Cells, organs and the systems that keep you alive.
Eight units, {{EXCOUNT}} interactive drills and a marked mock exam — built straight from the Year 8 Australian Curriculum descriptions AC9S8U01 and AC9S8U02.
Before MondayA three-session plan
You do not have to read all of this at once. Work in the order below and stop after each session — sleep is what turns study into memory.
How this worksFour ways to study
- Read. Every unit is written to be understood, not skimmed. Key words are underlined and collected in the glossary.
- Listen. Turn Voice on in the top bar, then press Listen next to any heading and the page reads that section to you.
- Drag. Labels, sorting bins and sequences — drag with a mouse or a finger, or tap a label then tap where it goes.
- Be tested. The oral quiz asks a question out loud, gives you a countdown to answer, then tells you if you were right. The mock exam marks you out of 100 and shows which topic let you down.
AC9S8U01 — cells are the basic unit of living things, with specialised structures and functions.
AC9S8U02 — multicellular organisms rely on coordinated and interdependent internal systems to respond to changes in their environment.
Everything in this course sits under one of those two sentences. If you can explain both in your own words and label the diagrams, you are ready.
Coming nextThe rest of school
This site is built to grow. Year 7, 9, 10, 11 and 12 courses sit beside this one — same diagrams, same drills, same exam engine. Open the course picker in the top bar to see what is planned.
Revision that sticks, for every year of high school.
The Learning Cycle turns each subject of the Australian Curriculum into short illustrated notes, drag-and-drop drills, a spoken quiz and a marked mock exam. No account, nothing to install, free for every student.
Start herePick your year, then your subject
Years 7–10 follow the national Australian Curriculum v9, so they match every state. Years 11 and 12 follow the Queensland QCAA senior syllabuses (Units 1–2, then Units 3–4 with the external exam). Cards marked Coming soon are on the way.
How it worksFour ways to study every topic
- Read. Each unit is a short, plain explanation with labelled diagrams — written to be understood, not skimmed. Key words are collected in a glossary.
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- Drag. Labels onto diagrams, cards into bins, steps into order — with a mouse or a finger, or tap a label then tap where it goes. Every drill marks itself.
- Be tested. The spoken quiz asks a question out loud and gives you a countdown to answer. The mock exam is timed, marked out of 100 and shows which topic let you down.
Who made thisA parent, for one student first
The Learning Cycle started as a weekend project to get one Year 8 student through a Biology exam. It worked, so it grew: every core subject and the Technologies electives from Year 7 to Year 12, built by JohnsonB Studio in Queensland and shared with anyone who can use it. It is free and will stay free. If it helps you or your child, the Donate button in the top bar keeps it growing.
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Sources. Curriculum content descriptions and codes are © ACARA and © QCAA, reused under their CC BY 4.0 licences. The explanations, drills, figures, quizzes and exams on this site are original work © JohnsonB Studio. Anatomical plates are free-licensed artwork credited in each course's glossary.
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Cells: the smallest thing that counts as alive
A cell is the smallest unit that can carry out all the processes of life. Nothing smaller feeds itself, gets rid of waste, responds or reproduces — which is why biology starts here.
1.1The three rules of cell theory
Cell theory is three sentences that took two hundred years and a lot of arguing to nail down. Learn them word for word — they are cheap marks.
- All living things are made of one or more cells. A bacterium, a gum tree and you are all built from the same kind of unit.
- The cell is the basic unit of structure and function in living things. Every job a body does — digesting, moving, sensing — happens because cells do it.
- All cells come from pre‑existing cells. Cells only ever appear by an existing cell dividing. Life does not start from nothing.
In 1665 Robert Hooke looked at a shaving of cork through his own microscope and saw thousands of empty boxes. They reminded him of the small rooms monks slept in — cellula in Latin — so he called them cells. He was looking at dead plant cell walls.
Ten years later Antonie van Leeuwenhoek, a Dutch draper who ground better lenses than anyone alive, looked at pond water and at scrapings from his own teeth, and saw things swimming. He called them "animalcules". They were the first living cells anyone had ever seen.
1.2Working the microscope
Cells are measured in micrometres (µm). One micrometre is a thousandth of a millimetre. A typical animal cell is about 20 µm across — you could line up fifty of them across a single millimetre. That is why you need a light microscope, and why the practical exam questions are always about using one properly.
Total magnification
You multiply the two lenses. Nothing else.
Total magnification = eyepiece magnification × objective magnification
Eyepiece ×10 with the ×40 objective gives ×400. The image is 400 times wider than the real object — so an object that appears 8 mm wide down the microscope is really 8 ÷ 400 = 0.02 mm, or 20 µm across.
Making a wet mount
- Put one drop of water in the middle of a clean slide.
- Add the specimen — a piece of onion epidermis, a cheek scraping, a leaf peel.
- Add a drop of stain. Iodine stains starch and plant nuclei; methylene blue stains animal nuclei. Without stain, most parts of a cell are transparent and you see almost nothing.
- Lower the coverslip at an angle using a mounting needle, then let it fall. Going slowly is what stops air bubbles — a bubble looks like a thick black ring and gets mistaken for a cell every year.
- Start on the lowest objective, focus with the coarse knob, centre what you want, then switch up and use only the fine focus.
Never use the coarse focus knob on the ×40 objective. It moves the stage far enough to drive the lens through the slide — broken glass, scratched lens, no result. Coarse focus is for low power only.
1.3One cell, or trillions
Unicellular organisms are a single cell that does everything: takes in food, releases energy, removes waste, reproduces. Bacteria, yeast, Amoeba, Paramecium and Euglena all live this way.
Multicellular organisms are made of many cells that have divided the work between them. A human is roughly 30 trillion cells, and a red blood cell has given up so much to carry oxygen that it cannot even divide any more. That is the trade: specialise, and depend on everyone else.
| Unicellular | Multicellular |
|---|---|
| One cell does every life process | Cells specialise and share the work |
| Exchange happens straight across the cell surface | Needs transport systems to reach inner cells |
| Usually microscopic | Can grow very large |
| Damage to the cell kills the organism | Damaged cells are replaced by cell division |
| Examples: bacteria, yeast, Amoeba, Paramecium | Examples: a mouse, a eucalypt, a mushroom, you |
1.4Why cells are so small
Everything a cell needs enters through its surface, and everything it makes has to leave the same way. As a cell grows, its volume grows faster than its surface area — so a big cell has proportionally less surface to feed a much bigger inside. Past a certain size the middle starves. Cells solve it by staying small and dividing.
Inside the cell: who does what
A cell is a workshop. Each part — each organelle — has one job, and the exam almost always asks you to match the part to the job, or to label it on a diagram.
2.1The animal cell
Study the labelled version first. Then scroll to the drag-and-drop drill below and do it from memory — that is the part that actually makes it stick.
2.2The plant cell
A plant cell has everything an animal cell has, plus three extras: a cell wall, chloroplasts and one large permanent vacuole. Those three explain almost everything else about plants — why they hold their shape, why they are green, and why a thirsty plant wilts.
2.3Every organelle, and its one job
| Organelle | What it does | Found in |
|---|---|---|
| Cell membrane | A thin, flexible, partially permeable boundary. Controls what enters and leaves. | Animal & plant |
| Cytoplasm | Watery jelly filling the cell. Most chemical reactions happen here; organelles float in it. | Animal & plant |
| Nucleus | Contains DNA (chromosomes). Controls the cell’s activities and holds the instructions for making proteins. | Animal & plant |
| Mitochondrion | Site of aerobic respiration — releases energy from glucose. Busy cells (muscle, liver) hold thousands. | Animal & plant |
| Ribosome | Tiny dot where proteins are made. Sits free in the cytoplasm or stuck to the ER. | Animal & plant |
| Rough ER | Folder and freight line for the proteins the ribosomes make. | Animal & plant |
| Golgi apparatus | Finishes, packages and ships molecules out in vesicles — the post room. | Animal & plant |
| Lysosome | Bag of digestive enzymes. Breaks down worn-out parts and invading bacteria. | Mainly animal |
| Cell wall | Rigid outer layer of cellulose. Gives shape and stops the cell bursting. Fully permeable. | Plant only |
| Chloroplast | Contains green chlorophyll; traps light energy for photosynthesis. | Plant only |
| Permanent vacuole | Large sac of cell sap. Its pressure keeps the plant firm (turgid). | Plant only (large one) |
Cell wall is not cell membrane. The wall is thick, rigid, cellulose and plant-only. The membrane is thin, flexible and in every cell — including plant cells, just inside the wall.
Not every plant cell is green. Root cells have no chloroplasts — no light gets down there. So "plant cell" does not automatically mean "has chloroplasts".
Chloroplast is the structure, chlorophyll is the pigment inside it. One is a place, one is a chemical.
From one cell to a whole organism
Multicellular life is built in five steps. Learn the ladder in order, because every body-system question later in the course is really a question about one rung of it.
3.1The five levels of organisation
Cell → tissue → organ → organ system → organism. A worked example gets full marks: "A muscle cell is one cell. Many muscle cells make muscle tissue. Muscle tissue plus glandular tissue plus lining tissue make the stomach, an organ. The stomach with the intestines and liver make the digestive system. All the systems together make the organism."
3.2Specialised cells
A cell that specialises changes its shape and its contents to suit one job. In the exam you are given a picture or a description and asked how is this cell adapted to its function? — and the answer is always structure first, then what that structure lets it do.
3.3How substances actually get in and out
Diffusion is the movement of particles from where they are more concentrated to where they are less concentrated, until they are spread evenly. It needs no energy — particles are already moving randomly, and spreading out is just what that randomness adds up to. Oxygen entering a cell and carbon dioxide leaving it both happen by diffusion.
Osmosis is the same idea but about water: water moves across a partially permeable membrane from a dilute solution to a more concentrated one. It is why a limp lettuce leaf crisps up in cold water, and why a plant with no water wilts — the vacuoles empty and stop pushing on the cell walls.
Three things make diffusion faster, and all three come back in the respiratory and digestive units: a steeper concentration gradient, a larger surface area, and a shorter distance to travel. Alveoli, villi and root hairs are all the same solution to the same problem.
The digestive system: turning food into fuel
Food is made of molecules far too big to cross a cell membrane. Digestion is one long job of breaking them down small enough to be absorbed — nine metres of tube doing chemistry on the way.
4.1The two kinds of digestion
Mechanical digestion is physical: teeth chewing, the stomach churning, bile emulsifying fat. It does not change the chemicals — it just breaks the food into smaller pieces, which gives the enzymes far more surface area to attack.
Chemical digestion uses enzymes to break the large molecules into small ones. Starch becomes glucose, proteins become amino acids, fats become fatty acids and glycerol. Only then are the molecules small enough to be absorbed into the blood.
4.2The journey, organ by organ
- Mouth. Teeth chew (mechanical). Saliva adds amylase, which starts breaking starch into sugars, and mucus to make a slippery ball of food called a bolus.
- Oesophagus. No digestion here. Rings of muscle squeeze in waves — peristalsis — pushing the bolus down. This is why an astronaut can swallow upside down; gravity is not doing the work.
- Stomach. A muscular bag that churns for 2–4 hours. It releases hydrochloric acid (kills most bacteria and gives protease the acidic pH it needs) and protease, which starts on proteins. Food leaves as a soup called chyme.
- Small intestine — digestion. The first part, the duodenum, receives bile from the gall bladder and enzymes from the pancreas. Chemical digestion is finished here.
- Small intestine — absorption. In the long second part, the small food molecules pass through the wall into the blood. About 6 m long and lined with millions of finger-like villi.
- Large intestine. What is left is mostly water and fibre. Water and some minerals are absorbed back into the blood; gut bacteria feed on the fibre and make some vitamins.
- Rectum and anus. The solid waste, faeces, is stored and then egested. Note the word: egestion is removing undigested food that never entered a cell — not the same as excretion.
4.3Enzymes: the three you must know
An enzyme is a biological catalyst — a protein that speeds up a reaction without being used up. Each one only fits one kind of molecule, and each works best at a particular temperature and pH. Learn this table as three rows of three.
| Enzyme | Breaks down | Into | Made in |
|---|---|---|---|
| Amylase (a carbohydrase) | Starch | Simple sugars (glucose) | Salivary glands, pancreas |
| Protease (pepsin in the stomach) | Proteins | Amino acids | Stomach, pancreas |
| Lipase | Fats (lipids) | Fatty acids + glycerol | Pancreas, small intestine |
Bile is made by the liver, stored in the gall bladder, and does two jobs: it neutralises stomach acid so the intestinal enzymes can work, and it emulsifies fat — breaking big fat drops into thousands of tiny ones. That is mechanical, not chemical: it gives lipase a far bigger surface area to work on. Bile speeds fat digestion up without digesting anything itself.
4.4Why the small intestine is shaped the way it is
Absorption is diffusion — so the small intestine is built for the three things that make diffusion fast: huge surface area, short distance, steep gradient.
The circulatory system: the delivery network
Every cell in your body needs oxygen and glucose delivered and carbon dioxide taken away. The heart is the pump, the vessels are the roads, and the blood is the truck. Beats about 100,000 times a day without ever being told to.
5.1The heart, chamber by chamber
Four chambers. Two on top called atria that receive blood, two underneath called ventricles that pump it out. The right side handles blood coming back from the body; the left side handles blood coming back from the lungs.
Heart diagrams are drawn as if the person is facing you. So the right side of the heart appears on the left of the page. Every year students lose marks by naming the chamber they can see on the left "the left atrium". Check the labels, not your instincts.
5.2Four structures, four reasons
| Structure | Why it is like that |
|---|---|
| Atria have thin walls | They only push blood down into the ventricle — a few centimetres. Little force needed. |
| Ventricles have thick, muscular walls | They pump blood out of the heart under pressure. |
| The left ventricle wall is thickest of all | It pushes blood all the way around the whole body; the right ventricle only reaches the lungs, which are next door. |
| Valves | Flaps that snap shut so blood can only travel one way. The "lub-dub" of a heartbeat is the sound of valves closing. |
| The septum | A wall of muscle keeping oxygenated and deoxygenated blood completely separate, so the blood sent to the body is fully loaded with oxygen. |
5.3Double circulation
Blood passes through the heart twice for every full lap of the body. That is what "double circulation" means, and it is why mammals can be so active: the blood is re-pressurised after the lungs instead of trickling on to the body.
5.4Three kinds of blood vessel
5.5What blood is made of
| Component | Job | Adaptation |
|---|---|---|
| Red blood cells | Carry oxygen | No nucleus (more room), biconcave disc (more surface area), full of haemoglobin which binds oxygen |
| White blood cells | Fight infection | Some engulf microbes, some make antibodies; they do have a nucleus |
| Platelets | Clot the blood | Cell fragments that plug a wound and trigger a mesh of fibrin |
| Plasma | Carries everything else | Straw-coloured liquid, about 90% water; transports glucose, amino acids, carbon dioxide, hormones and heat |
Haemoglobin contains iron, and iron plus oxygen is what makes blood red — the same chemistry that makes rust red. Low iron means less haemoglobin, less oxygen delivered, and constant tiredness: that is anaemia.
Carbon monoxide from a faulty heater or a fire binds to haemoglobin about 200 times more tightly than oxygen does, and will not let go. That is why it is deadly at concentrations you cannot smell.
The respiratory system: getting oxygen in
Your lungs are not muscles. They cannot pull air in on their own — the diaphragm and the ribs do that, and air rushes in behind them because the pressure has dropped. Understanding that one idea answers most breathing questions.
Breathing (ventilation) is the physical movement of air in and out of the lungs.
Respiration is a chemical reaction inside every cell that releases energy from glucose. It happens in the mitochondria, twenty-four hours a day, in every cell you have.
If a question says "respiration" and you write about the diaphragm, you get nothing. Read carefully.
6.1The route air takes
6.2How you breathe in and out
Air always moves from high pressure to low pressure. Your muscles change the volume of the chest, that changes the pressure inside, and air follows. Nothing sucks; everything is pushed.
6.3The alveolus: where the exchange happens
There are roughly 300 million alveoli in a pair of lungs. Spread flat they would cover about half a tennis court — all of it packed inside your chest, all of it one cell thick.
Asked "how is the alveolus adapted for gas exchange?", give all four and say what each one does:
1. Millions of them → enormous surface area. 2. Wall one cell thick → very short diffusion distance. 3. Surrounded by capillaries → blood carries gas away, keeping the gradient steep. 4. Moist lining → gases dissolve before they cross.
Excretion: taking out the chemical rubbish
Living cells constantly make waste, and some of it is poisonous. The excretory system removes it — and while it is at it, keeps the amount of water and salt in your blood almost perfectly steady.
Excretion is removing waste made by your cells — carbon dioxide, urea, excess water and salt. It was inside your cells.
Egestion is passing out undigested food as faeces. That material never entered a cell; it simply travelled through the tube. Faeces is not excretion.
7.1Three organs that excrete
| Organ | Waste removed | Where the waste came from |
|---|---|---|
| Lungs | Carbon dioxide, some water vapour | Cellular respiration in every cell |
| Kidneys | Urea, excess water, excess salt — as urine | The liver breaks down surplus amino acids into urea |
| Skin | Water, salt and a little urea — as sweat | Blood, filtered by sweat glands (cooling is the main purpose) |
7.2Homeostasis: staying the same on the inside
Homeostasis is keeping the conditions inside your body steady while the outside world changes. Enzymes only work in a narrow range, so your body defends that range hard: temperature near 37 °C, blood water and salt near constant, blood glucose near constant, blood pH near 7.4.
| The change | What the body does | Why it works |
|---|---|---|
| Too hot | Sweat is released; blood vessels near the skin widen (vasodilation) | Evaporating sweat takes heat away; more blood at the surface loses more heat |
| Too cold | Shivering; skin vessels narrow (vasoconstriction); hairs stand up | Shivering muscles release heat; less blood at the surface keeps heat in |
| Not enough water | Kidneys make less, more concentrated urine; you feel thirsty | Water is reabsorbed back into the blood instead of being lost |
| Blood glucose too high | The pancreas releases insulin; the liver stores glucose | Glucose leaves the blood, so the level falls back |
Every row above needs at least three systems talking to each other: something to detect the change (nervous system), something to carry the message (blood and hormones), and something to act (muscles, glands, kidneys). That is exactly what the curriculum means by "coordinated and interdependent internal systems".
Systems working together
This is the unit the curriculum actually cares about, and the one worth the most marks. No system works alone. Each one delivers something another one cannot get for itself.
8.1The reaction everything is for
glucose + oxygen → carbon dioxide + water + energy
It happens in the mitochondria of every cell, every second of your life. Read it as a shopping list and a bin bag: the digestive system supplies the glucose, the respiratory system supplies the oxygen, the circulatory system delivers both and collects the rubbish, and the respiratory and excretory systems throw the rubbish out.
8.2What happens when you sprint
Exam questions love this scenario, because answering it well means describing several systems responding together to one change.
- Muscle cells respire faster, so they use up glucose and oxygen quickly and produce more carbon dioxide.
- Sensors detect the rising carbon dioxide in the blood.
- Breathing rate and depth increase — more oxygen into the blood, more carbon dioxide out.
- Heart rate increases — blood is delivered to the muscles faster, so oxygen and glucose arrive faster and waste is removed faster.
- Blood vessels to the muscles widen; vessels to the digestive system narrow. Delivery is prioritised where it is needed.
- You get hot, so you sweat and your skin flushes — the excretory and circulatory systems cooling you down.
- If oxygen still cannot arrive fast enough, muscles switch to anaerobic respiration: glucose → lactic acid + a little energy. Lactic acid builds up, the muscle aches, and you keep breathing hard afterwards to repay the oxygen debt.
Name the system, name the change, then say why it helps. "The heart rate increases" is one mark. "The heart rate increases, so blood carries oxygen and glucose to the muscle cells faster and removes carbon dioxide faster, letting the muscle keep respiring aerobically" is three.
Everything is made of something.
Five units on what matter is made of and how it changes — built from the Year 8 Australian Curriculum descriptions AC9S8U06 and AC9S8U07.
The mapFive units
- The particle model — why solids hold their shape and gases fill the room.
- Atoms and elements — the hundred-ish ingredients everything is built from, and their symbols.
- Compounds — what happens when elements bond, and why water is nothing like hydrogen or oxygen.
- Mixtures and separation — filtering, evaporating, distilling and chromatography.
- Physical vs chemical change — the difference between melting ice and burning toast, and the clues that a new substance has formed.
AC9S8U06 — classify matter as elements, compounds and mixtures, and compare different representations of them.
AC9S8U07 — compare physical and chemical changes, and identify the indicators that a chemical change has happened.
The particle model: three states, one idea
All matter is made of particles far too small to see, always moving, with nothing between them. Every property of solids, liquids and gases follows from how those particles are arranged and how fast they move.
1.1Solid, liquid, gas
Particles do not melt, expand or change when a substance changes state. An ice particle is a water particle is a steam particle. What changes is the energy, spacing and movement of the particles — never the particles themselves.
1.2Changing state
- Melting — solid → liquid, at the melting point (ice: 0 °C).
- Evaporating / boiling — liquid → gas. Evaporation happens from the surface at any temperature; boiling happens throughout the liquid at the boiling point (water: 100 °C).
- Condensing — gas → liquid. Why a cold drink "sweats" on a hot day.
- Freezing — liquid → solid, at the same temperature as melting.
- Diffusion — particles of a gas or liquid spreading out and mixing by their own random movement — why perfume crosses a room.
Atoms and elements: the ingredients of everything
An atom is the smallest particle of matter that keeps its identity. An element is a substance made of only one kind of atom — and there are only about 118 of them, listed in the periodic table.
2.1Symbols: chemistry's alphabet
Every element has a one- or two-letter symbol. The first letter is always a capital, the second is always lowercase — Co is cobalt but CO is carbon monoxide, a compound of two elements. Some symbols come from Latin names, which is why they look nothing like the English word.
| Element | Symbol | Element | Symbol |
|---|---|---|---|
| Hydrogen | H | Chlorine | Cl |
| Helium | He | Iron (Latin ferrum) | Fe |
| Carbon | C | Copper (cuprum) | Cu |
| Nitrogen | N | Zinc | Zn |
| Oxygen | O | Silver (argentum) | Ag |
| Sodium (natrium) | Na | Gold (aurum) | Au |
| Magnesium | Mg | Mercury (hydrargyrum) | Hg |
| Aluminium | Al | Lead (plumbum) | Pb |
| Sulfur | S | Calcium | Ca |
| Potassium (kalium) | K | Silicon | Si |
2.2Metals and non-metals
| Metals (left side of the table) | Non-metals (right side) |
|---|---|
| Shiny when polished | Dull |
| Conduct heat and electricity | Insulators (except graphite) |
| Malleable — can be hammered into shape | Brittle when solid |
| Mostly solid at room temperature (mercury is the liquid exception) | Often gases; bromine is the liquid exception |
| Examples: iron, copper, gold, sodium | Examples: oxygen, carbon, sulfur, chlorine |
About three quarters of all elements are metals. Your body is mostly made of just six elements — oxygen, carbon, hydrogen, nitrogen, calcium and phosphorus — and the calcium in your bones and the iron in your blood were made inside dying stars.
Compounds: when elements join up
A compound is two or more elements chemically bonded in a fixed ratio. It is a genuinely new substance: sodium is a metal that explodes in water, chlorine is a poisonous green gas — bonded together they are table salt.
3.1Element, compound or mixture? Read the particles
3.2Reading a formula
A formula counts atoms. The little number applies only to the symbol just before it: H₂O is two hydrogens and one oxygen; CO₂ is one carbon and two oxygens. No number means one.
| Compound | Formula | Made of |
|---|---|---|
| Water | H₂O | 2 hydrogen + 1 oxygen |
| Carbon dioxide | CO₂ | 1 carbon + 2 oxygen |
| Table salt (sodium chloride) | NaCl | 1 sodium + 1 chlorine |
| Methane (natural gas) | CH₄ | 1 carbon + 4 hydrogen |
| Glucose | C₆H₁₂O₆ | 6 carbon + 12 hydrogen + 6 oxygen |
Bonding: in a compound the elements are chemically joined; in a mixture they just share space.
Ratio: a compound has a fixed recipe (water is always H₂O); a mixture can be any proportion.
Separating: a mixture can be separated physically (filter, evaporate); a compound needs a chemical reaction to break apart.
Mixtures, and how to un-mix them
Because the parts of a mixture are not bonded, you can always get them back — if you pick the technique that matches the property that makes the parts different.
4.1Solution words
- A solution is a mixture where one substance has dissolved in another — you cannot see the parts. Salt water is the classic.
- The solute is what dissolves (the salt). The solvent is what it dissolves in (the water).
- Soluble means it can dissolve; insoluble means it cannot (sand in water).
- A suspension is an insoluble solid floating through a liquid — muddy water. It settles if you wait.
4.2Pick the right separation
This is real, everyday engineering: water treatment plants filter your tap water, sea-salt farms evaporate ocean water in open pans, and forensic scientists use chromatography to match ink on a ransom note to a suspect's pen.
Physical or chemical? The most-asked question
In a physical change the substance stays the same substance — only its shape, size or state changes, and you can usually undo it. In a chemical change a new substance forms, and there is usually no going back.
5.1Two changes, side by side
5.2The five indicators of a chemical change
- A permanent colour change — toast browning, a copper roof turning green.
- A gas is produced (bubbles) when nothing was boiling — sherbet fizzing on your tongue, vinegar on bicarb.
- A precipitate forms — two clear liquids make a solid that clouds the mixture.
- Temperature changes by itself — the mixture gets hot (exothermic) or cold (endothermic) without a stove.
- Light or sound is given off — a firework, a glow stick, a burning match.
"Burning is a chemical change" is one mark. "Burning is a chemical change because a new substance (ash and carbon dioxide) is made, energy is released as heat and light, and you cannot get the wood back" is three. Always attach the indicator.
In every change, physical or chemical, atoms are never created or destroyed — they only rearrange. Burn 24 g of magnesium in 16 g of oxygen and you get exactly 40 g of magnesium oxide. If a burning log "loses" mass, the missing mass left as smoke and gas.
Energy: nothing happens without it.
Four units on what energy is, the forms it takes, and how it moves and changes — built from the Year 8 Australian Curriculum description AC9S8U05.
The mapFour units
- Forms of energy — kinetic and potential, and the family of forms under each.
- Energy transfer — energy moving from one object to another, without changing form.
- Energy transformation — energy changing form, and how to draw a flow diagram of it.
- Efficiency and conservation — where the "lost" energy really goes.
AC9S8U05 — classify different types of energy as kinetic or potential, and investigate energy transfer and transformations in simple systems.
Every form of energy is one of two kinds
Kinetic energy is the energy of things that are moving. Potential energy is stored energy — energy waiting because of position, shape or chemical make-up. Every other name you will meet is a member of one of these two families.
1.1The two family trees
Thermal energy is the movement of particles — a hot object's particles vibrate faster. That makes it kinetic, even though the object itself is sitting still. Same logic for sound (vibrating particles) and electricity (moving charges).
Energy transfer: same form, new owner
A transfer moves energy from one object to another without changing its form. A cue ball hits the eight ball: movement energy simply changes hands.
2.1Three ways heat travels
- Conduction — vibrating particles bump their neighbours, passing energy along. Works best in solids; metals are superb at it, which is why a metal seat feels colder than a wooden one at the same temperature.
- Convection — in liquids and gases, warm fluid expands, becomes less dense and rises; cooler fluid sinks to replace it, making a loop. Why heaters go near the floor and air conditioners near the ceiling.
- Radiation — energy travelling as rays that need no particles at all. The only transfer that works through empty space.
- An insulator is a material heat crosses slowly — wool, foam, trapped air. That is the whole science of a puffer jacket.
Transformation: energy changing its form
A transformation changes energy from one form into another. A torch transforms chemical energy into electrical energy, then into light. Writing that chain as a flow diagram is a guaranteed exam question.
3.1The skater: one story, told twice
3.2Flow diagrams: the exam's favourite
Write the forms in order with arrows. Name the object above the arrow if you can.
| System | Energy flow diagram |
|---|---|
| Torch | chemical (battery) → electrical → light + thermal |
| Eating then sprinting | chemical (food) → kinetic (muscles) + thermal |
| Toaster | electrical → thermal + light |
| Bow and arrow | elastic (bent bow) → kinetic (arrow) |
| Coal power station | chemical → thermal → kinetic (turbine) → electrical |
| Solar panel | light → electrical |
| Loudspeaker | electrical → sound + thermal |
Ask one question: did the form change? Cue ball to eight ball — movement stays movement: transfer. Battery to glowing bulb — chemical became light: transformation. Most real systems do both at once.
Nothing is lost: conservation and efficiency
The law of conservation of energy: energy cannot be created or destroyed, only transferred or transformed. So where does the energy "go" when a device wastes it?
4.1Useful energy and wasted energy
Efficiency = useful energy out ÷ total energy in × 100
An old bulb turning 100 J of electricity into 10 J of light is 10 ÷ 100 × 100 = 10% efficient. Every device on Earth is less than 100% — some energy always escapes as heat or sound.
This is why your phone warms up while gaming, why electric kettles are the rare near-100% device (their "waste" heat IS the job), and why a car engine at ~30% efficiency needs a radiator to dump the other 70%.
Rocks: the slowest recycling on Earth.
Four units on the three rock families, the cycle that turns each into the others, and the deep time it takes — built from the Year 8 Australian Curriculum description AC9S8U04.
The mapFour units
- Igneous rocks — born from cooling magma and lava, and why crystal size gives away where they formed.
- Sedimentary rocks — layers of squashed fragments, and the only family that keeps fossils.
- Metamorphic rocks — rocks cooked and squeezed into new ones without melting.
- The rock cycle and deep time — how each family becomes the others over millions of years.
AC9S8U04 — compare the processes of rock formation, including the timescales involved, for igneous, sedimentary and metamorphic rocks, and describe the rock cycle.
Igneous rocks: frozen fire
Igneous rocks form when molten rock cools and hardens. Underground it is called magma; the moment it erupts onto the surface it is called lava. Same stuff, two names, one rule to remember.
1.1Cooling speed writes the crystal size
Pumice is lava that cooled so fast around gas bubbles that it froze as stone foam — the only rock that floats. Obsidian cooled faster still: no crystals at all, just natural black glass, once prized for blades sharper than steel.
Sedimentary rocks: history in layers
Rain, wind and ice grind rocks into fragments. Rivers carry the fragments to lakes and seas, where they settle in layers — and over millions of years the layers become sedimentary rock.
2.1Four steps, millions of years
A creature buried gently in soft sediment can leave its shape as the layers harden around it. Igneous rock starts as molten magma — anything in it burns. Metamorphic rock is cooked and squeezed — any fossil is destroyed. So a rock with a fossil is sedimentary, every time. Two marks, almost every paper.
Metamorphic rocks: cooked, not melted
Bury any rock deep enough and the Earth will remake it. Metamorphic means "changed form": intense heat and pressure rearrange a rock's crystals into a new rock — without ever melting it. Melting would make magma, and that path leads back to igneous.
3.1Before and after
| Starts as | Heat + pressure make | Worth knowing |
|---|---|---|
| Limestone (sedimentary) | Marble | The sculptor's stone — the crystals fuse smooth |
| Mudstone / shale (sedimentary) | Slate | Splits into flat sheets — old roof tiles and blackboards |
| Sandstone (sedimentary) | Quartzite | Much harder than the sandstone it was |
| Granite (igneous) | Gneiss | Say "nice" — minerals squeezed into stripy bands |
- The heat comes from depth and from nearby magma; the pressure comes from kilometres of rock above and from colliding tectonic plates.
- Pressure often flattens the new crystals into stripes or sheets — that banding is a metamorphic giveaway.
- The change happens in the solid state, over thousands to millions of years.
"Heated until it melts" is never metamorphism. Melted rock is magma, and magma cools into igneous rock. Metamorphic rock is changed while still solid — cooked like clay in a kiln, which hardens into pottery without ever being liquid.
The rock cycle: every rock is another rock's future
No rock is permanent. Given heat, pressure, weather and enough time, each family turns into the others. The whole diagram below runs on two engines: the Sun (driving weather) and the Earth's inner heat (driving melting and metamorphism).
4.1The cycle
4.2Deep time
The cycle's clock does not tick in years. Lava can freeze to basalt in days, but growing granite's crystals takes tens of thousands of years, stacking sediment into stone takes millions, and one full lap of the cycle can take hundreds of millions of years. Geologists call this deep time.
Scale it down: if Earth's 4.5-billion-year history were one calendar year, the dinosaurs die on Boxing Day, and all of recorded human history fits into the last 30 seconds of New Year's Eve.
Igneous: molten rock cools — days (extrusive) to thousands of years (intrusive). Sedimentary: fragments compacted and cemented — millions of years. Metamorphic: existing rock changed by heat and pressure without melting — thousands to millions of years. Name the process AND the timescale for full marks.
Year 8 Maths: the six skills everything else uses.
Six units covering the core of the Year 8 Australian Curriculum: integers, index laws, percentages and ratios, algebra, linear graphs, and measurement.
The mapSix units
- Integers — negative numbers without fear, and the order of operations.
- Index laws — powers, and the three shortcuts for combining them.
- Percentages & ratios — discounts, increases, and sharing in a ratio.
- Algebra — simplifying expressions, expanding brackets, solving equations.
- Linear graphs — plotting lines and reading gradient and intercept from y = mx + c.
- Measurement — circle circumference and area, and volume of prisms.
Reading maths does almost nothing — doing it is everything. Do every drill with a pencil and paper beside you, and when you get one wrong, redo it by hand before moving on. Ten minutes of working problems beats an hour of reading them.
Integers: the rules for negatives
Negative numbers behave perfectly once you know three rules — and the number line settles every argument.
1.1Adding and subtracting
1.2Multiplying and dividing
| Signs | Answer's sign | Example |
|---|---|---|
| same × same (both + or both −) | positive | (−4) × (−3) = 12 |
| different (+ and −) | negative | 6 × (−5) = −30 |
| same rule for division | (−20) ÷ 4 = −5, (−20) ÷ (−4) = 5 |
Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right).
3 + 4 × 2 = 11, never 14. And (3 + 4) × 2 = 14 — brackets are how you demand the addition happens first.
Index laws: three shortcuts for powers
An index (power) counts repeated multiplication: 2⁴ means 2 × 2 × 2 × 2 = 16. The three laws below are just what happens when you write the multiplications out — learn them as patterns, check them by expanding.
2.1The three laws
| Law | Rule | Why it works |
|---|---|---|
| Multiplying | aᵐ × aⁿ = aᵐ₊ⁿ | 2³ × 2² = (2·2·2)(2·2) = 2⁵ |
| Dividing | aᵐ ÷ aⁿ = aᵐ⁻ⁿ | 2⁵ ÷ 2² = cancel two 2s = 2³ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ | (2³)² = 2³ × 2³ = 2⁶ |
| Zero index | a⁰ = 1 | 2³ ÷ 2³ = 1, and the law says 2⁰ |
2³ is not 6. It is 2 × 2 × 2 = 8. Powers multiply, they don't times-the-little-number.
The laws need the same base. 2³ × 5² cannot be combined — different bases, no shortcut.
Percentages and ratios: the shopping unit
Discounts, mark-ups, mixing cordial and splitting prize money — this is the maths you will actually use weekly for the rest of your life.
3.1Percentage of an amount
- Turn the percentage into a decimal (divide by 100): 35% → 0.35.
- Multiply: 35% of $80 = 0.35 × 80 = $28.
- Discount? Subtract from the original: $80 − $28 = $52. Shortcut: a 35% discount means you pay 65%, so 0.65 × 80 = $52 in one step.
- Increase? Same shortcut upward: a 10% rise means paying 110%, so × 1.10.
3.2Sharing in a ratio
Share $60 between two people in the ratio 2 : 3.
1. Add the parts: 2 + 3 = 5 parts. 2. One part = 60 ÷ 5 = $12. 3. Multiply out: 2 × 12 = $24 and 3 × 12 = $36. Check: 24 + 36 = 60 ✓
- Simplify a ratio like a fraction: 12 : 18 → divide both by 6 → 2 : 3.
- A rate compares different units: 180 km in 2 hours = 90 km/h. Divide to get the "per one".
- Best buy: work out the price per unit for each option and pick the smaller. 500 g for $6 (1.2 c/g) beats 300 g for $4.20 (1.4 c/g).
Algebra: letters are just unknown numbers
Every algebra rule is an arithmetic rule wearing a disguise. If a step looks wrong, test it with numbers: does it work when x = 5?
4.1The four skills
| Skill | Rule | Example |
|---|---|---|
| Collect like terms | Only identical letter-parts combine | 3x + 5x − 2 = 8x − 2 (the 2 stays alone) |
| Multiply terms | Multiply numbers, join letters | 4a × 3b = 12ab |
| Expand brackets | Multiply everything inside by the front | 3(x + 4) = 3x + 12 |
| Solve equations | Undo, same thing to both sides | 2x + 3 = 11 → 2x = 8 → x = 4 |
The equation wraps x in operations; you unwrap in reverse order, doing the same to both sides. For 2x + 3 = 11: the last thing done to x was "+3", so subtract 3 first (2x = 8), then undo "×2" by dividing (x = 4). Always check: 2(4) + 3 = 11 ✓ — a free mark, every time.
3(x + 4) is 3x + 12, not 3x + 4. The 3 multiplies everything in the bracket — draw the two arrows if it helps.
Linear graphs: reading y = mx + c
Every straight line has an equation of the form y = mx + c. Two numbers tell you everything: m, the gradient (steepness), and c, where the line crosses the y-axis.
5.1A live graph you can edit
5.2What m and c each do
- To plot a line: make a small table. For y = 2x + 1, x = 0 gives y = 1, x = 1 gives 3, x = 2 gives 5. Plot the points, rule the line.
- To read a graph: c is where it crosses the y-axis; m is rise ÷ run between any two grid points.
- To check a point is on a line: substitute. Is (3, 7) on y = 2x + 1? 2(3) + 1 = 7 ✓ yes.
Measurement: circles and prisms
Two circle formulas, one volume rule, and knowing which is which. The classic error is mixing up circumference and area — the figure below is built to stop that.
6.1The circle, labelled
6.2Volume of a prism
Volume = area of the end face × length.
A box 5 cm × 3 cm × 10 cm: end face 5 × 3 = 15 cm², so V = 15 × 10 = 150 cm³. A cylinder is just a circular prism: V = πr² × height. Volume is always in cubic units.
- Area of a triangle = ½ × base × height, so a triangular prism's volume = ½bh × length.
- Units stack with the dimension: length cm, area cm², volume cm³. Writing the wrong unit loses a mark even with the right number.
- 1 cm³ holds exactly 1 mL — volume and capacity are the same idea.
Control systems, and the systems nothing controls.
Four units: how your body detects and responds to change (nerves and hormones), and how ecosystems balance themselves with no controller at all — built from AC9S9U01 and AC9S9U02.
The mapFour units
- The nervous system — neurons, the stimulus–response chain, and the reflex arc.
- Hormones and homeostasis — the endocrine system, and negative feedback with blood glucose as the star example.
- Ecosystems — biotic and abiotic factors, and who eats whom: chains and webs.
- Energy and matter — why food chains are short, and how carbon cycles forever.
AC9S9U01 — the nervous and endocrine systems coordinate responses to changes in the internal and external environment.
AC9S9U02 — ecosystems consist of interdependent communities and their abiotic environment; matter cycles and energy flows through them.
The nervous system: fast wiring
Electrical messages at up to 120 metres per second, along dedicated cells, to exactly one destination. The nervous system is the body's fast, precise, short-lived control channel.
1.1The chain every response follows
- A neuron is a nerve cell: branched dendrites collect the signal, the long axon carries it, often wrapped in a fatty myelin sheath that speeds it up.
- Neurons never quite touch. The gap is a synapse, crossed by chemical messengers — this is where the signal briefly becomes chemistry.
- Receptors by sense: light → eye, sound and balance → ear, chemicals → nose and tongue, touch/heat/pain → skin.
1.2The reflex arc: skipping the brain
For dangerous stimuli, the sensory neuron connects — through a tiny relay neuron — straight to a motor neuron in the spinal cord. The response fires in about 50 milliseconds, and the "ouch" reaches your brain afterwards. A reflex is automatic, involuntary, and protective: hand off the hotplate, blink at a flying insect, knee-jerk at the doctor.
Hormones: the slow broadcast
The endocrine system is the body's second control channel: hormones, chemical messengers released by glands into the blood, reaching everywhere, acting slowly, lasting long.
2.1Nerves vs hormones
| Nervous system | Endocrine system | |
|---|---|---|
| Messenger | Electrical impulse | Chemical hormone |
| Travels by | Neurons | The bloodstream |
| Speed | Milliseconds | Seconds to days |
| Target | One precise spot | Every cell with the right receptor |
| Effect lasts | Very briefly | Long — minutes to years |
| Example | Pulling hand off a hotplate | Growth; puberty; blood sugar control |
- Pancreas → insulin (lowers blood glucose) and glucagon (raises it).
- Adrenal glands → adrenaline: the fight-or-flight surge — faster heart, wider airways, glucose released.
- Thyroid → thyroxine: sets the body's idle speed (metabolism).
- Pituitary → growth hormone, and the "master gland" signals that run other glands.
2.2Negative feedback: the thermostat trick
Ecosystems: everything eats, everything depends
An ecosystem is a community of living things plus the non-living world they share — and the network of who-eats-whom that ties it all together.
3.1The cast list
- Biotic factors are the living parts: plants, animals, fungi, bacteria — and their interactions (predation, competition).
- Abiotic factors are the non-living conditions: sunlight, temperature, water, soil, shelter.
- Producers (plants, algae) make their own food by photosynthesis. Every chain starts with one.
- Consumers eat others: herbivores eat plants, carnivores eat animals, omnivores eat both.
- Decomposers (fungi, bacteria) break down the dead and return nutrients to the soil — the recyclers nothing works without.
3.2A food web, read properly
"What happens to X if Y disappears?" Trace the arrows both ways: Y's food has fewer eaters (its numbers may rise), Y's predators lose a food source (their numbers may fall, or they switch prey and pressure a third species). Name both directions for full marks.
Energy flows through; matter goes around
Two different journeys through the same ecosystem. Energy arrives as sunlight, moves up the chain, and leaks away as heat — a one-way street. Matter (carbon, water, nitrogen) is never lost — it loops forever.
4.1The energy pyramid
4.2Matter loops: carbon in four moves
- Photosynthesis pulls carbon dioxide out of the air and locks the carbon into plant sugar.
- Feeding passes that carbon up the chain, body to body.
- Respiration — by plants, animals AND decomposers — breathes carbon dioxide back out.
- Decomposition returns the carbon in dead bodies and waste to the soil and air, ready to be used again. (Burning fossil fuels is a fifth, human-added move: it releases carbon that was locked away for millions of years.)
Almost every carbon atom in your body has been through this loop countless times — some of them were once in a dinosaur's breakfast. Matter cycles; only the energy is new each day, delivered fresh from the Sun.
Inside the atom, inside the reaction.
Four units: what atoms are made of, why the periodic table is arranged the way it is, and what really happens when substances react — built from AC9S9U06 and AC9S9U07.
The mapFour units
- Inside the atom — protons, neutrons, electrons, and the two numbers that describe any atom.
- The periodic table — why it has that shape, and what a column tells you.
- Chemical reactions — word equations, and why mass never changes.
- Reaction types — combustion, corrosion, acids at work, and energy in or out.
AC9S9U06 — all matter is made of atoms composed of protons, neutrons and electrons; natural radioactivity arises from the decay of nuclei.
AC9S9U07 — chemical reactions rearrange atoms into new substances, mass is conserved, and reactions absorb or release energy.
Inside the atom: three particles, two numbers
Last year the atom was the smallest thing. This year we open it: a tiny, dense nucleus of protons and neutrons, wrapped in shells of near-weightless electrons.
1.1A lithium atom, labelled
1.2The two numbers
| Number | Counts | For lithium |
|---|---|---|
| Atomic number | Protons — this IS the element's identity | 3 |
| Mass number | Protons + neutrons | 7 |
| So: neutrons = | mass number − atomic number | 7 − 3 = 4 |
| And: electrons = | protons (in a neutral atom) | 3 |
Some nuclei have an unstable mix of protons and neutrons. Sooner or later they decay — spitting out particles and energy (radiation) until they reach a stable form, sometimes becoming a different element in the process. That is natural radioactivity: not magic, just unstable nuclei settling down. It powers the Earth's inner heat and lets scientists date ancient rocks and fossils.
Change the number of neutrons and you get a heavier or lighter version of the same element. Change the number of protons and it is a different element entirely. Proton count is the element.
The periodic table: a map, not a list
Elements are arranged by atomic number, and the table's shape is doing real work: a period (row) adds electrons to the same outer shell; a group (column) collects elements with the same number of outer electrons — which is why families in a column behave alike.
2.1Three famous families
| Family | Where | Behaviour |
|---|---|---|
| Alkali metals (Li, Na, K) | Group 1, far left | Soft metals that react violently with water — and get MORE violent going down the column |
| Halogens (F, Cl, Br, I) | Group 17 | Reactive non-metals; form salts with metals (sodium + chlorine → table salt) |
| Noble gases (He, Ne, Ar) | Group 18, far right | Full outer shells → almost completely unreactive. Why helium balloons are safe and hydrogen ones explode |
- Metals fill the left and centre (about three quarters of the table); non-metals sit top-right; a staircase of semi-metals divides them.
- Same column = same outer-electron count = same chemistry family. That single idea is the table's superpower: it predicted undiscovered elements.
- Reading a table cell: the small whole number is the atomic number (protons); the larger number is the (average) atomic mass.
Dmitri Mendeleev built the table in 1869 by writing each element on a card and playing patience until the patterns lined up — then left gaps where the pattern demanded an element nobody had found. Gallium and germanium were discovered years later with almost exactly the properties his gaps predicted. That is what made chemists trust the table.
Reactions: atoms change partners, never number
A chemical reaction breaks some bonds and makes new ones. The atoms themselves are untouched — same atoms in, same atoms out, just rearranged into new substances.
3.1One reaction, drawn as atoms
3.2Word equations
- The starting substances are reactants; the new substances are products. The arrow means "react to make": reactants → products.
- Methane + oxygen → carbon dioxide + water.
- Iron + oxygen + water → hydrated iron oxide (rust).
- Signs a reaction happened are the Year 8 five: colour change, gas, precipitate, temperature change, light/sound.
Burn 4 g of methane in 16 g of oxygen inside a sealed container: the container still weighs exactly 20 g after. In an OPEN container a burning fuel seems to lose mass — because gas products escaped — and rusting iron seems to GAIN mass — because oxygen from the air joined it. Sealed system: mass never changes.
Reaction types you must recognise
Four patterns cover most of what Year 9 meets: burning, rusting, acids doing their two party tricks, and the energy question — does the reaction give heat out, or drink it in?
4.1The four patterns
| Type | General pattern | Everyday example |
|---|---|---|
| Combustion | fuel + oxygen → carbon dioxide + water | Gas stove, car engine, campfire |
| Corrosion (rusting) | iron + oxygen + water → rust | A bike left in the rain; slow, needs BOTH air and water |
| Acid + metal | acid + metal → salt + hydrogen gas | The squeaky-pop test lights the hydrogen |
| Acid + carbonate | acid + carbonate → salt + water + carbon dioxide | Vinegar fizzing on bicarb; limewater turns the CO₂ milky |
4.2Energy in, energy out
- Exothermic reactions release energy — the mixture (and its surroundings) get hotter. Combustion, hand warmers, respiration.
- Endothermic reactions absorb energy — the mixture gets colder. Instant cold packs, photosynthesis, baking soda + vinegar.
- Test in one line: put a thermometer in. Temperature up → exo; down → endo.
Burning "uses up" nothing. The fuel's atoms all leave as carbon dioxide and water vapour — mass is conserved, it just left as gas.
Rust needs water AND oxygen. Iron in dry air, or under boiled (air-free) water, barely rusts. That is why the classic three-test-tube experiment works.
Waves and circuits: energy on the move.
Four units on how energy travels without matter travelling with it — as sound, as light, and as electric current — built from AC9S9U05.
The mapFour units
- Waves — the vocabulary: wavelength, frequency, amplitude, and the two wave shapes.
- Sound — vibrations that need a medium; pitch, loudness, and speed.
- Light — rays that need nothing; reflection, refraction, and colour.
- Electric circuits — current, voltage, resistance, and series vs parallel.
AC9S9U05 — describe how energy is transferred through different mediums using wave and particle models, including sound, light and electricity.
Waves: energy travels, matter stays
Drop a stone in a pond: the ripple crosses the water, but the water itself only bobs. A wave is exactly that — a travelling disturbance that carries energy from place to place without carrying the material.
1.1Anatomy of a wave
1.2Two shapes of wave
| Transverse | Longitudinal | |
|---|---|---|
| Particles vibrate | Up and down, ACROSS the travel direction | Back and forth, ALONG the travel direction |
| Looks like | Ripples, a shaken rope | A pushed slinky: squashed zones (compressions) and stretched zones (rarefactions) |
| Examples | Light, water ripples | Sound |
Sound: vibrations passed hand to hand
Everything that makes sound is vibrating. The vibration shakes the air particles next to it, they shake their neighbours, and a longitudinal wave of squashes and stretches crosses the room to your ear.
2.1The two dials: pitch and loudness
| You hear | The wave property | Example |
|---|---|---|
| High pitch | High frequency (more vibrations per second) | A piccolo, a mosquito — thousands of Hz |
| Low pitch | Low frequency | A bass drum, thunder — tens of Hz |
| Loud | Large amplitude (bigger squashes) | A shout — more energy in each wave |
| Quiet | Small amplitude | A whisper |
- Humans hear roughly 20 Hz to 20,000 Hz. Dogs hear higher; whales and elephants rumble lower.
- Sound needs a medium. No particles → nothing to pass the vibration → silence. Space is silent; the bell-in-a-vacuum-jar experiment proves it.
- Speed depends on the medium: about 340 m/s in air, ~1,500 m/s in water, ~5,000 m/s in steel. Tighter-packed particles pass the shake faster — the old ear-on-the-railway-track trick.
- Light travels about a million times faster than sound — so you see lightning, then count the seconds to the thunder (3 seconds ≈ 1 km).
- An echo is sound reflected off a hard surface. Sonar and bat navigation both time the echo to measure distance.
Light: rays that need nothing
Light is a transverse wave that carries energy through empty space at 300,000 km per second — the universal speed limit. It travels in straight lines, which is why shadows are sharp and why we draw it as rays.
3.1Reflection and refraction, one diagram each
- White light is a mix. A prism refracts each colour by a slightly different amount and fans it into a spectrum — dispersion. Raindrops do the same thing: a rainbow.
- Red bends least, violet bends most.
- A red apple looks red because it reflects red light and absorbs the other colours. A white object reflects them all; a black one absorbs them all (and warms up).
- Materials are transparent (glass — light straight through), translucent (frosted glass — light through, scrambled), or opaque (wood — no light through; makes shadows).
Circuits: energy delivered by moving charge
A battery pushes charged particles around a closed loop of wire; whatever stands in the loop — a globe, a motor — taps energy off as they pass. Break the loop anywhere and everything stops.
4.1The three quantities
| Quantity | What it is | Unit | Measured with |
|---|---|---|---|
| Current (I) | How much charge flows per second — the traffic | amperes (A) | Ammeter, in the loop (in series) |
| Voltage (V) | The push — energy given to each unit of charge | volts (V) | Voltmeter, across a component (in parallel) |
| Resistance (R) | How hard the component fights the flow | ohms (Ω) | More resistance → less current for the same push |
4.2Series vs parallel: the diagram that decides your house wiring
Conductors (metals) let charge flow because some of their electrons are free to move; insulators (plastic, rubber) hold theirs tight — hence metal wire in a plastic coat. A switch is just a deliberate break in the loop.
A planet in slow motion.
Four units: the Earth's layered inside, the drifting plates that explain earthquakes and volcanoes, the evidence that convinced everyone, and the carbon that circulates through the whole planet — built from the Year 9 Earth & space descriptions.
The mapFour units
- Inside the Earth — crust, mantle, core, and the plates floating on top.
- Plate boundaries — the three ways plates meet, and what each one builds or breaks.
- The evidence — how a "crazy" drifting-continents idea became accepted science.
- The carbon cycle — carbon moving between air, life, ocean and rock, and what burning fossil fuels changes.
The theory of plate tectonics explains global patterns of geological activity — earthquakes, volcanoes and mountain building — and Earth's spheres exchange carbon in a global cycle that human activity is now shifting.
Inside the Earth: four layers, one engine
Nobody has drilled more than 12 km down — a scratch on a 6,371 km radius. Everything deeper is read from earthquake waves, and the picture is a layered planet with a heat engine at its heart.
1.1The layers
1.2The plates
- The rigid outer shell is cracked into about fifteen tectonic plates that fit together like a spherical jigsaw, carrying continents and ocean floor alike.
- They ride the mantle's convection currents at 2–10 cm a year — fingernail speed. Over 100 million years that is thousands of kilometres.
- Almost all earthquakes and volcanoes happen at plate edges. Map the quakes and you have drawn the plate boundaries — the Pacific's ring of them is the famous Ring of Fire.
- Australia sits mid-plate, which is why it has so few big quakes — and it is drifting north about 7 cm a year, fast enough that GPS maps must be corrected.
Plate boundaries: where the action is
Everything dramatic the Earth does — earthquakes, volcanoes, new ocean floor, the Himalayas — happens at one of three kinds of boundary. Learn the three arrows and you can explain the lot.
2.1The three boundaries
Plates at a boundary do not glide smoothly — friction locks them while stress builds for decades. When the rock finally snaps, the stored energy releases as seismic waves: an earthquake. The snap point underground is the focus; the surface point directly above it is the epicentre. Name the locked plates, the stored stress, and the sudden release.
The evidence: how a laughed-at idea won
In 1912 Alfred Wegener claimed the continents drift. He was mocked for fifty years — he had the evidence but no engine. The story of how his idea became plate tectonics is the best case study in how science actually works.
3.1Four lines of evidence
- The jigsaw fit. South America and Africa's coastlines match like torn halves of one page — and they fit even better at the true continental edges under the sea.
- Matching fossils. The same land reptile (Mesosaurus) and the same fern (Glossopteris) are fossilised on continents now separated by oceans no land animal could cross. Either the animals swam the Atlantic — or the lands were joined.
- Matching rocks and mountains. Rock bands in eastern South America line up exactly with bands in western Africa; the Appalachians continue into the Scottish Highlands.
- The clincher: seafloor spreading. In the 1960s, surveys found mid-ocean ridges with brand-new rock at the crest and progressively older rock further away, in matching stripes on both sides. The ocean floor is a conveyor belt made at ridges and consumed in trenches — the missing engine, found.
All the continents were once one supercontinent, Pangaea, which began breaking up about 200 million years ago. Run the movie forward instead: in another 250 million years they are forecast to merge again. And today the drift is not inferred — GPS measures it directly, centimetre by centimetre.
Not because his evidence was weak, but because he had no mechanism: nobody could see what force ploughed continents through solid ocean floor. When mantle convection and seafloor spreading supplied the engine, the same evidence convinced everyone. Lesson: a scientific theory needs evidence and a mechanism, and it must convince the community.
The carbon cycle: one atom, four spheres
Carbon shuttles constantly between the air (atmosphere), living things (biosphere), water (hydrosphere) and rock (geosphere). The cycle balanced itself for millions of years — until one flow got a new contributor.
4.1The cycle
- The four spheres: atmosphere (air), biosphere (life), hydrosphere (water and ice), geosphere (rock and soil). The carbon cycle threads through all four.
- The ocean holds far more carbon than the air and constantly trades CO₂ with it across the surface.
- CO₂ is a greenhouse gas: it lets sunlight in but slows heat's escape. More CO₂ in the air means more trapped heat — the mechanism behind the warming climate.
- Deforestation hits the cycle twice: fewer trees photosynthesising carbon in, and burning or rotting the wood sends its stored carbon out.
Four tools you'll use for years.
Index laws that tame huge numbers, algebra that multiplies brackets, live graphs you can bend with your own equations, and the two most famous triangle tools in mathematics — built from the Year 9 content descriptions.
The mapFour units
- Indices & scientific notation — the three index laws, zero and negative powers, and writing 149 000 000 km as 1.49 × 10⁸.
- Expanding & factorising — multiplying brackets out (including double brackets) and packing them back up.
- Linear graphs, live — gradient between any two points, parallel lines, and your first non-linear curve — on a graph you can edit.
- Pythagoras & trigonometry — finding missing sides of right-angled triangles two different ways.
Applying the index laws to numbers and variables, expanding binomial products, finding the gradient and midpoint on the Cartesian plane, and solving right-angled triangles with Pythagoras' theorem and the trigonometric ratios.
Index laws & scientific notation
You met powers in Year 8. Year 9 makes them a machine: three laws that work for any base — numbers or letters — plus a way to write the size of the Sun without running out of page.
1.1The three laws
| Law | Rule | Why it works | Example |
|---|---|---|---|
| Multiplying | aᵐ × aⁿ = aᵐ⁺ⁿ | 3² × 3³ = (3×3)×(3×3×3) — five 3s in total | x⁴ × x³ = x⁷ |
| Dividing | aᵐ ÷ aⁿ = aᵐ⁻ⁿ | 3⁵ ÷ 3² cancels two of the five 3s | x⁶ ÷ x² = x⁴ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ | (3²)³ = 3² three times over — six 3s | (x²)⁵ = x¹⁰ |
| Zero power | a⁰ = 1 (a ≠ 0) | 3² ÷ 3² = 1, and the law says it's 3⁰ | 7⁰ = 1, x⁰ = 1 |
The laws need the same base. 2³ × 5² cannot be combined with an index law — just calculate it: 8 × 25 = 200. And aᵐ + aⁿ has no law at all: laws are for multiplying and dividing, never adding.
1.2Scientific notation
A number in scientific notation is written as (a number from 1 up to but not including 10) × (a power of 10). The power counts how many places the decimal point moved.
- Big numbers, positive power. 149 000 000 = 1.49 × 10⁸ — the point moved 8 places left.
- Small numbers, negative power. 0.00052 = 5.2 × 10⁻⁴ — the point moved 4 places right.
- Check the first part. 14.9 × 10⁷ is not scientific notation — 14.9 is too big; shift once more: 1.49 × 10⁸.
Expanding & factorising
Expanding multiplies brackets out; factorising packs them back up. They are the same road driven in opposite directions — and the area model makes double brackets impossible to get wrong.
2.1Single brackets, both directions
- Expand: the outside term multiplies every term inside. 3(2x + 5) = 6x + 15. Watch signs: −2(x − 4) = −2x + 8.
- Factorise: pull out the highest common factor. 6x + 15 = 3(2x + 5). For 8x² + 12x the HCF is 4x: 4x(2x + 3).
- Check by expanding back. Factorising is only right if expanding your answer returns the original. This check takes ten seconds and catches everything.
2.2Double brackets: the area model
- Every term in the first bracket multiplies every term in the second. (x + 2)(x + 3) = x² + 3x + 2x + 6.
- Collect the like terms in the middle. 3x + 2x = 5x, so the answer is x² + 5x + 6.
- Signs ride along. (x − 4)(x + 2) = x² + 2x − 4x − 8 = x² − 2x − 8.
Linear graphs, live
Year 8 gave you y = mx + c. Year 9 asks for more: the gradient between any two points, the midpoint between them, spotting parallel lines — and a first meeting with a graph that isn't straight at all.
3.1Gradient from any two points
Between points (x₁, y₁) and (x₂, y₂): m = (y₂ − y₁) ÷ (x₂ − x₁) — rise over run. Between (1, 3) and (4, 9): m = (9 − 3) ÷ (4 − 1) = 6 ÷ 3 = 2. The midpoint is just the average of each coordinate: ((1+4)/2, (3+9)/2) = (2.5, 6).
3.2Your first curve
Pythagoras & trigonometry
Two tools, one triangle. If you know two sides of a right-angled triangle, Pythagoras finds the third. If you know one side and one angle, trigonometry finds the rest.
4.1Pythagoras' theorem
- Finding the hypotenuse: add. Sides 6 and 8: c² = 36 + 64 = 100, so c = 10.
- Finding a short side: subtract. Hypotenuse 13, one side 5: a² = 169 − 25 = 144, so a = 12.
- It only works with the right angle. No right angle, no Pythagoras — that's what the little square in the corner is telling you.
4.2SOH CAH TOA
- Label the sides from the angle you know (or want). Opposite, adjacent, hypotenuse.
- Pick the ratio that uses your two sides. Know the hypotenuse, want the opposite? That's O and H — sine.
- Solve. Hypotenuse 10, θ = 30°: opposite = 10 × sin 30° = 10 × 0.5 = 5.
sin 30° = 0.5 · cos 60° = 0.5 · tan 45° = 1. Everything else, the calculator knows — just make sure it is in degrees mode.
How English actually works.
Four units: the grammar that builds every sentence, the punctuation that can change a sentence's whole meaning, the tricks writers use to persuade you, and the devices that make stories and poems come alive — built from the Year 8 English language and literature descriptions.
The mapFour units
- The building blocks — word classes, phrases and clauses, and the three sentence types.
- Punctuation that changes meaning — apostrophes, commas, dialogue, and the homophones that trip everyone up.
- The art of persuasion — audience, purpose, and the techniques writers use to win you over.
- Stories and poetry — narrative structure, point of view, and figurative language.
Can you control sentences and punctuation in your own writing, and can you name what a writer is doing — the persuasive technique, the narrative choice, the figure of speech — and say what effect it has on the reader?
The building blocks: words, phrases, clauses
Every sentence ever written is built from the same small kit of parts. Learn the parts and their names, and suddenly you can see how any sentence is put together — and how to fix one that isn't working.
1.1Word classes: the job a word is doing
| Word class | Its job | Examples |
|---|---|---|
| Noun | Names a person, place, thing or idea | teacher, Sydney, bicycle, happiness |
| Verb | An action or a state of being | run, devour, is, seems |
| Adjective | Describes a noun | fragile, ancient, green |
| Adverb | Describes a verb (often how, when, where) — many end in -ly | quickly, rarely, yesterday |
| Pronoun | Stands in for a noun | she, it, they, who |
| Preposition | Shows position or relationship | under, before, with |
| Conjunction | Joins words or clauses | and, but, because, although |
A word's class is the job it is doing in that sentence, not a fixed label. In "I went for a run", run is a noun. In "I run every morning", it is a verb. Always ask: what is this word doing here?
1.2Phrase vs clause
- A phrase is a group of words without a subject–verb pair: "under the old bridge", "the tall girl", "before lunch". It adds detail but cannot stand alone.
- A clause has both a subject (who or what) and a verb (what they do): "the dog barked".
- A main clause makes sense on its own: "We went home." A subordinate clause starts with a word like although, when, because, if and leaves you hanging: "although it was late…" — it needs a main clause to lean on.
1.3The three sentence types
| Type | Recipe | Example |
|---|---|---|
| Simple | One main clause | The storm hit. |
| Compound | Main clause + main clause, joined by a coordinating conjunction (FANBOYS: for, and, nor, but, or, yet, so) | The storm hit, and the power went out. |
| Complex | Main clause + subordinate clause (joined by when, although, because, if…) | When the storm hit, the power went out. |
Variety is the point. A run of short simple sentences feels tense and punchy. Long complex sentences slow things down and add layers. Good writers choose the sentence type for the effect they want — and examiners reward you for doing the same, on purpose.
Punctuation that changes meaning
"Let's eat, Grandma" and "Let's eat Grandma" are one comma apart — and one of them is a dinner invitation for Grandma, the other a dinner invitation of Grandma. Punctuation is not decoration; it is part of the meaning.
2.1Apostrophes: two jobs, no more
- Contraction — the apostrophe marks missing letters: do not → don't, it is → it's.
- Possession — the apostrophe shows ownership: the student's book (one student), the students' books (more than one — apostrophe after the s).
- Apostrophes are never used just because a word is plural. "Banana's $2/kg" is the classic greengrocer's error.
- The famous pair: it's always means it is or it has. its (no apostrophe) means belonging to it — like his and hers, which take no apostrophe either.
2.2Commas — and the comma splice
- Commas separate items in a list, mark off extra information, and follow a subordinate clause that starts a sentence: "When the bell rang, we left."
- A comma splice is the error of gluing two complete sentences with only a comma: "It was late, we went home." A comma is not strong enough for that job.
- Three legal fixes: a full stop ("It was late. We went home."), a conjunction ("It was late, so we went home."), or a semicolon ("It was late; we went home.").
2.3Punctuating dialogue
- New speaker, new line. Every change of speaker starts a new paragraph.
- Speech marks wrap only the spoken words: "Let's go," said Sam.
- The punctuation before the closing quote stays inside it — a comma if a speech tag follows ("Let's go," said Sam), the full stop if not.
- The speech tag stays lower-case after speech: …" said Sam — unless it is a name.
2.4Homophones: same sound, different word
| Set | How to pick the right one |
|---|---|
| their / there / they're | their = belonging to them · there = a place (has here inside it) · they're = they are |
| your / you're | your = belonging to you · you're = you are. If "you are" fits, it's you're. |
| its / it's | its = belonging to it · it's = it is / it has. Test by expanding it. |
| to / too / two | to = direction or the verb form · too = also, or excessively · two = 2 |
| whose / who's | whose = belonging to whom · who's = who is |
The art of persuasion
Ads, speeches, opinion columns, that message convincing your parents you need a later bedtime — persuasion is everywhere, and it runs on a toolkit more than two thousand years old. Once you can name the tools, they stop working on you and start working for you.
3.1Start with audience and purpose
- Audience: who is this written for? A principal, Year 7s and grandparents need different language, examples and tone.
- Purpose: what is it trying to do — persuade, inform, entertain? Persuasive texts want you to think or do something.
- Every technique below is chosen to suit the audience. Statistics impress a school board; a sad story about one puppy moves the general public.
3.2The three appeals
3.3The techniques toolbox
| Technique | What it does to the reader | Example |
|---|---|---|
| Rhetorical question | Makes readers answer in their heads — and agree | Do we really want to live like this? |
| Rule of three | Three items in a row feel complete and memorable | Cheaper, cleaner and safer. |
| Emotive language | Words chosen to trigger feelings | innocent animals, cruelly abandoned |
| Statistics | Numbers make the claim feel proven | Nine out of ten dentists agree. |
| Expert opinion | Borrows a specialist's authority (ethos) | Professor Chen, a leading marine scientist, warns… |
| Inclusive language | "We" and "our" make it the reader's cause too | Together, we can fix our school. |
| Anecdote | One vivid personal story that puts a face on the issue | Last winter, one dog waited at the shelter for 200 days… |
| Repetition | Hammering a word or phrase makes it stick | Never again. Never. |
Never just spot the technique. The marks come in two halves: name it, then say what it does to this audience. "The rhetorical question 'Do we really want this?' pushes readers to answer 'no' in their own heads — so the writer's conclusion feels like their own idea."
Stories and poetry: the machinery of imagination
Stories feel like magic, but they are built — a structure that manages tension, a chosen point of view, and language that makes pictures in your head. Learn the machinery and you can both analyse it and drive it yourself.
4.1Narrative structure: the shape of tension
4.2Point of view: who is telling this?
- First person ("I") — a character inside the story tells it. Intimate, but we only know what they know — and they might be wrong, or lying.
- Third person limited ("she", "he") — an outside narrator who sticks to one character's thoughts and experiences.
- Third person omniscient — an all-knowing narrator who can enter any character's head and see everything, everywhere.
- POV is a choice with consequences: a mystery told by the detective hides different secrets than one told by the culprit.
4.3Figurative language: pictures made of words
| Device | What it is | Example |
|---|---|---|
| Simile | Compares using like or as | as brave as a lion |
| Metaphor | Says one thing is another | The classroom was a zoo. |
| Personification | Gives human qualities to non-human things | The wind danced through the trees. |
| Alliteration | Repeats the starting sound of nearby words | seven sleepy seagulls soared south |
| Onomatopoeia | A word that imitates its sound | sizzle, crash, buzz |
| Imagery | Language appealing to the five senses to build a picture | the sour tang of smoke on cold air |
| Hyperbole | Deliberate exaggeration for effect | I've told you a million times. |
If the comparison uses like or as, it is a simile. If it flatly claims one thing is another, it is a metaphor. "The moon was like a silver coin" — simile. "The moon was a silver coin" — metaphor.
Castles, plague ships and shoguns.
Four units from the thousand years between the ancient world and the modern one: how medieval Europe organised itself, the disease that broke that system open, the Japan that locked its doors for two centuries, and the Norse seafarers who raided, traded and settled half the known world.
The mapFour units
- Medieval Europe — the feudal pyramid, life on the manor, and why the Church touched everything.
- The Black Death — how a plague crossed the world in four years, what people thought caused it, and how it shook feudalism itself.
- Japan under the shoguns — the Tokugawa social order, the samurai, and 200 years of closed doors.
- The Vikings — raiders, traders and settlers, from Lindisfarne in 793 to the end of the Viking Age in 1066.
Not just remembering dates — using them. You should be able to put events in chronological order, explain cause and effect (the Black Death caused a labour shortage, which led to peasants demanding wages), and show how societies were organised and why they changed.
Medieval Europe: a society built like a pyramid
After the Roman Empire collapsed in western Europe, there was no police force, no standing army, no government you could appeal to. What grew in the gap was feudalism: a deal, repeated at every level of society — land and protection flowing down, loyalty and work flowing up.
1.1The feudal pyramid
1.2Life on the manor
- The manor was the basic unit of medieval life: the lord's house or castle, a village, farmland, common pasture and a church. Most people were born, worked and died on one manor.
- A serf was not a slave — he could not be bought and sold — but he was tied to the land: he could not leave, marry or even grind his grain elsewhere without the lord's permission, and he owed the lord several days of unpaid work every week.
- Villagers farmed long strips scattered across two or three great open fields, leaving one field fallow (unplanted) each year so the soil could recover.
- Famine was a constant fear: one bad harvest meant hunger, two in a row meant starvation. Most peasants never travelled more than a day's walk from home.
1.3The power of the Church
- Medieval western Europe had one Church — the Catholic Church, led by the Pope — and almost everyone belonged to it. People genuinely believed their eternal fate depended on it.
- The Church ran the things governments run today: schools, hospitals, care for the poor. Monasteries copied the books that kept learning alive.
- It was also enormously rich: every family paid a tithe — one tenth of what they produced — and the Church held vast lands.
- Its ultimate weapon was excommunication: being expelled from the Church, which people believed shut the gates of heaven. Even kings feared it.
A knight trained from about age 7 (page), served a knight from about 14 (squire), and was knighted around 21. The code of chivalry said he should be brave, loyal and protect the weak — an ideal, not always the reality. Castles began as quick wooden motte-and-bailey forts (a tower on a mound, plus a fenced yard) and evolved into stone keeps with curtain walls, moats and gatehouses as sieges got smarter.
The Black Death: four years that changed Europe
In 1347 ships from the Black Sea docked in Sicily carrying dying sailors. Within four years the plague had swept the length of Europe and killed somewhere between one third and one half of its people — the deadliest disaster in European history, and one that helped crack feudalism apart.
2.1How it spread
2.2What caused it — then and now
| What people believed in 1348 | What we know now |
|---|---|
| A punishment sent by God for humanity's sins | A disease caused by the bacterium Yersinia pestis |
| Miasma — poisonous "bad air" from swamps and filth | Mainly spread by fleas living on black rats aboard ships and in towns |
| An imbalance of the body's four "humours" | Its pneumonic form also spread person to person, by coughing |
| Deliberate poisoning of wells — a lie used to justify murdering Jewish communities | Today it is treatable with antibiotics; then, most victims died within about a week |
- The most common form, bubonic plague, caused fever and painful swollen lumps — buboes — in the armpits, neck and groin.
- Because people blamed sin, some became flagellants, marching from town to town whipping themselves in public to beg God's forgiveness — and spreading the disease as they went.
- Doctors' remedies — bleeding patients, sweet-smelling herbs, aromatic vinegar — did nothing, because the true cause was invisible to them: germs would not be discovered for another 500 years.
2.3The consequences
- Catastrophic death toll. Historians estimate between a third and a half of Europe's population died — roughly 25 to 50 million people. Some towns lost more; a few remote areas escaped almost untouched. (The exact number is contested — medieval record-keeping collapsed along with everything else.)
- Labour shortage. Suddenly there were too few workers for the land. Surviving peasants could demand wages, or walk to a lord who would pay them — unthinkable before.
- Lords pushed back. England's Statute of Labourers (1351) tried to freeze wages at pre-plague levels. Resentment at laws like this helped fuel the English Peasants' Revolt of 1381.
- Feudalism weakened. Serfdom didn't vanish overnight, but the old deal — work for protection, never for pay — was broken in western Europe. The Church's authority also suffered: prayers had not stopped the dying.
Plague → massive death toll → labour shortage → surviving workers demand wages and move freely → lords try to force old terms back → revolt and resistance → serfdom declines. Learn it as a chain, and you can answer almost any "consequences" question.
Japan under the shoguns: order, honour, closed doors
While Europe's pyramid was crumbling, Japan built one of the most tightly ordered societies in history — ruled not by its emperor but by a military lord, the shogun — and then sealed itself off from most of the world for over 200 years.
3.1The Tokugawa social order
After a century of civil war, Tokugawa Ieyasu won the decisive Battle of Sekigahara in 1600 and became shogun in 1603. The emperor remained in Kyoto as a revered figurehead — but real power sat with the shogun in Edo (today's Tokyo). Below him, society was frozen into ranked classes. You were born into your class, dressed according to it, and almost never left it.
| Rank | Who | Why they ranked there |
|---|---|---|
| Shogun | The military ruler — the Tokugawa family for 250+ years | Held real power, ruling in the emperor's name |
| Daimyo | Great lords governing their own domains | Powerful, but kept obedient — forced to spend alternate years at Edo, leaving their families there as hostages |
| Samurai | The warrior class, about 6–7% of Japan — only they could carry the two swords | Honoured as protectors; in the long peace many became officials and administrators |
| Peasants | Farmers — the great majority of the population | Respected in theory (they grew the rice everything ran on) but heavily taxed in practice |
| Artisans | Craftspeople — swordsmiths, carpenters, weavers | Made useful things with their hands |
| Merchants | Traders and money-lenders | Ranked lowest — they produced nothing themselves — yet many grew richer than samurai |
- Samurai lived by bushido, "the way of the warrior": absolute loyalty to your lord, courage, self-discipline and honour valued above life itself. A disgraced samurai was expected to die rather than live with shame.
- Compare this with European chivalry: both were warrior codes tied to a lord — but bushido put loyalty and honour first, where chivalry (in theory) put protecting the weak and serving God.
3.2Sakoku: the closed country
- Why close the country? The shoguns feared Christianity and European influence would divide Japanese loyalties and invite conquest — they had watched European powers colonise elsewhere in Asia.
- Isolation was not total: one carefully guarded window stayed open. Dutch and Chinese traders could dock at the tiny artificial island of Dejima in Nagasaki harbour — Japan's only official peephole on the world.
- The result was two centuries of internal peace: cities, roads, theatre, woodblock printing and literacy flourished — while Japan's military technology stood still, which is exactly what Perry's cannon exposed in 1853.
Both Tokugawa Japan and medieval Europe were strict hierarchies topped by a warrior elite bound by a code of honour. The big difference: Europe's system was loosening after the Black Death, while Japan's was deliberately frozen in place by law — and it stayed frozen until the outside world forced the doors open in 1853.
The Vikings: raiders, traders, settlers
"Vikings" were Norse people from Scandinavia — today's Norway, Denmark and Sweden. The stereotype is the axe-swinging raider, and the raids were real — but the same ships that carried raiders also carried merchants to the markets of the east and families to new farmland across the North Atlantic.
4.1The Viking Age, 793–1066
4.2Raiders, traders, settlers — three faces, one people
| Face | What it looked like | Evidence |
|---|---|---|
| Raiders | Fast hit-and-run attacks on coastal targets — monasteries were favourites: rich in silver, poor in defenders | Monastery chronicles like Lindisfarne's; buried treasure hoards hidden from raids |
| Traders | Furs, amber, walrus ivory and enslaved captives exchanged for silver, silk and spices; river routes ran east all the way to Constantinople | Thousands of Middle Eastern silver coins dug up in Scandinavian hoards |
| Settlers | Farming families claiming new land: eastern England (the Danelaw), Iceland, Greenland — briefly even North America | Norse place-names across England (-by, -thorpe); the excavated Norse site at L'Anse aux Meadows, Canada |
4.3The longship — the technology behind it all
- Longships were fast under sail or oar, and their genius was a shallow draught: they needed so little water that they could row far up rivers and land directly on beaches — no harbour required. That made surprise raids possible, and escape easy.
- The same shipbuilding skill produced broader, deeper cargo ships (knarrs) that carried settlers, livestock and trade goods across open ocean to Iceland and Greenland.
- Vikings navigated without compasses — by sun, stars, landmarks, birds and hard-won sea knowledge.
- Settlement changed them: in England the Danelaw Vikings became Christian farmers within a few generations, and their words — sky, egg, knife, they — are still in English.
"Were the Vikings just violent raiders?" The full-marks answer weighs both sides: yes, the raids were real and terrifying (Lindisfarne 793, and monks' chronicles say so — though remember the monks were the victims, so their accounts are hostile sources). But archaeology shows the bigger story: trade routes stretching to Constantinople, and generations of peaceful farming settlement from the Danelaw to Iceland.
The shape of the land, the pull of the city.
Four units in two halves: first the slow forces that carve mountains, coasts and Uluru — and the sudden ones that shake, erupt and flood. Then the biggest migration in human history: the world moving into cities, and where Australia fits in it.
The mapFour units
- Landforms and landscapes — weathering, erosion and deposition: the three processes behind every landscape, and what Country means.
- Geomorphic hazards — earthquakes, volcanoes, tsunamis and landslides: causes, impacts, and what people can actually do.
- Urbanisation and megacities — why over half of humanity now lives in cities, and what a city of ten million is like.
- Australia's urban future — where Australians live, why the coast won, and what makes a city worth living in.
Explaining how geomorphic processes create and change landscapes and produce hazards — and explaining the causes and consequences of urbanisation, using Australia and Asia as your evidence.
Landforms and landscapes: the slow sculptors
Every cliff, valley and dune you have ever seen is a work in progress. Three quiet processes — breaking rock, moving it, dropping it — have been running for billions of years, and they explain nearly everything about the shape of the land.
1.1Landscapes and landforms
A landform is a single natural feature — one mountain, one valley, one beach. A landscape is the whole scene those features add up to. Australia has nearly every kind:
| Landscape type | What defines it | An Australian example |
|---|---|---|
| Coastal | Shaped by waves and tides | The Great Ocean Road cliffs, Victoria |
| Arid (desert) | Shaped by wind and rare, violent rain | The Simpson Desert's parallel red dunes |
| Mountain | Uplifted land, carved by ice and rivers | The Australian Alps |
| Riverine | Built and re-built by rivers | The Murray–Darling floodplains |
| Karst | Limestone dissolved into caves and sinkholes | The Jenolan Caves, NSW |
1.2The three processes
- Physical weathering cracks rock without changing it: day–night heating and cooling, water freezing in cracks, salt crystals growing in coastal rock.
- Chemical weathering changes the rock itself: rainwater is very slightly acidic and slowly dissolves minerals — that is what hollowed out every limestone cave.
- Biological weathering is life doing the damage: tree roots widening cracks, lichens eating into stone.
- The agents of erosion are moving water, wind, ice and waves. Each one sorts and carries the broken pieces — and each one eventually deposits them.
1.3Landscapes in action
- Uluru. Around 550 million years ago, sand eroded off ancient mountains piled up in huge fans. Buried and squeezed, it hardened into tough sandstone, then earth movements tilted the layers nearly vertical. Ever since, weathering and erosion have stripped away the softer surrounding rock — leaving the hard remnant standing 348 m above the plain, with far more of it still below the surface.
- A river valley. A young river cuts downward, carving a narrow V-shaped valley; lower down it slows, swings side to side, and deposits floodplains of fertile silt.
- A coastline. Waves attack a headland's cracks, opening a cave; the cave punches through into an arch; the arch roof collapses, leaving a stack; the stack wears down to a stump. Victoria's Twelve Apostles are limestone stacks mid-story — despite the name, eight remain standing.
For Aboriginal and Torres Strait Islander peoples, land is Country: not property but a living whole of land, water, sky, ancestors and law, carrying creation stories and responsibilities of care. Uluru is sacred to its traditional owners, the Anangu, under their law, Tjukurpa — and at their request the climb was permanently closed in 2019. Practices such as cultural burning — small, cool, planned fires — managed Australian landscapes for tens of thousands of years, and are being used again today.
Geomorphic hazards: when the ground turns dangerous
The same Earth processes that build landscapes occasionally do it violently. A geomorphic hazard is any Earth-made threat to people — and the fascinating part is not the disaster, it is what people can do before it.
2.1The four big ones
| Hazard | Cause | Worst impacts | Best responses |
|---|---|---|---|
| Earthquake | Stress between locked plates suddenly snaps rock along a fault | Collapsing buildings — the shaking itself rarely kills directly | Strict building codes, drills, "drop, cover, hold on" |
| Volcano | Molten rock rises where plates collide or over hot spots | Ash, lava, fast-moving hot flows; flights grounded continents away | Monitoring gives warning days ahead — evacuation saves most lives |
| Tsunami | An undersea earthquake jolts the whole ocean above it | Walls of water flooding kilometres inland | Ocean sensor networks, sirens, and running to high ground fast |
| Landslide | Gravity wins on a slope weakened by water, quakes or clearing | Sudden burial of roads and buildings below | Drainage, planting slopes, not building on or under them |
- Earthquake size is measured by magnitude — and the scale is sneaky: each whole step means about 32 times more energy. A magnitude 7 is not "a bit worse" than a 5 — it releases roughly a thousand times the energy.
- Volcanoes give as well as take: volcanic soils are among the most fertile on Earth, which is exactly why millions of people farm on their slopes.
- The deadliest recent example: the 2004 Boxing Day tsunami. A magnitude-9.1 quake off Sumatra sent waves across the Indian Ocean, killing around 230,000 people in 14 countries — most of whom had no warning at all. The warning systems that now ring the Indian Ocean were built because of it.
2.2How a tsunami works
Australia sits in the middle of its tectonic plate, far from the edges where most quakes and volcanoes happen — that is why it is so quiet. But mid-plate stress still snaps sometimes: the 1989 Newcastle earthquake (magnitude 5.6) killed 13 people, and the 1997 Thredbo landslide killed 18. The mainland's youngest volcanoes, near Mount Gambier, last erupted only about 5,000 years ago — recent, by geological standards. And Australian coasts remain exposed to tsunamis crossing the oceans.
Urbanisation and megacities
In 1800, barely anyone lived in cities. Today more than half of all humans do, and the shift is still running — the largest movement of people in history, almost all of it happening in Asia and Africa.
3.1What is happening, and why
- Urbanisation means the share of people living in cities is rising. The world crossed the half-way mark around 2007; the UN projects about two-thirds urban by 2050.
- A megacity is a city of 10 million or more people. There were only two in 1950 (Tokyo and New York); today there are more than 30 — and most of them are in Asia.
- Greater Tokyo is the biggest of all — home to roughly 37 million people, more than all of Australia combined.
3.2Consequences of growing this fast
- Housing can't keep up. When millions arrive faster than homes can be built, people build their own: informal settlements (slums) without secure water, sewerage or land rights. Dharavi in Mumbai packs roughly a million people into about 2.5 km² — yet is also a hive of small businesses.
- Systems strain: traffic congestion, air pollution, waste, and water supplies stretched to the limit.
- But cities also deliver. On average, city dwellers are closer to work, schools and hospitals, and services are cheaper to provide per person than when the same people are scattered. That is why people keep coming — the move is usually rational.
Rich countries mostly urbanised before 1950 and have now levelled off; today's fast urbanisation is happening in Asia and Africa. So most new megacities are in lower-income countries — which is exactly why housing and services struggle to keep pace.
Australia's urban future
Australia is a giant continent that lives in a handful of coastal cities. Understanding why — and how migration keeps reshaping those cities — is understanding modern Australia.
4.1Where Australians actually live
- Why the coast, and why the south-east? Reliable rain, milder climate, better soils, and natural harbours. The colonial ports — Sydney, Melbourne, Brisbane, Perth, Adelaide — became the trade gateways, and jobs have snowballed around them ever since.
- The five biggest today (approx., 2024): Sydney ~5.5 million, Melbourne ~5.4 million, Brisbane ~2.9 million, Perth ~2.5 million, Adelaide ~1.5 million.
4.2Migration keeps redrawing the map
- Internal migration — Australians moving within Australia. Two famous currents: the sea change (city to coastal town) and tree change (city to country town). The biggest single flow of recent decades has been to south-east Queensland.
- International migration — most new migrants settle in the big cities, especially Sydney and Melbourne. It is the main engine of those cities' growth and diversity: about 30% of Australians were born overseas, one of the highest shares in the world.
- Young people flow toward the big cities for study and first jobs; families and retirees flow outward for space and affordability. Both currents run at once.
4.3Liveability — and planning for 40 million
- Liveability measures how good a city is to live in: safety, healthcare, education, transport, environment, culture. Australian cities routinely rank near the top of world surveys — Melbourne was ranked the world's most liveable city seven years running (2011–2017).
- The threats to that ranking are home-grown: urban sprawl (endless outward growth, leaving people far from jobs), congestion, and housing costs.
- Strategies on the table: build medium-density housing near transport instead of only sprawling outward; invest in public transport; protect green space; and grow regional centres so the capitals aren't the only choice (decentralisation).
Define it, measure it, improve it: liveability is the quality of living conditions; it is compared using factors like safety, health services, education, transport and environment; and any improvement strategy you name should match a factor — e.g. "extending the rail line improves transport access for outer suburbs".
Reading like a writer.
Four units: how word choice builds a voice, how arguments are constructed (and where they cheat), how to write the analytical paragraph that every English exam wants, and how to read the news without being played — built from the Year 9 English language and literacy descriptions.
The mapFour units
- Voice and tone — how word choice, register and sentence shape create a personality on the page.
- Rhetoric and argument — claims, evidence, appeals, and the fallacies that make bad arguments look good.
- The analytical paragraph — TEEL: the four-move structure for analysing any text.
- Reading the news — angle, bias, headlines, and telling fact from opinion.
Moving past "spot the technique" to analysis: how do a writer's specific language choices create voice, position an audience, and build an argument — and can you explain that in a structured analytical paragraph of your own?
Voice and tone: the personality in the words
Read one paragraph of a favourite author and you can often name them without a byline. That recognisable personality is voice — and it is built from choices you can point to: which words, which register, which sentence shapes.
1.1The three levers of voice
| Lever | What it means | The effect of moving it |
|---|---|---|
| Diction (word choice) | Which words, out of all the options — home or residence or shack? | Each option carries its own associations and formality |
| Register | The formality level, matched to audience and situation | Formal register signals authority and distance; informal signals closeness |
| Syntax (sentence shape) | Long and flowing, or short and clipped? | Short sentences: urgency, bluntness, tension. Long ones: reflection, detail, calm |
Voice is the writer's overall personality across a text — it stays fairly stable. Tone is the attitude to the subject at a given moment — sarcastic, mournful, outraged — and it can shift from paragraph to paragraph. You identify tone the same way every time: through the word choices on the page.
1.2Connotation: the charge a word carries
- Denotation is a word's literal, dictionary meaning. Connotation is the cloud of associations and feelings it carries with it.
- Slender, thin and scrawny all denote the same body — but one flatters, one is neutral, one insults. The connotation does the persuading.
- Writers pick the connotation, not just the meaning: freedom fighter vs rebel vs terrorist can describe the same person from three different sides.
| Positive | Neutral | Negative |
|---|---|---|
| slender | thin | scrawny |
| determined | firm | stubborn |
| home | house | shack |
| youthful | young | childish |
Never write "the author uses word choice" — every author does. Name the specific word, state its connotation, and say what it makes the reader feel: "Calling the shed a shack connotes poverty and neglect, positioning the reader to pity its owner."
Rhetoric and argument: how cases are built
An argument is a machine: a claim, supported by evidence, connected by reasoning. Learn the parts and you can build strong arguments — and, just as usefully, spot exactly where a weak one is cheating.
2.1The anatomy of an argument
- Claim — the statement the writer wants you to accept: "School should start at 10 am." A claim on its own proves nothing.
- Evidence — verifiable support: facts, data, examples, expert testimony. "Sleep studies of 3,000 teenagers found…"
- Reasoning — the link explaining why the evidence supports the claim. Evidence without reasoning is just trivia.
- The three appeals still apply at Year 9: ethos (credibility), pathos (emotion), logos (logic). Strong arguments lean on logos and use the others in support.
- A strong argument also anticipates the counter-argument and answers it, instead of pretending it doesn't exist.
2.2Fallacies: arguments that cheat
A fallacy is a flaw in reasoning that makes an argument look stronger than it is. Six to know by name:
| Fallacy | The cheat | Example |
|---|---|---|
| Ad hominem | Attacks the person instead of their argument | "Why listen to her plan? She failed Year 9 maths." |
| Straw man | Misrepresents the opposing view, then attacks the distortion | "So you want later starts? You clearly think school doesn't matter at all." |
| Bandwagon | Popularity offered as proof | "Every other school has done it, so we should too." |
| False dilemma | Pretends only two options exist | "Either we ban phones completely, or results will collapse." |
| Slippery slope | Claims one small step must lead to catastrophe, with no evidence for the chain | "Allow one late homework and soon nobody will hand in anything, ever." |
| Hasty generalisation | A sweeping conclusion from one or two cases | "My cousin's school tried it and hated it, so it fails everywhere." |
Full marks need two steps: name the fallacy, then explain why the reasoning fails here. "This is a false dilemma: banning phones and collapsing results are not the only options — phone lockers, class-time rules and partial bans all exist."
The analytical paragraph: TEEL
Every English essay you write from now to Year 12 is built from one repeating unit: the analytical paragraph. TEEL is its skeleton — four moves, in order, every time. Master the paragraph and essays become assembly.
3.1The four moves
3.2A worked example
- T — "Owen's Dulce et Decorum Est strips war of its glamour."
- E — "He opens by describing the marching soldiers as 'bent double, like old beggars under sacks'."
- E — "This simile replaces the recruiting-poster image of proud young soldiers with figures who are broken and prematurely aged."
- L — "From its first image, the poem begins dismantling the 'old Lie' that dying in war is sweet and honourable."
3.3Embedding quotes
- Short beats long. A phrase of two to eight words, woven into your own sentence, beats a copied paragraph every time.
- Embedded means grammatical: your sentence must read smoothly with the quote inside it — "Owen describes soldiers who march 'like old beggars', broken by the war."
- Exact words, in quotation marks. If you change or trim anything, the sentence around it must still be honest about what the text says.
- Never begin a sentence with a floating quote and no introduction — the dreaded "dropped quote".
Reading the news: the angle behind the story
No news story is just "what happened". Someone chose what to cover, whom to quote, which word to put in the headline and what to leave out. Reading the news well means seeing those choices — not assuming the worst, just seeing them.
4.1Angle, and the three faces of bias
- The angle is the perspective a story is told from — the same school-funding decision can be "a lifeline for students" or "a budget blowout", and both can be factually accurate.
- Bias by selection: which stories, facts and voices get included — and which are left out (omission).
- Bias by placement: front page or page 14? First paragraph or last? Position signals importance.
- Bias by language: loaded language — word choices whose connotations tilt the reader. "Prices soar" and "prices rise" report the same fact at different temperatures.
4.2Headline tricks
| Technique | Example | What it's doing |
|---|---|---|
| Emotive / loaded verb | Council slammed over pool closure | "Criticised" becomes a physical attack — drama sells |
| Pun / wordplay | Purr-fect ending for lost cat | Entertains; signals a light story |
| Alliteration | Beach ban battle begins | Rhythm makes it catchy and memorable |
| Sensationalism | CHAOS as trains delayed 20 minutes | Inflates scale to grab attention |
| Question headline | Is your suburb next? | Manufactures worry; makes you click to find out |
4.3Fact vs opinion
- A fact can be checked and verified against evidence: "The match ended 2–1." It can still be wrong — but it is checkable.
- An opinion is a judgement or preference: "The referee was a disgrace." It cannot be verified, only argued for.
- The danger zone is opinion dressed as fact: "Everyone knows the plan has failed." Ask: could evidence check this claim?
- Quality journalism separates the two: news reports lead with verifiable facts; opinion lives in clearly labelled columns.
Treat a news article exactly like a poem: quote the specific word, name the device (loaded language, emotive verb, selection of detail), and state the effect: "Slammed frames ordinary criticism as violent, positioning readers against the council before any facts arrive."
Steam, ships and the birth of a nation.
Four units spanning the century and a half that built the modern world: machines replace muscle in Britain, millions of people move across oceans — some in chains — six colonies argue their way into being Australia, and then the whole system marches into the First World War.
The mapFour units
- The Industrial Revolution — why Britain first, what the machines changed, and what factory life cost.
- Movement of peoples — convicts, enslaved people and free settlers: who moved, why, and what it was like.
- Making a nation — colonisation and frontier conflict, gold and Eureka, and the road to Federation in 1901.
- World War I — the causes, the trenches, Gallipoli, and the conscription fight that split Australia.
Cause and consequence at full depth: not "the war started in 1914" but why — long-term causes (militarism, alliances, imperialism, nationalism) versus the short-term trigger. Plus perspectives: the gold rush looked very different to a digger, a trooper, and the Wathaurong people of Ballarat.
The Industrial Revolution: when machines changed everything
For all of human history, work meant muscle — human or animal — plus wind and water. Then, in Britain from about 1750, coal-fired steam power broke that limit, and within a century everyday life changed more than it had in the previous thousand years.
1.1Why Britain first?
| Advantage | Why it mattered |
|---|---|
| Coal and iron | Huge, easily mined deposits — the fuel and the metal of the new machines |
| Empire and trade | Colonies supplied raw materials (like cotton) and bought the finished goods |
| Money to invest | Profits from trade — including the slave trade — funded factories and machines |
| Spare workers | Better farming methods fed more people with fewer hands, freeing labour for factories |
| Stability and transport | A stable government, plus rivers and new canals to move heavy goods cheaply |
1.2The machines
1.3What it cost: factories, children, cities
- The factory system replaced home workshops: hundreds of workers under one roof, working to the machine's pace and the owner's clock — shifts of 12 to 14 hours were common.
- Child labour was everywhere: children were cheap, obedient, and small enough to crawl under moving machinery or through narrow mine tunnels. Many were injured; some never saw daylight in winter.
- Urbanisation: people flooded from farms to factory towns. Manchester grew from about 25,000 people in 1770 to over 300,000 by 1850 — with housing, sewers and clean water nowhere near keeping up. Cholera swept the slums.
- Responses grew alongside: machine-smashing Luddites (1811–16), early trade unions, reform campaigners like Lord Shaftesbury, and eventually Parliament's Factory Acts and Mines Act.
Short term, for workers: brutal — hours, danger, slums, child labour. Long term: mass-produced goods, railways, rising wages, and the laws, unions and public-health reforms that the horrors themselves provoked. A top answer gives both, with evidence for each — and notes that the people who paid the costs were rarely the ones who collected the benefits.
Movement of peoples: chained, forced and free
Between 1750 and 1900 millions of people crossed the world's oceans — and the differences matter. Enslaved Africans were taken by force. British convicts were transported as punishment. Free settlers chose to go, pushed by hardship at home and pulled by promises abroad.
2.1Three very different journeys
- The transatlantic slave trade. Over roughly four centuries, about 12 million enslaved Africans were shipped across the Atlantic to the Americas. The crossing — the Middle Passage — packed people below decks in chains for weeks; huge numbers died at sea. Much of the cotton feeding Britain's mills was grown by enslaved labour.
- Convict transportation. Britain's answer to overflowing prisons: exile. From the First Fleet's arrival at Sydney Cove in 1788 to the last ship into Western Australia in 1868, about 162,000 convicts were transported to the Australian colonies — most for property crimes like theft, some for political protest (including the Tolpuddle Martyrs, transported in 1834 for forming a farm workers' union).
- Free settlers. Growing numbers chose the voyage — many with fares paid by assisted migration schemes hungry for workers, and a flood more after gold was found in 1851.
2.2Push and pull
| Push factors (drove people out) | Pull factors (drew people in) |
|---|---|
| Poverty and unemployment in industrial cities | Cheap land impossible to own at home |
| The Irish famine, 1845–49 — a million dead, a million emigrated | Gold, from 1851 |
| Overcrowded slums and disease | Assisted passage — the fare paid for you |
| Religious or political persecution | Higher wages, and family already there writing home |
2.3The timeline of forced migration's end
Slavery, convict transportation and free settlement all moved people across oceans — but with completely different legal status: enslaved people were property for life, with children born enslaved; convicts served a sentence with an end date and could earn freedom; free settlers kept every right they sailed with. Markers reward answers that keep these distinct.
Making a nation: from six colonies to one Australia
Australia wasn't born in 1901 out of nothing. It was built — on land taken from Aboriginal peoples in a long frontier conflict, transformed by a gold rush that tripled the population in a decade, and finally stitched together by referendum into a federation.
3.1Colonisation and the frontier
- Britain claimed the continent under the doctrine later called terra nullius — "land belonging to no one" — treating tens of thousands of years of Aboriginal ownership as if it didn't exist.
- As settlers and their sheep pushed inland, Aboriginal peoples resisted the loss of land and water — leaders like Pemulwuy fought a guerrilla campaign around Sydney in the 1790s. This frontier conflict ran for over a century, alongside devastating epidemics like the 1789 smallpox outbreak.
- The Myall Creek massacre (1838) stands out in the record because of what followed: seven colonists were tried and hanged for murdering 28 Aboriginal people — one of the very few times frontier killings were punished.
3.2Gold and Eureka
- Payable gold was found in New South Wales in 1851, then in far richer fields in Victoria (Ballarat, Bendigo). People poured in from Britain, Ireland, China, America and Europe — the non-Indigenous population roughly tripled in the 1850s.
- Every digger had to buy a monthly miner's licence — costly whether you found gold or not — enforced by brutal licence hunts.
- On 3 December 1854, diggers at Ballarat burned their licences, built a stockade at Eureka and swore an oath under the Southern Cross flag, led by Peter Lalor. Soldiers and police stormed it at dawn; around 22 diggers and at least 5 soldiers died.
- The rebels lost the battle and won the argument: juries refused to convict them, the hated licence was replaced by a cheap Miner's Right — which came with the vote. Eureka became a symbol of Australian democracy.
3.3Federation, 1901
Federation looked like a proud birth to most colonists. To Aboriginal peoples it delivered a constitution that excluded them from the census count and from federal law-making power — exclusions that stood until the 1967 referendum. A strong answer can hold both perspectives at once.
World War I: the war that made the modern world darker
One assassination in Sarajevo shouldn't have set the whole world on fire. That it did tells you the fuel was already stacked: rival empires, arms races, prickly nationalism — and a web of alliances that turned any local quarrel into everyone's war.
4.1The causes: MAIN + the spark
- M — Militarism: Europe's powers had spent decades building huge armies and navies (Britain and Germany raced to out-build each other's battleships) and glorifying war.
- A — Alliances: the Triple Alliance (Germany, Austria-Hungary, Italy) faced the Triple Entente (Britain, France, Russia) — promises that meant a quarrel between two nations dragged in six.
- I — Imperialism: rival empires competed for colonies, markets and resources, storing up resentments.
- N — Nationalism: fierce national pride — and in the Balkans, Serbian nationalists wanting Austria-Hungary's Slavic lands.
- The spark: on 28 June 1914, Archduke Franz Ferdinand, heir to Austria-Hungary's throne, was assassinated in Sarajevo by the Bosnian Serb nationalist Gavrilo Princip.
4.2Trenches and Gallipoli
- On the Western Front the armies dug in from the Channel to Switzerland: trench warfare. Machine guns and artillery made attacking across no-man's-land close to suicidal, so the line barely moved for four years.
- Trench life meant mud, rats, lice, "trench foot", shellfire — and going "over the top" into wire and machine guns.
- Gallipoli: to knock the Ottoman Empire out of the war and open a sea route to Russia, Allied forces landed on the Gallipoli peninsula on 25 April 1915 — the Australians and New Zealanders (the Anzacs) at what became Anzac Cove. The Turkish defenders held the heights; eight months of stalemate followed, and the peninsula was evacuated by early 1916. About 8,700 Australians died there.
- The Anzac legend — courage, endurance, mateship — was born at Gallipoli. Historians debate it: the campaign was a defeat, war correspondents wrote it up heroically at the time, and the Western Front (where about 46,000 Australians died, 1916–18) was far deadlier yet is far less remembered. You should be able to state both the legend and the debate.
4.3Australia divided: conscription
- All ~416,000 Australians who served enlisted voluntarily — but as casualties mounted, Prime Minister Billy Hughes tried to introduce conscription for overseas service.
- Two national votes — October 1916 and December 1917 — both said No, narrowly. The campaigns were bitter, splitting families, churches and the Labor Party itself.
- The war ended with the armistice of 11 November 1918. Around 60,000 Australians were dead — from a population under five million, one of the heaviest tolls per head among the Allies.
Never write "WWI started because Franz Ferdinand was shot" and stop. The assassination was the trigger; the MAIN factors were the fuel. The test: assassinations had happened before without world wars. Only a Europe already primed — armed, allied, and rivalrous — could turn one pistol shot into 20 million deaths.
Feeding, and connecting, eight billion people.
Four units: the great vegetation zones of the planet, how we turned them into the world's food supply, why hundreds of millions still go hungry anyway — and the trade, tourism and technology that stitch every place on Earth to every other.
The mapFour units
- Biomes — why two numbers, temperature and rainfall, predict the vegetation almost anywhere on Earth.
- Feeding the world — how farmers push past climate, soil and water limits, and what that costs the environment.
- Food security — who goes hungry, why it is mostly about poverty not shortage, and the 2050 challenge.
- Interconnections — trade, tourism, transport and the internet: how one phone in your pocket touches five continents.
Explaining how biomes produce food, the constraints on production and how people alter them, the causes and consequences of food insecurity — and how interconnections through trade, travel and technology change places and people.
Biomes: the world sorted by climate
Fly from the equator toward a pole and the vegetation changes in great bands: rainforest, savanna, desert, grassland, forest, tundra. Those bands are biomes — and they are not random. Two numbers place nearly every one.
1.1Two numbers rule everything
A biome is a huge region sharing one broad climate and one broad kind of vegetation and wildlife. What decides which biome grows where? Mostly just how hot it is and how much rain falls:
1.2Australia's share
- Australia is the driest inhabited continent: roughly 70% is arid or semi-arid (approx.) — the desert and scrub Australians call the outback.
- Across the north: tropical savanna with a drenching wet season and a long dry — cattle country.
- The south-east and south-west corners: temperate forests and grasslands — where the farms, and nearly all the people, are.
- Far north Queensland: tropical rainforest. The Daintree is often called the oldest continuously surviving tropical rainforest on Earth.
Lush rainforest, rich soil? Backwards. Rainforest nutrients are held in the living plants and recycled the moment anything falls; the heavy rain leaches (washes) goodness out of the soil itself, so cleared rainforest land exhausts quickly. It is the world's grasslands — with their deep, dark, organic-rich soils — that became the great wheat belts.
Feeding the world: pushing past the limits
Every meal you have ever eaten came out of a biome. Farming is the art of taking what a biome offers and pushing past what it refuses — and every push has a price.
2.1What limits a harvest — and how farmers fight back
- Humanity leans astonishingly hard on a few plants: just three crops — rice, wheat and maize — supply about half of all the calories people eat (approx.). Most grain grows on former grasslands, thanks to their deep fertile soils.
- What limits the harvest anywhere: climate (heat, frost, growing season), water, soil quality, and terrain.
| The limit | The fix | The catch |
|---|---|---|
| Not enough rain | Irrigation — channel, pump or drip water to the crop | Rivers and groundwater can be drained; salt builds up in soil |
| Worn-out soil | Fertiliser puts nitrogen and nutrients back | Runoff feeds algal blooms that choke waterways |
| Low-yielding plants | Better varieties — the Green Revolution's high-yield wheat and rice | Needs more water and fertiliser to deliver |
| Too little labour | Machinery — one driver harvests hundreds of hectares | Expensive; smallholders can't always afford it |
| Cold or short seasons | Greenhouses trap warmth and extend the season | Energy-hungry |
Australia's showcase is the Murray–Darling Basin: irrigation turned dry inland plains into the country's food bowl, growing about a third of Australia's food supply (approx.). The showcase warning is the Aral Sea in central Asia: so much river water was diverted to irrigate cotton from the 1960s that one of the world's largest lakes mostly disappeared.
2.2The salt problem — Australia's own goal
Food security: enough food, wrong places
Here is the uncomfortable fact of this unit: the world already grows enough food for everyone. Hundreds of millions go hungry anyway — which means hunger is mostly a problem of poverty, conflict and waste, not of farming.
3.1The definition, and the map
- Food security means all people, at all times, can get enough safe, nutritious food for an active, healthy life. Miss any part — not enough food, not always, not nutritious — and a person is food insecure.
- The count of undernourished people sits above 700 million — about one person in eleven — and moves with wars and food prices (approx.; it fell for decades, then rose again after 2019).
- The hungriest regions are sub-Saharan Africa and South Asia — not because their land can't grow food, but because poverty, conflict and weak infrastructure stand between people and meals.
3.2The leaky pipeline
3.3Causes — and the road to 2050
| What causes food insecurity | What improves it |
|---|---|
| Poverty — the food exists, the money doesn't | Incomes, jobs, small loans and training for farming families |
| Conflict — farms destroyed, aid blocked | Peace first; emergency food aid meanwhile |
| Drought and a changing climate | Drought-tolerant varieties, irrigation, climate-smart farming |
| Poor roads and storage — harvests rot | Infrastructure: roads, silos, cold chains |
| Waste — a third of food never eaten | Cutting waste at every stage of the pipeline |
By 2050 the world is expected to hold nearly 10 billion people, needing roughly 50% more food than the 2010s (approx.) — while climate change squeezes the very farmland doing the growing. The strongest answers name both sides: grow more sustainably (better yields without new land clearing) and lose less (waste, distribution, fairer access).
Interconnections: no place is an island
Your breakfast, your clothes and your phone each connect you to a dozen countries before nine in the morning. Geography's word for this is interconnection — the flows of goods, people, money and information that tie places together.
4.1Four connectors
- Trade. Australia earns its way selling iron ore (the biggest export), coal, gas, farm produce, education and tourism — mostly to Asia; China is the largest trading partner.
- Transport. The humble shipping container — a standard steel box any crane, ship or truck can handle — slashed the cost of moving goods and supercharged world trade. More than 80% of world trade travels by sea (approx.).
- ICT. Undersea fibre cables carry the internet between continents, letting money, work and ideas move instantly — though the digital divide means billions still lack fast, reliable access.
- Tourism. One of the world's biggest industries — about 1.4 billion international trips in 2019 (approx.). It funds jobs and conservation, and can also crowd, price out and wear down the very places people come to see.
4.2One phone, five continents
Interconnection questions want effects on places, both directions: "Tourism brings income and jobs to Bali but strains its water supply and roads." Goods, people, money and information flow — and every flow changes both ends.
The instruction book, and how it changes.
Four units: the DNA molecule every cell carries, how characteristics pass from parents to children, how populations change over generations, and the evidence that ties it all together — built from AC9S10U01 and AC9S10U02.
The mapFour units
- DNA and genes — the double helix, the base-pairing rule, and how genes sit on chromosomes.
- Inheritance — dominant and recessive alleles, Punnett squares, and predicting a cross's outcomes.
- Evolution by natural selection — the four-step engine that changes populations over generations.
- Evidence and applications — fossils, matching bones, DNA comparisons, and what we now do with DNA.
AC9S10U01 — DNA and genes carry the heritable information; inheritance of characteristics can be predicted, for example with Punnett squares.
AC9S10U02 — the theory of evolution by natural selection explains the diversity of life, and multiple independent lines of evidence support it.
DNA and genes: the instructions in every cell
Almost every cell in your body carries a complete copy of the same molecule: DNA. Stretched out, one cell's worth is about two metres long — folded into a nucleus a hundredth of a millimetre wide. This unit is about what that molecule is and how it stores instructions.
1.1A ladder with a rule
1.2From base to chromosome
- Base — one letter of the code: A, T, G or C. The order of the letters carries the information.
- Gene — a stretch of DNA, often thousands of bases long, holding the instructions for building one protein. Proteins do the actual work — enzymes, pigments, hormones, building materials — so genes control characteristics.
- Chromosome — one very long DNA molecule coiled up tightly with proteins. Humans have 46 chromosomes, arranged as 23 pairs — one of each pair from your mother, one from your father.
- Because chromosomes come in pairs, you carry two copies of each gene. The versions can differ: each version is called an allele. In pea plants, the height gene comes as a "tall" allele and a "short" allele.
- The full human genome is about 3 billion base pairs and roughly 20,000 genes. Every cell carries all of it; different cell types just switch different genes on.
- Occasionally the copying makes an error — a mutation. Most change nothing, a few are harmful, and a rare few are useful. Hold that thought for Unit 3: mutation is where new variation comes from.
DNA is the molecule. A gene is a meaningful stretch of it. A chromosome is a coiled-up package of it. Smallest to largest: base → gene → chromosome. And an allele is not a different thing again — it is simply one version of a gene.
Inheritance: predicting the next generation
You have two alleles of each gene; a parent passes exactly one of them to each child, at random. From that single fact, a monk counting pea plants in the 1860s worked out rules that let you predict inheritance — and a simple grid does the arithmetic.
2.1The vocabulary, fast
| Word | Means | Example (T = tall allele, t = short allele) |
|---|---|---|
| Dominant allele | Shows its effect with just one copy; written as a capital letter | T |
| Recessive allele | Only shows when both copies are recessive; lower case | t |
| Genotype | The allele pair an organism carries — the letters | TT, Tt or tt |
| Phenotype | What the organism actually looks like — the trait you see | tall or short |
| Homozygous | Both alleles the same | TT or tt |
| Heterozygous | The two alleles differ — the dominant one shows | Tt → tall |
2.2The Punnett square
Four moves, every time: (1) define the letters ("let T = tall, t = short"); (2) write the parents' genotypes; (3) draw the square and fill all four boxes; (4) state the ratios — genotype AND phenotype. A ratio is a prediction of chances, not a promise: a real family of four might easily be all tall.
2.3Boy or girl: the 23rd pair
- Twenty-two of your chromosome pairs match. The 23rd pair is the sex chromosomes: XX makes a female, XY makes a male.
- Every egg carries an X. Sperm carry either X or Y, half and half — so it is the sperm that settles the question, and each pregnancy is a 50 : 50 chance. (Draw it: XX × XY is just another Punnett square.)
Dominant only means "shows with one copy". A dominant allele can be rare (most people have no extra fingers, though that allele is dominant) and a recessive one can be everywhere. Never write "stronger gene" — markers cross it out.
Evolution by natural selection: the four-step engine
No individual ever evolves. What changes is a population, over generations, because some inherited variations help their owners survive and reproduce more than others. Four steps, endlessly repeated — that is the whole theory.
3.1The four steps
- Variation. Individuals in a population differ — in colour, speed, chemistry — and much of that variation is inherited. New variation keeps arriving by mutation.
- Selection pressure. Something in the environment — predators, disease, drought, a new chemical — makes survival a competition that not everyone wins.
- Survival and reproduction. Individuals whose variations suit the environment are more likely to live long enough to breed. Surviving is only half the job; the trait must reach offspring.
- Inheritance, over time. The helpful alleles are passed on, so the next generation has more of them. Repeat for many generations and the population as a whole shifts — it has evolved.
3.2Two textbook cases
- The peppered moth. Before industrial soot, England's tree trunks were pale with lichen, and the pale form of the moth was camouflaged; the rare dark form got eaten by birds. Soot blackened the trunks — suddenly the dark moths were hidden and the pale ones exposed. Within decades, dark moths dominated sooty regions. When clean-air laws lightened the trees again, the pale form came back. Same four steps, run twice in opposite directions.
- Antibiotic resistance. In any huge population of bacteria, a few carry mutations that happen to protect them from an antibiotic. The drug kills the rest — a massive selection pressure — and the survivors multiply into a resistant population. Bacteria breed in minutes, so this is evolution fast enough to watch, and it is why doctors say to use antibiotics carefully.
The moths did not "turn dark to adapt", and the bacteria did not "learn to resist". The variation already existed before the pressure arrived; the environment merely decided which existing variants survived to breed. Selection chooses — it never creates on demand.
3.3New species
- A species is a group whose members can breed together and produce fertile offspring.
- Speciation: split one population in two — an ocean, a mountain range — and each half faces different pressures and drifts its own way. Given enough generations, the two groups become so different they can no longer interbreed: one species has become two. Australia's long isolation is why so many of its species exist nowhere else.
The evidence — and what we do with DNA now
A scientific theory earns its keep through evidence from independent directions that all point the same way. Evolution has three classics — and the same DNA science now runs forensics labs and farms.
4.1Three lines of evidence
- The fossil record. Deeper rock layers are older, and reading upward the story is consistent: simpler organisms in ancient layers, later forms appearing above them, and transitional fossils — like whales with leg bones — capturing change mid-journey. No fossil has ever turned up in a layer that breaks the sequence.
- Comparative anatomy. A human arm, a whale flipper, a bat wing and a cat leg do utterly different jobs — yet inside they share the same layout of bones. These homologous structures make no sense as separate inventions, and perfect sense as one ancestral limb reshaped by selection for different lives.
- DNA comparison. If species share ancestors, their DNA should still show it — and it does. Humans and chimpanzees share roughly 98–99% of their DNA; more distant relatives share progressively less. The family tree built from DNA matches the one built from fossils and anatomy — three independent methods, one answer.
4.2Applications: DNA put to work
- DNA profiling. Except for identical twins, no two people share a whole DNA profile. Comparing a handful of highly variable DNA regions can match a crime-scene sample to a person, settle who a child's parents are, or identify remains. A profile match is powerful evidence — but courts still weigh how the sample was collected and handled.
- Genetically modified organisms (GMOs). Scientists can now move a gene directly into an organism's DNA — for example, most Australian cotton carries a bacterial gene that protects it from caterpillars, which has greatly cut insecticide spraying. Supporters point to less spraying and hardier crops; others raise questions about long-term ecosystem effects and want clear labelling. Both the benefits and the concerns are part of the science conversation — a good answer can state each side.
- Note the difference in speed: selective breeding has shaped crops and dogs for thousands of years by choosing parents; genetic modification edits the DNA directly in one step.
"Multiple independent lines of evidence support the theory." Fossils, anatomy and DNA don't rely on each other — any one could have contradicted the rest, and instead each confirms the same family tree. That agreement, not any single fossil, is why the theory is accepted.
Why atoms do what they do.
Four units: what the periodic table's shape really means, the three ways atoms stick together, how to balance a chemical equation properly, and what makes reactions run fast or slow — built from AC9S10U06 and AC9S10U07.
The mapFour units
- The periodic table, properly — periods, groups, and why one column behaves as a family.
- Bonding — ionic, covalent and metallic: three ways to a full outer shell.
- Reactions and equations — conservation of mass, balancing, acids, and the pH scale.
- Reaction rates — collision theory and the four dials that speed a reaction up.
AC9S10U06 — the periodic table's structure reflects atomic structure, and an element's position lets you predict its properties and how it bonds.
AC9S10U07 — chemical reactions can be represented by balanced equations because mass is conserved, and reaction rates depend on collisions between particles.
The periodic table, properly
Last year the table was a map. This year you get the reason for the map: electrons sit in shells, the shells fill in a fixed order — 2, then 8, then 8 at this level — and an atom's chemistry is decided almost entirely by its outermost shell.
1.1Two atoms that explain the table
1.2What the table's shape means
- A period (row) counts the shells: period 1 elements use one shell, period 2 use two, period 3 use three. Moving right along a period adds one electron at a time to the same outer shell.
- A group (column) collects elements with the same number of outer-shell electrons — sodium (2,8,1) sits under lithium (2,1) because both have one outer electron. Same outer shell, same chemical behaviour: that is why a column is a family.
- Metals fill the left and centre (about three quarters of the table); non-metals sit to the top-right; a staircase of metalloids (like silicon) runs between them, part-way in properties — silicon semi-conducts, which is why your phone is full of it.
1.3Three families, three trends
| Family | Outer shell | Behaviour and trend |
|---|---|---|
| Group 1 — alkali metals (Li, Na, K) | 1 electron | Desperate to lose it → very reactive; reactivity increases down the group — lithium fizzes in water, potassium bursts into lilac flame |
| Group 17 — halogens (F, Cl, Br, I) | 7 electrons | Desperate to gain one → very reactive; reactivity increases up the group — fluorine is the fiercest of all |
| Group 18 — noble gases (He, Ne, Ar) | Full | Nothing to gain or lose → almost completely unreactive. The whole point of bonding is to end up like them |
Elements in the same group have the same number of outer-shell electrons, so they react in the same way. Say it with an example — "sodium (2,8,1) and lithium (2,1) both have one outer electron to lose" — and the mark is yours.
Bonding: three roads to a full outer shell
Atoms bond for one reason: a full outer shell is stable, like a noble gas. There are three ways to get one — give electrons away, share them, or pool them — and each way builds materials with completely different personalities.
2.1Ionic bonding: the transfer
2.2Covalent bonding: the share
- Two non-metals have the same problem — both want electrons, neither will give any up. Solution: share pairs. Each shared pair counts toward both atoms' outer shells, and each shared pair is one covalent bond.
- Water, H₂O: oxygen (2,6) needs two more electrons; each hydrogen needs one. Oxygen shares one pair with each of two hydrogens — everyone full.
- Carbon dioxide, CO₂: carbon (2,4) needs four; each oxygen needs two. Carbon shares two pairs with each oxygen — a double bond on each side.
- Sharing builds small, self-contained molecules. The bonds inside a molecule are strong, but molecules barely grip each other — so covalent substances tend to be gases or liquids with low melting points, and they don't conduct electricity.
2.3Metallic bonding: the pool
- Metal atoms all want to lose outer electrons — so in a lump of metal, they all do. The freed electrons form a mobile "sea of electrons" drifting between a lattice of positive metal ions, and that shared glue is the metallic bond.
- The sea explains the metal personality: free electrons carry charge → metals conduct electricity; the glue is non-directional, so layers of ions can slide without shattering → metals bend and stretch; the grip is strong → high melting points.
2.4Match the bond to the properties
| Bond | Between | Electrons are… | Typical properties |
|---|---|---|---|
| Ionic | Metal + non-metal | Transferred → ions | Hard crystals, high melting point; conduct only when molten or dissolved (ions must be free to move) |
| Covalent | Non-metal + non-metal | Shared in pairs | Molecules; low melting points; don't conduct |
| Metallic | Metal atoms | Pooled into a mobile sea | Conduct when solid, bendable, mostly high melting points |
Solid sodium chloride does NOT conduct electricity — its ions are charged but locked in the lattice. Melt it, or dissolve it in water, and the ions can move: now it conducts. "Charged particles that are free to move" is the phrase that earns the mark.
Reactions and equations: making the books balance
Atoms are never created or destroyed in a reaction — only rearranged. A balanced equation is just honest bookkeeping: the same count of every atom on both sides of the arrow.
3.1One balanced equation, drawn
3.2How to balance any equation
- Write the correct formulas and never touch them again. Balancing may not change a formula's little subscript numbers — H₂O is water; H₂O₂ is bleach.
- Count every element on each side. A coefficient multiplies the whole formula: 2H₂O means 4 H and 2 O.
- Add coefficients — the big numbers in front — until the counts match. Adjust one element at a time; leave lone elements (like O₂) until last.
- Recount everything. Worked example: CH₄ + O₂ → CO₂ + H₂O. Carbon is fine; hydrogen needs 2H₂O; that makes 4 O on the right, so 2O₂. Result: CH₄ + 2O₂ → CO₂ + 2H₂O — 1 C, 4 H, 4 O each side.
3.3Acids, bases and pH
- The pH scale runs 0–14: below 7 acidic, 7 neutral, above 7 basic (alkaline). Each step is 10× — pH 3 is ten times more acidic than pH 4.
- Acid + base → salt + water — neutralisation. Example: HCl + NaOH → NaCl + H₂O. It's why antacid tablets calm an acid stomach.
- Acid + metal → salt + hydrogen gas. Example: Mg + 2HCl → MgCl₂ + H₂ — confirm the gas with the squeaky-pop test.
- Acid + carbonate → salt + water + carbon dioxide. Example: CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂ — the fizz on limestone, and the reason acid rain eats statues.
Changing a subscript to make the numbers work invents a different chemical. You may only ever add coefficients — the big numbers in front. If you catch yourself editing a formula, stop and start the count again.
Reaction rates: the collision game
Why does a bushfire race while a nail rusts for years? Same science: reactions happen only when particles collide hard enough to react. Everything that changes a reaction's speed works by changing how often, or how hard, particles collide.
4.1Collision theory in three lines
- Particles must collide to react — no contact, no reaction.
- The collision must carry enough energy to break the old bonds; a gentle bump just bounces.
- So the rate = successful collisions per second. More collisions, or harder collisions, means a faster reaction.
4.2The four dials
| Factor | Mechanism — why it works | Everyday example |
|---|---|---|
| Temperature | Particles move faster → they collide more often AND harder — the only dial that does both | Food spoils on the bench but keeps in the fridge; a glow stick glows brighter in hot water |
| Concentration | More particles packed in the same space → collisions come more often | Strong bleach cleans faster than diluted; pure oxygen makes embers flare |
| Surface area | Crushing a solid exposes buried particles → far more of them are available to be hit | Kindling catches before a log; flour DUST can explode though a bag of flour won't |
| Catalyst | Offers an easier reaction pathway needing less energy → far more collisions succeed — and the catalyst is not used up | A car's catalytic converter; the enzymes digesting your lunch right now |
- Slowing a reaction is the same game in reverse: fridges cut temperature, vacuum packs remove the oxygen concentration, paint keeps oxygen and water from ever colliding with the iron underneath.
- An explosion is only an ordinary reaction with the dials turned all the way up — fine powder, plenty of oxygen, plenty of heat.
Name the factor, then give the mechanism in collision language: "Raising the temperature makes particles move faster, so they collide more often and with more energy, so more collisions succeed each second and the reaction speeds up." Factor → collisions → rate. Never stop at "it reacts faster because it's hotter" — that repeats the question.
A catalyst is not a reactant. It comes out of the reaction unchanged and is never in the equation's reactants or products — one teaspoon can serve millions of collisions. If your answer says the catalyst "gets used up", cross it out.
Why things move the way they do.
Four units: how to describe motion with numbers and graphs, the three laws that explain every push and pull, the energy bookkeeping behind it all, and why physics is the reason cars have crumple zones — built from the Year 10 Physical sciences descriptions.
The mapFour units
- Describing motion — distance, displacement, speed, velocity, acceleration, and reading motion graphs.
- Forces and Newton's laws — the three laws, F = ma, and the difference between mass and weight.
- Energy — kinetic and potential energy, conservation, transformations and efficiency.
- Physics of safety — stopping distances, why speed is so dangerous, and how cars are built to save you.
Describing and predicting motion using Newton's laws and the formulas v = d/t, F = ma, KE = ½mv² and PE = mgh — and using the law of conservation of energy to follow energy through transformations, including in everyday systems like a braking car.
Describing motion: the language of movement
Before physics can explain why things move, it needs precise words and numbers for how they move. Four ideas do all the work: distance, displacement, speed and acceleration — plus two graphs that show a whole journey at a glance.
1.1Distance vs displacement, speed vs velocity
1.2The two formulas
- Speed = distance ÷ time, or v = d/t. A sprinter covering 100 m in 12.5 s averages 100 ÷ 12.5 = 8 m/s. Rearranged: d = v × t and t = d ÷ v.
- Acceleration = change in velocity ÷ time, or a = Δv/t. A car going from 0 to 24 m/s in 8 s accelerates at 24 ÷ 8 = 3 m/s² — its speed grows by 3 m/s every second.
- Slowing down is acceleration too — just negative. Braking from 30 m/s to 10 m/s in 5 s is a change of −20 m/s, so a = −4 m/s²: a deceleration of 4 m/s².
- Watch the units. Metres and seconds give m/s; a result in km/h is about 3.6 × the m/s value (60 km/h ≈ 16.7 m/s).
1.3Motion graphs
First check the vertical axis: distance–time or speed–time? On distance–time: gradient = speed, flat = stationary. On speed–time: gradient = acceleration, flat = constant speed — not stopped. Mixing these two up is the classic lost mark.
Forces and Newton's laws
Three sentences, written in 1687, still explain every push, pull, crash and launch — from a shopping trolley to a rocket. Learn the three laws and one formula, F = ma, and forces stop being mysterious.
2.1The three laws
- First law (inertia): an object keeps doing what it is doing — staying still, or moving at constant velocity — unless an unbalanced force acts on it. A braking car stops, but the loose phone on the seat keeps going forward: nothing braked the phone.
- Second law: an unbalanced force causes acceleration: F = ma. Bigger force, more acceleration; bigger mass, less. The same engine that flings a go-kart forward barely moves a truck.
- Third law: forces come in pairs — when A pushes B, B pushes back on A equally hard, in the opposite direction. You jump by pushing down on the ground; the ground pushes you up. A rocket pushes exhaust gas backward; the gas pushes the rocket forward.
2.2F = ma, and mass vs weight
- Worked example: a 1,200 kg car with an unbalanced forward force of 3,000 N accelerates at a = F ÷ m = 3,000 ÷ 1,200 = 2.5 m/s².
- Worked example: pushing a 20 kg trolley with 30 N of unbalanced force: a = 30 ÷ 20 = 1.5 m/s². Load it to 60 kg and the same push gives only 0.5 m/s² — triple the mass, a third of the acceleration.
- Weight is a force: weight = mg, with g ≈ 9.8 m/s² on Earth. A 50 kg student weighs 50 × 9.8 = 490 N.
- Mass is not weight. Mass (kg) is how much matter you are made of — the same everywhere. Weight (N) is gravity's pull on that mass. On the Moon (g ≈ 1.6 m/s²) the same student still has mass 50 kg but weighs only 50 × 1.6 = 80 N.
F is the net (unbalanced) force, not the biggest force. If an engine pushes with 2,000 N and friction pushes back with 500 N, use F = 2,000 − 500 = 1,500 N. Balanced forces mean F = 0, so a = 0 — which means constant velocity, not necessarily stopped.
Energy: the universe's strict accountant
Energy is never created and never destroyed — it only changes form and changes hands. That single rule, the law of conservation of energy, lets you audit anything from a dropped ball to a power station.
3.1Kinetic and potential energy
- Kinetic energy is the energy of movement: KE = ½mv², in joules (J). A 0.16 kg cricket ball bowled at 40 m/s carries KE = ½ × 0.16 × 40² = ½ × 0.16 × 1,600 = 128 J.
- The v² matters enormously. Double the speed and KE goes up four times; triple it and KE is nine times bigger. Speed is squared — mass is not.
- Gravitational potential energy is stored by lifting: PE = mgh. A 60 kg diver on a 10 m platform stores PE = 60 × 9.8 × 10 = 5,880 J.
- Conservation connects them. As the diver falls, PE converts to KE. At the water (ignoring air resistance) all 5,880 J is kinetic: ½ × 60 × v² = 5,880 gives v² = 196, so v = 14 m/s. No force measured, no timer used — the energy audit alone finds the speed.
3.2Transformations and efficiency
- Common transformations: a battery torch turns chemical → electrical → light (+ heat); a wind turbine turns kinetic → electrical; braking turns kinetic → heat in the brake discs.
- Efficiency = useful energy out ÷ total energy in × 100. An appliance that turns 300 J of input into 240 J of useful output is 240 ÷ 300 × 100 = 80% efficient.
- Wasted energy is almost always heat — and "wasted" means unusable, not destroyed. The books always balance.
- A pendulum swaps PE ↔ KE twice every swing: highest point, all PE; lowest point, maximum KE. Air resistance skims a little into heat each pass, which is why it eventually stops.
The physics of safety: why speed kills
Every road rule and every safety feature in a car is applied physics. Stopping distance comes straight from v = d/t and KE = ½mv²; crumple zones and airbags are Newton's laws, moulded in steel and nylon.
4.1Stopping distance = reaction + braking
4.2Why speed is the big one
- At twice the speed a car carries four times the kinetic energy (v is squared) — and the brakes must turn every joule of it into heat before the car stops. That is why braking distance quadruples.
- Reaction time barely changes with speed, but the distance covered during it doubles when speed doubles — and texting or tiredness stretches the reaction time itself, at any speed.
- A crash at 60 km/h involves more than twice the energy of one at 40 km/h (36 : 16 — speed squared again). Small speed differences make outsized differences to damage.
- Wet roads reduce friction, so braking distance stretches further still — the reaction part is unchanged, the braking part grows.
4.3How cars protect you: Newton, applied
- The problem (first law): when the car stops suddenly, you do not. Your body keeps moving at the car's old speed until a force stops it. The only question is which force, acting over how much time.
- The trick: stretch the time. A crash ends with the same change in velocity no matter what, but a force applied over a longer time can be a smaller force. Every safety feature buys time.
- Crumple zones are designed to collapse, so the car stops over a longer distance and time — smaller forces reach the people inside. A rigid car would stop almost instantly, with brutal forces.
- Seatbelts stop your body with the car instead of letting it fly into the windscreen — and spread the stopping force across the strong hips and chest.
- Airbags inflate in milliseconds so your head is stopped gently over a longer time by a cushion, not suddenly by the dashboard.
For any safety feature, write the same three-part logic: it increases the time taken to stop → so the force needed is smaller (same velocity change, spread out) → so less damage to the person. Crumple zone, airbag, seatbelt, bike helmet, gym crash mat — one explanation fits all.
From the first second to next summer.
Four units: how the universe began and how we know, the life stories of stars, the ocean and air currents that run Earth's climate machine, and the evidence that the machine is changing — built from the Year 10 Earth & space descriptions.
The mapFour units
- The Big Bang — the theory, and the two headline pieces of evidence behind it.
- Stars and galaxies — how stars are born, live and die, and where the Sun fits in.
- Global systems — the spheres, the ocean's conveyor belts, and El Niño vs La Niña.
- Climate in the balance — the greenhouse effect, the evidence for change, and the responses.
The Big Bang theory explains the origin of the universe, supported by evidence like galactic redshift and the cosmic microwave background — and Earth's global systems (atmosphere, oceans, carbon cycle) interact to set the climate, which human activity is now shifting.
The Big Bang: how everything began
About 13.8 billion years ago the entire universe — all its matter, energy, space and even time — began expanding from an unimaginably hot, dense state. That is the Big Bang theory, and it rests on two great pieces of evidence anyone can understand.
1.1What "expanding" actually means
1.2Evidence one: galactic redshift
1.3Evidence two: the afterglow
- If the universe began hot and dense, the glow of that early heat should still be out there — stretched by 13.8 billion years of expansion into faint microwaves coming from every direction.
- In 1964 two engineers found exactly that, by accident, as a stubborn "hiss" in their antenna: the cosmic microwave background (CMB) — the predicted afterglow, at almost exactly the predicted temperature (about 2.7 degrees above absolute zero).
- A theory earns trust by making predictions that come true. The Big Bang predicted the CMB before anyone found it — that is why the discovery was so convincing.
- Running the expansion backwards, with the measured rate, dates the beginning at about 13.8 billion years ago. (Earth, at 4.5 billion years, arrived two-thirds of the way through the story.)
Redshift: light from distant galaxies is stretched toward red, and more so the farther away they are — so the universe is expanding. CMB: faint microwave radiation arrives evenly from every direction — the leftover glow of the hot early universe. Name both, and say what each one shows.
Stars and galaxies: lives of the lights
Stars are born, burn, and die — and how a star dies depends entirely on how massive it is. Our Sun will end quietly; a star twenty times heavier goes out in the brightest explosion in nature.
2.1The life cycle — two roads out
2.2Our address in the universe
- The Sun is an ordinary main sequence star, about halfway through its roughly 10-billion-year life. In around 5 billion years it will swell into a red giant, then settle down as a white dwarf. It is far too small to ever go supernova.
- A galaxy is a gravity-bound city of billions of stars. Ours, the Milky Way, holds well over 100 billion stars; the Sun sits in one of its spiral arms, orbiting the centre. The universe holds billions of such galaxies.
- A light-year is a distance, not a time: how far light travels in a year, about 9.5 trillion km. The next star past the Sun is over 4 light-years away; the Milky Way is about 100,000 light-years across.
- Because light takes time to arrive, telescopes are time machines: see a galaxy 10 million light-years away and you see it as it was 10 million years ago.
- Supernovas matter to you: the explosion forges and scatters heavy elements. The iron in your blood and the calcium in your bones were made inside earlier generations of stars.
Global systems: the climate machine
Earth's air, water, land and life are one connected machine. Ocean currents shuttle heat around the planet, and when one Pacific pattern hiccups, Australia swings between drought and flood.
3.1The ocean's conveyor belt
- The four spheres from Year 9 — atmosphere, hydrosphere, biosphere, geosphere — constantly exchange energy and matter. A change in one ripples through the others: that is what "global systems" means.
- The tropics receive far more solar energy than the poles. Ocean currents and winds exist to move that surplus heat — they are the planet's heating ducts.
- Surface currents are pushed mainly by winds; the deep conveyor is driven by density differences from temperature and salt.
3.2El Niño and La Niña — Australia's mood swings
- Normal years: steady trade winds blow westward across the Pacific, piling warm surface water up near Australia and Indonesia. Warm sea makes rising moist air — and rain.
- El Niño: the trade winds weaken, and the warm water drifts back east toward South America. The rain-making machinery goes with it: eastern Australia turns hotter and drier — drought years, tougher bushfire seasons.
- La Niña: the trade winds strengthen, piling even more warm water against Australia. More evaporation, more storms: wetter years and higher flood risk in eastern Australia — as in the floods of 2010–11 and 2022.
- Each phase typically lasts around a year, returning every few years. It is a natural cycle, not caused by climate change — but it swings on top of the warming trend, like waves on a rising tide.
Follow the warm water: warm water near Australia → rain in Australia. La Niña piles it here — floods. El Niño lets it slump toward South America — drought here, and unusually wet weather over there. Wind strength is the lever: weaker trades = El Niño, stronger trades = La Niña.
Climate in the balance
The greenhouse effect is not the villain — without it Earth would be frozen. The issue is the extra blanket humans have added. Here is the mechanism, the evidence, and the two kinds of response, calmly and factually.
4.1The mechanism
4.2The evidence
- Thermometers: direct records since about 1850 show the global average temperature has risen roughly 1.2 °C, with the most recent decade the warmest on record.
- Ice cores: bubbles of ancient air trapped in Antarctic ice preserve an 800,000-year record. Across all of it, CO₂ stayed between about 180 and 300 parts per million — today it is above 420 ppm, and the rise tracks fossil-fuel use.
- Sea level: rising about 20 cm since 1900 and accelerating — warming water expands, and land ice adds meltwater.
- The carbon-cycle link (from Year 9): combustion returns carbon buried over millions of years to the air in centuries — faster than photosynthesis and the oceans can absorb it, so atmospheric CO₂ climbs.
- Multiple independent lines of evidence — thermometers, ice, oceans, satellites — all point the same way. That agreement is what makes the conclusion strong.
4.3Two kinds of response
- Mitigation — reduce the cause: renewable energy, electric transport, efficient buildings, protecting and planting forests that absorb CO₂.
- Adaptation — adjust to the change already underway: sea walls, drought-tolerant crops, better storm drains, smarter bushfire planning.
- They are partners, not rivals: mitigation limits how much the climate changes; adaptation manages the change that can no longer be avoided. Serious plans — including Australia's — use both.
Full marks needs the distinction: the greenhouse effect is natural and necessary (Earth habitable at all), and the problem is the enhanced effect — extra greenhouse gases from human activity trapping extra heat. One mechanism, two versions; name the gases (CO₂, methane, water vapour) and the human source (burning fossil fuels).
The year of the parabola.
Quadratics you can factorise and solve, parabolas you can bend on a live graph, pairs of equations solved at a glance — and trigonometry pointed at real buildings. Built from the Year 10 content descriptions.
The mapFour units
- Factorising quadratics — turning x² + 5x + 6 back into (x + 2)(x + 3), and why that instantly solves equations.
- Parabolas, live — roots, intercepts and turning points on a graph you can edit.
- Simultaneous equations — two equations, one answer: where the lines cross.
- Trigonometry at work — angles of elevation and depression, and finding angles with inverse ratios.
Expanding and factorising quadratic expressions, solving them with the null factor law, sketching parabolas and reading their key features, solving linear simultaneous equations graphically and algebraically, and applying trigonometry to practical problems.
Factorising & solving quadratics
Year 9 expanded (x + 2)(x + 3) into x² + 5x + 6. Year 10 runs the road backwards — and the payoff is huge: a factorised quadratic solves itself.
1.1Two numbers do all the work
To factorise x² + bx + c, hunt for two numbers that multiply to c and add to b.
- x² + 5x + 6: multiply to 6, add to 5 → 2 and 3. So (x + 2)(x + 3).
- x² − x − 12: multiply to −12, add to −1 → −4 and 3. So (x − 4)(x + 3).
- x² − 9: no middle term — difference of squares: (x − 3)(x + 3).
- Always check by expanding back. Ten seconds, catches everything.
1.2The null factor law
If two things multiply to zero, at least one of them is zero. That turns factorising into solving:
- x² + 5x + 6 = 0 → (x + 2)(x + 3) = 0.
- So x + 2 = 0 or x + 3 = 0.
- x = −2 or x = −3. Two solutions — quadratics usually have two.
(x − 1)(x − 2) = 6 does not mean x − 1 = 6 or x − 2 = 6. The product must equal 0 for the law to fire — move everything to one side first.
Parabolas, live
Every quadratic graphs as a parabola. Three features tell its whole story: where it crosses the x-axis (the roots), where it crosses the y-axis, and its turning point.
2.1Reading a parabola's features
2.2The family of curves
Simultaneous equations
Two equations, two unknowns, one pair of values that satisfies both. On a graph that pair is simply the point where the two lines cross.
3.1The graphical method
3.2The substitution method
Graphs are great for seeing; algebra is exact. Solve y = 2x and x + y = 6:
- Substitute the first equation into the second: x + 2x = 6.
- Solve: 3x = 6, so x = 2.
- Back-substitute: y = 2 × 2 = 4. Solution: (2, 4).
- Check in both originals: 4 = 2×2 ✓ and 2 + 4 = 6 ✓.
Parallel lines (same gradient, different intercepts) have no solution — the equations contradict each other. And two equations describing the same line have infinitely many. The picture explains the algebra every time.
Trigonometry at work
Year 9 found missing sides. Year 10 points the triangle at the world — heights of buildings, angles of ramps — and runs the ratios backwards to find angles.
4.1Angles of elevation and depression
4.2Finding the angle: inverse ratios
- When the sides are known and the angle isn't, run the ratio backwards with the calculator's sin⁻¹, cos⁻¹ or tan⁻¹ buttons.
- Example: a ramp rises 3 m over a 4 m run. tan θ = 3/4 = 0.75, so θ = tan⁻¹(0.75) ≈ 36.9°.
- Sanity-check the size. A ratio under 1 for tan means the angle is under 45°; steeper than 45° means opposite > adjacent.
Writing that argues.
Four units: building an essay around a real contention, comparing two texts without writing two separate essays, decoding irony and satire, and the final layer of polish — cohesion and register — that separates a good essay from a great one. Built from the Year 10 English descriptions.
The mapFour units
- Thesis and structure — the contention, topic sentences, and the architecture of an essay.
- Comparing texts — comparative language, integrated vs block structure.
- Satire, irony and tone — the three ironies, and how satire ridicules its targets.
- Polish: cohesion and register — cohesive ties, nominalisation, active and passive voice, and editing.
Sustained, structured argument: a defensible contention carried through an entire essay, evidence from texts (often two, compared), control of register, and the ability to read texts that don't say what they mean — irony and satire.
Thesis and structure: the essay as argument
An essay is not a container for everything you know. It is a single argument — your contention — sustained from the first sentence to the last, with every paragraph pulling in the same direction.
1.1The contention
- A contention is an arguable position — a claim a reasonable person could dispute. If nobody could disagree, it isn't a contention, it's a fact.
- It must answer the question actually asked, and be specific enough to steer every paragraph.
- Announcements are not contentions. "This essay will discuss themes in the novel" argues nothing.
| Weak | Why it fails | Strong |
|---|---|---|
| Nineteen Eighty-Four is about power. | A topic, not a position — nothing to dispute | Orwell presents power as inherently corrupting, not merely corruptible. |
| This essay will discuss Macbeth's ambition. | An announcement — it promises, but argues nothing | Macbeth's downfall owes more to Lady Macbeth's goading than to his own ambition. |
1.2Topic sentences: the contention's soldiers
- Each body paragraph opens with a topic sentence: one mini-claim that advances the contention from a new direction.
- Test: read your contention, then just your topic sentences. Alone, they should form the skeleton of the whole argument.
- A topic sentence that retells plot ("Then Macbeth kills Duncan") advances nothing — it must interpret, not narrate.
1.3The architecture
Comparing texts: one essay, two texts
The comparative essay is Year 10's signature task: two texts, one question. The trap is writing two separate essays stapled together. The skill is making the two texts talk to each other in every paragraph.
2.1What actually gets compared
- Not plots and not publication dates — you compare how each text handles a shared theme (power, belonging, justice…) and the techniques each uses to shape meaning around it.
- The strongest comparisons pair similarity with difference: "Both texts link power to fear, but where Orwell's state crushes the individual, Lee's town is resisted by one."
- Every comparison must serve your contention — a difference that proves nothing is trivia.
2.2Block vs integrated structure
2.3The language of comparison
| Signalling similarity | Signalling difference |
|---|---|
| similarly | whereas |
| likewise | by contrast |
| in the same way | conversely |
| both texts… | on the other hand |
| each writer… | while A does X, B… |
In an integrated paragraph, make at least one sentence hold both texts at once: "Both writers weaponise setting, but whereas Orwell's city surveils its citizens, Lee's town watches its neighbours." That single sentence proves genuine comparison.
Satire, irony and tone: texts that don't say what they mean
Irony is a gap — between what is said and meant, between what is expected and what happens, between what the audience knows and a character doesn't. Satire weaponises those gaps to ridicule its targets. Reading both means reading against the surface of the words.
3.1The three ironies
| Type | The gap | Example |
|---|---|---|
| Verbal irony | Said vs meant — the speaker means the opposite | "Lovely weather," she says, soaked to the skin. |
| Situational irony | Expected vs what happens | The fire station burns down. |
| Dramatic irony | What the audience knows vs what a character knows | We know Juliet is alive; Romeo does not. |
Sarcasm is verbal irony with a target and a sneer — meant to mock or wound. All sarcasm is verbal irony; not all verbal irony is sarcasm. "Lovely weather" mocks nobody; "Nice one, genius" does.
3.2Satire: ridicule with a purpose
- Satire uses humour, irony and exaggeration to ridicule vice or folly — usually in the powerful — with the aim of provoking change, not just laughs.
- Every satire has a target. Finding it is step one of any analysis: who or what is being ridiculed, and what is the satirist implying should change?
- Political cartoons, mock news programs and novels like Animal Farm are all satire — the packaging differs, the mechanism doesn't.
| Technique | How it works | Example |
|---|---|---|
| Exaggeration | Inflates a flaw until it cannot be ignored | A cartoon draws the CEO's pay cheque so long it wraps around the building |
| Parody | Imitates a familiar style or format to mock it | A sketch copies the nightly news format to expose its shallow coverage |
| Incongruity | Pairs things that don't belong together, so the absurdity shows | A billionaire lectures the nation on belt-tightening from a gold-plated podium |
| Understatement | Downplays something huge, making the gap the joke | After the budget disaster, the minister calls it "a minor hiccup" |
| Reversal | Flips normal roles or hierarchies to expose them | A world where children set the rules and adults get detention |
Three moves: name the technique, identify the target, and state the critique — what the satirist wants the audience to see or change. Satire analysis without a target is just describing jokes.
Polish: cohesion and register
Two essays can make the same argument and score differently — because one flows. Cohesion is the invisible stitching between sentences; register is the formality dial. Both are mechanical skills you can practise, not talents you're born with.
4.1Cohesive ties: the stitching
- Reference words — pronouns and pointers that reach back: "Macbeth hesitates. This hesitation is his last honest moment."
- Connectives — however, therefore, moreover, consequently — signal the logical relationship between sentences.
- Repetition of key nouns and their synonyms — the essay's key terms should echo through it (power… authority… control), keeping every sentence on-topic.
- Cohesion fails when a pronoun has no clear owner: "Macbeth tells Banquo his plan" — whose plan?
4.2Nominalisation and the passive: the formality dial
- Nominalisation turns verbs and adjectives into nouns: decide → decision, destroy → destruction, fail → failure. It packs actions into abstract concepts — the signature of formal, analytical writing.
- "Because they decided quickly, things went wrong" → "The decision's haste caused the failure." Fewer words, higher register.
- Active voice: the doer is the subject — "Sam kicked the ball." Direct and vivid. Passive voice: the receiver is the subject — "The ball was kicked (by Sam)."
- The passive is not an error — it is the right tool when the doer is unknown or unimportant ("the window was broken overnight"), or to keep the topic in the spotlight. It becomes a fault when it hides responsibility or drains energy from every sentence.
4.3The editing checklist
- Read it aloud. Your ear catches what your eye forgives — missing words, clunky rhythm, sentences that never end.
- Check the skeleton: contention in the intro, topic sentences that advance it, a link in every paragraph.
- Interrogate every pronoun: does it, this, their have one clear owner?
- Audit the register: hunt down contractions, slang and chatty phrases ("a heap of", "pretty good") in analytical writing.
- Cut the padding: "due to the fact that" → "because"; "in this day and age" → "today".
- Then proofread spelling and punctuation last — no point polishing sentences you might delete.
The century that made now.
Four units from 1918 to the present: how a punishing peace bred a second world war, how the fight for rights reshaped Australia and the world, how the globe divided into two armed camps and then reconnected, and how migration made modern Australia what it is.
The mapFour units
- World War II — from Versailles to the Holocaust, and Australia's own war: Darwin, Singapore, Kokoda.
- Rights and freedoms — from the Universal Declaration to Mabo and the Apology: the struggle for Indigenous rights.
- The globalising world — the Cold War, decolonisation, popular culture, and the wall that fell in 1989.
- Migration and multicultural Australia — from "populate or perish" to one of the world's most multicultural nations.
Everything from Years 8–9 plus significance and contestability: why the 1967 referendum matters (and what it did not do), how the Anzac and wartime stories are debated, and how to weigh sources with different perspectives. Dates still matter — but the marks are in the why.
World War II: the war after the war to end all wars
The Second World War killed more people than any event in human history — and its causes trace straight back to how the First one ended. Understand the Treaty of Versailles and you understand how a failed painter could talk a modern nation into catastrophe.
1.1From Versailles to war
- The Treaty of Versailles (1919) forced Germany to accept blame for WWI, pay crushing reparations, surrender territory and shrink its army to 100,000 men. Many Germans felt humiliated — and when the Great Depression hit in 1929, that humiliation became political fuel.
- Adolf Hitler and the Nazis promised to tear up Versailles, restore German greatness, and blamed scapegoats — above all, Jewish people. Hitler became Chancellor in January 1933 and rapidly built a dictatorship.
- Britain and France responded to his treaty-breaking — rearming, remilitarising the Rhineland (1936), annexing Austria (1938), demanding the Sudetenland (Munich Agreement, 1938) — with appeasement: giving him what he demanded, hoping each demand was the last. It wasn't.
- On 1 September 1939 Germany invaded Poland. Two days later Britain and France declared war — and Australia's Prime Minister Menzies announced that, as a result, Australia was at war too.
1.2The Holocaust
- The Holocaust was the Nazis' systematic, state-organised murder of six million Jewish people — alongside Roma, people with disabilities, Slavic peoples, political prisoners and others.
- It escalated by stages: legal persecution (the Nuremberg Laws, 1935), organised violence (Kristallnacht, 1938), ghettos and mass shootings after 1939, and from 1942 industrialised murder in death camps such as Auschwitz.
- It matters to history — not only to remember the victims, but because it shows how propaganda, fear and obedience can turn an educated modern society into an instrument of genocide. The world's answer included the UN's Universal Declaration of Human Rights (1948) and the Genocide Convention.
1.3Australia's war
- Singapore fell on 15 February 1942 — Britain's "impregnable fortress" gone in a week, with about 15,000 Australians among those marched into brutal captivity. The shield Australia had always relied on was broken.
- Four days later, 19 February 1942, Japanese aircraft bombed Darwin — the first foreign attack on the Australian mainland, killing at least 235 people. More air raids on northern Australia followed.
- Prime Minister John Curtin declared that Australia now looked to America, "free of any pangs" about its traditional links to Britain — the great turn in Australian foreign policy.
- On the Kokoda Track in Papua (July–November 1942), Australian troops — at first young, barely trained militia — fought a desperate withdrawal through the mountains and then pushed the Japanese army back, ending the threat of Port Moresby's capture. Kokoda sits beside Gallipoli in Australian memory — with the difference that this time the fight was in defence of Australia itself.
Versailles humiliates Germany → Depression wrecks its economy → Hitler promises revenge and greatness → dictatorship and rearmament → appeasement lets each gamble succeed → Poland is one gamble too far. Appeasement's lesson, as the exam wants it: concessions convinced Hitler the democracies would never fight, making the war bigger when it came.
Rights and freedoms: the long fight to be counted
After the horrors of WWII the world wrote down, for the first time, what every human being is owed: the Universal Declaration of Human Rights. In Australia, the gap between that promise and the lives of Aboriginal and Torres Strait Islander peoples powered a decades-long struggle — fought with petitions, bus rides, referendums and court cases.
2.1The milestones
2.2Each milestone, in a sentence or three
- Day of Mourning (26 January 1938). While white Australia celebrated 150 years since the First Fleet, Aboriginal leaders William Cooper, Jack Patten and William Ferguson held a protest conference in Sydney declaring the day one of mourning — the start of the modern Aboriginal rights movement.
- UDHR (10 December 1948). The UN's Universal Declaration of Human Rights — drafted by a committee chaired by Eleanor Roosevelt — set out rights belonging to every person. Australia helped draft it; Australian external affairs minister H.V. "Doc" Evatt presided over the UN General Assembly that adopted it.
- Freedom Ride (February 1965). Inspired by the US civil rights movement's freedom rides, Sydney University students led by Charles Perkins bussed through NSW towns like Walgett and Moree, confronting bans on Aboriginal people at RSLs and swimming pools — and putting segregation on the nightly news.
- 1967 referendum (27 May). 90.77% voted Yes — the biggest Yes in Australian referendum history — to count Aboriginal people in the census and let the Commonwealth make laws for them. Know the trap: it did not grant citizenship or the vote (Commonwealth voting rights had come in 1962).
- Tent Embassy (26 January 1972). Four activists planted a beach umbrella on the lawns opposite Parliament House, calling it the Aboriginal Embassy: if Aboriginal people were treated as strangers in their own land, they would have an embassy. It became a lasting symbol of the land rights struggle.
- Mabo (3 June 1992). After a ten-year case led by Eddie Koiki Mabo of Mer (Murray Island), the High Court rejected terra nullius and recognised native title — that Indigenous peoples' ownership of land survived colonisation where connection continued. The Native Title Act followed in 1993.
- Bringing Them Home (1997). The national inquiry's report on the Stolen Generations — the Aboriginal and Torres Strait Islander children forcibly removed from their families under government policy, from the early 1900s into the 1970s.
- The Apology (13 February 2008). Prime Minister Kevin Rudd, on behalf of the Parliament, formally said sorry to the Stolen Generations — the report's key unfinished recommendation, delivered eleven years on.
What it did: amended the Constitution so Aboriginal people were counted in the census and the Commonwealth could make laws for them. What it did NOT do: grant citizenship, the vote, or equal wages. Its real power was the 90.77% — an unmistakable national statement that change had to come.
The globalising world: two camps, then one planet
The allies of 1945 became the rivals of 1946: for four and a half decades the United States and the Soviet Union faced off in a Cold War — cold because the superpowers never fought each other directly, hot everywhere their proxies did. Meanwhile empires dissolved, and American music, movies and jeans conquered more territory than any army.
3.1The Cold War in one table
| The West | The East | |
|---|---|---|
| Superpower | United States | Soviet Union (USSR) |
| System | Capitalism, multi-party democracy | Communism, one-party state |
| Alliance | NATO (from 1949) | Warsaw Pact (from 1955) |
| How they fought | Never directly: an arms race (both nuclear-armed by 1949), a space race, spying, propaganda — and proxy wars where each backed a side, as in Korea (1950–53) and Vietnam | |
| The dividing line | The "Iron Curtain" across Europe — made concrete in the Berlin Wall, built 1961 to stop East Germans fleeing west | |
- The closest brush with catastrophe: the Cuban Missile Crisis (1962), thirteen days of nuclear stand-off over Soviet missiles in Cuba, resolved by negotiation at the brink.
- Australia fought in both big proxy wars — Korea and Vietnam — as a US ally under the ANZUS treaty (1951).
3.2Decolonisation and pop culture
- Decolonisation: after WWII the European empires unwound — India and Pakistan independent in 1947, most of Africa around 1960, Papua New Guinea from Australia in 1975. Dozens of new nations joined the UN, many becoming Cold War battlegrounds for influence.
- Popular culture went global — and mostly spoke American. Rock'n'roll arrived in 1950s Australia with Elvis and Bill Haley; television began here in 1956, just in time for the Melbourne Olympics; Beatlemania hit in 1964. Each wave sparked the same argument: is this exciting modern freedom, or the drowning of Australian identity?
- Culture was also a Cold War weapon: jeans, jazz and Hollywood carried "the American way of life" behind the Iron Curtain more effectively than any broadcast.
3.31989: the wall comes down
Migration: how Australia became multicultural
In 1945 Australia was overwhelmingly Anglo-Celtic by design — the White Australia policy had seen to that since 1901. Eighty years later, about half of all Australians were born overseas or have a parent who was. The change happened in deliberate steps, and this unit walks them.
4.1Populate or perish
- WWII's near-invasion convinced Australia's leaders the country was too small to defend itself. Immigration Minister Arthur Calwell put it bluntly in 1945: "populate or perish".
- The great post-war scheme followed: assisted passage for British migrants (the "ten pound Poms") — and, when Britain couldn't supply enough people, over 170,000 displaced persons from war-shattered Europe: Poles, Balts, Ukrainians, then Italians, Greeks and Yugoslavs through the 1950s–60s.
- Migrant labour built the icons of the era — most famously the Snowy Mountains Scheme, where workers from over 30 nations dug the tunnels. Australia's population soared from about 7.4 million (1945) past 13 million by the early 1970s.
4.2Dismantling White Australia — step by step
4.3Multicultural Australia today
- Multiculturalism — adopted as official policy in the 1970s — reversed the old expectation that migrants must shed their cultures. Instead: keep your heritage, share full citizenship.
- The results are visible everywhere: today nearly 30% of Australians were born overseas, and about half have at least one parent born overseas — among the highest proportions in the world.
- Migration remade even the national menu, from post-war Italian espresso and Greek delis to Vietnamese pho — the everyday evidence of the policy story above.
- The debates continue — over refugee policy, population size and national identity — which is exactly why the history matters: today's arguments echo 1901, 1945 and 1975.
Change: from a legally white-only immigration policy (1901) to one of Earth's most multicultural nations — via 1945's mass migration, the staged repeal of 1958–1973, and the Vietnamese resettlement test case. Continuity: immigration has been deliberately used as nation-building policy the whole way through — only the definition of who belongs has changed.
Managing the planet, measuring the people.
Four units in two halves: how humans change environments — and how those changes can be managed, with Australia's coasts as the working example. Then the other half of geography: how well are people actually living, how do we know, and why does it differ so sharply from place to place?
The mapFour units
- Environmental change — land clearing, pollution, invasive species and climate change, and what "sustainability" actually demands.
- Managing coasts — waves, drift and sea-level rise versus sea walls, sand pumping and planning: the Gold Coast as a live case study.
- Human wellbeing — GDP, life expectancy, literacy and the HDI: what each number measures, and what it hides.
- The wellbeing gap — between countries and inside them, including Australia's own gaps — and the programs that actually close them.
Explaining human-induced environmental change and evaluating management responses using environmental, economic and social criteria — and explaining the spatial variation in human wellbeing, between and within countries, using indicators as evidence.
Environmental change: the human fingerprint
Environments always changed — slowly. What is new is the speed, and the cause. Four human-driven changes dominate the modern story, and Australia has a front-row seat to every one of them.
1.1The big four
| Change | What is happening | The Australian angle |
|---|---|---|
| Land clearing | Forest and bushland removed for farms and suburbs; habitats cut into fragments | Nearly 40% of Australia's forests cleared since 1788 (approx.); koala habitat a running battleground |
| Pollution | Air, water and soil loaded with wastes; plastics drifting in every ocean | Fertiliser and sediment runoff is a major pressure on the Great Barrier Reef |
| Invasive species | Introduced organisms spreading unchecked, with no local predators | Cane toads (1935), rabbits, foxes and feral cats devastating native wildlife |
| Climate change | Extra greenhouse gases trapping extra heat worldwide | More extreme heat, worse fire weather, coral bleaching, shifting rainfall |
- The cane toad is the textbook backfire: introduced to Queensland in 1935 to eat cane beetles, it ignored them, spread across the north, and its poison now kills the native predators — quolls, goannas, snakes — that try to eat it.
- Invasive species run riot here for one clean reason: they evolved elsewhere. Native wildlife has no defences against them, and nothing here eats them.
- Atmospheric CO₂ has climbed from about 280 parts per million before industry to above 420 ppm today — the highest in at least 800,000 years of ice-core records.
1.2The greenhouse mechanism
Development that meets the needs of the present without compromising the ability of future generations to meet their own needs (the UN's Brundtland report, 1987). Evaluations in this course always weigh three things at once: environmental, economic and social costs and benefits. And notice that people hold different worldviews — human-centred (nature as a resource for people) versus earth-centred (nature valuable in its own right) — which is why they disagree about what "good management" means.
Managing coasts: holding the line, or moving it
Eighty-five per cent of Australians live within 50 km of the sea (approx.) — on a shoreline that was never standing still. Coastal management is a running argument between waves, property owners and physics, and the Gold Coast is where Australia has fought it longest.
2.1How sand travels: longshore drift
- The threats stack up: storm erosion, buildings placed on the dunes that were the coast's shock absorber, and sea-level rise — about 20 cm since 1900, and accelerating — which lets every storm bite further inland.
2.2The management menu
| Approach | Examples | For | Against |
|---|---|---|---|
| Hard engineering | Sea walls, groynes, rock revetments | Protects property now; lasts decades | Expensive; walls reflect wave energy and can strip the beach in front; groynes starve beaches down-drift |
| Soft engineering | Beach nourishment (pumping sand in), replanting dunes | Keeps a natural, usable beach; works with the drift | Must be repeated forever; sand is costly |
| Planning | Setback lines, no-build zones on dunes, planned retreat | Cheapest in the long run; avoids the fight entirely | Politically painful — someone's land loses value |
The problem. The Gold Coast's beaches are its economy — and they sit on a sand conveyor moving north. Training walls built to keep the Tweed River mouth navigable interrupted that drift, starving the southern Gold Coast beaches; cyclones in 1967 stripped them almost bare. The response, layered over decades: a boulder wall line behind the beaches (hard), repeated beach nourishment (soft) — and since 2001 the Tweed Sand Bypassing project, which pumps sand past the river mouth to the southern beaches, restarting the natural conveyor: roughly half a million cubic metres a year (approx.). Evaluation: the beaches are back and tourism thrives (economic ✓, social ✓), but it costs money forever and remains an engineered coastline (environmental: mixed) — a defensible trade-off, which is exactly how you should phrase it.
Human wellbeing: putting numbers on a good life
Is life better in one place than another? To answer without just guessing, geographers use indicators — and the skill this unit teaches is knowing exactly what each number measures, and what it quietly leaves out.
3.1The indicator toolkit
| Indicator | What it measures | Watch out |
|---|---|---|
| GDP per capita | A country's income divided by its population | An average — says nothing about how income is shared, unpaid work, or the environment |
| Life expectancy | How long a newborn can expect to live, on average | The single best one-number summary of health |
| Adult literacy | Share of adults who can read and write | A floor, not a ceiling — says little about quality of education |
| Infant mortality | Babies dying before age one, per 1,000 births | Brutally honest about healthcare, water and nutrition |
| Access to safe water | Share of people with clean drinking water | Underneath half the other indicators |
- Quantitative indicators are counted (years, dollars, percentages); qualitative ones must be asked (how safe people feel, how connected to culture). Good studies use both.
3.2The HDI — three numbers in a trench coat
A national average is one number stretched over millions of different lives. A country can post a healthy GDP per capita while wealth pools in one city and one class — and a rich country can contain regions whose indicators look like a much poorer one's. Whenever you quote an average, the next sentence should ask: averaged over whom? That question is the whole of Unit 4.
The wellbeing gap
Where you are born still largely decides how long you live, how many years you spend in school, and how much you earn. The gaps run between countries — and, less comfortably, straight through the middle of rich ones, Australia included.
4.1Between countries
| Indicator (UN figures, rounded) | Australia | Chad |
|---|---|---|
| Life expectancy | ≈ 83 years | ≈ 54 years |
| Average years of schooling | ≈ 13 | ≈ 3 |
| Income per person (PPP) | ≈ $50,000 | ≈ $1,500 |
| HDI | ≈ 0.95 — top 10 in the world | ≈ 0.39 — among the lowest |
- Life expectancy worldwide runs from the low 50s in the hardest-hit countries to the mid 80s in the healthiest — a gap of three decades of life.
- The pattern is spatial: the lowest-wellbeing countries cluster in sub-Saharan Africa, weighed down by combinations of poverty, conflict, disease and weak institutions — not by any shortage of human talent.
4.2Within countries — Australia's own gaps
- Wellbeing falls with distance from the cities: remote Australians live further from hospitals, specialists, schools and jobs, and every health statistic feels it.
- The sharpest national gap: on average, Aboriginal and Torres Strait Islander peoples live about eight years less than non-Indigenous Australians (approx.), with parallel gaps in child health, education and employment — widest in remote communities.
- The Closing the Gap national agreement sets targets across health, education, housing and employment. Its central lesson so far: programs designed and run with communities — like Aboriginal community-controlled health services — consistently outperform programs imposed from outside.
4.3What actually closes gaps
- Health first. Vaccination is the all-time champion: smallpox was eradicated worldwide in 1980, and polio has been driven to the edge of extinction. Clean water and maternal care follow close behind.
- Education — especially for girls. Each extra year of schooling lifts incomes, health and children's survival; educating girls is one of the strongest levers development economists have found.
- Money that reaches people. Microloans — tiny loans to people banks ignore — let poor families start small businesses; targeted aid builds the clinics, roads and schools that markets won't.
- A shared scoreboard. The UN's Sustainable Development Goals — 17 goals, adopted 2015, aimed at 2030 — put ending poverty and hunger, health, education and equality on every government's agenda at once.
Quote an indicator (with its number labelled approximate), name the scale (between countries / within a country), give a reason for the gap, and finish with a response — ideally one with evidence it works. "Chad's life expectancy is around 54 to Australia's 83; within Australia the Indigenous gap is about eight years; remoteness and access to services drive much of it; community-controlled health services are narrowing it." Four sentences, full marks.
Nothing on your desk happened by accident.
Every object around you — your chair, your drink bottle, your phone case — was designed: someone found a problem, imagined answers, built one, and judged it. Four units teach you to do the same, properly.
The mapFour units
- The design process — investigate, generate, produce, evaluate — and why the loop never really ends.
- Design thinking tools — briefs, constraints, criteria, annotated sketches and quick prototypes.
- Materials & making — strength, hardness, flexibility, durability: picking the right stuff, and working it safely.
- Evaluating & improving — testing against criteria, listening to users, and designing for a product's whole life.
Not whether your product is pretty — whether you can follow and explain the design process: define a problem and its constraints, generate several ideas before choosing, make a working version, and evaluate it honestly against criteria you wrote before you started.
The design process: a loop, not a line
Designers don't get it right first go — nobody does. What they have instead is a process that turns "I don't know" into "version 3 works": four stages, repeated until the design earns its keep.
1.1The four stages
1.2What each stage really means
- Investigate and define. Before designing anything, understand the problem: who has it, when it happens, what already exists, and what a good solution must do. Skipping this stage is the number-one cause of useless products — a brilliant answer to the wrong question.
- Generate ideas. This is divergent thinking: producing many different possibilities — wild ones included — before judging any of them. Quantity first, quality later. Only after the ideas exist do you switch to convergent thinking: narrowing down to the strongest one using your criteria.
- Produce. Turn the chosen idea into a real thing — measuring, cutting, joining, assembling — following your plan and working safely. Good producers keep notes on what they changed and why, because the plan never survives contact with real materials unchanged.
- Evaluate. Test the finished product against the criteria for success you wrote at the start — not against your feelings. "Do I like it?" is opinion; "does it hold 2 kg without bending, as criterion 3 required?" is evaluation.
A classic question asks why designers sketch many ideas instead of building the first one. The answer: the first idea is rarely the best; generating lots of options (divergent thinking) lets you compare them against the criteria and combine the best parts. Committing early to idea number one means never finding out ideas two to ten were better — and it's far cheaper to discard a sketch than a built product.
Design thinking tools: the paperwork that saves the project
Between "we have a problem" and "let's build it" sit a handful of simple tools. They look like paperwork. They are actually how designers avoid building the wrong thing beautifully.
2.1The brief, the constraints, the criteria
- A design brief is a short statement of the job: what is needed, who it is for, and the limits it must work within. Example: "Design a carry case that protects a school laptop from a 1 m drop, for a Year 8 student, costing under $15 in materials."
- Constraints are the limits the design cannot break: budget, time, size, available materials, safety rules. Constraints feel annoying but actually help — they shrink infinite possibilities down to a solvable problem.
- Criteria for success are measurable statements, written before you design, used after to judge the result. "It should be good" is useless; "it survives a 1 m drop onto concrete with the laptop undamaged" can be tested with a yes or no.
A constraint is a wall you must stay inside while designing (under $15, finished by week 8, no power tools). A criterion is a target the finished product is measured against (survives the drop, weighs under 400 g, opens one-handed). Walls during; targets after.
2.2Sketching, prototyping, and the user
- An annotated sketch is a quick drawing with written notes — arrows pointing out materials, sizes, how parts move or join. The annotations do the heavy lifting: a sketch shows what it looks like, the notes explain how it works.
- A low-fidelity prototype is a fast, rough, cheap model — cardboard, paper, tape, blu-tack. "Low-fidelity" means low detail, and that is the point: you can build it in twenty minutes, test the idea, and throw it away without pain. Finding a flaw in cardboard costs cents; finding it in the finished product costs the project.
- Designers study user needs with empathy — watching and asking the actual user rather than assuming. A pencil case designed for "everyone" fits no one; one designed after watching a left-handed user struggle with a right-zipping case fixes a real problem.
Markers want both halves: a prototype lets you test an idea early (does the mechanism work? does it fit the hand?) while changes are still cheap and fast. One sentence each, full marks.
Materials & making: the right stuff for the job
A chocolate teapot fails not because chocolate is bad, but because it's the wrong material for the job. Choosing well means matching a material's properties to what the product must survive.
3.1The properties that matter
| Property | What it means | Test it by… | Wanted in… |
|---|---|---|---|
| Strength | Withstands a force or load without breaking | pulling, pressing or loading it | a tow rope, a shelf, a bike frame |
| Hardness | Resists being scratched or dented | trying to scratch its surface | a bench top, a drill bit, floor tiles |
| Flexibility | Bends without breaking, then springs back | bending it and letting go | a hose, a ruler, a phone case |
| Durability | Stands up to wear, weather and time | using and weathering it for a long time | outdoor decking, playground gear |
| Absorbency | Soaks up liquid | dripping water on it | a towel — and NOT an umbrella |
- Strength and hardness are not the same thing. Glass is hard (very difficult to scratch) but not strong against a knock; a nylon rope is strong under load but soft enough to scratch with a fingernail.
- Choosing a material is a trade-off: list what the product must survive, rank which properties matter most, then compare candidates — including cost and availability, which are constraints, not properties.
- No material is "best". Steel beats pine for strength; pine beats steel for weight, cost, and ease of cutting in a school workshop. The job decides.
3.2Tools and safe work
- Basic workshop kit: measuring and marking tools (rule, square, pencil) come first — the rule is measure twice, cut once, because wood cut short stays short.
- Cutting (saws, scissors, craft knives), shaping (files, sandpaper), joining (glue, screws, nails, tape). Match the tool to the material — a wood saw fights sheet metal and loses.
- Safe work is not optional: PPE (personal protective equipment — safety glasses, apron, closed shoes), hair tied back, one person in a tool's working zone, tools checked before use and carried points-down, and a tidy bench — most workshop accidents are trips and slips, not blades.
- Report every fault and every injury, however small, to the teacher. A frayed cord or wobbly blade is the next person's accident.
Evaluating & improving: the honest stage
Anyone can build something. Designers find out whether it actually works — measured against the criteria, judged by real users, and considered across the product's whole life, from mine to landfill.
4.1Testing and feedback
- Evaluation means going back to the criteria for success and testing each one, honestly. Criterion met, partly met, or not met — with evidence. "The case survived two of three 1 m drops; the corner seam split on drop three" is an evaluation. "It went pretty well" is not.
- User feedback is the second test: hand the product to the person it was designed for and watch. Users find problems designers are blind to, because the designer knows how it's meant to be used. Ask open questions ("what was awkward?"), not leading ones ("it's good, right?").
- Every failure found is an improvement written for free: "the seam split" becomes "version 2: reinforce corner seams". That is the loop from Unit 1 closing — evaluation feeding the next iteration.
4.2The life of a product
- A product's life cycle runs: raw materials extracted → materials processed → product manufactured → distributed to shops → used → disposed of, recycled or reused. Every stage costs energy and resources and creates waste — not just the making.
- Sustainable design means choosing with the whole cycle in mind: renewable or recycled materials in, less material overall, products that can be repaired instead of replaced, and parts that can be separated for recycling at the end (a bottle that is all one plastic recycles; a toy of glued mixed plastics does not).
- The cheapest waste is the waste never made: designing a product to last twice as long halves everything upstream of it — mining, manufacturing, transport, packaging.
Judge it against named criteria (with evidence), report user feedback, and suggest a specific improvement tied to a failure you found. Criteria → evidence → improvement: three sentences, three marks, every time.
Teach a machine that can't guess.
Four units: how everything on a screen is secretly numbers, how those numbers cross the world in packets, how to write instructions so precise a machine can follow them, and your first real programs — built from the Year 7–8 Digital Technologies descriptions.
The mapFour units
- Everything is numbers — binary, bits and bytes, and how text and images become 0s and 1s.
- Networks — what the internet actually is, addresses, packets, and why passwords matter.
- Algorithms — precise steps, the three building blocks, flowcharts done properly, and tracing by hand.
- First programs — variables, input → process → output, IF/ELSE, loops, and hunting bugs.
Data of every kind is represented as binary numbers; networks move that data as addressed packets; and problems are solved by designing algorithms — sequence, selection and iteration — then implementing and testing them as programs.
Everything is numbers
Every photo, song, message and game on your phone is stored the same way: as numbers, written with only two digits. Learn to read binary and the whole machine stops being magic.
1.1Why 0 and 1?
- A computer is billions of microscopic switches. A switch is reliable at exactly two things: off and on — written 0 and 1. Ten different voltage levels would blur; two never do.
- One 0-or-1 is a bit — the smallest possible piece of information. Eight bits make a byte, the standard parcel size for data.
- Counting with two digits is called binary. Our everyday ten-digit counting is decimal. Same numbers, different costume.
1.2Reading binary: place values
In decimal, the columns are worth 1, 10, 100, 1000… — each ten times the last. In binary, each column is worth double the last: 1, 2, 4, 8, 16, 32, 64, 128. To read a binary number, add up the columns that hold a 1.
| Column value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Total |
|---|---|---|---|---|---|---|---|---|---|
| Binary 1101 | 1 | 1 | 0 | 1 | 8 + 4 + 1 = 13 | ||||
| Binary 11001 | 1 | 1 | 0 | 0 | 1 | 16 + 8 + 1 = 25 | |||
| Binary 11111111 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | all eight = 255 |
Work greedily from the biggest column down. For 13: does 8 fit? Yes — write 1, carry on with 5. Does 4 fit? Yes — 1, left with 1. Does 2 fit? No — 0. Does 1 fit? Yes — 1. Answer: 1101. Always check by adding back: 8 + 4 + 1 = 13.
1.3Text and images are numbers too
- Text: every character has an agreed code number — the ASCII table. Capital A is 65, B is 66, a space is 32. "CAT" is stored as 67, 65, 84 — each one a byte of binary.
- Images: a picture is a grid of tiny squares called pixels. Each pixel stores three numbers, 0–255 each: how much red, green and blue light to mix — the RGB system.
- (255, 0, 0) is pure red. (255, 255, 255) is white — all three lights on full. (0, 0, 0) is black — all off.
- Why 0–255? That is exactly the range one byte can hold: eight bits give 256 different patterns.
Networks: how your photo crosses the world
The internet is not a cloud. It is cables, radio waves and millions of machines passing numbered parcels of data — and once you can picture the journey, security stops being a lecture and starts making sense.
2.1What the internet is
- A network is any group of connected devices that can share data. Your home Wi-Fi is one; your school's computers are another.
- The internet is the worldwide network of networks — all of them agreeing to speak the same rules so any device can reach any other.
- Wired connections (cables) are usually faster and steadier; wireless (Wi-Fi, mobile data) trades some speed and reliability for the freedom to move. Radio waves also weaken with distance and walls.
- Every connected device gets an IP address — a number like 203.0.113.7 that works exactly like a postal address: it is how data finds the right machine among billions.
2.2The journey of a photo
2.3Why passwords and privacy matter
- Your accounts are doors, and a password is the key. A short or reused key is easy to copy: if one site leaks it, attackers try the same key on every other door you own.
- Strong passwords are long and unique per account. Length beats weird symbols: a passphrase of several random words is both stronger and easier to remember than "P@ss1".
- Whatever you post travels through machines you don't control and can be copied forever. Before sharing, ask: would I be fine with everyone — including future me — seeing this?
- Personal details (full name, school, address, photos with locations) are exactly what a stranger needs to pretend to know you. Give them out the way you'd give out your house key.
Algorithms: instructions with no wiggle room
Tell a friend "make me toast" and they fill in a hundred missing details. A computer fills in nothing. An algorithm is instructions written so precisely that even a machine that can't guess gets it right — every time.
3.1The three building blocks
Every algorithm ever written — from a recipe to a rocket launch — is built from just three patterns:
- Sequence — steps that run one after another, in order. Crack the eggs, then whisk, then pour.
- Selection — a choice made with a question. IF it is raining THEN take an umbrella ELSE wear a hat.
- Iteration — repetition. Keep stirring UNTIL the sauce thickens; repeat the chorus 3 times; WHILE lives remain, keep playing.
3.2Flowcharts, done properly
3.3Desk-checking: run it in your head first
A desk check (or trace) means being the computer: follow the algorithm line by line and write down every variable's value as it changes. It finds mistakes before a single line is typed. Trace this:
| Line | Pseudocode | total after the line |
|---|---|---|
| 1 | total ← 0 | 0 |
| 2 | total ← total + 4 | 4 |
| 3 | total ← total + 4 | 8 |
| 4 | PRINT total | prints 8 |
total ← total + 4 is not maths — it is an instruction: "work out the right side, then store the result in the box on the left." Read ← as "becomes". That is why a line like x ← x + 1 makes perfect sense to a computer and none to an algebra teacher.
First programs: from algorithm to code
A program is just an algorithm written in a language a computer accepts. We'll use pseudocode — structured English that every programming language translates from almost word for word.
4.1Variables, and the three-stage machine
- A variable is a named box in the computer's memory. score ← 10 puts 10 in a box called score; later lines can read it or replace it.
- Almost every program is the same machine: INPUT (get data in) → PROCESS (calculate, decide, repeat) → OUTPUT (show the result).
| Program | Input | Process | Output |
|---|---|---|---|
| Calculator | The numbers you type | The arithmetic | The answer on screen |
| Game | Taps and key presses | Physics, collisions, scoring | Graphics and sound |
| Step counter | Motion-sensor readings | Counting the jolts | Today's step total |
4.2Branching and looping in pseudocode
Selection and iteration, written the way we'll write them all course:
| Line | Pseudocode | What happens |
|---|---|---|
| 1 | INPUT temp | User types 18 — temp is now 18 |
| 2 | IF temp > 25 THEN | Is 18 > 25? No — skip to ELSE |
| 3 | PRINT "hot" | skipped |
| 4 | ELSE | — |
| 5 | PRINT "cool" | prints cool |
| 6 | END IF | the branch is over |
| Line | Pseudocode | Trace |
|---|---|---|
| 1 | count ← 3 | count = 3 |
| 2 | WHILE count > 0 | 3 > 0? yes — go round |
| 3 | PRINT count | prints 3, then 2, then 1 |
| 4 | count ← count − 1 | count = 2, then 1, then 0 |
| 5 | END WHILE | 0 > 0? no — loop ends |
4.3Finding bugs
- A bug is a mistake that makes the program behave wrongly. Programs never disobey — they obey a wrong instruction perfectly.
- To hunt one: trace the code with a desk check and find the first line where the value in your table differs from what you expected. The bug lives at or just before that line.
- Classic Year 8 bugs: forgetting the line that changes the loop variable (the loop never ends), testing with > when you meant <, and printing a variable before anything was put in it.
- Test with easy numbers first, then nasty ones: zero, negatives, huge values. A program that survives 0 has earned some trust.
Cooking is chemistry you can eat.
Four units take you from "don't poison anyone" to "plate it like you meant it": kitchen safety, what food actually does in your body, what heat does to food, and how a recipe becomes a meal.
The mapFour units
- Safe kitchens — the danger zone, cross-contamination, hygiene, and cleaning versus sanitising.
- Nutrition on the plate — the five food groups, the macronutrients, and how to read a food label.
- Cooking with method — moist heat, dry heat, how heat travels, and knife skills that keep fingers attached.
- Recipe to table — mise en place, scaling a recipe, Australian measurements, and judging food with your senses.
Safe food handling comes first and is marked hardest — know the danger zone (5–60 °C) and cross-contamination cold. Then: the five food groups and what the macronutrients do, which cooking method suits which food and why, and working from a recipe accurately.
Safe kitchens: the rules that stop food poisoning
Bacteria are invisible, tasteless, and everywhere — and in the right conditions their numbers can double roughly every twenty minutes. Kitchen safety is simply refusing to give them those conditions.
1.1The temperature danger zone
- Australia's rule of thumb for food left in the danger zone: under 2 hours — refrigerate or use it; 2 to 4 hours — use it immediately; over 4 hours — throw it away. The clock adds up across the day.
- Cooling leftovers: get them into the fridge promptly in shallow containers — a deep pot of warm soup can sit in the danger zone for hours in the middle.
1.2Cross-contamination and hygiene
- Cross-contamination is germs hitching a ride from one food to another — classically, raw chicken juice reaching salad via a shared board, knife or unwashed hands. The salad is never cooked, so the bacteria are never killed.
- Defence: separate boards and knives for raw meat and ready-to-eat food (or wash thoroughly between), raw meat stored below ready-to-eat food in the fridge so it cannot drip, and hands washed with soap for 20 seconds after touching raw meat.
- Personal hygiene: wash hands before cooking, tie hair back, wear a clean apron, cover cuts with a waterproof dressing, and do not cook for others while sick — your germs travel on everything you touch.
- Cleaning and sanitising are two different jobs, in a fixed order. Cleaning removes food scraps and grease with hot water and detergent. Sanitising then kills the germs that remain, with very hot water or a sanitiser. Clean first, then sanitise — sanitiser can't reach germs hiding under grease.
"Why is it dangerous to cut salad on the board just used for raw chicken?" Full marks needs the chain: raw chicken carries bacteria → they transfer to the board → then to the salad → the salad is eaten raw, so no cooking step ever kills them. That last link is the mark most people drop.
Nutrition on the plate: what food does once you eat it
Food isn't just fuel — it's building material, repair kit and spare parts. Australia sorts it into five groups, and the label on every packet tells you exactly what's inside, if you know where to look.
2.1The five food groups
The Australian Guide to Healthy Eating (AGHE) shows a plate divided into five groups — the bigger the slice, the more of your daily food should come from it. Vegetables and grains get the biggest slices; dairy and the meat group are smaller; and things like chips, lollies and soft drinks aren't on the plate at all — they're "sometimes foods", drawn outside it.
| Group | Examples | Star nutrients |
|---|---|---|
| Vegetables & legumes | broccoli, carrot, pumpkin, beans | vitamins, minerals, fibre |
| Fruit | apple, banana, berries | vitamins, fibre, natural sugars |
| Grain (cereal) foods | bread, rice, pasta, oats — mostly wholegrain | carbohydrates, fibre, B vitamins |
| Lean meat, fish, eggs, tofu, nuts & legumes | chicken, fish, eggs, lentils | protein, iron |
| Milk, yoghurt, cheese & alternatives | milk, yoghurt, cheese | calcium, protein |
2.2The macronutrients
- Carbohydrates are the body's main fuel — broken down to glucose to power everything from running to thinking. Wholegrain versions release energy slowly and steadily; sugary ones spike and crash.
- Protein is for growth and repair — building muscle, skin, blood and enzymes. You are literally built from it, which is why growing teenagers need plenty.
- Fats are the most concentrated energy store, and the body also needs them for insulation, protecting organs and absorbing certain vitamins. Some fat is essential — the aim is the right kinds (think oily fish, nuts, olive oil) in the right amounts.
- Two supporting acts: fibre (a plant carbohydrate we can't digest — it keeps the digestive system moving) and water (needed for every process in the body).
2.3Reading a food label
- The nutrition panel shows two columns: per serve and per 100 g. To compare two products fairly, always use per 100 g — serve sizes are chosen by the manufacturer and differ between brands.
- Ingredients are listed by weight, largest first. If sugar is ingredient number one, the product is mostly sugar — no matter what the front of the pack says.
- The front of the pack is advertising; the back is law. "Lite", "natural" and a cartoon farm prove nothing — the numbers on the panel do.
Cooking with method: what heat actually does
Boiled potato and roast potato start as the same vegetable — the method makes the meal. Every cooking method is just a different way of delivering heat, and each one changes food differently.
3.1Moist heat vs dry heat
| Family | Methods | How it cooks | What it does to food |
|---|---|---|---|
| Moist heat (water or steam) | boiling, simmering, steaming, poaching | hot water or steam surrounds the food — never hotter than about 100 °C | softens and tenderises; no browning or crisping; gentle — but boiling can leach vitamins into the water |
| Dry heat (air, fat or flame) | baking, roasting, grilling, frying | hot air, hot fat or direct radiant heat — well above 100 °C | browns and crisps the outside, building flavour; frying also adds fat to the food |
- The surprise of the table: frying is a dry-heat method. "Moist" means cooking in water or steam — oil is a fat, not water, and it gets far hotter than water can, which is exactly why fried food browns and boiled food never does.
- Steaming keeps the most nutrients of the moist methods: the food never touches the water, so water-soluble vitamins can't leach away into it.
- Method matching is about the food's needs: tough cuts want long, gentle moist heat to tenderise; tender foods want fast dry heat for flavour and crust.
3.2How the heat gets in
- Conduction: heat passes by direct contact — a steak sizzling where it touches the hot pan.
- Convection: currents of hot water or hot air carry heat around the food — a pot of boiling water, or a fan-forced oven.
- Radiation: heat travels as invisible rays from a glowing source — a grill's element browning the top of a lasagne, or a toaster.
- Real cooking usually combines them: a roast gets convection from the oven air and conduction from the hot tray beneath it.
3.3Knife skills
- The two safe grips: the claw — the holding hand's fingertips curled under, knuckles forward, so the blade can only meet knuckle, never fingertip — and the bridge — thumb and fingers make a bridge over the food and the knife cuts underneath it.
- A sharp knife is safer than a blunt one: blunt blades need force, and forced blades slip. Cut on a stable board (damp cloth underneath to stop sliding), blade away from you, and never walk around with a knife point-up.
- The standard cuts, by shape: slice (flat pieces), dice (even cubes), julienne (thin matchsticks). Even sizes are not just pretty — even pieces cook evenly.
Recipe to table: cooking like you've done it before
Watch a chaotic cook and a calm one make the same dish: the calm one did all the thinking before the heat went on. That habit has a French name, and it's the single biggest upgrade to anyone's cooking.
4.1Mise en place
- Mise en place (say "meez on plass") is French for "everything in its place": before any heat, read the whole recipe, get out every ingredient and piece of equipment, and do the washing, chopping, weighing and measuring.
- Why it works: once cooking starts, the recipe sets the pace — onions won't wait while you hunt for the paprika. With everything prepped, you just assemble.
- Read the whole recipe first, every time. It's the only way to discover "marinate for 2 hours" or "you'll need a blender" before those facts become emergencies.
4.2Measuring and scaling
- Australian standard measures: 1 cup = 250 mL, 1 tablespoon = 20 mL, 1 teaspoon = 5 mL. Watch the tablespoon: Australia's is 20 mL, but most other countries (and many internet recipes) use 15 mL.
- Measure accurately: dry ingredients levelled off with a knife, liquids read at eye level. In baking especially, the recipe is a chemistry formula — guessing changes the result.
- Scaling a recipe means multiplying every ingredient by the same factor. Serves 4 → serves 8: factor 2, double everything. Serves 4 → serves 2: factor ½, halve everything. The ratios between ingredients must not change — that's what keeps the recipe being the same recipe.
- One thing that doesn't simply scale: cooking time. Double the mixture is not double the minutes — test for doneness instead.
4.3Judging the result: sensory evaluation
- Food is judged with the senses, in four categories: appearance (colour, shape, how it's plated), aroma (smell), texture (how it feels to bite — crisp, tender, gluey), and flavour (taste, and the balance of sweet, salty, sour, bitter).
- Useful sensory words are specific: "the pastry was crisp outside and buttery inside" tells the cook something; "it was nice" tells them nothing.
- Sensory evaluation is the food version of Unit 4 in any design subject: honest testing against what you were aiming for, so the next attempt is better.
Design is decisions, not decoration.
Four units: designing for real users instead of imaginary ones, generating ideas worth choosing between, prototyping so failure is cheap, and designing responsibly for the planet and for everybody — the Year 9 design-thinking toolkit.
The mapFour units
- Design for real users — empathy, user research, defining the problem, and briefs with constraints and criteria.
- Generating better ideas — diverge then converge, SCAMPER, sketches that communicate, and choosing with a criteria matrix.
- Prototyping & iteration — fidelity levels, failing fast, testing with users, and improving from feedback.
- Design in the world — sustainable design, life cycle thinking, inclusive design, and who owns an idea.
Not whether your product is pretty — whether you can show a process: a real user need, a brief with constraints and measurable criteria, a range of ideas, prototypes tested with users, and a final design you can justify against the criteria.
Design for real users
Bad designs are usually designed for an imaginary "everyone". Good designs start with a specific person, a real frustration, and a designer who bothered to look.
1.1Start with people, not products
- User-centred design means the user's needs drive every decision — and the design is tested on real users, not just admired by its designer.
- Empathy is the working skill behind it: understanding the user's experience — what frustrates them, what they are trying to do, what gets in the way — from their point of view, not yours.
- The classic trap: designing for yourself. You are one user, and probably not a typical one.
1.2User research: look before you design
- Interviews — ask users open questions about what they do and what annoys them. "Tell me about the last time…" beats "would you like…".
- Observation — watch people actually doing the task. This is the gold standard, because what people do and what they say are different: someone who says their school bag is "fine" can be watched digging through it for two minutes to find a pen.
- Surveys — quick answers from many people; good for counting how common a problem is, weak at explaining it.
- Research ends with a problem statement that names the user, the need, and the insight: "Year 7 students (user) need a way to find equipment fast between classes (need), because digging through a full bag makes them late (insight)."
1.3The design brief
A design brief is the contract for the project: what is being designed, for whom, within what limits, and how success will be judged. Two of its parts are confused constantly, so pin them down:
| Part of the brief | What it is | Example |
|---|---|---|
| The problem & user | Who it is for and what need it meets | Year 7s who can't find equipment fast |
| Constraints | Limits set for you before designing starts — you must work inside them | Budget $15 · finished by week 8 · school materials only · safety rules |
| Criteria for success | The tests you will run on the finished design to judge whether it works | "8 of 10 testers find a pen in under 15 seconds" |
"It should be easy to use" cannot be tested — easy for whom, measured how? A criterion earns its place when it names a test and a number: "a first-time user finds the switch within 10 seconds". If you can't imagine the test, rewrite the criterion.
Generating better ideas
Your first idea is almost never your best one. Professionals generate many ideas cheaply, then choose between them fairly — open up first, narrow down second, never both at once.
2.1Diverge, then converge
2.2SCAMPER: seven ways to push an idea
SCAMPER takes an existing product and forces it somewhere new — one prompt per letter:
- S—Substitute. Swap a part or material. Metal frame → bamboo?
- C—Combine. Merge two things into one. Pencil case + phone stand?
- A—Adapt. Borrow an idea that already works elsewhere. What would a tackle box do here?
- M—Modify. Make a feature bigger, smaller, or exaggerated. Giant zip? Tiny footprint?
- P—Put to another use. Find it a new job. A bag that becomes a desk organiser?
- E—Eliminate. Remove a part. What isn't actually needed?
- R—Reverse. Flip the order, layout or roles. Opens from the bottom? User assembles it?
2.3Sketches and mood boards that communicate
- Design sketches are fast and plural — six rough ideas beat one polished drawing at this stage.
- Annotation does the heavy lifting: notes on the sketch that explain how it works and why you chose it ("lid clips here so it opens one-handed"), not just what it is ("lid").
- A mood board collects images, colours, materials and textures that capture the feel the design is aiming for — it sets a direction before any product is drawn.
2.4Choosing fairly: the criteria matrix
When it's time to converge, score every concept against the same criteria from the brief, out of 5, and add up. Here is one worked correctly for three pencil-case concepts:
| Criterion (score /5) | A — fold-flat case | B — rigid box | C — soft sleeve |
|---|---|---|---|
| Easy to carry | 5 | 2 | 4 |
| Cheap to make | 4 | 3 | 5 |
| Protects contents | 3 | 5 | 2 |
| Looks appealing | 3 | 4 | 2 |
| Total | 15 | 14 | 13 |
Concept A wins 15 to 14 to 13 — but the matrix also shows why: it trades some protection for portability and cost. The decision is now an argument you can defend with evidence, and a marker can follow it. That is exactly what "justify your design" means.
Prototyping & iteration
A prototype is a question made physical. You don't build one to show off — you build the cheapest thing that can tell you whether an idea works, before it's expensive to be wrong.
3.1Fidelity: how finished should it be?
- Low-fidelity prototypes are rough and fast — paper screens, a taped cardboard shape, acting out a service with sticky notes. Minutes to make, so failure costs nothing.
- High-fidelity prototypes look and work close to the real thing — a painted foam appearance model, a working coded app. Slow and costly, so they come late, when the big questions are already answered.
- Fail fast doesn't mean rushing to failure — it means finding the flaws early, at cardboard prices, instead of late, at final-material prices.
- Choose materials and processes to suit the prototype's question: cardboard answers "is it the right size and shape for a hand?"; a 3D-printed part answers "do these pieces actually fit together?"; final materials only when the question is "will it survive real use?"
3.2The iteration loop
3.3Testing with users, properly
- Give the user a real task ("pack this for a school day") and then watch silently. Every time you explain or defend the design, you erase the evidence of where it fails.
- Record what actually happened — where they hesitated, what they got wrong, what they said unprompted. Feelings fade; notes don't.
- Feedback is data about the design, not a verdict on the designer. "The tester couldn't find the opening" is a gift: it's the next iteration's to-do list.
Design in the world
Every designed object carries decisions about the planet, about who gets to use it, and about whose idea it was. Most of those decisions are locked in before anything is manufactured.
4.1Sustainable design: think in life cycles
- Around 80% of a product's environmental impact is locked in at the design stage — material choice, energy use, repairability and recyclability are all decided before manufacture begins.
- Design for disassembly: screws instead of glue, materials that separate cleanly — so at end of life the materials can actually be recovered.
- A product that mixes materials inseparably (foil-lined plastic, glued composites) usually can't be recycled, whatever the label implies.
4.2Inclusive design: design for everybody
- Accessibility asks: can people with different abilities — limited grip, low vision, a wheelchair, colour-blindness — actually use this?
- Inclusive design goes further: design for the widest range of people from the start. The famous pattern: solving for users at the extremes improves the design for everyone.
- Real examples: the easy-grip vegetable peeler designed for arthritic hands became everyone's favourite peeler; kerb ramps cut for wheelchairs turned out perfect for prams, bikes and delivery trolleys.
- Ethical designers also ask who is left out: a touchscreen-only kiosk excludes blind users; tiny grey text excludes half the room.
4.3Whose idea is it? Intellectual property basics
- Intellectual property (IP) is legal ownership of creations of the mind. It exists so inventors and creators can benefit from their work — which encourages more of it.
- A patent protects how an invention works — a mechanism, a process. It must be registered, and it expires.
- A trademark protects a brand's name and logo — the mark customers recognise.
- Copyright protects creative work — drawings, text, code, music — and applies automatically in Australia the moment the work is created.
- For your folio: being inspired by existing products is how design works; copying one and presenting it as yours is not.
From "it works" to "it's well built".
Four units: the number systems and file sizes underneath every app, the patterns that keep code readable, how real data is stored and questioned, and how to build something a stranger can actually use — built from the Year 9–10 Digital Technologies descriptions.
The mapFour units
- Data under the hood — binary, hexadecimal, colour codes, file sizes and compression.
- Programming patterns — functions, parameters, return values, arrays, and the bugs that bite everyone.
- Structured data — records and fields, tables, queries, validation, and why one big table isn't enough.
- Building for users — interface principles, wireframes, accessibility, user testing and staying safe online.
Representing data in different number systems and estimating its size; designing modular algorithms using functions and arrays; storing and querying structured data; and designing, testing and evaluating a digital solution against the needs of real users.
Data under the hood
You already know data is binary. This unit adds the shorthand professionals actually use — hexadecimal — then answers the two questions every project runs into: how big is this file, and can I make it smaller?
1.1Binary, fast review
- A bit is one 0 or 1; eight bits make a byte. Binary columns double: 128, 64, 32, 16, 8, 4, 2, 1.
- Read a binary number by adding the columns holding a 1. 1011 = 8 + 2 + 1 = 11. 11111111 = 255, the largest one byte can hold.
- Write decimal as binary by taking the biggest column that fits, then the next. 26 → 16 fits (1), 8 fits (1), 4 doesn't (0), 2 fits (1), 1 doesn't (0) = 11010. Check: 16 + 8 + 2 = 26.
1.2Hexadecimal: why 16 digits beat 2
Binary is correct but unreadable — nobody wants to dictate 11001010 over the phone. Hexadecimal ("hex") counts in 16s, so it needs six extra digits after 9: A B C D E F stand for 10, 11, 12, 13, 14, 15.
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Hex | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| Binary (4 bits) | 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |
Four bits have 16 patterns; hex has 16 digits — a perfect match. So converting is chunking, not arithmetic: split the binary into fours from the right and swap each chunk for its hex digit. 11001010 → 1100 1010 → C A = CA. Going to decimal: C is 12, so 12 × 16 = 192, plus A which is 10, gives 202. Two hex digits cover exactly one byte, 00 to FF (0 to 255) — which is why hex is everywhere bytes are.
| Hex | Working (left digit × 16, plus right digit) | Decimal |
|---|---|---|
| 1F | 1 × 16 = 16, plus F = 15 | 31 |
| 2A | 2 × 16 = 32, plus A = 10 | 42 |
| 80 | 8 × 16 = 128, plus 0 | 128 |
| FF | F = 15, so 15 × 16 = 240, plus 15 | 255 |
1.3Colour as #RRGGBB
1.4File sizes
- Sizes climb in steps of 1024 (210), because computers count in binary: 1024 bytes = 1 kilobyte (KB), 1024 KB = 1 megabyte (MB), 1024 MB = 1 gigabyte (GB). (Storage adverts often round to 1000 — that's why a "500 GB" drive shows less.)
- Estimating an uncompressed image is arithmetic: pixels × bytes per pixel. A 100 × 100 photo in RGB is 10,000 pixels × 3 bytes = 30,000 bytes (about 29 KB).
- Text is cheap: one character ≈ 1 byte, so a 500-word essay is a few KB. Video is brutal: it is many full images every second.
1.5Compression: lossy vs lossless
| Lossless | Lossy | |
|---|---|---|
| What it does | Records the data more cleverly — e.g. "40 white pixels" instead of listing 40 | Throws away detail people are unlikely to notice |
| Can you get the original back? | Yes — perfectly, every bit | No — the discarded detail is gone forever |
| Size saving | Modest | Large |
| Typical uses | ZIP archives, PNG images, program files, text | JPEG photos, MP3 audio, streamed video |
If losing a single byte would break the file — a program, a spreadsheet, a document — you must use lossless. If it is something human senses judge — a photo, a song — lossy buys a much smaller file for a loss most people never notice. Re-saving a lossy file again and again keeps discarding detail: the damage stacks up.
Programming patterns
Beginner code is one long list of instructions. Real code is built from small named parts that each do one job, and from lists of data walked through by loops. Both ideas are simple — and both come with a signature bug.
2.1Functions: why break code up
- A function is a named block of code that does one job. You call it by name instead of repeating its lines.
- Write it once, use it everywhere: one fix repairs every use. Duplicated code has to be fixed in every copy — and one copy always gets missed.
- A parameter is the input a function is given; an argument is the actual value passed in at the call. The return value is the answer it hands back.
- Names matter: calculateTotal tells the next reader what happens. doThing tells them nothing.
| Line | Pseudocode | What happens |
|---|---|---|
| 1 | FUNCTION areaOfRect(width, height) | width and height are the parameters |
| 2 | RETURN width × height | hands the answer back to whoever called |
| 3 | END FUNCTION | — |
| 4 | PRINT areaOfRect(5, 3) | 5 and 3 are the arguments; prints 15 |
| 5 | PRINT areaOfRect(10, 2) | same function, new values; prints 20 |
2.2Lists (arrays) and walking through them
- An array (or list) holds many values under one name: scores ← [7, 4, 9, 2].
- Each value has an index, and programming counts from 0. So scores[0] is 7, scores[1] is 4, scores[2] is 9, scores[3] is 2. The list's length is 4, but the last index is 3.
- A loop lets you visit every element without writing a line per value — and it works no matter how long the list grows.
| Pass | Pseudocode: total ← 0, then FOR EACH n IN [7, 4, 9, 2]: total ← total + n | n | total after |
|---|---|---|---|
| start | total ← 0 | — | 0 |
| 1 | total ← total + n | 7 | 7 |
| 2 | total ← total + n | 4 | 11 |
| 3 | total ← total + n | 9 | 20 |
| 4 | total ← total + n | 2 | 22 |
2.3The two bugs everyone meets
- Off-by-one. A list of 4 items has indexes 0 to 3. Asking for item 4 runs off the end; looping "1 to length" skips index 0. Always check the first and last item, never the middle — the middle is always fine.
- Infinite loop. The condition never becomes false, so the program hangs. Nearly always the line that changes the loop variable is missing, or changes it the wrong way. Before writing a loop, answer: what makes this stop?
2.4Trace tables
A trace table is a desk check with columns: one per variable, one row per line executed. Trace this and you can answer any exam question about it:
| Line executed | n | result | Condition n > 1 |
|---|---|---|---|
| n ← 5 / result ← 1 | 5 | 1 | — |
| WHILE test, then result ← result × n, n ← n − 1 | 4 | 5 | 5 > 1 true |
| same two lines again | 3 | 20 | 4 > 1 true |
| same two lines again | 2 | 60 | 3 > 1 true |
| same two lines again | 1 | 120 | 2 > 1 true |
| WHILE test fails, so PRINT result | 1 | 120 | 1 > 1 false — loop ends |
Write one column per variable and never erase — add a new row instead, so the history is visible. Update variables in the exact order the lines appear; a line that uses a variable it just changed is where most slips happen. Finally, record the condition's true/false at each pass: that column is what proves when the loop stopped.
Structured data
Data becomes useful the moment it has a shape. Give it fields and records and you can ask it questions — and stop people typing nonsense into it in the first place.
3.1Fields, records, tables
- A field is one piece of information about a thing — a column, like Title or Year. Each field has a data type: text, number, date, or true/false (boolean).
- A record is everything known about one thing — a row: one whole book, one whole student.
- A table is all the records of the same kind together, with the fields as its columns.
| BookID (number) | Title (text) | Author (text) | Year (number) | OnLoan (boolean) |
|---|---|---|---|---|
| 1 | Storm Boy | Thiele | 1964 | true |
| 2 | Playing Beatie Bow | Park | 1980 | false |
| 3 | Tomorrow, When the War Began | Marsden | 1993 | false |
Every column above is a field; every row is a record; the whole thing is a table. Choosing the type matters: a Year stored as text can't be compared or sorted numerically.
3.2Asking questions: filter and sort
- A query asks the data a question and returns only the records that answer it.
- Filter = keep only the records matching a condition. "Year > 1975" returns records 2 and 3 from the table above.
- Sort = put records in order by a field, ascending or descending. Sorting by Year ascending gives 1964, 1980, 1993.
- Filtering and sorting change what you see, not what is stored. The records themselves are untouched.
3.3Validation vs verification
| Validation | Verification | |
|---|---|---|
| Question it answers | Is this data sensible? | Is this data what was actually given? |
| Who does it | The computer, automatically | A person, or a double-entry check |
| Examples | Range check (age 0–120), type check (numbers only), presence check (not blank), format check (email has an @) | Typing a new password twice; proof-reading an address against the form |
Validation cannot tell you the data is true — only that it is possible. A birth year of 1804 fails a range check, but a wrong-but-plausible 2010 sails through. That is exactly what verification is for.
3.4One flat file, or linked tables?
A flat file is a single table holding everything. It works until the same information has to be repeated:
| Loan record | Member name | Member phone | Book |
|---|---|---|---|
| 1 | A. Nguyen | 0400 111 222 | Storm Boy |
| 2 | A. Nguyen | 0400 111 222 | Playing Beatie Bow |
| 3 | A. Nguyen | 0400 111 333 | Tomorrow, When the War Began |
- The phone number is stored three times — wasted space, and worse: when it changed, only one row was updated. Now the database contradicts itself and nobody knows which row is right.
- The fix is linked tables: a Members table holding each member's details once, and a Loans table that refers to the member by their ID. Change the number in one place and every loan is instantly correct.
- Splitting data into linked tables to remove repetition is the core idea you'll meet again in Year 10 as relational databases.
Building for users
Working code is half a solution. The other half is a person who has never seen your app, has one hand full, and gives up in about eight seconds. Design for them — and protect them.
4.1Interface principles
- Consistency — the same action looks and sits the same everywhere. Users learn your app once, not once per screen.
- Visibility — the important action is obvious without hunting. If a user has to search, the design failed, not the user.
- Feedback — every action gets a visible response: a button state, a spinner, a confirmation. Silence makes people tap again and send twice.
- Forgiveness — mistakes must be undoable, and destructive actions must confirm first.
- Simplicity — one screen, one main job. Everything competing for attention makes nothing stand out.
4.2Wireframes: plan before you build
4.3Accessibility basics
- Contrast. Text must stand out strongly from its background. Pale grey on white is unreadable in sunlight and for many users indoors too.
- Alternative text. Every meaningful image needs a written description, so a screen reader can say what it shows to someone who can't see it.
- Don't rely on colour alone. Add a word, an icon or a shape — a red-only error message is invisible to a colour-blind user.
- Keyboard access. Everything clickable must also be reachable and usable with the keyboard alone.
- Target size. Buttons must be big enough for a finger, and spaced so the wrong one isn't hit.
4.4Testing with real users
- Pick a real task ("find a book by Marsden and borrow it"). Never say "have a look around" — that tests nothing.
- Give them the task and then stay quiet. Every hint you give is a hint your app should have given.
- Watch where they hesitate, tap the wrong thing, or backtrack. Hesitation is data.
- Change the design, not the user. "They should have known" is not a finding.
- Test again after fixing — and with someone new, because the first person has now learnt the app.
4.5Cybersafety
- Phishing is a fake message pretending to be someone you trust, designed to make you hand over a password or click a bad link. Tells: false urgency ("your account closes today"), a slightly wrong sender address, a link whose real destination differs from its text, and a request nobody legitimate makes — your password.
- A passphrase of several unrelated words is both stronger and easier to remember than a short password with symbols. Length is what defeats guessing machines.
- Never reuse a password across accounts: one leaked site otherwise opens all of them.
- Two-factor authentication adds a second proof — a code from your phone or an app — so a stolen password alone is not enough to get in. Turn it on for email first: whoever controls your email can reset everything else.
How things push, pull, spin and decide.
Four units: the five ways forces attack an object, the simple machines that trade force for distance, how energy flows through every system, and the control loops that let machines steer themselves — the Year 9 Engineering Principles & Systems context of Design & Technologies.
The mapFour units
- Forces on things — tension, compression, shear, torsion and bending, and why triangles refuse to collapse.
- Simple machines & mechanisms — levers, pulleys, gears, cams and linkages: the parts every machine is built from.
- Energy in systems — input → process → output, energy changing form, and why no machine is 100% efficient.
- Control systems — open and closed loops, sensors, controllers and actuators, and where microcontrollers fit.
Engineered systems — a bike, a crane, a heater — can all be read the same way: forces act on their parts, mechanisms redirect motion and force, energy flows through and changes form, and control decides what happens next. Learn the four lenses and you can take any machine apart on paper.
Forces on things: five ways to break an object
Every part of every structure is being pushed, pulled, slid, twisted or bent — usually several at once. Engineers give each attack a name, because a part that shrugs off one can fail instantly under another.
1.1The five forces
1.2Static and dynamic loads
- A load is any force a structure must carry. A static load stays steady — the weight of the roof itself, a full water tank sitting on a stand.
- A dynamic load changes or moves — wind gusts, a truck crossing a bridge, a crowd jumping in a grandstand. Dynamic loads are harder on structures because they hit suddenly and repeat.
- Repeated dynamic loading can crack a part at forces far below what would break it once — engineers call this fatigue. Bend a paperclip once and it survives; bend it back and forth twenty times and it snaps.
- Engineers design for the worst realistic load, then add a safety margin on top — never for the average day.
1.3Why triangles win
Push on a square frame and it collapses sideways into a diamond without any side changing length — only the joints swing. Push on a triangle and it cannot change shape unless a whole side stretches or squashes, and solid material strongly resists both. That is why bridges, cranes, roof frames and pylons are full of triangles: adding a diagonal brace to a wobbly square turns it into two rigid triangles.
Simple machines: trading force for distance
No machine gives you free energy. What levers, pulleys and gears actually do is trade: less force over more distance, or more force over less. Every gadget you own is built from these few moves.
2.1Levers: three classes
Every lever has three players: the fulcrum (the pivot), the load (what you're moving) and the effort (the force you apply). The class of a lever is simply which of the three sits in the middle.
2.2Pulleys
- A single fixed pulley changes the direction of your pull — haul down to lift up — but not its size. Mechanical advantage: 1.
- Add a movable pulley attached to the load and two rope sections now share the weight: you pull with half the force, but pull twice as much rope. Mechanical advantage: 2.
- The rule for an ideal pulley system: mechanical advantage = the number of rope sections supporting the load. Four supporting sections → a quarter of the force, four times the rope.
- That is the machine trade in its purest form: force down, distance up, energy the same.
2.3Gears and gear ratio
- Worked example: driver 15 teeth, driven 45 teeth. Ratio = 45 ÷ 15 = 3. If the driver spins at 120 revolutions per minute, the driven gear spins at 120 ÷ 3 = 40 rpm.
- Gearing down (small drives big): slower, stronger — a car in first gear, a drill's chuck. Gearing up (big drives small): faster, weaker — a bike in top gear.
- A cam is a non-round wheel that converts rotation into a repeating push — up-down-up-down — as a follower rides its edge. Car engines use cams to open valves at exactly the right moment.
- A linkage is a chain of pivoting bars that carries motion somewhere else, changing its direction or size on the way — the mechanism behind vice-grips, folding clothes racks and digger arms.
Energy in systems: follow the flow
Engineers read any machine as a system: energy goes in, gets processed, and comes out — some as the useful thing you wanted, the rest as waste. Track the flow and you understand the machine.
3.1Input, process, output
3.2Energy changes form
- The forms worth knowing: kinetic (movement), gravitational potential (raised up), elastic potential (stretched or squashed), chemical (stored in fuel, food, batteries), electrical, thermal, light and sound.
- Machines are energy converters: an electric motor turns electrical energy into kinetic energy; a generator is the same idea run backwards — spin it, and kinetic energy becomes electrical.
- The law of conservation of energy: energy cannot be created or destroyed, only converted. If your machine outputs less useful energy than went in — and it always does — the difference left as waste, almost always heat.
- That's why "waste" heat is the universal clue: a warm phone charger, a hot laptop, a hot drill are all leaking energy that never became the useful output.
3.3Efficiency
Efficiency = useful energy out ÷ total energy in × 100. A motor fed 200 J that delivers 150 J of movement is 150 ÷ 200 × 100 = 75% efficient — the other 50 J became heat and sound. Nothing reaches 100%: an old incandescent bulb turned only about 5% of its energy into light, which is why LEDs replaced it. Higher efficiency means less fuel, less cost, less waste heat — a core design goal.
Control systems: machines that steer themselves
A toaster runs blind; a thermostat checks its own work. The difference — feedback — is the single most important idea in control, and it splits every automated system into one of two families.
4.1Open loop vs closed loop
4.2Sensor → controller → actuator
- Every closed-loop system has the same three jobs. The sensor measures the real world: temperature, light, distance, moisture, speed.
- The controller decides: it compares the measurement with the target and chooses an action. In old systems this was a mechanical switch; today it is usually a chip.
- The actuator acts on the world: a heater, motor, valve, buzzer or light — the muscle of the system.
- Examples everywhere: a fridge (sensor: thermometer → actuator: compressor), cruise control (speed sensor → throttle), automatic greenhouse (moisture sensor → water valve).
A microcontroller (like a micro:bit or Arduino) is a small, cheap computer that plays the controller role: sensors wire into its inputs, actuators hang off its outputs, and the decision rule is a program you write — if temperature < 21, switch heater on. Same loop as a 1950s thermostat, but the rule can now be as clever as you can code, and one chip can run dozens of loops at once.
Every good cook is running experiments.
Why does an egg set? Why does bread brown but boiled chicken doesn't? Why must rice be cooled fast? Four units answer the science questions behind the cooking — and follow food all the way from the paddock to the bin.
The mapFour units
- Food science — what heat does to protein, sugar and starch, and the four ways a mixture rises.
- Food safety systems — what bacteria need, which foods are high-risk, temperature control, HACCP and allergen law.
- Nutrition for life stages — changing energy needs, the adolescent's three key nutrients, and adapting recipes for dietary needs.
- The food system — paddock to plate, food miles and waste, and the preservation methods that beat spoilage.
Explaining why, not just what. Name the reaction (denaturation, Maillard, caramelisation, gelatinisation) and the conditions it needs; justify a safety decision with a temperature and a reason; adapt a recipe for a stated dietary need and say what the substitution replaces.
Food science: what heat does to food
Heat doesn't just make food hot — it rewrites it. Four reactions explain most of what happens in a kitchen, and knowing which one you are chasing tells you exactly how to cook.
1.1The four reactions
| Reaction | What changes | Needs | You see it in… |
|---|---|---|---|
| Denaturation (protein) | Heat unravels the folded protein molecules; they then tangle together and set. The change is permanent — a cooked egg never un-cooks. | heat (egg white sets from about 60 °C); acid and beating can denature proteins too | egg white turning white and firm, meat firming and shrinking, milk skin on custard |
| Maillard browning | Proteins (amino acids) react with sugars to make hundreds of new brown, savoury-smelling compounds. | protein and sugar together, a fairly dry surface, and high heat — roughly 140 °C and up | toast, bread crust, seared steak, roast coffee, browned onions |
| Caramelisation | Sugar alone breaks down and rebuilds into brown, bitter-sweet compounds. | sugar only — no protein needed — and strong heat (table sugar from about 160 °C) | toffee, caramel sauce, the dark edges of roasted pumpkin |
| Gelatinisation (starch) | Starch granules soak up water, swell, burst and release starch, thickening the liquid around them. | starch + liquid + heat — it begins around 60–70 °C; without water nothing happens | white sauce thickening, gravy, custard, rice absorbing water and swelling |
- Maillard and caramelisation both brown food, but they are not the same reaction. The tell: caramelisation is sugar on its own; Maillard needs protein as well as sugar. Golden toast is Maillard; molten toffee is caramelisation.
- This is why boiled or steamed food never browns: at about 100 °C, water-based cooking never reaches Maillard or caramelisation temperatures, and the wet surface keeps it cool.
- It is also why you pat a steak dry before searing — the pan must first boil off surface water before the surface can climb past 100 °C and brown.
- Gelatinisation is the odd one out: it is the only one of the four that needs water in order to happen.
1.2Raising agents: four ways to trap gas
A raised mixture is simply a mixture full of trapped gas bubbles that expand in the heat and are then held in place as the structure sets. There are four ways to get the gas in.
| Type | Agent | Gas, and where it comes from | Used in |
|---|---|---|---|
| Biological | Yeast — a living single-celled fungus | Carbon dioxide, from yeast feeding on sugars (fermentation). Needs warmth, moisture, food and time to prove. | bread, pizza dough, buns |
| Chemical | Baking powder, or bicarbonate of soda plus an acid | Carbon dioxide, from a chemical reaction between the bicarbonate and an acid once liquid is added; heat releases more. Works in minutes. | cakes, muffins, scones, pancakes |
| Mechanical | Air, beaten in by you | Air, from whisking, creaming butter and sugar, sifting, or folding. No reaction — pure physical work. | sponge cake, meringue, whipped mousse |
| Steam | Water already in the mixture | Steam: water turns to vapour at 100 °C and expands enormously, pushing layers apart. Needs a hot oven and a wet mixture. | choux pastry, puff pastry, Yorkshire puddings |
- Yeast and baking powder both produce carbon dioxide, but by completely different routes: yeast is alive and feeds (slow — an hour or more of proving); baking powder is a chemical reaction (fast — which is why cake batter goes into the oven straight away).
- Bicarbonate of soda on its own needs an acid partner in the recipe — lemon juice, yoghurt, buttermilk, golden syrup. Baking powder already contains its own dry acid, so it works in any mixture.
- Most recipes stack them: a scone uses baking powder and the steam from its milk; puff pastry uses steam alone and does the rest with folding.
"Why does bread have a brown crust but a pale crumb?" Because the crust dries out and reaches Maillard temperatures (about 140 °C and above), where protein and sugar react to brown it. The inside stays wet, so it cannot rise above about 100 °C and cannot brown. Same loaf, two temperatures.
Food safety systems: from rules to a system
In Year 8 food safety was a list of rules. At Year 9 it becomes a system: know what bacteria need, remove one of those needs, and check the points where it actually matters.
2.1What bacteria need — and which foods give it to them
- Food-poisoning bacteria need five things: food (especially protein), moisture, warmth (the 5–60 °C danger zone), time, and for most of them a near-neutral pH — they dislike acid. Take away any one and growth stops. Every preservation method in Unit 4 is exactly that: removing one need.
- High-risk foods are the ones that give bacteria everything they want: moist and protein-rich. Raw and cooked meat and poultry, seafood, dairy, eggs, cooked rice and pasta, prepared salads, and small goods. They must be kept out of the danger zone.
- Low-risk foods are missing something: dry (flour, biscuits, rice before cooking), very acidic (vinegar, pickles), very salty or sugary (jam, honey — sugar ties up the water so microbes cannot use it).
- Cooked rice deserves its own warning: Bacillus cereus spores survive cooking, so rice left to cool slowly on the bench grows toxins that reheating will not destroy. Cool it fast, refrigerate it, and don't keep it for days.
2.2Temperature control
- Cooling cooked food safely, the Australian rule: 60 °C down to 21 °C within 2 hours, then 21 °C down to 5 °C within a further 4 hours. Shallow containers and dividing large batches are how you hit it.
- Reheating is not the same as hot-holding: reheat quickly and thoroughly to 75 °C, then hold at 60 °C or above. Reheat once only.
- Never thaw frozen food on the bench: the outside sits in the danger zone for hours while the middle is still frozen. Thaw in the fridge.
2.3HACCP: checking where it counts
HACCP (say "hassup") stands for Hazard Analysis and Critical Control Points. It is the system every Australian food business runs on, and the idea is simple: instead of hoping the final product is safe, you find the few steps where safety is actually decided and control those.
- Identify the hazards — what could make someone ill at each step? (Bacteria in raw chicken; a metal fragment; an undeclared allergen.)
- Find the critical control points (CCPs) — the steps where you can actually remove or control that hazard: cooking, cooling, cold storage, reheating.
- Set a limit for each — a number, not a feeling: "cooked to 75 °C in the centre", "fridge at 5 °C or below".
- Monitor — measure it. A probe thermometer, a fridge log, checked at set times.
- Correct and record — if a limit is missed, act (keep cooking, discard the batch, fix the fridge) and write down what happened.
"Raw chicken carries Salmonella" is a hazard — a danger you have identified. "Cook to 75 °C in the centre" is the critical control point: the step that actually destroys it, with a limit you can measure. Hazards are what could go wrong; CCPs are where you stop it.
2.4Allergens and the label
- A food allergy is an immune reaction to a food protein. It can be severe: anaphylaxis is a life-threatening reaction affecting breathing and blood pressure, treated with adrenaline. A tiny trace can be enough — which is why "I picked the nuts off" is not a safe answer.
- An intolerance (such as lactose intolerance) is a digestive problem, not an immune one: unpleasant, but not life-threatening. Don't mix the two up in an exam.
- Australian food law requires certain allergens to be declared on the label whenever they are present, in plain English and in bold: peanuts, tree nuts, milk, egg, fish, crustacea, molluscs, sesame, soy, lupin, cereals containing gluten (such as wheat), and added sulphites.
- In the kitchen, allergen cross-contact is the risk: the same knife, board, oil, or a stir with the same spoon can carry enough protein to trigger a reaction. Prepare allergen-free food first, on clean, separate equipment.
Nutrition for life stages: same body, changing needs
A toddler, a fifteen-year-old and an eighty-year-old need very different food from the same five groups. And some people at every stage need a recipe changed, not just admired — which is a design problem.
3.1Energy and needs across life
| Life stage | What is happening | Food priorities |
|---|---|---|
| Childhood | Steady growth; small stomachs, high activity | regular meals and snacks; nutrient-rich food rather than bulk |
| Adolescence | The fastest growth since infancy — height, muscle, blood volume, bone | the highest energy needs of any stage; protein, iron and calcium especially |
| Adulthood | Growth has stopped; needs depend on activity level | energy matched to activity, to maintain a healthy weight |
| Pregnancy | Building another person | extra iron, folate (protects the baby's developing spine and brain) and calcium |
| Older adults | Energy needs fall, but nutrient needs do not; appetite often drops | fewer kilojoules but the same or more calcium, protein, fibre and fluids |
The pattern to remember: energy needs rise and fall across life, but nutrient needs don't follow them. An older adult eating less food still needs just as much calcium — so every mouthful has to work harder.
3.2The teenage three: protein, iron, calcium
- Protein — the material of growth: muscle, blood, skin, enzymes. Sources: meat, fish, eggs, dairy, legumes, tofu, nuts.
- Iron — makes haemoglobin, which carries oxygen in the blood. Too little causes anaemia: tiredness, paleness, poor concentration. Teenage girls need more than boys, because iron is lost with menstruation. Sources: red meat, chicken, fish, legumes, tofu, green leafy vegetables, iron-fortified cereal.
- Calcium — builds bone and teeth. Around 90% of adult bone mass is laid down by the end of the teens, so this is the one nutrient you cannot catch up on later; too little raises the risk of osteoporosis (weak, brittle bones) decades on. Sources: milk, yoghurt, cheese, calcium-fortified soy milk, tinned fish with soft bones.
Iron comes in two forms. Haem iron, from meat, fish and chicken, is absorbed easily. Non-haem iron, from plants — legumes, spinach, fortified cereal — is absorbed far less well, unless vitamin C is eaten in the same meal. Beans with tomato, cereal with orange juice, lentils with capsicum: the vitamin C markedly increases how much iron the body actually takes up. This matters most for vegetarians.
3.3Dietary needs, and how to adapt a recipe
| Need | What it means | Watch for | Adapting a recipe |
|---|---|---|---|
| Vegetarian | No meat (a vegan diet excludes all animal products, including dairy, eggs and honey) | protein, iron, vitamin B12, zinc | swap meat for legumes, tofu, eggs or dairy; add a vitamin C food to boost iron uptake; vegans need a reliable B12 source such as fortified foods |
| Coeliac disease | An autoimmune disease: gluten damages the lining of the small intestine, so nutrients stop being absorbed. Not an allergy, not a preference — and lifelong. | gluten in wheat, rye, barley (and oats, usually through contamination) | use gluten-free flours (rice, corn, buckwheat, besan); check every sauce and stock; use clean equipment — even crumbs in a shared toaster matter |
| Diabetes | The body cannot properly control blood glucose (with type 1, the pancreas makes little or no insulin) | the amount and type of carbohydrate, and meal timing | choose low-GI carbohydrates that release glucose slowly, keep portions and meal times regular, cut added sugar, add fibre |
| Lactose intolerance | Cannot digest lactose, the sugar in milk — a digestive problem, not immune | milk, cream, soft cheese, ice cream | use lactose-free or plant milks; choose calcium-fortified versions so calcium is not lost |
- The rule for a good substitution: replace the ingredient's function, not just its name. Butter in pastry is there for fat and flakiness; egg in a cake binds and traps air. Swap in something that does the same job, then test the result.
- An adapted dish still has to be worth eating. Sensory evaluation applies exactly as before — appearance, aroma, texture, flavour — and a gluten-free cake that no one enjoys has failed its brief.
The food system: paddock to plate, and what happens after
Between a paddock in the Riverina and a bowl on your table sit half a dozen industries, thousands of kilometres, and several inventions designed to stop food rotting on the way.
4.1Paddock to plate
- Food miles counts the distance food travels from producer to consumer. Long distances mean more fuel burned, more emissions and more refrigeration — part of why buying local and in season is usually the lower-impact choice.
- Food miles are not the whole story, though: a tomato trucked from a nearby heated greenhouse can carry more emissions than one grown in season further away. Distance is one factor, not the verdict.
- Reducing food waste at home: plan meals and shop to a list, store food properly (the fridge at 5 °C or below), understand the dates — use-by is a safety limit and must be obeyed, while best-before is about quality, and food is usually still safe after it — use leftovers, and compost what is genuinely left.
4.2Preservation: removing what spoilage needs
Every preservation method works by taking away one of the things micro-organisms need — water, warmth, a friendly pH, or access to the food at all.
| Method | How it works | What it defeats | Examples |
|---|---|---|---|
| Canning / bottling | Food is sealed in a container and heated enough to destroy micro-organisms and stop enzymes; the seal keeps new ones out. | Kills bacteria, yeasts and moulds already present, and blocks recontamination | tinned tomatoes, baked beans, bottled fruit |
| Freezing | Held at −18 °C or below, water is locked up as ice and everything slows to a halt. | Stops microbial growth — but does not kill: they resume on thawing | frozen peas, meat, bread |
| Drying / dehydrating | Water is removed, so microbes have nothing to grow in. | Bacteria and moulds cannot grow without moisture | sultanas, dried apricots, jerky, powdered milk |
| Fermenting | Helpful microbes are encouraged to convert sugars into acid (or alcohol), making the food too acidic for spoilage organisms. | Spoilage bacteria, which cannot survive the low pH | yoghurt, sauerkraut, kimchi, sourdough |
| Pickling / salting | Acid (vinegar) makes the food too sour for microbes; salt and sugar draw water out of them. | Bacteria and moulds, blocked by acid or by the loss of usable water | pickled onions, olives, salted fish, jam |
| Pasteurisation | A short, controlled heat treatment kills the disease-causing microbes without cooking the food. | Pathogens — the dangerous ones. Some harmless microbes survive, so milk still goes off eventually | milk, fruit juice, egg pulp |
Canning kills micro-organisms with heat and seals them out, so the food is shelf-stable for years at room temperature. Freezing only pauses them: nothing is killed, and once the food thaws, growth restarts from where it stopped. That is why thawed food must be treated as fresh food and never refrozen raw.
Why this thing is made of that stuff.
Four units: the properties that decide how a material behaves, the four great families and what separates them, the skills of marking out, shaping and joining, and how to choose the right material and defend the choice — the Year 9 Materials & Technologies Specialisations context of Design & Technologies.
The mapFour units
- Why materials behave — strength, hardness, toughness, elasticity and the rest, defined precisely enough to argue with.
- The big four families — timbers, metals, polymers, and textiles & composites.
- Working with materials — marking out, cutting, shaping, and the three ways to join.
- Choosing well — matching material to purpose, and counting cost, availability and sustainability.
Every object you touch is the answer to one question: which material, and why that one? A saucepan handle, a bike frame, a raincoat — each is a set of properties chosen against a set of needs, then processed and joined in ways that suit it. This course teaches you to read that answer and to write your own.
Why materials behave the way they do
"Strong" is the vaguest word in the workshop. Engineers split it into a handful of precisely different properties — and the two most often confused, hardness and toughness, are close to opposites.
1.1The properties that matter
| Property | What it actually means |
|---|---|
| Strength | How much force the material carries before it breaks. Ask "strong in what?" — rope is strong in tension, brick in compression. |
| Hardness | How well the surface resists scratching, denting and wear. |
| Toughness | How well the material absorbs a sudden impact without cracking. |
| Elasticity | The ability to change shape under load and spring back to the original shape. |
| Plasticity | The ability to be changed in shape permanently — and stay there — without breaking. |
| Durability | How well it survives its environment over time: rain, sun, salt, insects, chemicals. |
| Conductivity | How readily it carries heat or electricity. The opposite is an insulator. |
Glass is hard but not tough: you cannot scratch it with a fingernail, yet one knock shatters it. Rubber is tough but not hard: hit it with a hammer and it absorbs the blow, but you can scratch it with a coin. Hardness is about the surface resisting scratches and dents; toughness is about the whole part surviving a sudden impact. A chisel needs both, and steelmakers work hard to get them together: a hard edge that holds its sharpness, over a tough body that will not snap.
1.2Elastic, plastic, or broken
- Stretch a rubber band and let go — it returns. That is elasticity: temporary, reversible change.
- Bend a piece of soft copper wire — it stays bent. That is plasticity: permanent change without breaking. It is what makes a material malleable (hammerable into sheet) and ductile (drawable into wire).
- Push either too far and the part breaks. Where that happens is a question of strength, not of elasticity or plasticity.
- Design uses all three: a car body panel is pressed into shape using plasticity, a suspension spring works on elasticity, and both need enough strength to survive the road.
1.3Natural or manufactured
- Natural materials come out of the living world or the ground and are used with little change: timber, wool, cotton, leather, stone, clay.
- Manufactured materials are processed or synthesised until they are something new: steel (iron ore + carbon), plastics (from crude oil), MDF and plywood (wood fibres or veneers plus adhesive), glass, concrete.
- The point of manufacturing is control: you choose the properties. Plywood is engineered so its layers cross-grain, giving even strength in both directions — something a natural plank cannot do.
- The trade-off is usually energy and cost: manufactured materials nearly always take more energy to produce than the natural ones they replace.
The big four families
Almost everything made is timber, metal, polymer, or a textile or composite. Each family splits in two along one important line — and in three of the four cases, the line is not the one the names suggest.
2.1The four families at a glance
2.2Timbers
- Hardwood vs softwood is botanical, not a hardness test. Hardwoods come from broad-leaved trees that lose their leaves or flower; softwoods come from cone-bearing conifers. Balsa is a hardwood — and it is the softest timber in the workshop. Douglas fir is a softwood harder than several hardwoods.
- As a rough tendency hardwoods are denser, slower-growing and dearer; softwoods grow fast and are the cheap structural timber of house framing. Tendency, not rule.
- Timber is anisotropic: much stronger along the grain than across it. Split a plank along the grain and it parts easily; across the grain it fights you.
- Manufactured boards fix timber's weaknesses: plywood glues thin veneers with the grain crossed layer to layer, giving even strength and no splitting; MDF and chipboard are wood fibres or chips bonded with resin — cheap, perfectly flat, but weak at edges and ruined by water.
2.3Metals
- Ferrous metals contain iron: mild steel, cast iron. They are strong and cheap, and they rust unless painted, galvanised or alloyed. A magnet sticks to them — the workshop's quickest test.
- Non-ferrous metals contain no iron: aluminium, copper, zinc, lead, tin. They do not rust, and are usually lighter or better conductors — and usually dearer.
- An alloy is a metal mixed with other elements to get properties neither has alone. Steel = iron + a little carbon (harder and stronger than pure iron). Stainless steel = steel + chromium, which forms an invisible protective layer, so it resists corrosion. Brass = copper + zinc: harder than copper and easy to machine. Bronze = copper + tin.
- Most metals are good conductors of heat and electricity, and most are malleable and ductile — which is why metal can be rolled into sheet, drawn into wire and bent without cracking.
2.4Polymers
- Thermoplastics soften every time they are heated and can be reshaped again and again: acrylic, PET drink bottles, polypropylene, polythene. This is exactly why they can be recycled by melting.
- Thermosets set hard once during a chemical reaction and never soften again — heat them enough and they char or burn rather than melt: epoxy resin, melamine, Bakelite, vulcanised rubber. Great for saucepan handles and electrical fittings; very hard to recycle.
- Polymers in general: light, cheap to mould in huge numbers, excellent electrical and thermal insulators, corrosion-proof — but they soften or weaken with heat, most come from crude oil, and many take centuries to break down.
2.5Textiles and composites
A composite combines two materials so that each covers the other's weakness. Fibreglass = glass fibres, superb in tension but floppy alone, set in cured resin, rigid but brittle alone — together, a stiff, strong, light shell. Reinforced concrete = concrete, excellent in compression but feeble in tension, with steel bars laid exactly where the tension is — the pairing that makes modern buildings possible. Carbon fibre does the same trick with carbon fibres and epoxy, giving a stiffness-to-weight ratio no metal matches. In each case the composite outperforms both ingredients, because you get each one's strength and neither one's weakness.
- Textile fibres divide into natural (cotton, wool, linen, silk) and synthetic (nylon, polyester, acrylic — polymers spun into thread).
- Natural fibres breathe and absorb moisture; synthetics are stronger for their weight, dry fast, and resist rot — which is why outdoor gear blends them.
Working with materials
Four stages turn stock material into a part: mark it out, cut it, shape it, join it. Get the first stage wrong and no amount of skill in the other three will save the job.
3.1Marking out
- Start from a face side and face edge: one flat face and one straight edge, marked, and every measurement taken from those two. Measure from a rough edge and every error is passed on.
- Use the right marker for the material: a pencil on timber, a scriber that scratches a fine permanent line on metal, a fine marker on plastic film.
- A try square gives lines truly at 90° to the face edge. A marking gauge scores a line a set distance from the face edge, over and over, identically.
- The workshop's oldest rule: measure twice, cut once. Cutting is irreversible; measuring is free.
3.2Cutting and shaping
- Cutting removes material along a line: a tenon saw for fine straight cuts in timber, a coping saw for curves, a hacksaw's fine hard teeth for metal, tin snips for sheet.
- Shaping removes material to a form: chisels and planes pare timber; files and rasps work metal and edges; abrasive paper finishes.
- Some shaping moves material instead of removing it: bending sheet metal, hammering it (forming), or heating a thermoplastic in a strip heater and folding it while soft.
- Safety is part of the process, not an add-on: eye protection whenever material flies, the work clamped so both hands are free, cuts made away from the body, and long hair and loose sleeves secured near any machine.
3.3The three ways to join
- Match the join to the material: welding fuses steel; soldering joins copper pipe and electronics with a lower-melting-point filler; solvent cement welds acrylic chemically; PVA glues timber to timber — and a good PVA joint in timber is stronger than the wood beside it.
- Match the join to the load: adhesives are strong in shear (surfaces sliding) and weak in peel. Bolts handle heavy, changing loads and can be re-tightened; nails and glue alone are for light static loads.
- Match the join to the future: a chair frame you may need to repair should be bolted or joined with knock-down fittings; a laminated bench top is glued for life.
- Traditional timber joints — butt, lap, housing, mortise and tenon, dovetail — are mechanical joins made from the shape of the wood itself, usually glued as well. A butt joint is the weakest and fastest; a dovetail resists being pulled apart and is the slowest.
Choosing well, and being able to say why
"Because it looks good" is not a material selection. A defensible choice names the properties the job needs, tests candidates against them, and admits what it traded away.
4.1Selection criteria
- Functional: which properties does the job actually demand — strength in which direction, hardness, toughness, weight, conductivity, water resistance?
- Aesthetic: colour, grain, texture, finish, and whether it will still look right in five years.
- Economic: the price of the material, plus what it costs to work — a cheap material needing expensive tooling may lose to a dearer one you can cut in the workshop.
- Availability: can you buy it locally, in the size you need, in the time you have?
- Environmental: where it came from, how much energy it took, and what happens at the end of its life.
- Safety: does it splinter, shatter, give off fumes when heated, or need protective gear to work?
4.2Sustainability, embodied energy and recycling
- Embodied energy is the total energy used to extract, process, transport and make a material. Aluminium's is famously high — smelting it from ore takes enormous electricity — while recycled aluminium takes roughly a twentieth of that, which is why the drink-can loop is worth running.
- Timber from certified regrowth forests is the standout renewable structural material: it grows back, and the growing tree stores carbon while it does.
- Thermoplastics recycle by melting; thermosets do not. That single property difference decides a product's whole end-of-life story.
- Design choices that help: fewer different materials in one product, joins that come apart (bolts, not glue), and parts labelled so they can be sorted.
- Think in the order reduce, reuse, recycle — recycling is the last resort of the three, not the first answer.
4.3A worked selection: an outdoor park bench seat
The brief: slats for a public bench, outdoors year-round, sat on daily, must last ten years with minimal maintenance and survive the occasional skateboard.
| Candidate | Strength & toughness | Durability outdoors | Cost & workability | Verdict |
|---|---|---|---|---|
| Pine (softwood) | Adequate in bending | Rots and insect-attacks unless treated | Cheap, easy to cut | Rejected — fails the ten-year test |
| Hardwood (jarrah) | Strong and tough | Naturally durable, weathers greyly but soundly | Dearer; harder to cut but workshop-friendly | Chosen |
| Mild steel | Very strong | Rusts unless galvanised or painted | Cheap, but needs welding gear | Rejected — upkeep, and burning hot in summer sun |
| Recycled plastic lumber | Adequate; sags over long spans | Excellent — unaffected by rain | Dear; cuts like timber | Close second — best on sustainability |
Name the property, tie it to the need, then admit the trade-off. "Jarrah was chosen because it is naturally durable outdoors and tough enough to take impacts, so the bench meets the ten-year requirement without annual painting. It costs more than pine and is harder to cut, and I accepted that extra cost because replacing rotted pine slats twice over ten years would cost more in the long run." Property → need → trade-off. Every time.
The year that turns design into a discipline.
This course prepares you for QCAA Design (General) in Years 11–12. Four units: the formal designing process, the toolkit for opening ideas up, the toolkit for narrowing them down with evidence, and how designers communicate a decision to an audience.
The mapFour units
- The designer's process, formalised — explore, develop, resolve; stakeholders; needs, wants and constraints; measurable design criteria.
- Divergent toolkit — brainstorming rules, forced association, biomimicry, and sketching conventions that carry meaning.
- Convergent toolkit — weighted evaluation matrices, user testing, and writing a justification.
- Communicating design — presentation versus technical drawings, storyboards and user journeys, and the pitch.
Not the object — the reasoning. Senior Design assessment asks you to explore a need, develop ideas, and resolve a design solution, then justify it against criteria you wrote yourself, with evidence from testing. This year builds exactly those habits.
The designer's process, formalised
In senior Design the process has names, and the names matter: markers look for evidence that you explored, then developed, then resolved — in that order, with the work to prove it.
1.1Explore, develop, resolve
1.2Stakeholders: everyone the design touches
- A stakeholder is anyone affected by the design — not only the person who buys it.
- For a school canteen redesign the stakeholders include: students (the users), canteen staff (who must work in it), the school (which pays and owns the risk), suppliers, and the cleaners who deal with what the design leaves behind.
- Stakeholders conflict, and that is the point: students want more choice, staff want fewer items to prepare, the school wants a lower cost. A design decision usually trades one stakeholder's want against another's.
- Name your stakeholders early, because criteria that ignore one of them get punished at testing.
1.3Needs, wants and constraints
| Term | Test to tell them apart | Canteen example |
|---|---|---|
| Need | Remove it and the design fails its purpose | Food must be served hygienically |
| Want | Remove it and the design still works, just less well | The queue area should look modern |
| Constraint | A limit imposed from outside that you cannot design away | A $4,000 budget; the existing 6 m serving wall |
1.4Writing a design criterion that is measurable
A design criterion is a statement the finished design can be tested against. Three parts make it work: what is measured, how it is measured, and the target.
| Weak criterion | Why it fails | Rewritten, measurable |
|---|---|---|
| The queue should be quick | No number, no method | A student is served within 4 minutes of joining the queue, timed at peak lunch |
| It should be durable | Durable against what? | The lid survives 200 open–close cycles with no visible cracking |
| Users should like it | "Like" is not observable | At least 8 of 10 student testers rate it 4 or 5 out of 5 for ease of use |
Read your criterion and ask: "What experiment would prove this true or false?" If you cannot describe the test in one sentence, the criterion is not measurable yet — and it cannot be used to evaluate your solution later.
Divergent toolkit
Ideas are not luck. There are techniques that reliably produce more and stranger options, and drawing conventions that let those options be understood by someone who isn't inside your head.
2.1Brainstorming has rules
- Defer judgement. No criticism during the session — not even "yeah, but". Judging happens later, in the convergent phase.
- Go for quantity. Set a target (say 40 ideas in 20 minutes). Volume forces you past the obvious first five.
- Welcome wild ideas. An impossible idea is often a usable idea in disguise; it is easier to tame a wild idea than to energise a dull one.
- Build on others' ideas. "Yes, and…" — combining half-ideas is where the good ones usually come from.
- One conversation, and make it visual. Everything gets written or sketched where the group can see it, so nothing is lost or repeated.
2.2Forced association and biomimicry
- Forced association jams your problem against an unrelated word and makes you find a connection. Problem: a bike lock. Random word: umbrella. Umbrellas fold small and expand large → a lock that collapses to pocket size and expands around the frame. The random word is a crowbar for prising your brain off the obvious.
- Biomimicry borrows solutions that evolution already tested. Velcro came from burdock burrs hooking into dog fur. The Shinkansen bullet train's long nose was reshaped after the kingfisher's beak, which enters water with almost no splash — it cut the tunnel boom and the energy use.
- Ask of any problem: what living thing already solves this? Sticking, cooling, carrying loads, staying dry, being seen — nature has prior art for all of them.
2.3Sketching conventions: line hierarchy and annotation
- Sketch in pen, not pencil with an eraser. Rejected lines are evidence of thinking; erasing them destroys the record a folio is marked on.
- Draw many small sketches rather than one big one — a page of twelve thumbnails shows range; one careful drawing shows only commitment to your first idea.
- Annotation is the difference between a picture and a design document. "Handle" is a label. "Handle offset 15 mm so the lid clears the bench when open" is an annotation.
Convergent toolkit
Choosing is the hardest part, because "I prefer this one" is not a reason. Weighting turns a preference into an argument, and testing turns the argument into evidence.
3.1The weighted evaluation matrix
A plain matrix treats every criterion as equally important — which is almost never true. A weighted matrix gives each criterion a weight showing how much it matters, then multiplies. Here is one worked in full for three lunchbox concepts, each criterion scored out of 5:
| Criterion | Weight | A — stacking tiers | B — single deep tub | C — slim tray |
|---|---|---|---|---|
| Keeps food separate and intact (function) | 5 | 4 → 20 | 5 → 25 | 3 → 15 |
| Survives a school year (durability) | 4 | 3 → 12 | 4 → 16 | 5 → 20 |
| Within the $18 unit cost (cost) | 3 | 5 → 15 | 2 → 6 | 4 → 12 |
| Appeals to Year 7 buyers (appearance) | 2 | 3 → 6 | 4 → 8 | 2 → 4 |
| Unweighted total (raw scores added) | — | 15 | 15 | 14 |
| Weighted total (out of 70) | 14 | 53 | 55 | 51 |
Each cell is score × weight. Concept B: (5×5) + (4×4) + (2×3) + (4×2) = 25 + 16 + 6 + 8 = 55. Concept A: 20 + 12 + 15 + 6 = 53. Concept C: 15 + 20 + 12 + 4 = 51. The maximum possible is 5 × (5+4+3+2) = 5 × 14 = 70.
Now the lesson: A and B tie at 15 on raw scores. Weighting breaks the tie and reverses nothing dishonestly — it simply says that keeping food intact matters more than the price tag, and B is better at the thing that matters most. B wins, 55 to 53.
1. Set the weights before you score. Weights chosen after you have a favourite are just your preference in a costume — and a marker can spot it.
2. Weights come from the stakeholders and the brief, and you must say where each one came from: function is weighted 5 here because the brief's primary need was food arriving intact.
3.2User testing that produces evidence
- Test against a criterion, not in general. The criterion says a student is served in under 4 minutes — so you time students, and the result is a number.
- Give a real task, watch silently, and record what happened: time taken, errors, hesitations, and unprompted comments.
- Use enough testers that one odd result cannot decide anything — five to ten for a class project, and report how many.
- Report failures. A test where everything worked usually means the test was too easy, and markers know it.
3.3Justifying a decision in writing
A justification is not a description. Four moves, in this order:
- State the decision. "Concept B, the single deep tub, was selected."
- Give the evidence. "It scored 55 of 70 in the weighted matrix, ahead of A (53) and C (51), and 9 of 10 testers packed a full lunch into it without items mixing."
- Link to the criteria and stakeholders. "It leads on the highest-weighted criterion, keeping food intact — the primary need identified by student stakeholders."
- Acknowledge the trade-off. "B is the most expensive of the three at $19, $1 over the target, so the next iteration reduces wall thickness to bring the cost down."
Description says what. Justification says why, because of evidence. If your paragraph contains no number, no criterion and no "because", it is a description — and it will be marked as one.
Communicating design
A design nobody understands is a design nobody chooses. The last skill is translation: the same idea drawn one way to sell it, another way to build it, and spoken a third way to win the room.
4.1Presentation drawings vs technical drawings
| Presentation drawing | Technical drawing | |
|---|---|---|
| Its job | To make the audience understand and want it | To let someone build it exactly |
| Audience | Client, stakeholders, the public | Manufacturer, workshop, CNC operator |
| Looks like | Rendered pictorial view, colour, shadow, context, a person using it | Orthographic views, dimensions, scale, standard line types |
| Answers | "What is it and why is it good?" | "How big, how many, made of what?" |
| Follows | Graphic-design judgement | A standard — in Australia, AS 1100 |
They are not rivals: a folio needs both. A rendered view that carries no dimensions cannot be manufactured, and a dimensioned orthographic drawing will not persuade a client of anything.
4.2Storyboards and user journeys
- A storyboard is a sequence of frames showing a person using the design over time — like a comic strip. It communicates something a single product photo cannot: when and how the design is used.
- A user journey maps the whole experience step by step — before, during and after — and marks the pain points. For a canteen: leaving class → joining the queue → choosing → paying → finding a seat → returning waste. The pain point is often nowhere near the product you were designing.
- Both are diagnostic, not decorative: they routinely reveal a step nobody had designed for at all.
4.3The pitch: audience, message, evidence
- Audience. Who is in the room, and what do they care about? A principal hears cost, safety and timetable; a student hears speed and choice. Same design, different opening sentence.
- Message. One sentence they should repeat afterwards. "This cuts the lunch queue from nine minutes to under four." If you cannot compress it to one line, you do not yet know what you are proposing.
- Evidence. Every claim needs its proof visible: the test result, the matrix score, the user quote. "Users loved it" is worthless; "9 of 10 testers packed a full lunch with no mixing" is not.
- Show the design, not the slides. Lead with the drawing or the prototype; the words exist to explain it.
- Own the trade-off. Name the weakness before the audience finds it, and say what the next iteration does about it. That reads as confidence, not weakness.
Before any pitch, write your message as a single sentence containing a number. If the sentence has no number in it, you are pitching a feeling, and feelings are the first thing an audience forgets.
The year that makes Senior easy.
Four units built to land you in QCAA Digital Solutions (General) already fluent: thinking the way the exam asks, programming past the beginner ceiling, real databases with real SQL, and evaluating a solution against criteria instead of vibes.
The mapFour units
- Thinking like the exam — decomposition, abstraction, pseudocode written the QCAA way, and trace tables at speed.
- Programming deeper — AND/OR/NOT, nested loops, strings, arrays of records, and reading someone else's code.
- Data & databases — entities, attributes, primary keys, one-to-many relationships and SQL.
- User experience & evaluation — usability, prototypes, evaluation criteria, and privacy law in plain English.
The subject runs on four skills: generating a solution from a problem, evaluating it against criteria, and doing both through algorithms and data. Exam questions are rarely "define" — they are "trace this", "find the fault", "write the query", "justify this choice". This year builds exactly those four muscles.
Thinking like the exam
Senior questions don't reward knowing what an algorithm is. They reward breaking a messy problem into parts, ignoring what doesn't matter, and proving what code does — line by line, under time pressure.
1.1Decomposition and abstraction
- Decomposition is breaking a big problem into smaller sub-problems you can solve one at a time. "Build a canteen ordering app" is unanswerable; "log a student in", "show today's menu", "take an order", "total the price", "send it to the kitchen" are five jobs you can each write.
- Abstraction is deciding what to ignore. A train map abstracts away every curve and distance because the traveller only needs the order of stops. In code, a Student record keeps name, ID and year level — not eye colour — because the problem doesn't need it.
- They pull in opposite directions and that is the point: decomposition adds detail by splitting, abstraction removes detail by ignoring. Do both and you get parts that are small and simple.
1.2Pseudocode, written the way it is marked
Pseudocode is language-neutral but not freestyle. Markers look for consistent, readable structure — use these conventions all year:
| Purpose | Write it like this | Note |
|---|---|---|
| Store a value | total ← 0 | ← reads "becomes". Never use = for storing. |
| Compare values | IF total = 0 THEN | = only ever asks a question. |
| Input / output | INPUT mark · PRINT total | Keywords in capitals. |
| Selection | IF … THEN … ELSE … END IF | Always close the block. |
| Counted loop | FOR i FROM 1 TO 10 … END FOR | Both ends included: 10 passes. |
| Conditional loop | WHILE count > 0 … END WHILE | Something inside must change count. |
| Modules | FUNCTION name(params) … RETURN … END FUNCTION | One job per function. |
| Remainder | n MOD 2 | MOD gives the remainder: 7 MOD 2 = 1. |
Indent everything inside an IF, a loop or a function by one level, and close every block you open. A marker who can see the structure at a glance can award structure marks; a wall of unindented lines forces them to hunt, and hunting costs you.
1.3Trace tables under pressure
The exam gives you code you have never seen and asks what it outputs. The method never changes — and doing it in your head is how people lose marks. Draw the table.
- One column per variable, plus a column for the condition and one for output.
- Write the starting values on row one, before the loop.
- One row per pass. Never erase — add a row, so the history stays visible and a slip is findable.
- Update in the exact order the lines run. A line that uses a variable it just changed is where most errors happen.
- Record the condition's true/false each pass: that column proves why the loop stopped.
| Pass | Code: n ← 9, then WHILE n > 1 { IF n MOD 2 = 0 THEN n ← n ÷ 2 ELSE n ← n − 1, steps ← steps + 1 } | n | steps | n > 1 |
|---|---|---|---|---|
| start | n ← 9, steps ← 0 | 9 | 0 | — |
| 1 | 9 is odd → n ← n − 1 | 8 | 1 | 9 > 1 true |
| 2 | 8 is even → n ← n ÷ 2 | 4 | 2 | 8 > 1 true |
| 3 | 4 is even → n ← n ÷ 2 | 2 | 3 | 4 > 1 true |
| 4 | 2 is even → n ← n ÷ 2 | 1 | 4 | 2 > 1 true |
| end | loop test fails, PRINT steps | 1 | 4 | 1 > 1 false |
Programming deeper
Beyond one condition and one loop lies everything real programs are made of: combined logic, loops inside loops, text handled properly, and structured data held in memory. Half the marks are for reading such code, not writing it.
2.1Compound conditions: AND, OR, NOT
| A | B | A AND B | A OR B | NOT A |
|---|---|---|---|---|
| true | true | true | true | false |
| true | false | false | true | false |
| false | true | false | true | true |
| false | false | false | false | true |
- AND is strict: every part must be true. IF age >= 13 AND age <= 19 THEN is how you test a range — and both comparisons must name the variable. 13 <= age <= 19 is maths, not code.
- OR is generous: one true part is enough. IF day = "Saturday" OR day = "Sunday" THEN. Writing day = "Saturday" OR "Sunday" is the classic error — the right side of an OR must be a whole condition.
- NOT flips a condition. IF NOT (stock > 0) THEN means the same as IF stock <= 0 THEN — and the second is easier to read, so prefer it.
- Bracket anything mixed: IF (a AND b) OR c THEN is not the same as IF a AND (b OR c) THEN. Brackets cost nothing and settle the argument.
2.2Nested loops
A loop inside a loop. The inner loop completes fully on every single pass of the outer one — so the body runs outer × inner times.
| Code | Outer i | Inner j runs | Body runs |
|---|---|---|---|
| FOR i FROM 1 TO 3 FOR j FROM 1 TO 4 PRINT i × j END FOR END FOR | 1 | j = 1, 2, 3, 4 | 4 times |
| 2 | j = 1, 2, 3, 4 | 4 times | |
| 3 | j = 1, 2, 3, 4 | 4 times | |
| Total | 3 × 4 = 12 times | ||
Nested loops are how you walk a grid: the outer loop picks the row, the inner one walks its columns. They are also how a fast program becomes a slow one — double the data and a nested loop does four times the work.
2.3Strings
Text is a sequence of characters, indexed from 0 — the same rule as arrays, all year:
| Operation | Example with name ← "DIGITAL" | Result |
|---|---|---|
| LENGTH(text) | LENGTH(name) | 7 — D I G I T A L |
| Index a character | name[0] | "D" — the first, because counting starts at 0 |
| Last character | name[LENGTH(name) − 1] → name[6] | "L" |
| UPPERCASE / LOWERCASE | LOWERCASE(name) | "digital" |
| Join (concatenate) | "Hello " + "world" | "Hello world" — the space must be there on purpose |
"Smith" and "smith" are different strings. Before comparing user input, convert both sides with LOWERCASE — otherwise a correct login is rejected for a capital letter. Also: the number 7 and the text "7" are different things; adding them either fails or joins them, never adds.
2.4Arrays of records
Real data is a list of things, each with several fields. That is an array of records — and looping through it is the single most common pattern you will write.
| Index | .name | .mark |
|---|---|---|
| students[0] | "Ali" | 62 |
| students[1] | "Bea" | 81 |
| students[2] | "Cam" | 74 |
| Line | Pseudocode — count the marks of 70 or more | Trace |
|---|---|---|
| 1 | passes ← 0 | passes = 0 |
| 2 | FOR EACH s IN students | s is one whole record each pass |
| 3 | IF s.mark >= 70 THEN | 62 no · 81 yes · 74 yes |
| 4 | passes ← passes + 1 | passes = 1, then 2 |
| 5 | END IF | — |
| 6 | END FOR | — |
| 7 | PRINT passes | prints 2 |
2.5Reading code you didn't write
- Read the variable names first — they usually announce the purpose before you understand a line.
- Find the loops and ask what each one repeats over, and what stops it.
- Run one small example through by hand. Three items beats thirty.
- Watch the boundaries: the first item, the last item, an empty list, and zero.
- Then and only then say what the code does — in one sentence, about its purpose, not its lines. "It counts marks of 70 or more" earns the mark; "it loops and adds one" does not.
Data & databases
A relational database stores each fact once and links the rest. Learn entities, keys and four SQL words this year and Senior's database unit becomes revision.
3.1Entities, attributes, keys
- An entity is a kind of thing the database stores — Student, House, Book, Loan. Each entity becomes one table.
- An attribute is one property of that entity — FirstName, YearLevel. Each attribute becomes one column. One actual student is one row.
- A primary key is the attribute that identifies each row uniquely: StudentID. It can never be blank and never repeat. Names fail this — two students really can be called Sarah Chen.
- A foreign key is an attribute holding another table's primary key. It is the actual link between the tables.
3.2One-to-many
3.3SQL: asking the database
SQL is how you question a relational database. Four clauses cover almost everything at this level, and they must appear in this order:
| Clause | Means | Example |
|---|---|---|
| SELECT | which columns to show (* means all) | SELECT FirstName, LastName |
| FROM | which table to read | FROM Student |
| WHERE | keep only rows meeting a condition | WHERE YearLevel = 10 |
| ORDER BY | sort the results: ASC (default) or DESC | ORDER BY LastName ASC |
| Query | What it returns |
|---|---|
| SELECT * FROM Student; | Every column of every student. |
| SELECT FirstName, LastName FROM Student WHERE YearLevel = 10; | Just the two name columns, for Year 10 students only. |
| SELECT FirstName, LastName FROM Student ORDER BY LastName ASC; | All students, sorted A–Z by surname. |
| SELECT * FROM Student WHERE YearLevel >= 9 AND HouseID = 2; | Students in Year 9 or above who are also in house 2. |
| SELECT * FROM Student WHERE LastName = 'Nguyen'; | Students surnamed Nguyen. Text values go in single quotes; numbers do not. |
| SELECT HouseName FROM House WHERE HouseID = 3; | One value: the name of house 3. |
1. The clause order SELECT → FROM → WHERE → ORDER BY is fixed; swapping them is a syntax error. 2. Text in single quotes, numbers bare: = 'Nguyen' but = 10. 3. In SQL, = compares — there is no ← here, because a query never stores anything. 4. A query reads; it never changes the stored data, so no query can ever lose you data.
User experience & evaluation
Senior marks are not awarded for "it works". They are awarded for a solution justified against criteria — and for knowing what the law says about the personal data you just collected.
4.1Usability principles
- Learnability — can a first-time user achieve the main task without being taught?
- Efficiency — once learnt, how few steps does the common task take? Count the taps; the count is the evidence.
- Memorability — can someone returning after a month still use it without relearning?
- Error tolerance — are mistakes hard to make, clearly explained when made, and always undoable?
- Satisfaction — does using it feel pleasant rather than like a fight?
- Accessibility — can people with disability use it: contrast, alt text, keyboard access, adequate target sizes?
4.2Prototyping
| Low-fidelity prototype | High-fidelity prototype | |
|---|---|---|
| Looks like | Paper sketches, wireframes | Clickable screens that look like the real app |
| Costs | Minutes | Hours or days |
| Best for testing | Layout, priority, whether the idea makes sense at all | Detailed interaction, flow, visual design |
| Risk | Too rough for users to judge the experience | Looks finished, so testers hesitate to criticise it — and you hesitate to throw it away |
Prototype before building, cheaply and more than once. The whole point is that changing a sketch costs minutes and changing shipped code costs weeks.
4.3Evaluation criteria
An evaluation is only worth marks if it measures the solution against criteria agreed in advance. A criterion is useless unless it can be answered yes or no with evidence:
| Weak criterion | Why it fails | Usable criterion |
|---|---|---|
| "The app is easy to use" | Nobody can prove it either way | "A first-time user places an order in under 60 seconds without help" |
| "It looks good" | Pure opinion | "All text meets the contrast guideline and every image has alt text" |
| "It is fast" | Compared with what? | "Search results appear within 2 seconds on the school Wi-Fi" |
| "It handles errors" | Which errors, handled how? | "Entering a blank name shows a message naming the field, and no data is lost" |
State the criterion, give the evidence from testing, judge whether it was met, then say what you would change and why. "Criterion 2 was not met: two of three testers took over 90 seconds because the Order button sat below the fold. Moving it above the results would fix this." That is a full-mark evaluation — criterion, evidence, judgement, improvement.
4.4Personal data and privacy
- Personal information is any information that identifies someone, or could when combined with other data — name, email, photo, phone, location history, even a device ID.
- Australia's Australian Privacy Principles (APPs), under the Privacy Act 1988, set the rules for organisations handling it. The ideas you must be able to apply:
- Collect only what you need for a stated purpose. An ordering app has no business asking for a date of birth.
- Be open about it: say what you collect and why, in a privacy policy a human can actually read.
- Use it only for that purpose, unless the person agrees to another.
- Keep it secure, and destroy or de-identify it when it is no longer needed.
- Let people see and correct their own information.
- Design consequence: every extra field you collect is data you must now protect and could one day leak. The safest personal data is the data you never collected.
The year that makes senior Engineering easy.
Four units: forces in balance, the structures that carry them, the materials that resist them, and the method engineers use to decide anything — the groundwork for QCAA Engineering (General) in Years 11 and 12.
The mapFour units
- Statics — force as a vector, mass vs weight, equilibrium, and free-body diagrams.
- Structures — beams, columns and trusses, and the factor of safety that keeps them standing.
- Engineering materials — stress, stiffness vs strength, ductile vs brittle failure, and why steel is alloyed.
- The engineering method — the loop from problem to tested solution, and where the maths actually sits.
Three habits, drilled here until they are automatic: draw the free-body diagram before you calculate anything; carry the units through every line (N, mm², MPa); and state the assumption you made. Senior Engineering marks all three, and students who arrive without them lose marks on problems they actually understood.
Statics: everything in balance
Statics is the study of things that are not accelerating — bridges, buildings, a book on a table. The whole subject rests on one sentence: if it isn't moving, the forces on it add to zero.
1.1Force is a vector
- A force is a push or pull, measured in newtons (N). It is a vector: it has a size and a direction, and "300 N" without a direction is an incomplete answer.
- Forces along the same line add and subtract with sign. Two people pushing a crate right with 200 N and 150 N give 350 N right. If one pushes 200 N right and the other 150 N left, the resultant is 50 N right.
- The resultant is the single force that would have the same effect as all the forces together. Statics is largely the art of proving the resultant is zero.
- On a diagram, an arrow shows a force: its length suggests the size, its head shows the direction, and its tail sits at the point where the force acts.
1.2Mass is not weight
Mass is how much matter something contains, measured in kilograms. It does not change if you take the object to the Moon. Weight is the force gravity exerts on that mass, measured in newtons, and it does change — the same object weighs about a sixth as much on the Moon.
W = mg, with g = 9.8 N/kg on Earth. So a 10 kg toolbox has a weight of 10 × 9.8 = 98 N. A 50 kg student weighs 50 × 9.8 = 490 N. Writing "the load is 10 kg" in a force calculation is the single most common error in junior statics: convert to newtons first, every time.
1.3Equilibrium and free-body diagrams
An object is in equilibrium when it is at rest (or moving at constant velocity) and the forces on it sum to zero: ΣF = 0. Vertically, up must equal down; horizontally, left must equal right. To use that, you draw a free-body diagram: the object alone, stripped of its surroundings, with every force acting on it drawn as a labelled arrow.
- A symmetrical beam on two supports splits its load evenly. A 400 N plank load carried by two end supports gives 200 N at each — a result you will use constantly in Unit 2.
- Worked check: a 100 kg engine hangs from one chain. W = 100 × 9.8 = 980 N, so the chain tension is 980 N. Hang it from two vertical chains sharing equally and each carries 490 N.
Structures: beams, columns and trusses
Three members do nearly all the work in the built world. Learn what each carries, learn to spot which members of a truss are pulled and which are squashed, and learn the number that decides how much margin you keep.
2.1The three structural members
- A beam is loaded across its length and works in bending: its lower face stretches (tension) while its upper face squashes (compression). That is why an I-beam puts most of its steel in the top and bottom flanges — that is where the stress lives.
- A column is loaded along its length and works in compression. A long slender column fails by buckling — bowing sideways — long before the material is crushed, which is why columns are made fat, tubular or braced rather than merely thick.
- A truss is a frame of triangles whose members are (ideally) in pure tension or pure compression, with no bending at all. That is what makes trusses so efficient: material carrying only pull or push does far more work per kilogram than material being bent.
- Members are named by their job: a member in tension is a tie; a member in compression is a strut.
2.2Reading a truss
2.3Factor of safety
No engineer designs a part to carry exactly what it will be asked to carry. The factor of safety is the margin between them:
FoS = failure load ÷ working load
A lift cable that breaks at 12 000 N and is only ever asked to carry 3 000 N has FoS = 12 000 ÷ 3 000 = 4. A bracket that fails at 45 000 N under a working load of 9 000 N has FoS = 45 000 ÷ 9 000 = 5.
Rearranged, it tells you what you are allowed to load: a beam failing at 40 000 N designed to a factor of safety of 5 has a working load of 40 000 ÷ 5 = 8 000 N. Or what strength you must buy: a working load of 2 500 N at FoS 4 needs a part that fails no lower than 2 500 × 4 = 10 000 N.
The factor covers what you cannot know exactly: material flaws, corrosion and wear, overloading by users, and errors in your own assumptions. Higher stakes buy a higher factor — a garden shelf might use 2, a lift or a crane hook far more.
Engineering materials: stress, stiffness and failure
"Will it hold?" is not a question about force alone — it is a question about force spread over area. That is stress, and it is the number that lets you compare a thin wire with a thick beam on equal terms.
3.1Stress = force ÷ area
Stress = force ÷ cross-sectional area, written σ = F / A.
Use newtons (N) for force and square millimetres (mm²) for area, and the answer comes out in N/mm² — which is exactly the same unit as the megapascal (MPa). 1 N/mm² = 1 MPa. Getting that identity straight saves you constantly in senior Engineering.
Worked example 1. A steel rod of cross-section 25 mm² carries 5 000 N. σ = 5 000 ÷ 25 = 200 N/mm² = 200 MPa.
Worked example 2. A bar 20 mm wide and 5 mm thick has area 20 × 5 = 100 mm². Carrying 45 000 N: σ = 45 000 ÷ 100 = 450 MPa. If mild steel yields near 250 MPa, this bar has already failed — the calculation caught it before the workshop did.
Worked example 3. The same 45 000 N through a bar of 300 mm² gives 45 000 ÷ 300 = 150 MPa — comfortably under 250 MPa. Same force, three times the area, a third of the stress. Area is the design variable you control.
- Because stress divides out the size of the part, it lets you compare materials fairly: a material's strength is quoted as the stress at which it fails, in MPa, not as a force in newtons.
- Rough figures worth carrying: mild steel yields at about 250 MPa, aluminium alloys around 100–300 MPa, and timber along the grain is in the tens of MPa.
- The same logic explains snowshoes and stiletto heels: identical weight, wildly different area, wildly different stress on the ground.
3.2Strength is not stiffness
- Strength is the stress a material can take before it fails. Stiffness is how much it deflects under a load it is comfortably surviving.
- They are independent. A nylon rope is strong but not stiff — it holds a climber and stretches noticeably doing it. Cast iron is stiff but not especially strong in tension — it barely deflects, then cracks.
- Which one your design needs depends on the failure you fear. A bookshelf that visibly sags has not broken; it has failed a stiffness requirement, and a stronger timber of the same stiffness would not fix it.
- A machine tool bed is chosen for stiffness so the cut stays accurate; a lifting chain is chosen for strength.
3.3Ductile and brittle failure
- A ductile material stretches and visibly deforms before it breaks — mild steel, copper, aluminium. It gives warning: a sagging beam, a necked bolt, a bent bracket. Engineers prize that warning.
- A brittle material breaks suddenly with almost no deformation — glass, cast iron, concrete in tension, ceramics. No warning, and the failure is often explosive.
- This is why structural steel is favoured for buildings in earthquake zones: it bends, absorbs energy and announces distress rather than shattering.
- Brittle materials are not banned — they are used where the load is compressive and predictable, like concrete columns and cast iron machine bases.
3.4Why steel is alloyed
Pure iron is soft and weak. Steel is iron with a small, controlled amount of carbon — and that trace changes everything: raise the carbon and the steel gets harder and stronger but more brittle; lower it and the steel gets softer, tougher and easier to weld. Mild steel (low carbon) is the everyday structural choice because it is ductile, weldable and cheap. High-carbon steel makes chisels and springs, where hardness matters more than toughness. Add chromium (about 11% or more) and you get stainless steel, which forms a self-repairing oxide layer and resists corrosion. Alloying is how engineers order the properties they want instead of accepting what nature supplies.
The engineering method
Engineering is not "have an idea and build it". It is a loop that turns a vague problem into a specification you can test against, and then refuses to stop until the tested thing meets it.
4.1The loop
- Define the problem. Who has it, in what situation, and what would count as solved? Vague problems produce unmarkable projects.
- Specify. Turn needs into measurable requirements: "supports a 90 kg adult", "under 2.5 kg", "assembles in 10 minutes with one tool". A specification you cannot test is not a specification.
- Ideate. Generate several genuinely different concepts before falling in love with one. Sketch fast, cheap and plentifully.
- Analyse. Calculate before you cut: free-body diagram, forces, stress, factor of safety, material choice. This is where a bad idea should die — on paper, for free.
- Prototype. Build the cheapest thing that answers the question you are still unsure about. A cardboard mock-up that settles the ergonomics is a success, not a rough draft.
- Test. Load it, use it, measure it against the specification — the numbers you wrote in step 2, not your feelings about it.
- Iterate. Feed the results back and go round again. The loop, not the first idea, is what produces a good design.
- Communicate. Drawings, calculations and a justification, in a form somebody else could build from.
4.2Communicating with drawings
- A sketch explores an idea; a working drawing lets someone else make the part without asking you a single question.
- Orthographic projection shows the true shape of a part in separate flat views — front, top and side — so every dimension can be read exactly. Isometric or pictorial views show what it looks like as a whole, but distort the true sizes.
- A working drawing carries dimensions in millimetres, a stated scale, tolerances where fit matters, and a title block naming the part, the material, the drawer and the date.
- The test of a drawing is simple: hand it to someone who has never seen your project. If they can build the part, it is a working drawing.
Calculation is not decoration at the end of a project — it is how engineers choose between options and size the thing they chose. Deciding a shelf bracket: work out the load in newtons (W = mg), draw the free-body diagram, find the force in the member, divide by area to get the stress, compare it with the material's strength, and apply a factor of safety. That chain converts "I think it will hold" into "it holds 900 N with a factor of safety of 3". The second sentence is engineering; the first is a hope. In senior Engineering, marks follow the working, so show every line and carry every unit.
Wood, done properly.
Furnishing Skills is a hands-on subject — but the marks come from the theory behind the hands: which control actually removes a hazard, why a board warps, which joint carries the load, and why you cannot skip a sanding grit. Four units of the knowledge a workshop assumes you already have.
The mapFour units
- The safe workshop — the hierarchy of controls in order, machine guarding and isolation, and the PPE that comes last.
- Timber, properly — hardwood and softwood, seasoning and movement, and the manufactured boards that replaced solid timber for most jobs.
- Hand tools & joints — marking out, saws, chisels and planes, and the joint family ranked from weakest to strongest.
- Assembly & finishing — glue, screws and nails, the grit sequence, and what each finish actually does.
Applied subjects mark safe, correct practice and the reasoning behind it. Almost every written question is one of four kinds: name the control and say why it sits where it does in the hierarchy; choose a material and justify it; choose a joint or process and justify it; describe a sequence in the right order. Learn the orders and the reasons and you have the paper.
The safe workshop: controls in the right order
A workshop is not made safe by handing out earmuffs. Safety is a ranked list, and PPE is the bottom of it — the last resort, used when nothing better is possible. Get the order right and half the safety marks are yours.
1.1The hierarchy of controls
A hazard is anything with the potential to cause harm — a spinning blade, a bag of MDF dust, a solvent. The risk is how likely that harm is and how bad it would be. The hierarchy of controls ranks the six ways of dealing with a hazard from the most reliable to the least. You always work from the top down, and you only move down a level when the level above is genuinely not possible.
1.2Machines: guards, zones and isolation
- Guards stay on. A guard is an engineering control — it stops the body reaching the cutter. Removing a guard to "see better" moves you from level 4 protection to level 6 in one second.
- The exclusion zone. Every machine has a marked zone around the cutting point that hands never enter. On a table saw or docking saw the work is fed with a push stick, so the push stick is what gets close to the blade instead of your fingers.
- Isolate before you touch. Before changing a blade, clearing a jam or adjusting a fence, the machine is switched off at the isolator and left to stop completely — not just released at the trigger. In industry the isolator is then locked out and tagged so nobody else can restart the machine while a hand is inside it.
- Emergency stop. Know where it is before you start the machine, not after. It is a big red mushroom button you can hit with a knee, a hip or a palm.
- One operator, no spectators. The person running the machine controls it; everyone else stays outside the zone.
- Never leave a machine running and walk away, and never brush swarf or offcuts away while the cutter is still turning.
1.3Loose things and rotating things
Rotating machinery — a lathe, a drill press, a spindle moulder, a sander drum — catches anything that dangles and winds it in faster than a person can react. That is the reason for a rule list that sounds fussy until you understand it:
- No loose clothing. Sleeves rolled or buttoned, shirt tucked, no hoodie strings, no scarves. A caught sleeve pulls the arm in with it.
- Long hair tied back and, at a drill press or lathe, under a cap or net. Hair wrapped on a rotating spindle removes scalp.
- No rings, watches, bracelets or lanyards. A ring caught on a turning chuck degloves a finger.
- No gloves at rotating machines. This surprises people: gloves protect against splinters and sharp sheet edges, but at a drill or lathe they are exactly the kind of loose material that gets wound in — and a glove drags the whole hand with it.
- Enclosed non-slip footwear always, because dropped chisels and falling stock land on feet, and offcuts and dust make floors slippery.
1.4PPE: what each item is actually for
| PPE | Protects against | The detail that gets marked |
|---|---|---|
| Safety glasses / face shield | Flying chips, dust, splinters, splashed finish | Worn from the moment you enter the machine area — a chip thrown by someone else's cut still reaches your eye. A face shield goes over glasses for lathe work, not instead of them. |
| Hearing protection (earmuffs or plugs) | Noise from routers, thicknessers, saws and extraction | Hearing damage is cumulative and permanent — there is no repair and no warning pain. Protect from the first noisy minute, not once your ears ring. |
| P2 respirator (dust mask) | Fine wood dust, especially MDF and hardwood dust | Wood dust is a respiratory hazard and hardwood dust is a recognised cause of nasal cancer. A P2 mask must seal on the face — a beard or a loose strap makes it close to useless. |
| Gloves | Splinters, sharp edges, solvents and finishes | Handling and finishing only. Never near rotating machinery. |
| Enclosed footwear | Dropped tools and timber, offcuts underfoot | Steel cap in industry; enclosed, flat and non-slip at school. No thongs, no canvas slip-ons. |
"A student is exposed to loud noise from the thicknesser. Give the best control." The answer that scores highest is not earmuffs. Working down the hierarchy: can the noisy job be eliminated or the machine substituted for a quieter one? Can the machine be isolated in a separate enclosed bay? Can it be engineered — acoustic enclosure, better-maintained cutters? Only then rostering and time limits (administrative), and finally earmuffs. Earmuffs are the answer to "what PPE?", never to "what is the best control?".
Timber, properly: a material that keeps moving
Timber is not an inert material like steel. It was plumbing for a living tree, it is still full of water when it is cut, and for the rest of its life it swells and shrinks with the air around it. Everything a furniture maker does is shaped by that fact.
2.1Hardwood and softwood: a botanical split, not a hardness test
This is the single most commonly failed question in the subject. Hardwood and softwood describe the type of tree, not how hard the wood is. Hardwoods come from broadleaved, flowering trees that mostly lose their leaves or shed them gradually — the eucalypts (gums), blackwood, oak, maple. Softwoods come from conifers: needle-leaved, cone-bearing trees — pine, cypress, cedar, fir.
Most of the time hardwoods really are harder and denser, which is why the names stuck. But balsa is a hardwood — it is a broadleaved flowering tree — and you can dent it with a thumbnail. Meanwhile cypress pine, a softwood, is hard enough to blunt tools. Quote balsa in an exam answer and you have proved you know the rule rather than the rule of thumb.
| Hardwood | Softwood | |
|---|---|---|
| Tree type | Broadleaved, flowering (angiosperm) | Needle-leaved, cone-bearing conifer (gymnosperm) |
| Growth | Slow — decades to a century | Fast — plantation pine is harvested in about 30 years |
| Usual density & cost | Denser, harder-wearing, dearer | Lighter, cheaper, easier to work |
| Australian examples | Jarrah, spotted gum, blackbutt, Tasmanian oak, blackwood, silky oak | Radiata pine, hoop pine, cypress pine, Douglas fir |
| Typical use | Furniture, flooring, benchtops, decking — anywhere wear or looks matter | Framing, shelving, cheap carcases, mouldings, painted work |
| The exception to quote | Balsa — a hardwood softer than any softwood | Cypress pine — a softwood harder than some hardwoods |
2.2Seasoning, moisture and why timber warps
Freshly felled green timber can be more than half water by weight. Seasoning is drying it down to a stable moisture content before it is used — roughly 10–12% for indoor furniture in most of Australia. There are two ways to do it: air drying (stacked outdoors under cover, separated by spacer sticks so air passes between every board — cheap, slow, months to years) and kiln drying (a heated, humidity-controlled chamber — fast, weeks, controllable, but costs energy and can case-harden or check the timber if rushed).
- Seasoning matters because dry timber is stronger, lighter, holds glue and finish, and can be machined accurately. Green timber blunts tools, refuses to glue and rejects finish.
- Seasoning is not permanent. Timber is hygroscopic: it keeps exchanging moisture with the air, swelling in a humid summer and shrinking in a dry, heated winter. This is called movement, and good furniture is designed to allow for it — a solid tabletop is fixed with slotted holes or buttons so it can move without splitting itself.
- Timber moves a lot across the grain and almost nothing along it. A board gets narrower and thinner as it dries; its length barely changes.
- Because shrinkage differs between the growth rings and across them, a board dries unevenly and distorts. The named defects: cupping (the board curls across its width, away from the heart side), bowing (a curve along its length, face view), springing (a curve along the edge), twist or wind (corners no longer in one plane), and checks or splits (the surface dries and shrinks faster than the core and tears open).
- Before use, timber is left to acclimatise in the workshop for a week or two so it reaches the moisture content of the room it will live in. Machine it before it has settled and it will move after you have cut your joints.
- Knots (where a branch left the trunk) are the other common defect: they are hard, they blunt cutters, they weaken the board, and loose ones fall out.
2.3Manufactured boards
Most furniture today is not solid timber. Manufactured boards are made by gluing wood in some broken-down form back together, which buys three things solid timber cannot give: big flat sheets (typically 2400 × 1200 mm), uniform properties in every direction, and far less movement. What they lose is edge strength, water resistance and the look of real grain — which is why they are so often veneered or edge-banded.
| Board | Made from | Strengths | Weaknesses | Chosen when… |
|---|---|---|---|---|
| Plywood | Odd number of thin veneers glued with each layer's grain at 90° to the next | Strongest board for its weight; strong both ways; will not split; holds screws reasonably; marine grades exist | Dearest; edges show the plies and need banding or filling; face veneer is thin and easily sanded through | Strength or a thin panel matters — drawer bottoms, cabinet backs, curved work, boat and outdoor jobs |
| MDF (medium-density fibreboard) | Wood broken down to fine fibres, mixed with resin and pressed | Perfectly smooth faces and no grain, so it paints beautifully; cuts and routs to a crisp moulded edge; cheap; totally uniform | Heavy; swells irreversibly if it gets wet; weak screw holding in the edge; very fine dust that demands extraction and a P2 mask | The job will be painted — cabinet doors, shaped and routed edges, moulded panels |
| Particleboard (chipboard) | Wood chips and flakes mixed with resin and pressed | Cheapest sheet material; flat and stable; usually bought pre-faced with melamine so no finishing is needed | Weakest of the three; poor screw holding, especially in the edge; sags over a long span; destroyed by water | Cost rules and the panel is supported — flat-pack carcases, shelving, bench substrates |
| Solid timber | Sawn straight from the log | Real grain; can be re-sanded and re-finished for a lifetime; strongest joints; repairable | Moves with humidity; limited widths so boards must be edge-joined; defects and knots; expensive | The job is seen and expected to last — tabletops, chair frames, drawer sides |
A thin slice of expensive timber glued to a cheap stable board gives the look of solid timber with none of the movement — and one log stretches across a whole kitchen. The raw edge of a board is then covered with a strip of matching edge banding, usually iron-on. That is how nearly all commercial furniture is built.
Hand tools and joints: accuracy before speed
A joint is only as good as the line it was cut to. This unit runs in the order the work happens: mark it out, saw it, pare it to the line — then choose the joint that suits the load.
3.1Marking out
Everything is measured from a face side and a face edge — the one flat face and the one straight, square edge you prepare first and mark with the traditional face-side and face-edge symbols. Every later measurement is taken from those two surfaces, so small errors never add up. Measuring the second cut from the first cut is how a project ends up 4 mm out.
| Tool | What it makes | Use it when |
|---|---|---|
| Pencil (sharpened, or a flat carpenter's pencil) | A visible line about half a millimetre wide | Rough marking, waste marking, anything to be cut oversize and trimmed. Fast, erasable, but too thick for joinery. |
| Marking knife | A fine cut line that severs the surface fibres | Joinery. Two wins: the line is exactly one blade thick, and the severed fibres stop the saw or chisel tearing out. The knife line also gives the chisel a little trench to drop into. |
| Marking gauge | A scribed line parallel to an edge, set by the stock | Any line that must run parallel — a tenon shoulder, a rebate. The stock is held hard against the face side, so every board in the batch gets an identical line. |
| Mortise gauge | Two parallel scribed lines at once | Marking the width of a mortise and the matching tenon — set once, mark both parts, guaranteed to match. |
| Try square | A line square to the face side or edge | Squaring lines across a board and checking a sawn end or planed edge is truly at 90°. |
| Sliding bevel | Any angle, copied and repeated | Splayed legs, mitres that are not 45°, dovetail angles. |
3.2Saws, chisels and planes
- Rip saw — cuts along the grain. Its teeth are filed square across, like a row of tiny chisels, so they pare the fibres away lengthways. Fewer, larger teeth.
- Crosscut saw — cuts across the grain. Its teeth are filed to a bevel so each one is a small knife point that severs fibres before the gullet clears them. More teeth, finer finish. Use a rip saw across the grain and you get a torn, splintered edge.
- Set is the slight side-to-side bend of the teeth. It makes the saw cut a kerf wider than the blade, so the blade does not bind in its own cut.
- Tenon saw (backsaw) — fine teeth and a heavy brass or steel spine along the top to keep the thin blade rigid. This is the joint saw. A coping saw, with its thin removable blade, cuts curves and clears dovetail waste.
- Chisels pare and chop. Bevel-edge chisels get into a dovetail corner; a mortise chisel is thick and square to lever out waste. Cut with the bevel down for paring the last shavings, flat back down on the line, always with both hands behind the edge and the work clamped — never cut toward your hand.
- Planes flatten and true. The jack plane does the first rough flattening, the smoothing plane takes the final fine shavings, and a block plane (low blade angle) is for end grain and chamfers. Plane with the grain: if the surface tears out, turn the board around and plane the other way.
- Sharp is safe. A blunt tool needs force, and force is what makes a chisel skid off the work into a hand.
3.3The joint family
Joints are ranked by how well they resist being pulled apart and how much gluing surface they create. Glue is strong on long grain and weak on end grain — end grain drinks the glue in like a straw and leaves little to bond with. That single fact explains the whole ranking below: every stronger joint is a way of turning end-grain contact into long-grain contact, or of adding a mechanical interlock so the glue is not the only thing holding on.
| Joint | What it is | Strength | Where it is used |
|---|---|---|---|
| Butt joint | Two pieces simply pushed together and glued, usually end grain to long grain | Weakest. Almost no gluing surface and no interlock — always needs nails, screws, dowels or a block | Rough carcase work, painted boxes, anything reinforced by a back panel |
| Lap joint (half lap) | Half the thickness cut from each piece so they overlap flush | Better — a real long-grain gluing face and some resistance to twisting | Frames, cross-halvings, light rails |
| Housing (dado) | A square trench across one piece; the end of the other sits in it | Good — two long-grain faces glued instead of one, and the trench walls also carry the shelf's load directly | Shelves into a bookcase side, cabinet dividers |
| Mortise and tenon | A tongue on one piece fitted into a matching hole in the other | Very strong — large long-grain gluing area plus shoulders that resist racking | Chair and table frames, doors, anything with legs and rails |
| Dovetail | Interlocking wedge-shaped tails and pins | Strongest against being pulled apart — the wedges physically cannot withdraw, even with no glue | Drawer fronts, fine boxes — exactly where a joint is yanked repeatedly |
| Biscuit | A compressed beech oval glued into matching slots; it swells with the glue's moisture | Modest — mainly alignment plus a useful strength gain over a plain butt | Edge-joining boards, lining up panels and carcase parts fast |
| Domino (loose tenon) | A machined floating tenon glued into two routed mortises | Strong — effectively a mortise and tenon cut by machine in seconds | Production frames and carcases where hand-cut tenons would be too slow |
| Mitre | Both pieces cut at 45° so no end grain shows | Weak on its own — end grain to end grain — so it is keyed, splined or biscuited | Picture frames, boxes, anything where the corner must look seamless |
A full-mark answer names the joint, names the load, and links them. "A drawer front takes a repeated pull every time it is opened, so it needs a joint with a mechanical interlock rather than one relying on glue alone — a dovetail, whose wedge-shaped tails cannot withdraw." Compare: "a dovetail, because it's strong" earns a fraction of the marks.
Assembly and finishing: the last 10% everyone sees
A perfectly cut project can still be ruined in its final hour: glue that grabbed before the clamps went on, a screw that split a rail, or a coat of varnish laid over scratches that only became visible once it was wet. This unit is the order of operations for the end of a job.
4.1Adhesives
PVA (polyvinyl acetate — white or yellow woodworking glue) is the workshop default. It is water-based, non-toxic, cleans up with a damp cloth while wet, and when it is used properly a glued long-grain joint is stronger than the timber beside it — test it to destruction and the wood fails, not the glue line.
- Open time is the window between spreading the glue and closing the joint — roughly 5 to 10 minutes for standard PVA. Miss it and the surface skins over; the joint will look closed and be effectively unglued. On a complicated assembly you therefore dry-fit everything first, lay the clamps out ready, and only then open the bottle.
- Clamping does not squeeze the joint strong — it holds the parts in contact and squeezes out the excess so the glue line is thin. A thick glue line is a weak glue line. Use even pressure and cauls or scrap blocks so the clamp heads do not dent the work.
- Clamp time is around 30–60 minutes before the piece can be handled; full cure is about 24 hours before the joint takes real load or gets machined.
- Check for square while the glue is still wet — measure the two diagonals of a frame; if they are equal it is square. After the glue grabs, nothing can be adjusted.
- Wipe the squeeze-out now. Dried glue is invisible until you apply stain or oil, when it shows as a pale patch that refuses to take colour. Wipe with a damp cloth, or let it go rubbery and pare it off.
- Choosing the glue: interior PVA (D2) for indoor work; cross-linking PVA (D3/D4) where damp is possible; polyurethane for outdoor and oily timbers (it foams and needs moisture to cure); contact adhesive for laminates and veneers, coated on both faces, left to touch-dry, then pressed — there is no repositioning once the faces meet; hot melt only for temporary holds and jigs.
4.2Screws, nails and pilot holes
| Screws | Nails | |
|---|---|---|
| How it grips | A thread cuts into the timber and pulls the parts together | Friction only, as the fibres press back on the shank |
| Best at resisting | Withdrawal — being pulled straight out | Shear — a sideways load across the shank |
| Speed | Slower; needs drilling | Very fast |
| Removable? | Yes, cleanly — so it suits knock-down and repairable work | Not without damage |
| Typical use | Carcases, hinges and hardware, anything carrying load or needing to come apart | Framing, mouldings, holding a panel while glue cures |
A screw properly installed needs three holes, not one. The pilot hole in the lower piece is slightly smaller than the screw's core, giving the thread something to bite while stopping the wedge action from splitting the timber — essential in hardwood, and essential anywhere near an end or an edge. The clearance hole in the upper piece is the full shank diameter, so the thread does not grip the top piece and can pull the two boards tight together; skip it and the screw jacks the boards apart. The countersink is the cone at the top that lets a countersunk head sit flush or just below the surface. Nails split timber too, which is why they are staggered rather than driven in a line along one grain fibre, and blunting the point makes a nail crush its way through rather than wedge the fibres apart.
4.3Sanding: the sequence you cannot skip
Sandpaper does not smooth timber — it scratches it. Every grit leaves a field of scratches of its own size; the next grit's only job is to replace them with finer ones. That is why the sequence is coarse to fine and why skipping a grit does not work: 180 grit is not aggressive enough to remove 80-grit scratches, so it just polishes the ridges between them, and the coarse scratches sit there invisibly until a finish is applied and they suddenly appear as dark lines.
| Grit | Job | Notes |
|---|---|---|
| 80 | Levelling — machine marks, glue spots, badly out-of-flat surfaces | Coarse and fast. Removes a lot of material, so keep it moving or it will dish the surface. |
| 120 | Removing the 80-grit scratches | The workhorse grit; most of the time is spent here. |
| 180 | Removing the 120-grit scratches | Enough for a painted finish. |
| 240 | Final surface before oil, stain or varnish | Going much finer can burnish the surface so it stops absorbing stain evenly. |
- Sand with the grain, never across it. Cross-grain scratches are the ones that show most under a finish.
- Vacuum and wipe between grits. One stray 80-grit particle dragged along under a 180-grit sheet cuts a scratch you will then have to chase out from the beginning.
- Use a sanding block on flat work — fingers press unevenly and dig hollows, especially at edges.
- Ease the sharp edges ("break the arris") with a light pass. A knife-sharp edge is uncomfortable, dents easily, and finish will not stay on it.
- Before a water-based finish, wipe the surface with a damp cloth, let it dry, and sand lightly again: the water lifts the fibres (raises the grain) so you can cut them off now rather than have the first coat do it for you.
- Sanding dust is a hazard too — extraction on the machine, P2 mask on your face, especially with MDF.
4.4Finishes: what each one actually does
| Finish | How it works | Protection | Look & repair | Best for |
|---|---|---|---|---|
| Stain | Colour carried in a liquid that soaks into the fibres | None — it only colours | Deepens the grain; blotches on pine and any glue smear | Changing the colour before a protective finish goes over the top — a stain is never the last step |
| Oil (danish, tung, hardwax) | Soaks into the timber and cures there; no film on top | Low to moderate — water-resistant, not waterproof | Natural, low sheen, feels like wood; scratches are repaired by re-oiling the spot — no stripping | Furniture that will be handled and re-finished; anything a beginner must be able to repair |
| Wax | Buffed onto the surface as a soft film | Lowest of all — marks with water and heat | Soft glow, lovely feel; re-waxed whenever it dulls | A top coat over oil or shellac; low-wear items |
| Varnish / polyurethane | Cures into a hard plastic film on top of the timber | Highest — water, heat, scratches and spills | Glossy to satin, slightly plastic; damage means sanding back the area or the whole panel | Tabletops, benchtops, floors, outdoor work — anywhere that meets water and wear |
| Paint (over primer) | Opaque film; primer seals and grips first | High, and it hides the substrate | Any colour; chips are touched up | MDF and cheaper boards, where there is no grain worth showing |
Markers repeat one line: a finish magnifies the surface underneath it. It never hides a scratch, a glue smear or a torn edge — it makes all three more obvious. So the order is fixed: sand through every grit → remove all dust → stain if colour is wanted → apply thin coats of the protective finish → de-nib lightly between coats once dry → final coat. Thin coats, several of them, always beat one thick one: thick coats run, trap bubbles and stay soft.
Drawings that can be built from.
This course prepares you for Industrial Graphics Skills (Applied) in Years 11–12. Four units: the language of technical drawing, third-angle orthographic projection as Australia uses it, pictorial drawing, and CAD through to the machine that cuts the part.
The mapFour units
- The language of drawings — why the conventions exist, the four line types, and reading a scaled dimension.
- Orthographic projection — third angle to AS 1100, how the three views relate, and the dimensioning rules.
- Pictorial drawings — isometric at 30°, oblique, one-point perspective, and what happens to circles.
- CAD — sketch, constrain, extrude; file types; and the path from CAD to CNC and 3D printing.
A technical drawing is not artwork — it is an instruction. Someone you will never meet must build the part from it and get it right the first time. Every convention in this course exists to remove one more way of being misunderstood.
The language of drawings
Technical drawing is a language with a fixed grammar, and Australia's grammar book is AS 1100. Every line on a drawing means one particular thing — and its thickness and pattern are how it says which.
1.1Why technical drawing exists
- A sketch communicates an idea. A technical drawing communicates a specification: exact sizes, in a standard form, with no room for interpretation.
- It has to survive the journey. The drawing may be read by a machinist in another state, a supplier overseas, or a CNC operator years later — none of whom can ask you what you meant.
- Standards make that possible. In Australia, AS 1100 fixes the line types, the projection method, the dimensioning rules and the lettering, so every drawing reads the same way.
- It is also the legal and commercial record: a quote, a contract and a manufacturing check are all made against the drawing.
1.2The four line types you must know
Hidden lines start and finish with a dash, and a dash meets a visible line rather than crossing it — so the reader can see exactly where the hidden feature begins.
Centre lines cross at their long dashes at the centre of a circle, and extend a little past the feature. A centre line is never used as an edge.
1.3Scale: fitting a real object onto a page
A scale is written drawing : real. Read it as a ratio, and the arithmetic is always one multiplication or one division.
| Scale | Means | Real size → drawn size | Measured on paper → real size |
|---|---|---|---|
| 1:1 | Full size | 60 mm → 60 mm | 60 mm → 60 mm |
| 1:2 | Half size — divide by 2 | 90 mm → 45 mm | 45 mm → 90 mm |
| 1:5 | One fifth size — divide by 5 | 350 mm → 70 mm | 24 mm → 120 mm |
| 2:1 | Twice size — an enlargement, for small parts | 7 mm → 14 mm | 14 mm → 7 mm |
The number written beside a feature is always the true size of the real object, whatever the scale. On a 1:5 drawing, a 350 mm shelf is drawn 70 mm long — and labelled 350. Never write the paper measurement, and never measure a drawing to find a size when the dimension is written on it.
Orthographic projection
One picture of a 3D object always hides something. Orthographic projection solves it by giving several flat, square-on views — and Australia arranges those views in third angle.
2.1Third angle: where each view goes
In third-angle projection, each view is placed on the same side as the direction you looked from. Look down from above → the top view is drawn above. Look from the right → the right side view is drawn on the right. This is the method used in Australia under AS 1100, and in North America. (First angle, used across Europe, puts them on the opposite sides — know that it exists, but draw in third angle.)
2.2How the three views relate
- The front view is chosen first: pick the face that shows the object's most characteristic shape, and everything else follows from it.
- Top view shares WIDTH with the front view — it sits directly above, so every vertical projection line runs straight through both.
- Right side view shares HEIGHT with the front view — it sits directly beside, so every horizontal projection line runs straight across both.
- Top view and side view share DEPTH — the depth measured down the top view equals the depth measured across the side view. (In Figure 2.1 both are 40.)
- Draw only as many views as the object needs. Three is typical; a flat plate may need one plus a thickness note.
2.3The third-angle symbol
2.4Dimensioning rules
- Dimension each feature once, and once only. If the slot's width appears in both the front and the top view, the two can disagree after an edit — and then nobody knows which is right.
- Work from a datum. Measure every dimension from the same chosen edge or face rather than chaining each one off the last, so small errors cannot accumulate along the part.
- Millimetres, and don't write "mm". All dimensions are in millimetres, the unit symbol is left off each number, and a single note on the drawing states ALL DIMENSIONS IN MILLIMETRES.
- Put dimensions outside the outline where possible, on the view that shows the feature most clearly, and never let a dimension line cross another.
- Numbers read from the bottom or the right of the sheet, and sit above the dimension line, clear of it.
- Diameters are marked ⌀ and radii R — ⌀12 is a 12 mm hole; R6 is a 6 mm radius corner.
Pictorial drawings
Orthographic views are for building. Pictorial drawings show the object as a solid in one image — for explaining, selling and assembling. There are three you need, and each is right for a different job.
3.1Isometric: both axes at exactly 30°
3.2Oblique and one-point perspective
| Isometric | Oblique | One-point perspective | |
|---|---|---|---|
| How it is set out | Two axes at 30°, verticals vertical | Front face drawn square-on and true shape; depth goes back at an angle (usually 45°) | Front face square-on; all depth lines converge on one vanishing point on the horizon |
| Can you measure it? | Yes, along all three axes | Along the front face, yes; the depth is usually halved | No — sizes shrink with distance |
| Circles on the front face | Become ellipses (no face is square-on) | Stay true circles — that is the whole point of oblique | Become ellipses unless the face is parallel to the picture plane |
| Use it for | Engineering pictorials, assembly instructions | Objects with one complicated face — a dial, a wheel, a control panel | Realistic views: interiors, buildings, presentation renders |
- Cabinet oblique draws the depth at half its true length. Drawn at full depth (cavalier oblique) an object looks unnaturally long, so cabinet is the usual choice.
- In one-point perspective the vanishing point sits on the horizon line, at the viewer's eye level. Move the eye level and the whole drawing changes character — below it you look up at the object, above it you look down.
- Perspective is the only one of the three that matches what a camera sees — and the only one you must never measure a size from.
Ask: is the face square-on to me? A circle drawn on a square-on face stays a circle; on any face turned away from the viewer, it is drawn as an ellipse. That is why a wheel is easy in oblique and awkward in isometric — in isometric no face is square-on, so every circle becomes an ellipse.
CAD, and what happens next
Every convention in this course still applies in CAD — the software just enforces them. What CAD adds is that the model can go straight to a machine and become a real part.
4.12D CAD and 3D CAD
| 2D CAD | 3D CAD (parametric modelling) | |
|---|---|---|
| What you make | Flat views — lines, arcs and text on a sheet | A solid model with real volume |
| Views | You draw each view yourself | Views are generated from the model, so they cannot disagree |
| Changing a size | Redraw every view it affects | Change the dimension once; the model and all its views update |
| Typical use | Floor plans, laser-cut and CNC-router profiles | Parts, assemblies, 3D printing, machining |
4.2The workflow: sketch → constrain → extrude
- Choose a plane to sketch on — usually front, top or right, or a flat face of what you have already built.
- Sketch the profile roughly. Do not aim for accuracy here; aim for the right shape and the right connections.
- Constrain and dimension until the sketch is fully defined: geometric constraints (horizontal, vertical, parallel, tangent, equal, coincident) fix the relationships, and dimensions fix the sizes.
- Extrude the closed profile into a solid — or revolve it around an axis, for anything round.
- Add the next feature on the new solid: another extrusion, a cut, holes, fillets and chamfers.
An unconstrained sketch is a rubber band: drag one line and the whole shape distorts, and the next person to open the file has no idea what was meant to stay fixed. A fully defined sketch cannot be dragged out of shape at all — it records your design intent, so that when someone changes the width from 60 to 80, the holes stay centred and the walls stay parallel instead of drifting. Most CAD packages colour a fully defined sketch differently precisely because it matters this much.
4.3File types
| Format | What it holds | When you use it |
|---|---|---|
| Native (.dwg, .sldprt, .f3d) | The full model with its sketches, constraints and feature history | While you are still designing, in that one program |
| DXF | 2D geometry only — the flat profile | Sending a shape to a laser cutter, plasma cutter or CNC router |
| STEP (.stp) and IGES | Neutral 3D solid geometry, no editable history | Sending a 3D part to someone using different CAD software |
| STL | The surface only, approximated as thousands of triangles | 3D printing — it is the slicer's input |
| A fixed picture of the drawing sheet | Viewing, quoting and printing — never for machining |
Neutral formats are the reason a workshop can accept your part without owning your software — but they arrive with the history stripped out, so keep the native file: it is the only version you can properly edit.
4.4From CAD to a real part
- CAD → CAM → G-code → machine. CAM software plans the tool paths from your model, then posts them out as G-code — the numbered instruction list a CNC machine actually runs.
- CNC machining is subtractive: it starts with a block and cuts material away. A CNC router, mill or lathe follows the tool path exactly, as many times as you like.
- 3D printing is additive: a slicer cuts your STL into horizontal layers and writes G-code that builds the part up one layer at a time.
- The machine does exactly what the file says. A wrong dimension in CAD becomes a wrong part in metal — which is why the drawing conventions in Units 1 and 2 still decide whether the job succeeds.
Metal, measured to the millimetre.
Industrial Technology Skills is where a drawing becomes a fabricated object. The practical marks come from the workshop — but the written marks come from four things: assessing risk properly, measuring accurately, choosing the right cutting tool and speed, and choosing the right way to join two pieces of metal. That is this course.
The mapFour units
- Working safely with machines — risk assessment in four steps, the hierarchy of controls with metalwork examples, and the two hazards students underrate: noise and dust.
- Measuring & marking out — rules, squares and calipers, datum edges and tolerances, and marking metal so the line survives.
- Cutting, drilling, shaping — hacksaw blades and TPI, files, drilling speeds, threading with taps and dies, and the bench grinder.
- Joining & fabrication — rivets and bolts, the soldering–brazing–welding ladder, and why zinc protects steel long after the coating is scratched.
Applied questions almost always ask you to choose and justify: which control, which blade, which speed, which joining process, which coating. A bare name earns little. Name it, then give the reason in the same sentence — "24 TPI, because thin sheet needs at least three teeth in the cut at all times, or the teeth snag and strip."
Working safely with machines
Every machine in a metal workshop can do in a quarter of a second what a surgeon cannot undo in six hours. Safety here is not a list of rules to memorise — it is a repeatable process you can apply to a machine you have never seen before.
1.1Risk assessment: four steps, always in this order
- Identify the hazard. Walk the job and ask what could hurt someone: the rotating chuck, the swarf, the noise, the fume, the hot workpiece, the 6 kg bar that could drop on a foot. A hazard is anything with the potential to cause harm.
- Assess the risk. Two questions together: how likely is it to happen, and how badly would it hurt? A likely-but-minor hazard and an unlikely-but-fatal one are both worth controlling — assessing them tells you which to fix first.
- Control the risk. Work down the hierarchy of controls from the top and stop at the highest level you can actually achieve.
- Review. Did the control work? Has anything changed — a new machine, a new material, a near miss? A risk assessment written once and filed forever is not a risk assessment.
The output of that process is a safe work procedure (SWP): a short written sequence for one machine, stating the PPE required, the pre-start checks, the correct steps, and what to do if something goes wrong. In a school workshop you sign one before you are allowed on the machine, and it is the document a marker will ask you to write or complete.
1.2The hierarchy of controls, in metal
Six levels, most effective first. You never jump to the bottom because it is easier — and PPE is the bottom, because it changes nothing about the hazard itself.
| # | Level | What it means | In the metal workshop |
|---|---|---|---|
| 1 | Elimination | Remove the hazard completely | Have the supplier laser-cut the sheet, so nobody uses the guillotine at all |
| 2 | Substitution | Swap it for something less hazardous | Cut bar on a cold saw instead of an angle grinder — far less noise, no shower of sparks |
| 3 | Isolation | Separate people from the hazard | Weld inside a screened bay, so the arc flash cannot reach anyone walking past |
| 4 | Engineering | Design the risk out with hardware | Chuck guard, fume extractor at the arc, emergency stop within reach, interlocked door |
| 5 | Administrative | Change how people work | A written SWP, training and sign-off, machine signage, rostering noisy jobs |
| 6 | PPE | Protect the individual, last of all | Safety glasses, welding helmet, earmuffs, P2 respirator, leather gloves, boots |
PPE does nothing to the hazard. The grinder still throws sparks, the arc still emits ultraviolet, the fume is still in the air — PPE just puts a barrier in front of one person, and only while it is worn, undamaged and correctly fitted. Every level above it protects everyone in the room, all the time, without anyone remembering to do anything. That sentence is worth memorising; it answers half the safety questions on the paper.
1.3Machine rules that are never negotiable
- Guards on, always. A chuck guard or wheel guard is an engineering control. Removing it drops the protection five levels in one move.
- Isolate before adjusting. Switch off at the isolator, wait until everything has stopped turning, and lock and tag it out before changing a blade, a wheel or a chuck.
- Know the emergency stop before you press start — the big red mushroom button you can hit with a palm, a hip or a knee.
- Clamp the work. A drill that grabs will spin a plate into a spinning blade with your hand still on it. Use a machine vice or a clamp, every time.
- Swarf is not rubbish, it is razor wire. Long steel curls are sharp and hot. Clear it with a brush after the machine has stopped — never with fingers, never while it is running.
- No loose clothing, no long hair loose, no rings, no lanyards, and no gloves at rotating machines. Gloves protect against sharp sheet edges, but at a lathe or drill they are simply loose material that can be wound in with the hand inside them.
- Enclosed leather or steel-cap footwear. Dropped bar, hot sparks and sharp swarf all end up on the floor.
1.4The two hazards students underrate
- Noise. An angle grinder, a guillotine and a drop saw are all loud enough to damage hearing. The damage is cumulative and permanent: there is no warning pain, no healing, and no repair. Tinnitus — permanent ringing — usually arrives before people notice they cannot hear speech in a crowd. Control it high up the hierarchy where you can (quieter process, enclosed bay) and wear earmuffs or plugs the rest of the time, from the first minute.
- Dust and fume. Grinding dust, welding fume and the fine particles from cutting all reach deep into the lungs. Welding fume is a recognised carcinogen, and galvanised steel is especially dangerous to weld or grind: it releases zinc oxide fume, which causes metal fume fever. Extraction at the source beats a mask every time — it is level 4, the mask is level 6 — because extraction removes the fume from the whole room, protecting everyone, whether or not they remembered their respirator.
Measuring and marking out
In timber you can plane a millimetre away. In metal you cannot — a part is either within tolerance or it is scrap. Everything in this unit exists to stop small errors turning into a bin full of expensive off-cuts.
2.1The measuring tools
| Tool | What it does | Using it properly |
|---|---|---|
| Steel rule | Direct measurement, usually to 0.5 mm | Stand the rule on its edge so the graduations touch the work, and look straight down the line — viewing from an angle introduces parallax error. Measure from a graduation, not the worn end. |
| Try square | Marks and checks a true 90° | The stock is held hard against the datum face. To test a square itself, mark a line, flip the square over and mark again — the two lines must coincide. |
| Combination square | 90° and 45°, plus depths, heights and centres | The head slides and locks anywhere on the rule, so it doubles as a depth gauge and a marking gauge. With a centre head it finds the centre of round bar. |
| Vernier / digital calipers | Outside, inside, depth and step measurements to a fraction of a millimetre | Close the jaws first and check it reads zero. Use gentle, even pressure — squeezing gives a false small reading. |
| Scriber | Scratches a permanent fine line into the metal | A pencil line rubs off, smears with oil and is far too thick. A scribed line is one point wide and stays there through the whole job. |
| Centre punch | Punches a small dimple at a hole centre | The drill point drops into the dimple instead of skating across the surface. Check it is on the crossed lines before the hard hammer blow. |
| Engineer's / machinist's square, surface plate, scribing block | Reference surfaces for accurate marking out | Marking out is always done from a flat reference surface and a datum edge, not freehand on the bench. |
2.2Reading a vernier caliper
A metric vernier squeezes 50 divisions into the space of 49 millimetres, so each vernier division is 0.02 mm narrower than a main-scale millimetre. To take a reading: first read the whole millimetres on the main scale, up to the vernier's zero mark. Then run along the vernier until you find the one line that lines up exactly with a main-scale line, and multiply its number by 0.02 mm. Add the two. If the main scale reads 23 mm and the seventh vernier line coincides, the size is 23 + (7 × 0.02) = 23.14 mm. Digital calipers do the same job to 0.01 mm and can be zeroed anywhere, which makes comparison measurements easy — but they need a battery, and they lie silently when the jaws are dirty.
2.3Datum edges and tolerances
- A datum is the one edge or face that every measurement is taken from. Prepare it first: straight, flat and square. If you measure the second hole from the first hole and the third from the second, each small error is added to the last — cumulative error — and by the sixth hole nothing lines up. Measured from a single datum, each error stays its own size.
- A tolerance is the amount a size is allowed to vary and still be accepted. Written 40 ± 1 mm, it means anything from 39 mm to 41 mm passes. Tolerances exist because no process is perfect and because tighter tolerances cost more time, better machines and more rejects — so a designer specifies tight tolerances only where the fit actually matters.
- Where two parts must fit, the tolerance is what decides whether you get a clearance fit (it slides), a transition fit (it locates snugly) or an interference fit (it must be pressed in). This is why "close enough" is meaningless in fabrication and "±1 mm" is not.
- Always allow for the kerf — the width of material the blade turns into swarf. Four pieces cut from one bar means three cuts, and three cuts at a 2 mm kerf lose 6 mm of bar.
2.4Making the line show on metal
Bare steel is shiny, so a scribed line disappears into the reflections. Marking-out fluid — layout blue, brushed or sprayed on and dry in seconds — gives a dark matt coating; the scriber then cuts through it and the line appears as a bright metal streak against the blue, impossible to lose. The sequence is: clean and de-grease the surface → coat with marking-out fluid → set the rule or square from the datum edge → scribe the lines → centre punch every hole centre where the lines cross → check every dimension before a single cut is made.
Cutting, drilling and shaping
Every cutting tool in the workshop obeys the same two rules: match the tooth or the speed to the material, and let the tool cut instead of forcing it. Break either rule and you get a stripped blade, a burnt drill or a hospital visit.
3.1The hacksaw and the three-tooth rule
A hacksaw blade is fitted with the teeth pointing forward, away from the handle, because it cuts on the push stroke; the blade is tensioned in the frame so it cannot flex and wander. The number that matters is TPI — teeth per inch. The rule behind every choice is simple: at least three teeth must be in the cut at all times. Fewer than three and the teeth straddle the material, snag on the edge and strip off.
| TPI | Use it on | Why |
|---|---|---|
| 14 | Thick, soft sections — aluminium, brass, heavy mild-steel bar | Big gullets between big teeth clear the large soft chips instead of clogging |
| 18 | General-purpose mild steel | The default blade in a school workshop |
| 24 | Thinner sections, angle iron, thicker tube | Keeps three or more teeth in contact as the wall thickness drops |
| 32 | Thin sheet and small-diameter tube | Only very fine teeth keep three in the cut on a 1 mm wall — a coarse blade would snatch and strip |
- Long, steady strokes using the whole blade, about one per second, with pressure on the push and released on the return — dragging the teeth backwards under load just blunts them.
- Clamp the work in a vice close to the cut, or it will chatter, and support both sides as you finish so the offcut cannot pinch the blade.
- A new blade in a part-sawn cut will jam, because the old blade's kerf is wider than the new blade's set. Start a fresh cut.
3.2Files
| Term | Meaning |
|---|---|
| Single cut | One set of parallel teeth. Removes less, leaves a smoother surface — used for finishing and for sharpening. |
| Double cut | Two sets of teeth crossing each other, making individual cutting points. Removes metal fast; the general shaping file. |
| Rasp | Individual punched teeth for soft materials such as timber and plastic — far too coarse for steel. |
| Grades, coarse to fine | Rough → bastard → second cut → smooth → dead smooth. Work down the grades exactly as you work down sanding grits. |
| Cross filing | Filing across the work at an angle to remove material and bring a surface to size. |
| Draw filing | Holding the file sideways in both hands and drawing it along the work — the finishing cut, giving a flat, bright surface. |
| Pinning | Chips jammed between the teeth; they score deep scratches into the work. Clear them with a file card (wire brush) and rub chalk on the file to slow it happening. |
A file is only cut on the forward stroke, so lift or ease it on the return. And never use a file without a handle fitted over the tang: a bare tang is a spike, and if the file catches it drives that spike into the palm.
3.3Drilling
The speed rule is the one that gets examined: the bigger the drill or the harder the material, the slower the speed. A big drill's outer edge travels much further per revolution than a small one's, and the cutting edge burns if it moves through the metal too fast — a blued, blunt drill is a drill that was run too fast, pushed too hard, or run dry.
| Drill diameter (HSS in mild steel) | Roughly | The pattern |
|---|---|---|
| 3 mm | ~2000–2500 rpm | Double the diameter and you roughly halve the speed. Softer materials such as aluminium and plastic run faster; harder ones such as stainless steel run slower still, with plenty of cutting fluid. |
| 6 mm | ~1000–1300 rpm | |
| 10 mm | ~600–800 rpm | |
| 12 mm | ~500–650 rpm |
- Centre punch first, always. Without a dimple, the chisel edge of the drill skates across the surface and the hole ends up somewhere else.
- Clamp the work in a machine vice or to the table. Sheet metal is the worst offender: the drill grabs as it breaks through, and an unclamped sheet becomes a spinning blade.
- Cutting fluid on steel — it cools the edge and flushes the swarf. Aluminium can be cut dry or with kerosene; cast iron is drilled dry.
- Pilot holes. For a large hole, drill a small one first: the large drill's chisel edge does not cut well, and a pilot hole lets its cutting lips do the work.
- Countersinking cuts a cone at the mouth of the hole so a countersunk screw or rivet head finishes flush with the surface. Run the countersink slowly, or it chatters and leaves a fluted edge.
- Ease off as the drill breaks through — that is the moment it grabs.
3.4Threads: taps and dies
- A tap cuts an internal thread inside a drilled hole; a die cuts an external thread on a rod.
- The hole is drilled to the tap drill size, which for a standard metric thread is the diameter minus the pitch: M6 × 1.0 needs a 5.0 mm hole; M8 × 1.25 needs 6.8 mm; M10 × 1.5 needs 8.5 mm. Drill it too big and the thread has no metal to cut; too small and the tap jams and snaps — and a broken tap is hardened steel that cannot be drilled out.
- Taps come as a set of three, used in order: the taper tap (long lead-in, starts the thread square), the second or intermediate tap, and the plug or bottoming tap that finishes the thread to the bottom of a blind hole.
- Turn half a turn forward, then a quarter turn back to break the swarf, keep the tap square to the surface, and use cutting fluid.
3.5The bench grinder
- Sparks are metal. The stream leaving a grinding wheel is red-hot particles of steel — safety glasses and the wheel's eye shield, always, and never aim the stream at anyone.
- The tool rest is set close to the wheel — a couple of millimetres. A wide gap lets the work be dragged down into it and jam, wrecking the wheel and the hand holding the work.
- Stand to one side when starting up. A cracked wheel bursts in the first seconds at full speed, and the pieces leave in the plane of the wheel.
- Grind on the face of the wheel, never the side. The side is not designed to take the load and can shatter.
- Never grind aluminium, brass or timber on a wheel meant for steel: soft material loads the pores of the wheel, and a loaded wheel overheats and can break up.
- Dip the work to keep it cool. If a tool edge turns blue you have overheated it and lost the hardness — the temper — and no amount of sharpening brings it back.
Joining and fabrication
There are three ways to hold two pieces of metal together: a fastener through them, heat and a filler between them, or adhesive. Then there is the fourth question everyone forgets until the job rusts — what protects the steel afterwards.
4.1Mechanical fastening
| Fastener | How it works | Permanent? | Chosen when… |
|---|---|---|---|
| Blind (pop) rivet | A hollow rivet is pushed through both parts; the gun pulls a mandrel that swells the far end, then snaps it off | Permanent — removing it means drilling it out | You can only reach one side of the joint — a box, a duct, a closed tube. This is the answer markers look for. |
| Solid rivet | Hammered or pressed over to form a second head | Permanent | Heavier structural work, and where a joint must not vibrate loose |
| Bolt, nut and washer | Clamps the parts between the bolt head and the nut | Removable | Anything that must come apart for service, or carry a real load |
| Machine screw into a tapped hole | Threads directly into a thread cut in the part itself | Removable | Only one side is accessible but the part is thick enough to tap |
| Self-tapping screw | Cuts its own thread as it drives into a pilot hole in sheet | Removable, but the thread wears after a few cycles | Thin sheet metal, light fixings, fast assembly |
- A plain washer spreads the clamping load over a wider area, so the nut cannot pull through or dent thin material.
- A spring washer (or a nyloc nut) keeps tension in the joint so vibration cannot shake the nut loose — the reason every machine and vehicle uses them.
- Holes for bolts are drilled as clearance holes, a little larger than the bolt, so the parts can be lined up and the bolt is not bent into place.
4.2Heat: the soldering – brazing – welding ladder
All three use heat and all three make a joint, but they are separated by one question: does the parent metal melt?
| Process | Temperature | Does the parent metal melt? | Strength | Used for |
|---|---|---|---|---|
| Soft soldering | Filler melts below 450 °C — typically around 200 °C | No. Molten solder is drawn into the joint by capillary action | Weakest — it seals and conducts more than it holds | Electrical connections, copper pipe, sheet-metal seams, tinplate |
| Brazing (and silver soldering) | Filler melts above 450 °C — typically 600–900 °C | No. The parent metal is heated until the filler flows into the joint, but stays solid | Strong — and it can join dissimilar metals, such as steel to brass | Bike frames, tool joints, thin tube, anything that would burn through if welded |
| Welding (MIG, TIG, arc) | Steel melts at about 1500 °C | Yes. The parent metal melts and fuses; filler wire joins the same pool | Strongest — a good weld can be as strong as the parent metal itself | Structural steel, frames, trailers, gates — anything load-bearing |
- MIG (metal inert gas) is the common school welder because it is the easiest to learn: a motor feeds continuous wire through the torch as both electrode and filler, and a shielding gas flows around it to keep oxygen away from the molten pool. Squeeze the trigger and it just keeps going, so there is no rod to feed by hand.
- Flux does the same job as the shielding gas in soldering and brazing: it cleans the surface of oxide and stops it re-forming, so the filler can wet the metal. Nothing sticks to an oxidised surface.
- The joint must be clean and correctly fitted before heat is applied. Paint, rust, oil and galvanising all ruin the joint — and burning them produces fume.
- Welding hazards: the arc's ultraviolet burns eyes ("arc eye") and skin, so a helmet of the correct shade, a screened bay and covered skin are all needed; the fume needs extraction at the source; and everything you have just welded stays hot long after it stops glowing.
4.3Adhesives on metal
- Two-part epoxy is the structural metal adhesive: resin and hardener mixed in the right ratio, curing into a rigid joint that spreads the load over the whole glued area instead of concentrating it at a rivet hole.
- It adds no heat, so it cannot distort thin panels or destroy a heat treatment — and it can join metal to plastic or glass, which no welder can do.
- Its price: it is weak in peel (lift one corner and it unzips), it is degraded by heat and some chemicals, and the surface must be abraded and de-greased first or it will not bond at all.
4.4Protecting the steel afterwards
Steel rusts because iron, oxygen and water react to form iron oxide, which flakes off and exposes fresh metal to do it again. There are two completely different strategies for stopping that, and the difference between them is the most-asked question in this unit.
| Treatment | How it protects | What happens at a scratch | Typical use |
|---|---|---|---|
| Primer + topcoat paint | Barrier only — the primer grips and inhibits corrosion, the topcoat seals and colours | The exposed steel rusts, and the rust spreads under the film | Indoor and light outdoor steel; anywhere colour matters |
| Hot-dip galvanising | Barrier plus sacrificial protection — the zinc corrodes preferentially | The steel keeps being protected until the surrounding zinc is consumed | Outdoor structures, fencing, trailers, roof sheet, marine-adjacent work |
| Powder coating | A thick, tough, baked-on polymer barrier | Barrier only — a deep scratch will rust, so steel is often galvanised first, then powder coated | Furniture, gates, machine covers, anything wanting a hard coloured finish |
| Oil, grease or wax film | A temporary barrier keeping water and oxygen off | Wipes off — it must be renewed | Machine beds, tools, short-term storage of bright steel |
Heating zinc drives off zinc oxide fume, which causes metal fume fever — hours of shivering, aching and fever after the job. The correct practice is to grind the zinc back from the weld area first, work with extraction at the source and good ventilation, and re-coat the bare area afterwards with a zinc-rich paint.
Life, from one membrane to a whole body.
Senior Biology starts small and works outward: the cell and its membrane, the chemistry that keeps it powered, the exchange surfaces a large body needs, and the feedback loops that hold everything inside its tolerance limits. Four units, mapped straight onto Units 1 and 2 of the QCAA syllabus.
The mapFour topics, two units
- Cells as the basis of life (Unit 1, Topic 1) — cell theory, prokaryotes and eukaryotes, the fluid mosaic membrane, the five ways things cross it, and why surface area to volume sets a hard limit on cell size.
- Cellular energy (Unit 1, Topic 2) — enzymes and the active site, what temperature and pH really do to them, photosynthesis and aerobic respiration as balanced equations, and the anaerobic pathways.
- Exchange and transport (Unit 2, Topic 1) — what every gas exchange surface has in common, xylem and phloem, the transpiration stream, and why a large animal cannot survive on diffusion alone.
- Homeostasis and regulation (Unit 2, Topic 2) — the negative feedback loop named part by part, then thermoregulation, osmoregulation and the kidney, and blood glucose control.
Senior Biology marks explanation, not recall. A full-mark answer names the structure, states the process, and links the two: "the alveolar wall is one cell thick, so the diffusion distance is short, so oxygen crosses quickly." Every unit here is written to practise that chain.
Cells as the basis of life
Every living thing is cells, and every cell is defined by a membrane that decides what gets in and out. Get the membrane right and most of the rest of this course follows.
1.1Cell theory, stated properly
At senior level the cell theory has three parts, and you are expected to give all three:
- All living things are composed of one or more cells.
- The cell is the basic unit of structure and function in living things.
- All cells arise from pre-existing cells by cell division.
The third part is the one that did the real work historically: it ended spontaneous generation. It is also the part that viruses fail — a virus is not made of cells and cannot divide on its own, which is exactly why "is a virus alive?" is a live argument rather than a trick question.
1.2Prokaryotic and eukaryotic cells
| Feature | Prokaryotic cell | Eukaryotic cell |
|---|---|---|
| Nucleus | None — DNA sits free in a nucleoid region | Present, enclosed by a double membrane |
| DNA | One circular chromosome; often plasmids as well | Several linear chromosomes wound around histone proteins |
| Membrane-bound organelles | None | Mitochondria, endoplasmic reticulum, Golgi, lysosomes, and chloroplasts in plants |
| Ribosomes in the cytosol | Smaller, 70S | Larger, 80S |
| Typical size | About 0.1–5 µm across | About 10–100 µm across |
| Examples | Bacteria, archaea | Animals, plants, fungi, protists |
Both kinds share the essentials: a plasma membrane, cytosol, ribosomes, and DNA as the genetic material. That shared list is the evidence for common ancestry, and it is worth a mark on its own.
1.3The membrane: the fluid mosaic model
A phospholipid is a two-faced molecule: a hydrophilic phosphate head and two hydrophobic fatty acid tails. In water they arrange themselves automatically, tails inward and heads outward, into a bilayer. The consequence is the single most useful fact in the topic: the middle of the membrane is oily, so small non-polar molecules slip straight through, and charged or polar ones cannot — they need a protein.
1.4Five ways across the membrane
| Process | Direction | Protein needed? | ATP needed? | Example |
|---|---|---|---|---|
| Simple diffusion | Down the concentration gradient | No — straight through the bilayer | No | O₂ and CO₂ at the alveoli |
| Facilitated diffusion | Down the concentration gradient | Yes — a channel or carrier | No | Glucose entering a red blood cell |
| Osmosis | Water moves to where water is less concentrated (lower water potential) | Faster through aquaporin channels | No | Water entering a root hair cell |
| Active transport | Against the concentration gradient | Yes — a carrier that changes shape | Yes | The sodium–potassium pump in a neuron |
| Endocytosis / exocytosis | Bulk quantities in / out | The membrane itself folds and pinches | Yes | A white blood cell engulfing a bacterium |
Osmosis is not "water moving from high to low concentration". Water moves from the more dilute solution to the more concentrated one — that is from high water potential to low water potential. Say it in terms of water, not "concentration", and you cannot get it backwards.
Facilitated diffusion is still passive. Using a protein does not make it active. The only thing that makes transport "active" is moving something against its gradient using ATP.
1.5Surface area to volume: the constraint
Everything a cell needs enters through its surface; everything it makes leaves the same way. But if you double a cell's linear size, its surface area goes up by a factor of 2² = 4 while its volume goes up by 2³ = 8. Demand outruns supply. For a cube of side L, surface area is 6L² and volume is L³, so the ratio is exactly 6 ÷ L:
| Side length L | Surface area 6L² | Volume L³ | SA : V ratio |
|---|---|---|---|
| 1 | 6 | 1 | 6 : 1 |
| 2 | 24 | 8 | 3 : 1 |
| 3 | 54 | 27 | 2 : 1 |
| 4 | 96 | 64 | 1.5 : 1 |
| 6 | 216 | 216 | 1 : 1 |
So cells stay small and divide. Where a cell must be big, it cheats on the geometry instead: a root hair cell grows a long thin projection, and a cell lining the small intestine grows microvilli — both raise surface area without raising volume much. Multicellular bodies cheat the same way, with lungs and gills and leaves.
Cellular energy: enzymes, photosynthesis, respiration
Life runs on reactions that would otherwise be far too slow, and on two great opposing equations. This topic is where marks are won by writing formulae correctly and explaining denaturation properly.
2.1Enzymes and the active site
An enzyme is a biological catalyst — almost always a protein — that speeds a reaction up by lowering its activation energy, and is not used up in the process. The reactant it works on is the substrate; the small pocket it binds to is the active site.
Specificity comes from shape and chemistry together. The active site's shape is produced by the protein's folded tertiary structure, and its exposed side groups give it a particular pattern of charge. Only a substrate that is complementary on both counts will bind. The modern description is induced fit: the active site moulds slightly around the substrate as the enzyme–substrate complex forms, which strains the bonds that are about to break.
2.2What temperature and pH actually do
| Condition | What happens to the rate | The explanation the marker wants |
|---|---|---|
| Temperature below the optimum | Rate rises as temperature rises | Molecules gain kinetic energy, so enzyme and substrate collide more often and with enough energy to react |
| Temperature above the optimum | Rate falls sharply, and does not recover on cooling | Vibration breaks the hydrogen and ionic bonds holding the tertiary structure; the active site changes shape and can no longer bind the substrate — denaturation |
| pH at the optimum | Maximum rate | Charges on the side groups in the active site are exactly right for binding the substrate |
| pH away from the optimum | Rate falls; far from it, the fall is permanent | Excess H⁺ or OH⁻ changes the charge on those side groups, breaking ionic bonds and distorting the active site |
Optima are set by where the enzyme has to work. Most human enzymes peak near 37 °C; pepsin in the stomach peaks near pH 2, while trypsin in the small intestine peaks near pH 8. Two enzymes doing the same job (breaking down protein) with opposite pH optima is the cleanest possible evidence that the optimum is an adaptation, not a property of "enzymes" in general.
2.3Photosynthesis and aerobic respiration
| Photosynthesis | Aerobic respiration | |
|---|---|---|
| Summary equation | 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ | C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O |
| Where | Chloroplast — light reactions in the thylakoid membranes, the Calvin cycle in the stroma | Glycolysis in the cytosol; the Krebs cycle and electron transport chain in the mitochondrion |
| Energy | Light energy is converted to chemical energy stored in glucose | Chemical energy in glucose is transferred to ATP, the cell's usable currency |
| Requires | Light and chlorophyll | Oxygen |
| Yield | One glucose per six CO₂ | About 30–32 ATP per glucose (older texts quote 36–38) |
| Who does it | Plants, algae, cyanobacteria | Plants and animals — every aerobic cell, all the time |
Plants respire all the time, day and night, in every living cell. What changes in daylight is that photosynthesis runs as well, and usually faster — so the net exchange with the air reverses. Say "in the light, photosynthesis exceeds respiration, so the plant is a net absorber of CO₂".
2.4When the oxygen runs out
Glycolysis alone yields a net 2 ATP per glucose and needs no oxygen. What follows depends on the organism:
- Animals (lactic acid fermentation). C₆H₁₂O₆ → 2C₃H₆O₃ + energy (net 2 ATP). The lactic acid builds up in working muscle and is later oxidised or converted back to glucose in the liver.
- Yeast and plants (alcoholic fermentation). C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ + energy (net 2 ATP). This is the reaction behind bread and brewing — the CO₂ raises the dough, the ethanol does the rest.
- Both are far less efficient. 2 ATP against roughly 30–32 from aerobic respiration, because the glucose is only partly broken down — lactic acid and ethanol still hold most of the original energy.
Multicellular organisms: exchange and transport
A single cell exchanges everything across its own surface. A gum tree and a human cannot — so both evolved a huge folded exchange surface and a plumbing system to reach the cells that are nowhere near it.
3.1Why size forces the issue
Diffusion is quick over micrometres and hopeless over centimetres — the time it takes rises with the square of the distance. Combine that with the falling surface-area-to-volume ratio of a large body and you get the two requirements every big organism must meet: a specialised exchange surface with a large area, and a transport system to carry substances between that surface and every cell.
3.2What every gas exchange surface has in common
| Shared feature | Why it matters | How it looks in real organisms |
|---|---|---|
| Large surface area | Diffusion rate is proportional to area — more area, more molecules crossing per second | ~300 million alveoli in human lungs; stacked gill lamellae in a fish; spongy mesophyll air spaces in a leaf |
| Thin — often one cell thick | A short diffusion distance means fast exchange | Alveolar wall and capillary wall are each a single flattened cell |
| Moist | Gases must dissolve before they can diffuse across a membrane | The film of fluid lining every alveolus; gills work in water; leaf mesophyll walls are wet |
| Permeable | O₂ and CO₂ are small and non-polar, so they cross the bilayer by simple diffusion | No barrier layer of cuticle or keratin over the surface |
| A steep gradient, kept steep | If the gradient collapsed, net diffusion would stop | Ventilation refreshes the air; blood flow removes O₂ as fast as it arrives; fish gills use countercurrent flow |
3.3Transport in plants: xylem and phloem
| Xylem | Phloem | |
|---|---|---|
| Carries | Water and dissolved mineral ions | Sucrose and amino acids (the assimilates) |
| Direction | Upward only, root to leaf | Either way, from a source to a sink |
| Cells | Dead at maturity — hollow tubes, no end walls, walls thickened with lignin | Living sieve tube elements with perforated sieve plates, each supported by a companion cell |
| Driven by | Transpiration pull — evaporation at the leaf, no ATP used | Active loading of sucrose at the source, which requires ATP |
3.4The transpiration stream
Transpiration is the price of photosynthesis: stomata must open to let CO₂ in, and water vapour escapes through the same pores. Guard cells control the trade — they take in water and swell to open the stoma, and lose water to close it. Transpiration rate rises with light, temperature and wind, and falls as humidity rises.
3.5Transport in animals
- Mammals have a closed, double circulation: blood stays inside vessels, and passes through the heart twice per circuit — once to the lungs (pulmonary), once to the body (systemic).
- The point of the double circuit is pressure. Blood is slowed by the fine capillaries of the lungs, so it returns to the heart to be re-pressurised before being sent round the body.
- Arteries carry blood away from the heart: thick muscular and elastic walls, narrow lumen, high pressure, no valves (except at the heart itself).
- Veins carry blood back: thin walls, wide lumen, low pressure, and valves to stop backflow.
- Capillaries are built for exchange, not transport: walls one cell thick, an enormous total surface area, and slow flow that gives substances time to diffuse.
- Haemoglobin loads O₂ where the partial pressure of oxygen is high (the lungs) and unloads it where it is low and CO₂ is high (respiring tissue) — the gradient does the work at both ends.
Homeostasis: holding the inside steady
Enzymes only work inside narrow limits of temperature, pH and water concentration — so a body that wants working enzymes has to control its own internal conditions. One loop, five named parts, applied three times.
4.1The negative feedback loop
Homeostasis is the maintenance of a relatively constant internal environment within narrow tolerance limits, despite changes outside. It is achieved by negative feedback: a change is detected and a response is triggered that opposes it, pushing the variable back towards its set point. Name all five parts and you cannot lose the marks.
4.2Thermoregulation
The control centre is the hypothalamus, which compares blood temperature (and signals from skin thermoreceptors) with a set point near 37 °C.
| Effector | Too hot — response | Too cold — response |
|---|---|---|
| Skin arterioles | Vasodilation — more blood flows near the surface, so more heat is lost by radiation | Vasoconstriction — blood is kept away from the surface, conserving heat |
| Sweat glands | Secrete sweat; its evaporation removes latent heat from the skin | Little or no sweat produced |
| Erector muscles / hair | Hairs lie flat, so no insulating layer of air is trapped | Hairs are pulled upright, trapping a layer of still air |
| Metabolism | Metabolic rate falls, so less heat is generated | Metabolic rate rises (thyroxine, adrenaline); shivering — involuntary skeletal muscle contraction — releases heat |
Sweat sitting on skin cools nothing. It is the evaporation that cools: turning liquid water into vapour takes latent heat, and that energy comes from the skin. That is also why sweating works badly in humid air — evaporation is slow when the air is already near saturation.
4.3Osmoregulation and the kidney
The functional unit of the kidney is the nephron, and it works in three stages:
- Ultrafiltration at the glomerulus. Blood pressure forces water, ions, glucose, amino acids and urea out through the capillary wall into the Bowman's capsule. Blood cells and plasma proteins are too large to pass.
- Selective reabsorption, mostly in the proximal convoluted tubule. All the glucose and amino acids and most of the water and ions are taken back into the blood — glucose and Na⁺ by active transport, water by osmosis following them.
- Regulated reabsorption in the distal convoluted tubule and collecting duct. This is the stage under hormonal control, and it is what makes urine concentrated or dilute. The loop of Henle maintains the salt gradient in the medulla that makes this possible.
The loop itself: osmoreceptors in the hypothalamus detect a rise in blood solute concentration. The posterior pituitary releases ADH (antidiuretic hormone). ADH makes the collecting duct walls more permeable to water by inserting aquaporin channels, so more water is reabsorbed and a small volume of concentrated urine is produced — which restores the blood's water concentration and switches ADH off. Drink a litre of water and the whole loop runs in reverse: less ADH, a less permeable duct, and a large volume of dilute urine.
4.4Blood glucose regulation
The set point is roughly 4–6 mmol L⁻¹. Both the receptor and the control centre are in the pancreas — the islets of Langerhans detect blood glucose directly and secrete the hormone themselves.
| Blood glucose too HIGH (after a meal) | Blood glucose too LOW (fasting, exercise) | |
|---|---|---|
| Detected by | Beta cells of the islets of Langerhans | Alpha cells of the islets of Langerhans |
| Hormone released | Insulin | Glucagon |
| Target and effect | Liver, muscle and fat cells take glucose up faster; the liver converts glucose to glycogen (glycogenesis) | The liver breaks glycogen back down to glucose (glycogenolysis) and releases it into the blood |
| Result | Blood glucose falls back towards the set point | Blood glucose rises back towards the set point |
Type 1 diabetes: the beta cells are destroyed, so little or no insulin is made — treated with injected insulin. Type 2 diabetes: insulin is made but target cells respond poorly to it (insulin resistance) — managed with diet, exercise and medication. Both show up as blood glucose that stays high after a meal instead of returning to the set point, which is exactly a broken negative feedback loop.
From one atom to a counted reaction.
Senior Chemistry is built in one direction: what an atom is, how atoms hold together, what happens to the energy when those bonds are rearranged, and finally how to count the particles involved. Four topics, mapped straight onto Units 1 and 2 of the QCAA syllabus.
The mapFour topics, two units
- Properties and structure of atoms (Unit 1, Topic 1) — subatomic particles, isotopes and weighted relative atomic mass, electron configuration in shells and subshells, and the four periodic trends with the reasons behind them.
- Bonding and materials (Unit 1, Topic 2) — ionic, covalent, polar covalent and metallic bonding; the three intermolecular forces; and how structure explains melting point, conductivity and hardness.
- Chemical reactions (Unit 2, Topic 1) — balancing full and ionic equations, exothermic and endothermic changes, enthalpy signs, activation energy and catalysts.
- Quantifying chemistry (Unit 2, Topic 2) — the mole, molar mass, concentration, dilution, limiting reagent and percentage yield, all with exact working.
Avogadro's constant NA = 6.02 × 10²³ mol⁻¹. Relative atomic masses are the standard periodic-table values: H 1.008, C 12.01, N 14.01, O 16.00, Na 22.99, Mg 24.31, S 32.06, Cl 35.45, Ca 40.08. Every calculation on this site is worked with those figures, so your answers should match to the last digit.
Properties and structure of atoms
Everything the periodic table does — every trend, every bond, every reaction — comes from where the electrons are and how tightly the nucleus is holding them.
1.1The three subatomic particles
| Particle | Relative charge | Relative mass | Where it is |
|---|---|---|---|
| Proton | +1 | 1 | In the nucleus |
| Neutron | 0 | 1 | In the nucleus |
| Electron | −1 | about 1/1836 | In shells around the nucleus |
- The atomic number Z is the number of protons. It is what makes an element that element — change it and you have changed the element.
- The mass number A is protons + neutrons. So neutrons = A − Z.
- A neutral atom has electrons = protons. An ion does not: Na⁺ has 11 protons and 10 electrons; Cl⁻ has 17 protons and 18 electrons.
- Nearly all the mass is in the nucleus; nearly all the volume is the electron cloud. Both statements are worth marks in an atomic-model question.
1.2Isotopes and relative atomic mass
Isotopes are atoms of the same element (same number of protons) with different numbers of neutrons. They are chemically almost identical, because chemistry is done by electrons, but they have different masses.
The relative atomic mass (Ar) on the periodic table is therefore not a whole number: it is the weighted average of the isotope masses, weighted by natural abundance, on a scale where one carbon-12 atom is exactly 12.
Chlorine is 75.76% chlorine-35 (isotopic mass 34.969) and 24.24% chlorine-37 (isotopic mass 36.966).
Ar = (34.969 × 0.7576) + (36.966 × 0.2424)
= 26.4925 + 8.9606
= 35.45 (to 2 decimal places) — exactly the value printed on the periodic table.
Notice the answer sits closer to 35 than to 37, because the lighter isotope is three times as common. Use that as your sanity check: the weighted average always leans towards the more abundant isotope.
1.3Where the electrons go
The simple shell model fills 2, then 8, then 8 for the first twenty elements: sodium (11) is 2, 8, 1 and calcium (20) is 2, 8, 8, 2. It is enough to predict ion charges, but it does not explain why the fourth shell starts filling before the third is full.
The subshell model does. Each shell is divided into subshells: s holds 2 electrons, p holds 6, d holds 10. They fill in order of energy, which is 1s 2s 2p 3s 3p 4s 3d 4p — note that 4s fills before 3d.
| Element | Z | Shell notation | Subshell notation |
|---|---|---|---|
| Oxygen | 8 | 2, 6 | 1s² 2s² 2p⁴ |
| Sodium | 11 | 2, 8, 1 | 1s² 2s² 2p⁶ 3s¹ |
| Chlorine | 17 | 2, 8, 7 | 1s² 2s² 2p⁶ 3s² 3p⁵ |
| Calcium | 20 | 2, 8, 8, 2 | 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² |
The electrons in the outermost shell are the valence electrons, and they are the only ones that do chemistry. Sodium loses its single 3s electron to reach the configuration of neon; chlorine gains one to fill 3p and reach the configuration of argon. That single fact explains the whole of ionic bonding.
1.4Periodic trends, with the reasons
Two competing effects explain almost every trend. Going across a period, protons are added while electrons go into the same shell, so nuclear attraction on the outer electrons rises. Going down a group, a whole new shell is added, so outer electrons are further away and shielded from the nucleus by the filled inner shells.
| Trend | Across a period (left to right) | Down a group | Because |
|---|---|---|---|
| Atomic radius | Decreases | Increases | Across: more protons pulling the same shell in tighter. Down: each period adds a shell, and shielding weakens the pull on it |
| First ionisation energy | Increases | Decreases | The outer electron is held more tightly when it is close to a highly charged nucleus, and loosely when it is far away and shielded |
| Electronegativity | Increases | Decreases | Same reasoning applied to a shared pair: a small atom with a high nuclear charge pulls bonding electrons hardest |
| Metallic character | Decreases | Increases | Metals are the atoms that lose electrons easily — exactly the ones with low ionisation energy |
A trend question is marked on the reason. "Ionisation energy increases across period 3" is worth nothing on its own. "Ionisation energy increases across period 3 because nuclear charge rises while the outer electrons stay in the same shell, so they are held more tightly and more energy is needed to remove one" is the full-mark answer.
Fluorine is the most electronegative element (4.0 on the Pauling scale), which is exactly what "top right of the table, excluding the noble gases" predicts.
Bonding and materials
Why does salt melt at 801 °C and candle wax at 60 °C? Why does copper conduct and diamond not? Every one of those questions is answered the same way: name the structure, name the forces, then explain what breaking them costs.
2.1The three bonding types
| Ionic | Covalent | Metallic | |
|---|---|---|---|
| Between | Metal + non-metal | Non-metal + non-metal | Metal + metal |
| What electrons do | Transferred from metal to non-metal | Shared as pairs between two nuclei | Delocalised into a sea shared by all the cations |
| Held together by | Electrostatic attraction between oppositely charged ions, in a 3D lattice | Attraction of both nuclei for the shared pair | Attraction of the cation lattice for the electron sea |
| Melting point | High — NaCl melts at 801 °C | Molecular: low. Network (diamond, SiO₂): very high | Usually high — copper melts at 1085 °C |
| Conducts electricity? | Not as a solid (ions fixed); yes when molten or dissolved | No — no free charges. Graphite is the exception | Yes, solid or molten — the electrons are mobile |
| Mechanical behaviour | Hard but brittle: shift a layer and like charges meet, so it shatters | Molecular solids are soft; networks are extremely hard | Malleable and ductile: layers slide without breaking the non-directional bonding |
2.2When sharing is unequal
CO₂ contains two strongly polar C=O bonds, yet the molecule is non-polar — it is linear, so the two bond dipoles point in exactly opposite directions and cancel. H₂O has the same kind of polar bonds but is bent, so they do not cancel and the molecule has a net dipole. Always check the shape before you call a molecule polar.
2.3The forces between molecules
When a molecular substance melts or boils, the covalent bonds inside the molecules are untouched. What breaks is the much weaker attraction between molecules — which is why boiling water gives you steam made of intact H₂O molecules, not loose hydrogen and oxygen.
| Force | Occurs between | Relative strength | Evidence |
|---|---|---|---|
| Dispersion forces (London forces) | All molecules — caused by instantaneous, temporary dipoles in the electron cloud | Weakest, but they grow rapidly with the number of electrons and with contact area | The halogens: F₂ boils at −188 °C, Cl₂ at −34 °C, Br₂ at 59 °C, I₂ at 184 °C — identical bonding, more electrons |
| Dipole–dipole | Polar molecules only — the δ+ of one attracts the δ− of the next | Stronger than dispersion for molecules of similar size | Propanone boils at 56 °C but butane, of similar mass, boils at −0.5 °C |
| Hydrogen bonding | Only when H is bonded directly to N, O or F, and is attracted to a lone pair on the N, O or F of another molecule | Strongest of the three (still far weaker than a covalent bond) | Water boils at 100 °C; H₂S, a bigger molecule with no hydrogen bonding, boils at −60 °C |
Notice how the alkanes behave: methane boils at −162 °C, ethane at −89 °C, propane at −42 °C, butane at −0.5 °C. Same bonding, same kind of intermolecular force — only the number of electrons and the surface area available for contact change. That is dispersion forces getting stronger, and it explains why petrol is a liquid and natural gas is not.
Chemical reactions: reactants, products and energy
A chemical equation is an accounting statement: no atom is created or destroyed, so every element must balance. Then there is the energy ledger, which balances too — it just moves between the chemicals and their surroundings.
3.1Balancing, properly
You may only change the coefficients in front of formulae. Changing a subscript changes the substance — turning H₂O into H₂O₂ balances nothing, it produces hydrogen peroxide. Work through metals, then non-metals, then hydrogen, then oxygen last, and finish by counting every element on both sides.
| Reaction | Balanced equation | Check |
|---|---|---|
| Burning methane | CH₄ + 2O₂ → CO₂ + 2H₂O | C 1 / 1, H 4 / 4, O 4 / 4 |
| Burning propane | C₃H₈ + 5O₂ → 3CO₂ + 4H₂O | C 3 / 3, H 8 / 8, O 10 / 10 |
| Burning butane | 2C₄H₁₀ + 13O₂ → 8CO₂ + 10H₂O | C 8 / 8, H 20 / 20, O 26 / 26 |
| Making ammonia | N₂ + 3H₂ → 2NH₃ | N 2 / 2, H 6 / 6 |
| Rusting iron | 4Fe + 3O₂ → 2Fe₂O₃ | Fe 4 / 4, O 6 / 6 |
| Extracting iron | Fe₂O₃ + 3CO → 2Fe + 3CO₂ | Fe 2 / 2, C 3 / 3, O 6 / 6 |
| Acid on a carbonate | CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂ | Ca 1 / 1, C 1 / 1, O 3 / 3, H 2 / 2, Cl 2 / 2 |
| Acid on a metal | Zn + 2HCl → ZnCl₂ + H₂ | Zn 1 / 1, H 2 / 2, Cl 2 / 2 |
3.2Ionic and net ionic equations
In solution, soluble ionic compounds are not really molecules — they are separated ions drifting about. Writing them out shows which ions actually react and which are just watching. Those bystanders are the spectator ions, and a net ionic equation leaves them out.
- Full equation. AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)
- Complete ionic. Ag⁺(aq) + NO₃⁻(aq) + Na⁺(aq) + Cl⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq) — note the solid is not split up, because it is not dissolved.
- Cancel the spectators. Na⁺ and NO₃⁻ appear unchanged on both sides.
- Net ionic. Ag⁺(aq) + Cl⁻(aq) → AgCl(s)
Two more you should know by heart. Any strong-acid, strong-base neutralisation reduces to H⁺(aq) + OH⁻(aq) → H₂O(l). Any barium sulfate precipitation reduces to Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s). The full equation H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O collapses to that same one-line net ionic equation.
3.3Energy: the profile diagram
3.4Signs, and what a catalyst does
| Exothermic | Endothermic | |
|---|---|---|
| Energy flow | Released to the surroundings | Absorbed from the surroundings |
| Enthalpy change ΔH | Negative — products hold less energy than reactants | Positive — products hold more energy than reactants |
| The surroundings | Get warmer | Get colder |
| Bond energy balance | More energy released forming bonds than was used breaking them | More energy used breaking bonds than was released forming them |
| Examples | Combustion, respiration, neutralisation, most metal–acid reactions | Photosynthesis, thermal decomposition of CaCO₃, dissolving ammonium nitrate |
Complete combustion of methane is written CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH = −890 kJ mol⁻¹. The minus sign is not decoration — it is the statement that 890 kJ leaves the chemicals for every mole of methane burned.
A catalyst provides an alternative reaction pathway with a lower activation energy, so a greater fraction of collisions have enough energy to react and the rate rises. It is not consumed, and it can be recovered chemically unchanged.
What it does not do: it does not change ΔH, it does not lower the energy of the reactants or products, and it does not "give the reaction energy". On the profile diagram it lowers the peak only — both levels stay exactly where they were.
Quantifying chemistry: the mole
A balanced equation counts particles, but a balance counts grams. The mole is the bridge between them, and this topic is where senior Chemistry stops being descriptive and starts being arithmetic you must get exactly right.
4.1The mole and the four formulae
One mole is 6.02 × 10²³ particles — Avogadro's constant, NA. The number is chosen so that one mole of a substance has a mass in grams equal to its relative formula mass. That is the whole trick.
| Formula | Rearranged | Units | Use it when |
|---|---|---|---|
| n = m ÷ M | m = n × M · M = m ÷ n | m in g, M in g mol⁻¹, n in mol | You have a mass, or you want one |
| N = n × NA | n = N ÷ NA | N is a count of particles | The question asks "how many atoms/molecules/ions" |
| c = n ÷ V | n = c × V · V = n ÷ c | c in mol L⁻¹, V in litres | Anything in solution. Convert mL to L first, every time |
| c₁V₁ = c₂V₂ | c₂ = c₁V₁ ÷ V₂ | Any consistent volume unit | Diluting — the moles of solute do not change |
4.2Molar mass, worked
Add up the relative atomic masses in the formula. Using H 1.008, C 12.01, N 14.01, O 16.00, Na 22.99, S 32.06, Cl 35.45 and Ca 40.08:
| Substance | Working | M (g mol⁻¹) |
|---|---|---|
| H₂O | 2(1.008) + 16.00 = 2.016 + 16.00 | 18.02 |
| CO₂ | 12.01 + 2(16.00) = 12.01 + 32.00 | 44.01 |
| NaCl | 22.99 + 35.45 | 58.44 |
| NaOH | 22.99 + 16.00 + 1.008 = 39.998 | 40.00 |
| H₂SO₄ | 2(1.008) + 32.06 + 4(16.00) = 2.016 + 32.06 + 64.00 | 98.08 |
| CaCO₃ | 40.08 + 12.01 + 3(16.00) = 40.08 + 12.01 + 48.00 | 100.09 |
| NH₃ | 14.01 + 3(1.008) = 14.01 + 3.024 | 17.03 |
| C₆H₁₂O₆ | 6(12.01) + 12(1.008) + 6(16.00) = 72.06 + 12.096 + 96.00 | 180.16 |
Mass to moles. How many moles in 36.04 g of water? n = m ÷ M = 36.04 ÷ 18.02 = 2.000 mol.
Moles to mass. What is the mass of 0.250 mol of NaCl? m = n × M = 0.250 × 58.44 = 14.61 g.
Moles to particles. How many molecules in 2.00 mol of CO₂? N = 2.00 × 6.02 × 10²³ = 1.20 × 10²⁴ molecules. (Each one contains three atoms, so 3.61 × 10²⁴ atoms — read the question carefully.)
4.3Concentration and dilution
- Making a solution. 0.500 mol of solute in 250 mL. Convert: V = 0.250 L. c = n ÷ V = 0.500 ÷ 0.250 = 2.00 mol L⁻¹.
- Moles in a pipetted sample. 25.0 mL of 0.100 mol L⁻¹ solution. n = c × V = 0.100 × 0.0250 = 2.50 × 10⁻³ mol.
- Diluting. 25.0 mL of 2.00 mol L⁻¹ acid is made up to 250 mL. c₂ = c₁V₁ ÷ V₂ = (2.00 × 25.0) ÷ 250 = 0.200 mol L⁻¹. Diluting ten-fold divides the concentration by ten — adding water changes the volume, never the moles of solute.
4.4Limiting reagent and percentage yield
N₂(g) + 3H₂(g) → 2NH₃(g). You start with 4.00 mol of N₂ and 9.00 mol of H₂. Which runs out first, and how much ammonia can form?
Step 1 — test one reactant against the other. 9.00 mol of H₂ would need 9.00 ÷ 3 = 3.00 mol of N₂. You have 4.00 mol, which is more than enough. So H₂ is the limiting reagent and N₂ is in excess.
Step 2 — work from the limiting reagent only. The ratio H₂ : NH₃ is 3 : 2, so n(NH₃) = 9.00 × (2 ÷ 3) = 6.00 mol.
Step 3 — convert to mass if asked. M(NH₃) = 17.03 g mol⁻¹, so m = 6.00 × 17.03 = 102 g (3 significant figures). Left over: 4.00 − 3.00 = 1.00 mol of N₂.
That 102 g is the theoretical yield — what you would get if the reaction went perfectly and nothing was lost. It never does. The percentage yield compares reality with theory:
percentage yield = (actual yield ÷ theoretical yield) × 100
If the plant above actually collects 85.0 g of ammonia, the yield is 85.0 ÷ 102 × 100 = 83.3%. Losses come from incomplete reactions, side reactions, and product left behind on the glassware — not from atoms disappearing.
1. Volume in millilitres. c = n ÷ V only works with V in litres. 250 mL is 0.250 L, and forgetting it makes your answer wrong by a factor of 1000.
2. Ignoring the mole ratio. The coefficients in the balanced equation are the ratio. 9.00 mol of H₂ does not make 9.00 mol of NH₃.
3. Working from the reactant in excess. Always identify the limiting reagent first; everything else follows from it alone.
Energy, charge, motion — and the numbers behind them.
Senior Physics is a small set of equations applied with discipline: write the formula, substitute with units, solve, then check the answer is a sensible size. Four topics, mapped straight onto Units 1 and 2 of the QCAA syllabus.
The mapFour topics, two units
- Thermal physics (Unit 1, Topic 1) — temperature against heat, specific heat capacity, latent heat, the three transfer mechanisms, and the first law of thermodynamics.
- Electrical and nuclear physics (Unit 1, Topic 2) — charge, current, voltage, resistance, series and parallel circuits, power; then isotopes, alpha, beta and gamma decay, and half-life.
- Linear motion and force (Unit 2, Topic 1) — scalars and vectors, the SUVAT equations, Newton's three laws, free-body diagrams and friction.
- Momentum, energy and waves (Unit 2, Topic 2) — momentum and impulse, conservation in collisions, the work–energy theorem, and the wave model with v = fλ.
Acceleration due to gravity near the Earth's surface: g = 9.8 m s⁻², taken as downwards positive or negative depending on the sign convention you set up — state it every time. Specific heat capacity of water c = 4180 J kg⁻¹ °C⁻¹. Latent heat of fusion of water Lf = 3.34 × 10⁵ J kg⁻¹; of vaporisation Lv = 2.26 × 10⁶ J kg⁻¹. Elementary charge e = 1.60 × 10⁻¹⁹ C. Speed of light c = 3.00 × 10⁸ m s⁻¹. Every worked answer on this site uses exactly these.
Thermal physics: heat is not temperature
A spark from a sparkler is at 1000 °C and cannot hurt you. A cup of coffee is at 90 °C and can. The difference between those two sentences is the whole topic.
1.1Temperature, internal energy and heat
- Temperature is a measure of the average kinetic energy of the particles in a substance. It does not depend on how much substance there is.
- Internal energy is the total energy of all the particles — kinetic plus potential. A bath at 40 °C has far more internal energy than a cup at 90 °C, because it has vastly more particles.
- Heat is energy in transit because of a temperature difference, and it always flows from hotter to colder. An object does not "contain heat"; it contains internal energy.
- The Kelvin scale starts at absolute zero, where particle motion is minimal: 0 K = −273.15 °C, so T(K) = θ(°C) + 273.15. A change of 1 °C is the same size as a change of 1 K, which is why ΔT can be used in either unit.
1.2Specific heat capacity: Q = mcΔT
Specific heat capacity c is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Water's value of 4180 J kg⁻¹ °C⁻¹ is unusually high, which is why the ocean moderates coastal climates and why water is used as a coolant.
How much energy is needed to heat 2.0 kg of water from 20 °C to 70 °C?
ΔT = 70 − 20 = 50 °C
Q = mcΔT = 2.0 × 4180 × 50
Q = 4.18 × 10⁵ J (418 000 J, or 418 kJ)
Sanity check: a 2000 W kettle supplying that would need 418 000 ÷ 2000 = 209 s, about three and a half minutes. That is exactly how long a kettle takes.
1.3Latent heat: Q = mL
During a change of state the temperature does not change, even though energy is still going in. That energy is doing a different job: breaking the bonds between particles rather than speeding them up. The energy per kilogram is the specific latent heat — of fusion for melting and freezing, of vaporisation for boiling and condensing.
| Question | Working | Answer |
|---|---|---|
| Energy to melt 0.200 kg of ice at 0 °C | Q = mLf = 0.200 × 3.34 × 10⁵ | 6.68 × 10⁴ J |
| Energy to boil away 0.500 kg of water already at 100 °C | Q = mLv = 0.500 × 2.26 × 10⁶ | 1.13 × 10⁶ J |
| Energy to warm 0.500 kg of water by 10.0 °C | Q = mcΔT = 0.500 × 4180 × 10.0 | 2.09 × 10⁴ J |
Compare rows two and three: boiling that water away takes fifty times more energy than warming it by ten degrees. That is why a steam burn is so much worse than a hot-water burn — condensing steam dumps all of that latent heat into your skin before the temperature even starts to fall.
1.4Three ways heat moves
| Mechanism | How energy is carried | Needs a medium? | Example |
|---|---|---|---|
| Conduction | Particles vibrate and collide, passing energy along; in metals, free delocalised electrons carry it far faster | Yes — mainly solids | A metal spoon heating up in soup |
| Convection | Heated fluid expands, becomes less dense, rises, and cooler fluid sinks to replace it — a bulk circulation | Yes — liquids and gases only | A sea breeze; water circulating in a kettle |
| Radiation | Emitted as infrared electromagnetic waves; hotter and darker surfaces emit more | No — it crosses a vacuum | The Sun warming the Earth |
1.5The first law of thermodynamics
The first law is conservation of energy written for thermal systems: ΔU = Q + W, where ΔU is the change in the system's internal energy, Q is the heat added to the system, and W is the work done on the system. State the convention before you use it, because the law is also written ΔU = Q − W when W means work done by the system — same physics, opposite bookkeeping.
Two consequences worth knowing. A bicycle pump gets hot when you compress the air quickly: you do work on the gas, almost no heat escapes in the time available, so ΔU rises and the temperature climbs. And a perpetual motion machine of the first kind is impossible, because it would have to create internal energy from nothing.
Electrical and nuclear physics
Two topics that share a theme: what the nucleus does, and what its outermost electrons do when you push them. Both are dominated by a handful of exact equations.
2.1Charge, current, voltage, resistance
| Quantity | Symbol | Equation | Unit | In words |
|---|---|---|---|---|
| Charge | q | q = It | coulomb (C) | One electron carries 1.60 × 10⁻¹⁹ C, so one coulomb is 6.25 × 10₁⁸ electrons |
| Current | I | I = q ÷ t | ampere (A) | The rate of flow of charge: one amp is one coulomb per second |
| Potential difference | V | V = W ÷ q | volt (V) | Energy transferred per coulomb: one volt is one joule per coulomb |
| Resistance | R | R = V ÷ I | ohm (Ω) | How strongly a component opposes current |
| Power | P | P = VI = I²R = V² ÷ R | watt (W) | The rate at which energy is transferred; energy E = Pt |
Quick checks. A charge of 60 C passing in 20 s is a current of 60 ÷ 20 = 3.0 A. A 240 V appliance drawing 2.5 A uses P = 240 × 2.5 = 600 W, so in 120 s it transfers E = 600 × 120 = 7.2 × 10⁴ J.
2.2Series and parallel
| Series | Parallel | |
|---|---|---|
| Total resistance | R = R₁ + R₂ | 1/R = 1/R₁ + 1/R₂ |
| Current | The same through every component | Splits between branches, then adds back |
| Voltage | Divides between components, adding to the supply | The same across every branch |
| Remove one component | Everything stops — one path only | The other branch keeps working |
2.3Nuclear physics: what unstable nuclei do
A nucleus is written AZX: A is the mass number (protons + neutrons), Z is the atomic number (protons). Isotopes share Z and differ in A. When the ratio of neutrons to protons makes a nucleus unstable, it decays — and in every nuclear equation, the mass numbers must balance and the atomic numbers must balance.
| Decay | Emitted | Effect on the nucleus | Example | Stopped by |
|---|---|---|---|---|
| Alpha (α) | A helium nucleus, 42He | A falls by 4, Z falls by 2 | 23892U → 23490Th + 42He | A sheet of paper; a few cm of air. Most ionising |
| Beta-minus (β⁻) | An electron, 0−1e (a neutron becomes a proton) | A unchanged, Z rises by 1 | 146C → 147N + 0−1e | A few mm of aluminium |
| Gamma (γ) | A high-energy photon | A and Z both unchanged — the nucleus just loses excess energy | 6028Ni* → 6028Ni + γ | Only reduced — by thick lead or concrete. Least ionising |
Two more to be able to write from memory: 22688Ra → 22286Rn + 42He (alpha: 226 − 4 = 222 and 88 − 2 = 86) and 9038Sr → 9039Y + 0−1e (beta: mass unchanged, one more proton).
2.4Half-life
The half-life is the time for half the radioactive nuclei in a sample to decay. Decay is random for any single nucleus but utterly reliable in bulk, so after n half-lives the fraction remaining is (½)n.
| Half-lives elapsed | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Fraction remaining | 1 | 1/2 | 1/4 | 1/8 | 1/16 | 1/32 |
| Percentage remaining | 100% | 50% | 25% | 12.5% | 6.25% | 3.125% |
Iodine-131 has a half-life of 8.0 days. A hospital receives 80 g. How much is left after 24 days? 24 ÷ 8.0 = 3 half-lives, so 80 × (½)³ = 80 ÷ 8 = 10 g.
Carbon-14 has a half-life of 5730 years. A sample has 12.5% of the carbon-14 a living sample would have. How old is it? 12.5% = 1/8 = (½)³, so 3 half-lives have passed: 3 × 5730 = 17 190 years.
Always convert to a number of half-lives first. Halving three times is not "dividing by 6".
Linear motion and force
Five equations describe any object moving with constant acceleration, and three laws explain why it does. Learn to write down u, v, a, s and t before you pick an equation and most of this topic solves itself.
3.1Scalars and vectors
A scalar has size only. A vector has size and direction, and must be given one in every answer — "5 m s⁻¹" is an incomplete velocity. Scalars: distance, speed, mass, time, energy, temperature. Vectors: displacement, velocity, acceleration, force, momentum, weight.
The distinction bites immediately. Walk 300 m east then 100 m west: the distance travelled is 400 m, but the displacement is only 200 m east. Run a lap of a 400 m track in 50 s and your average speed is 8.0 m s⁻¹ while your average velocity is zero, because you finished where you started.
3.2The SUVAT equations
These apply whenever acceleration is constant. Vertical motion under gravity qualifies, with a = g = 9.8 m s⁻² directed downwards — decide once whether down is positive or negative and stay with it.
| Equation | What is missing from it | Reach for it when… |
|---|---|---|
| v = u + at | displacement s | You want a final velocity after a known time |
| s = ut + ½at² | final velocity v | You want a distance after a known time |
| v² = u² + 2as | time t | The question never mentions time — braking distances live here |
| s = ½(u + v)t | acceleration a | You know both velocities and the time |
| a = (v − u) ÷ t | displacement s | You want the acceleration itself |
1. A car accelerates from rest at 3.0 m s⁻² for 8.0 s. u = 0, a = 3.0, t = 8.0.
v = u + at = 0 + 3.0 × 8.0 = 24 m s⁻¹
s = ut + ½at² = 0 + ½ × 3.0 × 8.0² = ½ × 3.0 × 64 = 96 m
2. A stone is dropped from rest and falls for 2.0 s. u = 0, a = 9.8, t = 2.0.
v = 0 + 9.8 × 2.0 = 19.6 m s⁻¹ downwards
s = ½ × 9.8 × 2.0² = ½ × 9.8 × 4.0 = 19.6 m
3. A car travelling at 25 m s⁻¹ brakes to rest in 50 m. No time is given, so use v² = u² + 2as.
0 = 25² + 2a(50) → 0 = 625 + 100a → a = −625 ÷ 100 = −6.25 m s⁻²
The minus sign means the acceleration is opposite to the motion — it is a deceleration, and it must be there.
3.3Newton's three laws
- First law. An object stays at rest, or continues at constant velocity in a straight line, unless acted on by a net external force. The property that makes it do so is inertia, and inertia is measured by mass. Note the consequence: constant velocity means the forces are balanced, not that there are none.
- Second law. Fnet = ma. Acceleration is directly proportional to the net force, inversely proportional to mass, and in the direction of the net force. A 1200 kg car with a net forward force of 3600 N accelerates at 3600 ÷ 1200 = 3.0 m s⁻².
- Third law. If A exerts a force on B, then B exerts an equal and opposite force on A. The two forces are the same size, opposite in direction, of the same type — and crucially they act on different objects, which is why they never cancel each other out.
Weight is a force: W = mg. A 70 kg student weighs 70 × 9.8 = 686 N on Earth. Mass is a scalar measured in kilograms and never changes; weight is a vector measured in newtons and changes with location.
3.4Free-body diagrams and friction
- Friction always opposes relative motion (or attempted motion) between surfaces, and acts along the surface: f = μN, where μ is the coefficient of friction and N is the normal force.
- Static friction (before sliding starts) has a maximum value that is usually larger than kinetic friction (once sliding). That is why it takes a bigger shove to start a heavy box moving than to keep it moving.
- The normal force is perpendicular to the surface, and it is not automatically equal to the weight — push down on the block as well and N rises, which raises friction too.
- Normal force and weight are not a Newton's third law pair. Both act on the same object. The third-law partner of the block's weight is the block's gravitational pull on the Earth.
Momentum, energy and waves
Two conserved quantities and one model. Momentum and energy are both preserved in a closed system, which turns most collision problems into a single line of arithmetic — and waves are how energy travels without anything travelling with it.
4.1Momentum and impulse
Momentum is p = mv, measured in kg m s⁻¹. It is a vector, so in one dimension you must give it a sign: choose a positive direction and stick to it. A 1500 kg car at 20 m s⁻¹ has p = 1500 × 20 = 3.0 × 10⁴ kg m s⁻¹.
Impulse is the change in momentum, and it equals force multiplied by the time the force acts: FΔt = Δp = mΔv.
A 0.15 kg ball is served from rest to 30 m s⁻¹. The racquet is in contact for 0.010 s.
Δp = mΔv = 0.15 × 30 = 4.5 kg m s⁻¹
F = Δp ÷ Δt = 4.5 ÷ 0.010 = 450 N
Now read the equation the other way. For a given change in momentum, a longer contact time means a smaller force. That single rearrangement explains crumple zones, airbags, helmet padding, bending your knees when you land, and a cricketer drawing the hands back when catching.
4.2Conservation of momentum
In a closed system — no external net force — total momentum before = total momentum after. This holds in every collision and every explosion, elastic or not.
Perfectly inelastic (they stick together). A 2.0 kg trolley at 6.0 m s⁻¹ hits a stationary 4.0 kg trolley and they couple.
Before: p = (2.0 × 6.0) + (4.0 × 0) = 12 kg m s⁻¹
After: p = (2.0 + 4.0)v = 6.0v
6.0v = 12, so v = 2.0 m s⁻¹ in the original direction.
Check the energy: before, KE = ½ × 2.0 × 6.0² = 36 J; after, KE = ½ × 6.0 × 2.0² = 12 J. 24 J of kinetic energy has gone — into sound, heat and deformation. Momentum is conserved; kinetic energy is not.
Elastic. A 3.0 kg ball at 4.0 m s⁻¹ strikes a stationary 1.0 kg ball. Afterwards the 3.0 kg ball moves at 2.0 m s⁻¹ in the same direction. Find the speed of the 1.0 kg ball.
Before: p = 3.0 × 4.0 = 12 kg m s⁻¹
After: p = (3.0 × 2.0) + (1.0 × v) = 6.0 + v
6.0 + v = 12, so v = 6.0 m s⁻¹
Check the energy: before, KE = ½ × 3.0 × 16 = 24 J; after, KE = (½ × 3.0 × 4) + (½ × 1.0 × 36) = 6 + 18 = 24 J. Kinetic energy is conserved too, so this collision is elastic.
4.3Work, energy and the work–energy theorem
- Work W = Fs cos θ, in joules. Only the component of the force along the displacement does work — carrying a box horizontally does no work against gravity, because the force is vertical and the motion is not.
- Kinetic energy KE = ½mv². A 1000 kg car at 20 m s⁻¹ has ½ × 1000 × 400 = 2.0 × 10⁵ J. Because of the square, doubling the speed quadruples the kinetic energy — the reason speed limits matter so much.
- Gravitational potential energy GPE = mgh. Lifting 2.0 kg through 5.0 m stores 2.0 × 9.8 × 5.0 = 98 J.
- Work–energy theorem: the net work done on an object equals its change in kinetic energy, Wnet = ΔKE. A 20 N force acting over 5.0 m in the direction of motion does 100 J of work, so the object gains 100 J of kinetic energy.
- Conservation of energy: energy is never created or destroyed, only transferred or transformed. Drop something from 20 m with no air resistance and all the GPE becomes KE: mgh = ½mv², so v = √(2gh) = √(2 × 9.8 × 20) = √392 = 19.8 m s⁻¹. Note the mass cancels.
4.4The wave model
| Question | Working | Answer |
|---|---|---|
| A wave of frequency 50 Hz has a wavelength of 6.0 m. Its speed? | v = fλ = 50 × 6.0 | 300 m s⁻¹ |
| Sound travels at 340 m s⁻¹. Wavelength of a 170 Hz note? | λ = v ÷ f = 340 ÷ 170 | 2.0 m |
| Light of frequency 5.0 × 10₁⁴ Hz. Wavelength? | λ = c ÷ f = (3.00 × 10⁸) ÷ (5.0 × 10₁⁴) | 6.0 × 10⁻⁷ m (600 nm) |
| A wave has a period of 0.25 s. Its frequency? | f = 1 ÷ T = 1 ÷ 0.25 | 4.0 Hz |
Senior maths begins here.
Year 11 Methods is where algebra stops being a puzzle and becomes a language for change. Four topics — the functions themselves, the exponential and circular functions, the calculus that measures how they change, and the counting and probability that measure how likely things are. This is Units 1 and 2 of the QCAA General syllabus, and it counts.
The mapFour topics, two units
- Unit 1, Topic 1 — Functions and graphs. Function notation, domain and range, quadratics, the discriminant, completing the square, and the four transformations that move any graph.
- Unit 1, Topic 2 — Exponentials, logarithms and trigonometry. Index laws, growth and decay, logarithms as the undo button, radians, the unit circle, and the sine and cosine waves.
- Unit 2, Topic 1 — Calculus: differentiation. Limits, average versus instantaneous rate, first principles, the power rule, tangents, stationary points and optimisation.
- Unit 2, Topic 2 — Statistics and counting. Permutations and combinations, discrete random variables, probability distributions, expected value and the binomial idea.
QCAA assessment rewards three things you can practise separately: correct routine procedures (differentiate this, solve that), communication (working set out so a reader can follow it, with the answer stated in context and to the required accuracy), and justification (why your method is valid, and why your answer is reasonable). A right answer with no working is worth far less than it was in Year 10.
Rounding too early (carry full accuracy, round once at the end); dropping units and context («$15,360», not «15360»); and answering a different question from the one asked (a maximum area is not the x that produced it).
Functions and graphs
A function is a machine with one rule: put a number in, get exactly one number out. Everything in Methods — every derivative, every wave, every model — is built on that one idea and on knowing what its graph looks like before you calculate anything.
1.1Function notation
A function is a rule that assigns to each input exactly one output. Write it f(x) — read «f of x», and note that it does not mean f times x.
- Substituting. If f(x) = x² − 4x + 3 then f(2) = 4 − 8 + 3 = −1, and f(−1) = 1 + 4 + 3 = 8. Bracket the negatives or you will lose the sign.
- Solving f(x) = k is a different job: it asks which inputs give that output. f(x) = 3 means x² − 4x + 3 = 3, so x² − 4x = 0, x(x − 4) = 0, and x = 0 or x = 4.
- The vertical line test. A graph is a function only if no vertical line crosses it twice — that is the picture of «exactly one output». A circle fails it; a parabola passes.
1.2Domain and range
The domain is the set of inputs the rule is allowed to take; the range is the set of outputs it actually produces. In Methods you must state both, and there are only three things that ever restrict a domain.
| Function | What restricts it | Domain | Range |
|---|---|---|---|
| f(x) = 3x − 7 | Nothing — every real number works | all real x | all real y |
| f(x) = x² − 4x + 3 | Nothing restricts the input; the turning point restricts the output | all real x | y ≥ −1 |
| f(x) = √(x − 5) | You cannot square-root a negative | x ≥ 5 | y ≥ 0 |
| f(x) = 1 ÷ (x − 3) | You cannot divide by zero | all real x, x ≠ 3 | all real y, y ≠ 0 |
| Height of a ball, h(t) | The context: time cannot be negative, and the ball lands | 0 ≤ t ≤ landing time | 0 ≤ h ≤ max height |
It is not «all real y». The parabola opens upward and its lowest point is (2, −1), so no output below −1 is ever produced. Find the turning point first, then read the range off it — that is what completing the square is for.
1.3Quadratics and the discriminant
Every quadratic can be written y = ax² + bx + c. The discriminant Δ = b² − 4ac is the part of the quadratic formula under the square root, and on its own it tells you how many times the parabola meets the x-axis — before you solve anything.
| Example | Δ = b² − 4ac | Sign | What the graph does |
|---|---|---|---|
| x² − 4x + 3 | 16 − 12 = 4 | Δ > 0 | Two distinct real roots — cuts the x-axis twice (at x = 1 and x = 3) |
| x² − 4x + 4 | 16 − 16 = 0 | Δ = 0 | One repeated root — just touches the x-axis at x = 2 |
| x² − 4x + 5 | 16 − 20 = −4 | Δ < 0 | No real roots — never meets the x-axis at all |
| 2x² + 3x + 5 | 9 − 40 = −31 | Δ < 0 | No real roots; the whole parabola sits above the x-axis |
1.4Completing the square
Turning-point form y = a(x − h)² + k hands you the vertex (h, k) for free. Getting there is one move: halve the coefficient of x, square it, add it and take it straight back off.
- x² − 4x + 3. Half of −4 is −2; (−2)² = 4. So x² − 4x + 3 = (x² − 4x + 4) − 4 + 3 = (x − 2)² − 1. Vertex (2, −1); minimum value −1; range y ≥ −1.
- x² + 6x + 1. Half of 6 is 3; 3² = 9. So it becomes (x + 3)² − 9 + 1 = (x + 3)² − 8. Vertex (−3, −8).
- Check by expanding back. (x − 2)² − 1 = x² − 4x + 4 − 1 = x² − 4x + 3 ✓. Ten seconds, catches every sign slip.
- The axis of symmetry is x = h, which is also x = −b ÷ (2a). For x² − 4x + 3 that is 4 ÷ 2 = 2 ✓ — two routes, same answer.
1.5Transformations of graphs
Once you know the shape of a basic function, you never have to plot points again. Every change to the equation does exactly one thing to the picture.
| Written as | What happens to the graph of y = f(x) | Watch out |
|---|---|---|
| y = f(x) + k | Translation k units up (down if k is negative) | Nothing surprising — the sign matches the movement |
| y = f(x − h) | Translation h units to the right (left if h is negative) | Inside the bracket the sign is reversed: f(x + 3) moves 3 left |
| y = a f(x) | Dilation by factor a from the x-axis — stretched taller if a > 1 | x-intercepts do not move; every y-value is multiplied |
| y = f(bx) | Dilation by factor 1/b from the y-axis — squashed inward if b > 1 | Again reversed: f(2x) makes the graph narrower, not wider |
| y = −f(x) | Reflection in the x-axis — the whole graph flips upside down | A minimum becomes a maximum |
| y = f(−x) | Reflection in the y-axis — the graph flips left to right | y = x² looks unchanged because it is already symmetric |
Exponentials, logarithms and trigonometry
Two new families of function. One models anything that multiplies itself — money, populations, radioactive decay — and comes with its own undo button, the logarithm. The other models anything that repeats — tides, sound, seasons — and needs a new unit for angle: the radian.
2.1Index laws, revisited properly
| Law | Example | Why it is true |
|---|---|---|
| am × an = am+n | 2⁵ × 2³ = 2⁸ | Five twos next to three twos is eight twos |
| am ÷ an = am−n | x⁸ ÷ x⁵ = x³ | Five of the eights cancel |
| (am)n = amn | (x³)⁴ = x¹² | Four lots of three x’s |
| a0 = 1 | 7⁰ = 1 | an ÷ an = a0, and anything over itself is 1 |
| a−n = 1 ÷ an | 5⁻² = 1/25 | Keep subtracting indices past zero |
| a1/2 = √a | 91/2 = 3 | Because a1/2 × a1/2 = a1 |
2³ × 5² cannot be combined — different bases. Just evaluate: 8 × 25 = 200. And (a + b)² is not a² + b²; that is expansion, not an index law.
2.2Exponential growth and decay
An exponential function y = a·bx multiplies by the same factor b for every step in x. That is the definition of growth (b > 1) and decay (0 < b < 1), and it is why exponentials outrun every polynomial in the end.
- Doubling. A colony of 200 bacteria doubles every 3 hours. In 12 hours there are 12 ÷ 3 = 4 doublings, so N = 200 × 2⁴ = 200 × 16 = 3,200.
- Decay by a percentage. A car worth $30,000 loses 20% of its value each year, so it keeps 80%: V = 30000 × 0.8n. After 3 years V = 30000 × 0.512 = $15,360. (Check the chain: 30000 → 24000 → 19200 → 15360 ✓)
- Half-life. If a quantity halves every h units of time, the model is A = A₀ × (½)t/h. Carbon-14 has a half-life of about 5,730 years, so after 11,460 years exactly one quarter is left.
- The horizontal asymptote. y = 2x gets closer and closer to the x-axis on the left but never touches it. Exponential quantities approach zero; they never reach it.
2.3Logarithms — the undo button
A logarithm answers «what power?». By definition:
loga b = c means exactly the same as ac = b. So log₂32 = 5 because 2⁵ = 32; log₁₀1000 = 3 because 10³ = 1000; log₃81 = 4 because 3⁴ = 81. Read every logarithm out loud as a question about a power and it stops being mysterious.
| Log law | Worked example | Where it comes from |
|---|---|---|
| log(mn) = log m + log n | log 8 + log 2 = log 16 | Multiplying numbers adds their indices |
| log(m/n) = log m − log n | log 20 − log 2 = log 10 = 1 | Dividing numbers subtracts their indices |
| log(mp) = p log m | log 8 = log 2³ = 3 log 2 | A power is repeated multiplication |
| loga a = 1 and loga 1 = 0 | log₅ 5 = 1, log₅ 1 = 0 | a¹ = a and a⁰ = 1 |
- Exact solving. 3x = 81. Write 81 as 3⁴, so x = 4. Whenever both sides can be written to the same base, do that — it is exact and it is faster.
- When they cannot. 2x = 20 has no nice power. Take logs of both sides: x log 2 = log 20, so x = log 20 ÷ log 2 = 4.32 to 2 decimal places. (Sanity check: 2⁴ = 16 and 2⁵ = 32, so x must sit between 4 and 5 ✓)
- Domain. You can only take the logarithm of a positive number — there is no power of 10 that produces zero or a negative.
2.4Radian measure and the unit circle
Degrees are an arbitrary human choice (360 because the Babylonians liked 60). A radian is defined by the circle itself: the angle at the centre subtended by an arc equal in length to the radius. Since the whole circumference is 2πr, a full turn is 2π radians.
| Degrees | Radians | Degrees | Radians |
|---|---|---|---|
| 30° | π/6 | 120° | 2π/3 |
| 45° | π/4 | 180° | π |
| 60° | π/3 | 270° | 3π/2 |
| 90° | π/2 | 360° | 2π |
- Converting. Multiply by π/180 to go degrees → radians; by 180/π to come back. So 1 radian ≈ 57.3°.
- Arc length l = rθ, with θ in radians. A radius of 10 cm and an angle of 1.2 rad gives an arc of 12 cm — no π, no fractions of 360. That simplicity is the whole point of radians.
- Sector area A = ½r²θ. With r = 6 cm and θ = π/3, A = ½ × 36 × π/3 = 6π ≈ 18.85 cm².
2.5Sine and cosine graphs
Unroll the unit circle and you get a wave. For y = a sin(bx) and y = a cos(bx):
- Amplitude = |a| — how far the wave rises above and falls below its centre line. y = 4 sin(3x) has amplitude 4.
- Period = 2π ÷ b — how far along x before the pattern repeats. y = 4 sin(3x) has period 2π/3; y = sin x has period 2π.
- The difference between them is only a head start: cosine starts at its maximum (cos 0 = 1), sine starts at zero and rises (sin 0 = 0). Cosine is sine shifted a quarter-period left.
- Both are bounded. Whatever a and b are, the range of y = a sin(bx) is −|a| ≤ y ≤ |a| — because the unit circle never lets sine leave the interval from −1 to 1.
The drill below plots three of these waves live. Read the amplitude off the height and the period off the repeat distance, then type each equation and watch your guess snap onto the target.
Calculus: differentiation
Every rate you have ever met — speed, growth, cost per extra unit — was an average over an interval. Calculus asks the harder question: how fast is it changing right now, at a single instant? The answer is the gradient of a tangent, and there is a rule that finds it in one line.
3.1Average versus instantaneous rate of change
| Average rate of change | Instantaneous rate of change | |
|---|---|---|
| Question it answers | How much did y change per unit of x, over an interval? | How fast is y changing at one exact value of x? |
| On the graph | The gradient of the chord joining two points | The gradient of the tangent at one point |
| Formula | [f(b) − f(a)] ÷ (b − a) | f′(x), the derivative |
| For f(x) = x² | From x = 1 to x = 4: (16 − 1) ÷ 3 = 5 | At x = 1: f′(1) = 2 |
| Real-world name | Your average speed over the whole trip | What the speedometer reads at one moment |
3.2The limit idea, and first principles
You cannot find the gradient at a single point directly — gradient needs two points. So take a second point a distance h away, find the chord gradient, and then let h shrink towards zero. The value the chord gradients close in on is the limit, and that is the tangent gradient.
- The definition. f′(x) = the limit, as h approaches 0, of [f(x + h) − f(x)] ÷ h.
- Do it for f(x) = x². The numerator is (x + h)² − x² = x² + 2xh + h² − x² = 2xh + h².
- Divide by h (legal, because h is not yet zero): the chord gradient is 2x + h.
- Let h → 0: f′(x) = 2x. So at x = 1 the tangent gradient is 2, at x = 3 it is 6.
Putting h = 0 into [f(x + h) − f(x)] ÷ h gives 0 ÷ 0, which is meaningless. The whole method is: simplify first while h is still alive, cancel the h, and only then let it vanish. That is what a limit is for.
3.3The power rule
Nobody uses first principles for every function. Doing it once for x², x³, x⁴… reveals a pattern, and the pattern is the rule.
If y = xn then dy/dx = n xn−1 — bring the index down in front, then knock one off it.
If y = k·f(x) then dy/dx = k·f′(x) — constants come along for the ride.
If y = f(x) + g(x) then dy/dx = f′(x) + g′(x) — differentiate term by term.
| Function | Derivative | Note |
|---|---|---|
| y = x⁴ | dy/dx = 4x³ | Index 4 comes down, 4 − 1 = 3 left behind |
| y = 5x³ | dy/dx = 15x² | 5 × 3 = 15 |
| y = 3x² − 4x + 7 | dy/dx = 6x − 4 | The 7 vanishes: a constant does not change |
| y = x | dy/dx = 1 | x is x¹, so 1·x⁰ = 1 |
| y = 9 | dy/dx = 0 | A horizontal line has gradient zero everywhere |
| y = x⁵ − 2x³ | dy/dx = 5x⁴ − 6x² | Term by term, signs kept |
3.4Tangents, stationary points and their nature
- Gradient of a tangent. For f(x) = x² − 4x + 3, f′(x) = 2x − 4. At x = 3 the gradient is 2, and f(3) = 0, so the tangent is y − 0 = 2(x − 3), that is y = 2x − 6.
- Stationary points are where the tangent is horizontal: solve f′(x) = 0. For f(x) = x³ − 3x, f′(x) = 3x² − 3 = 0 gives x² = 1, so x = −1 or x = 1.
- Find the y-values too. f(−1) = −1 + 3 = 2 and f(1) = 1 − 3 = −2. The stationary points are (−1, 2) and (1, −2).
- Determine the nature with a sign test on f′. Just left of x = −1 (say x = −2): f′ = 12 − 3 = 9, positive. Just right (x = 0): f′ = −3, negative. Rising then falling is a local maximum. At x = 1, f′ goes from −3 (at x = 0) to 9 (at x = 2): falling then rising is a local minimum.
3.5Simple optimisation
Optimisation is stationary points with a story. The method never changes.
Problem. A rectangular paddock is fenced on three sides, using a straight river as the fourth side. There are 40 m of fencing. What dimensions give the greatest area?
1. Name the variables. Let the two sides perpendicular to the river be y metres each, and the side parallel to the river be x metres.
2. Constraint. Only three sides are fenced: x + 2y = 40, so x = 40 − 2y.
3. One-variable model. A = xy = (40 − 2y)y = 40y − 2y².
4. Differentiate and solve. dA/dy = 40 − 4y. Setting 40 − 4y = 0 gives y = 10.
5. Justify the maximum. dA/dy is positive for y < 10 and negative for y > 10, so y = 10 is a maximum, not a minimum.
6. Answer the actual question, in context. y = 10 m, x = 40 − 20 = 20 m, and the greatest area is A = 20 × 10 = 200 m².
Stopping at y = 10 without ever stating the area, and never justifying that it is a maximum. Both are explicitly assessed. Also check the domain makes sense: 0 < y < 20, since x must stay positive.
Statistics and counting
Probability begins with counting: to say how likely something is, you first have to know how many ways it can happen. Then a random variable turns a chance experiment into a number, and its expected value tells you what to bet on in the long run.
4.1Factorials, permutations and combinations
n! («n factorial») is n × (n−1) × … × 2 × 1, and it counts the arrangements of n distinct objects. 4! = 24, 5! = 120. By convention 0! = 1.
| Permutation — nPr | Combination — nCr | |
|---|---|---|
| Counts | Ways to choose r from n and arrange them | Ways to choose r from n, order irrelevant |
| The test question | Would swapping two chosen items give a different outcome? Yes | Would swapping two chosen items give a different outcome? No |
| Formula | n! ÷ (n − r)! | n! ÷ [r!(n − r)!] |
| Relationship | nCr = nPr ÷ r! — combinations are permutations with the r! reorderings divided out | |
| Example with n = 5, r = 3 | 5 × 4 × 3 = 60 | 60 ÷ 3! = 60 ÷ 6 = 10 |
| In words | Gold, silver and bronze from 5 runners | A 3-person committee from 5 people |
- Exact values worth knowing. 10C2 = (10 × 9) ÷ 2 = 45. 12C3 = (12 × 11 × 10) ÷ 6 = 1320 ÷ 6 = 220. 9C4 = (9 × 8 × 7 × 6) ÷ 24 = 3024 ÷ 24 = 126.
- The shortcut. For nCr, multiply r descending factors starting at n, then divide by r!. You never need to compute 12! itself.
- Symmetry. nCr = nCn−r, because choosing 3 of 12 to include is the same act as choosing 9 to leave out. 12C9 is also 220.
4.2Discrete random variables and distributions
A discrete random variable X assigns a number to each outcome of a chance experiment — the number of heads in five tosses, the score on a die, the number of faulty items in a box. Its probability distribution lists every value X can take alongside its probability.
Every probability lies between 0 and 1 inclusive, and they add to exactly 1. If a table is missing one probability, that second rule finds it: if P(1) = 0.2 and P(2) = 0.5, then the remaining value must carry 1 − 0.7 = 0.3.
| x | 0 | 1 | 2 | 3 | Total |
|---|---|---|---|---|---|
| P(X = x) | 0.1 | 0.3 | 0.4 | 0.2 | 1.0 ✓ |
| x × P(X = x) | 0 | 0.3 | 0.8 | 0.6 | E(X) = 1.7 |
- Expected value E(X) = Σ x × P(X = x) — a probability-weighted average. Above: 0(0.1) + 1(0.3) + 2(0.4) + 3(0.2) = 1.7.
- It need not be a possible outcome. For one roll of a fair die, E(X) = (1+2+3+4+5+6) ÷ 6 = 21/6 = 3.5 — and you can never roll 3.5. E(X) is the long-run average, not a prediction of one trial.
- Reading it as a decision tool. A $2 raffle ticket with E(prize) = $1.40 loses 60 cents per ticket on average. That is what expected value is for.
4.3The binomial idea
A huge family of problems shares one shape. A situation is binomial when all four conditions hold:
| Condition | Coin tossed 5 times, counting heads | Counterexample |
|---|---|---|
| Fixed number of trials, n | n = 5, decided in advance | «Toss until you get a head» — n is not fixed |
| Only two outcomes per trial | Head or tail | Rolling a die and recording the number — six outcomes |
| Constant probability p | p = 0.5 every toss | Drawing cards without replacement — p changes each draw |
| Independent trials | One toss tells you nothing about the next | Drawing names from a hat without replacing them |
- The count of ways is a combination: the number of ways to get exactly 2 heads in 5 tosses is 5C2 = 10 — HHTTT, HTHTT, and eight more.
- The probability. P(X = k) = nCk × pk × (1 − p)n−k. So P(exactly 2 heads in 5 fair tosses) = 10 × (0.5)² × (0.5)³ = 10 ÷ 32 = 0.3125.
- Expected value. E(X) = np. A basketballer who makes 60% of shots and takes 20 shots expects 20 × 0.6 = 12 baskets.
Maths you will actually use.
General Mathematics is not «easy Methods». It is the mathematics of decisions: what a loan really costs, how much concrete a slab needs, which mobile plan wins, and what a set of data is honestly telling you. Four topics across QCAA Units 1 and 2, and every one of them turns up in adult life within a year of leaving school.
The mapFour topics, two units
- Unit 1, Topic 1 — Money and financial mathematics. Percentage change, simple against compound interest, depreciation, loans and repayments, budgeting.
- Unit 1, Topic 2 — Measurement and geometry. Units and conversions, perimeter, area, volume and surface area, Pythagoras and right-angle trigonometry, similar figures and how area and volume scale.
- Unit 2, Topic 1 — Graphs, networks and linear relationships. Linear models, simultaneous equations in context, step graphs, and reading a network of vertices and edges.
- Unit 2, Topic 2 — Data and statistics. Types of data, summary statistics, box plots and five-number summaries, outliers, comparing distributions, scatterplots and correlation.
Almost every question is set in a context, and the marks follow the context: choose a reasonable model, carry out the calculation accurately, then interpret the answer in the situation with correct units and sensible rounding. «20230» is not the answer; «the car is worth $20,230 after two years» is.
Round once, at the end. Rounding $4,764.064 to $4,764.06 is correct; rounding the interest rate or an intermediate balance first will drift your answer by dollars. Money is written to the cent, measurements to the accuracy the question gives you.
Money and financial mathematics
Interest is the price of time. Learn the difference between the two ways it is charged and you can already see through a car ad, a credit card and a home loan — because all three run on the same three formulas.
1.1Percentage change, and the one-step multiplier
Percentage change = (new value − old value) ÷ old value × 100. The sign carries the meaning: positive is an increase, negative is a decrease.
- A price rises from $80 to $92. Change = 12 ÷ 80 × 100 = 15% increase.
- A price falls from $250 to $200. Change = −50 ÷ 250 × 100 = 20% decrease.
- Use one multiplier, not two steps. A 20% discount means paying 80%: $65 × 0.8 = $52. A 10% rise means × 1.10.
- GST. Adding 10% GST multiplies by 1.1. Going backwards, a price that already includes 10% GST is 11 parts, so the GST inside $264 is 264 ÷ 11 = $24 (and the pre-GST price is $240).
$100 × 1.2 = $120, and $120 × 0.8 = $96. The percentages are taken from different bases. Always ask «percentage of what?»
1.2Simple interest against compound interest
| Simple interest | Compound interest | |
|---|---|---|
| Formula | I = Prt | A = P(1 + r)n |
| Interest is charged on | The original principal, every period | The current balance — so on the interest as well |
| $4,000 at 6% p.a. for 3 years | I = 4000 × 0.06 × 3 = $720 | A = 4000 × 1.06³ = $4,764.06 |
| Interest earned | $720 — total $4,720.00 | $764.06 — $44.06 more |
| Growth over time | A straight line | A curve that steepens — it is an exponential |
Use A = P(1 + r/k)kn, where k is the number of compounding periods per year. $5,000 at 6% p.a. compounded monthly for 2 years: the monthly rate is 0.06 ÷ 12 = 0.005 and there are 24 periods, so A = 5000 × 1.00524 = $5,635.80, and the interest is $635.80. Compounded annually the same deposit would reach only $5,618.00, so the extra $17.80 is purely the effect of compounding twelve times a year.
1.3Depreciation: two models, two answers
| Straight-line (flat rate) | Declining balance (reducing) | |
|---|---|---|
| Formula | V = V₀ − Dn | V = V₀(1 − r)n |
| Loses | The same dollar amount each year | The same percentage of the current value each year |
| $28,000 car, after 2 years | At $3,500 a year: 28000 − 7000 = $21,000 | At 15% a year: 28000 × 0.85² = $20,230.00 |
| The same car, after 3 years | 28000 − 10500 = $17,500 | 28000 × 0.85³ = $17,195.50 |
| Which is realistic? | Rare — used mainly for tax purposes | How cars actually behave: the big loss is in year one |
1.4Loans and repayments
A reducing-balance loan charges interest on what you still owe. Each repayment first pays that month’s interest; only what is left over reduces the debt. That is why the early repayments barely touch the principal.
| Month | Opening balance | Interest at 0.75% (9% p.a. ÷ 12) | Repayment | Closing balance |
|---|---|---|---|---|
| 1 | $20,000.00 | $150.00 | $500.00 | $19,650.00 |
| 2 | $19,650.00 | $147.38 | $500.00 | $19,297.38 |
| 3 | $19,297.38 | $144.73 | $500.00 | $18,942.11 |
- Read row 1. Of that first $500, exactly $150 vanished as interest; only $350 reduced the debt.
- The balance falls, so the interest falls. $147.38 in month 2, $144.73 in month 3 — and the amount coming off the principal grows every month.
- Why a longer term costs so much more. Stretching the same loan over more months means more interest charged on a slowly shrinking balance. The monthly repayment falls; the total repaid rises sharply.
1.5Budgeting
A budget is a subtraction with consequences: net income − total expenses = surplus or deficit. Work in one consistent period — usually per week or per fortnight.
| Weekly item | Amount | Fixed or variable? |
|---|---|---|
| Net pay (after tax) | $1,250 | Income |
| Rent | $480 | Fixed — the same every week |
| Food and groceries | $180 | Variable — where a budget can flex |
| Transport and fuel | $95 | Variable |
| Utilities and phone | $60 | Mostly fixed |
| Everything else | $150 | Variable |
| Total expenses | $965 | 480 + 180 + 95 + 60 + 150 |
| Weekly surplus | $285 | 1250 − 965 — savings, or a buffer |
Measurement and geometry
Every trade runs on this topic: how much turf, how much concrete, how long a rafter, what angle a ramp makes. The mathematics is not hard — the marks are lost on units, on forgetting to halve a diameter, and on rounding too soon.
2.1Units and conversions
| Kind | Conversion | Why the number is what it is |
|---|---|---|
| Length | 1 m = 100 cm = 1,000 mm; 1 km = 1,000 m | One dimension, so the factor is used once |
| Area | 1 m² = 10,000 cm² | 100 × 100 — the factor is used twice |
| Area (land) | 1 hectare = 10,000 m² | A square 100 m by 100 m |
| Volume | 1 m³ = 1,000,000 cm³ | 100 × 100 × 100 — three times |
| Capacity | 1 cm³ = 1 mL, so 1 L = 1,000 cm³ and 1 m³ = 1,000 L | The bridge between space and liquid |
1 m² is not 100 cm². Draw the square: it is 100 cm along each side, so 100 × 100 = 10,000 cm². The same logic makes 1 m³ a million cubic centimetres.
2.2Perimeter, area, volume, surface area
| Shape or solid | Formula | Worked example |
|---|---|---|
| Circle | C = 2πr, A = πr² | r = 5 cm: C = 31.42 cm, A = 78.54 cm² |
| Trapezium | A = ½(a + b)h | a = 8, b = 12, h = 5: ½(20)(5) = 50 cm² |
| Any prism | V = end-face area × length | Triangle 6 × 4: ½(24) = 12 cm², × 10 = 120 cm³ |
| Cylinder | V = πr²h | r = 5, h = 20: π(25)(20) = 500π = 1,571 cm³ = 1.571 L |
| Cylinder surface | SA = 2πr² + 2πrh | Same cylinder: 50π + 200π = 250π = 785.40 cm² |
| Rectangular prism surface | SA = 2(lw + lh + wh) | 5 × 3 × 10: 2(15 + 50 + 30) = 190 cm² |
2.3Pythagoras and right-angle trigonometry, applied
a² + b² = c² holds in every right-angled triangle, with c the hypotenuse — the side opposite the right angle, and always the longest. A 5 m ladder with its foot 1.4 m from the wall reaches √(25 − 1.96) = √23.04 = 4.8 m up the wall.
- Finding a length. A tower’s angle of elevation is 32° from a point 45 m away. Height = 45 × tan 32° = 45 × 0.62487 = 28.1 m (1 decimal place).
- Finding an angle. A roof rises 7 m over a horizontal run of 24 m. tan θ = 7/24 = 0.29167, so θ = tan⁻¹(0.29167) = 16.3°.
- Sanity-check every answer. The hypotenuse must be the longest side; an angle of elevation to something taller than you must be under 90°; and a tan ratio below 1 always means an angle below 45°.
2.4Similar figures: k, k² and k³
Two figures are similar when one is an exact enlargement of the other: all matching angles equal, all matching lengths in the same ratio. That ratio is the scale factor k — and it does not apply equally to lengths, areas and volumes.
| Quantity | Multiplied by | Scale factor k = 2 | Model at 1 : 20 (k = 20) |
|---|---|---|---|
| Any length — side, height, perimeter | k | × 2 | × 20 |
| Any area — surface, cross-section | k² | × 4 | × 400 |
| Any volume — capacity, mass if the material is the same | k³ | × 8 | × 8,000 |
- Worked example. Two similar cylinders have radii 3 cm and 6 cm, so k = 2. If the smaller holds 54 cm³, the larger holds 54 × 2³ = 432 cm³ — eight times, not twice.
- Why this matters outside the classroom. Doubling the length of a shipping container multiplies its steel surface by 4 and its capacity by 8. It is also why a photograph enlarged by a factor of 3 needs 9 times as much ink.
Graphs, networks and linear relationships
A straight line is the most useful model in applied mathematics: a fixed amount plus a steady rate. Then two lines meeting solves a real choice, a step graph handles the charges that jump, and a network turns roads, cables and friendships into mathematics.
3.1Linear models and what the numbers mean
In y = mx + c applied to a real situation, the two numbers always mean the same two things: c is the fixed amount you pay before anything happens, and m is the rate — the extra cost for each extra unit. Interpreting them in context is worth as many marks as the calculation.
3.2Simultaneous equations in context
- Comparing two plans. Plan A costs $20 a month plus 20c a minute: C = 0.2m + 20. Plan B costs $5 plus 50c a minute: C = 0.5m + 5. They cost the same when 0.2m + 20 = 0.5m + 5, so 15 = 0.3m and m = 50 minutes, both costing $30. Below 50 minutes Plan B is cheaper; above 50 minutes Plan A wins.
- A ticket problem. Adult tickets are $18 and child tickets $12. Two hundred tickets were sold for $3,120. With a + c = 200 and 18a + 12c = 3120, substitute c = 200 − a: 18a + 2400 − 12a = 3120, so 6a = 720 and a = 120 adults, c = 80 children. Check: 120(18) + 80(12) = 2160 + 960 = 3120 ✓
- Always check in BOTH original equations and answer in words. A pair of numbers that satisfies only one equation is not a solution.
Two lines with the same gradient but different intercepts are parallel: they never meet, so the equations have no solution — in context that usually means one option is always cheaper. Two equations describing the same line have infinitely many solutions.
3.3Piecewise and step graphs
Not every charge grows smoothly. A step graph stays flat across a whole bracket and then jumps — parking, postage, and income tax brackets all behave this way.
| Time parked | Fee | Reading it |
|---|---|---|
| Up to 2 hours | $5 | Every stay from 1 minute to 2 hours costs the same |
| Over 2 and up to 4 hours | $9 | A 3½-hour stay costs $9 — not $9 plus a part-hour |
| Over 4 and up to 8 hours | $14 | Staying 4 hours 1 minute costs $5 more than staying 4 hours |
| Over 8 hours | $20 | The final step, flat for the rest of the day |
On a step graph one end of each step is filled (included) and the other is open (excluded). «Up to and including 2 hours» charges $5 at exactly 2 hours; the $9 step starts the instant after. Reading the wrong end of a step is the classic lost mark.
3.4Graphs and networks
A network (or graph, in this sense) is just dots and lines: a vertex is a point — a town, a person, a router — and an edge is a connection between two vertices. The degree of a vertex is the number of edges meeting at it.
Data and statistics
Statistics is the art of saying what a pile of numbers actually shows — and of noticing when someone is using the same numbers to say something they do not show. Centre, spread, shape, outliers: four questions, asked in that order, every time.
4.1Types of data
| Type | Meaning | Examples | Sensible display |
|---|---|---|---|
| Categorical — nominal | Named groups with no natural order | Eye colour, suburb, favourite sport | Bar chart, frequency table |
| Categorical — ordinal | Named groups that do have an order | T-shirt size S/M/L/XL, agree-to-disagree scales | Bar chart kept in order |
| Numerical — discrete | Counted; only whole values are possible | Number of siblings, cars in a car park | Column graph, dot plot |
| Numerical — continuous | Measured; any value in a range is possible | Height, time, mass, temperature | Histogram, box plot |
A postcode, a jersey number and a phone number are written with digits but are nominal categorical data — the average of a set of postcodes means nothing. Ask whether arithmetic on the values would make sense.
4.2Summary statistics, worked in full
Take these eleven values, already sorted:
4, 7, 8, 11, 11, 14, 15, 18, 21, 24, 43
| Statistic | Value | How it was found |
|---|---|---|
| n | 11 | Count the values |
| Mean | 16 | Total 176 ÷ 11 = 16 exactly |
| Median | 14 | The 6th value of 11, once sorted — five below, five above |
| Mode | 11 | The only value appearing twice |
| Range | 39 | 43 − 4 |
| Q1 (lower quartile) | 8 | Median of the lower five: 4, 7, 8, 11, 11 |
| Q3 (upper quartile) | 21 | Median of the upper five: 15, 18, 21, 24, 43 |
| IQR | 13 | Q3 − Q1 = 21 − 8 — the spread of the middle half |
| Standard deviation (s) | ≈ 10.8 | The typical distance of a value from the mean, the ÷(n−1) version your calculator calls s |
The median is the 6th value. The lower half is the five values below it and the upper half is the five above it — the median itself belongs to neither. (With an even n, split straight down the middle and both halves are complete.)
4.3Outliers and the box plot
A value is an outlier if it lies more than 1.5 × IQR beyond a quartile. Here 1.5 × 13 = 19.5, so the fences are at 8 − 19.5 = −11.5 and 21 + 19.5 = 40.5. The minimum 4 sits comfortably inside; the maximum 43 is above 40.5, so it is an outlier and is plotted as its own dot.
4.4Comparing distributions
When two box plots are set side by side, compare them in a fixed order and always in context:
- Centre. Which median is higher, and by how much? «Class B’s median of 68 is 9 marks above Class A’s 59.»
- Spread. Compare the IQRs (and the ranges). A smaller IQR means more consistent results, which is often the more useful finding.
- Shape. Symmetric, or skewed? A long right whisker is positive skew; a long left whisker is negative skew.
- Outliers. Note any, and say what they might mean — a data-entry error, or a genuinely unusual case worth investigating.
The mean uses every value, so a single extreme value drags it. The median only cares about position, so it barely moves. In our set, deleting the outlier 43 drops the mean from 16 all the way to 13.3, but moves the median only from 14 to 12.5. That is why house prices and incomes are reported as medians.
4.5Scatterplots, correlation and causation
- Set the axes properly. The explanatory variable (the one you think does the explaining) goes on the horizontal axis; the response variable goes on the vertical.
- Describe a scatterplot in four words: direction (positive or negative), form (linear or curved), strength (strong, moderate, weak) and outliers.
- Correlation is not causation. Ice-cream sales and drownings rise together every summer. Ice cream does not drown anyone: hot weather drives both. That hidden third variable is a confounding variable.
- Other explanations to rule out before claiming cause: coincidence in a small sample, and reversed causation (does A cause B, or does B cause A?).
Nobody writes by accident.
Senior English is not about liking a text. It is about proving how a text works on the person reading it, and why the writer built it that way. Four topics across QCAA Units 1 and 2: reading perspective, reading culture, writing analysis, and writing persuasion.
The mapFour topics, two units
- Unit 1, Topic 1 — Perspectives and texts. How texts represent a perspective; purpose, audience and context; denotation and connotation; register; and the choices a writer makes.
- Unit 1, Topic 2 — Texts and culture. How people and places are represented, the cultural assumptions a text carries, whose voice is heard and whose is missing, and intertextuality.
- Unit 2, Topic 1 — Textual analysis: the craft. Close analysis of language and structure, embedding evidence, and building the analytical essay paragraph by paragraph.
- Unit 2, Topic 2 — Persuasion and the public sphere. Ethos, pathos and logos; argument and rebuttal; logical fallacies; analysing persuasive media; and writing to persuade a defined audience.
A C-grade response says what the text contains: «the writer uses a metaphor». An A-grade response says what that choice does, and to whom: «by reducing the city to a furnace, the writer makes the heat feel industrial and inescapable, positioning the reader to read a weather report as a warning». Naming the technique is the cheapest mark in the paper; the effect is where the marks live.
Retelling — the marker has read the text; describing the plot proves nothing. Quote dumping — a quotation parachuted in on its own sentence, unexplained. Feelings as evidence — «this makes the reader sad» with no language named and no reason given.
Perspectives and texts
Every text is written from somewhere, by someone, for someone. Once you can name the position a text is written from, you stop being a passenger in it and start being a reader of it.
1.1Perspective and representation
- A perspective is the position or point of view from which a text presents its subject — the angle the world is seen from. It is not the same as an opinion, and it is not always stated.
- A representation is the version of a person, place, event or idea that a text constructs for its reader. The word is deliberate: a representation is made, not found. A tourism advertisement does not record a beach; it builds one.
- Representations are made by selection (what goes in), omission (what is left out), emphasis (what is placed first, repeated, or given most space) and word choice.
- Texts position readers: they invite you to feel a certain way about what they show. Noticing the invitation is the first act of analysis.
1.2Purpose, audience and context
1.3Denotation and connotation
Denotation is a word’s literal, dictionary meaning. Connotation is the freight it carries — the associations, attitudes and feelings that come with it. Two words can denote the same thing and connote opposite things, and that gap is where persuasion lives.
| Shared denotation | Approving word | Disapproving word | What the choice does |
|---|---|---|---|
| Careful with money | thrifty | stingy | Turns a virtue into a meanness without changing a single fact |
| Will not change position | determined | stubborn | Praises or condemns the identical behaviour |
| Wants to know things | curious | nosy | Recasts interest as intrusion |
| Sure of oneself | confident | arrogant | Decides for the reader how to judge the person |
| A place one lives | home | residence | Warmth and belonging, against distance and officialdom |
1.4Register, tone and mood
- Register is the level of formality and the kind of language a situation calls for. A safety notice, a text to a friend and a job application describe the same person in three registers — and getting it wrong is itself a message.
- Tone is the attitude the text takes towards its subject and its reader: sardonic, urgent, affectionate, clinical. Tone is created by word choice, sentence length, punctuation and what the writer chooses to dwell on.
- Mood is the feeling created in the reader. Tone belongs to the text; mood belongs to you. A cheerful tone can create an uneasy mood — and a writer who does that on purpose is worth writing about.
- Diction is the technical name for a writer’s choice of words; syntax is the arrangement of those words into sentences. Short sentences can create urgency; a long accumulating sentence can create weight or exhaustion.
Never write «the writer uses language». Name the level: diction (which word), syntax (how the sentence is built), structure (where it sits in the text), register (how formal), tone (what attitude). Then say what it does. Precision in the naming buys you precision in the explanation.
Texts and culture
Texts do not float free of the culture that made them. They carry its assumptions, repeat its habits, amplify some voices and leave others out — usually without ever announcing that they are doing it.
2.1Cultural assumptions and values
- A cultural assumption is a belief a text takes for granted rather than argues for — that success means owning things, that the bush is empty, that a family looks a particular way. Because it is assumed, it is never defended, which is exactly what makes it powerful.
- Values are what a text treats as good; attitudes are the stances it takes towards particular things. A text can state neither and still make both perfectly clear.
- A stereotype is a fixed, simplified representation of a whole group, in which one trait stands in for every member. Its giveaway is predictability: every character from that group behaves the same way.
- To find the assumptions, read for what is never questioned. The argument a text does not bother to make is the one it is most confident you already accept.
2.2Whose voice, and whose silence
Representation is also a question of who gets to speak. In any text, ask: who narrates? Who is described but never speaks? Whose experience would change the story if it were included?
| Question | What to look for | Why it matters |
|---|---|---|
| Who narrates? | First or third person; whose thoughts we are allowed inside | The narrator’s access decides whose interior life feels real |
| Who is spoken about but not heard? | Groups that appear only as description, scenery or problem | Being described rather than heard is a form of powerlessness |
| What is the silence? | An experience the text never mentions at all | What is absent shapes a reader as strongly as what is present |
| Who is the assumed reader? | What the text expects you to already know or accept | It reveals which audience the text was really built for |
A dominant (or preferred) reading accepts the position the text invites. A negotiated reading accepts some of it and resists the rest. A resistant reading questions the position deliberately — reading against the text. A resistant reading is not a misreading: it is a reading that declines the invitation, and it must still be argued from evidence in the text.
2.3Intertextuality
Intertextuality is the way texts take part of their meaning from other texts — echoing them, adapting them, mocking them, or answering back to them. Spot the borrowed text and you gain a second layer of meaning for free.
| Kind | What it does | Example |
|---|---|---|
| Allusion | A brief, indirect reference that assumes you will recognise it | Calling a policy a Trojan horse, or a speech echoing a famous refrain |
| Parody | Imitates the style of another text in order to mock it or its subject | A sketch that copies the look and voice of a nightly news bulletin |
| Adaptation | Moves a text into another form or setting, keeping the story | A stage play made from a well-known novel; a film that relocates a Shakespeare plot to a modern school |
| Retelling | Tells a known story from a different point of view — often a silenced one | Jean Rhys’s Wide Sargasso Sea, which gives a voice and a history to the first wife locked away in Charlotte Brontë’s Jane Eyre |
Do three things: name the text being drawn on, say what the reader is expected to bring from it, and say what the new text does with that expectation — confirm it, complicate it, or overturn it. A retelling that gives the silenced character a voice is doing the third.
Textual analysis: the craft
This is the topic where marks are actually won. Close analysis means reading at the level of the individual choice — this word, this sentence break, this order of events — and then building an essay that argues one claim from beginning to end.
3.1What close analysis actually looks at
| Level | What to notice | Terms you should be using |
|---|---|---|
| Word | The exact word chosen over its near-synonyms, and its connotations | Diction, connotation, emotive language, jargon |
| Image | Comparisons and sensory detail, and what the comparison smuggles in | Metaphor, simile, personification, imagery, symbol |
| Sentence | Length, rhythm, what is delayed to the end, what is repeated | Syntax, repetition, anaphora, tricolon, short declarative |
| Sound | How the line moves when read aloud | Alliteration, assonance, sibilance, rhythm |
| Structure | Order of events, framing, what is placed beside what, what recurs | Juxtaposition, motif, foreshadowing, framing, climax |
| Whole text | Who speaks, how formal it is, what attitude it takes | Point of view, register, tone, perspective |
3.2Embedding evidence
A quotation is not evidence until it is inside your own sentence, doing grammatical work. Compare:
| Sentence | Why | |
|---|---|---|
| Weak | The writer uses a metaphor. «The city was a furnace.» This shows it was hot. | The quotation stands alone, the technique is only named, and the effect is a restatement of the literal meaning |
| Better | The writer describes the city as «a furnace», which suggests extreme heat. | Embedded and grammatical, but «suggests extreme heat» still only paraphrases |
| Strong | By reducing the city to «a furnace», the writer makes the heat feel industrial and inescapable, positioning the reader to read a weather report as a warning. | Technique, evidence and effect in one sentence, with the effect on the reader named |
- Keep quotations short — a phrase, often a single word. Long quotations fill space without proving anything, and they hide your argument.
- Square brackets mark a word you have altered or added so the quotation fits your sentence grammatically. An ellipsis marks words you have cut from the middle.
- Analytical present tense. The writer argues; the poem opens. Use it consistently, and write in third person.
- Never quote to prove a fact of plot. Quote to prove a claim about how the text works.
3.3Building the analytical essay
A contention must be arguable. «The poem is about loss» is a topic, not a contention — nobody could disagree. «The poem refuses the comfort its own imagery keeps offering, leaving the reader without the consolation the form promises» is a contention: someone could argue the opposite, which means it is worth proving.
Persuasion and the public sphere
Every day someone tries to move you: an editorial, an advertisement, a post, a politician. The tools they use are two and a half thousand years old and have not changed. Learn to name them and you can both resist them and use them.
4.1The three appeals
Aristotle named three ways a speaker can move an audience, and every persuasive text still runs on some mixture of them.
| Appeal | Works on | Sounds like | Its weakness |
|---|---|---|---|
| Ethos — credibility | Whether you trust the speaker | «As a nurse of twenty years…», «I have no financial interest in this» | Credentials in one field do not transfer to another |
| Pathos — emotion | What you feel about the subject | «Picture your own child waiting in that corridor» | Feeling strongly is not the same as being right |
| Logos — reasoning | Whether the argument holds together | «Here is the arithmetic: 400 beds for 1,200 patients» | Numbers can be true and still be selected to mislead |
| Kairos — timing | Why this argument, now | «We have three weeks before the decision is made» | Manufactured urgency is a common trick |
«This is pathos» earns almost nothing. Say what the appeal is doing and to whom: «by asking the reader to picture their own child in the corridor, the writer converts a funding statistic into a personal threat, making disagreement feel like indifference». Same observation, three times the marks.
4.2The shape of an argument
- Contention. The single position the piece exists to prove, stated early and never lost sight of.
- Arguments and evidence. Each reason gets its own paragraph, supported by something a reader can check: statistics, expert opinion, examples, precedent.
- Rebuttal. Name the strongest objection to your own case and answer it. Anticipating it makes you look considered; ignoring it lets a reader think you did not know.
- Concession. Granting a small, true point that costs you nothing buys credibility for the point that matters.
- Call to action. End by saying what should now happen and who should do it. A persuasive piece that ends in agreement but no action has half-finished its job.
| Device | What it is | What it does to a reader |
|---|---|---|
| Inclusive language | «We», «our», «all of us» | Places the reader inside the writer’s group before any argument is made |
| Rhetorical question | A question asked for effect, not for an answer | Makes the reader supply the answer themselves, so it feels like their own conclusion |
| Anaphora | Repeating the same opening words across successive clauses | Builds rhythm and insistence; the repetition itself feels like accumulating proof |
| Tricolon | A group of three — the rule of three | Sounds complete and memorable, which makes a claim easier to accept |
| Emotive language | Words chosen for their connotations, not their denotation | Decides the reader’s judgement before they have weighed the facts |
| Anecdote | A short personal story | Makes an abstract issue concrete and hard to argue with, though one case is not evidence |
4.3Logical fallacies
A fallacy is an argument that looks like reasoning but is not. Naming the fallacy is the cleanest possible rebuttal.
| Fallacy | What it does | Example |
|---|---|---|
| Ad hominem | Attacks the person instead of the argument | «You would say that — you have never run a business.» |
| Straw man | Misrepresents the opposing case so it is easier to defeat | «They want a bike lane, so they want to ban cars.» |
| False dilemma | Offers only two options when more exist | «Either we build the road or the town dies.» |
| Slippery slope | Claims one small step must lead to an extreme end, with no reason given | «Allow this and within a year nothing will be legal.» |
| Bandwagon | Treats popularity as proof | «Nine out of ten people agree, so it must be right.» |
| Hasty generalisation | Draws a sweeping conclusion from far too few cases | «Two students were late, so this generation has no discipline.» |
| Circular reasoning | Uses the conclusion as its own reason | «It is the best option because nothing else is as good.» |
| Post hoc | Assumes that because B followed A, A caused B | «Crime fell after the cameras went in, so the cameras cut crime.» |
4.4Analysing persuasive media, and writing your own
- Find the contention first. Everything else in the text is in service of it. If you cannot state it in one sentence, you cannot analyse the text.
- Track the tone as it shifts. Persuasive pieces often open reasonably and harden later, or open in outrage and end in appeal. The shift is a deliberate choice and worth writing about.
- Read the visuals as argument. A photograph’s angle, a headline’s size, the colour of a graph, what is cropped out — these persuade alongside the words, and the analysis is the same: technique, effect, purpose.
- Writing your own: define the audience before the first sentence. The register, the evidence you choose and the objections you must answer all follow from who is reading. A letter to a council, a school assembly speech and an online comment on the same issue are three different texts.
History is an argument about evidence.
Senior Modern History is not a memory test. It is a skill: read a source, judge what it can and cannot tell you, and build a case. Four topics — the craft itself, the ideas that broke the old world, the movements that widened who counted as a citizen, and Australia's own version of the same story.
The mapUnits 1 and 2, four topics
- Unit 1, Topic 1 — The historian's craft. Provenance, reliability, usefulness, corroboration, and why interpretations change.
- Unit 1, Topic 2 — Ideas that changed the world. The Enlightenment, the French Revolution of 1789, and the spread of nationalism.
- Unit 2, Topic 1 — Movements for change. Abolition, women's suffrage, the US civil rights movement, and what makes a movement win.
- Unit 2, Topic 2 — National experiences: Australia in the modern world. Federation, the World Wars, White Australia and its dismantling, and Indigenous rights.
Knowledge — the right event, the right year, the right order. Source analysis — a judgement about a source that names its provenance and separates reliability from usefulness. Argument — a contention, supported by specific evidence, that answers the question actually asked.
A dateless generalisation earns nothing. "Conditions were bad" is worth no marks; "the Commonwealth Franchise Act of 1902 enfranchised women federally while excluding most Aboriginal and Torres Strait Islander people" is worth several.
The historian's craft: evidence, and what it will bear
Every other topic in this course depends on this one. History is not a list of things that happened; it is a set of claims about the past, each of which must be defended from sources — and every source was made by someone, for a reason.
1.1Primary and secondary sources
The division is about the source's relationship to the event, not about how old or how serious it looks.
| Primary source | Secondary source | |
|---|---|---|
| Definition | Created at the time of the event, by someone connected to it | Created later, interpreting the event using other sources |
| Examples | A trench diary from 1916; the printed Declaration of the Rights of Man, 1789; a 1963 news photograph; a census return; a ration book | A textbook chapter; a documentary; a historian's journal article; an encyclopedia entry |
| What it gives you | Direct traces — but always one person's angle on the event | Context, synthesis and an argument — but at second hand |
| The catch | Being "there" does not make it true or complete | A secondary source is a primary source for the time it was written in |
A 2020 documentary about the Terror is a secondary source about 1793. But if your question is "how did the twenty-first century remember the French Revolution?", exactly the same film becomes a primary source. Always classify a source against the question you are asking.
1.2Provenance: the first question, every time
Provenance is the origin of a source: who made it, when, where, for whom, and why. Nothing sensible can be said about a source until its provenance is established, because every judgement that follows depends on it.
- Who. A general's despatch, a private's letter and a war correspondent's report describe the same battle from three positions with three different sets of interests.
- When. Written on the day, or in a memoir forty years later? Later means more perspective — and more time for memory to reshape the story into something the writer can live with.
- For whom. A private diary, a letter home passed by the censor, and a recruiting poster have three different audiences and therefore three different levels of candour.
- Why. Purpose is the strongest single clue to distortion. Sources made to persuade, to recruit, to excuse or to sell are shaped by that job.
1.3Reliability and usefulness are different judgements
This is the distinction senior History examiners test hardest, and the one students most often collapse into one.
| Reliability | Usefulness | |
|---|---|---|
| The question it answers | Can I trust this source to be accurate about what it claims? | Does this source help me answer my question? |
| What it depends on | The source alone — its author, purpose, distance from the event, and whether other evidence corroborates it | The source and the question. Change the question and the usefulness changes |
| Worked case | A 1917 recruiting poster is unreliable about the reality of the trenches: it was made to persuade, and it shows what the state wanted believed | The same poster is highly useful as evidence of government propaganda technique and of the appeals thought likely to work on the public |
| The rule | A source can be completely unreliable and still be extremely useful. What it is unreliable about is precisely what it is useful for. | |
Bias is not a reason to throw a source away, and "this source is biased" is not an analysis. Every source has a position. The analytical move is to say which way it leans, why its provenance makes it lean that way, and what it is still good evidence of.
Corroboration is the test that turns a single claim into a supported one: check it against sources that are independent of it. Two newspapers that both reprinted the same wire report are not independent, so their agreement proves nothing.
1.4Historiography: why interpretations change
Historiography is the study of how historians' accounts of a topic have changed over time. Interpretations shift for four reasons, and none of them is that the past changed.
- New evidence. Archives open — Soviet archives after 1991 rewrote a great deal of Cold War history.
- New questions. Once historians began asking about women, workers, colonised peoples and children, sources that had sat unread for a century suddenly mattered.
- New methods. Oral history, statistical analysis and digitised records reach material that traditional political history could not.
- The historian's own context. Writers work inside their own society's concerns. That is why contestability — genuine, informed disagreement between historians — is normal rather than a failure.
1. Provenance. Name the type, author, date and purpose in one sentence: "a British recruiting poster issued in 1915 by the Parliamentary Recruiting Committee, intended to raise volunteers."
2. Content. Quote or describe one specific detail. Not "it shows soldiers" — "it shows a smiling, uninjured soldier waving from a clean trench."
3. Reliability. Judge accuracy and give the reason from the provenance: "as a persuasive document it omits casualties, so it is not reliable evidence of trench conditions."
4. Usefulness, tied to the question. "It is nevertheless very useful for the question of how recruitment was sold to the public in 1915." Then, if you have another source, corroborate.
Ideas that changed the world: reason, rights, revolution
In 1750 almost every European was a subject of a monarch who ruled by the grace of God. Within two generations millions had begun to describe themselves as citizens of a nation, holding rights nobody had granted them. That change of vocabulary is the subject of this topic.
2.1The Enlightenment
The Enlightenment was an eighteenth-century movement of thinkers who argued that human affairs — government, law, religion, economics — should be examined by reason and evidence rather than accepted on the authority of tradition, church or king. Immanuel Kant summed up its motto in 1784 as sapere aude: dare to know.
| Thinker | Key work | The idea that mattered |
|---|---|---|
| John Locke | Two Treatises of Government, 1689 | People hold natural rights to life, liberty and property; government exists by their consent and may be replaced if it breaks that trust |
| Montesquieu | The Spirit of the Laws, 1748 | Separation of powers — legislative, executive and judicial — so that no single body can dominate |
| Voltaire | Letters and pamphlets, from the 1730s | Religious toleration and freedom of expression, against censorship by church and state |
| Denis Diderot | The Encyclopédie, 1751–1772 | Collect and publish all useful knowledge, so that ordinary readers could judge for themselves |
| Jean-Jacques Rousseau | The Social Contract, 1762 | Legitimate authority comes from the general will of the people, not from a hereditary ruler |
| Adam Smith | The Wealth of Nations, 1776 | Wealth grows through free exchange and the division of labour, not through hoarding by the state |
| Mary Wollstonecraft | A Vindication of the Rights of Woman, 1792 | If rights follow from reason, and women reason, then rights and education must extend to women |
The American Declaration of Independence of 1776 and the United States Constitution of 1787, with its Bill of Rights ratified in 1791, put Locke's consent and Montesquieu's separated powers into working institutions. French officers who fought in that war — Lafayette among them — carried the demonstration home: the ideas were not merely arguable, they had been built.
2.2Case study: the French Revolution from 1789
France in 1789 was bankrupt from war, taxed through a system in which the two privileged orders paid least, and legally divided into three Estates: the clergy, the nobility, and everybody else — the Third Estate, about 97 per cent of the population. Louis XVI summoned the Estates-General in May 1789 for the first time since 1614, to solve the deficit. He lost control of it within weeks.
Causes: why 1789 and not some other year
- Financial. France's support for the American revolutionaries left the crown effectively bankrupt by 1788. Calling the Estates-General was a last resort to raise taxes.
- Social and legal. Privilege was written into law. The First and Second Estates held exemptions the Third Estate paid for, and the Third Estate contained the wealthy, educated bourgeoisie who resented it most articulately.
- Economic and immediate. The harvest of 1788 failed; by July 1789 bread took a very large share of a labourer's daily wage. Hunger supplied the crowds.
- Intellectual. Enlightenment vocabulary gave the grievance a language: not "the king is unjust to us" but "sovereignty belongs to the nation."
The Declaration of the Rights of Man and of the Citizen, 26 August 1789
Adopted by the National Constituent Assembly three weeks after the Bastille fell, the Declaration set out the principles the new France claimed to rest on: that men are born and remain free and equal in rights; that sovereignty resides in the nation; that law is the expression of the general will; and that liberty, property, security and resistance to oppression are natural rights. On 4 August 1789 the Assembly had already voted away feudal privileges.
The 1789 Declaration used the word homme — man. Women received no political rights, and in September 1791 Olympe de Gouges published the Declaration of the Rights of Woman and of the Female Citizen, rewriting each article to include them. She was guillotined in 1793. Slavery in the French colonies was not abolished until 1794, and Napoleon restored it in 1802; the enslaved people of Saint-Domingue had already taken the Declaration at its word, rising in 1791 and winning independence as Haiti on 1 January 1804. The gap between a declaration of universal rights and the list of people it actually covered is one of the great essay questions of this topic.
The Terror, and Napoleon
- The monarchy was abolished in September 1792 and Louis XVI executed on 21 January 1793. Foreign invasion, civil war in the Vendée and food riots followed.
- The Terror ran from September 1793 to July 1794 under the Committee of Public Safety, dominated by Maximilien Robespierre. Roughly 17,000 people were formally executed after trial by the revolutionary tribunals; many thousands more died in prison or without trial, and historians' totals for the whole period differ considerably. It ended when the Convention turned on Robespierre: he fell on 27 July 1794 and was executed the next day.
- Napoleon Bonaparte seized power in the coup of 18 Brumaire, 9 November 1799, crowned himself Emperor on 2 December 1804, and issued the Civil Code in 1804. He was finally defeated at Waterloo on 18 June 1815.
- Napoleon's paradox is worth stating in an essay: he destroyed the Republic while exporting its administrative achievements — equality before the law, careers open to talent, secular civil codes — across the whole of Europe.
2.3The spread of nationalism
Nationalism is the belief that humanity divides into nations, that each nation has a right to govern itself, and that the state should match the nation. Before 1789 loyalty was owed to a dynasty; after 1789 it was increasingly claimed by a people.
- Revolutionary France invented the mass citizen army: the levée en masse of 1793 conscripted men to fight for the nation rather than for a king.
- Napoleon's conquests spread the model twice over — by imposing French codes and administration, and by provoking resistance in Spain, the German states and Italy that taught those peoples to think of themselves as nations.
- The Congress of Vienna, 1814–15, tried to restore the dynastic order; the revolutions of 1848 showed it could not be restored for long.
- The logic worked itself out in two new great powers: the Kingdom of Italy proclaimed on 17 March 1861 (with Rome added in 1870), and the German Empire proclaimed on 18 January 1871.
- The same idea had a darker edge. If the state should match the nation, then people inside the borders who are defined as outside the nation become a problem to be solved — a logic that runs directly into the twentieth century.
Movements for change: how the excluded got in
The Enlightenment declared rights for "man" and then spent two centuries arguing about who counted. Three movements — against slavery, for women's votes, for Black American civil rights — forced the answer wider. Studied together, they reveal a repeatable method.
3.1The abolition of slavery
| Date | Event | Why it mattered |
|---|---|---|
| 1772 | Somerset's case, England | An English court found that slavery had no support in English law — a legal foothold campaigners used for decades |
| 1787 | The Society for Effecting the Abolition of the Slave Trade is founded | Invented the modern campaign: mass petitions, a logo, boycotts of slave-grown sugar, and printed eyewitness evidence |
| 1789 | Olaudah Equiano publishes his life story | A formerly enslaved author testifying in his own voice, touring Britain to sell the book — testimony that could not be dismissed as hearsay |
| 1791–1804 | The Haitian Revolution | Enslaved people of Saint-Domingue took the Declaration of 1789 literally and won; Haiti declared independence on 1 January 1804 |
| 1807 | The Slave Trade Act (Britain) | Abolished the trade in enslaved people in the British Empire — not slavery itself |
| 1833 | The Slavery Abolition Act (Britain) | Abolished slavery through most of the Empire, in force from 1 August 1834. Compensation of about £20 million was paid to slave owners, and none to the enslaved |
| 1865 | The 13th Amendment (United States) | Ratified on 6 December 1865, after the Civil War, abolishing slavery in the United States |
| 1888 | Brazil abolishes slavery | The last country in the Americas to do so |
Note the two-step in Britain — 1807 the trade, 1833 the institution. Confusing them is the most common error in this topic. Note too that abolition was never only a gift from parliaments: resistance, escape and revolt by enslaved people themselves made the system expensive and unstable.
3.2The campaign for women's suffrage
| Date | Where | What was won |
|---|---|---|
| 1893 | New Zealand | The first self-governing country in the world where women won the vote in national elections. Women could not yet stand for parliament there until 1919 |
| 1894 | South Australia | Women won the vote and the right to stand for parliament — the first place in the world to grant both. The Act passed in December 1894 and came into force in 1895 |
| 1899 | Western Australia | The second Australian colony to enfranchise women |
| 1902 | Commonwealth of Australia | The Commonwealth Franchise Act 1902 gave women a federal vote and the right to stand for federal parliament — while its section 4 excluded most Aboriginal and Torres Strait Islander people from the federal roll |
| 1918 | United Kingdom | The Representation of the People Act gave the vote to women over 30 who met a property qualification — a partial win, deliberately limited |
| 1920 | United States | The 19th Amendment was ratified on 18 August 1920. In practice, Black women in the South remained barred by the same devices used against Black men until 1965 |
| 1928 | United Kingdom | The Equal Franchise Act lowered the age to 21, finally equalising the franchise with men |
- Two British methods, and the argument between them: the suffragists (National Union of Women's Suffrage Societies, led by Millicent Fawcett) petitioned, lobbied and argued; the suffragettes (Women's Social and Political Union, founded by Emmeline Pankhurst in 1903) used militant direct action, imprisonment and hunger strikes. Emily Wilding Davison stepped in front of the King's horse at the Derby on 4 June 1913 and died of her injuries four days later.
- Australia's early success owed much to its colonies being small, new and already experimenting: an unusually wide male franchise made extending it to women a smaller step than in Britain.
- Australia's 1902 franchise is the course's sharpest example of a right being widened and restricted in the same Act — and the restriction was not lifted federally until 1962.
3.3The United States civil rights movement
| Date | Event | Significance |
|---|---|---|
| 1954 | Brown v. Board of Education, 17 May | The Supreme Court held that segregated public schools were unconstitutional, overturning the "separate but equal" doctrine of 1896 |
| 1955–56 | The Montgomery bus boycott | Began after Rosa Parks was arrested on 1 December 1955 and ran to 20 December 1956 — just over a year of sustained, disciplined economic pressure. It made Martin Luther King Jr a national figure |
| 1957 | Little Rock Central High School | Federal troops escorted nine Black students into a white school, forcing Washington to choose a side |
| 1960 | The Greensboro sit-ins, from 1 February | Student-led non-violent direct action spread to dozens of cities within weeks |
| 1961 | The Freedom Rides | Integrated bus rides through the South; the televised violence against them moved national opinion |
| 1963 | The March on Washington, 28 August | About a quarter of a million people; King's "I Have a Dream" speech put the moral case to a mass television audience |
| 1964 | The Civil Rights Act, 2 July | Outlawed segregation in public accommodation and discrimination in employment |
| 1965 | Selma marches, March; the Voting Rights Act, 6 August | Suspended literacy tests and put federal officers into counties that had used them — the law that finally delivered the vote |
| 1968 | King is assassinated, 4 April | The movement fragmented, but the legislative gains held |
3.4How movements succeed
Compare the three and the same six ingredients appear. This is the framework to use when an exam asks you to evaluate the effectiveness of a movement.
- A clear, single demand. "Abolish the trade." "Votes for women." "Register to vote." A demand you can put on a placard can be conceded; a general complaint cannot.
- Organisation that outlasts individuals. Committees, subscriptions, newspapers and local branches keep a campaign alive across decades.
- Testimony from the people affected. Equiano's book, hunger-strike accounts, Parks's arrest — first-hand evidence is far harder to dismiss than argument alone.
- Sympathetic publicity, and the moral contrast it creates. Non-violent marchers met with violence made the case in a way words could not, because the pictures reached people who were not looking for an argument.
- Allies inside the institutions. Wilberforce in the Commons, Fawcett's parliamentary lobbying, President Johnson signing in 1964 and 1965. Pressure from below needs a lever at the top.
- A change in the law — then enforcement. This is the step students forget. The 19th Amendment of 1920 did not enfranchise Black women in the South; the Voting Rights Act of 1965 did. A right that is not enforced is not yet a right.
Australia in the modern world: 1901 to 2008
A nation founded in 1901 on a restricted definition of who belonged, tested by two world wars, and then spending half a century widening that definition — in immigration law, and in the rights of the people who had been here for tens of thousands of years.
4.1Federation, 1901 — and who was excluded
On 1 January 1901 six self-governing British colonies became the Commonwealth of Australia, under a Constitution drafted in the 1890s and enacted by the British Parliament. Federation was argued for on defence, free trade between the colonies, a common railway gauge and a shared immigration policy — and that last argument was, in plain terms, the desire for a "white" Australia.
- The Immigration Restriction Act 1901 was among the first laws of the new parliament, passing in December 1901. Its instrument was the dictation test: an officer could require an intending immigrant to write fifty words dictated in a European language (from 1905, any prescribed language). Because the officer chose the language, anyone could be failed, and the Act avoided naming a race in its text.
- The Pacific Island Labourers Act 1901 provided for the deportation of Pacific Islander workers, most of whom had been brought to Queensland's cane fields, many of them by coercion or kidnapping ("blackbirding").
- Section 127 of the Constitution excluded Aboriginal people from being counted in reckoning the population, and section 51(xxvi) gave the Commonwealth power over "the people of any race" except Aboriginal people — leaving them to the states. Both provisions were altered by the 1967 referendum.
4.2Australia in the World Wars
| First World War, 1914–18 | Second World War, 1939–45 | |
|---|---|---|
| Entry | Automatically at war when Britain declared war on 4 August 1914 | Prime Minister Menzies announced on 3 September 1939 that Australia was at war, following Britain |
| Defining campaign | The landing at Gallipoli on 25 April 1915; the peninsula was evacuated in December 1915. Far heavier losses followed on the Western Front in 1916–18 | The bombing of Darwin on 19 February 1942, the naval Battle of the Coral Sea in May 1942, and the Kokoda campaign in Papua from July to November 1942 |
| Losses | About 60,000 Australian deaths from a population of fewer than five million; more than 8,000 of them at Gallipoli | About 39,000 Australian deaths; more than 22,000 Australians were taken prisoner by Japan, and about a third of them died in captivity |
| Political fracture | Two conscription plebiscites, on 28 October 1916 and 20 December 1917 — both defeated, splitting the Labor Party and the country | The fall of Singapore on 15 February 1942 ended faith in British protection; Prime Minister Curtin had already turned to the United States in a New Year message published on 27 December 1941 |
1942 is the hinge of twentieth-century Australian foreign policy. Singapore fell, Darwin was bombed, and Curtin recalled Australian divisions from the Middle East against Churchill's wishes. The alliance formalised in the ANZUS Treaty of 1951 is the direct descendant of that decision. Explain it as a shift in strategic dependence, not as a sudden dislike of Britain.
4.3Dismantling White Australia, 1958–1973
The policy was not repealed in a single stroke. It was taken apart over fifteen years by three governments, under pressure from post-war labour shortages, decolonisation in Asia, and the embarrassment of defending a racial policy at the United Nations.
- 1958 — the Migration Act. Abolished the dictation test and replaced it with a system of entry permits. The discretion remained, but the most notorious instrument was gone.
- 1966 — the Holt government's review. Non-European people could apply to settle on the basis of their qualifications and suitability, and residence requirements for citizenship were equalised. This is the point at which the policy stopped operating as a blanket bar.
- 1973 — the Whitlam government. The last racial criteria were removed from immigration policy and all migrants became eligible for citizenship after three years' residence regardless of origin. The Racial Discrimination Act 1975 then made selection by race unlawful.
The post-war programme that ran alongside all this was itself huge: from 1945 Australia took in millions of migrants, at first from Britain, then from displaced-persons camps across Europe, then from southern Europe, and from the mid-1970s from Vietnam and the rest of Asia — the shift from assimilation to multiculturalism as official policy.
4.4Indigenous rights milestones
| Date | Milestone | What it actually did |
|---|---|---|
| 1962 | Commonwealth Electoral Act | Gave all Aboriginal and Torres Strait Islander people the right to enrol and vote in federal elections. Enrolment remained voluntary for them until 1984. Queensland was the last state to grant state voting rights, in 1965 |
| 1965 | The Freedom Ride | Charles Perkins and Sydney University students toured western New South Wales towns in February 1965, exposing segregation in pools, cinemas and clubs to national media |
| 1966 | The Wave Hill walk-off | Vincent Lingiari led Gurindji stockmen off a Northern Territory station on 23 August 1966. A strike over wages became a claim for the land itself |
| 1967 | The referendum, 27 May | Carried with 90.77% voting yes. It deleted section 127 so Aboriginal people were counted in the census, and amended section 51(xxvi) so the Commonwealth could make laws for them |
| 1971 | Neville Bonner enters the Senate | The first Aboriginal member of the federal parliament |
| 1972 | The Aboriginal Tent Embassy | Established on the lawns of Parliament House on 26 January 1972, reframing the claim as one of sovereignty and land rights |
| 1975–76 | Land rights | The Racial Discrimination Act 1975; the Gurindji handback at Wattie Creek in August 1975; the Aboriginal Land Rights (Northern Territory) Act 1976 |
| 1992 | Mabo v Queensland (No 2), 3 June | The High Court rejected terra nullius and recognised native title at common law where a continuing connection to country could be shown. The Native Title Act 1993 then built a process around it |
| 1997 | Bringing Them Home | The national inquiry's report on the forced removal of Aboriginal and Torres Strait Islander children — the Stolen Generations — and the evidentiary basis for what followed |
| 2008 | The National Apology, 13 February | Prime Minister Kevin Rudd apologised in Parliament to the Stolen Generations, eleven years after the report recommended it |
It did not give Aboriginal people the vote — that was 1962 federally. It did not grant citizenship, which they already held. It did not by itself deliver equal pay, land or rights. Writing "in 1967 Aboriginal people got the vote" is a factual error that examiners look for. What it did was remove section 127 and change section 51(xxvi) — and give the movement an overwhelming public mandate.
Design is a decision you can defend.
Senior Design is not judged on whether your idea looks good. It is judged on whether you found the real need, generated enough options to have a genuine choice, tested them, and can show why the one you resolved is the right answer. Four topics take you through that argument.
The mapUnits 1 and 2, four topics
- Unit 1, Topic 1 — Design in practice. What designers do, human-centred design, explore–develop–resolve, stakeholders, and measurable criteria.
- Unit 1, Topic 2 — Exploring needs. Observation, interviews and surveys; empathy and personas; framing and reframing the problem.
- Unit 2, Topic 1 — Developing ideas. Divergent techniques, convergent evaluation with a weighted matrix, prototyping, and iteration.
- Unit 2, Topic 2 — Communicating and evaluating design. Sketching and drawing, storyboards, pitching, evaluation, ethics, sustainability and IP.
Every decision gets a reason attached to evidence. Not "I chose stainless steel because it looks better", but "I chose stainless steel because criterion 2 requires the bottle to survive 200 drops, and the drop test destroyed the polymer sample at 60." Design folios lose marks for undefended decisions far more often than for weak ideas.
Design in practice: what designers actually do
Most of a designer's work happens before anything is drawn. It is finding out who the design is for, agreeing what "good" would mean, and writing that down in a form that can be tested later.
1.1The job, honestly described
- Designers frame problems. The brief you are given is rarely the problem you should solve; part of the job is to find out what is actually going wrong.
- Designers work inside constraints — budget, materials, standards, time, existing equipment. A design that ignores a constraint is not bold, it is unusable.
- Designers generate options and then choose. One idea is not a design process; it is a guess.
- Designers test with people and change the design when the test says so, not when they personally lose interest in it.
- Designers communicate — to clients, to makers, to users. An undocumented design cannot be built or bought.
1.2Human-centred design
Human-centred design means the needs, capabilities and behaviour of real people drive the design, and the design is then tested against those people rather than against the designer's taste. It rests on four commitments.
- Understand the users, their tasks and their environment. A hospital ward at 3 a.m. is not the same environment as a showroom.
- Involve users throughout, not just at the end in a satisfaction survey. Design with people, not merely for them.
- Iterate. Design, test, change, test again. The first version is a question, not an answer.
- Address the whole experience — finding it, buying it, unpacking it, learning it, using it, maintaining it, disposing of it. Not only the moment of use.
Human-centred design is not "ask people what they want and build it." People are excellent witnesses to their problems and unreliable designers of solutions. Your job is to take their problem seriously and then do the designing.
1.3The design process: explore, develop, resolve
| Phase | What you do | What you must have at the end |
|---|---|---|
| Explore | Investigate the situation, identify stakeholders and needs, research existing solutions, define the problem | A written problem statement and a set of measurable design criteria |
| Develop | Generate many ideas, combine and refine them, prototype, test with users, evaluate against the criteria | One resolved concept, and the evidence that chose it over the others |
| Resolve | Finalise details, produce presentation and technical drawings, pitch, evaluate the outcome | A communicated solution and an honest evaluation against the original criteria |
1.4Stakeholders, needs, wants and constraints
A stakeholder is anyone affected by the design, not just the person paying for it. For a school locker redesign the stakeholders include students, cleaners, teachers on duty, the maintenance staff who repair them and the business manager who buys them — and their interests conflict. Naming them early is what stops a design that pleases one group and fails the rest.
| Term | The test that identifies it | Locker example |
|---|---|---|
| Need | Remove it and the design fails its purpose | A bag and a laptop must fit and be securable |
| Want | Remove it and the design still works, just less well | Students would like to choose the colour |
| Constraint | A limit set from outside that you cannot design away | A $180 per locker budget; a 2.4 m ceiling; the corridor must stay 1.5 m wide for egress |
1.5Writing a design criterion that can be tested
A design criterion is a statement the finished design can be measured against. Three parts make it usable: what is measured, how it is measured, and the target that counts as a pass.
| Weak criterion | Why it fails | Rewritten so it can be tested |
|---|---|---|
| The locker should be strong | Strong against what, measured how? | The door withstands a 400 N horizontal push at its centre without permanent deformation |
| It should be easy to use | "Easy" is not observable | A Year 7 student, untrained, opens and closes it within 10 seconds on the first attempt |
| It should be sustainable | No boundary and no measure | At least 80% of its mass by weight is recyclable steel, and it separates into materials with hand tools in under 5 minutes |
Read your criterion and ask: what experiment would prove this true or false? If you cannot say the test in one sentence, the criterion is not measurable yet — and it will be useless in the evaluation, which is where the marks are.
Exploring needs: research, empathy and the real problem
The most expensive mistake in design is solving the wrong problem beautifully. This topic is the discipline that prevents it: find out what people actually do, understand why, and write the problem down before you draw anything.
2.1Research methods, and what each is actually for
| Method | Best for | Its weakness | How to run it well |
|---|---|---|---|
| Observation | Finding out what people do, including the workarounds they never mention | Tells you what, rarely why; people behave differently when watched | Watch a real task in the real place. Record actions and times, not opinions |
| Interview | Finding out why — motives, frustrations, history | Small numbers; easy to lead the answer you want | Open questions. Ask about the last real time it happened, then ask "why" again |
| Survey | Breadth — how common is the problem across many people | Shallow; a badly worded question produces confident nonsense | Short, one idea per question, no leading wording, and pilot it on five people first |
| Product / competitor analysis | Learning from what already exists, and finding the gap | Anchors you to existing solutions | Compare against your criteria, and note what each existing product refuses to solve |
| Secondary research | Standards, dimensions, materials data, market and demographic figures | Not specific to your users | Cite the source. Anthropometric data and Australian Standards belong here |
People under-report the embarrassing and over-report the virtuous. Ask students whether they use the recycling bin and most say yes; watch the courtyard at lunch and count. Where an interview and an observation disagree, the observation is usually closer to the truth — and the disagreement itself is a finding worth writing down.
Research ethics. Explain what you are doing and get consent, especially with minors. Do not photograph people without permission. Store names separately from responses, and report findings in a way that does not identify an individual.
2.2Empathy and personas
Empathy in design is a working method, not a feeling: it is the deliberate effort to understand a situation from the user's position, including the constraints you do not personally share — arthritic hands, a shift that ends at midnight, no home internet.
- An empathy map organises what you learned into four boxes for one user: what they say, think, do and feel. Contradictions between the boxes are the most useful part.
- A persona is a one-page fictional character that stands for a group of real users: a name, a photograph or sketch, a context, goals, frustrations, and the constraints that matter. It is a summary of research, not an invention.
- A persona with no research behind it is worse than useless, because it lets the team argue confidently about somebody who does not exist. Every claim on the page should be traceable to an interview, an observation or a survey result.
- Design for the edges as well as the average: a door handle that works for someone with limited grip works for everyone carrying a box.
2.3Defining the design problem
A problem statement written before the research is a guess. One written after it should name who, what and why it matters, and it must not contain a solution.
| Statement | Verdict |
|---|---|
| "Design a bigger bin for the courtyard." | Not a problem statement — it names a solution and closes off every other option |
| "The courtyard is messy." | Too vague — no user, no evidence, nothing to measure |
| "Year 7–9 students eating in the courtyard leave about 40 items of litter per lunch break, because the nearest bin is 25 m away and out of sight from the seating." | Usable — names the users, quantifies the problem, and states an observed cause without prescribing the fix |
2.4Framing and reframing
Framing is choosing which problem to solve. Reframing is deliberately restating it a different way to open up options that the first frame hid.
- The classic case: tenants complain the lift is too slow. Framed as "make the lift faster", the answer is a costly mechanical upgrade. Reframed as "make the wait feel shorter", the answer is mirrors and a floor indicator in the lobby — and the complaints stop. Same evidence, different frame, far cheaper solution.
- How might we… is the standard reframing device. "How might we make litter easier to dispose of than to drop?" is broader than "how might we design a bin?" but still bounded.
- Test a frame by asking what solutions it makes impossible. If the answer is "all but one", the frame is too narrow.
- Reframing has a limit. Widen the frame far enough and you can no longer test anything — "how might we improve society?" is not a design brief.
Developing ideas: diverge, then converge, then prototype
Developing is two opposite skills used in strict order. First widen — generate far more ideas than you need, without judging any of them. Then narrow — evaluate them against the criteria you wrote in Unit 1, using arithmetic you can show a client.
3.1Divergent techniques
Brainstorming, with the rules that make it work
- Defer judgement. No criticism during generation — including your own, and including "that's too expensive."
- Go for quantity. Set a target and a timer: forty ideas in fifteen minutes. Volume is what shakes loose the unobvious ones.
- Welcome wild ideas. An impossible idea is often a usable idea wearing a disguise, and it is easier to tame a wild idea than to enliven a dull one.
- Build on the ideas of others. "Yes, and…" rather than "yes, but…".
- One conversation at a time, and stay on topic. Write and sketch every idea where everyone can see it.
SCAMPER — seven prompts against a stuck idea
| Prompt | Question to ask | Applied to a school water bottle |
|---|---|---|
| Substitute | What material, part or step could be swapped? | Replace the plastic body with recycled aluminium |
| Combine | What could be merged with it? | Combine the lid with the carry loop so the loop cannot be lost |
| Adapt | What works elsewhere that could be adapted? | Adapt the bayonet lock used on camera lenses for a one-quarter-turn lid |
| Modify | What could be made bigger, smaller or a different shape? | Flatten the cross-section so it sits in a laptop sleeve |
| Put to another use | What else could it be, or serve? | The cap doubles as a measuring cup |
| Eliminate | What could be removed entirely? | Remove the separate silicone seal by moulding the thread as a seal |
| Reverse / rearrange | What if the order or orientation were reversed? | Open it from the base for cleaning instead of through the neck |
Biomimicry
Biomimicry borrows a strategy from nature, not a shape. Ask what problem an organism has already solved, and how.
- Velcro — George de Mestral examined the burdock burrs stuck to his dog under a microscope in the 1940s and copied the hook-and-loop mechanism.
- The Shinkansen 500 series nose — reshaped after the kingfisher's beak to reduce the pressure wave, and therefore the boom, as the train left a tunnel.
- Lotus-effect surfaces — microscopic bumps on the lotus leaf make water bead and roll off, carrying dirt with it; copied in self-cleaning paints and glass.
- The discipline is to state the function first: "how does nature reduce drag?", then look. Copying a leaf's outline onto a chair is styling, not biomimicry.
Morphological analysis
Break the design into independent parameters, list options under each, then combine across the columns — including combinations you would never have thought of deliberately.
| Body material | Lid mechanism | Carry method | Insulation |
|---|---|---|---|
| Stainless steel | Screw thread | Moulded finger loop | None |
| Recycled aluminium | Quarter-turn bayonet | Carabiner clip | Double wall vacuum |
| Co-polyester | Flip-top with button | Silicone sleeve strap | Neoprene sleeve |
With 3 options in each of 4 columns there are 3 × 3 × 3 × 3 = 81 combinations. You will not evaluate 81, but generating them is how you find the ones nobody proposed out loud.
3.2Converging: the weighted decision matrix
Once you have many ideas you need a defensible way to choose. A weighted decision matrix scores each concept against each criterion, multiplies by how much that criterion matters, and totals the result. The arithmetic is trivial; the value is that the weights and scores are visible and arguable, so a client can challenge a number rather than your taste.
The brief. A refillable water bottle sold to a school. The school states that durability matters most (bottles get dropped daily for five years), cost and cleaning matter equally and moderately, and portability matters least. Weights are agreed with the client before scoring, and total 10. Each concept is scored out of 5 on each criterion.
| Criterion | Weight | A — steel score | A weighted | B — aluminium score | B weighted | C — co-polyester score | C weighted |
|---|---|---|---|---|---|---|---|
| Durability | 5 | 5 | 5 × 5 = 25 | 4 | 4 × 5 = 20 | 2 | 2 × 5 = 10 |
| Unit cost | 2 | 2 | 2 × 2 = 4 | 4 | 4 × 2 = 8 | 5 | 5 × 2 = 10 |
| Ease of cleaning | 2 | 4 | 4 × 2 = 8 | 3 | 3 × 2 = 6 | 5 | 5 × 2 = 10 |
| Portability | 1 | 2 | 2 × 1 = 2 | 4 | 4 × 1 = 4 | 5 | 5 × 1 = 5 |
| Weighted total (out of 50) | 10 | — | 39 | — | 38 | — | 35 |
| Unweighted total (out of 20) | — | 13 | — | 15 | — | 17 |
Check the arithmetic yourself. A: 25 + 4 + 8 + 2 = 39. B: 20 + 8 + 6 + 4 = 38. C: 10 + 10 + 10 + 5 = 35. The maximum possible is 5 × 10 = 50, because the weights total 10 and the highest score on any criterion is 5.
Add the raw scores and C wins, 17 to 13. Apply the client's weights and A wins, 39 to 35. Nothing about the concepts changed — only the statement of what this client values. That is exactly the argument a matrix exists to make visible, and it is why the weights must be agreed with the client before any concept is scored. Agreeing them afterwards is just choosing your favourite and reverse-engineering the numbers.
Two honest limits to state in a folio: the scores are still judgements, so say what evidence each one rests on; and totals of 39 and 38 are not a real difference — when concepts finish that close, the matrix has told you to test both, not to pick one.
3.3Prototyping and iteration
| Low-fidelity prototype | High-fidelity prototype | |
|---|---|---|
| What it is | Paper, card, foam, tape, a wireframe sketch, a cardboard mock-up at full size | CAD model, 3D print, working mechanism, a coded and clickable interface |
| What it tests | Concept, layout, size, sequence, whether the idea makes sense at all | Fit, function, materials, tolerances, real usability, manufacturability |
| Cost and speed | Hours, almost free — so you can build five and throw four away | Days to weeks, and expensive |
| The hidden effect | People criticise it freely, because it clearly is not finished — which is what you want | People comment on the finish instead of the idea, and the team becomes reluctant to change something they spent a fortnight making |
| Use it when | Early, while the concept is still in question | Late, once the concept is settled and the details need proving |
- Iteration is a loop driven by test results: build, test with real users on a real task, record what the design caused, change the design, test again with someone new.
- Record what the design did wrong, not what the user "should have known". "Three of five testers pulled the handle that was meant to be pushed" is a design finding; "users were confused" is not.
- Change one significant thing at a time where you can, or you will not know which change fixed the problem.
- Keep every version and the test data. In senior Design the trail of evidence is assessed, not just the final object.
Communicating and evaluating: making the case
A design that cannot be understood cannot be built, bought or judged. This topic covers the drawings that carry an idea, the pitch that sells it, the evaluation that tests it honestly — and the responsibilities that come with putting something into the world.
4.1Sketching conventions and annotation
- Thumbnails are small, fast and many — twenty on a page. They exist to compare options, so do not render them.
- Crating (construction lines) means blocking the object inside a light box first, so proportion and perspective are right before any detail is drawn. Leave the construction lines visible: they show the method.
- Line weight carries meaning. Thick for the outline of the object, medium for the edges of surfaces, thin for internal detail and construction, and dashed for hidden detail behind a surface.
- Exploded views pull the parts apart along their assembly axis to show how they fit and in what order.
- Annotation is the difference between a drawing and a design. A useful annotation names the material, the function and the reason: "1.2 mm 304 stainless — chosen for the 400 N door-push criterion". "Looks cool" is not an annotation.
4.2Presentation drawing and technical drawing
| Presentation drawing | Technical drawing | |
|---|---|---|
| Audience | The client, the user, the public | The maker, the engineer, the manufacturer |
| Job | Make the design understood and wanted — context, materials, mood, scale relative to a person | Let someone build it exactly, without asking you a single question |
| Typical form | Rendered pictorial or perspective view, in context, often with people for scale | Dimensioned orthographic views to scale, in third-angle projection, drawn to AS 1100 |
| Test of success | The client can picture owning it | Two different workshops build the same object from it |
4.3Storyboards and user journeys
- A storyboard is a short sequence of frames showing a person using the design over time: the situation, the action, the outcome. It tests whether the design makes sense as a sequence, which a single beautiful render cannot.
- A user journey maps the whole experience — before, during and after — and marks the pain points: hearing about it, choosing it, unpacking it, first use, everyday use, cleaning, repair, disposal.
- Both are cheap ways to discover that the design solves the moment of use and fails everything around it. Most product complaints live in the "after" section of the journey.
4.4Pitching to a client
A pitch is an argument, and it has three ingredients: the audience, the message and the evidence.
- Audience. A business manager wants cost, lifespan and maintenance. A student user wants weight and whether it looks acceptable. Same design, two different pitches — lead with what that audience actually decides on.
- The problem, in their words and with a number. "About 40 items of litter per lunch break in the courtyard."
- The message — one sentence. If you cannot say what the design is and why it wins in a single sentence, you do not yet know.
- The evidence. Test results, the weighted matrix, user quotes, the prototype in their hands. Evidence is what separates a pitch from a preference.
- The ask. Say exactly what you want the client to decide, and what happens next.
4.5Evaluating against the original criteria
Evaluation is not a paragraph saying you enjoyed the project. It is a return to the criteria written in the explore phase, one at a time, with the test result and a verdict.
| Criterion (from the brief) | How it was tested | Result | Verdict |
|---|---|---|---|
| Survives 200 drops from 1 m onto concrete without leaking | Drop rig, 1.0 m, concrete slab, lid fitted | Passed 200; small dent at 140 | Met — cosmetic damage only |
| Unit cost at 500 units is $15 or less | Quotation from two suppliers | $16.40 | Not met — $1.40 over; a thinner wall would meet it but risks the drop criterion |
| Year 7 student opens it in under 10 seconds, untrained | 12 students, timed, first attempt | Median 6 s; 2 of 12 took over 10 s | Partly met — both failures gripped the sleeve, not the lid |
Saying a criterion was not met costs no marks. Hiding it does. Finish with the specific change you would make next and the evidence that prompted it — that is the iteration loop closing.
4.6Ethics, sustainability and intellectual property
Design ethics
- Inclusion. Who does this design exclude — by grip strength, height, language, colour vision, cost or connectivity? Exclusion is usually an accident of designing for yourself.
- Honesty. No claim in the marketing the evidence does not support, and no dark patterns: interfaces designed so the user does something they did not intend, such as a subscription that is one click to start and six to cancel.
- Safety and consequence. Ask what happens when the design fails, is misused, or is used by someone it was not designed for.
- Cultural respect. Aboriginal and Torres Strait Islander designs, symbols and stories are held under Indigenous Cultural and Intellectual Property. Using them requires permission and proper attribution — not admiration.
Sustainability across the life cycle
- Materials. What was extracted, and at what energy cost? Recycled aluminium takes roughly a twentieth of the energy of new aluminium.
- Manufacture. Energy, water, waste and offcuts. Can the part be nested to cut less scrap?
- Distribution. Mass, volume and packaging. A shape that stacks halves the trucks.
- Use. Energy or consumables while in service — usually the largest share for anything powered.
- End of life. Design for disassembly: screws rather than glue, one material rather than three bonded together, and no unnecessary composites. Ask whether it can be repaired, reused, then recycled.
Intellectual property in Australia
| Right | Protects | How you get it | How long |
|---|---|---|---|
| Copyright | The expression — your drawings, photographs, text and code | Automatically, on creation. No registration in Australia | Generally the creator's life plus 70 years |
| Registered design | The visual appearance of a product: shape, configuration, pattern, ornamentation | Registration under the Designs Act 2003, before you publish it | 5 years, renewable once to a maximum of 10 |
| Standard patent | A new and inventive way something works | Application and examination | Up to 20 years |
| Trade mark | A sign that distinguishes your goods or services — name, logo, shape | Registration | 10 years, renewable indefinitely |
Two practical rules for a folio: copyright protects how you expressed an idea, never the idea itself; and publishing your design before registering it can destroy the novelty a registered design needs. Credit every image, dataset and standard you used.
Senior starts here.
Four units covering QCAA Digital Solutions Units 1 and 2. Year 10 taught you the tools; Year 11 makes you accountable for them — a specification you can defend, code you can prove correct on paper, a database that cannot contradict itself, and an evaluation backed by recorded test evidence.
The mapFour units, two QCAA units
- Understanding digital problems — Unit 1, Topic 1. Decomposition and abstraction on a real brief, requirements elicitation, functional vs non-functional requirements, user experience principles, prototyping an interface.
- Data and programming fundamentals — Unit 1, Topic 2. Data types, variables, arrays and records, compound conditions, functions with parameters and return values, pseudocode, and desk-checking with trace tables.
- Data-driven solutions — Unit 2, Topic 1. Entities, keys, one-to-many relationships, normalisation to 1NF and 2NF, and SQL including JOIN.
- Building and evaluating — Unit 2, Topic 2. Algorithm efficiency, linear vs binary search, unit / boundary / user testing, security and privacy, and evaluating against the requirements you agreed.
Year 10 asked "what does this code do?". Year 11 asks "prove it, and justify why you built it this way rather than another". Every answer now needs three parts: the claim, the evidence, and the reason. A trace table is evidence. A recorded test result is evidence. "It worked when I tried it" is not.
Pseudocode conventions (← stores, = compares, keywords in capitals, close every block), AND/OR/NOT, nested loops, strings indexed from 0, entities and keys, and the four SQL clauses. Those are assumed here, not re-taught — go back to the Year 10 course if any of them feel shaky.
Understanding digital problems
A client describes a mess in three sentences. Your job is to turn that into a specification precise enough that two different programmers would build the same thing — and precise enough that, at the end, anyone can check whether you succeeded.
1.1Decomposition and abstraction, at senior level
You met both last year. What changes now is that you must justify each split and each omission, because a marker will ask why.
- Decomposition stops when every leaf is one job you could write as a single function — not when the diagram looks tidy. "Take an order" is still too big; "add one item to the cart", "recalculate the cart total", "apply the student discount" are each one function.
- Abstraction is a decision with a reason attached. Modelling a Lesson as subject, teacher, room and period — and ignoring the room's paint colour — is defensible because no rule of the timetable depends on paint. If the school ever timetabled by "rooms with natural light", that abstraction would become wrong.
- Test every abstraction with one question: could this detail ever change the output? If yes, keep it. If no, drop it and say so.
- Decomposition and abstraction produce different artefacts: decomposition gives you the module list; abstraction gives you the data model — the fields each record will hold.
1.2Requirements elicitation
Elicitation is the work of finding out what people actually need, as opposed to what they first say or what you assume. Clients describe solutions ("we need an app with a big green button"); your job is to dig out the underlying problem ("orders get lost at the busiest ten minutes of lunch").
| Technique | What it is good at | What it misses |
|---|---|---|
| Interview | Depth, reasons, exceptions, the "yes, but on Fridays…" cases | People describe what they think they do, not what they do |
| Observation | What really happens, including the workarounds nobody mentions | Slow; people behave differently while watched |
| Survey | Many users cheaply; numbers you can quote as evidence | Only answers the questions you already thought to ask |
| Studying existing systems | The real data, the real volumes, the real forms in use | Copies the old system's faults into the new one if you are not careful |
After eliciting, write the requirements back to the client and get them confirmed. An unconfirmed requirement is a guess wearing a suit. In an exam answer, saying "I would confirm the list with the client in writing before designing" is worth a mark on its own.
1.3Functional and non-functional requirements
A functional requirement says what the solution must do. A non-functional requirement says how well it must do it — a quality it must have. Both are testable; neither is an opinion.
| Functional — what it DOES | Non-functional — how WELL | Quality being specified |
|---|---|---|
| A student can add an item to their order | Any screen loads in under 2 seconds on the school Wi-Fi | Performance |
| The app calculates the order total, including GST | Thirty students can order at once without slowdown | Capacity |
| The app emails a receipt when an order is placed | It runs on Android 10 or later and iOS 15 or later | Compatibility |
| A staff member can mark an order as collected | No password is ever stored or sent as plain text | Security |
"The app should be fast" is not a requirement — nothing can settle it. "Any screen loads in under 2 seconds on the school Wi-Fi" is, because you can hold a stopwatch. Any requirement you cannot imagine testing is still a wish, and must be rewritten before you design anything.
1.4User experience principles
These are general design principles — they apply to every interface, not just yours. They are not requirements; they are what you appeal to when justifying an interface decision.
| Principle | What it demands | Broken when… |
|---|---|---|
| Visibility of system status | Every action produces visible feedback, immediately | Submit is pressed and nothing at all happens for three seconds |
| Consistency | The same control looks and behaves the same everywhere | "Back" is top-left on one screen and bottom-right on the next |
| Error prevention | Make the wrong action hard to take in the first place | A free-text date field, when a date picker would refuse 31 February |
| Error recovery | Let people undo a mistake, not merely read about it | Deleting an order is instant and permanent |
| Recognition over recall | Show the options; do not make people remember codes | The user must type an item code they saw two screens ago |
| Accessibility | Sufficient contrast, alt text, keyboard access, large enough targets | Pale grey 10 px text on white, reachable only by mouse |
1.5Prototyping the interface
- Wireframe first. Boxes and labels only — no colour, no font choices, no logo. The question a wireframe answers is "is the right thing in the right place, and is the main task obvious?"
- One screen per task from the decomposition. If a screen serves two unrelated jobs, that is usually a sign the decomposition was not finished.
- Map the flow. Draw the arrows between screens and count the taps for the most common task. The count is evidence you can quote in the evaluation.
- Test it with a real user, cheaply. Hand them the sketch and a task, say nothing, and write down where they hesitate. Hesitation is the data.
- Iterate before writing code. Redrawing a sketch costs minutes; rebuilding a screen costs days. Two rounds of sketching routinely saves a week.
Data and programming fundamentals
Types, structures, functions and proof. The new skills this year are parameters and return values — splitting an algorithm into pieces small enough to test on their own — and desk-checking, which is how you show an algorithm is correct without running it.
2.1Data types
Choosing the type is a design decision, and the wrong one causes faults that are hard to find later.
| Type | Holds | Use it for | Trap |
|---|---|---|---|
| Integer | Whole numbers, no decimal part | A mark out of 100, a quantity, a year level | Integer division may discard the remainder — use MOD to see it |
| Real (float) | Numbers with a decimal part | A price, an average, a measurement | Tiny rounding errors mean you rarely test two reals for exact equality |
| Boolean | Exactly true or false | isPaid, hasConsent, a tick box | Storing "yes"/"no" as text instead — then every comparison is a string comparison |
| String | A sequence of characters, indexed from 0 | Names, addresses, item codes, phone numbers | Phone numbers are strings: leading zeros survive, and you never do arithmetic on them |
| Date | A calendar date, stored as a date | Order date, due date, date of birth | Stored as text, sorting gives 01/12 before 02/01 of the next year |
2.2Arrays and records
An array is a numbered list of values of the same type, indexed from 0. A record is one thing with several named fields of possibly different types. Real data is nearly always an array of records.
| Idea | Written as | Meaning |
|---|---|---|
| Array literal | scores ← [12, 7, 30, 5] | Four integers in a fixed order |
| First element | scores[0] | 12 — counting starts at 0 |
| Third element | scores[2] | 30 |
| Last index | LENGTH(scores) − 1 → 3 | 4 elements, so the highest valid index is 3 |
| Walk it safely | FOR i FROM 0 TO LENGTH(scores) − 1 | Ending at LENGTH would read index 4, which does not exist |
| Record field | order.item · order.qty | Named fields of one record, reached with a dot |
| Array of records | FOR EACH o IN orders | o is one whole record on each pass |
2.3Control structures with compound conditions
- Every part of an AND/OR must be a complete condition. IF o.qty >= 2 AND o.price < 8 THEN is right; IF o.qty >= 2 AND < 8 is not a condition at all.
- An OR that is always true filters nothing. mark >= 50 OR mark <= 100 is true for every possible mark, because any number below 50 is still at most 100. A range test always needs AND.
- Order the branches so the narrowest case comes first. In IF…ELSE IF…, once a branch matches, the rest are skipped — so testing mark >= 50 before mark >= 80 means no one ever reaches the 80 branch.
- WHILE when you do not know how many passes; FOR when you do. Every WHILE must contain something that can eventually make its condition false, or it never ends.
- Bracket anything mixed: (a AND b) OR c is not a AND (b OR c).
2.4Functions and procedures
| FUNCTION | PROCEDURE | |
|---|---|---|
| Gives back | A value, via RETURN | Nothing — it just performs an action |
| Called as | net ← applyDiscount(20, 10) | printReceipt(order) |
| Typical job | Calculate and hand back an answer | Display, save, send |
- Parameters are the named inputs in the definition; arguments are the actual values passed in at the call. They are matched by position: the first argument fills the first parameter.
- A parameter is a local copy. Changing it inside the function does not change the caller's variable — the only thing that travels back out is the RETURN value.
- One job per function, and a name that says the job. applyDiscount tells you what it returns; doStuff tells you nothing.
- The real payoff: a function can be tested on its own. You cannot unit-test a 90-line block, but you can call applyDiscount(100, 10) and check it returns 90.
2.5Algorithm design in pseudocode — and a flowchart
Pseudocode and flowcharts say the same thing in two notations. Flowcharts are marked on their shapes, so use the right one every time.
2.6Desk-checking with trace tables
Desk-checking means running the algorithm by hand, on paper, before any computer is involved. It is how you find a fault in five minutes instead of an hour, and it is examined directly.
Worked example one — a function with parameters and a return value:
| FUNCTION applyDiscount(price, pct) RETURN price − (price × pct ÷ 100) END FUNCTION total ← 0 · FOR EACH p IN [20, 50, 30] total ← total + applyDiscount(p, 10) END FOR · PRINT total | ||||
|---|---|---|---|---|
| Pass | p | price × pct ÷ 100 | RETURN value | total after |
| start | — | — | — | 0 |
| 1 | 20 | 20 × 10 ÷ 100 = 2 | 20 − 2 = 18 | 18 |
| 2 | 50 | 50 × 10 ÷ 100 = 5 | 50 − 5 = 45 | 63 |
| 3 | 30 | 30 × 10 ÷ 100 = 3 | 30 − 3 = 27 | 90 |
| end | — | list exhausted | — | PRINT 90 |
Worked example two — walking an array to find the largest value:
| temps ← [18, 24, 21, 27, 19] · best ← temps[0] · FOR i FROM 1 TO 4 IF temps[i] > best THEN best ← temps[i] END FOR · PRINT best | ||||
|---|---|---|---|---|
| Pass | i | temps[i] | temps[i] > best? | best after |
| start | — | temps[0] = 18 | — | 18 |
| 1 | 1 | 24 | 24 > 18 true | 24 |
| 2 | 2 | 21 | 21 > 24 false | 24 |
| 3 | 3 | 27 | 27 > 24 true | 27 |
| 4 | 4 | 19 | 19 > 27 false | 27 |
| end | — | — | loop finished | PRINT 27 |
One column per variable plus one for the condition and one for output. Never erase — add a row, so the history stays visible. Update in the exact order the lines run. Seeding best from temps[0] and then starting the loop at i = 1 is deliberate: seeding it from 0 instead would break for a list of negative numbers, and markers look for exactly that reasoning.
Data-driven solutions
A relational database earns its keep by making certain kinds of mistake impossible. Normalisation is the technique; keys are the mechanism; SQL is how you get the answers back out — including from two tables at once.
3.1The worked schema for this unit
Every example and every drill below uses these two tables. Learn the rows — the questions depend on them.
| MEMBER | |||
|---|---|---|---|
| MemberID PK | FirstName | LastName | JoinYear |
| 1 | Ava | Nguyen | 2024 |
| 2 | Ben | Okafor | 2023 |
| 3 | Chloe | Tran | 2025 |
| 4 | Dev | Patel | 2023 |
| LOAN | |||
|---|---|---|---|
| LoanID PK | MemberID FK | BookTitle | DaysOut |
| 101 | 1 | Dune | 5 |
| 102 | 2 | Frankenstein | 21 |
| 103 | 1 | Persuasion | 14 |
| 104 | 3 | Dracula | 3 |
Note what the data already tells you: member 1 has two loans, member 4 has none. One member, many loans — and "many" is allowed to mean zero.
3.2The relationship, drawn properly
3.3Normalisation to 1NF and 2NF
Normalisation is reorganising tables so that each fact is stored exactly once. The payoff is that the data cannot contradict itself — not neatness.
| Form | The rule | Broken by | The fix |
|---|---|---|---|
| 1NF | Every field holds one single value, and there are no repeating groups of columns | A Books column holding "Dune, Persuasion"; or columns Book1, Book2, Book3 | Move the repeating thing into its own table, one row per value |
| 2NF | It is in 1NF, and every non-key attribute depends on the whole primary key | A composite key (MemberID, BookTitle) in a table that also stores LastName — LastName depends on MemberID alone | Move the partly-dependent attributes into a table keyed by the part they depend on |
2NF only ever bites when the primary key is a composite key — two or more attributes that identify a row only together. With a single-attribute key there is no "part of the key" to depend on, so a 1NF table with a single-attribute key is automatically in 2NF.
If a member's surname is stored on every one of their loan rows, then correcting a misspelling means finding and changing every row — and the day you miss one, the database says two different things at once. Stored once in MEMBER and referenced by MemberID, that is not possible.
3.4SQL, including JOIN
| Query against the tables above | What it returns, exactly |
|---|---|
| SELECT LastName FROM Member WHERE JoinYear = 2023 ORDER BY LastName ASC; | 2 rows: Okafor, then Patel — in that order, because O comes before P. |
| SELECT * FROM Loan WHERE DaysOut > 7; | 2 rows: loan 102 (21 days) and loan 103 (14 days). |
| SELECT BookTitle FROM Loan WHERE DaysOut > 7 ORDER BY DaysOut DESC; | Frankenstein, then Persuasion — DESC puts the longest first. |
| SELECT FirstName, LastName FROM Member WHERE LastName = 'Tran'; | 1 row: Chloe Tran. Text goes in single quotes; numbers do not. |
| SELECT M.FirstName, L.BookTitle FROM Member M JOIN Loan L ON M.MemberID = L.MemberID; | 4 rows, one per loan: Ava–Dune, Ben–Frankenstein, Ava–Persuasion, Chloe–Dracula. Dev has no loan, so he does not appear. |
| SELECT M.LastName, L.BookTitle FROM Member M JOIN Loan L ON M.MemberID = L.MemberID WHERE L.DaysOut > 7; | 2 rows: Okafor–Frankenstein (21 days) and Nguyen–Persuasion (14 days). The JOIN happens first, then WHERE filters the joined rows. |
- JOIN combines two tables; ON states the matching condition, which is almost always foreign key = primary key.
- A plain JOIN keeps only rows that match on both sides. Member 4 has no loan, so a joined query never mentions him — a fact worth stating explicitly in an exam answer.
- An alias (Member M) shortens the table name; M.FirstName then says unambiguously which table a column came from. With two columns both called MemberID, that is not optional.
- Clause order is still fixed: SELECT → FROM → JOIN…ON → WHERE → ORDER BY.
- A query only reads. Nothing in this unit can alter or lose the stored data.
Building and evaluating
Working is the minimum. This unit is about the three things that separate a pass from a high mark: knowing why one algorithm costs more than another, testing in a way that produces evidence, and protecting the data you have just made yourself responsible for.
4.1Algorithm efficiency, at concept level
You are not asked for formal big-O notation. You are asked to say how the work grows as the data grows, and why.
- A single loop over n items does about n steps. Double the data, double the work.
- A nested loop over the same n items does about n × n steps. Double the data and the work goes up four times, because (2n) × (2n) = 4 × n × n. Ten times the data is a hundred times the work.
- That is why a nested loop that compares every item with every other item is the first thing to look at when a program is slow.
- Efficiency is not only speed: memory matters too. Copying a whole array inside a loop is cheap for 10 items and ruinous for 10 million.
4.2Linear search versus binary search
Linear search checks item 1, then item 2, then item 3… In the worst case it checks all n. Binary search checks the middle item, throws away the half that cannot contain the target, and repeats — so each comparison halves what is left.
| Items in the list | Linear search, worst case | Times you can halve it down to one | Binary search, worst case |
|---|---|---|---|
| 8 | 8 comparisons | 8 → 4 → 2 → 1 = 3 halvings | about 4 comparisons |
| 16 | 16 comparisons | 16 → 8 → 4 → 2 → 1 = 4 halvings | about 5 comparisons |
| 1,000 | 1,000 comparisons | 9 halvings | about 10 comparisons |
| 1,000,000 | 1,000,000 comparisons | 19 halvings | about 20 comparisons |
Binary search only works on a sorted list — discarding half depends entirely on knowing which half the target must be in. On an unsorted list it is simply wrong, and sorting first costs time of its own. The full answer is therefore: binary search wins on a list that is already sorted, or one you will search many times.
4.3Testing that produces evidence
| Kind of test | What it checks | Example |
|---|---|---|
| Unit test | One function, in isolation, against a hand-calculated answer | applyDiscount(100, 10) must return 90 |
| Boundary test | The edges, where off-by-one faults live: lowest valid, highest valid, one outside each, and empty | A field accepting 0–100: try 0, 100, −1, 101, and blank |
| User (acceptance) test | Whether a real user can complete the real task, unaided | Three students who have never seen the app each place an order while you time and watch them |
A test case is only evidence if it is written down before you run it. The exam-standard table has five columns:
| ID | What is tested | Input | Expected output | Actual output |
|---|---|---|---|---|
| T1 | Discount calculation | price 100, pct 10 | 90 | 90 — pass |
| T2 | Lower boundary of the mark field | 0 | Accepted | Accepted — pass |
| T3 | Just outside the upper boundary | 101 | Rejected, with a message naming the field | Rejected, message says only "invalid" — fail |
| T4 | Empty order submitted | no items | Rejected, nothing sent to the kitchen | Rejected — pass |
Notice T3: a recorded failure is worth more marks than a table of four passes, because it gives you something specific to justify improving.
4.4Security and privacy
- Authentication answers "are you who you say you are?" — a password is something you know. Two-factor authentication adds something you have (a code on your phone) or something you are (a fingerprint), so a stolen password alone is not enough to get in.
- Authorisation is the separate question "what are you allowed to do?" A student and a canteen manager may both be authenticated, and still see different screens.
- Encryption scrambles data with a key so that intercepting it yields nothing readable. Encrypt in transit (HTTPS, so Wi-Fi traffic cannot be read) and at rest (so a stolen drive is useless). Encryption does not stop interception; it makes interception pointless.
- Passwords should be stored hashed, never encrypted and never plain: the system needs to check a password, not to read it back.
- The Australian Privacy Principles under the Privacy Act 1988 still apply: collect only what you need for a stated purpose, be open about it, keep it secure, and let people see and correct their own information. At senior level the design consequence is the point — a field you never collected is a field that can never leak.
4.5Evaluating against the requirements
The evaluation is judged against the requirements you agreed in Unit 1 — not against how you feel about the finished thing. Take them one at a time:
- State the requirement, in the words it was agreed in.
- Give the evidence: the test ID, the input, and what actually happened.
- Judge it: met, or not met. No third option, and no hedging.
- Say what you would change and why, tied to the evidence you just gave.
"Requirement 3 — an invalid mark is rejected with a message naming the field — was not met. Test T3 entered 101 and the system rejected it, but the message read only 'invalid', so the user is not told which field is wrong. Naming the field in the message would meet the requirement, and costs one line; I would also add the valid range to the message so the user does not have to guess it."
Engineering is arithmetic with consequences.
Four topics: what materials do under load, how forces balance, how machines trade force for distance, and the professional method that turns all of it into a decision somebody's life may depend on. Every number on this page has been worked, not asserted.
The mapUnits 1 and 2, four topics
- Unit 1, Topic 1 — Engineering materials. The four families, the mechanical properties defined precisely, stress, strain and the stress–strain curve.
- Unit 1, Topic 2 — Statics and forces. Vectors, components, W = mg, moments, equilibrium, free-body diagrams and beam reactions.
- Unit 2, Topic 1 — Machines and mechanisms. Levers, mechanical advantage, gear trains, pulleys, torque, power and efficiency.
- Unit 2, Topic 2 — Engineering practice. The design process, factor of safety, failure modes, standards and testing, and life-cycle thinking.
Draw the free-body diagram first. Most statics problems solve themselves once every force on the object is drawn and labelled.
Carry the units through every line. Newtons and square millimetres give megapascals directly, because 1 MPa = 1 N/mm². A stress answer without a unit is worth nothing.
State the assumption. "Beam weight ignored", "friction neglected", "g = 9.8 m s⁻²". An assumption stated is engineering; an assumption hidden is a defect.
Engineering materials: what happens under load
Choosing a material is a numerical argument, not a preference. To make it you need four families, six properties defined precisely enough to be measured, and one curve that contains most of the answers.
1.1The four families
| Family | What holds it together | Typical behaviour | Examples |
|---|---|---|---|
| Metals | Metallic bonding — a lattice of ions in a sea of free electrons | Stiff, strong, generally ductile, tough, conduct heat and electricity, can be alloyed and heat-treated | Mild steel, stainless steel, aluminium alloy 6061, copper, titanium |
| Polymers | Long covalently bonded chains, held to each other weakly | Low stiffness and low density, mouldable, corrosion-resistant, soften with heat, creep under sustained load | Polypropylene, nylon, ABS, polycarbonate, epoxy |
| Ceramics | Strong ionic and covalent bonds in a rigid network | Very hard, very stiff, strong in compression, weak in tension, brittle, heat- and wear-resistant | Alumina, fired clay brick, glass, concrete, tungsten carbide tooling |
| Composites | A stiff, strong reinforcement held in a matrix that transfers load between the fibres | Properties are designed, not inherited: excellent strength-to-weight, but anisotropic and hard to recycle | Carbon-fibre reinforced polymer, glass-fibre, reinforced concrete, plywood |
Reinforced concrete is the clearest illustration of the composite idea: concrete is strong in compression and weak in tension, steel is strong in tension, so steel bars are placed exactly where the tension will be. Neither material could do the job alone.
1.2Mechanical properties, defined precisely
| Property | Precise definition | How it is measured | Watch out |
|---|---|---|---|
| Strength | The stress a material can carry before it yields or fractures | Tensile test; quoted as yield strength or ultimate tensile strength, in MPa | Say which strength: yield or ultimate |
| Stiffness | Resistance to elastic deformation — how much stress is needed per unit of strain | Young's modulus E, the gradient of the elastic part of the curve, in GPa | Not the same as strength. Every steel has E ≈ 200 GPa, whatever its strength |
| Hardness | Resistance to localised surface indentation or scratching | Brinell, Rockwell or Vickers test — press an indenter and measure the mark | Hardness is not toughness. Hardening steel usually makes it less tough |
| Toughness | The energy absorbed before fracture — the area under the stress–strain curve | Charpy impact test, in joules | A tough material can be soft; a hard material is often brittle |
| Ductility | The ability to deform plastically a long way before fracture | Percentage elongation at fracture in a tensile test | Ductility gives warning before failure — a safety property |
| Brittleness | Fracturing with almost no plastic deformation first | Observed as a low elongation and a flat, sudden break | Brittle failure gives no warning at all |
A glass sheet is hard (you cannot scratch it with steel) and utterly not tough (it shatters, absorbing almost no energy). A car body panel in mild steel is comparatively soft and very tough — it crumples and absorbs energy, which is exactly what you want in a crash. Hardness is about the surface; toughness is about energy absorbed to fracture.
1.3Stress: σ = F ÷ A
Stress is the force carried per unit of cross-sectional area: σ = F ÷ A. Work in newtons and square millimetres and the answer comes out directly in megapascals, because 1 MPa = 1 N/mm².
| Problem | Area A | Force F | σ = F ÷ A |
|---|---|---|---|
| Steel rod, area 200 mm², carrying 50 kN | 200 mm² | 50 000 N | 50 000 ÷ 200 = 250 MPa |
| Rectangular bar 20 mm × 10 mm, carrying 12 kN | 20 × 10 = 200 mm² | 12 000 N | 12 000 ÷ 200 = 60 MPa |
| Round bar, diameter 20 mm, carrying 25 kN | πd²/4 = π × 400 ÷ 4 = 314 mm² | 25 000 N | 25 000 ÷ 314 = 79.6 MPa |
| Tie of area 150 mm², carrying 45 kN | 150 mm² | 45 000 N | 45 000 ÷ 150 = 300 MPa |
Strain is the deformation per unit of original length: ε = ΔL ÷ L₀. It has no units, because it is a length divided by a length. A tie 2000 mm long that stretches 1.6 mm has a strain of 1.6 ÷ 2000 = 0.0008, which is 0.08 per cent.
Young's modulus is stress divided by strain in the elastic region: E = σ ÷ ε. If that same steel tie reached 160 MPa at a strain of 0.0008, then E = 160 ÷ 0.0008 = 200 000 MPa = 200 GPa — the standard figure for steel.
| Material | Young's modulus E (approx.) | Meaning |
|---|---|---|
| Steel (any grade) | 200 GPa | Very stiff; grade changes the strength, not E |
| Titanium alloy | 110 GPa | About half as stiff as steel, at about 57% of the density |
| Aluminium alloy | 70 GPa | About a third of steel's stiffness, about a third of its density |
| Concrete | 30 GPa | Stiff, but weak in tension — hence reinforcement |
| Engineering polymers | 1–3 GPa | Roughly a hundredth of steel: they flex noticeably under load |
1.4The stress–strain curve
- Below the yield point the deformation is elastic: remove the load and the sample returns to its original length. Above it the deformation is plastic and permanent.
- Mild steel yields at roughly 250 MPa and reaches an ultimate tensile strength of roughly 400–550 MPa, depending on grade.
- After the UTS the sample necks — it thins locally, so the true stress there keeps rising even though the plotted engineering stress, which uses the original area, falls.
- Heat treatment and alloying move the curve up and usually shorten it: harder and stronger, but less ductile and less tough. That trade-off is the whole of materials selection in one sentence.
Statics and forces: everything adds to zero
Statics is the study of things that are not accelerating — a bridge, a bracket, a beam. Two equations cover almost all of it: the forces sum to zero, and the moments sum to zero.
2.1Force as a vector, and mass against weight
- A force is measured in newtons (N) and is a vector: it has a magnitude and a direction. "300 N" without a direction is an incomplete answer.
- Mass is the quantity of matter, in kilograms, and does not change with location. Weight is the force gravity exerts on that mass, in newtons, and does.
- W = mg, with g = 9.8 m s⁻² on Earth. A 12 kg toolbox: W = 12 × 9.8 = 117.6 N. A 65 kg person: 65 × 9.8 = 637 N. A 250 kg machine: 250 × 9.8 = 2450 N.
- Putting a mass in kilograms into a force equation is the single most common error in senior statics. Convert first, every time.
2.2Resolving a force into components
An angled force can be replaced by two perpendicular forces that together do exactly the same job. With the angle θ measured from the horizontal: the horizontal component is F cos θ and the vertical component is F sin θ.
2.3Moments
A moment is the turning effect of a force about a point: M = F × d, where d is the perpendicular distance from the pivot to the line of action of the force. The unit is the newton metre (N·m).
| Situation | Force F | Perpendicular distance d | Moment M = F × d |
|---|---|---|---|
| Pushing on a lever | 250 N | 0.4 m | 250 × 0.4 = 100 N·m |
| Pulling on a spanner | 150 N | 0.30 m | 150 × 0.30 = 45 N·m |
| A door handle | 40 N | 0.25 m | 40 × 0.25 = 10 N·m |
Double the distance and you double the moment for the same force — which is why a longer spanner loosens a tighter nut. A force whose line of action passes through the pivot has zero perpendicular distance and therefore no moment at all.
2.4Equilibrium and free-body diagrams
A body is in equilibrium when it is at rest or moving at constant velocity. Two conditions must both hold:
- ΣF = 0 — the forces balance. Vertically, up equals down; horizontally, left equals right.
- ΣM = 0 — the moments balance about any point. Clockwise equals anticlockwise.
- A free-body diagram is the object drawn alone, with every support deleted and replaced by the force it applies — each force drawn as an arrow labelled with its size, direction and cause.
2.5Reactions on a simply supported beam
An 8 m beam on supports A and B at its ends carries 600 N at 2 m from A and 400 N at 6 m from A.
Moments about A: R(B) × 8 = (600 × 2) + (400 × 6) = 1200 + 2400 = 3600, so R(B) = 450 N.
ΣF = 0: R(A) = (600 + 400) − 450 = 550 N.
Check about B: R(A) × 8 = (600 × 6) + (400 × 2) = 3600 + 800 = 4400, so R(A) = 550 N. It agrees.
And the symmetrical special case worth memorising: a single load at mid-span splits exactly in half, so a 2 kN central load gives 1 kN at each support.
Machines and mechanisms: trading force for distance
No machine creates energy. Every one of them takes the energy you put in and hands it back in a more convenient shape — usually more force over a shorter distance, or less force over a longer one. Levers, gears and pulleys are three versions of the same bargain.
3.1Levers and the three classes
Mechanical advantage is MA = load ÷ effort. For an ideal lever it also equals effort arm ÷ load arm, because the moments about the fulcrum must balance.
- Crowbar. Effort arm 1.2 m, load arm 0.15 m. MA = 1.2 ÷ 0.15 = 8. So 200 N of effort lifts 200 × 8 = 1600 N.
- Wheelbarrow. An 800 N load sits 0.4 m from the wheel (the fulcrum); the handles are 1.2 m from it. Effort = (800 × 0.4) ÷ 1.2 = 266.7 N, and MA = 1.2 ÷ 0.4 = 3.
- The bargain is never free. Multiplying the force by 8 means the effort end must move 8 times further than the load end.
3.2Gears and gear trains
Gear ratio = driven teeth ÷ driver teeth. The driver is the gear on the input shaft; the driven is the one on the output shaft. Because gears in mesh must have teeth of the same size, tooth count is proportional to pitch radius — so a 3 : 1 ratio by teeth is also 3 : 1 by radius.
- Speed. Output speed = input speed ÷ gear ratio. A 20-tooth driver at 1500 rpm driving 60 teeth gives 1500 ÷ 3 = 500 rpm.
- Reversed. A 60-tooth driver turning at 800 rpm driving a 24-tooth gear: ratio = 24 ÷ 60 = 0.4, so output = 800 ÷ 0.4 = 2000 rpm. Speed up, torque down.
- Compound trains multiply. A 15-tooth driver into 45 teeth is 3 : 1; a 20-tooth driver on that same shaft into 80 teeth is 4 : 1. Overall 3 × 4 = 12 : 1, so 1200 rpm in gives 1200 ÷ 12 = 100 rpm out.
- An idler gear between driver and driven reverses the output's direction but leaves the overall ratio unchanged — its tooth count cancels out.
- Belt and chain drives follow the same rule with diameters or sprocket teeth instead: ratio = driven diameter ÷ driver diameter.
3.3Pulleys
- A single fixed pulley has MA = 1: it changes the direction of the effort, which is often worth having on its own.
- A single movable pulley has MA = 2, because two rope sections share the load.
- In a block and tackle, the ideal MA equals the number of rope sections supporting the load. With 4 supporting sections and a 1200 N load, the ideal effort is 1200 ÷ 4 = 300 N — but you must pull 4 m of rope for every 1 m the load rises.
3.4Torque, power and efficiency
- Torque is a moment about a rotating shaft: T = F × r. A 200 N force on a 0.25 m radius pulley gives 200 × 0.25 = 50 N·m.
- Rotational power is P = 2πNT ÷ 60, with N in rpm and T in N·m. That 50 N·m at 600 rpm gives (2π × 600 × 50) ÷ 60 = 3142 W, about 3.14 kW.
- Efficiency = useful output ÷ total input × 100%. A gearbox taking in 4000 W and delivering 3600 W is (3600 ÷ 4000) × 100 = 90% efficient; the missing 400 W leaves as heat, sound and vibration.
- Efficiency for a machine can also be found as actual MA ÷ ideal MA. That block and tackle with an ideal MA of 4 that actually needs 350 N to lift 1200 N has an actual MA of 1200 ÷ 350 = 3.43, so its efficiency is (3.43 ÷ 4) × 100 = 85.7%.
- No machine reaches 100%. Anything that claims to has an unmeasured energy path.
Engineering practice: method, margin and consequence
The calculations are the easy part. Engineering practice is the method that decides which calculation to do, the margin you keep because reality is untidy, the failure modes you check for, and the standards that carry a century of other people's accidents.
4.1The engineering design process
- Define the problem. What must the thing do, for whom, under what conditions and loads?
- Research and specify. Gather data, standards and materials properties. Write the specification: measurable criteria and the constraints.
- Generate concepts. More than one, always. A single concept cannot be justified because nothing was rejected.
- Analyse and model. This is where the calculations live — free-body diagrams, stresses, deflections, ratios, factor of safety. Do them on paper before anything is built.
- Select. Compare concepts against the specification, using the numbers.
- Prototype and test. Test against the specification, not against your hopes for it. Record everything.
- Evaluate and iterate. Feed test results back into the design and go round again.
- Communicate and implement. Drawings to AS 1100, calculations, and the assumptions written down for whoever maintains it in twenty years.
The difference from the Design subject's process is emphasis, not shape: engineering puts an analysis step in the middle and requires the decision to be defended numerically.
4.2Factor of safety
Factor of safety = failure load ÷ working load. Equivalently, in stress terms, FoS = ultimate stress ÷ allowable working stress. It is the margin that covers everything the calculation could not know: material variation, manufacturing defects, corrosion, wear, overload, and simple error.
| Problem | Working | Answer |
|---|---|---|
| A cable fails at 24 kN and is used at a working load of 6 kN. Find the FoS. | 24 ÷ 6 | FoS = 4 |
| A lifting eye must carry 3.2 kN with a required FoS of 5. What failure load is needed? | 3.2 × 5 | 16 kN |
| Steel with an ultimate tensile strength of 400 MPa, with FoS 2.5. Find the allowable working stress. | 400 ÷ 2.5 | 160 MPa |
| At 160 MPa allowable, what area is needed to carry 40 kN? | 40 000 ÷ 160 | 250 mm² |
| A beam fails at 18 kN and works at 4 kN. Find the FoS. | 18 ÷ 4 | FoS = 4.5 |
The factor chosen is a judgement, not a constant. It rises when the loading is uncertain or shock-loaded, when failure would kill someone, when the material is brittle or its properties vary, and when inspection is difficult. It falls when loads are well known, the material is well characterised, and weight is critical — aircraft structures run low factors precisely because they are analysed, tested and inspected obsessively. An unnecessarily large factor is not "safer": it costs mass, material and money, and heavier parts impose larger loads on everything else.
4.3Failure modes
| Mode | What happens | Where you see it | How it is designed against |
|---|---|---|---|
| Tensile | The member is pulled apart once the stress exceeds its tensile strength | Ties, cables, bolts in tension | Increase the cross-sectional area, or use a stronger material |
| Compressive / crushing | The material is squashed and fails locally | Short posts, bearing surfaces, packers | Spread the load over a larger bearing area |
| Shear | Layers slide across each other — the member is cut | A bolt cut through by the plates it joins; a pin in a clevis | Larger pin diameter, or two shear planes rather than one |
| Buckling | A slender column bows sideways at a load far below the one that would crush it | Long thin struts, scaffold tubes, thin webs | Shorten it, brace it, fix the ends, or use a hollow tube or I-section with more material away from the centre |
| Fatigue | Repeated load cycles below the yield stress start a crack at a stress raiser, grow it, then it snaps suddenly | Rotating shafts, aircraft skins, springs, welds | Remove stress raisers — generous radii instead of sharp corners — polish surfaces, and inspect at scheduled intervals |
| Creep | Slow permanent stretching under a steady load, mainly at high temperature | Turbine blades, boiler tubing, polymers under sustained load | Choose creep-resistant alloys, lower the stress, lower the temperature |
Fatigue happens at stresses a static calculation says are perfectly safe. The crack starts at a stress raiser — a sharp internal corner, a bolt hole, a weld toe, a scratch — grows a fraction of a millimetre per cycle, and gives no visible warning until the remaining section fails all at once. It is why engineers round internal corners, and why fatigue-critical parts are given inspection schedules and finite service lives rather than being trusted forever.
4.4Standards and testing
- Australian Standards (AS and joint AS/NZS) are published by Standards Australia and are the accumulated record of what has worked and what has failed. AS 1100 covers technical drawing; the AS/NZS 1170 series covers structural design actions such as wind and floor loads; AS 4100 covers steel structures.
- Working to a standard means a part made in one workshop fits one made in another, an inspector can check it against a published rule, and liability is defensible.
- Destructive testing uses up the sample: tensile test (gives the whole stress–strain curve), Charpy impact test (toughness in joules), hardness testing, fatigue testing to a set number of cycles.
- Non-destructive testing leaves the part usable: dye penetrant for surface cracks, ultrasonic and radiographic testing for internal flaws, magnetic particle inspection for ferrous surfaces. This is how a bridge or an aircraft is checked without being taken apart.
- Testing is only meaningful with a sample size and a stated method. One test is an anecdote.
4.5Sustainability and life-cycle thinking
- Raw materials. Extraction and processing carry an embodied energy. New aluminium costs in the order of 200 MJ per kilogram to produce; recycled aluminium costs roughly 5 per cent of that. Steel is far lower again per kilogram, at roughly 30 MJ.
- Manufacture. Energy, water, scrap and emissions. Nesting parts to reduce offcuts is an engineering decision with a measurable result.
- Distribution. Mass and volume become fuel. A part that stacks or nests halves the trucks.
- Use. For anything powered, the use phase usually dominates the whole life-cycle total — so a small efficiency gain can outweigh a large manufacturing cost.
- End of life. Design for disassembly: mechanical fasteners rather than adhesives, fewer bonded material combinations, and parts marked with their material so they can be sorted. Repair first, then reuse, then recycle.
The engineering point is that these are numbers in the decision, not sentiments beside it. If recycled aluminium meets the strength criterion at a twentieth of the embodied energy, that belongs in the selection matrix with everything else — and stating the whole-of-life cost is often what wins the argument with the client.
The machine, the network, the work.
Four units covering QCAA Information & Communication Technology Units 1 and 2. This is an Applied subject: it is judged on what you can actually do — diagnose a fault, explain a network, choose the right file format, build a spreadsheet that gives the right number.
The mapFour units, two QCAA units
- Hardware and operating systems — Unit 1, Topic 1. The fetch–decode–execute cycle, RAM versus storage, input and output devices, the three buses, what an operating system actually does, and a troubleshooting method that works.
- Networks and the internet — Unit 1, Topic 2. LAN and WAN, wired and wireless, what a switch, router, modem and access point each really do, IP addresses and DNS, client–server versus peer-to-peer, cloud services, and network security.
- Digital media and design — Unit 2, Topic 1. Raster and vector, resolution and DPI, RGB and CMYK, file formats and compression with the arithmetic, layout and typography, and accessibility.
- ICT in the workplace — Unit 2, Topic 2. Spreadsheet formulas and charts, documents and templates, project workflow and version control, the 3-2-1 backup rule, workstation health and safety, and copyright and Creative Commons.
Questions are practical and situational: "the printer will not print — what do you check, in what order, and why?"; "which file format, and justify it"; "what does this formula return?". Vague answers lose marks. Name the component, name the step, give the number.
Hardware and operating systems
Every computer, from a phone to a server, does the same three things over and over, billions of times a second. Once you can name those three stages and say what each part of the machine contributes, most hardware questions answer themselves.
1.1The fetch–decode–execute cycle
1.2RAM, storage and the buses
| RAM (main memory) | Secondary storage (SSD, hard disk) | |
|---|---|---|
| Volatile? | Yes — contents vanish when power is lost | No — contents survive a shutdown |
| Speed | Very fast; the CPU works directly with it | Much slower, even for an SSD |
| Size | Typically 8–32 GB | Typically 256 GB–4 TB |
| Holds | Whatever is running right now, and its data | Every file, program and the operating system itself |
| So… | Unsaved work lives here, which is why a power cut loses it | Saving means copying from RAM to here |
The CPU talks to memory over three buses — bundles of wires, each with one job:
| Bus | Carries | Direction | Why |
|---|---|---|---|
| Address bus | The address being read from or written to | One way, CPU → memory | Only the CPU ever chooses the location; memory never chooses one for itself |
| Data bus | The actual data or instruction | Two way | Data must travel both to memory (write) and from memory (read) |
| Control bus | Signals such as read, write and clock | Mostly CPU → devices, with replies back | Something has to say whether this is a read or a write |
- Input devices put data in: keyboard, mouse, touchscreen, microphone, camera, barcode scanner, sensors.
- Output devices present results: monitor, printer, speakers, projector.
- Some devices are both: a touchscreen (input by touch, output by display), a headset, a network card, and any storage device (read and write).
1.3What the operating system actually does
| OS role | What it means in practice | Visible when… |
|---|---|---|
| File management | Folders, names, permissions, and knowing which blocks on the disk hold which file | You rename a file and nothing else breaks |
| Memory management | Deciding which program gets which part of RAM, and stopping one program from reading another's | A crashing program takes down only itself |
| Process scheduling | Sharing the CPU between programs fast enough that they seem simultaneous | Music keeps playing while you type |
| Device drivers | The translation layer between the OS and one particular piece of hardware | A new printer needs its driver before it will print |
| User interface | The desktop, windows and menus — or a command line | Always |
| Security and accounts | Logins, permissions, and what each user is allowed to reach | A student account cannot install software |
1.4A troubleshooting method
Guessing is not a method. The order below is the one used in industry, and it is examined:
- Identify the problem. Ask exactly what happens, exactly when it started, and what changed just before.
- Gather information. Error messages word for word, what still works, whether anyone else is affected.
- Establish a probable cause — and test the simplest, cheapest one first. Power and cables before motherboards.
- Test the theory, changing one thing at a time. Change three things and a fix tells you nothing about which one worked.
- Apply the fix and verify the whole system, not just the symptom you were shown.
- Document the fault and the fix, so the next person — probably you — does not start from zero.
If you swap the cable, reinstall the driver and restart the printer all at once and it works, you have not diagnosed anything — and you may have introduced a new fault you will meet next week. Changing one variable at a time is the same discipline as a controlled experiment.
Networks and the internet
Four boxes do almost all the work of any small network, and most people cannot say which is which. Learn what each one decides, and you can draw, explain and fault-find a network you have never seen.
2.1LAN and WAN, wired and wireless
| LAN — local area network | WAN — wide area network | |
|---|---|---|
| Covers | One site: a home, a school, an office floor | Large distances: cities, states, the globe |
| Owned by | You — your cabling, your switches | A carrier; you rent a connection across it |
| Speed | Fast, and free to use once installed | Slower, and billed |
| Example | The computers in one school building | The link joining a company's Brisbane and Perth offices — and the internet itself, the largest WAN of all |
| Wired (Ethernet) | Wireless (Wi-Fi) | |
|---|---|---|
| Speed and reliability | Higher and steadier; the cable is yours alone | Shared between everyone in range; drops with distance and walls |
| Interference | Essentially none | Microwaves, other networks, thick walls |
| Security | An attacker needs physical access to the cable | The signal leaves the building; it must be encrypted |
| Best for | Desktops, servers, printers, anything that never moves | Laptops, phones, tablets, and rooms you cannot cable |
2.2The four boxes, and what each decides
| Device | What it actually does | Decides using |
|---|---|---|
| Switch | Connects devices within one LAN and sends each message only out of the port where the destination sits — not to everybody | The destination device's hardware (MAC) address |
| Router | Passes traffic between two different networks — typically your LAN and the internet | The destination IP address |
| Modem | Converts between the digital signal your network uses and the signal the carrier's line carries (fibre, cable or copper) | Nothing — it translates, it does not choose |
| Wireless access point | Adds Wi-Fi coverage by bridging wireless devices onto the wired LAN | Nothing about routes — it is a radio doorway into the same LAN |
The box on a wall at home is usually all four in one case, which is exactly why people confuse them. In an exam, describe the function, not the box.
2.3Addresses and names
- Every device on a network has an IP address. An IPv4 address is four numbers from 0 to 255 separated by dots — 192.168.1.15. It identifies where a device is on the network.
- Addresses starting 192.168 are private: they work inside your LAN only, and the router presents one public address to the world on behalf of all of them.
- DNS — the Domain Name System — translates a name people can remember into the IP address machines need. It is the internet's phone book: you look up the name, you get the number, then you make the connection.
- Which is why "the internet is down" is often really "DNS is down": the connection works, but no name can be resolved into an address.
2.4How the work is shared
| Client–server | Peer-to-peer | |
|---|---|---|
| Structure | Clients request; one dedicated server provides | Every device is both client and server to the others |
| Accounts and files | Central: one login works anywhere, files live in one place | Scattered: each machine has its own users and its own files |
| Backup | Back up the server and you have everything | Every machine must be backed up separately, so in practice some are not |
| Cost and complexity | Server hardware and administration | Nearly free; nothing extra to buy |
| Suits | A school or business — any place needing control | Two or three machines sharing a printer |
Cloud services move some of that off your site altogether:
- IaaS — infrastructure as a service. You rent raw machines, storage and network, and you still install and manage the operating system and software. Maximum control, maximum work.
- SaaS — software as a service. You just use finished software over the internet — web email, an online office suite — and the provider runs everything underneath. Minimum work, minimum control.
- The trade-off in one line: the more the provider manages, the less you can change — and the more your work depends on your internet connection and on their business surviving.
2.5Network security
- A firewall inspects traffic entering or leaving a network and allows or blocks it against a set of rules. It is a gate with a list, not a virus scanner.
- A strong passphrase is long, unique to that account, and not built from your own details. Four unrelated words beat one word with letters swapped for symbols, because length defeats guessing far better than punctuation does.
- Two-factor authentication adds something you have or are, so a stolen password alone is not enough. It is the single most effective thing an ordinary user can turn on.
- Phishing is a fake message designed to make you hand over credentials. Its signature is manufactured urgency plus a link to a login page it supplies. Real organisations do not close your account in an hour.
- Social engineering attacks the person rather than the computer: a phone call from "IT" asking for your password, or a stranger held the door for you into the server room. No firewall filters a polite request.
- Which is why staff training is a genuine security control, and why "check the sender before clicking" belongs on the same list as encryption.
Digital media and design
Choosing a file format is an engineering decision with numbers behind it. So is choosing a colour model, a resolution and a typeface. This unit is about being able to justify each choice — and to calculate the consequences.
3.1Raster and vector
| Raster (bitmap) | Vector | |
|---|---|---|
| Made of | A fixed grid of coloured pixels | Shapes described by maths: points, lines, curves, fills |
| Enlarged | The pixels just get bigger — it goes blocky | Redrawn at the new size; perfectly sharp at any scale |
| File size grows with | Pixel dimensions and colour depth | The number of shapes, not the display size |
| Right for | Photographs, scans, screenshots, anything with continuous tone | Logos, icons, diagrams, maps, technical drawings, type |
| Formats | JPEG, PNG, GIF, WebP, TIFF | SVG, AI, EPS, and PDF when it holds vector art |
A club supplies its logo as a 200 × 60 pixel JPEG and wants it on a three-metre banner. It cannot be fixed by "increasing the resolution": the detail was never captured, and enlarging a raster image only enlarges its pixels. The answer is to obtain or redraw the logo as a vector file, which prints sharply at any size.
3.2Resolution, DPI and file size
- Resolution is the pixel dimensions of the image itself: 1920 × 1080 means 1920 across and 1080 down — 2,073,600 pixels in total.
- DPI (dots per inch, or PPI on screen) is how densely those pixels are laid down on paper. It only means something once you state a physical size.
- Screen work is typically 72–96 ppi; quality print is typically 300 dpi. So an image to be printed 6 inches wide at 300 dpi needs 6 × 300 = 1800 pixels across.
- Uncompressed file size = width × height × bytes per pixel. Full 24-bit colour is 3 bytes per pixel (one each for red, green and blue).
| Image | Pixels | × 3 bytes each | Uncompressed size |
|---|---|---|---|
| 800 × 600 | 480,000 | 1,440,000 bytes | 1.44 MB |
| 1600 × 1200 | 1,920,000 | 5,760,000 bytes | 5.76 MB — four times as big |
| 1920 × 1080 | 2,073,600 | 6,220,800 bytes | 6.22 MB |
Note the middle row: doubling both dimensions quadruples the file, because you doubled the width and the height. This is the same arithmetic as a nested loop, and it is why "just send the full-size photo" fills an inbox.
3.3Colour: RGB and CMYK
3.4Formats and compression
| Format | Raster or vector | Compression | Use it for |
|---|---|---|---|
| JPEG | Raster | Lossy | Photographs, where discarded detail is hard to see and the size saving is huge |
| PNG | Raster | Lossless, supports transparency | Screenshots, logos on a web page, anything with sharp edges or text |
| GIF | Raster | Lossless, 256 colours only | Simple animation; poor for photographs |
| SVG | Vector | Lossless (it is text) | Logos, icons and diagrams on the web, at any size |
| Either | Depends what was placed in it | Sending a finished document that must look the same everywhere |
- Lossy compression permanently discards detail the eye is unlikely to notice. Far smaller files — but the loss accumulates: re-saving the same JPEG repeatedly degrades it a little further each time.
- Lossy is wrong for sharp edges. Text and line art develop blurry halos, which is why a screenshot saved as JPEG looks dirty and the same shot as PNG does not.
- Lossless compression rebuilds the original exactly, bit for bit. Larger files, but nothing is lost no matter how often you re-save.
- Rule of thumb: photograph → JPEG; anything with text, sharp edges or transparency → PNG; logo or diagram → SVG. Always keep an untouched master in a lossless format and export copies from it.
3.5Layout, typography and accessibility
- Alignment. Everything lines up with something else. A single invisible left edge does more for a page than any amount of decoration.
- Proximity. Things that belong together sit together; unrelated things get white space between them. Space is what shows the reader the structure.
- Contrast and hierarchy. Make the important thing obviously bigger or heavier. If everything is emphasised, nothing is.
- Repetition. The same heading style, the same spacing, the same colours on every page — consistency is what makes a set of pages look designed.
- Readable type. Body text around 10–12 pt in print; line length about 50–75 characters; at most two or three typefaces in one document; never a whole paragraph in capitals or italics.
- Accessibility. Body text needs a contrast ratio of at least 4.5:1 against its background. Every meaningful image needs alt text saying what it conveys; a purely decorative image takes an empty alt attribute so a screen reader skips it rather than announcing "image".
ICT in the workplace
Spreadsheets that give the right number, documents that stay consistent, work that can be found again next month, backups that survive the fire, a chair that does not wreck your back, and images you are actually allowed to use.
4.1The worked spreadsheet for this unit
Every formula below and every question in the drills refers to this sheet. Cell E1 holds the GST rate, 0.1.
| A | B | C | |
|---|---|---|---|
| 1 | Item | Sold | Price |
| 2 | Wrap | 12 | 6.50 |
| 3 | Juice | 30 | 2.00 |
| 4 | Salad | 8 | 8.00 |
| 5 | Muffin | 20 | 3.50 |
4.2References: relative, absolute and mixed
| Written as | Called | Copied from D2 down to D3, it becomes | Use it when |
|---|---|---|---|
| B2 | Relative | B3 — the row shifts with the formula | Each row should use its own data |
| $E$1 | Absolute | $E$1 — unchanged | Every row must use the same one cell, such as a tax rate |
| $E1 | Mixed | $E2 — the column is locked, the row moves | Copying across columns but down rows |
| E$1 | Mixed | E$1 — the row is locked, the column would move | Copying across a header row |
Writing =B2*C2*E1 and copying it down. Row 3 quietly becomes =B3*C3*E2, which multiplies by an empty cell — so every GST figure below the first is zero, and nothing looks obviously broken. $E$1 prevents it. The dollar sign locks whatever follows it.
4.3Formulas, with their exact results
| Formula | What it does | Result on the sheet above |
|---|---|---|
| =SUM(B2:B5) | Adds every value in the range | 12 + 30 + 8 + 20 = 70 |
| =AVERAGE(B2:B5) | Adds them, divides by how many | 70 ÷ 4 = 17.5 |
| =COUNTIF(B2:B5,">15") | Counts only the cells meeting the condition | Only 30 and 20 are above 15: 2 |
| =IF(B2>=20,"Restock","OK") | Test, then the true value, then the false value | B2 is 12, so the test is false: OK (the same formula on row 3, where B3 is 30, gives Restock) |
| =B2*C2 in D2 | Revenue for that row | 12 × 6.50 = 78 |
| =B3*C3 in D3, after copying D2 down | The relative references both moved one row | 30 × 2.00 = 60 |
| =SUM(D2:D5) with D2:D5 = 78, 60, 64, 70 | Total revenue | 78 + 60 + 64 + 70 = 272 |
| =D2*$E$1 | GST on row 2, using the locked rate in E1 | 78 × 0.1 = 7.8, and copying it down still uses E1 |
4.4Choosing a chart that suits the data
| Chart | Right when | Wrong when |
|---|---|---|
| Column / bar | Comparing a value across categories — sales per item | Rarely wrong; the safe default |
| Line | Showing change over time — monthly sales across two years | The horizontal axis is not ordered, so the line means nothing |
| Pie | Parts of one whole, a handful of slices, adding to 100% | Many slices, or values from different wholes — the eye cannot compare angles |
| Scatter | Looking for a relationship between two numeric variables | One axis is categories rather than numbers |
Whatever the chart: title it, label both axes with units, and start a bar chart's value axis at zero. A truncated axis exaggerates a difference, and doing it on purpose is misleading.
4.5Documents, templates and workflow
- Format with styles (Heading 1, Body), not by selecting text and changing the font. Change the style once and every instance updates; manual formatting has to be hunted down one paragraph at a time.
- A template fixes layout, styles and branding so every document from it matches, and nobody rebuilds the letterhead from scratch.
- A project runs brief → plan → produce → review → deliver. The plan lists the tasks, who owns each, how long it should take, and the milestones — the checkpoints where you find out early that you are behind.
- Version control at concept level: one shared master, numbered versions (v1.0, v1.1, v2.0), and a change log recording what changed, when, and who changed it. Never a folder of report_final, report_final2 and report_FINAL_use_this — none of those names says which is current or what differs.
- The reason it matters is recovery: version control lets you go back to the state before a bad change, and tells you who to ask about it.
4.6Backups: the 3-2-1 rule
| Rule | Means | Protects against |
|---|---|---|
| 3 copies | The working file plus two backups | One backup that turns out to be corrupt |
| 2 different media | Not all on the same drive or the same kind of device | A single drive failing, or one technology failing |
| 1 copy off-site | Another building, or a cloud service | Fire, flood, theft, and ransomware that encrypts everything attached |
And the step people skip: test a restore. A backup nobody has ever restored from is a hope, not a backup.
4.7Health and safety at a workstation
- Monitor: top of the screen at or just below eye level, about an arm's length away, tilted to avoid glare from windows and lights.
- Chair and posture: feet flat on the floor or a footrest, knees roughly 90°, lower back supported, shoulders relaxed.
- Keyboard and mouse: close enough that the forearms stay roughly horizontal and the wrists straight, not bent up over a raised keyboard.
- Breaks: stand up and look at something distant every 20–30 minutes. Sustained close focus tires the eye's focusing muscle, and that is what causes the headaches and the gritty eyes.
- The room: enough light to read by without straining, no glare on the screen, cables routed out of walkways, ventilation and no trip hazards.
- These are not fussiness. Repetitive strain injury and back damage are the ordinary occupational injuries of desk work, and they are cumulative.
4.8Copyright, licensing and Creative Commons
- Copyright exists automatically the moment an original work is created — no symbol, registration or fee is needed. Anything you find online has an owner unless you are told otherwise.
- A licence is permission to use someone's work on stated conditions. "Free to download" is not a licence to republish.
- Creative Commons licences let a creator grant permission in advance:
- CC BY — use and adapt it, commercially too, provided you credit the creator.
- CC BY-SA — as above, but your version must carry the same licence (share alike).
- CC BY-ND — you may share it but not change it (no derivatives).
- CC BY-NC — non-commercial use only. Selling anything that contains it is out.
- CC0 — the creator has waived their rights; effectively public domain.
- A proper attribution names four things: the title, the creator, the source (a link) and the licence.
Senior furnishing: the reasoning behind the hands.
In Year 10 you learned the workshop's rules. Senior Furnishing Skills asks you to justify them: which duty the law actually places on you, why a board cups the way it does and not the other way, why one joint is specified over another for a named load, and how a finished job is proved to be within tolerance. Four topics across Units 1 and 2.
The mapTwo units, four topics
- Unit 1, Topic 1 — Workplace health and safety. The WHS Act's duty of care, the risk management cycle, the hierarchy of controls, SWMS, isolation and lockout, and the cumulative hazards of dust and noise.
- Unit 1, Topic 2 — Timber technology. How a tree is built, what seasoning really removes, fibre saturation point, why boards distort, and where each manufactured board is correctly specified.
- Unit 2, Topic 1 — Cabinetmaking practice. Setting out and cutting lists, the machining sequence, the joint family matched to load, carcase against frame-and-panel, and the hardware that makes a cabinet work.
- Unit 2, Topic 2 — Finishing and quality. Surface preparation, adhesives and assembly times, the five finishes compared, and quality control with real tolerances.
Applied assessment rewards correct practice and the justification for it. Nearly every written response asks you to select and justify: name the control and say why it outranks the one below; name the material and link its property to the demand; name the joint and link it to the load it carries; name the finish and link it to the service conditions. A bare noun scores almost nothing. Noun + property + consequence scores the mark.
Workplace health and safety: duty, risk, control
Safety in a senior workshop is not a poster on the wall. It is a legal duty with named duty holders, a repeatable four-step cycle, and a ranked list of controls that decides which answer earns the marks.
1.1Duty of care under the WHS Act
Australia's workplaces run under harmonised Work Health and Safety laws — in Queensland, the Work Health and Safety Act 2011 and its Regulation, supported by Codes of Practice published by Safe Work Australia. The Act does not simply say “be careful”. It names who owes a duty, to whom, and how far that duty goes.
| Duty holder | Who that is in a furnishing workshop | What they must do |
|---|---|---|
| PCBU — the person conducting a business or undertaking | The cabinet shop, the school, the contractor | Ensure, so far as is reasonably practicable, the health and safety of workers and of anyone else affected by the work — safe plant, safe systems of work, training, supervision, information and facilities. |
| Officers | Directors and managers who make the decisions | Exercise due diligence: know the hazards, provide the resources, and check that the PCBU's duties are actually being met. |
| Workers | You, on the machine | Take reasonable care for your own health and safety; take reasonable care that what you do (or fail to do) does not harm others; comply with reasonable instruction; and co-operate with the workplace's policies. |
| Other persons at the workplace | Visitors, a delivery driver, a client viewing a job | Take reasonable care for themselves and others, and follow reasonable instructions. |
It is not “whatever is convenient”. Deciding what is reasonably practicable weighs, together: how likely the hazard is to cause harm; how serious that harm would be; what the person knows or ought to know about the hazard and the ways of removing it; the availability and suitability of those controls; and only then the cost — and cost counts as a reason not to act only where it is grossly disproportionate to the risk. A dust extractor is never grossly disproportionate to a cancer risk, which is why “we couldn't afford it” is not a defence.
1.2The risk management cycle
1.3The hierarchy of controls, at senior level
Safe Work Australia groups the controls into three levels of protection, which the workshop then teaches as six steps. Knowing both the six steps and the three groupings is what separates a senior answer from a Year 10 one: the groupings explain why the order is what it is.
| Level of protection | # | Control | What it does to the hazard | Furnishing example |
|---|---|---|---|---|
| Level 1 — the most effective: the hazard is gone | 1 | Elimination | The hazard no longer exists | Order the panels cut and edged by the supplier, so nobody rips or edges them at all |
| Level 2 — the hazard remains, but it is kept away from people | 2 | Substitution | A less hazardous thing does the same job | A water-based lacquer in place of a solvent-based one; a pre-finished board in place of spraying |
| 3 | Isolation | A barrier or distance separates people from it | The spray booth; the thicknesser in its own enclosed, interlocked bay | |
| 4 | Engineering | Hardware removes the exposure | Blade guard and riving knife, extraction at each machine's cutting point, a power feeder, an emergency stop | |
| Level 3 — the least effective: the hazard is untouched, only the person's behaviour changes | 5 | Administrative | Changes what people do | The SWMS, induction and training, machine sign-off, job rotation away from noise, signage |
| 6 | PPE | A barrier on one person, while worn | Safety glasses, Class 5 earmuffs, a fit-tested P2 respirator, enclosed footwear |
- You work down the list and stop at the highest level that is reasonably practicable — you do not choose the easiest.
- Controls can be combined. Extraction (level 4) plus a fit-tested P2 respirator (level 6) is normal practice for MDF machining; the respirator is the backup, never the plan.
- Levels 5 and 6 fail the moment a person forgets, is rushed, or is new. Levels 1–4 keep working whether or not anyone remembers them — which is the whole argument for the order.
1.4Safe Work Method Statements, isolation and lockout
- A SWMS (Safe Work Method Statement) is a written document that sets out, for one activity: the task and its high-risk elements, the hazards, the control measures chosen from the hierarchy, and how those controls will be put in place, monitored and reviewed. It is prepared before the work starts, kept where the work happens, and revised when the job or the risk changes.
- A safe work procedure or machine SWP is the same discipline applied to one machine: PPE, pre-start checks, the correct steps in order, and what to do if something goes wrong. In a school workshop you sign one before you are allowed on the machine.
- Guarding is an engineering control, so removing a guard is a five-level demotion in one movement. Guards that must be removed for setting are interlocked, so the machine cannot run with the guard open.
- Isolation and lockout/tagout: before any blade change, jam clearing or setting, the machine is switched off at its isolator, all movement is allowed to stop, the isolator is locked with a personal lock and tagged with the name of the person working on it. The person who fits the lock is the only person who removes it — that is what makes it a control rather than a promise.
- Emergency stop is located before the machine is started, not after something has gone wrong.
1.5Dust, noise and chemicals: the cumulative hazards
- Wood dust is a health hazard, not just a mess. The fine fraction reaches deep into the lungs, and hardwood dust is classified as a carcinogen — it is an established cause of cancer of the nose and sinuses, which is why its workplace exposure standard is far stricter than the standard for softwood dust. MDF adds a very fine, resin-bearing dust of its own. The control order is extraction at the cutting point (level 4) first, general ventilation and housekeeping next, and a fit-tested P2 respirator last. A respirator that does not seal — on a beard, or with a slack strap — provides close to nothing.
- Noise damage is cumulative, painless and permanent. The Australian exposure standard is an eight-hour equivalent of 85 dB(A), with a peak limit of 140 dB(C) that must never be exceeded. Routers, thicknessers and extraction fans sit above that all day. There is no warning ache and no recovery: every unprotected hour adds to a total that only moves one way.
- Chemicals: read the SDS. Every hazardous chemical in the workshop — solvent lacquer, two-pack polyurethane, contact adhesive, thinners — must have a current Safety Data Sheet supplied by the manufacturer, kept readily accessible to everyone who uses it. The SDS names the hazards, the required ventilation and PPE, the first-aid response, the fire response, and safe storage and disposal. Containers must be correctly labelled, and decanted product labelled too. Two-pack finishes containing isocyanates need a level of respiratory protection and ventilation that ordinary spraying does not.
- Manual handling is the quiet one: sheet goods are heavy, awkward and sharp-edged. A full sheet of 18 mm MDF is a two-person or mechanical lift, and a panel saw or a lifter is an engineering control, not a luxury.
Timber technology: the material explained, not just named
Year 10 taught you that timber moves. Senior Furnishing Skills asks how much, in which direction, and why — and expects you to predict what a board will do before you cut it.
2.1How a tree is built
| Hardwood | Softwood | |
|---|---|---|
| Botanical class | Angiosperm — broadleaved, flowering, seeds in a fruit or capsule | Gymnosperm — needle-leaved conifer, seeds in a cone |
| Cell structure (the senior-level difference) | Has vessels (pores) for conducting sap, plus fibres for strength — a more complex structure, and the pores are what make the grain look open | No vessels. Tracheids do both jobs, conducting and supporting — a simpler, more uniform structure |
| Growth | Slow, decades to a century | Fast; plantation radiata pine is harvested at about 30 years |
| Australian examples | Jarrah, spotted gum, blackbutt, Tasmanian oak, blackwood, silky oak | Radiata pine, hoop pine, cypress pine, Douglas fir |
| The exception to quote | Balsa — a hardwood you can dent with a thumbnail | Cypress pine — a softwood hard enough to blunt tools |
2.2Seasoning, moisture content and fibre saturation point
Water sits in green timber in two different places, and that is the whole key to seasoning. Free water fills the hollow cell cavities. Bound water is held chemically inside the cell walls themselves. Drying removes the free water first, and while only free water is leaving, the timber does not shrink at all — the cell walls are still full.
The point at which the cavities are empty but the walls are still saturated is the fibre saturation point, at roughly 30% moisture content. Below that, bound water starts leaving the cell walls, the walls themselves get thinner, and the timber shrinks. Above 30% MC the timber is also wet enough for decay fungi to work. Both facts come from the same number.
MC% = (wet mass − oven-dry mass) ÷ oven-dry mass × 100. Notice you divide by the oven-dry mass, not the wet mass. That is why moisture contents above 100% are perfectly possible: a green board can hold more water than it holds wood. A board of 900 g that oven-dries to 500 g has lost 400 g of water from 500 g of wood — a moisture content of 80%.
| Air drying | Kiln drying | |
|---|---|---|
| How | Stacked outdoors under cover on bearers, every layer separated by stickers so air passes between all faces | A chamber with controlled temperature, humidity and air flow, run to a schedule for that species and thickness |
| Time | Months to years — a rough guide is a year per 25 mm of thickness | Days to weeks |
| How dry it gets | Only down to the local outdoor equilibrium — typically 12–18% MC, too wet for indoor furniture on its own | Any target: 10–12% for indoor furniture is normal, and it is repeatable |
| Other effects | Cheap, low energy, gentle — but uncontrolled, and it does not kill insects or set the resin | Kills borers and their eggs and can set resin in pine — but energy costs money, and a rushed schedule causes collapse, honeycombing and case hardening |
- Equilibrium moisture content (EMC) is the moisture content at which timber neither gains nor loses moisture in the surrounding air. It is set by the air's temperature and relative humidity, so it changes with the season and with air conditioning. Timber is hygroscopic: it chases its EMC forever, which is why seasoning is not permanent and why a job is always acclimatised in the room it will live in before it is machined.
- Case hardening is the kiln fault most worth knowing: the outer shell dries and sets while the core is still wet, leaving the shell in compression and the core in tension. The board looks perfect — until it is ripped, when it pinches the blade and springs violently out of straight.
2.3Movement, sawing method and the named defects
Timber moves by very different amounts in its three directions, and the ratio is the reason boards distort rather than simply getting smaller:
| Direction | Movement | Consequence for the maker |
|---|---|---|
| Tangential — along the growth ring, around the log | Greatest — about twice the radial movement | A back-sawn board's width changes most, and it cups |
| Radial — across the rings, out from the centre | About half the tangential movement | A quarter-sawn board is the most dimensionally stable across its width |
| Longitudinal — along the length of the grain | Negligible — a fraction of one per cent | Length can be treated as fixed; only width and thickness need allowances |
| Defect | What it looks like | Cause |
|---|---|---|
| Cupping | The board curls across its width, like a shallow gutter | Tangential shrinkage exceeds radial — the face further from the heart shrinks more |
| Bowing | A curve along the length, seen on the face | Uneven drying along the board, or poor stacking with too few stickers |
| Spring (crook) | A curve along the length, seen on the edge | Released growth stresses, or grain that runs out of the edge |
| Twist (wind) | The four corners no longer lie in one plane | Spiral or interlocked grain drying unevenly |
| Checking | Small splits opening along the grain on the surface or the end | The surface dried far faster than the core — drying too hard, or unsealed end grain |
| Collapse | The board looks washboarded and undersized | Cell cavities crushed by drying too fast at high temperature, above fibre saturation point |
2.4Manufactured boards: specifying, not just naming
| Board | Construction | Specify it when… | Do not specify it when… |
|---|---|---|---|
| Plywood | An odd number of veneers, each at 90° to its neighbours and balanced in pairs about the central core, so both faces run the same way and the sheet stays flat | Strength-to-weight or a thin panel matters; the panel is curved; the job meets moisture and an A-bond (phenolic) grade is used | A crisp routed profile is wanted — the plies show and the face veneer is thin enough to sand through |
| MDF | Wood broken to individual fibres, blended with resin and hot-pressed — no grain, uniform right through | The work will be painted or veneered, or routed to a moulded edge; a dead-flat surface is needed | It will get wet (it swells irreversibly), or screws must hold in the edge; and never without extraction — the dust is very fine |
| Particleboard | Wood chips and flakes with resin, pressed with finer chips at the faces; usually supplied melamine-faced | Cost governs and the panel is supported: flat-pack carcases, shelving on short spans, bench substrates | Long unsupported spans (it sags), edge screwing, or anywhere water can reach |
| Veneered board | A sliced decorative veneer on an MDF or particleboard substrate, with a balancing veneer on the back | The look of solid timber is wanted on a stable, wide, cheap panel — the whole basis of commercial furniture | The surface must survive repeated re-sanding — the veneer is often under 0.6 mm thick |
A veneer glued to one face only will shrink as it dries and pull that face concave — the panel bows. A balancing (backing) veneer of similar thickness on the opposite face pulls equally the other way, and the panel stays flat. It is the same principle that makes plywood's ply count odd and its layers mirrored about the core: symmetry about the centre keeps a panel flat.
Cabinetmaking practice: from cutting list to cabinet
A cabinet is made twice: once on paper as a set-out and a cutting list, and once in timber. Get the first one wrong and no amount of skill at the machines will rescue it.
3.1Setting out and the cutting list
- A setting-out rod is a full-size drawing of the job's critical sections on a board or a strip of MDF. Because it is full size there is no scale to misread and no arithmetic to get wrong: every part is taken directly off the rod, and every part therefore agrees with every other.
- A cutting list is the ordered table of every component: part name, quantity, material, and finished length × width × thickness, with the grain direction noted where it matters. Machining allowances are added to the sawn sizes, never to the finished sizes on the list.
- Order the list by material and by machine setting, not by where the parts end up. Everything that gets the same thicknesser or fence setting is cut together — parts machined at one setting are identical, parts machined at two settings are only nearly identical.
- Work from a face side and face edge, marked on every component, and take every later measurement from those two surfaces. This is what stops small errors accumulating along a job.
- Check the list against the drawing before cutting anything, and check the total stock needed, remembering that every saw cut turns a kerf's width of timber into dust.
3.2The machining sequence
Solid timber is prepared in a fixed order, and the order is not arbitrary: each step provides the reference surface that the next machine needs. Skip the buzzer and the thicknesser will faithfully copy the bend already in the board.
| # | Step | Machine | Why it must be here |
|---|---|---|---|
| 1 | Dock and rip oversize — roughly to length and width, with allowance left on | Docking saw, rip saw | Shorter, narrower pieces are easier to straighten, and cutting releases growth stresses now rather than later |
| 2 | Machine one face side flat | Buzzer (surface planer / jointer) | Creates the first true reference surface — nothing before this is trustworthy |
| 3 | Machine one face edge square to the face side | Buzzer, against the fence | Gives a second reference, at a known 90° to the first |
| 4 | Thickness the opposite face parallel to the face side | Thicknesser | The thicknesser copies whatever face rides on its bed — so that face must already be flat |
| 5 | Rip to finished width, face edge against the fence | Panel or rip saw | Both reference surfaces now exist, so the cut is parallel and square |
| 6 | Dock to finished length, face edge against the fence, using a stop for repeats | Docking saw | Length last, so nothing that follows can shorten it — and a stop makes every repeat identical |
After that the joints are cut: routing for housings, rebates, grooves and moulded profiles; mortising for frames; docking with a stop for repeated shoulders. Cut the joints while the components are still square-ended and unshaped — curves and mouldings go last, because they destroy the flat reference faces every jig needs.
3.3Choosing the joint for the load
| Joint | What it resists best | Correct application | Why not something else |
|---|---|---|---|
| Butt | Almost nothing on its own — end grain gives no useful glue bond | Only where a fastener, dowel or block does the real work, or where a back panel braces the box | Any load at all needs an interlock or extra glue area |
| Lap (half lap) | Racking in a light frame; gives one long-grain gluing face | Cross-halvings, light face frames, jigs | Weaker than a tenon and it shows on both faces |
| Housing (dado) | Downward load — the trench walls carry the shelf directly | Fixed shelves and dividers in a carcase; stopped at the front so it does not show | A butt joint would rely on screws alone in end grain |
| Rebate | Location and a right-angled seat; two glue faces | Cabinet backs, glazing, drawer bottoms, box corners | Not a structural corner on its own — it is usually nailed or screwed as well |
| Mortise and tenon | Racking — large long-grain cheeks plus shoulders that stop the rail rotating | Chair and table frames, doors, anything with legs and rails; haunched where the joint runs out at the top of a stile, so the groove is filled and the tenon cannot twist | Dowels give far less glue area and no shoulder resistance |
| Dovetail | Withdrawal — the wedged tails cannot pull out even unglued | Drawer fronts and backs, fine boxes. Lapped (half-blind) at a drawer front so no end grain shows on the face | Any glue-only joint eventually fails under a repeated pull |
| Dowel | Alignment plus modest shear; adds long-grain surface inside end grain | Face frames and light carcases where machinery for tenons is not available | Accuracy is unforgiving — the holes must match exactly in both parts |
| Biscuit | Mainly alignment, with a useful gain over a plain butt | Edge-joining boards, lining up panels and carcase parts quickly | Not a substitute for a tenon in a frame — the biscuit is short and thin |
| Domino / loose tenon | Racking and shear, like a mortise and tenon | Production frames and carcases — effectively a machine-cut mortise and tenon in seconds | Needs the specific machine; otherwise cut a real tenon |
Three parts, one sentence: the load, the joint, the property that answers the load. “A drawer front is pulled straight out several times a day, so it needs a mechanical interlock rather than glue alone: a lapped dovetail, whose wedge-shaped tails cannot withdraw and whose lap hides the end grain on the drawer face.” Compare with “a dovetail, because it is strong” — same joint, a fraction of the marks.
3.4Carcase construction and frame-and-panel
3.5Hardware
| Hardware | How it works | Specified when |
|---|---|---|
| Butt hinge | Two leaves let into the door edge and the carcase; the knuckle sets the pivot | Traditional and inset doors; nothing is adjustable afterwards, so the fitting must be right first time |
| Concealed cup hinge (European) | A 35 mm cup bored into the door, on a mounting plate screwed to the carcase side; adjustable for height, depth and sideways alignment after fitting | Almost all modern cabinets: it is invisible when closed, and the three-way adjustment lets a run of doors be aligned perfectly on site |
| Side-mounted ball-bearing runners | A runner each side, needing a fixed clearance between drawer box and opening | General drawer work; simple to fit, and the standard clearance is 12.5 mm each side, so the box is made 25 mm narrower than the opening |
| Undermount runners | Hidden beneath the drawer box, gripping the underside of the drawer bottom | Higher-quality work where the drawer sides must be seen without hardware showing; the drawer box sizes are set by the manufacturer's specification |
| Cam lock fitting (knock-down) | A steel dowel screwed into one panel engages a cam housed in the other; a quarter turn draws the parts tight | Flat-pack and knock-down furniture: it must assemble with a screwdriver and come apart again |
| Confirmat screw | A coarse-threaded screw into a stepped pilot hole in the panel edge | Permanent particleboard and MDF carcase assembly — it holds far better in a board edge than an ordinary screw |
| Shelf pins on the 32 mm system | Rows of 5 mm holes at 32 mm centres up both cabinet sides, taking pins, hinge plates and runners | Adjustable shelving and any production cabinet — one drilling pattern serves every fitting |
Finishing and quality: proving the job is right
The finish is the only part of your work a client ever touches, and quality control is what turns “it looks all right” into a measured statement. Both are examined, and both are about doing things in a fixed order.
4.1Surface preparation
Abrasive paper does not smooth timber — it scratches it in a controlled way. Every grit leaves a field of scratches of its own size, and the next grit's only job is to replace them with finer ones. That is why the sequence runs coarse to fine and why a grit cannot be skipped: 180 is not aggressive enough to cut out 80-grit scratches, so it merely polishes the ridges between them and the coarse scratches stay, invisible on bare timber, until the first coat of finish makes them appear as dark lines.
- A typical schedule is 80 → 120 → 180 → 240. Start at the coarsest grit the job actually needs — starting too coarse creates damage you then have to sand away.
- Vacuum and wipe between grits. One stray 80-grit particle dragged along under a 180-grit sheet cuts a scratch you must chase out from the beginning.
- Sand with the grain and use a block or a machine platen on flat work; fingers dig hollows, especially near edges.
- Do not go finer than the finish needs. Beyond about 240 the surface begins to burnish, closing the pores so that stain and penetrating oil are absorbed unevenly and blotch.
- Raise the grain before a water-based finish: wipe with a damp cloth, let it dry, and cut the lifted fibres off with a light pass of the final grit. Otherwise the first coat does the lifting and the surface dries rough.
- Ease the arris — a knife-sharp edge holds almost no finish and dents at a touch.
- Dried glue is the classic preparation failure: it is invisible on bare timber and shows as a pale patch that refuses stain. Remove squeeze-out at assembly, and check the surface under a low raking light before the first coat.
4.2Adhesives and the assembly window
PVA (polyvinyl acetate) is the workshop default, and on long grain a properly made PVA joint is stronger than the timber beside it — loaded to destruction, the wood fails and the glue line does not. Senior work separates two different times that Year 10 treats as one:
| Term | Definition | What happens if you exceed it |
|---|---|---|
| Open assembly time | From spreading the adhesive until the two parts are brought together | The surface skins over. The joint closes and looks perfect but is effectively unglued. |
| Closed assembly time | From bringing the parts together until full clamping pressure is applied | The glue has begun to set before the joint is pulled tight, so the glue line stays thick and weak. |
| Clamp (press) time | How long the clamps stay on before the assembly can be handled | Handled early, the joint creeps and the assembly loses square. |
| Full cure | Around 24 hours before the joint takes design load or is machined | Machining a green glue line tears it open and clogs the cutter. |
- Clamping pressure does not make a joint strong; it makes the glue line thin and even. Too little and you get a thick, weak line and gaps. Too much and you squeeze out so much adhesive that the joint is starved — and you can bow the components. The target is firm, even pressure that produces a small continuous bead of squeeze-out along the whole joint.
- Always dry-fit first, with every clamp and caul laid out and adjusted, before the bottle is opened. The clock starts when the glue is spread, not when you are ready.
- Check for square while it is still wet: measure both diagonals of a frame or carcase — equal diagonals mean square. Also sight across the assembly for wind.
- Choosing the adhesive: interior PVA for dry indoor work; cross-linking PVA where moisture or heat is possible; polyurethane for exterior and oily timbers (it needs moisture to cure and foams as it goes); contact adhesive for laminates — coated on both faces, left to touch-dry, then pressed, with no repositioning at all once the faces meet; hot melt for edge banding and temporary holds; epoxy where gap filling and water resistance both matter.
4.3The five finishes compared
| Finish | How it cures | Protection | Application | Repairability |
|---|---|---|---|---|
| Oil (danish, tung, hardwax) | Penetrates and cures inside the fibres | Low to moderate — water-resistant, not waterproof; no heat resistance | Wiped or brushed on and the excess wiped off; several thin applications | Excellent — clean and re-oil the damaged spot; no stripping |
| Wax | A soft buffed film; the solvent flashes off | Lowest of all — marks with water, heat and fingerprints | Applied on a cloth and buffed | Excellent — re-wax and buff whenever it dulls |
| Shellac | A resin dissolved in alcohol; the alcohol evaporates | Low — poor against water, heat and alcohol (a spilled drink marks it) | Brushed, padded or French polished; dries in minutes | Very good — new shellac re-dissolves the coat below, so repairs blend in |
| Lacquer (nitrocellulose, pre-catalysed) | Solvent evaporates; each coat softens and melts into the one below | Good — the standard commercial furniture finish; less heat- and solvent-resistant than polyurethane | Sprayed, in a booth with extraction and correct respiratory protection; dries very fast | Very good — because coats burn into each other, a damaged area can be re-sprayed and blended |
| Polyurethane / varnish | Cures by chemical reaction into a hard cross-linked film | Highest — water, heat, solvents and abrasion | Brushed, wiped or sprayed in thin coats, de-nibbed between coats | Poorest — a cured coat will not re-dissolve, so repair means abrading the area (or the whole panel) and recoating |
Name the service conditions first, then the finish, then the property that answers them. A café tabletop meets spilled drinks, hot cups and constant abrasion, and will be cleaned daily by staff who cannot re-oil it — so a two-pack polyurethane is specified for its water, heat and abrasion resistance, accepting that damage will need the panel sanded and recoated. A hand-made timber jewellery box that its owner will handle for decades takes a hardwax oil, because the low protection is enough and the owner can repair a scratch themselves. Same question, two different correct answers — the conditions decide.
4.4Quality control, tolerances and rectification
- A tolerance is the permitted variation from a stated size. Written 400 ± 0.5 mm, it accepts anything from 399.5 to 400.5 mm — a tolerance band 1 mm wide. Tighter tolerances cost more machine time and produce more rejects, so they are specified only where the fit actually matters.
- In furnishing, the tolerances that matter are usually about fit and consistency rather than absolute size: a run of doors with even 3 mm gaps looks right even if all of them are 0.5 mm narrower than drawn, whereas one door 2 mm out among five looks broken.
- Inspect at each stage, not at the end. Check components off the cutting list before joints are cut; check joints dry-fitted before glue; check square and wind before the glue grabs; check the surface under raking light before the first coat. A defect found at its own stage costs minutes; the same defect found after finishing can cost the component.
- Standard checks: diagonals equal for square; a straight edge and feeler for flatness; winding sticks sighted across a frame for twist; a consistent gap measured with the same offcut used as a gauge; hinges and runners checked for full travel and self-closing before the job leaves.
- Rectification is graded: re-sand and re-coat a finish defect; fill and colour-match a small blemish where the panel is not visible in raking light; re-machine or replace a component that is outside tolerance. Deciding which of the three is honest — rather than filling something that should be remade — is part of what is assessed.
- Record what you did. In an Applied subject, a quality record — the checks made, the results, and the action taken — is evidence, and evidence is what is marked.
Drawings that a stranger can build from.
Senior Industrial Graphics is a language subject: the vocabulary is AS 1100, the grammar is third-angle projection, and the test of fluency is whether a person you will never meet can make your part correctly from your sheet alone. Four topics across Units 1 and 2 — standards, orthographic, pictorial, and CAD through to the machine.
The mapTwo units, four topics
- Unit 1, Topic 1 — Drawing standards. AS 1100, the full set of line types including section and cutting-plane lines, lettering, sheet layout and title block, and scale arithmetic done exactly.
- Unit 1, Topic 2 — Orthographic projection. Third angle as Australian practice, view selection and alignment, the dimensioning rules, sectional views and hatching, and auxiliary views.
- Unit 2, Topic 1 — Pictorial and presentation drawing. Isometric and its ellipses, cavalier and cabinet oblique, one- and two-point perspective, exploded assemblies with balloons and a parts list.
- Unit 2, Topic 2 — CAD and digital documentation. Parametric modelling, constraints and design intent, assemblies and mates, drawings generated from the model, file formats, and the route to CNC and 3D printing.
A technical drawing is not a picture — it is an instruction that has to survive the journey. It may be read by a machinist in another state, a supplier overseas or a CNC operator in five years' time, none of whom can ask you what you meant. Every convention in this course exists to remove one more way of being misunderstood, and every mark in the exam is given for applying one.
Drawing standards: the grammar of AS 1100
Every line on a drawing means one particular thing, and its thickness and pattern are how it says which. Get the line types and the sheet conventions right and a large part of the paper is already yours.
1.1The standard, and why there is one
- AS 1100 is the Australian Standard for technical drawing. It fixes the line types and their thicknesses, the projection method, the dimensioning rules, the lettering and the sheet layout, so that every drawing produced in this country reads the same way.
- A drawing is also a legal and commercial record: quotes are priced from it, contracts refer to it, and a finished part is inspected against it. If the drawing is ambiguous, the cost of the mistake follows the ambiguity.
- Lettering is upright, single-stroke and in capitals, of a consistent height — typically 3.5 mm for notes and dimensions and larger for titles. It is chosen for legibility after photocopying, faxing, scanning and printing at half size, not for looks.
- Standards are what let the work be split up. The designer, the estimator, the machinist and the inspector are usually four different people in three different places, and the drawing is the only thing they share.
1.2The line types
1.3Sheet layout and the title block
1.4Scale, done exactly
A scale is written drawing : real. Read it as a ratio and every calculation is one multiplication or one division.
| Scale | Means | Real size → size on paper | Measured on paper → real size |
|---|---|---|---|
| 1:1 | Full size | 60 → 60 | 60 → 60 |
| 1:2 | Half size — divide by 2 | 290 → 145 | 145 → 290 |
| 1:5 | One fifth size — divide by 5 | 350 → 70 | 86 → 430 |
| 1:10 | One tenth size — divide by 10 | 2400 → 240 | 63 → 630 |
| 2:1 | Twice size — an enlargement, for small parts | 7.5 → 15 | 15 → 7.5 |
The number written beside a feature is always the true size of the real object, whatever the scale. On a 1:5 drawing a 350 mm shelf is drawn 70 mm long and labelled 350. Never write the paper measurement; and never measure a drawing to find a size that is already written on it, because the sheet may have been printed at a reduced size.
Choosing a scale: work out what the largest dimension becomes at each standard scale, and take the largest scale that still fits the space, because bigger is easier to read. A 900 mm door in a 200 mm space becomes 900 at 1:1, 450 at 1:2, 180 at 1:5 and 90 at 1:10 — so 1:5 is the answer.
Orthographic projection: views that agree
One picture of a solid always hides something. Orthographic projection answers with several flat, square-on views — and Australia arranges them in third angle. The test of a correct drawing is that the views agree with each other in width, height and depth.
2.1Third angle: each view on the side you looked from
In third-angle projection every view is placed on the same side as the direction you looked from. Look down from above and the top view is drawn above the front view; look from the right and the right side view is drawn to the right. This is Australian practice under AS 1100, and it is also North American practice. First angle, used across Europe and much of Asia, puts the views on the opposite sides — which is exactly why the projection symbol in the title block is not optional.
- Choose the front view first: the face that shows the object's most characteristic shape, in its normal working position, and with the fewest hidden lines. Every other view then follows from it.
- Draw only as many views as the object needs. Three is typical; a turned part often needs one plus a diameter; a flat plate needs one plus a thickness note. Extra views cost time and add ways to disagree.
- The third-angle symbol is a truncated cone drawn in two views, placed in the title block. In third angle the end-on view (two concentric circles) sits on the left and the side view of the cone on the right. In first angle they are the other way round.
2.2Dimensioning rules
- Dimension each feature once, and once only. If a slot width appears in both the front and the top view, an edit can leave the two disagreeing and nobody can tell which is right.
- Work from a datum. In parallel (datum) dimensioning, every dimension is measured from the same chosen edge or face, so errors cannot accumulate. In chain dimensioning each dimension starts where the last one finished; it reads well and is correct where each individual step matters, but the tolerances add up along the chain, so it is not used where the overall length must be exact.
- Millimetres, and do not write “mm”. All dimensions are in millimetres, the unit symbol is left off each number, and one note on the sheet states ALL DIMENSIONS IN MILLIMETRES.
- Put dimensions outside the outline wherever possible, on the view that shows the feature most clearly, and never let a dimension line cross another.
- Numbers read from the bottom or the right of the sheet, and sit above the dimension line, clear of it.
- Diameters are marked ⌀ and radii R. ⌀12 is a 12 mm hole; R6 is a 6 mm radius corner. A diameter is dimensioned on the view where the feature appears as a circle wherever that is clearer.
- Extension lines run out from the object with a small gap at the object, and extend a little past the dimension line. They never carry the size themselves.
2.3Sectional views
When a part has enough internal detail that the hidden lines become a thicket, you section it: imagine the object cut through, throw away the piece in front of the cut, and draw what is left. Everything that was hidden becomes visible, and the hidden lines are no longer needed.
| View | What it is | Used when |
|---|---|---|
| Full section | The cutting plane passes right through; everything in front of it is imagined removed | The internal detail runs the whole way through and hidden lines would be unreadable |
| Half section | One quarter of the object is removed, so half the view is a section and half is an ordinary outside view | The part is symmetrical — one drawing then shows both the outside and the inside |
| Auxiliary view | An extra view projected square-on to a sloping face, on a plane parallel to that face | A face is not parallel to any of the three principal planes, so it appears foreshortened in every normal view — the auxiliary view gives its true shape and size |
Hatching runs at 45°, evenly spaced, and is thin. Where two different parts are cut in the same assembly section, their hatching is drawn at different angles or different spacings, so the reader can see where one part ends and the next begins. And some parts are never hatched even when the plane passes along them — shafts, bolts, nuts, keys, pins, ribs and webs — because hatching them would suggest they had been cut lengthways when the drawing is clearer showing them whole.
Pictorial and presentation drawing
Orthographic views are for building. Pictorial drawings show the whole object in one image — for explaining, selling and assembling. Each of the four is right for a different job, and choosing the wrong one is a mark lost.
3.1Isometric, and what happens to circles
Isometric has three axes and only three: one truly vertical, and two at 30° to the horizontal. In isometric drawing all three axes are measured full size, so an isometric drawing can be scaled along its axes — which is why it is the engineer's pictorial. The price is that nothing gets smaller with distance, so a long object can look faintly wrong.
The consequence students lose marks on is circles. In isometric no face is square-on to the viewer, so every circle is drawn as an ellipse — and the ellipse has a fixed shape and a fixed orientation.
3.2Oblique and perspective
| Isometric | Cavalier oblique | Cabinet oblique | Perspective | |
|---|---|---|---|---|
| How it is set out | Two axes at 30°, verticals vertical | Front face square-on and true shape; depth back at an angle (often 45°) at full length | Front face square-on and true shape; depth back at an angle at half length | Front face square-on (one point) or turned (two point); receding edges converge on vanishing points |
| Can you measure it? | Yes, along all three axes | Yes, on all three — but it looks stretched | Front face yes; depth is halved deliberately | No — sizes shrink with distance |
| Circles on the front face | Ellipses — no face is square-on | True circles | True circles | True circles only if the face is parallel to the picture plane |
| Best for | Engineering pictorials and assembly instructions | Quick sketching where measured depth matters more than looks | Objects with one complicated face — a dial, a wheel, a control panel | Presentation: interiors, buildings, product renders |
- One-point perspective: the object's front face is parallel to the picture plane, so it stays true shape, and every edge running away from you converges on a single vanishing point on the horizon line. Use it for a corridor, a room interior, a street looked straight along.
- Two-point perspective: the object is turned so no face is parallel to the picture plane. Vertical edges stay vertical, but the two sets of horizontal edges converge on two vanishing points, both on the horizon. Use it for a building corner or a product seen from a natural angle.
- The horizon line is the viewer's eye level. Put it above the object and you look down on it; put it below and you look up at it. Moving that one line changes the character of the whole drawing.
- Perspective is the only one of these that matches what a camera sees, and the only one you must never take a size from.
3.3Exploded assembly drawings
| Item | Part | Qty | Material / specification |
|---|---|---|---|
| 1 | Hexagon head bolt | 1 | M8 × 40, zinc plated |
| 2 | Plain washer | 1 | M8, zinc plated |
| 3 | Upper plate | 1 | Mild steel, 6 thick |
| 4 | Lower plate | 1 | Mild steel, 6 thick |
| 5 | Hexagon nut | 1 | M8, zinc plated |
Ask: is the face square-on to the viewer? If yes, a circle on it is drawn as a circle. If no, it is drawn as an ellipse. That single test explains why a wheel is easy in oblique (put the wheel on the square-on front face) and awkward in isometric (no face is square-on, so every circle is an ellipse), and why perspective keeps circles true only on faces parallel to the picture plane.
CAD and digital documentation
Every convention in Units 1 and 2 still applies in CAD — the software just enforces them. What CAD adds is that the model itself becomes the master: the views, the parts list and the machine code are all generated from it, so they cannot disagree.
4.12D CAD and 3D parametric modelling
| 2D CAD | 3D parametric CAD | |
|---|---|---|
| What you make | Flat views — lines, arcs, hatching and text on a sheet | A solid model with real volume, mass and surface area |
| Views | You draw each view yourself, and must keep them consistent | Views are generated from the model, so they cannot disagree with each other |
| Changing a size | Redraw every view the change affects | Change the dimension once; the model, every view and the parts list all update |
| What it carries | Geometry only | Geometry plus the feature history — the sequence of sketches and operations that built it |
| Typical use | Floor plans, laser and CNC-router profiles, schematics | Parts, assemblies, 3D printing, machining, simulation |
4.2The parametric workflow
- Choose a plane or a flat face to sketch on — front, top or right, or a face of what you have already built.
- Sketch the profile roughly. Do not chase accuracy here; get the shape right and get the ends of lines actually joined.
- Apply geometric constraints — horizontal, vertical, parallel, perpendicular, tangent, equal, concentric, coincident, symmetric. These say what must stay true no matter what size the part becomes.
- Apply dimensions until the sketch is fully defined: every degree of freedom removed, so no line can be dragged out of shape.
- Extrude or revolve the closed profile into a solid.
- Add features on the new solid: further extrusions and cuts, holes, fillets, chamfers, patterns.
- Assemble the parts, using mates or joints — coincident faces, concentric holes, distance and angle — to say how they locate against each other.
- Generate the drawing: place the views, add the section and auxiliary views you need, dimension them, balloon the assembly and let the parts list build itself.
An under-constrained sketch is a rubber band: drag one line and the whole shape distorts, and the next person to open the file has no idea what was meant to stay fixed. A fully defined sketch records your design intent — so when the width goes from 60 to 80, the holes stay centred, the walls stay parallel and the fillets stay equal, instead of drifting. Most CAD packages colour a fully defined sketch differently precisely because it matters this much. If an exam asks “why constrain?”, the two words that earn the mark are design intent.
4.3File formats
| Format | What it holds | When it is used |
|---|---|---|
| Native (.dwg, .sldprt, .f3d, .ipt) | The full model with its sketches, constraints and feature history | While you are still designing, in that one program — keep it, because it is the only version you can properly edit |
| DXF | 2D geometry only — the flat profile, no solid | Sending a shape to a laser cutter, plasma cutter or CNC router |
| DWG | AutoCAD's drawing format; widely read as an exchange format for 2D work | Sending drawings to a client or contractor who works in 2D |
| STEP (.stp) and IGES | Neutral 3D solid geometry, with the feature history stripped out | Sending a 3D part to someone running different CAD software |
| STL | The surface only, approximated as thousands of triangles — no exact curves and no history | 3D printing: it is the slicer's input |
| A fixed picture of the drawing sheet | Viewing, quoting, checking and printing — never for machining |
4.4From the model to a real part
- CAD → CAM → G-code → machine. CAM software plans the tool paths from the model — which cutter, what depth of cut, what feed and speed, in what order — then posts them out as G-code, the numbered instruction list the CNC machine actually runs.
- CNC machining is subtractive: it starts with a block or a bar and cuts material away. A router, mill or lathe follows the tool path exactly, as many times as you like.
- 3D printing is additive: a slicer cuts the STL into horizontal layers and writes G-code that builds the part up one layer at a time. Layer height, infill, wall count and support are all decided in the slicer, not in the CAD model.
- Digital documentation is more than the drawing: a released job carries the model, the drawing sheets, the parts list, the revision history and the file the machine was actually run from. The revision letter on the sheet is what tells a workshop it has the current version — and an uncontrolled printout is how the wrong revision gets made.
- The machine does exactly what the file says. A wrong dimension in CAD becomes a wrong part in metal, which is why the conventions in Units 1 and 2 still decide whether the job succeeds.
Metal, to the hundredth of a millimetre.
Senior Industrial Technology Skills is where a drawing becomes a fabricated object. The practical marks come from the workshop; the written marks come from four things — assessing risk properly, knowing what a material will do and measuring it, selecting the right process and speed, and selecting the right way to join and protect the finished job.
The mapTwo units, four topics
- Unit 1, Topic 1 — Safety and workplace practice. Duty of care, risk assessment with a risk matrix, the hierarchy of controls in order, SWMS, guarding and emergency stops, PPE selection, hazardous substances and manual handling.
- Unit 1, Topic 2 — Engineering materials and measurement. Ferrous and non-ferrous metals and their alloys, mechanical properties, heat treatment, and precision measurement to 0.01 mm with tolerances, limits and fits.
- Unit 2, Topic 1 — Fabrication processes. Marking out on metal, sawing with the three-tooth rule, filing, drilling speeds, threading with taps and dies, turning and milling, and sheet-metal bending and riveting.
- Unit 2, Topic 2 — Joining and finishing. Mechanical fasteners, the soldering–brazing–welding ladder around 450 °C, welding processes and defects, and surface protection against corrosion.
Applied questions almost always ask you to select and justify: which control, which material, which blade, which speed, which joining process, which coating. A bare name earns almost nothing. Name it, then give the reason in the same sentence — “a 32 TPI blade, because a 1 mm tube wall needs at least three teeth in the cut at all times or the teeth straddle the wall and strip.”
Safety and workplace practice
Every machine in a metal workshop can do in a quarter of a second what a surgeon cannot undo in six hours. Senior safety is not a rule list to memorise — it is a process you can apply to a machine you have never seen.
1.1Duty of care
Under the Work Health and Safety Act 2011 the primary duty falls on the PCBU — the person conducting a business or undertaking — who must ensure, so far as is reasonably practicable, the health and safety of workers and of anyone else affected by the work. Officers must exercise due diligence. Workers must take reasonable care for their own safety and for others, comply with reasonable instruction, and co-operate with the workplace's policies. Visitors owe the same care within their power.
“Reasonably practicable” is decided by weighing, together: the likelihood of harm, the degree of harm, what is known about the hazard and the ways of removing it, the availability and suitability of controls, and last, the cost — which counts against acting only where it is grossly disproportionate to the risk.
1.2Risk assessment and the risk matrix
Risk management runs in four steps, always in this order: identify the hazards, assess the risks, control the risks, review the controls. Assessing means asking two questions at once — how likely is harm, and how serious would it be? A risk matrix is the tool that combines them into a single rating, so that limited time and money go to the worst risks first.
1.3The hierarchy of controls in the metal workshop
| # | Control | What it does to the hazard | In the metal workshop |
|---|---|---|---|
| 1 | Elimination | The hazard no longer exists | Have the supplier laser-cut the sheet, so nobody uses the guillotine at all |
| 2 | Substitution | Something less hazardous does the same job | Cut bar on a cold saw instead of an angle grinder — far less noise, and no shower of hot sparks |
| 3 | Isolation | A barrier or distance separates people from it | Weld in a screened bay, so the arc flash cannot reach anyone walking past |
| 4 | Engineering | Hardware removes the exposure | Chuck guard, interlocked door, fume extraction at the arc, emergency stop within reach |
| 5 | Administrative | Changes what people do | The SWMS, induction and machine sign-off, signage, rostering noisy jobs |
| 6 | PPE | A barrier on one person, while worn | Safety glasses, welding helmet of the correct shade, earmuffs, P2 respirator, leather gloves and boots |
PPE is last because it does nothing to the hazard. The grinder still throws sparks, the arc still emits ultraviolet, the fume is still in the air — PPE just puts a barrier in front of one person, and only while it is worn, undamaged and correctly fitted. Every level above it protects everyone in the room, all the time, without anyone having to remember anything.
- A SWMS sets out, for one activity: the task and its high-risk elements, the hazards, the controls chosen from the hierarchy, and how those controls will be implemented, monitored and reviewed. It is written before the work starts and revised when the job changes.
- Guards stay on, and guards that must come off for setting are interlocked. Isolate, lock and tag before changing a wheel, a blade or a chuck — the person who fits the lock is the only person who removes it.
- Clamp the work. A drill that grabs turns an unclamped plate into a spinning blade with your hand still on it. Machine vice or clamp, every time.
- Swarf is razor wire, hot. Clear it with a brush after the machine has stopped — never with fingers, never while it turns.
- No gloves at rotating machinery, no loose clothing, no rings or lanyards, long hair tied and covered. Gloves are for handling sharp sheet and hot work, never for a lathe or a drill.
- Noise: the Australian exposure standard is an eight-hour equivalent of 85 dB(A), with a peak that must never exceed 140 dB(C). Grinders, guillotines and drop saws all sit above it, and the damage is cumulative, painless and permanent.
- Hazardous substances: every chemical — degreaser, cutting fluid, flux, paint, thinners — needs a current Safety Data Sheet kept readily accessible, giving the hazards, the ventilation and PPE required, first aid, firefighting, and safe storage and disposal. Containers must be labelled, including anything decanted.
- Manual handling: assess the load, the task, the workplace and the person. Steel is dense — a 3 m length of 50 mm bar is a two-person or mechanical lift, and a trolley or a hoist is an engineering control, not a convenience.
Engineering materials and measurement
In timber you can plane a millimetre away. In metal a part is either within tolerance or it is scrap — so this topic runs from what a metal is, through what heat can do to it, to measuring it to a hundredth of a millimetre.
2.1Ferrous and non-ferrous
The first division in metals is simple: ferrous metals contain iron; non-ferrous metals do not. It matters because iron rusts and is magnetic, and most non-ferrous metals do neither.
| Metal | Class | Made of | Properties that decide its use | Typical use |
|---|---|---|---|---|
| Mild steel | Ferrous | Iron with about 0.1–0.3% carbon | Strong, tough, ductile, cheap, easy to weld and machine — but it rusts, and it cannot be hardened by quenching because it has too little carbon | The workshop default: frames, brackets, gates, trailers |
| Medium and high carbon steel | Ferrous | Iron with roughly 0.3–1.5% carbon | The higher the carbon, the harder and stronger it can be made — and the more brittle and the harder to weld | Springs, chisels, punches, cutting tools |
| Cast iron | Ferrous | Iron with about 2–4% carbon | Very hard in compression, excellent at damping vibration, easily cast to shape — but brittle, and it cracks rather than bends | Machine beds and bases, engine blocks, vices |
| Stainless steel | Ferrous | Steel with at least about 11% chromium | The chromium forms a thin, invisible, self-repairing oxide film on the surface, so it resists corrosion; tougher to machine and dearer | Food equipment, marine fittings, chemical and medical work |
| Aluminium | Non-ferrous | Aluminium, usually alloyed with silicon, magnesium or copper | About one third the density of steel, corrosion-resistant through its own oxide layer, an excellent conductor — but softer, and it needs different welding technique | Frames, extrusions, boats, heat sinks, aircraft |
| Copper | Non-ferrous | Copper | The best common conductor of heat and electricity, very ductile, easily soldered | Wiring, plumbing, heat exchangers, roofing |
| Brass | Non-ferrous | Copper + zinc | Machines beautifully, corrosion-resistant, non-sparking, good looking | Fittings, valves, decorative and marine hardware |
| Bronze | Non-ferrous | Copper + tin | Hard, corrosion-resistant and low friction against steel | Bearings, bushes, marine propellers |
Strength (resisting load), hardness (resisting scratching and indentation), toughness (absorbing shock without fracturing), ductility (drawing into wire without breaking), malleability (hammering or rolling into sheet), brittleness (fracturing with little deformation), elasticity (returning to shape), conductivity, density and corrosion resistance. Notice that hard and tough are opposites in practice — a file is hard and will shatter; a mild-steel bracket is tough and will bend. That trade-off is the whole reason heat treatment exists.
2.2Heat treatment
| Process | What you do | What it achieves | Why you would |
|---|---|---|---|
| Annealing | Heat to the critical temperature, hold, then cool as slowly as possible — usually in the furnace or in sand | The softest, most ductile condition, with internal stresses relieved | To make hardened steel machinable again, or to soften work-hardened metal so it can be bent further without cracking |
| Normalising | Heat above the critical temperature, then cool in still air | A refined, uniform grain structure; slightly harder and stronger than annealed | To remove the effects of forging, welding or heavy machining before a part goes into service |
| Hardening | Heat to the critical temperature, then quench rapidly in water, oil or brine | Very hard and wear-resistant — and brittle, with big internal stresses | To make a cutting edge or a wear surface. It only works on steel with enough carbon, which is why mild steel cannot be hardened this way |
| Tempering | Reheat the hardened steel to a lower temperature, then cool | Gives up a little hardness to buy back toughness and relieve the quenching stresses | Always, after hardening. Untempered hardened steel is too brittle to trust — a cold chisel would shatter at the first blow |
| Case hardening | Add carbon to the surface of a low-carbon steel, then harden it | A hard, wear-resistant skin over a core that stays tough | When a part must resist wear on the outside but survive shock — gears, shafts, pins |
2.3Precision measurement
| Instrument | Reads to | How you read it |
|---|---|---|
| Steel rule | About 0.5 mm | Stand the rule on edge so the graduations touch the work, and sight straight down the line — looking from an angle introduces parallax error. Measure from a graduation, never from the worn end. |
| Vernier caliper | 0.02 mm on a 50-division metric scale | Read the whole millimetres on the main scale up to the vernier's zero. Then find the one vernier line that coincides exactly with a main-scale line, and multiply its number by 0.02. Add them: main scale 31 with the 12th line coinciding gives 31 + 0.24 = 31.24 mm. |
| Digital caliper | 0.01 mm | Same jaws, an electronic scale. It can be zeroed anywhere, which makes comparison measurements easy — but it needs a battery, and it lies silently when the jaws are dirty. |
| Micrometer | 0.01 mm, and to 0.001 mm with a vernier on the sleeve | Whole and half millimetres on the sleeve, plus the thimble division × 0.01 mm. Always close it on the ratchet stop so the force is the same every time. |
2.4Tolerances, limits and fits
- A tolerance is the permitted variation from a stated size. 25 ± 0.05 mm means the limits are 24.95 and 25.05 mm, a tolerance band 0.10 mm wide. Anything inside passes; anything outside is scrap or rework.
- Tolerances cost money: tighter bands need better machines, slower work and more inspection, and they produce more rejects. A designer specifies a tight tolerance only where the fit actually matters, and opens it up everywhere else.
- Where a shaft goes into a hole, the two tolerance bands together decide the fit: clearance fit — the shaft is always smaller than the hole, so the parts always go together and can slide or rotate; transition fit — the bands overlap, so the assembly may be a slight clearance or a slight interference, giving accurate location; interference fit — the shaft is always larger, so the parts must be pressed together, or the hole heated and the shaft chilled.
- Work the extremes to prove a fit. For a hole of 20.00–20.03 mm and a shaft of 19.96–19.98 mm: the maximum clearance is the largest hole minus the smallest shaft, 20.03 − 19.96 = 0.07 mm, and the minimum clearance is 20.00 − 19.98 = 0.02 mm. Both are positive, so it is a clearance fit under every combination.
- Measure from a single datum, not from the last feature you cut. Chained measurements add each error to the last, and by the sixth hole nothing lines up.
- Allow for the kerf. Four pieces from one bar means three cuts, and three cuts at a 2 mm kerf remove 6 mm of bar.
Fabrication processes
Every cutting tool in the workshop obeys the same two rules: match the tooth or the speed to the material, and let the tool cut rather than forcing it. Break either and you get a stripped blade, a burnt drill or a hospital visit.
3.1Marking out on metal
Bare steel is shiny, so a scribed line disappears into the reflections. Marking-out fluid — layout blue, brushed or sprayed on and dry in seconds — gives a dark matt coating that the scriber cuts through, so the line appears as a bright streak against the blue. The sequence is fixed: clean and de-grease → coat with marking-out fluid → set the rule or square from the datum edge → scribe the lines → centre punch every hole centre where the lines cross → check every dimension before a single cut is made. Marking out is done from a flat reference surface, never freehand on the bench.
3.2Sawing: the three-tooth rule
| TPI | Use it on | Why |
|---|---|---|
| 14 | Thick, soft sections — aluminium, brass, heavy mild-steel bar | Big gullets between big teeth clear large soft chips instead of clogging |
| 18 | General-purpose mild steel | The default blade in a school workshop |
| 24 | Thinner sections, angle iron, thicker tube | Keeps three or more teeth in contact as the wall thickness drops |
| 32 | Thin sheet and small-diameter tube | Only very fine teeth keep three in the cut on a 1 mm wall |
- Long, steady strokes using the whole blade, about one a second, pressure on the push and released on the return — dragging teeth backwards under load only blunts them.
- Clamp the work in a vice close to the cut or it will chatter, and support the offcut as you finish so it cannot pinch the blade.
- A new blade will jam in a part-sawn cut, because the old blade's kerf is wider than the new blade's set. Start a fresh cut.
- Filing: single cut for finishing, double cut for fast shaping; grades run rough → bastard → second cut → smooth → dead smooth, worked down like sanding grits. Cross filing brings a surface to size; draw filing gives the flat bright finishing cut. Clear pinning with a file card, and never use a file without a handle over its tang.
3.3Drilling, speeds and threads
The rule to remember is that the bigger the drill or the harder the material, the slower the spindle speed. A large drill's outer cutting edge travels much further per revolution than a small one's, and the edge burns if it moves through the metal too fast. A blued, blunt drill was run too fast, pushed too hard, or run dry.
N = 1000 × Vc ÷ (π × D) — where N is the spindle speed in rpm, Vc is the recommended cutting speed in metres per minute for that tool-and-material pair, and D is the diameter in millimetres. For a high-speed-steel drill in mild steel, Vc is around 30 m/min. So a 10 mm drill needs N = 30 000 ÷ (π × 10) = 30 000 ÷ 31.42 = 955 rpm. Double the diameter to 20 mm and the answer halves to about 477 rpm — which is exactly the “bigger drill, slower speed” rule, written as arithmetic.
- Centre punch first, always, or the drill's chisel edge skates and the hole ends up somewhere else. Clamp the work — sheet metal is the worst offender, because the drill grabs as it breaks through. Ease off at breakthrough, which is the moment it grabs.
- Pilot holes for large diameters: the big drill's chisel edge does not cut well, and a pilot lets its cutting lips do the work. Cutting fluid on steel to cool the edge and flush the swarf; aluminium dry or with kerosene; cast iron dry.
- Countersinking cuts the cone that lets a countersunk head finish flush. Run it slowly or it chatters and leaves a fluted edge.
- Taps and dies: a tap cuts an internal thread, a die cuts an external one. The hole is drilled to the tap drill size, and for a standard metric thread the formula is diameter − pitch: M6 × 1.0 gives 5.0 mm; M10 × 1.5 gives 8.5 mm; M8 × 1.25 gives 6.75 mm, for which the nearest stocked drill is 6.8 mm. Drill it too large and there is no metal for the thread to be cut in; too small and the tap jams and snaps, and a broken tap is hardened steel that cannot be drilled out.
- Taps come as a set of three, used in order: taper (a long lead-in that starts the thread square), second or intermediate, then plug or bottoming, which finishes the thread to the bottom of a blind hole. Turn half a turn forward and a quarter turn back to break the swarf, keep the tap square, and use cutting fluid.
3.4Turning, milling and sheet metal
| Process | What moves | What it produces |
|---|---|---|
| Turning (centre lathe) | The work rotates in the chuck; a single-point tool is fed along and across it | Round work: parallel turning to a diameter, facing an end square, drilling on centre, boring, knurling, parting off and screw cutting |
| Milling | The cutter rotates; the work is fed past it on a table that moves in three axes | Flat faces, steps, slots, keyways and pockets on square work — the complement of the lathe |
| Shearing / guillotining | A moving blade passes a fixed one | Straight cuts in sheet, fast and with no swarf — but it cannot cut an internal shape, and it slightly distorts the cut edge |
| Folding / bending | Sheet clamped along a line and folded over a nose bar | Boxes, trays, flanges and stiffening returns — a fold makes thin sheet far more rigid without adding material |
Bending sheet metal needs one idea that catches everybody: a bend does not simply add the two leg lengths together. As the sheet bends, the outside stretches and the inside compresses, and only a line inside the material — the neutral axis — keeps its original length. The bend allowance is the length of material actually consumed in the bend, measured along that neutral axis. Cut a blank to the sum of the outside legs and the finished part comes out oversize; the developed (flat) length is always the legs plus the bend allowance, and the bend allowance depends on the material thickness, the bend radius and the angle.
- Bend across the grain of rolled sheet where you can — bending along it invites cracking on the outside of the bend.
- A tighter radius stretches the outside fibres more, so every material has a minimum bend radius below which it splits.
- Riveting is the classic sheet-metal joint: a blind (pop) rivet when only one side of the joint can be reached, a solid rivet hammered or pressed over where the joint is structural and must not vibrate loose.
- Deburr every sheared or drilled edge. A sheet-metal burr is sharp enough to open a hand and it stops parts sitting flat.
Joining and finishing
Two pieces of metal can be held together by a fastener through them, by heat and a filler between them, or by adhesive. Then comes the question everybody forgets until the job rusts: what protects the steel afterwards, and what happens when that protection is scratched?
4.1Mechanical fasteners
| Fastener | How it works | Permanent? | Specified when… |
|---|---|---|---|
| Blind (pop) rivet | A hollow rivet goes through both parts; the gun pulls a mandrel that swells the far end, then snaps it off | Permanent — removal means drilling it out | You can only reach one side of the joint — a box, a duct, a closed tube. This is the answer markers look for. |
| Solid rivet | Hammered or pressed over to form a second head | Permanent | Structural work, and joints that must not vibrate loose |
| Bolt, nut and washer | Clamps the parts between the head and the nut | Removable | Anything that must come apart for service, or carry a real load. The plain washer spreads the clamping force so the nut cannot pull through thin material. |
| Spring washer or nyloc nut | Keeps tension (or friction) in the joint after tightening | Removable | Vibration is present — every machine and vehicle. Without them the nut works loose. |
| Machine screw into a tapped hole | Threads into a thread cut in the part itself | Removable | Only one side is accessible, but the part is thick enough to tap |
| Self-tapping screw | Cuts its own thread as it drives into a pilot hole in sheet | Removable, but the thread wears after a few cycles | Thin sheet, light fixings, fast assembly |
Holes for bolts are drilled as clearance holes, slightly larger than the bolt, so parts can be lined up and the bolt is not bent into place. And a bolted joint works by clamping friction between the parts, not by the bolt acting as a pin — which is why correct tightening matters as much as the right bolt.
4.2Thermal joining: soldering, brazing and welding
All three use heat and all three make a joint, but they are separated by one question, and it is the question an exam will ask: does the parent metal melt?
- MIG (metal inert gas) is the common school welder because it is the easiest to learn: a motor feeds continuous wire through the torch as both electrode and filler, and a shielding gas keeps oxygen away from the molten pool. TIG uses a non-consumable tungsten electrode with filler added by hand — slower, but the most controllable and the cleanest, and the choice for thin material, stainless and aluminium. Manual metal arc (stick) uses a flux-coated electrode whose flux burns to make its own shielding gas and a protective slag — rugged, portable, and it works outdoors where wind would blow a shielding gas away.
- Flux in soldering and brazing does the same job the shielding gas does in MIG: it removes the surface oxide and stops it re-forming, so the filler can wet the metal. Nothing sticks to an oxidised surface.
- The joint must be clean and correctly fitted before heat is applied. Paint, rust, oil and galvanising all ruin the joint — and burning them produces fume.
- Welding hazards: the arc's ultraviolet burns eyes (“arc eye”) and skin, so a helmet of the correct shade, a screened bay and covered skin are all required; welding fume is a recognised carcinogen and needs extraction at the source; and the work stays hot long after it stops glowing.
| Weld defect | What it looks like | Usual cause |
|---|---|---|
| Porosity | Gas bubbles trapped in the weld metal, seen as holes on a cut or an X-ray | Lost or contaminated shielding gas, a draught blowing it away, or a dirty, damp, painted or oily surface |
| Undercut | A groove melted into the parent metal along the edge of the weld and left unfilled | Too much current or too fast a travel speed. It leaves a thinner section and a stress raiser where cracks start. |
| Lack of fusion / incomplete penetration | The weld metal sits on the joint without fusing to it, or does not reach the root | Too little heat, too fast a travel, or a joint preparation with no gap or bevel |
| Excess spatter | Balls of metal thrown onto the surface around the weld | Current or voltage set wrong, or a contaminated surface. It is cosmetic, but it hides other defects and has to be chipped off. |
| Distortion | The part pulls out of shape or out of square as it cools | Uneven heating and cooling shrinking the weld. Controlled by tacking, clamping in a jig, balancing the welds either side, and using shorter runs. |
4.3Corrosion and surface protection
Steel rusts because iron, oxygen and water react to form hydrated iron oxide. Rust is the problem and the mechanism: it is porous and it flakes off, so it never seals the surface, and fresh metal is exposed to corrode again. Corrosion is also faster where two dissimilar metals are in contact with moisture between them — the more reactive of the two corrodes preferentially, which is called galvanic corrosion, and which is also exactly what galvanising puts to work on purpose.
| Treatment | How it protects | What happens at a scratch | Typical use |
|---|---|---|---|
| Primer + topcoat paint | Barrier only — the primer grips the steel and inhibits corrosion; the topcoat seals and colours | The exposed steel rusts immediately, and the rust creeps along under the film, lifting more of it | Indoor and light outdoor steel; anywhere colour matters |
| Hot-dip galvanising | A barrier plus sacrificial protection: zinc is more reactive than iron, so the zinc corrodes in the steel's place | The bare steel keeps being protected until the surrounding zinc is used up | Outdoor structures, fencing, trailers, roof sheet, marine-adjacent work |
| Powder coating | A thick, tough, electrostatically applied and oven-baked polymer barrier | Barrier only — a deep scratch will rust, so quality work is galvanised first and then powder coated | Furniture, gates, machine covers, anything wanting a hard coloured finish |
| Anodising (aluminium only) | Thickens aluminium's own oxide layer electrolytically, and it can be dyed | The oxide is part of the metal, not a coating, so it does not peel — but a deep gouge exposes bare aluminium | Architectural extrusions, window frames, consumer products |
| Oil, grease or wax film | A temporary barrier keeping water and oxygen off | Wipes off — it must be renewed | Machine beds, tools, short-term storage of bright steel |
Zinc is more reactive than iron. Where the coating is scratched and moisture bridges the two metals, the zinc corrodes preferentially and the steel does not — the zinc is sacrificed to protect it, and it keeps protecting the bare strip until the surrounding zinc is consumed. Paint cannot do this, because paint is not a metal and takes no part in the reaction; it protects only while it is unbroken. That single comparison — barrier versus sacrificial — is the most-asked question in this topic.
Heating zinc drives off zinc oxide fume, which causes metal fume fever — hours of shivering, aching and fever after the job. Correct practice is to grind the zinc back from the weld area first, work with extraction at the source and good ventilation, and re-coat the bare area afterwards with a zinc-rich paint so the sacrificial protection is restored.
Every living thing has a place.
Four units: what makes something alive and how scientists sort the living world into groups, how to use a key to name what you find, how energy moves from grass to eagle, and how ecosystems hold together — or fall apart when people change them. Built from the Year 7 Biological sciences descriptions.
The mapFour units
- Sorting the living world — the seven signs of life, the ladder from kingdom to species, and the big animal groups.
- Dichotomous keys — reading and building a yes/no key, and why every species has a two-word Latin name.
- Food chains and food webs — producers, consumers, decomposers, and which way the arrows point.
- Ecosystems and people — habitats, living and non-living factors, introduced species, and caring for Country with fire.
Classification — living things are grouped by the features they share, and a dichotomous key lets anyone identify an organism step by step. Ecosystems — energy flows from producers through food chains and food webs, and changing one part of the web, including through human activity, affects the rest.
Sorting the living world
About two million species have been named and millions more are waiting. Nobody could keep track of that without a system — so biologists sort living things into groups inside groups, from the giant kingdoms down to a single species.
1.1Alive, or not?
Fire moves, grows and "eats" wood, but it is not alive. A seed lies still for years, but it is. The test is not one thing but seven — a living thing does all of them. The initials spell MRS GREN.
| Process | What it means | Example |
|---|---|---|
| Movement | Moving the whole body, or parts of it | A sunflower head turns to follow the sun |
| Respiration | Releasing energy from food inside cells (not breathing) | A seed uses stored energy to sprout |
| Sensitivity | Detecting and responding to change | A snail pulls in its eye-stalks when touched |
| Growth | Getting bigger, or making more cells | A joey grows into an adult kangaroo |
| Reproduction | Making new individuals of the same kind | A frog lays eggs in a pond |
| Excretion | Getting rid of waste the body makes | Plants release oxygen and water through their leaves |
| Nutrition | Taking in or making food | A gum tree makes sugar from sunlight; a possum eats the leaves |
Respiration is not breathing. Breathing moves air in and out; respiration is the chemical release of energy from food that happens in every living cell — in a tree, a mushroom and a bacterium, none of which have lungs.
1.2The ladder of groups
In the 1700s the Swedish naturalist Carl Linnaeus set up the system we still use: groups nested inside bigger groups. Going down the ladder, each group is smaller and its members share more features.
1.3The five kingdoms
| Kingdom | How they get food | Made of | Examples |
|---|---|---|---|
| Animals | Eat other living things | Many cells | Kangaroo, magpie, snail, coral |
| Plants | Make their own food from sunlight | Many cells | Eucalypt, wattle, grass, moss |
| Fungi | Absorb food from dead or living material | Many cells (yeast: one) | Mushroom, mould, yeast |
| Protists | Some make food, some eat | Mostly one cell | Amoeba, algae in a pond |
| Bacteria | Some make food, most absorb it | One tiny cell | Soil bacteria, the bacteria in yoghurt |
It looks rooted and it does not move, but a mushroom cannot make its own food — it has no green colour and absorbs what it needs from rotting wood or soil. Feeding is the feature that separates fungi from plants, and it is the feature exams ask about.
1.4Vertebrates and invertebrates
Within the animal kingdom, the first big split is a backbone. Animals with one are vertebrates — only about 5% of animal species. The other 95%, the invertebrates, have no backbone at all.
| Vertebrate class | Skin | Young | Body temperature | Australian example |
|---|---|---|---|---|
| Mammals | Fur or hair | Born alive (mostly), fed on milk | Warm-blooded | Kangaroo, dingo, platypus |
| Birds | Feathers | Hard-shelled eggs | Warm-blooded | Emu, kookaburra, magpie |
| Reptiles | Dry scales | Leathery eggs, laid on land | Cold-blooded | Crocodile, goanna, blue-tongue lizard |
| Amphibians | Moist, no scales | Jelly eggs in water; tadpoles | Cold-blooded | Green tree frog, cane toad |
| Fish | Wet scales; breathe with gills | Eggs in water (mostly) | Cold-blooded | Barramundi, Murray cod, shark |
- Insects — six legs, three body parts, usually wings: ants, beetles, butterflies. The biggest group of animals on Earth.
- Arachnids — eight legs, two body parts, no wings: spiders, scorpions, ticks.
- Crustaceans — hard shell, many jointed legs, mostly in water: crabs, prawns, yabbies.
- Molluscs — soft body, often a shell: snails, oysters, octopus.
- Worms — long soft body, no legs: earthworms.
- The platypus lays eggs but has fur and feeds its young on milk — so it is a mammal. Classification goes by the set of shared features, not a single odd one.
Dichotomous keys: naming what you find
A dichotomous key is a chain of questions with exactly two answers each — dichotomous means "cut in two". Answer one question, follow the branch, answer the next, and you end up with a name. It is how a ranger identifies a frog, or a doctor a tick.
2.1Reading a key
2.2Building your own key
- List the organisms and the features you can see or measure: legs, wings, shell, scales, number of body parts.
- Pick a feature that splits the group in two. "Does it have wings?" is a good first question if about half the group has them.
- Keep splitting each smaller group with a new feature until every branch ends at one organism.
- Test it on every organism. If two end up in the same place, you need one more question.
Anything that depends on opinion or on the moment: "Is it big?", "Is it scary?", "Is it moving?" Two people must get the same answer from the same organism, so use fixed, countable features — "Does it have six legs?" never changes.
2.3Scientific names
- The same animal can have many common names: Macropus rufus is the red kangaroo, the red roo, the plains kangaroo, and has a different name in every language. It has exactly one scientific name, used by scientists in every country.
- The name is two words — the genus, then the species. Two species in the same genus are close relatives: the eastern grey kangaroo is Macropus giganteus.
- Writing rules: genus with a capital letter, species in lowercase, both in italics when typed and underlined when handwritten. Homo sapiens, never "homo Sapiens".
- Linnaeus chose Latin because in the 1700s it was the shared language of scholars — and because it belongs to no country, it offends nobody.
Food chains and food webs: following the energy
Every bite of energy in an ecosystem started as sunlight caught by a plant. A food chain traces that energy from one organism to the next; a food web shows all the chains tangled together, the way real bush actually works.
3.1The chain
- A chain always starts with a producer — a plant or alga that makes its own food from sunlight. No producer, no chain.
- Everything that eats is a consumer. Herbivores eat plants (kangaroo, koala). Carnivores eat animals (dingo, eagle). Omnivores eat both (magpie, emu, humans).
- The first animal in the chain is the primary consumer, the next the secondary consumer, then the tertiary consumer. Each step is a trophic level — a feeding level.
- Decomposers — fungi and bacteria — break down dead plants, animals and droppings, returning nutrients to the soil for the producers to use again. They are the recyclers that close the loop.
- The arrow means "is eaten by". It points from the food to the eater, because that is the direction the energy travels. Grass → grasshopper → magpie: the grass does not eat the grasshopper.
Draw a food chain with the arrows backwards and the whole answer is wrong. Say it to yourself as you draw: the arrow shows where the energy goes — out of the thing eaten, into the thing eating.
3.2A food web
3.3Pull one thread
Because everything is connected, removing one species sends ripples through the web. Work it out step by step, and say which arrows are affected.
- The grasshoppers die out (say a dry year, or a new pesticide). The frogs and magpies lose a food source: fewer frogs, and magpies must rely on seeds. Fewer frogs means less food for snakes. Meanwhile, with no grasshoppers chewing it, the grass grows thicker.
- The dingoes are removed (as they were across much of farmland). Kangaroos lose a predator and their numbers climb. More kangaroos eat more grass, so there is less for the grasshoppers — the ripple goes down the web as well as up.
- The grass fails (drought, overgrazing). Every chain in the web starts there, so everything above it suffers — producers are the foundation.
Only about a tenth of the energy at one level reaches the next. The rest is used up moving, keeping warm and simply staying alive. That is why there is so much grass, fewer kangaroos, and only a handful of eagles: each step up has far less energy to share.
Ecosystems and people
An ecosystem is all the living things in a place plus the non-living things they depend on — a rock pool, a patch of mallee, a farm dam. Humans are part of every ecosystem in Australia, sometimes as the damage and sometimes as the cure.
4.1Habitats, and what shapes them
A habitat is the place an organism lives, with everything it needs: food, water, shelter, space. What lives in a habitat is decided by two kinds of factor.
| Biotic factors (living) | Abiotic factors (non-living) | |
|---|---|---|
| What they are | Other organisms and their effects | Physical conditions of the place |
| Examples | Food plants, predators, competitors, disease, decomposers | Sunlight, temperature, rainfall, soil type, wind, salt in the water |
| In a rock pool | Seaweed, crabs, gulls hunting at low tide | Tide height, water temperature, how salty the pool gets in the sun |
- Predation: one organism (the predator) kills and eats another (the prey). Dingo and kangaroo; kookaburra and lizard. Predators keep prey numbers in check.
- Competition: two organisms need the same limited resource — food, water, light, nest hollows. Two magpies over one worm; a gum seedling in the shade of its parent. Rabbits compete with bilbies for burrows and grass.
- A population is all the members of one species in a place; a community is all the populations living there together.
4.2Human impacts
Australia has lost more mammal species since European settlement than any other continent. Most of the damage traces back to three things.
| Impact | What happened | Effect on the ecosystem |
|---|---|---|
| Introduced species | Rabbits released for hunting in 1859; cane toads brought to Queensland in 1935 to eat beetles; foxes and cats arrived with settlers. | Rabbits strip plants and out-compete native grazers. Toads poison the quolls, goannas and snakes that eat them. Cats and foxes hunt small mammals that never evolved to escape them. |
| Habitat loss | Bush cleared for farms, roads and suburbs; wetlands drained; old trees with hollows cut down. | Animals lose food and shelter. Koalas need connected forest; a patch cut in two by a highway is two smaller, weaker populations. |
| Big, hot bushfires | Long droughts and years of built-up fuel make fires that burn huge areas at once, as in the 2019–20 summer. | Every part of a habitat burns together, leaving nowhere to escape or return to. Slow-moving animals suffer worst. |
An introduced species arrives without the predators, diseases and competitors that kept it in check at home. Nothing here eats it safely, so its numbers explode. Solutions include fences, baits, and biological control — bringing in the pest's own enemy, as the cactoblastis moth was brought in to eat the prickly pear cactus that had swallowed farmland in the 1920s.
4.3Caring for Country with fire
- Aboriginal and Torres Strait Islander peoples have managed Australian ecosystems for tens of thousands of years, with detailed knowledge of which plants and animals live where, when they breed, and what they need.
- Cultural burning uses small, cool, patchy fires, lit on purpose in the cooler months. They burn slowly along the ground, clearing leaf litter and dead grass while the tree canopy and the soil are barely touched.
- Animals can walk away from a cool fire and come back to fresh green shoots. A patchwork of burnt and unburnt ground means there is always food and shelter somewhere nearby.
- Because fuel never builds up, a summer bushfire has far less to burn. Today many fire services work with Traditional Owners to bring cultural burning back.
Some Australian plants need fire: banksia cones only open in heat, and grass trees flower after a burn. An ecosystem shaped by fire for thousands of years does not thrive with no fire at all — it needs the right kind of fire.
Mixed up, and how to un-mix it.
Four units: what "pure" really means and what a mixture is, how dissolving works and the words that go with it, the toolkit for separating mixtures — sieves, filters, evaporation, distillation, chromatography — and where the same tricks run whole cities. Built from the Year 7 Chemical sciences description.
The mapFour units
- Pure substances and mixtures — one thing, or several things jumbled; and why sea water is not "pure" even when it is clean.
- Solutions — solute, solvent, soluble, saturated; why dissolving is not melting; and how to make it go faster.
- Separating mixtures — eight techniques, and the one question that tells you which to use.
- Separation in the real world — tap water, desalination, recycling and gold, and the particle picture that explains why any of it works.
Mixtures, including solutions, contain a combination of pure substances that can be separated using a range of techniques — and each technique works by using a physical property (size, solubility, boiling point, density, magnetism) that is different between the parts.
Pure substances and mixtures
"Pure" on a juice carton means nothing was added. "Pure" in science means something stricter: one substance, and only that substance, all the way through. By that rule almost everything around you is a mixture.
1.1What "pure" means in science
- A pure substance is made of one kind of particle only. Pure water is water and nothing else; sugar is sugar; the oxygen in a hospital cylinder is oxygen. A pure substance has fixed properties — pure water always freezes at 0 °C and boils at 100 °C.
- A mixture contains two or more substances jumbled together but not joined. They can be in any amounts, each keeps its own properties, and they can be separated again. Sea water, air, soil, milk, muesli, a cup of tea: all mixtures.
- Tap water is a mixture: water plus dissolved minerals, a little chlorine, and gases. It is clean and safe, but it is not pure. That is why "pure" and "clean" are different words.
1.2The particle picture
1.3Two kinds of mixture
| Homogeneous mixture | Heterogeneous mixture | |
|---|---|---|
| Looks like | One substance — the same all the way through | You can see the different parts |
| Every spoonful | Identical | Different — more raisins in one, more oats in the next |
| Examples | Salt water, cordial, vinegar, air, clear apple juice | Muesli, soil, a salad, sand in water, oil and water, pizza |
| Memory hook | homo = same | hetero = different |
Asked why air is a mixture and not a pure substance, do not just say "it has lots of things in it". Say the parts — nitrogen, oxygen, water vapour, carbon dioxide — are not joined, can be in varying amounts (humid days have more water vapour), and can be separated. Three ideas, three marks.
Solutions: where did the sugar go?
Stir sugar into tea and it vanishes. It has not gone anywhere — every particle is still in the cup, spread too thinly to see. That is a solution, and this unit gives you the words to describe it exactly.
2.1The words
- The solute is the substance that dissolves — the sugar, the salt, the cordial syrup.
- The solvent is what it dissolves into — usually water, "the universal solvent", though nail-polish remover and turpentine are solvents too.
- Solute + solvent = solution: a homogeneous mixture, clear (you can see through it, even if coloured), and the solute never settles out.
- Soluble means it can dissolve in that solvent; insoluble means it cannot. Sugar is soluble in water. Sand is insoluble — stir all you like, it sinks. Chalk is insoluble in water but a wax crayon mark dissolves in turpentine: solubility depends on the pair.
- An insoluble solid floating through a liquid is a suspension — muddy water. Leave it and the solid settles; a real solution never does.
2.2Dissolving, particle by particle
Melting needs heat and one substance: solid ice becomes liquid water at 0 °C, with no second substance involved. Dissolving needs a solvent and can happen cold: the sugar stays solid-type particles, just separated and surrounded by water. Chocolate in your hand melts; chocolate in hot milk dissolves. Exams love this pair.
2.3How much, and how fast
- Concentration describes how much solute is in the solvent. A dilute solution has a little (weak cordial); a concentrated solution has a lot (the syrup in the bottle).
- Keep adding solute and eventually no more will dissolve — it piles up at the bottom however hard you stir. The solution is saturated: it holds all it can at that temperature.
- Warm water can usually hold more solute than cold water, which is why sugar dissolves so easily in hot tea and so badly in iced water.
| To dissolve it faster… | Why it works (particle model) |
|---|---|
| Stir it | Keeps fresh water particles bumping the crystal instead of the same saturated layer |
| Heat the solvent | Faster-moving water particles hit the crystal harder and more often |
| Crush it | Small grains have far more surface for water particles to attack — caster sugar beats sugar cubes |
Separating mixtures: the toolkit
Because the parts of a mixture are not joined, you can always get them apart — provided you find a property that is different between them and pick the technique that uses it. Every separation question is really that one question in disguise.
3.1The simple ones
- Sieving — uses particle size. Big pieces stay on the mesh, small ones fall through. Flour through a sieve; pasta in a colander; gravel from sand.
- Decanting — uses density (heavy sinks). Let the solid settle, then pour the liquid gently off the top. Rinsing rice; separating oil floating on water.
- Magnetic separation — uses magnetism. A magnet lifts iron or steel out of everything else. Iron filings from sand; steel cans from recycling.
- Hand-picking — uses appearance. Slow but real: the raisins out of the muesli.
3.2Filtration
3.3Evaporation, crystallisation and distillation
- Evaporation — uses boiling point. Heat a solution and the solvent turns to gas and leaves; the dissolved solid stays behind. Salt from salt water. You lose the water.
- Crystallisation — evaporation done slowly. Warm the solution until it is nearly saturated, then let it cool and sit. The solute comes out as neat crystals, bigger and purer than fast boiling gives. Copper sulfate crystals in the lab; sugar crystals on a string.
- Distillation — evaporation plus condensing. Boil the liquid off, cool the vapour back to liquid, and collect it. Now you keep the solvent: pure water from sea water, alcohol from a fermented mix.
3.4Chromatography
3.5The whole toolkit
| Technique | Property it uses | Separates | Example |
|---|---|---|---|
| Sieving | Particle size (big vs small) | Solid from solid | Gravel from sand |
| Filtration | Particle size (solid vs liquid) | Insoluble solid from liquid | Sand from water |
| Decanting | Density | Settled solid, or a floating liquid, from a liquid | Oil off water |
| Magnetic separation | Magnetism | Iron or steel from anything else | Iron filings from sand |
| Evaporation | Boiling point | Dissolved solid from a solution (keep the solid) | Salt from sea water |
| Crystallisation | Boiling point, slowly | Dissolved solid as pure crystals | Copper sulfate crystals |
| Distillation | Boiling point | Solvent from a solution (keep the liquid) | Pure water from sea water |
| Chromatography | Solubility | Dyes in a mixture of colours | The colours in black ink |
"Separate a mixture of sand, salt and water." Do it in order: filter first (sand is insoluble — it is the residue), then evaporate the filtrate to get the salt back — or distil it if the question wants the water too. Always name the technique and the property that makes it work.
Separation in the real world
The same techniques you use with a funnel and a beaker run at city scale: every glass of tap water, every recycled can and every gram of gold ever mined was separated from a mixture by using a property that was different.
4.1How tap water is made
- Screening — river or dam water passes through metal grids that stop sticks, leaves and rubbish. That is sieving.
- Settling — in wide, still tanks the mud and grit sink to the bottom and the clearer water flows on. That is decanting, done slowly and continuously. A chemical is added first that makes tiny bits clump into bigger, heavier flakes so they settle faster.
- Filtering — the water trickles down through beds of sand and gravel, which trap the fine particles that never settled. That is filtration.
- Disinfecting — a small, carefully measured amount of chlorine is added to kill germs. This is not a separation: bacteria are too small to filter cheaply, so they are killed instead. Fluoride is added in most Australian cities to protect teeth.
None of these steps removes dissolved salt — and that is fine for river water. Which is exactly why turning sea water into drinking water needs a different tool.
4.2Desalination: drinking the sea
- Perth gets close to half its water from two desalination plants; Sydney, Melbourne, Adelaide and the Gold Coast have them for dry years. Salt is dissolved, so filtering and settling cannot touch it.
- The old way is distillation — boil the sea water, condense the steam — but boiling that much water costs an enormous amount of energy.
- Modern plants use reverse osmosis: the sea water is pushed at very high pressure against a membrane with holes so fine that water particles fit through and the dissolved salt does not. Think of it as filtration taken to the extreme — it still uses particle size, just at the scale of single particles.
- The leftover, extra-salty water (brine) is returned to the ocean and mixed in carefully so it does not harm sea life.
4.3Recycling and gold
- At a recycling centre the mixed contents of yellow bins ride a conveyor. Rotating screens sieve out small bits and flat cardboard; powerful magnets lift out steel cans; a different device using electricity flicks aluminium cans off the belt; jets of air blow light plastic one way while heavy glass drops the other — separation by density.
- Panning for gold is decanting with a swirl: gold is about seven times denser than sand, so as water washes the light sand over the rim of the pan, the heavy gold stays at the bottom. The 1850s gold rushes at Ballarat and Bendigo ran on this one property.
- In the kitchen: draining pasta (sieving), skimming fat off a stock (decanting), a tea bag (filtration), reducing a sauce (evaporation).
4.4Why any of it works
All matter is made of tiny particles. In a mixture the different particles are mixed together but not joined, so each keeps its own properties — its size, its density, its boiling point, whether a magnet pulls it. A separation technique simply finds a property the particles of one part have and the other part's do not, and uses it to pull them apart. Filter paper holes stop sand particles but pass water particles (size); heat makes water particles fly off as gas while salt particles stay (boiling point); a magnet grabs iron particles and ignores sand (magnetism). Name the property every time.
Pushes, pulls and the machines that cheat them.
Four units: what a force is and how to draw one, what happens when forces cancel and when they don't, the difference between how heavy you are and how much stuff you are made of, and the simple machines that let a small push do a big job — built from the Year 7 Physical sciences description AC9S7U06.
The mapFour units
- What a force is — pushes and pulls, newtons, force arrows, and the forces that need contact versus the ones that reach across empty space.
- Balanced and unbalanced — adding forces up, and why a balanced object keeps doing exactly what it was doing.
- Gravity, mass, weight and friction — kilograms versus newtons, why you would weigh less on the Moon, and friction as friend and enemy.
- Simple machines — levers, ramps, pulleys, gears and the wheel-and-axle: how they change the size or direction of a force.
AC9S7U06 — investigate and represent balanced and unbalanced forces, including gravitational force, acting on objects, and relate changes in an object's motion to its net force. You should be able to name contact and non-contact forces, draw force arrows, tell mass from weight, and explain how a simple machine helps.
What a force is: every push and every pull
You cannot see a force. You can only see what it does: a netball changes direction, a trolley starts rolling, a bike slows down, a can gets crushed. A force is simply a push or a pull, and this unit is about naming them, measuring them and drawing them.
1.1What forces do
- A force can make a still object start moving, make a moving object speed up, slow down, stop or change direction, and it can change an object's shape (squash a sponge, stretch a rubber band, bend a ruler).
- Forces are measured in newtons, symbol N. A small apple pulls down on your hand with about 1 N. A full 2 L milk bottle is about 20 N. A strong adult push is a few hundred newtons.
- Forces always come in a direction as well as a size. "10 N" is not a full answer; "10 N to the left" is.
- We draw a force as an arrow: it starts on the object, points the way the force acts, and its length shows the size. A picture with all the force arrows on one object is a force diagram.
1.2Measuring a force
1.3Contact and non-contact forces
Most forces need the two objects to touch. A few reach across empty space. That split is the first thing the exam asks for.
| Force | Contact or non-contact? | What it does | Australian example |
|---|---|---|---|
| Applied force (push or pull) | Contact | Whatever your hands, feet or a machine push or pull on | Shoving a jammed sliding door |
| Friction | Contact | Resists two touching surfaces sliding past each other | Thongs gripping a wet pool deck |
| Air resistance (drag) | Contact | Friction with the air that pushes against anything moving through it | A cyclist crouching low on the Tour Down Under |
| Support (normal force) | Contact | A surface pushing up on whatever rests on it | The wharf holding up a parked ute |
| Tension | Contact | The pull along a stretched rope, cable or chain | A tow rope pulling a water-skier |
| Upthrust (buoyancy) | Contact | Water pushing up on whatever is in it | A tinnie floating on the Murray |
| Gravity | Non-contact | Pulls every object towards the centre of the Earth | A dropped cricket ball falling |
| Magnetic force | Non-contact | Pulls on iron, steel, nickel and cobalt; magnets can also push each other apart | A fridge magnet holding a shopping list |
| Electrostatic force | Non-contact | Pull or push between charged objects | A rubbed balloon lifting the hairs on your arm |
Only three forces on the Year 7 list act at a distance: gravity, magnetic and electrostatic. Everything else needs contact. If an exam question describes something happening "without touching", it is one of those three — and if it mentions iron, steel or a compass needle, it is magnetic.
Balanced and unbalanced: adding the arrows up
Objects almost never have just one force on them. What matters is the net force — what is left over once you add the arrows up. If nothing is left over, the forces are balanced and the object carries on exactly as it was. If something is left over, its motion changes.
2.1Net force
- Forces in the same direction add: two people each pushing a car with 200 N give a net force of 400 N.
- Forces in opposite directions subtract: 500 N to the right and 300 N to the left give a net force of 200 N to the right. The net force always points the way of the bigger force.
- If the opposite forces are equal, the net force is 0 N. The forces are balanced.
- A net force is never "just a number": say its size and its direction.
2.2The rule
When the forces on an object are balanced, it keeps doing what it was already doing: if it was still, it stays still; if it was moving, it keeps moving at the same speed in the same direction. When the forces are unbalanced, the object speeds up, slows down or changes direction — in the direction of the net force.
- A book on a desk: weight down, support up, equal. Balanced, so it stays put.
- A car cruising at a steady 100 km/h: the engine's forward push equals friction plus air resistance pulling back. Balanced — steady speed does not need a net force. This is the point most people get wrong.
- A car braking: the brakes add a large backward friction force. Backward now beats forward, the net force points backward, the car slows.
- A netball hitting the ring: the ring pushes on the ball for a moment; that unbalanced push changes the ball's direction.
Gravity, mass, weight — and friction
"How much do you weigh?" is a trick question in physics. The number on the bathroom scales is your mass in kilograms. Your weight is the force gravity pulls you down with, in newtons — and it would be different on the Moon.
3.1Gravity
- Gravity is a non-contact force of attraction between any two objects that have mass. Everything pulls on everything — but only enormous things like planets and moons pull hard enough to notice.
- The Earth pulls every object toward its centre. That direction is what we call "down" — which is why "down" in Perth and "down" in London point in different directions in space.
- Gravity also holds the Moon in orbit around the Earth, and the Earth in orbit around the Sun. It works across empty space; nothing needs to touch.
- A bigger planet pulls harder. The Moon is much smaller than Earth, so its gravity is about one-sixth as strong.
3.2Mass versus weight
| Mass | Weight | |
|---|---|---|
| What it is | The amount of matter (stuff) in an object | The force of gravity pulling on that matter |
| Unit | kilograms (kg) | newtons (N) |
| Measured with | A balance (compares against known masses) | A spring balance or force meter |
| Changes if you move to the Moon? | No — you are made of the same stuff | Yes — about one-sixth of your Earth weight |
| On Earth | 50 kg student | 50 × 10 = about 500 N |
On Earth, gravity pulls each kilogram with about 10 N. So weight (N) ≈ mass (kg) × 10. A 30 kg bag of cement weighs about 300 N; a 1.5 kg cat weighs about 15 N. On the Moon it is only about 1.6 N per kilogram, so that same cat would weigh about 2.4 N — but it would still be a 1.5 kg cat.
3.3Falling
- Drop a hammer and a feather on Earth and the hammer lands first — but only because air resistance holds the feather back. In 1971 an Apollo 15 astronaut dropped both on the airless Moon and they hit the ground together.
- Air resistance depends on shape, size and speed. A flat sheet of paper drifts down; scrunch the same sheet into a ball and it drops fast. Same mass, same gravity, less air resistance.
- The faster you fall, the bigger the air resistance gets, until it balances your weight — the steady-speed stage of Figure 2.2.
3.4Friction: friend and enemy
Friction is the contact force that resists two surfaces sliding across each other. It always acts against the direction something is moving (or trying to move), and it turns motion into heat — rub your hands together and feel it.
| Friction is useful when… | Friction is a nuisance when… |
|---|---|
| Your shoes grip the floor so you can walk — try it on a wet tiled pool deck | Engine and bike parts rub, get hot and wear away |
| Tyres grip the road; the tread channels water away on a wet day | Air resistance slows a cyclist or a car, wasting fuel |
| Brake pads squeeze the wheel and slow the bike | A stiff, dry hinge squeaks and sticks |
| A match lights; a gymnast's chalked hands hold the bar | Water resistance slows a swimmer or a boat |
- To reduce friction: lubricate with oil or grease, polish the surfaces smooth, put the load on wheels or ball bearings, and streamline the shape to cut air or water resistance (teardrop helmets, smooth car bodies, swimmers' caps).
- To increase friction: roughen the surface (tyre tread, sandpaper, non-slip strips on stairs), add grip (rubber soles, chalk, rosin on a violin bow), or press the surfaces together harder.
Simple machines: a small force doing a big job
You cannot lift a car engine with your hands, but you can with a crowbar, a ramp or a pulley. A simple machine has no motor and no electronics — it just changes the size or the direction of a force. The catch: a smaller force always has to move a longer distance.
4.1Levers
A lever is a stiff bar that turns about a fixed point, the fulcrum (or pivot). You apply the effort; the lever moves the load. Where the fulcrum sits relative to the effort and the load decides the class of lever.
The further from the fulcrum you push, the smaller the force you need — but the further your hand has to move. A long crowbar lifts a rock a child could not budge, yet the rock rises only a few centimetres while the crowbar's end swings through half a metre. Less force, more distance: every simple machine makes this same trade.
4.2Ramps, pulleys, wheels and gears
| Machine | What it changes | How | Examples |
|---|---|---|---|
| Inclined plane (ramp) | Size of force | Push a load up a gentle slope with a smaller force, over a longer distance, instead of lifting it straight up | Wheelchair ramps, a plank into a ute, a mountain road's zigzags |
| Wedge | Size and direction | A moving ramp: push it forward and it pushes the material apart sideways | Axe, knife, door stop, chisel |
| Screw | Size of force | A ramp wrapped around a cylinder: many turns for a little forward travel, so a small twist gives a big push | Wood screws, jar lids, a car jack |
| Pulley | Direction (one pulley); size too (two or more) | A rope over a grooved wheel lets you pull down to lift up; add pulleys and each rope section shares the load | Flagpole, window blinds, a builder's crane, a well |
| Wheel and axle | Size of force | Turn the big wheel with a small force and the small axle turns with a big force | Steering wheel, door knob, screwdriver, tap handle |
| Gears | Size of turning force, and speed | Toothed wheels lock together; a small gear driving a big one turns it slower but harder | Bike gears, hand egg-beater, clockwork |
Your body is full of levers. Your forearm is a third-class lever: the elbow is the fulcrum, the biceps pulls just in front of it (the effort), and the load is in your hand. That is a poor arrangement for strength — the biceps pulls much harder than the weight you hold — but a superb one for speed, which is why you can throw a cricket ball at 100 km/h.
One planet, one Sun, one Moon — and everything we take from them.
Four units: the resources Earth gives us and which ones run out, the water that never stops moving, why we have day, night and seasons, and what the Moon does to our skies and our oceans — built from the Year 7 Earth & space descriptions AC9S7U03 and AC9S7U04.
The mapFour units
- Earth's resources — renewable versus non-renewable, and why the answer depends on how fast we use them.
- The water cycle — evaporation to precipitation and back, driven by the Sun, and where the water in your tap actually comes from.
- Day, night and seasons — a spinning, tilted Earth on a year-long lap around the Sun.
- The Moon, eclipses and tides — phases, two kinds of eclipse, and the pull that lifts the ocean twice a day.
AC9S7U03 — classify Earth's resources as renewable or non-renewable and describe the water cycle. AC9S7U04 — model the relative movements of the Earth, Sun and Moon and explain day and night, seasons, Moon phases, eclipses and tides.
Earth's resources: what runs out and what doesn't
Everything you own started as something dug up, cut down, pumped out or grown. A natural resource is anything we take from the Earth and use. The big question about each one is simple: does nature make more of it as fast as we use it up?
1.1Renewable or non-renewable
- A renewable resource is replaced by natural processes about as fast as we use it — or faster. Sunlight, wind, flowing water, tides, crops, wool, and timber from forests that are replanted.
- A non-renewable resource took millions of years to form, so once it is used it is gone on any human timescale. Coal, oil, natural gas, and minerals such as iron ore, bauxite, gold and uranium.
- Coal, oil and gas are the fossil fuels: the remains of plants and tiny sea creatures buried and squeezed for hundreds of millions of years. Burning a tonne of coal takes an afternoon; making it took an age.
- Some resources sit on the line. A forest is renewable if it is logged slower than it regrows. A fishery is renewable if the catch is smaller than the number of fish born. Groundwater is renewable if rain refills it faster than bores pump it out.
1.2The Australian picture
| Resource | Renewable? | Where Australia gets it | What it is used for |
|---|---|---|---|
| Iron ore | No | The Pilbara, WA — Australia is the world's biggest exporter | Steel for buildings, cars, bridges |
| Coal | No | Hunter Valley (NSW), Bowen Basin (Qld) | Electricity, steel-making, export |
| Natural gas | No | Off the north-west coast, Bass Strait | Cooking, heating, power stations, export as LNG |
| Bauxite | No | Weipa (Qld), the Darling Range (WA) | Aluminium for cans, planes, window frames |
| Sunlight | Yes | Everywhere — about one in three Australian homes has rooftop solar, the highest rate in the world | Electricity, hot water |
| Wind | Yes | South Australia, western Victoria, Tasmania | Electricity |
| Flowing water | Yes | The Snowy Mountains, Tasmania's dams | Hydro-electricity |
| Timber | Yes, if replanted | Pine plantations in SA, Vic and NSW | House frames, paper, furniture |
A resource is renewable if it is replaced by natural processes at least as fast as it is used, and non-renewable if it forms so slowly that our use will exhaust it. Name the resource, say how fast nature makes it, and compare that with how fast we take it.
The water cycle: the same water, round and round
The water in your glass has been rain, ocean, cloud, river and probably a dinosaur at some point. Earth has had roughly the same water for billions of years; it just keeps changing state and moving. The engine that drives it all is the Sun.
2.1The cycle
| Process | Change of state | Where it happens |
|---|---|---|
| Evaporation | Liquid → gas (water vapour) | Ocean, lakes, wet roads, washing on the line |
| Transpiration | Liquid → gas | Leaves of plants, which pull water up from the soil |
| Condensation | Gas → liquid | High in the sky where the air is cold; also on a cold drink can |
| Precipitation | Falls as liquid or solid | Rain, drizzle, hail, snow |
| Runoff | No change — liquid flows | Over the land surface into creeks, rivers and lakes |
| Infiltration | No change — liquid soaks down | Into soil and porous rock, becoming groundwater |
2.2Where your tap water comes from
- Of all the water on Earth, about 97% is salty ocean, about 2% is locked in ice, and less than 1% is the fresh liquid water in rivers, lakes and underground that we can actually drink.
- Most Australian cities drink dam water: rain runs off a protected catchment into a reservoir — Warragamba for Sydney, Wivenhoe for Brisbane, the Thomson for Melbourne. It is filtered and a little chlorine is added to kill germs before it reaches the pipes.
- Perth gets about half its water from desalination — taking the salt out of sea water — and much of the rest from groundwater pumped from bores.
- Outback towns and farms rely on the Great Artesian Basin, a vast underground store of water that fell as rain thousands of years ago, and on rainwater tanks.
Water is renewable — the cycle keeps delivering it — but only at the rate rain falls. Australia is the driest inhabited continent, and droughts can last years. That is why we build dams and tanks to store the wet years, put restrictions on sprinklers in the dry ones, rate appliances with WELS water stars, and recycle treated water for parks and industry. The cycle is free; managing it is not.
Day, night and seasons: a spinning, tilted Earth
The Earth does two things at once. It spins on its axis once every 24 hours, and it orbits the Sun once every year. Add one more fact — the axis is tilted — and you can explain sunrise, midnight, summer holidays and why Christmas is hot in Australia and cold in London.
3.1Day and night
- One spin = one day (24 hours). One orbit = one year (365¼ days — the quarter is why we add 29 February every four years).
- The Earth's axis is an imaginary line through the North and South Poles. It is tilted at 23.5° and it always points the same way in space as the Earth goes around the Sun.
- The Sun does not move across the sky — we turn. Sunrise is your part of the Earth spinning into the light.
3.2Seasons come from tilt, not distance
- The hemisphere leaning toward the Sun gets sunlight that is more direct (concentrated on a smaller patch of ground, so it heats more) and more hours of daylight. Both make it hotter.
- The hemisphere leaning away gets slanting sunlight spread over a bigger area, and shorter days. Winter.
- Distance is not the reason. Earth is actually closest to the Sun in early January — the middle of the northern winter. The orbit is very nearly a circle; the tilt does all the work.
- Near the equator neither hemisphere leans much, so Darwin has a wet and a dry season rather than a hot and a cold one.
| Month | Hemisphere leaning toward the Sun | Australia | Europe and North America |
|---|---|---|---|
| December | Southern | Summer — longest day about 21 Dec | Winter |
| March | Neither (in between) | Autumn | Spring |
| June | Northern | Winter — shortest day about 21 June | Summer |
| September | Neither (in between) | Spring | Autumn |
"It is summer because the Earth is closer to the Sun." No. If that were true, the whole planet would have summer at the same time — but December is summer in Sydney and winter in London. Seasons are opposite in the two hemispheres, which only a tilt can explain.
The Moon: phases, eclipses and tides
The Moon makes no light of its own. What you see is sunlight bouncing off a ball of grey rock that orbits us once a month. Everything in this unit — the changing shape, the rare eclipses, the ocean rising and falling twice a day — comes from where that ball is on its lap around the Earth.
4.1Phases
- The Moon orbits the Earth and reflects sunlight. Half of it is always lit — we just cannot always see that half.
- The order: new → waxing crescent → first quarter → waxing gibbous → full → waning gibbous → last quarter → waning crescent → new. About a week between each quarter.
- From Australia a waxing Moon is lit on its left side and a waning Moon on its right — the opposite of what northern-hemisphere books show, because we are looking at it "upside down".
- Phases are not Earth's shadow. Earth's shadow only touches the Moon during a lunar eclipse.
4.2Eclipses
4.3Tides
"Spring tide" has nothing to do with the season — it means the water springs up, and it happens twice every month. The biggest tides in Australia are in the Kimberley: at Derby, WA, the sea rises and falls up to 11 metres twice a day, among the largest tidal ranges on Earth, which is why the town's wharf stands on such tall legs.
Year 7 Maths: the six foundations.
Six units covering the core of the Year 7 Australian Curriculum: integers and number properties, fractions and percentages, first algebra, the Cartesian plane, angles and shapes, and measurement with data and chance.
The mapSix units
- Integers and number properties — negatives on the number line, order of operations, squares, primes and factor trees.
- Fractions, decimals and percentages — equivalent fractions, adding and multiplying, switching between the three forms, discounts and ratios.
- First algebra — what a letter means, substituting, like terms, solving equations, and the rule behind a pattern.
- The Cartesian plane — plotting points in four quadrants, and turning a rule into a line of points.
- Angles and shapes — angle types, angle facts, parallel lines, and the angle sums of triangles and quadrilaterals.
- Measurement, data and chance — perimeter, area and volume; mean, median, mode and range; probability as a fraction.
Reading maths does almost nothing — doing it is everything. Keep a pencil and paper beside you for every drill, and when you get one wrong, redo it by hand before moving on. Ten minutes of working problems beats an hour of reading them.
Integers and number properties
Negative numbers are just the left half of the number line. Once you can walk along it, adding and subtracting them is easy — and the rest of this unit is about the personalities of the whole numbers: squares, primes and powers.
1.1Ordering, adding and subtracting on the number line
Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right).
2 + 3 × 4 = 14, never 20. And (2 + 3) × 4 = 20 — brackets are how you demand the addition happens first. 20 − 12 ÷ 4 = 20 − 3 = 17.
1.2Squares, square roots, factors and primes
| Word | Meaning | Example |
|---|---|---|
| Square number | A number times itself | 7² = 7 × 7 = 49. The first twelve: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 |
| Square root √ | Undoes squaring: which number, squared, gives this? | √49 = 7 because 7² = 49. √81 = 9 |
| Factor | A number that divides in exactly | Factors of 12: 1, 2, 3, 4, 6, 12 (six of them) |
| Multiple | The times-table of a number | Multiples of 4: 4, 8, 12, 16, 20 … |
| Prime number | Has exactly two factors: 1 and itself | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 … (2 is the only even prime) |
| Composite number | Has more than two factors | 9 = 3 × 3, 15 = 3 × 5, 21 = 3 × 7 |
1 is not prime — it has only one factor (itself), and a prime needs exactly two. It is not composite either. It is simply 1.
1.3Index notation and prime factor trees
An index (or power) is a shortcut for repeated multiplication: 2³ = 2 × 2 × 2 = 8. The small 3 says "multiply three 2s together" — it does not mean 2 × 3. Every composite number can be split into primes, and a factor tree does the splitting.
Fractions, decimals and percentages: three costumes, one number
½, 0.5 and 50% are the same amount written three ways. This unit is about moving between the costumes, adding and multiplying fractions, and using percentages on real prices.
2.1Equivalent fractions
2.2Adding, subtracting and multiplying
- Same denominator? Just add the tops. 2/5 + 1/5 = 3/5. The bottom names the size of the pieces; it does not change.
- Different denominators? Make them the same first. 1/2 + 1/3: the smallest number both 2 and 3 go into is 6. So 1/2 = 3/6 and 1/3 = 2/6, and 3/6 + 2/6 = 5/6.
- Subtracting works the same way. 3/4 − 1/2 = 3/4 − 2/4 = 1/4.
- Multiplying is the easy one: top × top, bottom × bottom. 2/3 × 3/4 = 6/12 = 1/2.
- "Of" means multiply. 3/4 of 20 = 20 ÷ 4 × 3 = 15.
1/2 + 1/3 is not 2/5. Adding the tops and adding the bottoms is wrong every time — check it: 2/5 is less than 1/2, but you started with 1/2 and added more. You must find a common denominator first.
2.3Switching between the three forms
| Fraction | Decimal | Percentage | How to get there |
|---|---|---|---|
| 1/2 | 0.5 | 50% | fraction → decimal: divide top by bottom (1 ÷ 2 = 0.5) |
| 1/4 | 0.25 | 25% | decimal → percentage: multiply by 100 (0.25 × 100 = 25) |
| 3/4 | 0.75 | 75% | percentage → fraction: write it over 100 and simplify (75/100 = 3/4) |
| 1/5 | 0.2 | 20% | 1 ÷ 5 = 0.2, then × 100 = 20% |
| 1/10 | 0.1 | 10% | the easiest to memorise |
| 1/3 | 0.333… | 33.3% | the decimal never ends, so it is rounded |
2.4Percentage of a quantity, and discounts
- Turn the percentage into a fraction or decimal: 20% = 20/100 = 0.2.
- Multiply: 20% of $45 = 0.2 × 45 = $9.
- Discount? Subtract it from the price: a $45 game with 20% off costs $45 − $9 = $36.
- The 10% trick: 10% is just "divide by 10". 10% of $80 = $8, so 30% of $80 = 3 × $8 = $24, and 5% of $80 = half of $8 = $4.
2.5Ratios: sharing fairly-by-the-rules
Share $40 between two people in the ratio 3 : 5.
1. Add the parts: 3 + 5 = 8 parts. 2. One part = 40 ÷ 8 = $5. 3. Multiply out: 3 × 5 = $15 and 5 × 5 = $25. Check: 15 + 25 = 40 ✓
- A ratio compares parts in order: cordial to water 1 : 4 means 1 part cordial for every 4 parts water.
- Simplify a ratio like a fraction: 8 : 12 → divide both by 4 → 2 : 3.
- Ratios and fractions are cousins: in 3 : 5 the first person gets 3/8 of the money, not 3/5.
First algebra: a letter is a number you don't know yet
Algebra is arithmetic with a placeholder. If a step ever looks strange, put a number in for the letter and see whether it still works — that test never lies.
3.1Reading an expression, and substituting
Say n is the number of tickets you buy. Then 3n + 2 means "3 times n, then add 2" — perhaps $3 a ticket plus a $2 booking fee. Writing 3n instead of 3 × n is the only new notation: a number next to a letter means multiply. To substitute, replace the letter with its value and calculate.
| Expression | In words | Value when n = 4 |
|---|---|---|
| 3n + 2 | three times n, then add 2 | 3 × 4 + 2 = 14 |
| n − 5 | 5 less than n | 4 − 5 = −1 |
| n / 2 | half of n | 4 ÷ 2 = 2 |
| 2(n + 1) | add 1 to n, then double | 2 × 5 = 10 |
| n² | n times itself | 4 × 4 = 16 |
3.2Simplifying: collect like terms
- Like terms have exactly the same letter part. 4a + 3a = 7a (four apples plus three apples).
- Numbers on their own are their own kind: 5x + 2 + x = 6x + 2. The 2 has no x, so it stays alone.
- Different letters do not combine: 3a + 2b is already as simple as it gets.
- Subtracting works too: 9y − 4y = 5y.
3.3Solving equations: same thing to both sides
An equation has an equals sign, and the two sides balance. Whatever you do to one side you must do to the other, or the balance breaks. To solve, undo what was done to x, in reverse order.
3.4Number patterns and their rules
The pattern 5, 8, 11, 14, … goes up by 3 each step, so the rule starts with 3n. Test n = 1: 3 × 1 = 3, but the first term is 5 — 2 more. So the rule is 3n + 2. Check n = 4: 3 × 4 + 2 = 14 ✓. Now any term is instant: the 10th term is 3 × 10 + 2 = 32.
| Position n | 1 | 2 | 3 | 4 | 10 |
|---|---|---|---|---|---|
| Term (3n + 2) | 5 | 8 | 11 | 14 | 32 |
The Cartesian plane: every point has an address
Two number lines crossed at right angles give every point a pair of coordinates (x, y). Once you can plot points, a rule like y = x + 2 becomes a picture — and the picture is always a straight line.
4.1Reading and plotting points
4.2From a rule to a line of points
A rule like y = x + 2 is a machine: put in an x, get out a y. Make a table, plot each (x, y) pair, and look.
| x | −2 | −1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| y = x + 2 | 0 | 1 | 2 | 3 | 4 | 5 |
| y = 2x | −4 | −2 | 0 | 2 | 4 | 6 |
- To plot a rule: make a table with 3 or 4 x-values (include 0 — it is the easiest), work out each y, plot the points, rule a line through them.
- To check a point is on a line: substitute. Is (3, 6) on y = 2x? 2 × 3 = 6 ✓ yes. Is (3, 5)? 2 × 3 = 6, not 5, so no.
- Negative x-values work the same way: for y = x + 2, x = −5 gives y = −3.
Angles and shapes: a handful of facts that unlock every diagram
Five angle types, four angle facts, three parallel-line pairs, and two angle sums. Learn them as a kit and almost any "find the missing angle" question becomes a two-line calculation.
5.1The five angle types
5.2Four angle facts
5.3Parallel lines and a transversal
5.4Triangles and quadrilaterals
The three angles of any triangle add to 180°. Tear the corners off a paper triangle and put them together: they make a straight line. The four angles of any quadrilateral add to 360° — a diagonal cuts it into two triangles, 2 × 180°.
Missing angle in a triangle with 50° and 60°: 180 − 50 − 60 = 70°. Missing angle in a quadrilateral with 90°, 90° and 120°: 360 − 300 = 60°.
| Quadrilateral | Sides | Angles |
|---|---|---|
| Square | 4 equal, opposite sides parallel | 4 right angles |
| Rectangle | opposite sides equal and parallel | 4 right angles |
| Rhombus | 4 equal, opposite sides parallel | opposite angles equal (a pushed-over square) |
| Parallelogram | opposite sides equal and parallel | opposite angles equal (a pushed-over rectangle) |
| Trapezium | exactly one pair of parallel sides | no rule |
| Kite | two pairs of adjacent equal sides | one pair of opposite angles equal |
Measurement, data and chance
Three area formulas and one volume rule; four ways to summarise a list of numbers; and probability as a fraction between 0 and 1. All of it is arithmetic once you pick the right formula and the right unit.
6.1Perimeter and area
Perimeter is the distance around the outside — add up the sides, answer in cm. Area is the space inside — use a formula, answer in cm² (square centimetres), because you are counting squares.
6.2Volume of a rectangular prism
A box 4 cm × 3 cm × 2 cm: V = 4 × 3 × 2 = 24 cm³. You are counting centimetre cubes: 12 in the bottom layer, two layers. Volume is always in cubic units.
- Units stack with the dimension: length cm, area cm², volume cm³. Writing the wrong unit loses a mark even with the right number.
- 1 cm³ holds exactly 1 mL, so a 24 cm³ box holds 24 mL of water.
6.3Mean, median, mode and range
| Measure | How to find it | For 2, 5, 5, 8, 10 |
|---|---|---|
| Mean | Add them all, divide by how many | 30 ÷ 5 = 6 |
| Median | Put in order, take the middle one (or the average of the middle two) | 5 |
| Mode | The most common value | 5 |
| Range | Biggest minus smallest (how spread out) | 10 − 2 = 8 |
For 4, 6, 9, 11 there is no single middle. The median is the average of the two middle values: (6 + 9) ÷ 2 = 7.5. And always order the data first — the median of 9, 4, 11, 6 is still 7.5.
Test scores 23, 27, 31, 35, 35, 42, 48, 50 written with tens as the stem and units as the leaves:
2 | 3 7 3 | 1 5 5 4 | 2 8 5 | 0 (key: 3 | 1 means 31)
Because the leaves are already in order you can read straight off it: mode 35, range 50 − 23 = 27, and with 8 scores the median is the average of the 4th and 5th: (35 + 35) ÷ 2 = 35.
6.4Probability of a single event
How texts are built — and how to build your own.
Four units: the shape every story shares, the toolbox of words and sentences writers reach for, what makes a poem a poem, and how to persuade or inform a reader in a paragraph that actually works — built from the Year 7 English language, literature and literacy descriptions.
The mapFour units
- How stories work — the five stages of a narrative, character, setting, point of view, and showing instead of telling.
- The writer's toolbox — simile, metaphor and friends; the four big word classes; three sentence types; punctuating speech.
- Poetry — rhyme, rhythm, stanzas, repetition and sound, with an original poem to pull apart.
- Persuade and inform — purpose and audience, the persuasive techniques, the TEEL paragraph, and how informative texts are laid out.
Two things. Can you read a text and say how it works — name the stage of the story, the language device, the persuasive trick — and can you write clearly on purpose: a story with a shape, a paragraph with a point, sentences that are punctuated so a stranger can read them?
How stories work
A picture book, a film, a game's storyline and a novel all climb the same mountain: something is normal, something goes wrong, it gets worse, it comes to a head, and it settles. Learn the shape and you can find it in anything you read — and use it in anything you write.
1.1The narrative mountain
Here is the whole shape in one tiny story, stage by stage:
| Stage | The Missing Key |
|---|---|
| Orientation | Every morning before school, Jai unlocked the gate of the community garden and watered the seedlings. |
| Complication | One Tuesday the key was not on its hook. |
| Rising action | He emptied his bag, retraced his steps to the bus stop, and even dug through the compost. Meanwhile the sun climbed higher and the seedlings began to wilt. |
| Climax | Then he saw a glint in the mud under the tap: someone had dropped the key while filling a can. |
| Resolution | He soaked the seedlings just in time, and from that day the key lived on a string around his neck. |
1.2Character and setting
- The setting is where and when the story happens — a flooded town in 1974, a space station, a Year 7 classroom on the last day of term. Setting sets the mood and limits what can happen.
- A character is anyone the story is about. The main character (protagonist) has the problem; whatever gets in their way — a person, a storm, their own fear — is the obstacle.
- We learn about characters from four clues: what they say, what they do, what they think, and how others react to them.
1.3Show, don't tell
Telling hands the reader a label. Showing hands them the clues and lets them work it out — which is why it feels more real.
| Telling | Showing |
|---|---|
| Maya was nervous. | Maya's hands would not keep still. She read the first line of her speech four times and still could not remember what it said. |
| The room was messy. | Socks hung from the lamp. Somewhere under the pizza boxes, a phone was ringing. |
"The bus was late again. Priya checked her phone for the fifth time, then kicked the bus-stop pole." The writer never says frustrated — but the fifth check and the kick show it. In a test, quote the action and name the feeling it shows.
1.4Point of view: who is telling this?
| Point of view | Pronouns | The same moment |
|---|---|---|
| First person — a character tells their own story | I, me, my, we | I gripped the rope and told myself not to look down. |
| Third person — a narrator outside the story tells it | he, she, they, their | Sam gripped the rope and told himself not to look down. |
- First person feels close — we are inside one head — but we only know what that character knows.
- Third person can step back and follow more than one character, and can tell us things the characters don't know.
- The choice changes the story. A mystery told by the detective keeps different secrets from one told by an outside narrator.
The writer's toolbox
Writers don't have magic; they have tools. Some make pictures in the reader's head, some control the speed of a sentence, and some just stop the reader getting lost. This unit names the tools so you can spot them in a text and pick them up yourself.
2.1Language devices: pictures made of words
| Device | What it does | Example |
|---|---|---|
| Simile | Compares two things using like or as | The puppy's ears were as soft as velvet. |
| Metaphor | Says one thing is another — no like or as | The playground was a battlefield at lunchtime. |
| Personification | Gives a non-human thing human feelings or actions | The old house groaned and shivered in the wind. |
| Alliteration | Repeats the same starting sound in nearby words | Big brown bears bumbled by. |
| Onomatopoeia | A word that sounds like the noise it names | The fireworks fizzed, whizzed and banged. |
| Imagery | Detail aimed at the senses — sight, sound, smell, taste, touch | Hot bitumen, the smell of sunscreen, a magpie warbling somewhere. |
| Hyperbole | Exaggeration on purpose, for effect | My bag weighs about a thousand kilos. |
Look for like or as. "The crowd roared like a jet engine" is a simile. "The crowd was a jet engine at full power" is a metaphor. Same picture, different tool.
2.2The four big word classes
| Word class | Its job | In a sentence |
|---|---|---|
| Noun | Names a person, place, thing or idea | The surfer waited for a wave. |
| Verb | The action, or the state of being | The surfer paddled; the wave was enormous. |
| Adjective | Describes a noun | The enormous wave; the rusty gate. |
| Adverb | Describes a verb — how, when, where (many end in -ly) | The surfer paddled quickly; she arrived late. |
- A word's class depends on the job it does in that sentence. "A light rain" (adjective) · "turn on the light" (noun) · "light the candle" (verb).
- Strong writing usually swaps a weak verb plus an adverb for one precise verb: "walked slowly" → "trudged"; "said loudly" → "shouted".
2.3Three sentence types
Short simple sentences hit hard: "The lights went out." Longer compound and complex sentences carry more information and slow the pace. A whole paragraph of one type gets dull — mix them on purpose.
2.4Punctuating what people say
- Speech marks around the spoken words only: "Watch out!" shouted Mia.
- Punctuation before the closing speech mark, inside it: a comma if a speech tag follows ("It's over here," said Tom), otherwise a full stop, question mark or exclamation mark.
- The speech tag stays lower-case unless it starts with a name: …" shouted Mia.
- New speaker, new line. Each time a different person speaks, start a new paragraph.
Poetry: what makes a poem a poem
A poem is a text where the sound and the shape carry meaning as much as the words do. Lines end where the poet chooses, sounds repeat on purpose, and a beat runs underneath. This unit gives you the names for those choices and a short poem to test them on.
3.1The poet's terms
| Term | Meaning |
|---|---|
| Stanza | A group of lines set apart by a blank line — a poem's paragraph. Four lines make a quatrain; two rhyming lines make a couplet. |
| Rhyme | Words that end with the same sound: grey / tray, blue / new. |
| Rhyme scheme | The pattern of rhymes at line ends, written in letters. Lines that rhyme share a letter: ABAB, AABB. |
| Rhythm | The beat, made by stressed and unstressed syllables: the SKY turned BLACK at HALF past THREE — da-DUM, da-DUM. |
| Repetition | The same word, phrase or line used more than once, so it sticks and builds a beat. |
| Sound devices | Alliteration and onomatopoeia (from Unit 2) — in poetry they are everywhere, because poems are meant to be heard. |
| Free verse | Poetry with no regular rhyme or beat — the lines are shaped by sense and breath instead. |
3.2Read this: an original poem
The sky turned black at half past three,
the wind chased clouds of grey,
and rain came drumming down on me
like marbles on a tray.
Then just as fast the sky turned blue,
the gutters gurgled, brown;
the steaming footpath shone like new
across the sleepy town.
| What to look for | In "After the Storm" | Effect |
|---|---|---|
| Structure | Two stanzas of four lines (quatrains): storm, then calm | The shape mirrors the event — the break between stanzas is the moment the rain stops |
| Rhyme scheme | three / grey / me / tray → ABAB, and again in stanza two (blue / brown / new / town) | Rhyme makes the lines feel finished and easy to remember |
| Rhythm | Lines swap between four beats and three: the SKY turned BLACK at HALF past THREE / the WIND chased CLOUDS of GREY | A bouncing, song-like beat — the same one many nursery rhymes use |
| Simile | "like marbles on a tray" | You hear the hard, bouncing rain |
| Personification | "the wind chased clouds" | The weather becomes a character with intentions |
| Onomatopoeia & alliteration | "drumming", "gutters gurgled" | The words make the noise of the storm; the repeated g sounds thick and wet |
| Imagery | "the steaming footpath shone like new" | Sight and touch — you can feel the heat coming back |
Name the device, quote the words, then say the effect: "The simile 'like marbles on a tray' makes the rain sound hard and noisy, so the reader hears the storm rather than just seeing it." Device → quote → effect, every time.
3.3Write your own
- Pick one small moment — a storm, a lost sock, the last bell — not a whole day.
- Choose a shape: two quatrains with an ABAB scheme, or free verse if you'd rather shape the lines by sense.
- Put one picture in every line and at least one sound device in every stanza.
- Read it aloud. If a line trips your tongue, the rhythm is wrong — change a word, not the idea.
Persuade and inform
Not every text is a story. A poster, a speech at assembly, a science explanation and a letter to the council each have a job to do and a reader to do it for. Work out the job and the reader first, and the right techniques choose themselves.
4.1Purpose and audience
- Purpose is what the text is for. The three big ones: to persuade (change what the reader thinks or does), to inform (give the reader facts they can use), to entertain (tell a story, make them laugh).
- Audience is who it is for. A letter to the principal, a talk to Year 3s and a text to a friend about the same problem use different words, different examples and a different tone.
- Ask both questions before you write a word: what do I want this reader to think or do by the end?
4.2Persuasive techniques
| Technique | What it does to the reader | Example |
|---|---|---|
| Rhetorical question | A question with an obvious answer — the reader answers it silently and agrees | Wouldn't you rather breathe clean air? |
| Emotive language | Words picked to stir feelings | Helpless, terrified kittens are dumped every single week. |
| Facts and statistics | Numbers and facts make the claim feel proven | Students who eat breakfast score 15% higher on tests. |
| Rule of three | Three items in a row feel complete and stick in the memory | Faster, fairer, friendlier. |
| Personal pronouns | We, our, you pull the reader onto the writer's side | We all want our school to be safe. |
| Repetition | Saying the key idea again so it cannot be missed | More shade. More seats. More bins. |
"Who could say no to a longer lunch break?" — a rhetorical question, and the marks come from finishing the sentence: it makes the reader answer 'nobody' in their head, so they agree before the argument has even started.
4.3The TEEL paragraph
4.4Informative texts: built to be found
An informative text — a science explanation, a how-to, a report — is not read from start to finish. It is searched. So it is built to help a reader find things fast:
- Headings and subheadings break the text into sections, so you can jump straight to the part you need.
- Diagrams, tables and captions show what would take a paragraph to say. Every figure gets a caption telling you what you are looking at.
- Topic sentences start each paragraph with its main idea; bold key terms flag the vocabulary; a glossary defines it.
- The tone is neutral and precise: facts, present tense, no "I think" and no emotive words — the opposite of a persuasive text.
Inform: "Magpies swoop for about six weeks in spring, while chicks are in the nest." Persuade: "Every spring, terrified students are ambushed on their way to school — when will the council act?" Same bird. One text gives you facts; the other wants something from you.
Stone tools, pharaohs and the Roman roads.
Four units from the longest stretch of human history: how historians and archaeologists actually find out about the past, the oldest continuous cultures on Earth here in Australia, the civilisation the Nile made possible, and the two Mediterranean powers whose ideas — democracy, theatre, the alphabet, concrete — are still all around you.
The mapFour units
- How historians work — sources and evidence, archaeology, dates and centuries, and telling fact from opinion.
- Deep time: Australia's First Peoples — at least 65 000 years of continuous culture, Country, Songlines and technology.
- Ancient Egypt — the Nile, the pharaoh, the social pyramid, hieroglyphs, and beliefs about the afterlife.
- Ancient Greece and Rome — Athens and Sparta, the Olympics, Rome from republic to empire, and why it fell.
Three skills more than three hundred facts: putting events in chronological order (with BCE and CE the right way round), telling a primary source from a secondary one and saying what it is evidence of, and explaining why a society was organised the way it was — why the Nile made Egypt, why Sparta trained soldiers, why Rome built roads.
How historians work
Nobody alive saw ancient Egypt. Everything we know about it comes from things that survived — a tomb wall, a broken pot, a tax record on papyrus — and from people who asked those things careful questions. History is not a list of facts; it is the detective work that produces them.
1.1Primary and secondary sources
| Kind of source | What it is | Examples |
|---|---|---|
| Primary source | Something made at the time being studied, or by someone who was there | A tomb painting, a Roman coin, a stone tool, a letter from a soldier, the Rosetta Stone |
| Secondary source | Something made later, by someone studying the time, usually using primary sources | A textbook, a documentary, a historian's book, a museum label |
- Primary sources are closer to the event — but not automatically true. A pharaoh's monument boasts about victories; it is not going to mention defeats.
- So historians ask every source the same questions: who made it, when, why, for whom — and what it can't tell us.
- Written sources only begin about 5 000 years ago. For everything before that — most of human history — the sources are objects and places, and the experts are archaeologists.
1.2From source to evidence
1.3Archaeology: reading objects
- An artefact is any object made or used by people — a spear point, a bead, a cooking hearth. Where it was found matters as much as what it is, so archaeologists dig slowly and record every layer.
- Deeper usually means older: soil builds up over time, so the layers of a site are a rough calendar. This is called stratigraphy.
- Carbon dating gives actual ages. Everything alive takes in a tiny amount of a radioactive form of carbon (carbon-14). When it dies, that carbon slowly breaks down at a known rate — so measuring how much is left in bone, charcoal or shell tells scientists roughly how long ago it died. It works back to about 50 000 years; older sites need other methods, such as dating the sand grains around a find.
- That is why historians say "about 40 000 years" or "at least 65 000 years": scientific dates come with a range, and a new dig can push them back.
1.4Dates, centuries and timelines
| Word | How long | Working it out |
|---|---|---|
| Decade | 10 years | the 2020s |
| Century | 100 years | Centuries count from year 1, so the years 1–100 CE are the 1st century. Rule of thumb: drop the last two digits and add 1 — 650 CE is in the 7th century CE; 1250 BCE is in the 13th century BCE. |
| Millennium | 1 000 years | The pyramids at Giza were built about 4 500 years ago — four and a half millennia. |
1.5Fact, opinion, interpretation
| What it is | Example | |
|---|---|---|
| Fact | Something that can be checked against evidence | The Great Pyramid was built about 4 500 years ago. |
| Opinion | A personal view that can't be proved either way | The Great Pyramid is the most beautiful building ever made. |
| Interpretation | A historian's conclusion built from evidence — reasoned, but open to debate | The pyramids were built by paid workers, not slaves — supported by the workers' village and bakeries found beside them. |
"Is this source reliable?" Never just say yes or no. Say who made it and why, what that means they might leave out or exaggerate, and what it is still useful as evidence of. A pharaoh's boastful monument is unreliable about the battle — but excellent evidence of how pharaohs wanted to be seen.
Deep time: at least 65 000 years on this continent
When the pyramids were new, Aboriginal peoples had already been living, trading, burying their dead and managing the land here for tens of thousands of years. Aboriginal and Torres Strait Islander peoples hold the oldest continuous cultures on Earth — and they are not ancient history: those cultures are alive today.
2.1The evidence for deep time
| Site | Where | What was found | What it is evidence of |
|---|---|---|---|
| Madjedbebe | A rock shelter in Arnhem Land, Northern Territory, on Mirarr Country | Stone tools, ground ochre and some of the world's oldest ground-edge axe heads, in layers dated to at least 65 000 years | People were living in northern Australia at least 65 000 years ago — the oldest firm date on the continent so far |
| Lake Mungo | The dry Willandra Lakes, south-west New South Wales | The remains of Mungo Lady and Mungo Man, buried about 40 000 years ago — Mungo Lady is the world's oldest known cremation | Complex beliefs and ceremony around death, deep in the Ice Age |
| Budj Bim | Gunditjmara Country, south-west Victoria | Stone channels, weirs and ponds for trapping and farming eels, about 6 600 years old, beside the remains of stone houses | Permanent settlement and engineered food production — older than the pyramids or Stonehenge |
- The dates come from science — carbon dating for the younger sites, dating the sand grains around the tools at Madjedbebe — which is why they are given as "about" and "at least".
- People arrived by sea, during the Ice Age, when lower sea levels joined Australia to New Guinea and shrank the water gaps from South-East Asia. It still needed boats: the crossing was never dry land.
- These are not the only sources. Aboriginal and Torres Strait Islander peoples' own oral histories record events like the rising of the seas at the end of the Ice Age — stories that match what geologists have found.
2.2Country, Songlines and oral history
- Country, with a capital C, is more than land. It is the land, waters and sky of a particular people, with all its plants, animals, stories and ancestors — something people belong to and are responsible for, rather than something they own. There are hundreds of different Countries, languages and nations across the continent, which is why we say Aboriginal and Torres Strait Islander peoples, plural.
- Songlines are routes across Country recorded in songs, dances and stories. Sung in order, they carry directions to water and food, the law of the land, and the story of how the ancestors made it. Some cross the whole continent, passing from one language group to the next.
- Oral history is knowledge passed on by speaking, singing and showing, generation to generation, with strict rules about who may tell what. It is a primary source in its own right, and it has proved accurate over thousands of years.
2.3Technology and managing the land
| Technology | How it worked |
|---|---|
| Fish and eel traps | At Budj Bim, channels and stone weirs guided eels into ponds and woven baskets, so they could be held live and harvested all year. Stone fish traps on rivers and coasts elsewhere used the tide the same way. |
| Boomerangs | Curved throwing sticks. The returning kind is the famous one, but most were heavier hunting and fighting boomerangs that flew straight; the oldest found is about 10 000 years old. |
| Grinding stones | Flat stones for grinding seeds into flour, which was baked into bread — some of the earliest bread-making anywhere. Ground-edge axes, sharpened on stone, are among the world's oldest. |
| Cultural burning | Small, cool fires lit deliberately in the right season, clearing old grass so fresh growth drew in kangaroos, keeping paths open and preventing huge bushfires. Sometimes called fire-stick farming. |
Say Aboriginal and Torres Strait Islander peoples (plural: many nations), or name the specific people — the Gunditjmara at Budj Bim, the Mirarr at Madjedbebe. Write about cultures in the present tense where they continue: Songlines are sung today. And say "at least 65 000 years", not "65 000 years" — the evidence gives a minimum, not a start date.
Ancient Egypt: the gift of the Nile
Egypt is desert — except for a green ribbon a few kilometres wide either side of one river. Every year the Nile flooded, left a layer of rich black mud, and went back down. That one fact fed a civilisation for three thousand years, paid for pyramids, and shaped what Egyptians believed happened after death.
3.1The river that made a country
- Each year from about July the Nile rose and spread over the fields: the inundation. When it fell in October it left fresh black silt, so the same fields could be farmed every year without wearing out.
- Farmers planted wheat and barley in the mud, dug channels to carry water further, and harvested in spring. Surplus grain was stored, taxed and used to feed the workers who built temples and tombs.
- The river was also the highway: boats carried stone, grain and people north with the current and south with the wind. Egypt's two halves, Upper (south) and Lower (north), were joined into one kingdom under one ruler in about 3100 BCE.
- The Greek historian Herodotus called Egypt "the gift of the Nile" — and the Egyptians agreed: they called their farmland Kemet, "the Black Land", and the desert beyond it Deshret, "the Red Land".
3.2The social pyramid
3.3Writing: hieroglyphs and the Rosetta Stone
- Hieroglyphs are Egypt's picture-writing: several hundred signs, some standing for sounds and some for whole words, carved on temples and tombs and painted on papyrus, a paper-like sheet made from Nile reeds.
- After Egypt became part of the Roman world the skill of reading them died out, and for about 1 400 years nobody on Earth could read them.
- In 1799 French soldiers near the town of Rosetta found a stone carved with the same decree in three scripts: hieroglyphs, everyday Egyptian, and Greek. Scholars could read the Greek. Using it as a key, Jean-François Champollion cracked the hieroglyphs in 1822 — and Egypt's own words could be read again.
3.4Death, mummies and the afterlife
- The belief. Egyptians thought a person's spirit lived on after death — but needed its body to return to. So the body had to be preserved.
- Mummification. Embalmers removed the internal organs (the heart was left in place, as the seat of thought), dried the body for about 40 days in a natural salt called natron, then wrapped it in linen with protective charms. The whole process took about 70 days.
- The tomb. The mummy was buried with food, furniture, tools and painted walls — everything the spirit would need. For early pharaohs that tomb was a pyramid; the largest, at Giza, was built about 4 500 years ago from more than two million blocks. Later pharaohs were hidden in rock-cut tombs in the Valley of the Kings, where Tutankhamun's was found almost untouched in 1922.
- The judgement. The dead person's heart was weighed against a feather, the symbol of truth. A heart lighter than the feather meant a good life — and entry to a paradise that looked a lot like Egypt in flood season.
Most Egyptians lived in mud-brick houses, ate bread, onions and beer, and wore linen. Children of scribes went to school; most others learned their parents' trade. Women could own property, run businesses and go to court — unusual in the ancient world. Egypt stayed independent, with breaks, for about three thousand years, until it became a Roman province after the death of Cleopatra in 30 BCE.
Ancient Greece and Rome
Greece was never one country: it was hundreds of small city-states that shared a language and gods but ran themselves in wildly different ways. Rome started as one of those small cities and ended up ruling everything from Scotland to Egypt. Between them they invented, or perfected, an astonishing amount of the world you live in.
4.1Athens and Sparta: two ways to run a city
| Athens | Sparta | |
|---|---|---|
| Government | Democracy from about 508 BCE — citizens met in the Assembly and voted on laws and war directly | Two kings, a council of elders, and a small group of officials — ordinary Spartans had little say |
| Who counted | Only free men over 18 born to Athenian parents — not women, foreigners or slaves, who together were most of the population | A small warrior class ruled over the helots, a conquered people forced to farm for them |
| Childhood | Boys of citizens learned reading, music and athletics; girls stayed home | Boys left home at seven for brutal military training; girls also trained hard, to bear strong soldiers |
| Famous for | Philosophy, theatre, the Parthenon, a strong navy and trade across the Aegean Sea | The best army in Greece — and the 300 who held the pass at Thermopylae in 480 BCE |
- The Olympic Games were held every four years at Olympia, in honour of the god Zeus, from 776 BCE (the first recorded games). Wars were paused so athletes from rival cities could travel safely. Winners got a wreath of olive leaves — and hero status back home.
- The Greek legacy: the first plays — tragedy and comedy — performed in open-air theatres; philosophy, with Socrates, Plato and Aristotle asking how to live and think; the first alphabet with vowels, which became the Roman alphabet you are reading now; and the idea that ordinary citizens can govern themselves.
4.2Rome: from republic to empire
- Kingdom, 753–509 BCE. By legend Rome was founded by Romulus in 753 BCE and ruled by kings.
- Republic, 509–27 BCE. The Romans threw out their last king and swore never to have another. Instead, two consuls were elected each year, advised by the Senate of wealthy families. The rich patricians and ordinary plebeians fought for centuries over who got a say. Meanwhile Rome's citizen army conquered Italy, then defeated Carthage, then Greece.
- Civil wars. Success made generals too powerful. Julius Caesar conquered Gaul, marched on Rome, and made himself dictator for life — and was stabbed to death by senators in 44 BCE.
- Empire, 27 BCE – 476 CE. Caesar's heir won the wars that followed and in 27 BCE became Augustus, the first emperor. The republic's titles stayed; the power was now one man's. At its largest the empire ringed the whole Mediterranean, from Britain to Egypt.
4.3Roman engineering and Roman society
| Engineering | What it did |
|---|---|
| Roads | Straight, layered, paved — about 80 000 km of them — so legions and messages could move fast. Many modern European roads still follow them. |
| Aqueducts | Channels sloping gently for tens of kilometres, carrying spring water into cities for fountains, baths and toilets. |
| Concrete | Made with volcanic ash, it set hard even under water — harbours, domes and the Colosseum (opened 80 CE) are still standing because of it. |
- Citizens had rights: to vote (under the republic), to a trial, to own property. Citizenship spread slowly across the empire until, in 212 CE, almost every free person in it was a Roman citizen.
- Slaves had none. Prisoners of war and their children were bought and sold to work farms, mines and households; some were trained as gladiators to fight in the arena. Slaves were a large part of the population, and revolts — the most famous led by Spartacus in 73–71 BCE — were crushed.
- Roman cities had apartment blocks, public baths, markets, theatres and free grain for the poor — and, for the rich, villas with heated floors.
4.4Why Rome fell — briefly
The Western Roman Empire ended in 476 CE, when a Germanic general removed the last emperor in Rome. Historians point to several causes working together, not one: the empire had grown too big and expensive to defend; invasions by Germanic peoples pushed across the frontiers; a string of weak, short-lived emperors fought each other for the throne; and the empire had been split into western and eastern halves, so the richer East could not, or would not, save the West. The eastern half carried on for another thousand years — which is where Year 8's medieval world begins.
"What did the Greeks and Romans leave us?" Have three concrete examples ready for each. Greece: democracy, theatre, the alphabet (or philosophy, the Olympics). Rome: roads, concrete and aqueducts, the Latin behind half of English (or the calendar, law, citizenship). Then say how each one reaches you today — that is the mark.
Where the water is, and where people want to live.
Four units in two halves. First, water: where it is on Earth, how a river collects it, why some places run short and what Australians do about it. Then liveability: what makes a place a good place to live, how that is measured, and how it can be improved — including by you, with a clipboard and a map.
The mapFour units
- Water as a resource — the world's water, catchments and rivers, groundwater, and how Australians use water.
- Water scarcity and hazards — running short, drought and flood, how water is managed, and what water means on Country.
- Liveability — what makes a place good to live in, how cities are ranked, and how a city, a country town and a remote community compare.
- Improving liveability — planning, green space, transport, what young people want, and a fieldwork project of your own.
Describing where water is and how it moves, explaining why it is scarce in some places and how it is managed — and explaining what makes a place liveable and how liveability can be improved. Every answer needs an Australian example and, when you can, one from another country. Maps and graphs are marked on BOLTSS.
Water as a resource: where it is and how we use it
Earth looks like a water planet from space, and it is — but almost none of that water is the kind you can drink. Geography starts with the question of where the useful water actually is, and who gets to use it.
1.1Where the world's water is
A resource is anything people use to meet a need. Water is the most important one there is: no water, no drinking, no crops, no showers, no factories. The catch is how it is shared out.
1.2The water cycle, the geographer's way
- The Sun heats the sea and the land; water evaporates into the air, cools and condenses into cloud, then falls as precipitation (rain, hail, snow).
- What happens next is the part geographers care about. Rain that lands on the ground either runs off the surface into creeks and rivers, soaks in (infiltration) to become groundwater, or evaporates straight back up — in Australia, most of it evaporates.
- Because the cycle never stops, water is a renewable resource. But it is renewed unevenly: some places get metres of rain a year, some get almost none. Australia is the driest inhabited continent — only Antarctica gets less.
1.3Catchments and rivers
A catchment (also called a river basin) is all the land that drains into the same river. Its edge is the high ground — the ridge line. Rain that lands on one side of the ridge ends up in one river; rain on the other side ends up in another.
| Catchment word | What it means |
|---|---|
| Source | Where a river begins, usually in high ground |
| Tributary | A smaller river or creek that flows into a bigger one |
| Floodplain | The flat land beside a river that it spreads across in a flood |
| Wetland | Land that is wet for most of the year — a natural filter and a home for birds and fish |
| Mouth | Where the river reaches the sea or a lake; an estuary is a mouth where fresh and salt water mix |
| Upstream / downstream | Towards the source / towards the mouth — water and pollution only ever travel downstream |
The Murray–Darling Basin covers about one million square kilometres — roughly 14% of Australia, across Queensland, New South Wales, the ACT, Victoria and South Australia. The Murray is Australia's longest river at about 2,500 km. The basin grows around 40% of Australia's food and supplies drinking water to more than two million people living in it, plus Adelaide at the very end. Because five states share the one river system, every state wants water and the last one in line — South Australia — gets whatever is left. That argument is the reason the Basin Plan exists.
1.4Groundwater: the water you can't see
- Rain that soaks into the ground fills the tiny gaps in sand, gravel and porous rock. A layer of rock that holds water like this is an aquifer, and the water in it is groundwater. People reach it by drilling a bore.
- The Great Artesian Basin lies under about 22% of Australia — most of Queensland and parts of NSW, SA and the NT. It is one of the largest groundwater stores in the world. The water is under pressure, so in many places it rises up a bore by itself (that is what artesian means). Some of it fell as rain thousands of years ago.
- Groundwater is what lets cattle stations, towns and mines exist in the outback. But it refills very slowly — pump it faster than rain replaces it and the level drops for good.
1.5How Australians use water
| Who uses it | Share of Australia's water use | What for |
|---|---|---|
| Farming | The biggest user by far — well over half | Irrigating cotton, rice, fruit, vegetables, pasture for cattle and dairy |
| Households | About one-tenth | Showers, toilets, washing, gardens, drinking and cooking |
| Industry and mining | The rest | Making things, cooling machines, washing minerals |
- An Australian uses roughly 150–200 litres a day at home (approx.). The biggest slices are the shower, the toilet, the washing machine and the garden — drinking and cooking are tiny by comparison.
- Farming uses the most because growing food takes staggering amounts: about a thousand litres of water for a single litre of milk, once you count what the cow eats and drinks (approx.).
Water scarcity and hazards: too little, too much
About two billion people cannot get safe drinking water at home. Meanwhile Australia swings between years when the rivers stop and years when they swallow whole towns. Both problems have the same answer: manage the water you have.
2.1Two kinds of scarcity
- Water scarcity means not having enough clean water for people's needs. It comes in two flavours, and the difference matters in every exam answer.
- Physical scarcity: the water simply isn't there. Deserts, places in a long drought, rivers that run dry every summer. Central Australia and much of the Middle East are physically short of water.
- Economic scarcity: the water exists — there may even be a river nearby — but people can't afford the wells, pipes, pumps and treatment plants to make it safe and bring it home. This is the story across much of sub-Saharan Africa. Economic scarcity is fixed with money and engineering, not rain.
- Around 2 billion people lack safely managed drinking water, and unsafe water is one of the biggest killers of young children in the world. It is a solvable problem — it is being solved, slowly.
2.2Drought and flood in Australia
| Drought | Flood | |
|---|---|---|
| What it is | A long period with much less rain than normal, so rivers, dams and soil dry out | Water covering land that is usually dry — a river bursting its banks, or rain falling faster than drains can cope |
| Big Australian examples | The Millennium Drought, 1997–2009, across south-east Australia; the Murray stopped reaching the sea | Brisbane, January 2011: thousands of homes under water; Lismore, February 2022: the river reached a record 14.4 m |
| Impacts | Failed crops, dead stock, dust storms, towns trucking in water, farming families leaving the land | Drowning, destroyed homes and roads, mud and disease afterwards, months of clean-up |
| Responses | Water restrictions, drought relief for farmers, new dams and desalination plants, drought-tolerant crops | Warnings and evacuations, levees, dams that hold back floodwater, not building on floodplains |
- Why the swings? The Pacific Ocean has a rhythm. In an El Niño year, eastern Australia is usually drier and hotter (drought risk up). In a La Niña year it is usually wetter (flood risk up). The 2011 and 2022 floods both came in strong La Niña years.
- Floods are among Australia's costliest natural hazards — partly because so many of our towns were built on floodplains, right where the river goes when it is full.
2.3Same planet, different taps
| A household in Queensland | A village household in rural Ethiopia | |
|---|---|---|
| Where the water comes from | A tap — piped from a dam, treated so it is safe to drink | A well, spring or river, often a walk of 30 minutes or more each way |
| Who collects it | Nobody — it arrives by itself | Mostly women and girls, carrying 20-litre containers on their heads or backs |
| Is it safe? | Yes — tested every day | Often not; children get sick with diarrhoea from dirty water |
| How much per person, per day | Roughly 150–200 litres | Often under 20 litres — less than one short shower |
| What it costs | A water bill of a few dollars a week | Hours of time every day — hours a girl might otherwise spend at school |
Ethiopia is not short of rain in most of the country — that is economic scarcity. A well with a hand pump, costing a few thousand dollars, can change a whole village's daily life. Australia's problem is usually the opposite: plenty of money, not always enough rain — physical scarcity, managed with engineering.
2.4Managing water in Australia
| Strategy | How it works | Example | The catch |
|---|---|---|---|
| Dams | A wall across a river stores water in a reservoir for dry times; big dams can also hold back floodwater | Wivenhoe Dam supplies Brisbane; Warragamba supplies most of Sydney | Drowns a valley; needs rain to fill; nothing for downstream if it holds too much |
| Desalination | Pushes seawater through fine filters to remove the salt | Perth gets close to half its water from desalination; the Gold Coast plant opened in 2009 | Uses huge amounts of energy, so it is expensive water |
| Recycling | Treats used water so it can be used again on gardens, sports fields and in industry (purple pipes) | Many new suburbs have a purple recycled-water tap outside | People are uneasy about drinking it, even when it is cleaner than river water |
| Water restrictions | Rules that limit water use during drought — sprinklers only on certain days, no hosing driveways | Brisbane's target of 140 litres per person per day in 2008 | Only cuts demand; it can't make more water |
| Rainwater tanks & efficient appliances | Catch roof water for the garden and toilet; use taps, showers and machines with more WELS stars | Tanks are standard on new Queensland homes | Tanks run dry in exactly the droughts you need them for |
2.5Water on Country
For Aboriginal and Torres Strait Islander peoples, water is part of Country — alive, sacred and tied to stories and law. Knowing every waterhole, soak and spring and the rules for using them is what allowed people to live in the desert for tens of thousands of years. At Brewarrina on the Barwon River in NSW, the Ngemba people built stone fish traps — Baiame's Ngunnhu — among the oldest human-made structures on Earth, engineered to harvest fish as the river rose and fell. Today, cultural flows are water set aside for Aboriginal nations to use for cultural, spiritual and economic purposes, so that rivers like the Murray and Darling are managed with the people who have always managed them.
Liveability: what makes a place good to live in
Ask ten people what makes a place great to live and you get ten answers — beach, jobs, family, no traffic. Geographers turn those answers into a checklist, so that any two places on Earth can be compared fairly.
3.1The liveability checklist
Liveability is how good a place is to live in — whether it meets people's needs for a safe, healthy, comfortable life. It is judged on a set of factors, and the trick is remembering that they are a set: a place can be beautiful and still score badly if there is no work and no doctor.
- Liveability is partly personal. A surfer, a farmer and a grandparent with a heart condition do not want the same place. What you value depends on your age, health, job and culture — which is why geographers ask people, not just measure things.
3.2Rankings — and why Australian cities do well
- The best-known ranking is the Global Liveability Index, published every year by the Economist Intelligence Unit. It scores more than 170 cities on five things: stability (safety), healthcare, culture and environment, education and infrastructure (transport, housing, water, power).
- Australian cities are regulars near the top. Melbourne was ranked number one for seven years in a row (2011–2017); Vienna has held the top spot recently; Melbourne, Sydney, Adelaide, Perth and Brisbane usually land in the top twenty.
- Why: they are safe, with good public hospitals and schools, mild climates, clean air, beaches and parks, and stable government. What drags them down: housing costs, traffic, and suburbs that sprawl a long way from jobs.
- A warning about rankings: the index was designed to help companies decide how much extra to pay staff moving to a city. It measures what suits a business traveller. It says nothing about skate parks, sports fields or whether it is safe to ride to school — a 12-year-old's checklist looks different.
3.3Reading a climate graph
Climate is a liveability factor, and geographers show it with a climate graph. Learn the layout and any climate graph in the world becomes readable:
- The months run along the bottom, January to December.
- Bars show average rainfall for each month, in millimetres, read on the right-hand axis.
- A line shows average temperature, in °C, read on the left-hand axis.
- Brisbane's graph: the temperature line peaks in January (average maximum about 29 °C) and dips in July (about 21 °C); the rain bars are tallest in summer (roughly 130–160 mm a month) and shortest in winter (about 30–40 mm). In one sentence: warm, wet summers and mild, dry winters — which is most of why Brisbane scores well on climate.
3.4Three Queensland places, one checklist
| Factor | Brisbane (big city, about 2.5 million) | Warwick (country town, about 15,000) | Aurukun (remote community, Cape York, about 1,200) |
|---|---|---|---|
| Services | Major hospitals, universities, every kind of shop | A small hospital, high schools, main-street shops; specialists mean a trip to Brisbane or Toowoomba | A health clinic and a school to Year 10; a hospital is a flight away |
| Transport | Trains, buses, ferries, motorways — and traffic jams | A car for almost everything; two hours' drive to Brisbane | The road is cut for months in the wet season; light planes and barges bring supplies |
| Jobs | Huge choice, most jobs in Queensland | Farming, food processing, shops, schools; fewer choices | Council, school, clinic, ranger work; many young people leave to find work |
| Environment & climate | Warm, wet summers; river and coast; heat, storms and flooding | Cooler and drier — frosty winters; floods on the Condamine | Tropical: a hot wet season and a dry season; crocodiles, cyclones |
| Community | Diverse but anonymous — easy to know nobody | Everyone knows everyone; strong sports clubs and shows | Wik people on their own Country: language, family, ceremony — a connection no city offers |
| Housing | Among the most expensive in Australia | Far cheaper than Brisbane | Crowded houses; very few new ones built |
No column wins everything. The city wins on services, transport and jobs; the town wins on housing and community; the remote community has a connection to Country and culture the others cannot match — and the hardest liveability problem in Australia, distance from services. Remote Australians live shorter lives on average largely because help is so far away.
Improving liveability: from planning to fieldwork
Places are not fixed. Every park, bus route and bike lane was somebody's decision — and the decisions keep being made. This unit is about how liveability gets improved, and how to gather the evidence that makes a council listen.
4.1Planning a better place
- Urban planning is deciding what goes where: homes here, shops there, a park in between, and how people move about. Councils and state governments do it; residents get a say.
- Green space. Trees and parks cool a suburb by several degrees on a hot day, clean the air, soak up storm water and give people somewhere to meet. Dark roofs and car parks do the opposite — the urban heat island.
- Public transport and paths. Trains, buses, bike lanes and safe footpaths mean people are not stuck in traffic and children can get around without a lift. Brisbane's Cross River Rail and Queensland's 50-cent fares (from 2024) are both liveability projects.
- The 20-minute neighbourhood. Melbourne's plan aims for most daily needs — shops, school, doctor, park, a bus stop — to be within a 20-minute walk or ride of home. Less driving, more chance of bumping into people you know.
- Sustainability. A liveable place stays liveable: rainwater tanks, solar panels, recycling, protecting bushland and creeks, and not building on floodplains.
4.2Liveability through young people's eyes
- When young Australians are surveyed about their suburbs, the same things come up: a safe way to walk or ride to school, sports fields and skate parks, shade and drinking fountains, a library or somewhere to hang out that is free, decent internet, and buses that actually come. Many councils now run youth councils to hear exactly this.
- For remote and regional places, some of the biggest liveability improvements shrink distance rather than cross it: the Royal Flying Doctor Service (flying since 1928), telehealth video appointments with city specialists, and distance education that lets students stay on their family's station or in their community.
4.3Your fieldwork project
Fieldwork is geography done outside: collecting your own evidence about a real place. A good fieldwork project follows the same steps every time.
- Ask a geographic question. Small and answerable: "How could the crossing outside our school be made safer?" beats "Is our suburb good?"
- Plan. Decide what data will answer it, and how: a tally count of cars per five minutes, a survey of 20 students, photos, observation of shade and seats, a sketch map.
- Collect the data in the field — same place, same method, written down straight away.
- Record it: tables, an annotated photo, and a map.
- Analyse: graph it, compare it, look for the pattern. "Cars peaked at 8:25 — 47 in five minutes."
- Conclude and propose an improvement that matches a liveability factor — then say who you would send it to.
4.4Map skills: BOLTSS and grid references
Every map you draw or read is checked against BOLTSS. Miss one and you lose a mark; miss the legend and nobody can read the map at all.
| Letter | Stands for | What it does |
|---|---|---|
| B | Border | A frame showing where the map ends |
| O | Orientation | A north arrow, so you know which way is which |
| L | Legend (key) | Explains every symbol and colour on the map |
| T | Title | Says what the map shows, and where |
| S | Scale | Shows how a distance on the map matches real distance |
| S | Source | Where the information came from, and when |
- Grid references pin a location on a gridded map. Read the easting first (the numbers along the bottom, going across), then the northing (the numbers up the side). The memory trick: along the corridor, then up the stairs. A four-figure reference such as 2437 names the square whose bottom-left corner is at easting 24, northing 37.
- On a fieldwork sketch map, a scale can be as simple as "one pace = 1 metre" — as long as it is written on the map.
Name the place, name the factor that is weak, propose a specific strategy, and say who it helps. "Warwick's transport score is low because there is no bus to Toowoomba; a twice-daily bus would give students and older people access to specialists and TAFE without needing a car." Four parts, four marks.
Somebody designed your pencil case.
The zip, the shape, the fabric, the price — every one of those was a decision. Four units take you from "what is a designer, anyway?" to a finished object you made, tested and improved yourself.
The mapFour units
- What designers do — needs and wants, the design brief, the four-step loop, and famous everyday designs.
- Sketching ideas — thumbnails, annotated sketches, 2D and 3D drawing, shading, and dimensions in millimetres.
- Materials & tools — timber, plastics, metals, card and fabric; picking by property; hand tools used safely.
- Make, test, improve — a real project from brief to test plan, with a criteria table and an honest "what I would change".
Whether you can read a brief, sketch more than one idea, choose materials for a reason, make safely, and then test your product against the brief and say clearly what worked and what you would change. A wobbly product with an honest evaluation scores better than a perfect one with "it was good".
What designers do
A designer is someone who notices a problem, works out exactly who has it, and makes a thing that solves it. Not magic — a method. This unit is the method.
1.1Needs and wants
- A need is something the design must have to do its job. A drink bottle needs to hold liquid without leaking. No leak-proof lid, no drink bottle — just a wet bag.
- A want is something that would be nice but the design still works without it. Your favourite colour, a sticker, a name printed on the side.
- Designers sort needs from wants before they start, because needs are non-negotiable and wants are where you make trade-offs when time or money runs short.
| Product | Needs (must have) | Wants (nice to have) |
|---|---|---|
| School drink bottle | Holds 600 mL, doesn't leak in a bag, fits a bag pocket | Favourite colour, a carry loop, a name label |
| Phone stand for a desk | Holds the phone upright, doesn't tip, phone can't slide off | Matching the desk, a slot for the charging cable |
| Bike light | Bright enough to be seen, clips on securely, survives rain | Flashing modes, USB charging, a fancy shape |
1.2The design brief: who, what, limits
- A design brief is the job written down in a few sentences. Every brief answers three questions: who is it for, what must it do, and what are the limits.
- The limits are called constraints: how much money, how much time, which materials you are allowed, how big it can be. Example brief: "Design a stand that holds a phone upright on a desk for a Year 7 student, made only from card and glue, costing under $2, finished in two lessons."
- Read a brief the way a detective reads a clue. "For a grandparent whose hands aren't strong" changes everything: big buttons, no tiny zips, light to lift. Miss the who and you design the wrong thing well.
1.3The four-step loop
- Investigate. Read the brief, look at products that already exist, ask the user what annoys them. Write the needs down.
- Generate. Sketch several ideas — three is the minimum — before picking one. The first idea is rarely the best; you only find that out by drawing a second and a third.
- Produce. Measure, mark, cut, join. Work safely and keep notes on anything you changed from the sketch.
- Evaluate. Test the finished thing against the brief. Then say what you would change — and that becomes the start of the next loop.
1.4Famous designs and the problem each solved
| Design | The problem | The clever bit |
|---|---|---|
| Paper clip (1890s) | Hold papers together without punching holes or damaging them | One bent wire that springs back — no moving parts, reusable, costs almost nothing |
| Zip (1910s) | Fasten clothes and bags fast, without a row of fiddly buttons | Two rows of teeth that a slider locks together in one pull |
| Velcro (1941) | A fastening that a child, or one hand, can open and close again and again | Copied from burrs the inventor found stuck to his dog: tiny hooks catching tiny loops |
| Ring-pull can (1960s) | Open a drink anywhere without carrying a separate opener | A lever built into the lid, using the can's own metal |
| Wheelie bin (1960s–70s) | Move a heavy bin to the kerb without lifting it | Two wheels and a handle turn a lift into a tilt-and-roll |
The marks are not for saying what it looks like. They are for naming the problem it solves, who it solves it for, and the one idea that makes it work. Problem → user → clever bit: three short sentences.
Sketching ideas: thinking on paper
You do not need to draw well. You need to draw fast, draw lots, and write on the drawing so that someone else could build it. This unit is the difference between a doodle and a design.
2.1Thumbnails, then annotation
- A thumbnail is a small, quick sketch — a minute each, six to a page. The point is not to finish any of them; it is to get many different ideas down so you can compare them. Wobbly lines are fine. Blank pages are not.
- Pick the strongest thumbnail and turn it into an annotated sketch: a bigger drawing with notes and arrows saying what each part is made of, how big it is, and how it works. The notes carry the thinking; the drawing just shows where things go.
- The test of a good annotated sketch: could a classmate build it from the page alone, without asking you a single question?
2.22D and 3D: flat views and isometric
- A 2D drawing shows one flat view: the front, the side or the top. Flat views are the easiest place to write dimensions, which is why makers use them.
- A 3D drawing shows three faces at once, so the viewer sees the shape. The school standard is isometric: vertical edges drawn straight up, and the other edges sloping at 30° to the horizontal, all at true length.
- Oblique is the quick alternative: draw the front face flat and true, then push the side edges back at 45°. Easier, less realistic.
2.3Shading and dimensions
- Rendering means adding shade so a drawing looks solid. Decide where the light comes from, keep the face nearest the light lightest, the face away from it darkest, and the top in between. Three tones are enough.
- Texture tells the viewer the material: short parallel strokes for timber grain, a few dots for card, a clean highlight streak for shiny plastic or metal.
- Dimensions are the sizes written on the drawing. In Design Technology they are always in millimetres — no units written, no decimals to worry about: 100, not 10 cm. Draw a thin dimension line with an arrowhead at each end and write the number above the middle of it.
- One page should tell the whole story: the brief in a sentence, thumbnails, the annotated sketch of the chosen idea, a flat view with dimensions, and a materials list. That is communicating a design.
Multiply by 10: 4.5 cm is 45 mm, 12 cm is 120 mm. Going back, divide by 10. Rulers in the workshop are marked in mm for a reason — the tiny lines are the ones you use.
Materials & tools: the right stuff, used safely
Card, pine, acrylic, aluminium, felt. Each is brilliant at some jobs and hopeless at others. Choosing well means knowing a handful of properties — and then cutting, shaping and joining without anyone getting hurt.
3.1Five families of materials
| Family | Examples | Good at | Watch out for |
|---|---|---|---|
| Timber | pine, balsa, plywood | strong for its weight, easy to cut and sand, warm to touch | splinters, splits along the grain, swells when wet |
| Plastics | acrylic, PVC, polystyrene | waterproof, can be transparent, easy to keep clean | scratches, can crack, edges cut sharp |
| Metals | aluminium, steel | hard, strong, keeps its shape | heavy, hard to cut by hand, steel rusts |
| Card & paper | corrugated card, mounting board | cheap, cuts with a knife, folds, quick to test ideas | goes soft when wet, bends under weight |
| Fabric | cotton, felt, canvas | flexible, soft, folds flat | frays at cut edges, no stiffness of its own |
3.2Choosing by property
- A property is how a material behaves: hard (doesn't scratch or dent easily), flexible (bends and springs back), waterproof (water can't soak in), strong for its weight (carries a load while staying light), transparent (you can see through it).
- Start from the job, not the material. Ask: what must this part survive? A phone-stand back rest must not bend → stiff. A raincoat must keep water out → waterproof. A ruler must survive being dropped → hard and a little flexible.
- Then check the constraints from the brief: is it allowed, can you afford it, can you actually cut it with the tools you have? Aluminium might be the "best" material for a stand and still be the wrong choice in a two-lesson card project.
3.3Hand tools, used safely
| Tool | Job | The rule |
|---|---|---|
| Steel ruler | Measure and mark in mm; guide the knife | Measure twice, cut once — a piece cut short stays short |
| Craft knife + cutting mat | Cut card and thin plastic | Mat under, ruler on, fingers back, light passes, blade retracted after |
| Hand saw | Cut timber to length | Clamp the wood, start the cut slowly with a few backward strokes, let the teeth do the work |
| Sandpaper | Smooth edges, remove splinters | Coarse grit first, fine grit last; sand along the grain |
| Hot glue gun | Join card, timber, plastic quickly | The nozzle and fresh glue burn — never touch either; rest the gun on its stand |
- PPE — personal protective equipment — goes on before the work starts: safety glasses when cutting or sanding, closed shoes always, an apron, hair tied back, sleeves rolled up.
- Carry tools points-down at your side, put them back where they live, and keep the bench clear — most workshop injuries are trips and slips, not blades.
- Blunt, loose or damaged tools are not "still fine": stop and tell the teacher. Report every cut, however small.
Make, test, improve
Here is the whole loop run once, on one small project: a cardboard phone stand. Follow it and you have a template for every project you will ever be set — brief, criteria, make, test, improve, present.
4.1The project, step by step
The brief: "Design a stand that holds a phone upright on a desk for watching videos, for a Year 7 student, made only from card and glue, costing under $2, finished in two lessons."
- Turn the brief into criteria. Before touching card, write what "success" means as things you can test: holds the phone upright; doesn't tip when the desk is nudged; phone can't slide off; card and glue only; under $2; done in two lessons.
- Three thumbnails. A folded wedge, an L-shape with a lip, a slotted two-piece stand. Pick one using the criteria — the wedge folds from a single piece, so it is fastest.
- Annotated sketch with dimensions. Base 100 mm, back rest 130 mm, lip 15 mm, all from 3 mm corrugated card. (Figure 2.1 is exactly this sketch.)
- Make. Measure and mark in mm, cut on the mat along the steel ruler, score the fold lines lightly so the card bends cleanly, fold, and glue the lip.
- Test against every criterion, write down what happened, and say what you would change.
4.2The test plan and the criteria table
- A test plan is written before testing: one test per criterion, saying exactly what you will do and what counts as a pass. "Put the phone on the stand, nudge the desk three times, it must stay up" is a test. "See if it works" is not.
- Record the result honestly in a criteria table: met, partly met, or not met — with the evidence. A tick you didn't earn teaches you nothing; a cross tells you what version 2 fixes.
| Criterion (from the brief) | How I tested it | What happened | Met? |
|---|---|---|---|
| Holds the phone upright | Placed the phone, watched for 10 minutes | Stayed up the whole time | ✓ met |
| Doesn't tip when the desk is nudged | Nudged the desk three times, portrait and landscape | Fine in portrait; wobbled in landscape | △ partly |
| Phone can't slide off | Tilted the desk edge slightly, 5 tries | Lip caught it every time | ✓ met |
| Card and glue only | Checked the materials list | Card, glue — nothing else | ✓ met |
| Costs under $2 | Added up the materials | $1.20 | ✓ met |
| Finished in two lessons | Checked the time | Needed ten minutes of a third lesson | ✗ not met |
4.3"What worked / what I would change" — and presenting it
- What worked: name the criteria you met and why the design met them. "The 15 mm lip stopped the phone sliding in all five tries."
- What I would change: pair every failure with a specific fix. "It wobbled in landscape because the back rest is only 100 mm wide, so I would make it 160 mm wide." Not "make it better".
- "It looks awesome" and "my friend liked it" are opinions. They are allowed in the presentation — they are not evaluation. Evaluation is criterion → test → evidence → verdict.
- Presenting: one page or one minute, in this order — the brief, your thumbnails, the product, the criteria table, and what you would change. Show the sketches you didn't choose too: they prove you generated ideas.
"Criterion 2 was partly met: it wobbled in landscape during the nudge test, so version 2 would have a 160 mm back rest." Criterion, evidence, fix. Write one of those for every row of the table and you cannot lose the evaluation marks.
The machine only knows two things.
Off and on. From those two, a computer stores your photos, plays your games and sends your messages around the planet. Four units open the box: what is inside, how it counts, how it follows instructions, and how you stay in charge of it.
The mapFour units
- Inside a computer — hardware and software, input → process → output → storage, the parts, files and folders, and how a message travels.
- Data as numbers — why binary, counting to 31 with five bits, bits and bytes, and how letters and pictures become numbers.
- Algorithms — exact instructions, sequence, selection and repetition, flowcharts, tracing by hand and spotting bugs.
- First programs & staying safe — events, loops and variables in pseudocode, a guess-the-number game traced line by line, and digital citizenship.
Naming the parts of a digital system and what each does; showing that all data is stored as binary numbers; writing and following algorithms using sequence, selection and repetition; tracing a small program by hand; and explaining how to be safe and respectful online.
Inside a computer
A phone, a laptop, a games console and a smart watch are all the same machine underneath: something comes in, something is worked out, something comes out, and some of it is kept for later.
1.1Hardware and software
- Hardware is every part you could touch: the screen, the keyboard, the chips inside, the cable. If you dropped it, it would make a noise.
- Software is the instructions the hardware follows: apps, games, the web browser, and the operating system underneath them all. You cannot drop software.
- Hardware without software is a very expensive paperweight. Software without hardware is just an idea. A computer is the two working together.
1.2Input, process, output, storage
1.3The parts and what each one does
| Part | What it does | Think of it as… |
|---|---|---|
| CPU (processor) | Carries out the program's instructions, one after another, billions of times a second | the brain — it does the actual working-out |
| RAM (memory) | Fast working space for whatever is open right now; wiped when the power goes off | the desk you spread your work on |
| Storage (SSD, hard drive, USB stick) | Keeps files and programs safe when the power is off | the filing cabinet |
| Screen | Shows the output as pictures and text | the window onto the results |
| Keyboard, mouse, touchscreen | Turn your taps and presses into input | the doors data comes in through |
- The operating system (Windows, macOS, Android, iOS) is the software that starts the computer, runs every other program, draws the windows and buttons, and looks after your files. Apps ask it for things; they never touch the hardware directly.
- A file is one saved item: a photo, a document, a song. Its name ends in an extension that says what kind it is —
.jpgfor a photo,.docxfor a document,.mp3for a song. - A folder is a named container for files — and for other folders.
School → Year 7 → Science → volcano.docxis a path: the route from the top folder down to one file. Good folder names save you from a desktop with 400 files on it.
1.4How a message gets to your friend
- Your phone doesn't beam a message straight to your friend's phone. It sends it to your Wi-Fi router, which passes it to the internet — a giant web of cables and machines that connects networks all over the world.
- Every device on the internet has an address (a number, a bit like a postal address), so the message can be steered to the right place.
- The message goes to a server — a computer in a data centre that never switches off — run by the messaging app. The server holds the message until your friend's phone asks for new messages, then sends it on. That is why a message still arrives when your friend's phone was off when you sent it.
- Long messages, photos and videos are chopped into small pieces for the trip and put back together at the far end. You never see the pieces; you just see the photo.
Device → router → server → device. Add that every device has an address and that the server holds the message until the other phone collects it, and you have full marks. No need for anything more technical in Year 7.
Data as numbers
A computer cannot store a letter, a colour or a sound. It can only store numbers — and only numbers made of 0 and 1. Everything on your screen is a trick played with those two digits.
2.1Why two digits?
- Inside a chip are billions of tiny switches. A switch is either off or on — nothing in between — so the computer writes off as 0 and on as 1. Two states are impossible to mix up; ten would be.
- Counting with only 0 and 1 is called binary. Our normal counting with ten digits is decimal. They are the same numbers wearing different clothes: binary 101 and decimal 5 are the same amount.
- One 0-or-1 is a bit. Eight bits together make a byte. A byte is the usual parcel size for data: one letter of text takes one byte.
2.2Counting in binary with five bits
In decimal, the columns are worth 1, 10, 100 — each ten times the last. In binary, each column is worth double the last: 1, 2, 4, 8, 16. To read a binary number, add up the columns that hold a 1 and ignore the ones that hold a 0.
| Decimal | 16 | 8 | 4 | 2 | 1 | Binary |
|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 1 | 00001 |
| 2 | 0 | 0 | 0 | 1 | 0 | 00010 |
| 3 | 0 | 0 | 0 | 1 | 1 | 00011 |
| 7 | 0 | 0 | 1 | 1 | 1 | 00111 |
| 10 | 0 | 1 | 0 | 1 | 0 | 01010 |
| 19 | 1 | 0 | 0 | 1 | 1 | 10011 |
| 31 | 1 | 1 | 1 | 1 | 1 | 11111 |
To write 19 in binary: does 16 fit into 19? Yes — write 1, and 3 is left. Does 8 fit into 3? No — 0. Does 4? No — 0. Does 2? Yes — 1, and 1 is left. Does 1? Yes — 1. Answer: 10011. Always check by adding back: 16 + 2 + 1 = 19.
2.3Letters and pictures are numbers too
- Text: every letter, digit and symbol has an agreed code number, listed in the ASCII table. Capital H is 72, capital I is 73, so "HI" is stored as 72, 73 — each one a byte of binary. Lowercase letters have their own numbers (a is 97), which is why passwords care about capitals.
- Pictures: a digital image is a grid of tiny squares called pixels. In the simplest kind, a bitmap in black and white, each pixel is just one bit: 1 for black, 0 for white. The picture is the list of bits, row by row.
- More pixels means a sharper picture and a bigger file. Colour pictures need more bits per pixel to say which colour — that is the Year 8 story.
Algorithms: instructions a machine can follow
Tell a friend "make a sandwich" and they manage. Tell a computer and nothing happens, because it doesn't know what "make" means, or "sandwich", or where the bread is. An algorithm is the instructions written so exactly that nothing is left to guess.
3.1Precise steps, in order
- An algorithm is a list of exact steps, in order, that solves a problem. A recipe, the instructions for a board game, and the way you sharpen a pencil are all algorithms — if they are precise enough.
- The test: could someone who has never done it follow your steps without asking a question? "Add some flour" fails the test. "Add 200 g of flour" passes.
- Order matters. "Spread the butter, then put the bread in the toaster" is the same four words as the right version, in the wrong order, and it ruins the toaster.
3.2The three building blocks
- Sequence — steps one after another. Put on socks, then shoes, then tie the laces.
- Selection — a choice made by asking a yes/no question. IF homework is finished THEN play ELSE keep working.
- Repetition — doing steps again. REPEAT 10 star jumps. Keep asking UNTIL the user types yes.
Every program ever written — games, maps, the app that took your photo — is built from just those three patterns, stacked and nested. Learn to spot them and code stops looking like a foreign language.
3.3Flowcharts: the shapes and what they mean
3.4Tracing by hand, and spotting a bug
To trace an algorithm, be the computer: follow it one step at a time and write down what changes. Here is Figure 3.1 as a trace table. Read ← as "becomes".
| Step | What happens | count is now | Said out loud |
|---|---|---|---|
| count ← 1 | the box called count gets 1 | 1 | — |
| Say count | output | 1 | 1 |
| count ← count + 1 | 1 + 1 | 2 | — |
| count > 3? | 2 > 3? No — loop back | 2 | — |
| Say count | output | 2 | 2 |
| count ← count + 1 | 2 + 1 | 3 | — |
| count > 3? | 3 > 3? No — loop back | 3 | — |
| Say count | output | 3 | 3 |
| count ← count + 1 | 3 + 1 | 4 | — |
| count > 3? | 4 > 3? Yes — End | 4 | — |
- A bug is a mistake in the steps. The computer does not notice — it follows the wrong step perfectly. The trace table finds it: the first row where the value is not what you expected is where the bug lives.
- Classic Year 7 bugs: steps in the wrong order (butter before toast), a question that asks the wrong thing (> when you meant <), and a loop with nothing inside it that changes the count — so it never ends.
Your first programs — and staying safe
A program is an algorithm written in a language the computer accepts. Block coding like Scratch snaps the pieces together for you; here we write the same ideas as plain pseudocode, so you can see exactly what each block means.
4.1Events, loops and variables
| Block idea | In Scratch it looks like | In pseudocode | What it means |
|---|---|---|---|
| Event | "when green flag clicked", "when space key pressed" | WHEN space is pressed | Something happens, so the script starts |
| Loop | "repeat 10", "forever" | REPEAT 10 TIMES … END REPEAT | Do the steps inside again and again |
| Variable | "set score to 0", "change score by 1" | score ← 0, then score ← score + 1 | A named box that holds a value the program can change |
| Selection | "if … then … else" | IF guess < secret THEN … ELSE … | Choose one of two paths |
- A variable is a named box in the computer's memory. score ← 0 puts 0 in the box; score ← score + 1 takes what is in the box, adds 1, and puts the answer back. The arrow means "becomes".
- An event is the trigger: a click, a key press, a sprite being touched. Nothing in an event script runs until the event happens.
4.2Guess the number, traced line by line
| Line | Pseudocode |
|---|---|
| 1 | secret ← 7 |
| 2 | tries ← 0 |
| 3 | REPEAT |
| 4 | INPUT guess |
| 5 | tries ← tries + 1 |
| 6 | IF guess < secret THEN PRINT "too low" |
| 7 | ELSE IF guess > secret THEN PRINT "too high" |
| 8 | END IF |
| 9 | UNTIL guess = secret |
| 10 | PRINT "You got it in", tries, "tries" |
The player guesses 5, then 9, then 7. Trace it:
| Go round | guess | tries | Line 6/7 says | Line 9: guess = 7? |
|---|---|---|---|---|
| 1st | 5 | 1 | 5 < 7 → too low | No — go round again |
| 2nd | 9 | 2 | 9 > 7 → too high | No — go round again |
| 3rd | 7 | 3 | neither — nothing printed | Yes — leave the loop |
| Line 10 prints: You got it in 3 tries | ||||
- Testing means running the program with inputs you already know the answer for, and checking it does what you expected. Test the easy case (a right guess first go), the loop case (wrong, wrong, right), and a silly input (a letter instead of a number). A program that survives all three has earned some trust.
- If a test fails, trace it — the first line where your table disagrees with the program is where the bug is.
4.3Staying safe and being decent online
- Passwords. Long beats clever: three or four random words is stronger than "P@ss1" and easier to remember. Different for every account, and told to nobody — not your best friend, not someone who says they are from the game's support team.
- Privacy. Keep private: your full name with your school, your address, your phone number, your date of birth, your passwords, and photos that show your school uniform or street. These are exactly the details a stranger needs to pretend they know you. Fine to share: your opinion of a movie, your favourite colour, that you like a game.
- Being kind. Whatever you post can be screenshotted and kept forever, by anyone. Before you send, THINK: is it True, Helpful, Inspiring, Necessary, Kind? Would you say it to their face with a teacher standing there?
- When something feels wrong — a stranger asking questions, a message that scares you, someone being nasty — don't reply, keep the evidence, and tell a trusted adult. That is not telling tales; it is what the adults are for.
Could this detail help a stranger find me or pretend to know me? School name, address, phone number, birthday, photos with locations: yes, so keep them private. Favourite colour, opinion of a film: no, so share away.
Everyone eats. Not everyone can cook.
Four units take you from your first day in a school kitchen to designing a snack of your own: staying safe, knowing what a balanced plate looks like, following a recipe without panic, and knowing where the food on your fork actually came from.
The mapFour units
- Safe in the kitchen — hygiene, holding a knife, hot things, the danger zone and colour-coded boards.
- Food groups and a balanced plate — the five food groups, sometimes foods, reading a label, and water.
- Reading and following a recipe — the parts of a recipe, measuring, the basic techniques, and getting the timing right.
- Where food comes from — paddock to plate, eating with the seasons, food waste, and your first design brief.
Working safely and hygienically comes first, every lesson. Then: naming the five food groups and using them to judge a meal, following a recipe accurately (measuring, techniques, timing), and being able to plan a simple food product for a purpose and say honestly how it turned out.
Safe in the kitchen: the habits that keep everyone well
A kitchen has sharp things, hot things and invisible things that can make people sick. None of them are a problem if you build a few habits so deep you do them without thinking. This unit is those habits.
1.1Hygiene: you are the biggest risk in the room
- Wash your hands with soap and warm water for 20 seconds — before you start, after touching raw meat or eggs, after the toilet, and after touching your face, hair or phone. Dry them on a clean towel or paper, not your clothes.
- Tie long hair back, put on a clean apron, take off watches and rings, and roll up sleeves. Hair and jewellery carry germs and end up in the food.
- Cover any cut with a blue bandaid — blue because no food is blue, so it is easy to spot if it falls off.
- Don't cook for other people when you are sick with a cold, a cough or an upset stomach. Tell the teacher.
- Never taste with a spoon and put it back in the pot. Use a clean spoon each time.
1.2Holding a knife
- Carry a knife point down, by your side, and tell people you are coming through. Never run with one, never wave one about, never try to catch one that is falling — step back and let it drop.
- Never leave a knife in a sink of soapy water where someone will reach in and find it. Wash it straight away, blade pointing away from you, and put it back in the block.
- Cut away from your body, on a board that can't slip, with your eyes on the blade. A blunt knife is more dangerous than a sharp one, because you push harder and it slips.
1.3Hot things
- Turn pot handles in, away from the edge of the stove, so nobody catches one and tips boiling water on themselves.
- Lift a lid away from your face — steam burns worse than boiling water. Use dry oven mitts, never a tea towel: a wet cloth conducts heat straight through to your hand.
- Hot oil and water do not mix. If oil in a pan catches fire, never pour water on it — turn off the heat and smother the flames with a lid or a fire blanket. Tell the teacher immediately.
- Burn first aid: cool running water for 20 minutes. Not ice, not butter, not toothpaste. Then tell someone.
1.4The danger zone
Food-poisoning bacteria are already on most raw food. Whether they become a problem depends on temperature: cold slows them down, cooking kills them, and everything in between is where they multiply.
1.5Keeping germs where they are
- Cross-contamination is germs travelling from one food to another — usually from raw meat, chicken or eggs to something that will be eaten without cooking, like salad or bread. The knife, the board, the tea towel and your hands are the usual taxis.
- School and restaurant kitchens stop it with colour-coded chopping boards: one colour per kind of food, so raw chicken and salad never share a board.
| Board colour | Used for |
|---|---|
| Red | Raw meat |
| Blue | Raw fish and seafood |
| Green | Fruit, salad and vegetables |
| Yellow | Cooked meat |
| White | Bread and dairy |
- In the fridge, raw meat goes on the bottom shelf in a covered container so it cannot drip on anything below.
- At the end of a lesson: clean the bench (hot soapy water removes the food and grease), then sanitise it (a spray that kills the germs left behind). Cleaning first — sanitiser can't get through grease.
"Why does the school kitchen use a red board for raw chicken and a green one for salad?" The full answer has three links: raw chicken carries bacteria → a shared board would move them onto the salad → salad is eaten raw, so nothing ever kills them. Separate boards break the chain at the second link.
Food groups and a balanced plate
"Eat healthy" is useless advice until someone tells you what that looks like on an actual plate. Australia has an official picture of it, and once you know the five groups you can judge any meal — including the one in front of you right now.
2.1The five food groups
The Australian Guide to Healthy Eating draws a plate cut into five slices. Each slice is a food group, and the size of the slice shows how much of your daily food should come from it.
| Food group | Everyday examples | Why your body wants it |
|---|---|---|
| Vegetables and legumes | pumpkin, spinach, corn, capsicum, lentils | vitamins, minerals and fibre; hardly any is too much |
| Grain foods | wholemeal bread, rice, pasta, porridge oats, Weet-Bix | slow-burning energy to get you through the day |
| Lean meat, fish, eggs, tofu, nuts and beans | chicken, tuna, eggs, tofu, baked beans | protein for growing and repairing muscle, skin and blood; iron |
| Milk, yoghurt, cheese and alternatives | milk, yoghurt, cheese, calcium-added soy milk | calcium for bones and teeth — teenagers are building bone right now |
| Fruit | mango, strawberries, apples, bananas | vitamins, fibre, and a sweet that comes with the good stuff attached |
- A quick test for any meal: how many groups are on the plate? Chicken, rice and steamed broccoli scores three. A bowl of chips scores none — potato chips are deep-fried, so they count as a sometimes food, not a vegetable.
2.2Reading a food label
- Every packet has a nutrition information panel. Use the per 100 g column to compare two products — it is the same ruler for both, no matter how big the packet's "serve" is.
- Sugar: about 4 grams is one teaspoon. A cereal with 24 g of sugar per 100 g is nearly a quarter sugar — six teaspoons in every 100 g. Under about 15 g per 100 g is a better choice.
- Salt appears on the label as sodium. Under 400 mg per 100 g is a good choice; under 120 mg is low.
- The ingredients list runs from the largest ingredient to the smallest. If sugar is first, the product is mostly sugar — whatever the front of the packet says.
2.3Water, and the drinks that aren't
- Your body is about 60% water, and you lose it all day in sweat, breath and the toilet. Water is the everyday drink — roughly 6 to 8 glasses a day, more in the heat or after sport.
- A 375 mL can of soft drink holds about 10 teaspoons of sugar (around 40 g). Juice is not much better, because the fibre of the fruit is gone. Sports drinks are soft drinks with salt — for a two-hour match, not a maths lesson.
Reading and following a recipe
A recipe is a set of instructions written by someone who has already made the mistakes for you. Read it the right way, measure properly, and know what the words mean — and the dish comes out the way the photo promised.
3.1The parts of a recipe
| Part | What it tells you | Read it for… |
|---|---|---|
| Title | What you are making | whether it is actually what you want |
| Serves | How many people it feeds | whether you need to double or halve it |
| Prep time and cook time | How long the chopping takes, and how long the cooking takes | when you must start |
| Ingredients | Every item and exactly how much, usually in the order you use them | your shopping list, and your mise en place |
| Equipment | The bowls, pans, tray and tools you'll need | getting everything out before you start |
| Method | The numbered steps — what to do, in order | surprises like "chill for one hour" hiding in step 6 |
- Read the whole recipe before you touch anything. Then do your mise en place ("meez on plass") — French for everything in its place: ingredients out and measured, vegetables chopped, oven on, pans ready. Cooking then becomes just assembling.
3.2Measuring
| Measure | Short form | Australian standard |
|---|---|---|
| Teaspoon | tsp | 5 mL |
| Tablespoon | tbsp | 20 mL (most other countries use 15 mL — check whose recipe it is) |
| Cup | cup | 250 mL |
| Grams and kilograms | g, kg | weighed on scales; 1 kg = 1000 g |
| Millilitres and litres | mL, L | measured in a jug; 1 L = 1000 mL |
- Dry ingredients: fill the cup or spoon, then level it off with the back of a knife. "Heaped" is only right if the recipe says heaped.
- Liquids: put the jug on the bench and read it at eye level. Looking down at it, you will always pour too much.
- Baking is the strict one — a cake is a chemistry experiment, and a quarter cup of extra flour is a brick. Soups and stir-fries forgive; cakes don't.
3.3What the words mean
| Technique | What you actually do |
|---|---|
| Slice | Cut into flat, even pieces — a tomato for a sandwich |
| Dice | Cut into small, even cubes — an onion for a sauce |
| Grate | Rub against a grater to make fine shreds — cheese, carrot |
| Mix / stir | Combine ingredients with a spoon until even |
| Whisk | Beat fast with a whisk to blend, or to get air in — eggs, pancake batter |
| Boil | Cook in water at 100 °C, big rolling bubbles — pasta |
| Simmer | Cook gently just below boiling, small bubbles — a sauce or soup |
| Bake | Cook in the dry heat of the oven — muffins, a tray of vegetables |
| Fry | Cook in a little hot oil in a pan — an egg, stir-fry vegetables |
- Even pieces matter more than pretty pieces: a big chunk and a small chunk in the same pan means one is raw when the other is burnt.
3.4Ovens and timing
- "Preheat the oven to 180 °C" means turn it on before you start, so it is already hot when the food goes in. An oven takes 10–15 minutes to heat up.
- Oven temperatures: slow about 150 °C, moderate about 180 °C, hot 200–220 °C. A fan-forced oven cooks hotter, so set it about 20 °C lower than the recipe says.
- Work backwards from serving time. Dinner at 6:00 pm and a recipe that takes 45 minutes means you start at 5:15 pm — and earlier if the oven needs preheating.
- Use a timer. Every time. Nobody remembers when the muffins went in.
Where food comes from
A banana in a Brisbane lunchbox was hanging on a tree in Far North Queensland a week or two ago. Everything you eat has a journey, and every step of it costs something — which is why the food you throw away matters more than you think.
4.1Paddock to plate
- Australia grows most of its own food. Queensland grows nearly all the country's bananas and most of its sugar and mangoes; Tasmania is apples and salmon; the Murray–Darling grows the rice, cotton, oranges and much of the vegetables; wheat comes from the dry inland belt across every mainland state.
- The distance food travels from paddock to plate is its food miles. Fewer miles usually means fresher food, less fuel, and a cheaper price.
4.2Eating with the seasons
| Season | In season in Queensland (examples) |
|---|---|
| Summer (Dec–Feb) | mangoes, lychees, watermelon, sweet corn, tomatoes |
| Autumn (Mar–May) | apples, pears, pumpkin, sweet potato, avocados |
| Winter (Jun–Aug) | strawberries (Queensland's season is winter), oranges and mandarins, broccoli, cauliflower |
| Spring (Sep–Nov) | pineapples, bananas (all year), asparagus, peas, zucchini |
- Food in season is picked ripe, close by and in bulk — so it tastes better, costs less and has travelled less. Mangoes in July have come from overseas or a cold store, and the price tag shows it.
4.3Food waste and packaging
- Australia throws away about 7.6 million tonnes of food a year (approx.); households throw away roughly one in five bags of groceries they buy. Every wasted bag wasted the water, fuel, work and money that got it home.
- Cut the waste: plan meals and shop from a list; store food properly (the fridge, sealed containers, older food at the front); use leftovers for tomorrow's lunch; freeze what you can't eat in time; compost the scraps.
- Use by versus best before: a use-by date is about safety — don't eat it after that day. A best-before date is about quality — it is still safe afterwards, just not at its best. Most food thrown out is best-before food that was perfectly fine.
- Packaging keeps food safe and fresh, but most of it is used once. Buy loose fruit instead of the plastic-wrapped tray, refill a water bottle, bring your own bags, and check the Australasian Recycling Label on the packet before you decide which bin.
4.4Your first design brief
Technology subjects are about designing: making something for a purpose, then judging it honestly. In food, the project might be: "Design a healthy snack for a Saturday morning sports team."
- Understand the brief. Who is it for, what is it for, and what are the limits? A sports team is hungry, in a hurry, and eating outdoors.
- Write the criteria for success — the things your snack must do to count as a success: at least two food groups; no nuts (school rule); no cooking on the day; costs under a dollar a serve; survives two hours in an esky.
- Generate ideas — several, quickly. Fruit kebabs. Wholemeal pikelets. Yoghurt cups with berries. Cheese and crackers.
- Choose and plan. Pick the idea that meets the most criteria; write the recipe, the shopping list and the timing.
- Make it — safely and hygienically, following your own plan.
- Evaluate. Test it against every criterion, ask the people it was for, and write down what you would change. "It was nice" is not an evaluation; "the pikelets went soggy in the esky — next time, pack them separately from the fruit" is.
Go back to your criteria, one at a time, and give each a yes or no with a reason. Then add one improvement. Markers are looking for honesty and specifics, not for a snack that scored a perfect ten.
From a whole ecosystem down to one gene, and back out to four billion years.
Units 1 and 2 built the organism. Units 3 and 4 zoom out to populations and ecosystems, then in to the DNA that makes each generation resemble the last, and finally out again to the process that has shaped every species. Four topics, mapped straight onto Units 3 and 4 of the QCAA syllabus — the ones the external examination is written on.
The mapFour topics, two units
- Describing biodiversity (Unit 3, Topic 1) — how to measure diversity so two sites can actually be compared, Simpson's index worked from raw counts, classification and cladistics, and reading a cladogram as a hypothesis about ancestry.
- Ecosystem dynamics (Unit 3, Topic 2) — energy flow and the 10 % rule with real numbers, nutrient cycles at senior level, exponential and logistic population growth, keystone species, succession, and the Great Barrier Reef as the Queensland case study.
- DNA, genes and the continuity of life (Unit 4, Topic 1) — replication, meiosis, gene expression, mutation, the inheritance patterns you must be able to work as ratios and pedigrees, and the biotechnology toolkit.
- Continuity of life on Earth (Unit 4, Topic 2) — the evidence for evolution, natural selection explained as a chain, the four microevolutionary forces, speciation, and mass extinctions.
QCAA Biology is graded on four instruments. IA1, the data test (10 %), rewards the ability to read an unfamiliar table or graph, calculate from it (Simpson's index, percentage change, a Lincoln index) and draw a conclusion the data actually supports. IA2, the student experiment (20 %), rewards a refined research question, a controlled method, and honest evaluation of your own uncertainty. IA3, the research investigation (20 %), rewards finding real evidence for a claim and judging its quality. The external examination (50 %) covers Units 3–4 in two papers: Paper 1 is multiple choice and short response; Paper 2 is short response with extended reasoning. Every drill on this site is written for the exam papers, and the calculation drills double as data-test practice.
Senior Biology rewards a chain of reasoning: name the structure or process, state what it does, and link it to the consequence with "so" or "because". "Coral bleaching reduces biodiversity" is a claim; "warm water makes coral expel its zooxanthellae, so the coral loses its main energy source, so reef fish that depend on live coral decline, so species richness falls" is an answer.
Describing biodiversity
"This forest is more diverse than that one" is not a scientific statement until you can put a number on it and say how you counted. This topic gives you the numbers, then the tree diagrams that show how the species are related.
1.1Three levels, and what a species is
Biodiversity is measured at three levels. Genetic diversity is the variety of alleles within a species; species diversity is the variety of species in an area; ecosystem diversity is the variety of habitats and communities across a region. A question that only says "biodiversity" usually wants species diversity — but say which level you mean.
The biological species concept defines a species as a group of organisms that can interbreed to produce fertile offspring. It works well for living, sexually reproducing organisms and badly for everything else: it cannot be applied to fossils, to bacteria that reproduce asexually, or to populations that never meet. That is why biologists also use a morphological concept (shared physical form) and, increasingly, a phylogenetic concept (the smallest group sharing a common ancestor, judged from DNA). The exam expects you to know the definition and its limits.
1.2Measuring diversity: richness is not enough
Species richness is simply the number of species present. It is easy to count and easy to compare, but it ignores how the individuals are shared out. Two woodlands can each have three bird species and be nothing alike: one with the birds in roughly equal numbers, the other with one species making up 90 % of every sighting. The second is dominated by one species, and a single disease or cold snap could empty it. That second property is species evenness, and a diversity index is a number that combines both.
The QCAA formula is SDI = 1 − Σ n(n − 1) ÷ N(N − 1), where n is the number of individuals of one species and N is the total number of individuals of all species. SDI runs from 0 (one species only) up towards 1 (many species, evenly shared).
Site A: 50 wrens, 30 robins, 20 honeyeaters. N = 100.
Σ n(n−1) = 50×49 + 30×29 + 20×19 = 2450 + 870 + 380 = 3700. N(N−1) = 100×99 = 9900.
SDI = 1 − 3700 ÷ 9900 = 1 − 0.374 = 0.63.
Site B: 90 wrens, 5 robins, 5 honeyeaters. N = 100, so the richness is identical.
Σ n(n−1) = 90×89 + 5×4 + 5×4 = 8010 + 20 + 20 = 8050. SDI = 1 − 8050 ÷ 9900 = 1 − 0.813 = 0.19.
Same three species, same hundred birds — and the index drops from 0.63 to 0.19 because site B is dominated by wrens. That is the sentence a data-test answer needs: "Site A has the higher diversity (0.63 vs 0.19); the richness is the same, so the difference is due to evenness."
Always show Σ n(n−1) and N(N−1) as separate lines before you divide. If you subtract from 1 at the wrong step, or forget to subtract at all, a marker can still give working marks if the lines are there. And quote the index to two decimal places unless told otherwise.
1.3Sampling: how the counts are made
| Method | Used for | What it gives you | Its weakness |
|---|---|---|---|
| Quadrat | Plants and slow or fixed animals | Density (individuals per m²) or percentage cover, from randomly placed frames | Random placement is essential; a few quadrats in a patchy habitat give a wildly wrong mean |
| Transect | Change along a gradient — shore to dune, creek to ridge | How abundance changes with distance, usually with quadrats at intervals along the line | Only samples along the line; it is not a random sample of the whole area |
| Mark–recapture | Mobile animals | A population estimate from the Lincoln index: N = M × n ÷ m | Assumes marks do not affect survival, no births, deaths or migration between samples, and thorough mixing |
| Camera trap / acoustic survey | Shy, nocturnal or rare animals | Presence and relative activity | Gives presence, not a reliable count |
Lincoln index, worked: 40 skinks are caught, marked and released (M = 40). A week later 50 are caught (n = 50), of which 8 carry a mark (m = 8). Estimate N = 40 × 50 ÷ 8 = 250. The logic is a proportion: marked animals are 8 in 50 of the second catch, so the 40 marked animals should be 8 in 50 of the whole population.
1.4Classification and cladistics
Linnaean classification files species into nested ranks — domain, kingdom, phylum, class, order, family, genus, species — and gives each a two-part binomial name (Macropus rufus, genus first, both italic). It is a filing system. Cladistics is a claim about history: it groups organisms by shared derived characteristics, features that arose in a common ancestor and were inherited by all of its descendants, and it draws the result as a cladogram.
A feature shared because it was in the common ancestor of the whole group (a backbone, for these five) is ancestral and tells you nothing about who is closest to whom. Only derived characters build the tree. Similarity that evolved separately — wings in bats and birds, streamlined bodies in dolphins and sharks — is analogous, the product of convergent evolution, and must be excluded. That is why DNA sequences have become the preferred data: they are inherited, they change at a roughly known rate, and a sequence match of thousands of bases is very unlikely to be a coincidence.
Building a tree from DNA follows one rule: fewer differences means a more recent common ancestor. If species X and Y differ at 4 bases in a gene while each differs from Z at 20, X and Y are sister taxa and Z branched off earlier. The principle of parsimony then chooses, among all possible trees, the one that requires the fewest evolutionary changes.
1.5Two ways to spend a life: r and K
| r-selected species | K-selected species | |
|---|---|---|
| Strategy | Many offspring, little or no parental care | Few offspring, heavy investment in each |
| Maturity and lifespan | Reproduce early, die young | Mature late, live long |
| Population size | Booms and crashes, rarely near carrying capacity | Stable, close to carrying capacity K |
| Suits | Unstable or newly opened habitats — the first colonisers after a fire | Stable, crowded habitats where competition decides who survives |
| Examples | Cane toads, locusts, dandelions | Koalas, humpback whales, kauri pines |
The letters come from the population-growth equation in Unit 3, Topic 2: r is the intrinsic growth rate and K the carrying capacity. Most real species sit somewhere between the two extremes; the value of the model is that it predicts which kind of species recovers first after a disturbance, and which is most at risk when one is lost.
Ecosystem dynamics
An ecosystem is energy flowing one way and matter going round in circles, with populations rising and falling in between. Every question in this topic comes back to one of those three ideas — and the Great Barrier Reef is where the exam likes to ask them.
2.1Energy flow and the 10 % rule
Producers capture light and store it as chemical energy; the rate at which they do so is gross primary productivity (GPP). They respire some of it away, and what is left to build tissue is net primary productivity (NPP = GPP − respiration). Only NPP is available to the next trophic level — and of that, only about a tenth ends up as tissue in the consumer.
Efficiency = energy in the higher level ÷ energy in the level below × 100.
Producers in a reef flat fix 8500 kJ m⁻² yr⁻¹ as NPP; the herbivorous fish that graze them store 950 kJ m⁻² yr⁻¹. Efficiency = 950 ÷ 8500 × 100 = 11.2 %. That is close to the 10 % rule of thumb, which is all the rule ever was: real transfers run from about 5 % to 20 %.
2.2Matter goes round: the cycles
| Cycle | Main reservoir | Key processes to name | Human disruption |
|---|---|---|---|
| Carbon | Oceans (dissolved CO₂ and carbonate), then fossil fuels and rock | Photosynthesis takes CO₂ out of the air; respiration, decomposition and combustion return it. Ocean uptake forms carbonic acid | Burning fossil fuels and clearing forests raise atmospheric CO₂, which warms the planet and acidifies the sea — both hit reefs directly |
| Nitrogen | The atmosphere, 78 % N₂ — but plants cannot use it | Nitrogen fixation (bacteria, lightning) makes ammonium; nitrification makes nitrite then nitrate; plants assimilate nitrate; decomposers ammonify dead matter; denitrification returns N₂ to the air | Fertiliser run-off adds nitrate to waterways, causing algal blooms, oxygen depletion and dead zones — the crown-of-thorns starfish outbreaks on the reef are linked to it |
| Water | Oceans | Evaporation, transpiration, condensation, precipitation, run-off and infiltration | Land clearing raises run-off and sediment; irrigation drains rivers before they reach the sea |
You are not expected to know genus names. You are expected to say that nitrogen-fixing bacteria in root nodules and soil convert N₂ to ammonium, that nitrifying bacteria convert ammonium to nitrate, and that denitrifying bacteria in waterlogged soil convert nitrate back to N₂. The three verbs are the marks.
2.3Population growth: exponential and logistic
A population changes by four routes: change = (births + immigration) − (deaths + emigration). When resources are unlimited, the number added each generation is proportional to the number already there, and the population grows exponentially — a J-shaped curve that doubles at a fixed interval. No population does this for long. As it grows, food, space and shelter run short, predators and disease find it, and the growth rate falls until births balance deaths. The result is a logistic, S-shaped curve that levels off at the carrying capacity, K: the maximum population the environment can support indefinitely.
| Phase of the logistic curve | What is happening | Growth rate |
|---|---|---|
| Lag | Few individuals, so few births; colonisers are settling in | Low |
| Exponential (log) | Plenty of resources; each generation adds proportionally more | Highest — the steepest part of the curve |
| Deceleration | Resources tightening, competition and predation rising | Falling |
| Plateau (at K) | Births equal deaths; the population fluctuates around carrying capacity | About zero |
The factors that pull a population back towards K are density-dependent: competition, predation, parasitism and disease all bite harder as the population becomes crowded. Density-independent factors — a cyclone, a flood, a bushfire, a marine heatwave — kill a similar proportion whether the population is large or small, and they are what knock a population off its plateau in the first place.
A dugong population of 500 records 60 births, 20 deaths, 10 arrivals and 5 departures in a year. Change = (60 + 10) − (20 + 5) = 70 − 25 = +45. The new population is 545, and the growth rate is 45 ÷ 500 × 100 = 9 % per year. If the same numbers repeated each year the curve would be exponential; the data test will usually then give you a later year in which deaths have risen, and ask why.
2.4Keystone species and succession
A keystone species has an effect on its community out of all proportion to its abundance: remove it and the community collapses or changes state. Sea otters on the Pacific coast eat urchins; without otters, urchins strip the kelp forest bare. On Australian reefs, large predatory fish and the giant triton snail keep the crown-of-thorns starfish in check, and parrotfish keep algae from smothering coral. The test is not "is it important?" but "does the community reorganise when it is removed?"
Ecological succession is the predictable sequence of communities that replace one another after a disturbance. Primary succession starts on bare rock or new sand with no soil — a lava flow, a retreating glacier, a new dune — and its pioneer species (lichens, mosses, then grasses) must build the soil before anything larger can grow. Secondary succession starts where soil already exists, after fire, flood or clearing, and is much faster. Both end in a climax community in balance with the local climate. As succession proceeds, species richness, biomass and the complexity of food webs all rise, and the early r-selected pioneers give way to K-selected competitors.
2.5The Queensland case: the Great Barrier Reef
Reef-building corals are animals that host photosynthetic algae, zooxanthellae, inside their tissue. The algae supply up to 90 % of the coral's energy and give it its colour; the coral supplies shelter and nutrients. That mutualism only works within a narrow temperature window. When water stays about 1 °C above the normal summer maximum for weeks, the algae produce damaging reactive oxygen and the coral expels them. The coral is now white — bleached — and starving. If the water cools within a few weeks the algae return; if it does not, the coral dies and algae overgrow the skeleton.
| Pressure | Mechanism | Effect on the reef community |
|---|---|---|
| Marine heatwaves (mass bleaching 1998, 2002, 2016, 2017, 2020, 2022, 2024) | Density-independent: the whole reef is hit regardless of coral density | Loss of live coral cover; the fish, crustaceans and molluscs that need live coral decline, so richness and Simpson's index fall; fast-growing branching corals die first, so the reef becomes dominated by fewer, tougher species — lower evenness |
| Ocean acidification | Dissolved CO₂ lowers pH and the carbonate available for skeletons | Slower coral growth and weaker skeletons; recovery after bleaching is slower |
| Nutrient and sediment run-off | Cleared catchments and fertiliser feed algal blooms; sediment blocks light | Algae outcompete coral larvae; more phytoplankton feeds crown-of-thorns larvae, so outbreaks follow wet seasons |
| Crown-of-thorns starfish outbreaks | A native predator of coral whose numbers explode when its own predators are fished and its larvae are well fed | Each starfish eats up to 10 m² of coral a year; outbreaks are the largest single cause of coral loss after bleaching |
The examiners want the chain, not the headline. Warmer water → zooxanthellae expelled → coral loses its energy source → coral dies if heat persists → habitat and food for coral-dependent species disappear → species richness and evenness both fall → the community may shift to an algae-dominated state that is stable and hard to reverse. Then, if asked about management: reduce run-off (local, fast), control starfish (local, ongoing), cut emissions (global, the only fix for the cause).
DNA, genes and the continuity of life
One molecule copies itself, is read to make proteins, is shuffled at meiosis and occasionally miscopied. Everything in this topic — ratios, pedigrees, PCR — is a consequence of those four facts.
3.1DNA structure and semi-conservative replication
DNA is a double helix of two antiparallel strands. Each strand is a chain of nucleotides — a deoxyribose sugar, a phosphate, and one of four bases — joined by a sugar–phosphate backbone. The strands are held together by hydrogen bonds between complementary base pairs: adenine with thymine (two hydrogen bonds), guanine with cytosine (three). Complementarity is the whole point: either strand contains the information to rebuild the other.
3.2The cell cycle and meiosis
The cell cycle is interphase (G₁ growth, S for DNA synthesis, G₂ preparation) followed by division. Mitosis produces two genetically identical diploid cells for growth and repair. Meiosis produces four genetically different haploid gametes, and it is the source of almost all the variation on which natural selection works.
| Stage | What happens | Why it matters for variation |
|---|---|---|
| Prophase I | Homologous chromosomes pair up; non-sister chromatids swap segments at chiasmata | Crossing over makes new combinations of alleles on one chromosome — recombinant chromatids that existed in neither parent |
| Metaphase I | Homologous pairs line up on the equator; which member of each pair faces which pole is random | Independent assortment: with 23 pairs a human can make 2²³ (about 8 million) different gametes from this alone |
| Anaphase I | Homologous chromosomes are pulled apart — the number is halved here | Each daughter cell gets one chromosome from each pair, so the gametes are haploid |
| Meiosis II | Sister chromatids separate, like mitosis, in both cells | Four haploid cells, each genetically unique |
| Fertilisation | Any sperm meets any egg | Random fertilisation multiplies the combinations again: 8 million × 8 million |
3.3Gene expression: transcription and translation
- Transcription (in the nucleus). RNA polymerase binds the promoter, unwinds the gene, and builds a strand of pre-mRNA complementary to the template strand — uracil in place of thymine. In eukaryotes the non-coding introns are cut out and the exons spliced together to make mature mRNA, which leaves through a nuclear pore.
- Translation (at a ribosome). The ribosome reads the mRNA three bases at a time. Each codon is matched by a tRNA carrying the complementary anticodon and one specific amino acid. The ribosome joins the amino acids by peptide bonds, from the start codon AUG to a stop codon (UAA, UAG or UGA).
- Folding. The polypeptide folds into its tertiary structure. Its shape — and so its function — is set by the order of amino acids, which was set by the order of bases. That chain is what "the gene codes for the protein" means.
The code is triplet (three bases per amino acid), degenerate (64 codons for 20 amino acids, so most amino acids have several codons), non-overlapping and universal. Degeneracy is why some base substitutions are silent: change GAA to GAG and you still get glutamic acid. Universality is why a human gene inserted into a bacterium is read correctly — the basis of recombinant insulin.
3.4Mutations
| Type | What changes | Effect on the protein |
|---|---|---|
| Substitution (point mutation) | One base replaced by another | Silent if the new codon gives the same amino acid; missense if it gives a different one (sickle-cell: GAG → GTG swaps glutamic acid for valine); nonsense if it creates a stop codon, truncating the protein |
| Insertion or deletion | One or more bases added or removed | Unless a multiple of three, it causes a frameshift: every codon downstream is misread, so the protein is usually non-functional |
| Chromosomal | Whole segments duplicated, deleted, inverted or moved; or whole chromosomes gained or lost (non-disjunction at meiosis) | Many genes affected at once — trisomy 21 (Down syndrome) is one extra chromosome 21 |
Mutations happen spontaneously through copying errors and are made more frequent by mutagens — UV and ionising radiation, and chemicals such as those in tobacco smoke. Only mutations in gametes (germline) are inherited; a mutation in a skin cell may cause a cancer but dies with the individual. And because mutation is the only source of new alleles, it is the raw material of evolution even though most individual mutations are neutral or harmful.
3.5Inheritance patterns you must be able to work
| Cross | Parents | Offspring ratio | How to see it |
|---|---|---|---|
| Monohybrid, both heterozygous | Aa × Aa | 3 : 1 phenotypes (AA, Aa, Aa, aa — 1 : 2 : 1 genotypes) | A 2 × 2 Punnett square; one in four shows the recessive trait |
| Test cross | A? × aa | All dominant if the parent is AA; 1 : 1 if it is Aa | The way to find an unknown genotype |
| Dihybrid, both heterozygous, genes on different chromosomes | AaBb × AaBb | 9 : 3 : 3 : 1 | Each parent makes four gamete types (AB, Ab, aB, ab); a 4 × 4 square. The ratio only holds because of independent assortment |
| Codominance | IAIB × ii (blood groups) | 1 : 1 group A to group B | Both alleles are fully expressed; AB blood shows both antigens |
| Sex-linked recessive | XBXb (carrier mother) × XBY | Half the sons affected; no daughters affected, half are carriers | Males have one X, so one recessive allele is enough — which is why red–green colour blindness and haemophilia are mostly seen in males |
3.6Biotechnology: the toolkit
| Technique | How it works | What it is for |
|---|---|---|
| PCR (polymerase chain reaction) | Cycles of denaturing at ~95 °C to separate the strands, annealing at ~55 °C so primers bind either side of the target, and extension at ~72 °C as heat-stable Taq polymerase copies it. Each cycle doubles the target: 2n copies after n cycles, so 30 cycles give about a billion | Amplifying a tiny sample — a crime-scene trace, an ancient bone, a viral test swab — into enough DNA to analyse |
| Gel electrophoresis | DNA is cut by restriction enzymes at specific recognition sequences, loaded into a gel, and pulled towards the positive electrode because DNA is negatively charged. Smaller fragments move further. A ladder of known sizes runs alongside | DNA profiling (comparing fragment patterns between individuals), paternity, checking a PCR product |
| Recombinant DNA | The same restriction enzyme cuts a gene and a bacterial plasmid, leaving matching sticky ends; DNA ligase joins them; the plasmid is put into bacteria which then express the gene | Human insulin, growth hormone, and vaccines made in bacteria or yeast |
| DNA sequencing | Reading the base order of a fragment or a whole genome | Building cladograms from sequence differences; diagnosing inherited disease |
Why Taq? Because the 95 °C denaturing step would destroy an ordinary polymerase every cycle; Taq comes from a hot-spring bacterium and survives it. Which way do fragments run? Towards the positive electrode, because the phosphate backbone is negative, and the small ones run furthest because they thread through the gel more easily. "Bigger fragments move further" costs the whole question.
Continuity of life on Earth: evolution
Natural selection is not "survival of the fittest" — it is a chain of four links, and an exam answer that skips one scores like an answer that skips them all. This topic writes the chain out, then follows it from a single population to the whole fossil record.
4.1The evidence for evolution
| Line of evidence | What is observed | What it shows |
|---|---|---|
| Fossil record | Simpler organisms in older rock, transitional forms (Tiktaalik between fish and tetrapods), and absolute dates from radiometric decay | Life has changed over time, in a sequence |
| Comparative anatomy | Homologous structures: the same bones in a human arm, whale flipper and bat wing, doing different jobs. Vestigial structures: the human appendix, hind-limb bones in whales | Common ancestry, with structures modified for new functions |
| Comparative embryology | Vertebrate embryos share gill pouches and a tail early in development | Shared developmental programs inherited from a common ancestor |
| Biogeography | Marsupials dominate Australia; island species resemble the nearest mainland; Darwin's finches | Species evolve where they are, from whatever got there |
| Molecular biology | A universal genetic code; the more similar two species' DNA and proteins, the more recently they diverged (humans and chimpanzees share ~98 % of DNA) | All life is related, and the differences accumulate with time — a molecular clock |
| Direct observation | Antibiotic resistance in bacteria, insecticide resistance in mosquitoes, industrial melanism in peppered moths | Natural selection happening on human timescales |
Homologous structures share an origin and may differ in function (arm, flipper, wing — same bones). Analogous structures share a function but not an origin (a bird's wing and an insect's wing). Homology is evidence of divergent evolution from a common ancestor; analogy is evidence of convergent evolution, where similar environments select similar solutions. Examiners set this distinction every year.
4.2Natural selection as a chain
In biology fitness is reproductive success — the number of fertile offspring an individual leaves relative to others — not strength or health. A trait is only "adaptive" in a particular environment: the dark allele is a liability on pale lichen-covered bark, which is exactly what happened to the peppered moth once air pollution fell.
4.3Microevolution: four ways allele frequencies change
| Mechanism | What happens to allele frequencies | Random or directed? | Example |
|---|---|---|---|
| Mutation | A new allele appears — the only source of new variation | Random | The dark allele in the beetles above |
| Natural selection | Alleles that raise fitness become more common | Directed by the environment | Antibiotic resistance; industrial melanism |
| Gene flow | Migrants bring alleles in or take them out; populations become more alike | Depends on who moves | Pollen blown between two eucalypt stands |
| Genetic drift | Frequencies change by chance from one generation to the next; strongest in small populations, and some alleles are lost altogether | Random | The bottleneck effect: a population crashes and the survivors carry only a subset of the alleles (cheetahs, northern elephant seals). The founder effect: a few colonists start a new population with only the alleles they happened to carry (island populations, the Amish) |
Drift and selection are the pair students confuse. Ask one question: did the allele spread because it helped, or because of luck? If the individuals that survived a cyclone were simply the ones in the right place, that is drift, even if the population is now genetically different. Drift reduces genetic diversity, which is why the small surviving populations of many endangered species are so vulnerable: they have lost the variation on which any future selection could act.
4.4Speciation
A new species has formed when two populations can no longer interbreed to produce fertile offspring — when they are reproductively isolated. The standard route is allopatric speciation:
- A geographic barrier splits one population into two: a river changes course, sea level rises and cuts off an island, a mountain range lifts, rainforest fragments into patches separated by dry woodland.
- Gene flow between the two stops.
- Each population experiences its own selection pressures and its own mutations and drift, so the allele frequencies diverge.
- Over many generations the populations become so different that, if they meet again, they cannot produce fertile offspring. Reproductive isolation is complete.
Sympatric speciation is the rarer case with no barrier: a population splits within the same area, usually because of a shift in habitat or timing — insects that switch to a new host plant and then mate only on it, or plants that double their chromosome number (polyploidy) and can no longer cross with the parent form. The Queensland examples worth knowing are the wet-tropics rainforest fauna, split into separate species by dry corridors during past ice ages, and the Lake Eacham rainbowfish, isolated in a single crater lake.
| Isolating mechanism | Prezygotic or postzygotic? | How it works |
|---|---|---|
| Temporal | Prezygotic | Breeding at different seasons or times of day |
| Behavioural | Prezygotic | Different courtship songs or displays are not recognised |
| Mechanical / gametic | Prezygotic | Incompatible reproductive structures, or sperm that cannot fertilise the egg |
| Hybrid inviability or sterility | Postzygotic | The zygote forms but dies, or grows into a sterile adult — the mule from a horse and a donkey |
4.5Macroevolution and mass extinctions
Microevolution is change within a species; macroevolution is the pattern above species level — the origin of new groups, and their loss. Two patterns recur. Divergent evolution and adaptive radiation: one ancestor gives rise to many species filling different niches, fastest when niches are empty (marsupials across Australia; Darwin's finches on the Galapagos). Convergent evolution: unrelated lineages arrive at similar forms because they face similar pressures (the marsupial and placental moles).
The fossil record shows five mass extinctions, in which a large fraction of species vanished in a geologically short time. The end-Permian (about 252 million years ago), driven by enormous volcanic eruptions in Siberia, removed roughly 90 % of marine species. The end-Cretaceous (66 million years ago), driven by an asteroid impact and volcanism, removed the non-avian dinosaurs. Each one was followed by adaptive radiation into the vacated niches — mammals only diversified once the dinosaurs were gone. Many biologists argue a sixth mass extinction is under way now, driven by habitat loss, invasive species, overharvesting and climate change; the current extinction rate is estimated at 100 to 1000 times the background rate seen in the fossil record.
The link the examiners want you to make: extinction removes genetic diversity within species (drift in small populations), species diversity (lower richness and Simpson's index), and ecosystem function (keystone species lost, food webs simplified). Conserving a species means conserving a population large enough for selection, not drift, to be in charge of its future.
Reactions that go both ways, electrons that go one way, and carbon that goes everywhere.
Units 1–2 built the tools: the mole, bonding, the balanced equation. Units 3–4 use them on the chemistry that runs industry — equilibria you can push, batteries and electrolysis, the whole family of organic compounds, and how a chemist designs a synthesis that is safe, efficient and green. This is the half the external exam is written on.
The mapFour topics, two units
- Chemical equilibrium systems (Unit 3, Topic 1) — reversible reactions and dynamic equilibrium, Kc with a worked calculation, Le Chatelier's principle applied to concentration, pressure and temperature, and acids and bases: Brønsted–Lowry, strong and weak, Ka, pH, titration curves, indicators and buffers.
- Oxidation and reduction (Unit 3, Topic 2) — oxidation numbers, half-equations, galvanic cells and standard electrode potentials, electrolytic cells and electroplating, and corrosion.
- Properties and structure of organic materials (Unit 4, Topic 1) — homologous series and functional groups, IUPAC naming, isomers, physical properties from intermolecular forces, the key reactions, polymers, and reading IR, mass and ¹H NMR spectra.
- Chemical synthesis and design (Unit 4, Topic 2) — reaction pathways, yield and atom economy, green chemistry, an industrial synthesis worked through, and the analytical checks on purity.
IA1 — data test (10%). Short responses to unseen data: calculations from a table, reading a graph, identifying a trend. Rewards accuracy with units and significant figures. IA2 — student experiment (20%). You modify a practical, collect data and write it up: rewards a testable research question, error analysis and a conclusion that goes only as far as the data. IA3 — research investigation (20%). A claim evaluated from published evidence: rewards judging sources and linking evidence to chemistry. External examination (50%). Two papers on Units 3–4: multiple choice and short response, then extended calculations and explanations. Every mark on it is on this page.
Chemical equilibrium systems
Most reactions do not run to completion; they run to a balance, where the forward and reverse reactions are going at the same rate and the concentrations stop changing. Industry lives on tilting that balance — and acids and bases are the equilibrium you meet every day.
1.1Dynamic equilibrium
In a reversible reaction the products can re-form the reactants. In a closed system the forward rate falls as reactants are used up and the reverse rate rises as products build, until the two rates are equal. That is dynamic equilibrium: both reactions still run, nothing stops, but the concentrations stay constant. It is reached from either side, and it says nothing about how much product there is — an equilibrium can lie far to the left, far to the right, or anywhere between.
1.2The equilibrium constant, Kc
For aA + bB ⇌ cC + dD, the equilibrium constant is Kc = [C]c[D]d ÷ [A]a[B]b: products over reactants, each raised to its coefficient, using equilibrium concentrations in mol L⁻¹. Solids and pure liquids are left out (their concentration does not change). Kc depends on temperature only: change the temperature and you get a new constant; change anything else and the system shifts until the same Kc is satisfied again.
From Figure 1.1. N₂O₄ ⇌ 2NO₂. Kc = [NO₂]² ÷ [N₂O₄] = (0.0400)² ÷ 0.0100 = 0.00160 ÷ 0.0100 = 0.160. Small: the equilibrium lies to the left at this temperature.
H₂(g) + I₂(g) ⇌ 2HI(g). At equilibrium [H₂] = 0.200, [I₂] = 0.200, [HI] = 1.60 mol L⁻¹. Kc = (1.60)² ÷ (0.200 × 0.200) = 2.56 ÷ 0.0400 = 64.0. Large: the equilibrium lies to the right. Kc here has no units because the powers cancel; when they do not, the unit is written.
Reading Kc: much greater than 1, mostly products; much less than 1, mostly reactants; near 1, comparable amounts. The reaction quotient Q is the same expression with any concentrations: if Q < Kc the reaction moves right to reach equilibrium; if Q > Kc it moves left.
1.3Le Chatelier's principle
Le Chatelier's principle: if a system at equilibrium is disturbed, it shifts in the direction that partially counteracts the disturbance. It is a prediction tool, not an explanation — the explanation is always rates: the change makes one rate larger than the other until they are equal again.
| Disturbance | Shift | Why, in terms of rates | Effect on Kc |
|---|---|---|---|
| Add a reactant (or remove a product) | Right, to use it up | More reactant collisions raise the forward rate | None |
| Add a product (or remove a reactant) | Left | Reverse rate rises | None |
| Increase pressure (gases) by reducing volume | To the side with fewer moles of gas | All concentrations rise; the side with more particles gains more rate | None |
| Decrease pressure | To the side with more moles of gas | The reverse of the above | None |
| Increase temperature | In the endothermic direction (absorbs the heat) | Both rates rise, the endothermic one by more | Changes: Kc rises for an endothermic forward reaction, falls for an exothermic one |
| Decrease temperature | In the exothermic direction | Both rates fall, the endothermic one by more | Changes, the other way |
| Add a catalyst | No shift | Both rates rise equally; equilibrium is reached sooner, at the same position | None |
| Add an inert gas at constant volume | No shift | Partial pressures of the reacting gases are unchanged | None |
N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH = −92 kJ mol⁻¹. Four moles of gas become two, so high pressure favours ammonia (200 atm in practice). The reaction is exothermic, so low temperature favours ammonia — but too low and the rate is uselessly slow. The compromise is about 450 °C, an iron catalyst to get the rate back, and removing ammonia by liquefying it so the equilibrium keeps shifting right. Every choice is Le Chatelier against rate against cost, and the exam wants all three named.
1.4Acids and bases: Brønsted–Lowry, strong and weak
A Brønsted–Lowry acid is a proton (H⁺) donor; a base is a proton acceptor. Every acid–base reaction is a proton transfer, and it makes a conjugate pair: HCl gives away H⁺ and becomes its conjugate base Cl⁻; water accepts it and becomes its conjugate acid H₃O⁺. Water does both jobs (it is amphiprotic) and even reacts with itself: 2H₂O ⇌ H₃O⁺ + OH⁻, with Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.
| Strong | Weak | |
|---|---|---|
| Acid | Fully ionised in water: HCl, HNO₃, H₂SO₄. Written with a one-way arrow. [H₃O⁺] = the acid concentration | Partly ionised, an equilibrium lying left: CH₃COOH, HF, H₂CO₃. Written with ⇌. [H₃O⁺] is much less than the concentration |
| Base | Fully dissociated: NaOH, KOH. [OH⁻] = the base concentration | Partly protonated: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ |
| Do not confuse with | Concentrated and dilute, which describe how much is dissolved. 0.01 mol L⁻¹ HCl is a dilute strong acid; 5 mol L⁻¹ ethanoic acid is a concentrated weak acid. | |
The acid dissociation constant, Ka = [H₃O⁺][A⁻] ÷ [HA], measures how far a weak acid ionises: the larger Ka, the stronger the acid. Ethanoic acid has Ka = 1.8 × 10⁻⁵; HF, 6.8 × 10⁻⁴, is the stronger of the two. pKa = −log Ka runs the other way: smaller pKa, stronger acid.
1.5pH, worked
Strong acid. 0.0250 mol L⁻¹ HCl: [H₃O⁺] = 0.0250, pH = −log(0.0250) = 1.60.
Strong base. 0.0100 mol L⁻¹ NaOH: [OH⁻] = 0.0100, pOH = 2.00, pH = 14 − 2.00 = 12.00.
Weak acid. 0.100 mol L⁻¹ ethanoic acid, Ka = 1.8 × 10⁻⁵. Because so little ionises, [HA] ≈ 0.100 and [H₃O⁺] = [A⁻] = x: Ka = x² ÷ 0.100, so x = √(1.8 × 10⁻⁵ × 0.100) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³, and pH = 2.87. Compare 0.100 mol L⁻¹ HCl at pH 1.00: the weak acid is nearly two pH units higher at the same concentration.
Dilution. Each tenfold dilution of a strong acid raises the pH by one unit (pH 1 → 2 → 3), until it approaches 7. A weak acid rises by less than one, because dilution also shifts its equilibrium towards more ionisation.
1.6Titration curves, indicators and buffers
25.0 mL of 0.100 mol L⁻¹ NaOH needs 22.4 mL of HCl to reach the end point. n(NaOH) = 0.100 × 0.0250 = 2.50 × 10⁻³ mol. The ratio is 1 : 1, so n(HCl) = 2.50 × 10⁻³ mol in 0.0224 L: c = 2.50 × 10⁻³ ÷ 0.0224 = 0.112 mol L⁻¹ (3 s.f.). Always: moles of the known, ratio, moles of the unknown, then concentration.
A buffer resists pH change when small amounts of acid or base are added. It is a weak acid and its conjugate base together, in similar amounts — ethanoic acid with sodium ethanoate, or carbonic acid with hydrogen carbonate in your blood. Add H⁺ and the conjugate base absorbs it (A⁻ + H⁺ → HA); add OH⁻ and the acid neutralises it (HA + OH⁻ → A⁻ + H₂O). The equilibrium shifts, the pH barely moves. Blood is buffered at 7.4; a shift of 0.4 either way is fatal, which is the point.
Oxidation and reduction
Every battery, every rusting gate and every electroplated tap is the same chemistry: one substance loses electrons, another gains them. Learn to track the electrons and the whole topic — cells, potentials, electrolysis, corrosion — is one idea applied four ways.
2.1Oxidation numbers and half-equations
Oxidation is loss of electrons; reduction is gain (OIL RIG). The substance that is reduced takes the electrons and is the oxidising agent; the one oxidised gives them and is the reducing agent. To see who lost what, assign oxidation numbers:
- Free element: 0. Simple ion: its charge. In compounds: F −1; O −2 (except peroxides, −1); H +1 (except metal hydrides, −1); Group 1 +1, Group 2 +2.
- The numbers in a neutral compound add to 0; in a polyatomic ion, to its charge. So Mn in MnO₄⁻: x + 4(−2) = −1, x = +7. Cr in Cr₂O₇²⁻: 2x − 14 = −2, x = +6. S in H₂SO₄: 2 + x − 8 = 0, x = +6. N in NH₃: x + 3 = 0, x = −3.
- Oxidation number goes up = oxidised; goes down = reduced. In Zn + Cu²⁺ → Zn²⁺ + Cu, Zn goes 0 → +2 (oxidised, the reducing agent) and Cu goes +2 → 0 (reduced; Cu²⁺ is the oxidising agent).
Balance the main atoms, then O with H₂O, then H with H⁺, then charge with e⁻. Permanganate reduced: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O. Iron(II) oxidised: Fe²⁺ → Fe³⁺ + e⁻. Multiply so the electrons cancel (×5 on the iron), add, and cancel anything on both sides: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺. Check: atoms balance and charge balances (+17 each side).
2.2Galvanic cells
The standard electrode potential, E°, of a half-cell is its voltage against the standard hydrogen electrode (0.00 V) at 1 mol L⁻¹, 100 kPa and 25 °C. The table lists reductions: the more positive E°, the more readily the species is reduced (the stronger oxidising agent); the more negative, the more readily the reverse happens (the stronger reducing agent). Cu²⁺/Cu is +0.34 V, Zn²⁺/Zn is −0.76 V, Ag⁺/Ag is +0.80 V.
Zn–Cu: copper has the higher E°, so it is the cathode. E°cell = 0.34 − (−0.76) = +1.10 V. Positive means the reaction is spontaneous as written.
Cu–Ag: silver is the cathode. E°cell = 0.80 − 0.34 = +0.46 V. Copper is now the anode — a metal's role depends on what it is paired with.
A negative E°cell means the reaction will not go on its own; it needs an electrolytic cell. Note that multiplying a half-equation does not multiply its E°.
2.3Electrolytic cells and electroplating
An electrolytic cell is a galvanic cell run backwards: a power supply forces a non-spontaneous reaction. The same rules hold — oxidation at the anode, reduction at the cathode — but now the anode is positive (connected to the supply's positive terminal, which pulls electrons out) and the cathode is negative. In molten NaCl, Na⁺ is reduced to sodium metal at the cathode and Cl⁻ oxidised to chlorine at the anode. In aqueous solution water competes: the species with the most positive reduction potential is reduced at the cathode, the one with the most negative is oxidised at the anode. That is why electrolysing NaCl(aq) gives hydrogen at the cathode, not sodium.
Electroplating uses this to coat one metal with another: the object to be plated is the cathode, the plating metal is the anode (it dissolves to replenish the ions), and the electrolyte contains the plating metal's ions. Silver-plating a spoon: spoon at the cathode (Ag⁺ + e⁻ → Ag), silver bar at the anode (Ag → Ag⁺ + e⁻), in silver nitrate. The mass deposited is proportional to the charge passed.
2.4Corrosion
Rusting is an electrochemical cell on the surface of the iron. At an anodic spot, Fe → Fe²⁺ + 2e⁻; the electrons travel through the metal to a cathodic spot where O₂ + 2H₂O + 4e⁻ → 4OH⁻; the ions meet and form Fe(OH)₂, which oxidises to rust, hydrated iron(III) oxide. It needs oxygen and water together; salt speeds it by making the water a better electrolyte. Protection follows from the cell: barrier (paint, oil, plastic) keeps oxygen and water off; sacrificial protection attaches a metal with a more negative E° — zinc on galvanised steel, magnesium blocks on a ship's hull — which becomes the anode and corrodes instead; cathodic protection connects the structure to the negative terminal of a supply so it cannot lose electrons. Tin plating on a can is a barrier only: scratch it and the iron, more negative than tin, corrodes faster.
Properties and structure of organic materials
Carbon makes four bonds, bonds to itself in chains and rings, and hangs a small set of functional groups off the result. Learn the groups, the naming rules and the intermolecular forces each group brings, and you can predict the properties and reactions of a compound you have never seen.
3.1Homologous series and functional groups
A homologous series is a family with the same functional group and general formula, each member differing by CH₂: the same chemistry, with physical properties that change steadily along the series. The functional group is the atom or group that gives the family its reactions.
| Series | Functional group | General formula | Suffix / prefix | Example | Chemistry |
|---|---|---|---|---|---|
| Alkane | C–C single bonds only | CnH2n+2 | -ane | propane C₃H₈ | Saturated; combustion, substitution with halogens in UV light |
| Alkene | C=C | CnH2n | -ene | propene CH₃CH=CH₂ | Unsaturated; addition reactions; decolourises bromine water |
| Alkyne | C≡C | CnH2n−2 | -yne | ethyne C₂H₂ | Addition, twice |
| Haloalkane | C–X (F, Cl, Br, I) | — | fluoro-, chloro-, bromo-, iodo- | 2-bromopropane | Substitution with OH⁻ to alcohols |
| Alcohol | –OH (hydroxyl) | CnH2n+1OH | -ol | propan-2-ol | Hydrogen bonding; oxidation; esterification; dehydration |
| Aldehyde | –CHO (carbonyl at the end) | — | -al | ethanal | From a primary alcohol; oxidises further to the acid |
| Ketone | C=O inside the chain | — | -one | propanone | From a secondary alcohol; resists further oxidation |
| Carboxylic acid | –COOH | — | -oic acid | ethanoic acid | Weak acid; hydrogen bonding; makes esters |
| Ester | –COO– | — | -yl -oate | ethyl ethanoate | From acid + alcohol; sweet smells; hydrolysis back |
| Amine | –NH₂ | — | -amine | ethanamine | Weak base; hydrogen bonding |
| Amide | –CONH₂ / –CONH– | — | -amide | ethanamide | The peptide link in proteins and nylon |
3.2IUPAC naming and isomers
- Find the longest chain that contains the functional group: that gives the stem (meth-, eth-, prop-, but-, pent-, hex-, hept-, oct-).
- Number from the end that gives the functional group the lowest number; if there is none, the first branch the lowest number.
- Name the substituents as prefixes with their numbers (methyl, ethyl, chloro), in alphabetical order; use di-, tri- for repeats (not counted for the alphabet).
- Write it: numbers separated from letters by hyphens, numbers from numbers by commas. 2-methylbutan-2-ol; 3-methylpent-1-ene; 1,2-dichloroethane.
| Isomer type | What differs | Example | Consequence |
|---|---|---|---|
| Chain (structural) | The carbon skeleton | butane and 2-methylpropane, both C₄H₁₀ | The branched one has a lower boiling point: less surface for dispersion forces |
| Position (structural) | Where the functional group sits | propan-1-ol and propan-2-ol | Different oxidation products: aldehyde vs ketone |
| Functional group (structural) | Which group the atoms make | ethanol and methoxymethane, both C₂H₆O | Completely different chemistry |
| Geometric (cis/trans) | Arrangement about a C=C that cannot rotate, each carbon carrying two different groups | cis- and trans-but-2-ene | Different shapes, so different packing and melting points |
| Optical (enantiomers) | A chiral carbon with four different groups: two mirror images that cannot be superimposed | the two forms of butan-2-ol | Identical physically, except they rotate polarised light oppositely; biology tells them apart |
3.3Properties from intermolecular forces
- Dispersion forces act between all molecules and grow with size: boiling points rise along every homologous series (methane −162 °C, butane −1 °C, octane 126 °C). Branching lowers them.
- Dipole–dipole forces add for polar groups (C=O in ketones and aldehydes, C–X): propanone boils at 56 °C, butane at −1 °C, similar mass.
- Hydrogen bonding (O–H, N–H) adds most: propan-1-ol boils at 97 °C; ethanoic acid at 118 °C, because acids form hydrogen-bonded pairs.
- Solubility in water needs hydrogen bonding with water: small alcohols, acids and amines dissolve; the hydrocarbon tail wins as the chain grows (hexan-1-ol is barely soluble). Alkanes, alkenes and esters do not dissolve.
3.4The reactions
| Reaction | Equation (example) | Conditions | Type |
|---|---|---|---|
| Halogenation of an alkane | CH₄ + Cl₂ → CH₃Cl + HCl | UV light | Substitution (free radical) |
| Bromination of an alkene | CH₂=CH₂ + Br₂ → CH₂BrCH₂Br | Room temperature; orange bromine water goes colourless — the test for C=C | Addition |
| Hydration of an alkene | CH₂=CH₂ + H₂O → CH₃CH₂OH | Steam, phosphoric acid catalyst, 300 °C, 60 atm | Addition — industrial ethanol |
| Hydrogenation | C=C + H₂ → C–C | Nickel catalyst; margarine from oils | Addition |
| Haloalkane to alcohol | CH₃CH₂Br + OH⁻ → CH₃CH₂OH + Br⁻ | Warm aqueous NaOH | Substitution |
| Oxidation of a primary alcohol | CH₃CH₂OH → CH₃CHO → CH₃COOH | Acidified K₂Cr₂O₇ (orange → green) or KMnO₄ (purple → colourless); distil for the aldehyde, reflux for the acid | Oxidation |
| Oxidation of a secondary alcohol | CH₃CH(OH)CH₃ → CH₃COCH₃ | As above; stops at the ketone | Oxidation. A tertiary alcohol does not oxidise |
| Esterification | CH₃COOH + CH₃CH₂OH ⇌ CH₃COOCH₂CH₃ + H₂O | Concentrated H₂SO₄ catalyst, heat | Condensation (water released); reversible |
| Hydrolysis of an ester | Ester + H₂O → acid + alcohol | Dilute acid, or NaOH (saponification, makes soap from fats) | Hydrolysis |
The alcohol gives the first word (-yl), the acid the second (-oate). Ethanoic acid + methanol → methyl ethanoate. Butanoic acid + ethanol → ethyl butanoate. Write the ester so the acid's carbon chain carries the C=O: CH₃COOCH₃ is methyl ethanoate.
3.5Polymers and biomolecules
Addition polymers form when alkene monomers open their C=C and join, nothing lost: ethene → polyethene; propene → polypropene; chloroethene → PVC; tetrafluoroethene → PTFE. The repeat unit is the monomer with the double bond opened. Condensation polymers form when two functional groups react and a small molecule (water) leaves: a diacid with a diol makes a polyester (PET); a diacid with a diamine makes a polyamide (nylon-6,6). Proteins are condensation polymers of amino acids joined by the peptide (amide) link; carbohydrates (starch, cellulose) are condensation polymers of glucose; fats are triesters of glycerol with three fatty acids — saturated fats have no C=C, unsaturated fats have one or more.
3.6Reading spectra
| Technique | What it measures | What it tells you | Key values |
|---|---|---|---|
| Infrared (IR) | Bonds absorbing IR at their vibration frequency | Which functional groups are present | O–H (alcohol) broad 3200–3600 cm⁻¹; O–H (acid) very broad 2500–3300; C=O sharp 1680–1750; C–H 2850–3000; N–H 3300–3500 |
| Mass spectrometry (MS) | Mass-to-charge of the molecular ion and its fragments | The molar mass (the molecular-ion peak, M⁺, furthest right) and pieces of the structure from fragments | Fragment at M−15 = lost CH₃; M−17 = lost OH; M−29 = lost C₂H₅; a chlorine compound shows M and M+2 peaks 3 : 1 |
| ¹H NMR | Hydrogen nuclei in a magnetic field | How many H environments, how many H in each, and what is next door | As Figure 3.1 |
Chemical synthesis and design
Knowing a reaction is not the same as making a tonne of product safely and cheaply. Synthesis asks: which pathway, how many steps, how much do we get, how much do we waste, and what does it cost the people and the planet? Those questions have numbers, and the exam wants them.
4.1Reaction pathways
A reaction pathway links a starting material to a target through the reactions of Unit 4 Topic 1. To make ethyl ethanoate from ethene: ethene → (hydration) → ethanol; ethanol → (oxidation, reflux with acidified dichromate) → ethanoic acid; ethanoic acid + ethanol → (esterification) → ethyl ethanoate. Three steps, and each step has a yield, so the overall yield is their product: 90% × 80% × 70% = 50%. Fewer steps almost always wins, which is why a chemist looks for the shortest pathway first, then for the one with the safest reagents.
4.2Yield and atom economy
Salicylic acid (C₇H₆O₃, M 138.12) + ethanoic anhydride (C₄H₆O₃, M 102.09) → aspirin (C₉H₈O₄, M 180.16) + ethanoic acid (M 60.05). A student starts with 5.00 g of salicylic acid and excess anhydride, and collects 4.85 g of dry aspirin.
Theoretical yield. n(salicylic) = 5.00 ÷ 138.12 = 0.0362 mol. Ratio 1 : 1, so n(aspirin) = 0.0362 mol; m = 0.0362 × 180.16 = 6.52 g.
Percentage yield = 4.85 ÷ 6.52 × 100 = 74.4%. The rest was lost to incomplete reaction, to the recrystallisation, and to the filter paper.
Atom economy = (M of desired product ÷ sum of M of all reactants) × 100 = 180.16 ÷ (138.12 + 102.09) × 100 = 180.16 ÷ 240.21 × 100 = 75.0%. A quarter of the reactant mass leaves as ethanoic acid, by design, before a single practical loss.
Percentage yield measures how well the reaction was run; atom economy measures how well it was designed, and it is fixed by the equation alone. Addition reactions have 100% atom economy (every reactant atom ends up in the product: ethene + water → ethanol). Substitution and elimination reactions are lower, because something leaves. Fermentation of glucose to ethanol, C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂, has an atom economy of 2(46.07) ÷ 180.16 = 51.1% — half the sugar leaves as carbon dioxide — yet it wins on renewability and mild conditions. Atom economy is one criterion among several.
4.3Green chemistry
| Principle | In practice | Example |
|---|---|---|
| Prevent waste | Better not to make it than to treat it | Choose a pathway with fewer by-products |
| Maximise atom economy | Prefer addition to substitution | Ethanol by hydration of ethene (100%) over routes that lose a leaving group |
| Less hazardous synthesis | Avoid toxic reagents and intermediates | Replace phosgene, replace chromium(VI) oxidants with catalytic oxygen |
| Safer solvents | Water, supercritical CO₂, or no solvent at all | Decaffeination with supercritical CO₂ instead of dichloromethane |
| Energy efficiency | Room temperature and pressure where possible | Enzyme catalysis; a catalyst that lets the Haber process run cooler |
| Renewable feedstocks | Biomass instead of oil | Ethanol from sugar cane; bioplastics (PLA) from corn starch |
| Catalysis | Catalytic, not stoichiometric, reagents | A catalyst is used in tiny amounts and recovered; a stoichiometric reagent becomes waste |
| Design for degradation | Products that break down after use | Biodegradable polyesters over polyethene |
4.4An industrial synthesis: ethanol two ways
| Hydration of ethene | Fermentation of glucose | |
|---|---|---|
| Equation | C₂H₄ + H₂O ⇌ C₂H₅OH | C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ |
| Feedstock | Ethene from cracking crude oil — non-renewable | Sugar cane, corn, waste starch — renewable |
| Conditions | 300 °C, 60–70 atm, phosphoric acid catalyst; continuous | 30–40 °C, 1 atm, yeast enzymes, no oxygen; batch |
| Rate and yield | Fast; single-pass conversion low (equilibrium) but unreacted ethene is recycled to ~95% overall | Slow (days); stops at about 15% ethanol because the yeast dies |
| Product | Pure, anhydrous ethanol | Dilute; needs fractional distillation, which costs energy |
| Atom economy | 100% | 51.1% |
| Chosen when | Industrial solvent and chemical feedstock; cheap oil | Fuel ethanol and beverages; a renewable mandate; sugar is cheap |
Not with one criterion. Name the criteria — atom economy, yield, rate, energy, feedstock, safety, product purity, cost — give each a value or a comparison, and then judge. “Hydration has 100% atom economy and gives pure ethanol at high rate, but it depends on crude oil and 300 °C; fermentation is renewable and runs at 35 °C, but wastes half its carbon as CO₂ and needs energy to distil. For fuel ethanol in Queensland, with cane and a renewable target, fermentation is the better fit.” That is the shape of a full-mark answer.
4.5Checking purity
A synthesis is not finished until the product is shown to be the product, pure. Melting point: a pure solid melts sharply at its literature value (aspirin 135 °C); impurities lower it and spread it over a range. Chromatography (TLC or HPLC): a pure sample gives one spot or one peak; the Rf matches a standard. Titration: the amount of acid in the sample against what the mass predicts — an assay. Spectroscopy: IR confirms the functional groups (aspirin's ester C=O at 1750 and acid C=O at 1690 cm⁻¹, and no broad phenol O–H from leftover salicylic acid), MS confirms the molar mass (M⁺ at 180), NMR confirms the structure. Recrystallisation is the purification step that precedes them: dissolve hot in the minimum solvent, cool slowly, filter the crystals, wash cold, dry — the impurities stay in the solution.
From falling apples to the Higgs boson.
Units 3 and 4 take the tools of Year 11 — vectors, forces, energy, fields — and point them at the biggest questions physics has: what holds the planets in orbit, what electricity and magnetism really are, what happens near the speed of light, and what matter is made of. The method has not changed: formula, substitution with units, answer, sanity check.
The mapFour topics, two units
- Gravity and motion (Unit 3, Topic 1) — vectors in two dimensions, projectiles, inclined planes, uniform circular motion, Newton's law of universal gravitation, gravitational fields, orbits and Kepler's third law.
- Electromagnetism (Unit 3, Topic 2) — Coulomb's law and electric fields, charges moving in fields, magnetic fields from currents, F = qvB and F = BIL, electromagnetic induction, transformers and power transmission.
- Special relativity (Unit 4, Topic 1) — Einstein's two postulates, simultaneity, time dilation, length contraction, relativistic momentum, E = mc² and the muon evidence.
- Quantum theory and the Standard Model (Unit 4, Topic 2) — black-body radiation and Planck, the photoelectric effect, wave–particle duality, the Bohr atom, the Standard Model, Feynman diagrams and particle accelerators.
g = 9.8 m s⁻². Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻². Earth: mass 5.97 × 10²⁴ kg, radius 6.37 × 10⁶ m. Coulomb constant k = 8.99 × 10⁹ N m² C⁻². Permeability of free space μ₀ = 4π × 10⁻⁷ T m A⁻¹. Elementary charge e = 1.60 × 10⁻¹⁹ C; electron mass 9.11 × 10⁻³¹ kg; proton mass 1.67 × 10⁻²⁷ kg. Speed of light c = 3.00 × 10⁸ m s⁻¹. Planck's constant h = 6.626 × 10⁻³⁴ J s. 1 eV = 1.60 × 10⁻¹⁹ J. Every worked answer on this site uses exactly these.
IA1 — data test (10 %): analyse and interpret a set of data you are given. IA2 — student experiment (20 %): modify an experiment, collect data, evaluate. IA3 — research investigation (20 %): investigate a claim using published evidence. External examination (50 %): two papers covering Units 3 and 4 — multiple choice, short response and extended calculations. Half the marks are the exam, so the drills here are built to look like it.
Gravity and motion: the same force, from a thrown ball to a satellite
Year 11 kept everything in a straight line. This topic lets motion turn corners — a ball in flight, a car on a bend, a satellite in orbit — and the trick every time is the same: split the vector into components, and treat each one separately.
1.1Vectors in two dimensions
A vector at an angle θ to the horizontal has a horizontal component v cos θ and a vertical component v sin θ. Going the other way, a pair of perpendicular components adds back to a magnitude √(vx² + vy²) at an angle tan⁻¹(vy ÷ vx). Draw the triangle every time: the mistake that costs most marks in this topic is swapping sine and cosine.
A velocity of 20 m s⁻¹ at 30° above the horizontal is therefore 20 cos 30° = 17.3 m s⁻¹ horizontally and 20 sin 30° = 10.0 m s⁻¹ vertically. Check: √(17.3² + 10.0²) = √(299 + 100) = √399 ≈ 20. Good.
1.2Projectile motion
With air resistance ignored, a projectile is two independent motions happening at once. Horizontally there is no force, so the velocity is constant: sx = uxt. Vertically gravity acts, so the SUVAT equations apply with a = −9.8 m s⁻² (taking up as positive). The only thing the two share is the time — which is why time is nearly always what you solve for first.
Components. ux = 20 cos 30° = 17.3 m s⁻¹; uy = 20 sin 30° = 10.0 m s⁻¹.
Time to the top. At the peak vy = 0: v = u + at → 0 = 10.0 − 9.8t → t = 10.0 ÷ 9.8 = 1.02 s. By symmetry the whole flight lasts 2 × 1.02 = 2.04 s.
Maximum height. v² = u² + 2as → 0 = 10.0² − 2(9.8)s → s = 100 ÷ 19.6 = 5.10 m.
Range. Horizontal velocity is constant, so sx = uxt = 17.3 × 2.04 = 35.3 m.
Sanity check: a good throw of a cricket ball goes about 35 m. Right size.
A stone is thrown horizontally at 6.0 m s⁻¹ from a cliff 19.6 m high. Here uy = 0, so the vertical motion is a straight drop.
Time in the air (vertical): s = ut + ½at² → 19.6 = 0 + ½(9.8)t² → t² = 4.0 → t = 2.0 s.
Range (horizontal): sx = 6.0 × 2.0 = 12 m.
Landing velocity. vy = 0 + 9.8 × 2.0 = 19.6 m s⁻¹ down; vx = 6.0. Speed = √(6.0² + 19.6²) = √420 = 20.5 m s⁻¹, at tan⁻¹(19.6 ÷ 6.0) = 73° below the horizontal. The throwing speed does not change the time in the air — only how far away it lands.
1.3Inclined planes
On a slope, the useful axes are along the surface and perpendicular to it — not horizontal and vertical. Weight is the only force that then has to be resolved: mg sin θ acts down the slope and mg cos θ presses into it. The normal force balances the perpendicular component, so N = mg cos θ, and friction (if any) is μN acting up the slope while the block slides down.
Now let the coefficient of kinetic friction be μ = 0.20.
N = mg cos 30° = 5.0 × 9.8 × 0.866 = 42.4 N → f = μN = 0.20 × 42.4 = 8.5 N up the slope.
Fnet = 24.5 − 8.5 = 16.0 N down the slope → a = 16.0 ÷ 5.0 = 3.2 m s⁻².
Without friction it was 4.9 m s⁻² = g sin θ, which does not depend on the mass at all — the reason Galileo could slow gravity down with a ramp and time it.
1.4Uniform circular motion
An object moving in a circle at constant speed is still accelerating, because its velocity keeps changing direction. That acceleration points to the centre and has size a = v² ÷ r. By Newton's second law something must supply a net force F = mv² ÷ r toward the centre — the centripetal force. It is not a new kind of force: it is whatever real force happens to be doing the job — tension in a string, friction on tyres, gravity on a planet.
A 0.50 kg ball is whirled in a horizontal circle of radius 1.2 m, completing one revolution every 0.80 s.
v = 2πr ÷ T = 2π × 1.2 ÷ 0.80 = 9.42 m s⁻¹
F = mv² ÷ r = 0.50 × 9.42² ÷ 1.2 = 0.50 × 88.8 ÷ 1.2 = 37 N — the tension in the string.
Now the car again: the maximum friction on a dry road is about 0.60 of the weight, so the fastest safe speed round a 50 m bend is v = √(μgr) = √(0.60 × 9.8 × 50) = √294 = 17.1 m s⁻¹ (about 62 km/h). Notice the mass cancelled: a truck and a bicycle have the same limit.
1.5Newton's law of universal gravitation
Every mass attracts every other mass with a force F = G m₁m₂ ÷ r², where r is the distance between their centres and G = 6.67 × 10⁻¹¹ N m² kg⁻². It is an inverse-square law: double the distance and the force falls to a quarter; triple it and the force falls to a ninth. The two forces in the pair are equal and opposite (Newton's third law) — the Earth pulls you with 686 N and you pull the Earth with 686 N.
| Question | Working | Answer |
|---|---|---|
| Force of the Earth on a 1.0 kg mass at its surface | F = (6.67 × 10⁻¹¹)(5.97 × 10²⁴)(1.0) ÷ (6.37 × 10⁶)² | 9.81 N — which is g |
| Force between the Earth and the Moon (7.35 × 10²² kg, 3.84 × 10⁸ m away) | F = (6.67 × 10⁻¹¹)(5.97 × 10²⁴)(7.35 × 10²²) ÷ (3.84 × 10⁸)² | 1.98 × 10²⁰ N |
| Force between two 70 kg people 1.0 m apart | F = (6.67 × 10⁻¹¹)(70)(70) ÷ 1.0² | 3.3 × 10⁻⁷ N — gravity is feeble unless a mass is planet-sized |
1.6Gravitational fields and potential energy
A gravitational field is the region around a mass where another mass feels a force. Its strength at a point is the force per kilogram: g = F ÷ m = GM ÷ r², in N kg⁻¹ — which is the same unit as m s⁻², because the field strength is also the acceleration of anything falling freely there.
Near the surface, GPE = mgh works because g is nearly constant. Over planetary distances it is not, and the general expression is U = −GMm ÷ r. The minus sign is bookkeeping: potential energy is taken as zero infinitely far away, and it falls (becomes more negative) as an object comes closer, because the field does work on it. To escape a planet entirely, an object needs kinetic energy equal to the depth of that well: ½mv² = GMm ÷ R, giving the escape speed v = √(2GM ÷ R). For Earth: √(2 × 3.98 × 10¹⁴ ÷ 6.37 × 10⁶) = 1.12 × 10⁴ m s⁻¹, about 11 km per second, whatever the mass of the object.
1.7Orbits and Kepler's third law
A satellite in a circular orbit is in uniform circular motion with gravity as the centripetal force. Set the two equal and the mass of the satellite cancels:
GMm ÷ r² = mv² ÷ r → v = √(GM ÷ r) and, since v = 2πr ÷ T, T² = (4π² ÷ GM) r³
That last line is Kepler's third law: for everything orbiting the same central body, T² ∝ r³. Kepler found it in 1619 from Tycho Brahe's observations of the planets; Newton explained it seventy years later. Kepler's first two laws: orbits are ellipses with the central body at one focus, and a line from the body to the orbiting object sweeps out equal areas in equal times — so a planet moves fastest when closest to the Sun.
Orbital radius r = 6.37 × 10⁶ + 0.63 × 10⁶ = 7.00 × 10⁶ m (always add the planet's radius — r is measured from the centre). GM = 6.67 × 10⁻¹¹ × 5.97 × 10²⁴ = 3.98 × 10¹⁴.
Speed. v = √(GM ÷ r) = √(3.98 × 10¹⁴ ÷ 7.00 × 10⁶) = √(5.69 × 10⁷) = 7.54 × 10³ m s⁻¹
Period. T = 2πr ÷ v = 2π × 7.00 × 10⁶ ÷ 7.54 × 10³ = 5.83 × 10³ s = 97.2 minutes. Low-orbit satellites really do circle the Earth in about an hour and a half.
A geostationary satellite must have T = 24 h = 86 400 s. Rearranging Kepler: r³ = GMT² ÷ 4π² = 3.98 × 10¹⁴ × (86 400)² ÷ 39.5 = 7.53 × 10²², so r = 4.22 × 10⁷ m — an altitude of about 35 800 km, where every communications satellite sits.
Ratios need no constants. Mars orbits at 1.52 times the Earth's distance from the Sun, so TMars = 1.523/2 × 1 year = 1.87 years (the measured value is 1.88).
Electromagnetism: charges, currents and the fields between them
Year 11 treated circuits as plumbing. This topic asks what is actually pushing: a stationary charge makes an electric field, a moving charge makes a magnetic field too, and a changing magnetic field makes electricity — which is how every power station on Earth works.
2.1Coulomb's law and electric fields
Two point charges exert a force on each other of F = k q₁q₂ ÷ r², with k = 8.99 × 10⁹ N m² C⁻² — the same inverse-square shape as gravity, but enormously stronger and able to repel as well as attract. Like charges repel; unlike charges attract.
An electric field is the region where a charge feels a force, and its strength is the force per coulomb: E = F ÷ q, in N C⁻¹. Around a point charge, E = kQ ÷ r². Between two parallel plates a distance d apart with a potential difference V across them, the field is uniform and E = V ÷ d, which gives the equivalent unit V m⁻¹. Field lines point in the direction a positive charge would be pushed: away from positive, toward negative.
Charges of +2.0 μC and −3.0 μC are 5.0 cm apart. Convert first: 2.0 × 10⁻⁶ C, 3.0 × 10⁻⁶ C, 0.050 m.
F = k q₁q₂ ÷ r² = (8.99 × 10⁹)(2.0 × 10⁻⁶)(3.0 × 10⁻⁶) ÷ (0.050)² = 5.39 × 10⁻² ÷ 2.5 × 10⁻³ = 21.6 N, attractive
Work out the size from the magnitudes and state the direction in words. A minus sign in the working just means "attract".
2.2Charges moving in an electric field
- A charge released in a uniform field accelerates uniformly along the field lines, so the SUVAT equations apply with a = qE ÷ m.
- A charge entering a uniform field sideways follows a parabola, exactly like a projectile: constant velocity along the plates, constant acceleration across them. That is how the beam was steered in old cathode-ray televisions.
- Moving a charge q through a potential difference V transfers energy W = qV. An electron accelerated from rest through 400 V gains KE = 1.60 × 10⁻¹⁹ × 400 = 6.4 × 10⁻¹⁷ J, so ½mv² = 6.4 × 10⁻¹⁷ gives v = √(2 × 6.4 × 10⁻¹⁷ ÷ 9.11 × 10⁻³¹) = 1.19 × 10⁷ m s⁻¹ — four per cent of the speed of light, from a battery-sized voltage.
- This is where the electron-volt comes from: 1 eV is the energy an electron gains through 1 V, so that electron has 400 eV. You will use the unit constantly in Unit 4.
2.3Magnetic fields from currents
A moving charge — a current — produces a magnetic field. Around a long straight wire the field lines are concentric circles, found by the right-hand grip rule: thumb along the conventional current, fingers curl the way the field goes. Its strength is B = μ₀I ÷ 2πr, falling off with distance (not distance squared). Inside a long coil — a solenoid — the field is uniform and B = μ₀nI, where n is the number of turns per metre; grip the coil with your fingers following the current and your thumb gives the north end.
| Question | Working | Answer |
|---|---|---|
| Field 0.10 m from a wire carrying 5.0 A | B = (4π × 10⁻⁷)(5.0) ÷ (2π × 0.10) | 1.0 × 10⁻⁵ T — a fifth of the Earth's field |
| Field inside a solenoid of 1000 turns per metre carrying 2.0 A | B = (4π × 10⁻⁷)(1000)(2.0) | 2.5 × 10⁻³ T |
| Field on the page from a current flowing up the page, to the right of the wire | Grip rule: thumb up, fingers curl anticlockwise seen from above | Into the page (drawn as ×) |
Drawing convention: a field pointing out of the page is a dot (the tip of an arrow coming at you); into the page is a cross (the tail feathers going away).
2.4Force on a moving charge, and on a current
A magnetic field exerts a force on a charge only if the charge is moving, and only on the part of its velocity that is perpendicular to the field: F = qvB sin θ. The force is at right angles to both v and B, found with the right-hand palm rule: thumb along v (for a positive charge), fingers along B, and the palm pushes in the direction of F. For a negative charge, reverse it.
A wire is a stream of moving charges, so a current-carrying wire in a magnetic field feels a force too: F = BIL sin θ, where L is the length of wire inside the field. Same palm rule, with the thumb along the conventional current. A 0.50 m wire carrying 3.0 A at right angles to a 0.20 T field feels 0.20 × 3.0 × 0.50 = 0.30 N. Put a loop of wire in a field and the two sides feel opposite forces — a turning effect — and you have a DC motor; a commutator reverses the current every half-turn so it keeps turning the same way.
2.5Electromagnetic induction: Faraday and Lenz
The magnetic flux through a loop is the field times the area it threads: Φ = BA cos θ, in webers (Wb), with θ the angle between the field and the perpendicular to the loop. Faraday's law: whenever the flux through a coil changes, an emf is induced equal to the rate of change of flux, times the number of turns: emf = −N ΔΦ ÷ Δt. Change the field, change the area, or turn the coil — any of them will do. A steady flux induces nothing.
The minus sign is Lenz's law: the induced current flows in the direction that opposes the change causing it. Push a north pole toward a coil and the coil's near face becomes north to push back; pull it away and the face becomes south to hold on. It has to be so — if the induced current helped the change, you would get energy for nothing.
A coil of 200 turns and area 0.010 m² sits with its face perpendicular to a 0.50 T field. The field is switched off and falls to zero in 0.20 s.
ΔΦ = ΔB × A = 0.50 × 0.010 = 5.0 × 10⁻³ Wb
emf = N ΔΦ ÷ Δt = 200 × 5.0 × 10⁻³ ÷ 0.20 = 5.0 V
By Lenz's law the induced current makes a field in the same direction as the vanishing one, trying to keep it. Switch the field on again and the current runs the other way.
A generator is a coil rotated in a field: the flux through it rises and falls sinusoidally, so the emf does too — alternating current. Spin the coil faster and both the frequency and the peak voltage go up.
2.6Transformers and AC transmission
A power station sends 100 kW down a line of total resistance 2.0 Ω. The power lost as heat in the line is Ploss = I²R.
At 1000 V: I = P ÷ V = 100 000 ÷ 1000 = 100 A. Loss = 100² × 2.0 = 20 000 W — a fifth of everything sent.
At 100 kV: I = 100 000 ÷ 100 000 = 1.0 A. Loss = 1.0² × 2.0 = 2.0 W.
Raising the voltage a hundredfold cuts the current a hundredfold and the loss ten-thousandfold. That is the whole argument for AC: transformers can step it up for the journey and down again for the home, and transformers do not work on DC.
Special relativity: what the speed of light does to space and time
In 1905 Einstein took one experimental fact seriously — light always arrives at the same speed, no matter how you move — and followed it wherever it led. It led to moving clocks running slow, moving rulers shrinking, and mass turning out to be a form of energy. Every one of those has since been measured.
3.1Frames of reference and the two postulates
An inertial frame of reference is one that is not accelerating — a lab at rest, or a train at constant velocity. Galileo already knew that no experiment done inside a smoothly moving ship can tell you it is moving; Newton's laws work the same in every inertial frame. The trouble came with light. Maxwell's equations gave light one definite speed, c, and nineteenth-century physicists assumed that was its speed relative to a medium filling space, the "ether". In 1887 Michelson and Morley tried to detect the Earth's motion through that ether by comparing the speed of light in two perpendicular directions. They found no difference at all.
- First postulate. The laws of physics are the same in every inertial frame of reference. There is no experiment that can identify a state of "absolute rest".
- Second postulate. The speed of light in a vacuum is the same, c = 3.00 × 10⁸ m s⁻¹, for all observers in inertial frames, regardless of the motion of the source or of the observer.
The second one is the strange one. Fire a torch forward from a train doing 0.5c, and someone on the platform measures the light passing at c — not 1.5c. Since speed is distance over time, and the speed refuses to change, it is distance and time that must give way.
3.2Simultaneity is relative
3.3Time dilation and length contraction
Everything is governed by the Lorentz factor γ = 1 ÷ √(1 − v²/c²), which is 1 at rest and grows without limit as v approaches c.
| v | 0.1c | 0.5c | 0.6c | 0.8c | 0.9c | 0.99c | 0.995c |
|---|---|---|---|---|---|---|---|
| γ | 1.005 | 1.155 | 1.25 | 1.667 | 2.294 | 7.09 | 10.0 |
- Time dilation: t = γt₀. The proper time t₀ is the interval measured by a clock that is at rest relative to the events — the clock that sees both events happen at the same place. Every other observer measures a longer interval. Moving clocks run slow.
- Length contraction: L = L₀ ÷ γ. The proper length L₀ is measured by someone at rest relative to the object. Every other observer measures it shorter, along the direction of motion only. Moving rulers shrink.
- The effects are symmetric: the astronaut sees Earth's clocks running slow and Earth's rulers shortened, too. The asymmetry in the "twin paradox" arises only because the travelling twin turns around, which means changing frames.
A spacecraft passes Earth at 0.8c. γ = 1 ÷ √(1 − 0.64) = 1 ÷ √0.36 = 1 ÷ 0.6 = 1.67.
Time. The crew's clock records 10.0 years on the voyage. That is proper time (the crew are with their clock the whole way). Earth measures t = γt₀ = 1.67 × 10.0 = 16.7 years.
Length. The ship is 100 m long as built. Earth measures L = L₀ ÷ γ = 100 ÷ 1.67 = 60 m. The crew, meanwhile, measure the distance to their destination as 0.6 of the value Earth quotes — which is exactly why they age less: they have less distance to cover.
The check that catches most errors: the moving clock must read less, the moving length must come out shorter. If your γ ended up on the wrong side, the numbers will tell you.
3.4Muons: relativity measured
Cosmic rays hitting the upper atmosphere create muons about 10–15 km up. A muon at rest lives on average only 2.2 μs before decaying. At their typical speed of about 0.995c they should therefore travel about 0.995 × 3.00 × 10⁸ × 2.2 × 10⁻⁶ = 660 m on average before decaying, and almost none should ever reach the ground. Yet detectors at sea level count them by the hundreds per square metre per second. In the classic experiment of 1963, Frisch and Smith counted muons at the top of Mount Washington and again about 1.9 km lower, and found far more survived the descent than a 2.2 μs lifetime allows.
Relativity resolves it both ways. From the ground: at 0.995c, γ = 10, so the muon's lifetime is dilated to 22 μs and its average range becomes about 6.6 km — enough for a large fraction to arrive. From the muon: its clock is normal, but the 10 km of atmosphere rushing past is contracted to about 1 km, which it can cross in its short life. Two descriptions, one prediction, and the counts match it.
3.5Relativistic momentum and E = mc²
- Momentum: p = γmv. As v approaches c, γ explodes and so does the momentum, which means the force needed to accelerate further grows without limit. That is the operational reason c cannot be reached: an accelerator can keep adding energy and momentum forever while the speed creeps closer to c without arriving. An electron at 0.9c has p = 2.294 × 9.11 × 10⁻³¹ × 2.7 × 10⁸ = 5.6 × 10⁻²² kg m s⁻¹, more than double the Newtonian value.
- Mass–energy equivalence: E = mc². A mass m at rest has a rest energy mc². Because c² = 9.00 × 10¹⁶, a tiny mass stands for a huge energy: one gram is 0.001 × 9.00 × 10¹⁶ = 9.0 × 10¹³ J, roughly the output of a large power station for a day. An electron's rest energy is 9.11 × 10⁻³¹ × 9.00 × 10¹⁶ = 8.2 × 10⁻¹⁴ J = 0.51 MeV, a number you will meet again in particle physics.
- Total energy E = γmc², so the kinetic energy is KE = (γ − 1)mc². At 0.8c that is 0.67mc² — already two-thirds of the rest energy, far more than the ½mv² = 0.32mc² Newton would give.
- The Sun radiates 3.85 × 10²⁶ W, so it converts m = E ÷ c² = 3.85 × 10²⁶ ÷ 9.00 × 10¹⁶ = 4.3 × 10⁹ kg of mass into energy every second — and has done so for four and a half billion years without losing a noticeable fraction of itself. Nuclear fission and fusion are the same bookkeeping on a smaller scale: the products weigh less than the reactants, and the difference has left as energy.
Quantum theory and the Standard Model
Around 1900 three experiments refused to fit the wave theory of light, and the fix — that energy comes in lumps — turned out to describe atoms, electrons and, eventually, every particle there is. This topic runs from Planck's desperate guess to the table of everything.
4.1Black-body radiation and Planck's constant
A black body absorbs all radiation that falls on it and, when hot, radiates a spectrum that depends only on its temperature. Two features were measured long before they were explained: the total power grows steeply with temperature, and the peak wavelength shifts shorter as the body gets hotter (Wien's law, λmax = 2.898 × 10⁻³ ÷ T).
| Body | Temperature | Peak wavelength | What you see |
|---|---|---|---|
| A human | 310 K | 9.3 μm (infrared) | Nothing — but a thermal camera does |
| An incandescent bulb filament | 3000 K | 970 nm | Yellowish; most of its output is wasted as infrared |
| The Sun's surface | 5800 K | 500 nm | White, peaking in the green — the band our eyes evolved for |
Classical wave theory predicted that a hot body should radiate ever more strongly at shorter wavelengths, without limit — the "ultraviolet catastrophe", which is plainly not what happens. In 1900 Max Planck obtained the correct curve by assuming that the oscillating charges in the body could only emit energy in discrete packets, or quanta, of size E = hf, with h = 6.626 × 10⁻³⁴ J s. He regarded it as a mathematical trick. It was not.
A photon of red light at 600 nm has f = c ÷ λ = 3.00 × 10⁸ ÷ 6.00 × 10⁻⁷ = 5.00 × 10¹⁴ Hz, so E = hf = 6.626 × 10⁻³⁴ × 5.00 × 10¹⁴ = 3.31 × 10⁻¹⁹ J, which is 3.31 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = 2.07 eV. Visible photons carry a few electron-volts; that is the scale of chemistry, which is why light drives photosynthesis and photography.
4.2The photoelectric effect
Shine light on a clean metal surface in a vacuum and, under the right conditions, electrons come out. The observations, first made carefully around 1902, were impossible for a wave to explain:
- Below a threshold frequency f₀ that depends on the metal, no electrons are emitted, however intense the light.
- Above it, emission is instantaneous — no time to "build up" energy.
- The maximum kinetic energy of the electrons depends on the frequency of the light, not on its brightness.
- Brightness controls only how many electrons are emitted per second — the current.
Einstein, 1905: light arrives as photons of energy hf, and one photon gives all its energy to one electron. The electron spends the work function W — the minimum energy to escape that metal — and keeps the rest: KEmax = hf − W. If hf < W nothing escapes, and no number of too-small photons will add up. This is the work that won Einstein the Nobel Prize.
Sodium's work function is 2.28 eV. Light of wavelength 400 nm falls on it.
f = c ÷ λ = 3.00 × 10⁸ ÷ 4.00 × 10⁻⁷ = 7.50 × 10¹⁴ Hz
hf = 6.626 × 10⁻³⁴ × 7.50 × 10¹⁴ = 4.97 × 10⁻¹⁹ J = 4.97 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = 3.11 eV
KEmax = hf − W = 3.11 − 2.28 = 0.83 eV = 1.32 × 10⁻¹⁹ J, so the stopping voltage is 0.83 V.
Threshold. f₀ = W ÷ h = (2.28 × 1.60 × 10⁻¹⁹) ÷ 6.626 × 10⁻³⁴ = 3.65 × 10⁻¹⁹ ÷ 6.626 × 10⁻³⁴ = 5.51 × 10¹⁴ Hz, a wavelength of 545 nm. Red light at 650 nm (4.6 × 10¹⁴ Hz) is below threshold: a red floodlight gets nothing out of sodium, a faint violet glimmer does.
4.3Wave–particle duality
If light waves behave as particles, do particles behave as waves? Louis de Broglie proposed in 1924 that everything with momentum has a wavelength λ = h ÷ p = h ÷ mv. Three years later Davisson and Germer fired electrons at a nickel crystal and saw a diffraction pattern — the unmistakable signature of a wave, at exactly the wavelength de Broglie predicted. Electron microscopes exploit it: a short de Broglie wavelength resolves details that visible light, at 500 nm, cannot.
| Object | Momentum p = mv | λ = h ÷ p | Consequence |
|---|---|---|---|
| An electron at 2.0 × 10⁶ m s⁻¹ | 9.11 × 10⁻³¹ × 2.0 × 10⁶ = 1.8 × 10⁻²⁴ | 3.6 × 10⁻¹⁰ m | About the spacing of atoms in a crystal — so it diffracts |
| A cricket ball, 0.16 kg at 40 m s⁻¹ | 6.4 | 1.0 × 10⁻³⁴ m | Unmeasurably small — no wave behaviour is ever seen |
Neither "wave" nor "particle" is the truth; both are pictures that work in their own regime. Light and matter alike are quantum objects that propagate as waves and are detected as particles.
4.4The Bohr model and emission spectra
Hot hydrogen gas does not glow with a smooth rainbow: it emits a few sharp lines of definite colour. In 1913 Niels Bohr explained them by proposing that the electron can only occupy certain allowed orbits, each with a fixed energy En = −13.6 ÷ n² eV, and that it radiates only when it jumps between them. The photon carries exactly the energy difference: hf = Eupper − Elower. Absorption is the same in reverse, which is why the dark lines in a star's spectrum sit at the same wavelengths as the bright ones in a lamp.
Electron drops from n = 3 to n = 2. ΔE = E₃ − E₂ = (−1.51) − (−3.40) = 1.89 eV = 1.89 × 1.60 × 10⁻¹⁹ = 3.02 × 10⁻¹⁹ J.
λ = hc ÷ E = (6.626 × 10⁻³⁴)(3.00 × 10⁸) ÷ 3.02 × 10⁻¹⁹ = 6.58 × 10⁻⁷ m, about 658 nm. The measured H-α line is at 656 nm — the small gap is rounding in the level energies.
Bohr's model works only for hydrogen and hydrogen-like ions, and it never explained why those orbits were allowed. De Broglie did: an orbit is allowed when a whole number of electron wavelengths fits around it — a standing wave. The full quantum mechanics of 1925–26 replaced orbits with orbitals and kept the energies.
4.5The Standard Model
By the 1960s accelerators had found hundreds of "elementary" particles, far too many to all be fundamental. The Standard Model reduces them to twelve matter particles (fermions) in three generations, plus the force-carrying bosons. Ordinary matter needs only the first generation: up and down quarks, and the electron.
| Generation 1 | Generation 2 | Generation 3 | Charge | |
|---|---|---|---|---|
| Quarks | up (u) | charm (c) | top (t) | +⅔ e |
| down (d) | strange (s) | bottom (b) | −⅓ e | |
| Leptons | electron (e⁻) | muon (μ⁻) | tau (τ⁻) | −1 e |
| electron neutrino (νe) | muon neutrino (νμ) | tau neutrino (ντ) | 0 |
| Interaction | Carrier (gauge boson) | Acts on | Range | Relative strength |
|---|---|---|---|---|
| Strong | gluon (g) | Quarks — binds them into hadrons, and nucleons into nuclei | About 10⁻¹⁵ m | 1 |
| Electromagnetic | photon (γ) | Anything with charge | Infinite | about 10⁻² |
| Weak | W⁺, W⁻, Z⁰ | All quarks and leptons — changes one flavour into another; beta decay | About 10⁻¹⁸ m | about 10⁻⁶ |
| Gravity | (graviton — hypothetical; not part of the Standard Model) | Anything with mass or energy | Infinite | about 10⁻³⁹ |
- Every particle has an antiparticle of the same mass and opposite charge: the positron e⁺, the antiproton, antiquarks written with a bar. Particle meets antiparticle and both annihilate into photons; the reverse, pair production, needs at least 2mc² of energy.
- Quarks are never seen alone. They combine into hadrons: baryons of three quarks — the proton is uud (+⅔ +⅔ −⅓ = +1), the neutron udd (+⅔ −⅓ −⅓ = 0) — and mesons of a quark and an antiquark, such as the pion π⁺ = u anti-d.
- Leptons do not feel the strong force. Neutrinos feel only the weak force, which is why trillions pass through you each second unnoticed.
- Three quantities are conserved in every interaction and let you check any proposed reaction: charge, baryon number (+1 per baryon, −1 per antibaryon, 0 for leptons and mesons) and lepton number (+1 per lepton, −1 per antilepton).
- The Higgs boson, predicted in 1964 and found at CERN in 2012, is the quantum of the field that gives the W, Z, quarks and leptons their mass.
4.6Reading a Feynman diagram
4.7Particle accelerators
Everything in this unit comes together in the machines that test it. An accelerator uses electric fields to speed charged particles up (W = qV, over and over) and magnetic fields to steer them (r = mv ÷ qB, which is why a ring needs stronger magnets as the energy rises). A linear accelerator is a straight line of accelerating gaps; a synchrotron such as the Large Hadron Collider at CERN is a ring 27 km round in which two proton beams circulate in opposite directions and collide at energies of 13 TeV.
- Why so much energy? Two reasons, both from this course. De Broglie: a higher momentum means a shorter wavelength, and a shorter wavelength resolves smaller structures — you cannot see inside a proton with a probe whose wavelength is bigger than the proton. And E = mc²: to create a particle of mass m you must bring at least mc² of energy into the collision. The Higgs, at 125 GeV, needed the LHC.
- Why relativity matters here. LHC protons travel at 0.999999990c, with γ about 7000. Their momentum is γmv, not mv; the magnets are designed around the relativistic value, and the accelerating fields are timed for a speed that barely changes while the energy climbs a thousandfold.
- Detectors wrap the collision point in layers: tracking chambers in a magnetic field measure momentum from the curvature of each track (and the sign of the charge from which way it bends), calorimeters absorb particles to measure their energy, and muon chambers on the outside catch the one charged particle that gets through everything else.
The year the calculus pays off.
Units 3 and 4 finish what Year 11 started. The exponential function gets its own derivative, three new rules let you differentiate almost anything, and integration — the reverse of differentiation — turns out to measure area. Then the sine wave becomes a function you can differentiate, the binomial idea becomes a full distribution, and the normal curve lets you estimate a whole population from one sample. Everything here is examined externally, and everything here is worth exactly the working you show.
The mapSeven QCAA topics, four units here
- Unit 3 — Logarithmic functions and further differentiation. Log laws with base e, the functions ex and ln x and their derivatives, the chain, product and quotient rules, and the second derivative as a test of concavity.
- Unit 3 — Applications of differentiation, and integrals. Optimisation with the new rules, kinematics (displacement, velocity, acceleration), anti-differentiation, the fundamental theorem of calculus, and the definite integral as a signed area.
- Unit 4 — Trigonometric functions and discrete random variables. Amplitude, period and phase, the derivatives of sin and cos, Bernoulli trials and the full binomial distribution with its mean np and variance np(1 − p).
- Unit 4 — Continuous random variables and inference. Probability density functions, the normal distribution and z-scores, the 68–95–99.7 rule, sample proportions and a confidence interval for a proportion.
Four pieces. IA1, a problem-solving and modelling task (20%). IA2, an examination (15%). IA3, an examination (15%). Then the external examination (50%), set and marked by QCAA in two papers: Paper 1 is technology-free — exact values, log laws, derivatives and integrals by hand — and Paper 2 is technology-active, where the calculator does the arithmetic and the marks are for setting up, interpreting and justifying. Practise both modes: every worked example in this course says which one it belongs to.
Forgetting the chain rule factor (the derivative of e3x is 3e3x, not e3x); dropping the + c on an indefinite integral, or the minus sign when an area sits below the x-axis; and reading a confidence interval as a probability about the population. Each one is a single line of working that markers look for by name.
Logarithmic functions and further differentiation
In Year 11 you differentiated polynomials. Now the world gets bigger: exponential growth, logarithms, and anything built by composing, multiplying or dividing simpler functions. Three rules cover all of it, and one special number, e, makes the exponential function the only function that is its own derivative.
1.1The number e and the natural logarithm
e ≈ 2.71828 is the base at which an exponential curve’s gradient equals its own height. The natural logarithm ln x is loge x: the power you raise e to in order to get x. The two functions undo each other, and every log law from Year 11 applies with base e.
| Fact | Example | Why |
|---|---|---|
| ln e = 1, ln 1 = 0 | ln e² = 2 | e¹ = e and e⁰ = 1; the power law then gives 2 ln e = 2 |
| eln x = x and ln(ex) = x | eln 5 = 5 | Each is the inverse of the other |
| ln(mn) = ln m + ln n | ln 6 = ln 2 + ln 3 | Multiplying adds the powers |
| ln(m/n) = ln m − ln n | ln 20 − ln 2 = ln 10 | Dividing subtracts them |
| ln(mp) = p ln m | ln(e3x) = 3x | A power is repeated multiplication |
| loga b = ln b ÷ ln a | log₂ 20 = ln 20 ÷ ln 2 = 4.32 | Change of base — the calculator only needs ln |
- Solving e2x = 10. Take ln of both sides: 2x = ln 10, so x = ln 10 ÷ 2 = 1.151 (3 decimal places). On Paper 1 you stop at the exact form x = ½ ln 10.
- Solving ln(x − 1) = 2. Rewrite as a power: x − 1 = e², so x = e² + 1 ≈ 8.389. Always check the argument of the log is positive: x − 1 = e² > 0 ✓
- Continuous growth. A population modelled by P = 500e0.03t reaches 1000 when e0.03t = 2, so 0.03t = ln 2 and t = ln 2 ÷ 0.03 = 23.1 years. The doubling time of any ekt model is ln 2 ÷ k.
1.2ex and ln x as functions — and their derivatives
If y = ex then dy/dx = ex — the curve’s gradient at every point equals its height there.
If y = ln x then dy/dx = 1/x (for x > 0) — the gradient of the log curve dies away as x grows, but never reaches zero.
1.3The chain rule
A composite function is one function inside another: e3x, (2x + 1)³, ln(x² + 1), √(4x − 3). The chain rule says: differentiate the outside, keep the inside unchanged, then multiply by the derivative of the inside. In symbols, if y = f(u) and u = g(x), then dy/dx = dy/du × du/dx.
| Function | Outside → inside | Derivative |
|---|---|---|
| y = (2x + 1)³ | cube → 2x + 1 | 3(2x + 1)² × 2 = 6(2x + 1)² |
| y = e3x | eu → 3x | e3x × 3 = 3e3x |
| y = e−x² | eu → −x² | e−x² × (−2x) = −2x e−x² |
| y = ln(x² + 1) | ln u → x² + 1 | 1/(x² + 1) × 2x = 2x/(x² + 1) |
| y = √(4x − 3) = (4x − 3)½ | square root → 4x − 3 | ½(4x − 3)−½ × 4 = 2/√(4x − 3) |
The derivative of e3x is 3e3x, not e3x. The derivative of (2x + 1)³ is 6(2x + 1)², not 3(2x + 1)². Ask «what is the inside, and what is its derivative?» every single time — it is the most common lost mark on Paper 1.
1.4The product and quotient rules
| Product rule: y = uv | Quotient rule: y = u/v | |
|---|---|---|
| Rule | dy/dx = u′v + uv′ | dy/dx = (u′v − uv′) ÷ v² |
| In words | Differentiate each factor in turn, keep the other, add | Same idea on top, but a minus, and divide by the bottom squared |
| Example | y = x²ex: u = x², v = ex | y = x/(x² + 1): u = x, v = x² + 1 |
| Working | 2x·ex + x²·ex = x(x + 2)ex | [1·(x² + 1) − x·2x] ÷ (x² + 1)² = (1 − x²)/(x² + 1)² |
| Second example | y = x ln x: 1·ln x + x·(1/x) = ln x + 1 | y = ex/x: (ex·x − ex·1)/x² = ex(x − 1)/x² |
- Factorise the answer. 2xex + x²ex becomes x(x + 2)ex, which shows at a glance that the gradient is zero at x = 0 and x = −2 — the stationary points, for free.
- Order matters in the quotient rule. The top is u′v − uv′: derivative of the top times the bottom, first. Swap them and every sign is wrong.
- Where the rules stack. y = x²e3x is a product whose second factor needs the chain rule: 2x·e3x + x²·3e3x = xe3x(2 + 3x).
1.5The second derivative and concavity
Differentiate f′(x) again and you get f″(x), the second derivative: the rate at which the gradient itself is changing. It tells you which way the curve bends.
| Sign of f″(x) | Shape | At a stationary point it means |
|---|---|---|
| f″(x) > 0 | Concave up — the gradient is increasing, the curve holds water | A local minimum |
| f″(x) < 0 | Concave down — the gradient is decreasing, the curve sheds water | A local maximum |
| f″(x) = 0 and changes sign | A point of inflection — the bend switches direction | Test with the sign of f′ either side instead |
- Worked: f(x) = x³ − 3x². f′(x) = 3x² − 6x = 3x(x − 2), so the stationary points are at x = 0 and x = 2. f″(x) = 6x − 6.
- Classify them. f″(0) = −6 < 0, so (0, 0) is a local maximum. f″(2) = 6 > 0, so (2, −4) is a local minimum. One substitution each — faster than a sign table.
- Inflection. f″(x) = 0 at x = 1, and it changes from negative to positive there, so (1, −2) is a point of inflection: the curve stops bending down and starts bending up.
Applications of differentiation, and integrals
Differentiation answers «how fast?» and «where is the best?». Integration asks the reverse question — given the rate, what was the total? — and the surprising answer is that the total is an area under a graph. The fundamental theorem of calculus is the bridge, and it is the single most important line in the whole course.
2.1Optimisation with the new tools
Problem. A square of cardboard 24 cm by 24 cm has a square of side x cm cut from each corner; the flaps fold up to make an open box. Find the value of x that maximises the volume, and the maximum volume.
1. Model. The base is (24 − 2x) by (24 − 2x) and the height is x, so V = x(24 − 2x)², with 0 < x < 12.
2. Differentiate (product rule with a chain rule inside): V′ = 1·(24 − 2x)² + x·2(24 − 2x)(−2) = (24 − 2x)[(24 − 2x) − 4x] = (24 − 2x)(24 − 6x).
3. Solve V′ = 0. x = 12 (which gives no box at all) or x = 4.
4. Justify. Expand V = 4x³ − 96x² + 576x, so V″ = 24x − 192 and V″(4) = −96 < 0: a maximum.
5. Answer in context. V(4) = 4 × 16² = 1024 cm³, with corner cut-outs of 4 cm.
x = 12 solves V′ = 0 but is not in the domain (the base would vanish), so say so. Then give the volume, not just the x. Then write cm³. Three separate marks.
2.2Kinematics: displacement, velocity, acceleration
If displacement x(t) is a particle’s position relative to an origin, then velocity v = dx/dt and acceleration a = dv/dt = d²x/dt². Differentiate to go down the chain; integrate to go back up.
| Quantity | For x(t) = t³ − 6t² + 9t (metres, seconds) | What it tells you |
|---|---|---|
| Displacement | x(t) = t³ − 6t² + 9t | Position: x(0) = 0, x(1) = 4, x(3) = 0 |
| Velocity | v(t) = 3t² − 12t + 9 = 3(t − 1)(t − 3) | Zero at t = 1 and t = 3: the particle is at rest and turns around |
| Acceleration | a(t) = 6t − 12 | a(1) = −6 m/s²: at t = 1 it is slowing to a halt then reversing |
| Distance in the first 3 s | |x(1) − x(0)| + |x(3) − x(1)| = 4 + 4 | 8 m travelled, even though the displacement after 3 s is 0 |
The particle goes 4 m out and 4 m back: displacement 0, distance 8 m. Whenever velocity changes sign inside the interval, split the interval at the turning instant and add the absolute values.
2.3Anti-differentiation
An anti-derivative of f(x) is any function whose derivative is f(x). Because a constant differentiates to zero, there is a whole family of them, which is why every indefinite integral ends in + c.
| ∫ f(x) dx | Result | Check by differentiating |
|---|---|---|
| ∫ xn dx | xn+1 ÷ (n + 1) + c, n ≠ −1 | Raise the power by one, divide by the new power |
| ∫ (6x − 4) dx | 3x² − 4x + c | d/dx(3x² − 4x) = 6x − 4 ✓ |
| ∫ ekx dx | ekx ÷ k + c | The chain rule would multiply by k, so divide by k |
| ∫ 1/x dx | ln|x| + c | The missing case n = −1 — it is the log |
| ∫ (2x + 1)³ dx | (2x + 1)⁴ ÷ 8 + c | Divide by the new power 4 and by the inside derivative 2 |
- Finding c. If f′(x) = 6x − 4 and f(1) = 5, then f(x) = 3x² − 4x + c and 3 − 4 + c = 5, so c = 6: f(x) = 3x² − 4x + 6.
- Velocity to displacement. If v(t) = 6t − 12 and the particle starts at x = 5, then x(t) = 3t² − 12t + 5.
2.4The fundamental theorem and definite integrals
If F is any anti-derivative of f, then ∫ab f(x) dx = F(b) − F(a), and that number is the signed area between the curve and the x-axis from x = a to x = b. Regions above the axis count positive, regions below count negative. No + c is needed: it cancels in the subtraction.
- ∫₀³ (x² + 1) dx = [x³/3 + x]₀³ = (9 + 3) − 0 = 12.
- Area under y = 4 − x² from x = −2 to 2. [4x − x³/3] from −2 to 2 = (8 − 8/3) − (−8 + 8/3) = 16 − 16/3 = 32/3 ≈ 10.67 units². The curve is above the axis on the whole interval, so the integral is the area.
- Below the axis. ∫₀² (x² − 4) dx = [x³/3 − 4x]₀² = 8/3 − 8 = −16/3. The integral is negative because the region is under the axis; the area is 16/3. Always sketch first.
- With e and ln. ∫₁e 1/x dx = ln e − ln 1 = 1. ∫₀¹ ex dx = e¹ − e⁰ = e − 1 ≈ 1.718.
- Between two curves. y = x lies above y = x² between x = 0 and x = 1, so the area between them is ∫₀¹ (x − x²) dx = [x²/2 − x³/3]₀¹ = 1/2 − 1/3 = 1/6. Top curve minus bottom curve, always.
Trigonometric functions and discrete random variables
Two things that repeat. A wave repeats in space and time, and once you can shift and stretch it, you can model tides, sound and daylight — then differentiate it, because the derivative of a sine wave is another sine wave. A Bernoulli trial repeats in probability, and counting its successes gives the binomial distribution, with a mean and variance you can write down without a table.
3.1The general sine and cosine: y = a sin(b(x − c)) + d
| Parameter | Controls | In y = 2 sin(2x) + 1 | In y = 3 cos(x − π/2) |
|---|---|---|---|
| a | Amplitude |a|, the height above and below the centre line | 2 | 3 |
| b | Period 2π/b, the distance before it repeats | 2π/2 = π | 2π |
| c | Phase shift: the graph moved c to the right | 0 | π/2 right (which turns cos into sin) |
| d | Vertical shift: the centre line is y = d | 1, so the range is −1 ≤ y ≤ 3 | 0 |
- Maximum and minimum are d + |a| and d − |a|. For y = 2 sin(2x) + 1 they are 3 and −1.
- Solving on a domain. sin x = ½ for 0 ≤ x ≤ 2π: the reference angle is π/6, and sine is positive in the first and second quadrants, so x = π/6 or 5π/6. Check the number of solutions against the number of periods in the domain.
- Modelling. A tide with high water 3 m, low water 1 m and a 12-hour cycle: amplitude 1, centre 2, period 12 so b = 2π/12 = π/6. If high tide is at t = 0, h = cos(πt/6) + 2.
3.2Differentiating and integrating sin and cos
d/dx sin x = cos x and d/dx cos x = −sin x (x in radians — the results are false in degrees).
So ∫ cos x dx = sin x + c and ∫ sin x dx = −cos x + c. Differentiating goes sin → cos → −sin → −cos → sin.
| Function | Derivative (chain rule) | Note |
|---|---|---|
| y = sin(3x) | 3 cos(3x) | Inside derivative 3 comes out the front |
| y = cos(2x) | −2 sin(2x) | The minus from cos, the 2 from the chain |
| y = 3 sin(2x) + 1 | 6 cos(2x) | The + 1 vanishes; 3 × 2 = 6 |
| y = x sin x | sin x + x cos x | Product rule |
| y = ex cos x | ex(cos x − sin x) | Product rule, then factorise |
- Gradient of y = sin x at x = 0 is cos 0 = 1; at x = π/3 it is cos(π/3) = ½; at x = π/2 it is 0 — the crest of the wave.
- ∫₀π/2 cos x dx = [sin x]₀π/2 = sin(π/2) − sin 0 = 1. The area under one quarter-wave of cosine is exactly 1 unit².
- ∫₀π sin x dx = [−cos x]₀π = −cos π + cos 0 = 1 + 1 = 2. One full hump of sine has area 2.
3.3Bernoulli trials and the binomial distribution
A Bernoulli trial has exactly two outcomes: success with probability p, failure with probability 1 − p. Its mean is p and its variance is p(1 − p). Count the successes in n independent Bernoulli trials and you get a binomial random variable, X ~ Bin(n, p).
P(X = k) = nCk pk (1 − p)n−k, E(X) = np, Var(X) = np(1 − p), so the standard deviation is √[np(1 − p)].
| Worked: a machine produces faulty parts with probability 0.1; a box holds 8. X ~ Bin(8, 0.1) | Calculation | Result |
|---|---|---|
| P(no faulty parts) | 0.9⁸ | 0.430 |
| P(exactly 2 faulty) | ⁸C₂ × 0.1² × 0.9⁶ = 28 × 0.01 × 0.531441 | 0.149 |
| P(at least 1 faulty) | 1 − P(X = 0) = 1 − 0.430 | 0.570 |
| Mean | np = 8 × 0.1 | 0.8 faulty parts per box |
| Variance and SD | np(1 − p) = 8 × 0.1 × 0.9 = 0.72; √0.72 | Var 0.72, SD 0.849 |
- «At least one» is always the complement. 1 − P(none). Never add P(1) + P(2) + … + P(8) by hand.
- A guessing test. Ten multiple-choice questions with four options, guessed at random: X ~ Bin(10, 0.25), E(X) = 2.5 correct, Var(X) = 10 × 0.25 × 0.75 = 1.875. Guessing gets you a quarter, on average, and no more.
- Bin(4, 0.5) in full: P(0) = 1/16, P(1) = 4/16, P(2) = 6/16, P(3) = 4/16, P(4) = 1/16 — the row of Pascal’s triangle divided by 2⁴. Symmetric because p = 0.5; skewed whenever p is not.
- On Paper 2 the calculator’s binomial functions do the arithmetic; your marks are for writing X ~ Bin(8, 0.1), the probability statement, and the answer in context.
Continuous random variables and inference
Heights, times and masses do not come in whole numbers, so their probabilities cannot be listed — they have to be areas under a curve, which is exactly what you just learned to compute. The most important such curve is the normal distribution. The last step of the course turns it around: from one sample, how confident can you be about the whole population?
4.1Probability density functions
A continuous random variable X has a probability density function f(x) with two rules: f(x) ≥ 0 everywhere, and the total area under it is 1. Probabilities are areas: P(a ≤ X ≤ b) = ∫ab f(x) dx, and P(X = one exact value) is 0.
| Worked: f(x) = kx for 0 ≤ x ≤ 2, and 0 elsewhere | Working | Result |
|---|---|---|
| Find k | ∫₀² kx dx = [kx²/2]₀² = 2k = 1 | k = ½ |
| P(X ≤ 1) | ∫₀¹ x/2 dx = [x²/4]₀¹ | ¼ |
| Mean E(X) = ∫ x f(x) dx | ∫₀² x²/2 dx = [x³/6]₀² = 8/6 | 4/3 ≈ 1.33 |
| Median m | ∫₀m x/2 dx = m²/4 = ½ | m = √2 ≈ 1.41 |
4.2The normal distribution and z-scores
The normal distribution X ~ N(μ, σ²) is the bell-shaped density that measurements cluster into: symmetric about the mean μ, with the standard deviation σ setting how wide the bell is. Any normal value is converted to a z-score by z = (x − μ) ÷ σ: the number of standard deviations above (or below) the mean.
| The 68–95–99.7 rule | Interval | For heights with μ = 170 cm, σ = 8 cm |
|---|---|---|
| About 68% of values lie within | μ ± 1σ | 162 to 178 cm |
| About 95% lie within | μ ± 2σ | 154 to 186 cm — so 2.5% are above 186 |
| About 99.7% lie within | μ ± 3σ | 146 to 194 cm — only 0.15% are above 194 |
- A z-score. A height of 182 cm is z = (182 − 170) ÷ 8 = 1.5: one and a half standard deviations above the mean. The calculator gives P(Z < 1.5) = 0.9332, so about 93% of people are shorter.
- Comparing across scales. A mark of 75 in Maths (μ = 65, σ = 8) has z = 1.25; a mark of 70 in English (μ = 60, σ = 10) has z = 1. The Maths result is the stronger one, even though 70 out of 100 and 75 out of 100 look similar.
- Working backwards. The tallest 10% start at z = 1.2816, so x = 170 + 1.2816 × 8 = 180.3 cm. Inverse-normal on the calculator; the mark is for the setup x = μ + zσ.
4.3Sample proportions
Take a random sample of n people and let X be the number with some property. The sample proportion is p̂ = X ÷ n. It varies from sample to sample, but predictably:
| Fact about p̂ | Formula | Worked: p = 0.4, n = 100 |
|---|---|---|
| Its mean is the true proportion | E(p̂) = p | 0.4 |
| Its standard deviation shrinks with n | SD(p̂) = √[p(1 − p) ÷ n] | √(0.24 ÷ 100) = 0.049 |
| Its shape is approximately normal for large n | p̂ ≈ N(p, p(1 − p)/n) | About 95% of samples give p̂ between 0.30 and 0.50 |
| Four times the sample halves the spread | √(1/4) = 1/2 | n = 400 gives SD 0.0245 |
4.4A confidence interval for a proportion
p̂ ± z × √[p̂(1 − p̂) ÷ n], with z = 1.645 for 90% confidence, 1.96 for 95%, and 2.576 for 99%. The part after the ± is the margin of error.
Problem. In a random sample of 400 students, 140 say they walk to school. Find a 95% confidence interval for the proportion of all students who walk.
1. Sample proportion. p̂ = 140 ÷ 400 = 0.35.
2. Standard error. √(0.35 × 0.65 ÷ 400) = √0.00056875 = 0.02385.
3. Margin of error. 1.96 × 0.02385 = 0.0467.
4. Interval. 0.35 ± 0.0467, so (0.303, 0.397).
5. Interpret. We are 95% confident that between 30.3% and 39.7% of all students walk to school. The method captures the true proportion in 95% of samples; this particular interval either does or does not, and we cannot know which.
- Wider or narrower? A 99% interval is wider (z = 2.576, margin 0.0614); a 90% interval is narrower (z = 1.645, margin 0.0392). More confidence costs precision.
- Halving the margin needs four times the sample: with n = 1600 the margin is 1.96 × √(0.2275 ÷ 1600) = 0.0234.
- Does it support a claim? If the principal claimed «40% of students walk», 0.40 lies outside (0.303, 0.397), so the sample gives evidence against the claim at the 95% level. If the claim were 35%, it sits inside and the sample is consistent with it.
«There is a 95% probability that p is in (0.303, 0.397)» is wrong: p is a fixed number, not a random one. The randomness is in the sample. Say «95% confident», and, if asked to explain, say that 95% of intervals built this way contain the true proportion.
The maths of decisions, senior edition.
Units 3 and 4 take the Year 11 tools and point them at bigger questions. Does one variable really predict another, and by how much? What is a business’s sales trend once you strip out Christmas? What will a loan actually cost, and how long will a retirement fund last? And when a project has twenty tasks, which ones must not slip? Every topic here is examined externally, and every answer is a number with a sentence attached.
The mapSeven QCAA topics, four units here
- Unit 3 — Bivariate data analysis and time series. Scatter plots, Pearson’s r, the least-squares line, residuals, interpolation against extrapolation; then trend, seasonality, moving averages and seasonal indices.
- Unit 3 — Growth and decay in sequences, and Earth geometry. Arithmetic and geometric sequences written as recurrence relations, growth and decay models, latitude and longitude, distance along a meridian, and time-zone arithmetic with UTC.
- Unit 4 — Loans, investments and annuities. Compound interest as a recurrence, effective against nominal rates, reducing-balance loans, annuities and perpetuities, all worked line by line.
- Unit 4 — Graphs and networks, and decision mathematics. Network vocabulary, Euler and Hamiltonian paths, minimum spanning trees by Prim’s algorithm, shortest paths by Dijkstra’s method, critical path analysis and maximum flow.
IA1, a problem-solving and modelling task (20%). IA2, an examination (15%). IA3, an examination (15%). Then the external examination (50%), set and marked by QCAA, in two papers with a calculator allowed in both. The marks are for choosing a model, calculating accurately, and interpreting the answer in context — «the loan is repaid in 37 months, costing $966.80 in interest», not a bare number.
Extrapolating a regression line far beyond the data and reporting the nonsense it produces; rounding a seasonal index or an interest rate before the final step; and quoting a network answer (a total distance, a project duration) without naming the path or the activities that produce it.
Bivariate data analysis and time series
Two variables, one question: does knowing one help you predict the other? A scatter plot shows the answer, Pearson’s r measures it, and the least-squares line turns it into a prediction. Then the same idea runs along time: a series of sales figures has a trend hiding under its seasonal ups and downs, and there is a method for finding it.
1.1Scatter plots and the least-squares line
The explanatory variable goes on the horizontal axis and the response variable on the vertical. Eight students recorded their weekly study hours (x) and their test score (y):
| Hours, x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Score, y | 57 | 55 | 59 | 69 | 73 | 71 | 75 | 85 |
| Predicted ŷ = 4x + 50 | 54 | 58 | 62 | 66 | 70 | 74 | 78 | 82 |
| Residual y − ŷ | +3 | −3 | −3 | +3 | +3 | −3 | −3 | +3 |
1.2Pearson’s r and the coefficient of determination
| Value of r | Strength | What the scatter plot looks like |
|---|---|---|
| |r| from 0.75 to 1 | Strong | Points hug a straight line |
| |r| from 0.5 to 0.75 | Moderate | A clear band with some scatter |
| |r| from 0.25 to 0.5 | Weak | A tendency you can only just see |
| |r| below 0.25 | None | A cloud; knowing x tells you nothing about y |
| Sign of r | Direction | Positive: y rises with x. Negative: y falls as x rises |
- Describe in four words. The plot above is strong, positive, linear, no outliers; r = 0.95 puts a number on «strong».
- The coefficient of determination r² = 0.95² = 0.90 means 90% of the variation in test score is explained by the variation in study hours. The other 10% is everything else — sleep, prior knowledge, luck. That sentence, in that form, is what the marker wants.
- r only measures linear association. A perfect curve can have r near 0. Always look at the plot before trusting the number.
- Correlation is still not causation — the Year 11 warning applies with more force now that you can compute a precise r. A strong r between two variables can be the work of a third.
1.3Using the line: interpret, interpolate, extrapolate
- Interpret the gradient in context. b = 4 means: each extra hour of weekly study is associated with a score 4 marks higher, on average. The intercept 50 is the predicted score with no study at all.
- Interpolation — predicting inside the data range — is reliable. At x = 5.5 hours, ŷ = 4(5.5) + 50 = 72.
- Extrapolation — predicting outside the range — is not. At x = 20 hours the line gives ŷ = 130, a score above 100%. The model is only known to hold between 1 and 8 hours; say so.
1.4Time series: the four components
| Component | Meaning | Example |
|---|---|---|
| Trend | The long-term direction once the wobbles are removed | A shop’s sales growing year on year |
| Seasonal | A pattern that repeats over a fixed period — a year, a week, a day | Ice-cream sales peaking every summer |
| Cyclical | Rises and falls over longer, irregular periods | A building boom followed by a slump |
| Irregular | Random one-off effects with no pattern | A flood closing the shop for a fortnight |
Quarterly sales (in $000) for a surf shop over two years:
| Quarter | Q1 24 | Q2 24 | Q3 24 | Q4 24 | Q1 25 | Q2 25 | Q3 25 | Q4 25 |
|---|---|---|---|---|---|---|---|---|
| Sales | 160 | 200 | 280 | 160 | 190 | 260 | 340 | 210 |
| 4-point moving average | 200 | 207.5 | 222.5 | 237.5 | 250 | |||
| Centred moving average | 203.75 | 215 | 230 | 243.75 |
- Why 4 points? One full year of quarters. Averaging a whole cycle cancels the seasonal pattern and leaves the trend. The first 4-point average is (160 + 200 + 280 + 160) ÷ 4 = 200; the next slides one quarter along: (200 + 280 + 160 + 190) ÷ 4 = 207.5.
- Why centre? An average of four values sits between the second and third of them — between quarters, not on one. Averaging neighbouring 4-point averages puts it back on a quarter: (200 + 207.5) ÷ 2 = 203.75, lined up with Q3 2024.
- Read the trend. 203.75, 215, 230, 243.75: rising by roughly 13 a quarter. That is the growth the seasonal swings were hiding.
1.5Seasonal indices and deseasonalising
A seasonal index says how a season compares with the average season: an index of 1.38 means «38% above a typical quarter». The indices for one cycle always average to 1 (so four quarterly indices add to 4).
| Q1 | Q2 | Q3 | Q4 | Yearly mean | |
|---|---|---|---|---|---|
| 2024 sales ÷ 200 | 0.80 | 1.00 | 1.40 | 0.80 | (160 + 200 + 280 + 160) ÷ 4 = 200 |
| 2025 sales ÷ 250 | 0.76 | 1.04 | 1.36 | 0.84 | (190 + 260 + 340 + 210) ÷ 4 = 250 |
| Seasonal index (average) | 0.78 | 1.02 | 1.38 | 0.82 | Sum = 4.00 ✓ |
- Deseasonalise by dividing: Q3 2025 sales of 340 ÷ 1.38 = 246.4. Q1 2025: 190 ÷ 0.78 = 243.6. Once the season is stripped out, the two quarters are almost the same — the summer «boom» was just the season.
- Re-seasonalise by multiplying. If the trend predicts 260 for Q3 2026, the actual forecast is 260 × 1.38 = 358.8, about $359,000.
- Interpret an index in a sentence. «Q1 sales are typically 22% below the quarterly average» (index 0.78), or «Q3 sales are typically 38% above it» (index 1.38).
Growth and decay in sequences; Earth geometry and time zones
A recurrence relation is a rule for getting the next term from the one before — add the same amount, or multiply by the same factor. Those two rules describe simple interest and compound interest, straight-line and declining-balance depreciation, and every population model you will meet. Then the unit turns to the globe itself: where you are, how far apart two places are, and what time it is there.
2.1Arithmetic sequences: add the same amount
| Recurrence relation | Explicit rule | Example: 5, 9, 13, 17, … | |
|---|---|---|---|
| Form | tn+1 = tn + d, with t₁ = a | tn = a + (n − 1)d | tn+1 = tn + 4, t₁ = 5 |
| Common difference d | The fixed amount added each step | Negative d means decay | d = 9 − 5 = 4 |
| A far term | Would take 19 steps | One line | t₂₀ = 5 + 19 × 4 = 81 |
| Graph | Points on a straight line of gradient d — linear growth | ||
- Simple interest is arithmetic. $2,000 at 5% p.a. simple interest earns $100 every year: tn+1 = tn + 100, t₀ = 2000, giving 2000, 2100, 2200, 2300, …
- Straight-line depreciation is arithmetic with d < 0. A $28,000 car losing $3,500 a year: tn+1 = tn − 3500.
2.2Geometric sequences: multiply by the same factor
| Recurrence relation | Explicit rule | Example: 3, 6, 12, 24, … | |
|---|---|---|---|
| Form | tn+1 = r × tn, with t₁ = a | tn = a × rn−1 | tn+1 = 2tn, t₁ = 3 |
| Common ratio r | The fixed multiplier each step | Growth if r > 1, decay if 0 < r < 1 | r = 6 ÷ 3 = 2 |
| A far term | Would take 9 doublings | One line | t₁₀ = 3 × 2⁹ = 1536 |
| Graph | Points on an exponential curve — it outruns every arithmetic sequence eventually | ||
- Compound interest is geometric. $5,000 at 4% p.a. compounded yearly: tn+1 = 1.04 tn, t₀ = 5000. After 3 years, 5000 × 1.04³ = $5,624.32.
- Population growth. A town of 12,000 growing 2.5% a year: tn+1 = 1.025 tn. After 5 years, 12000 × 1.025⁵ = 13,577 people (nearest whole).
- Decay. Declining-balance depreciation at 15% is tn+1 = 0.85 tn; a drug leaving the body at 20% an hour is tn+1 = 0.8 tn. The ratio is 1 minus the percentage.
- Which model? Ask whether the change each step is a fixed amount (arithmetic) or a fixed percentage (geometric). Interest of $100 a year is arithmetic; interest of 4% a year is geometric.
2.3Latitude, longitude and distance along a meridian
Latitude measures degrees north or south of the equator (0° to 90°); longitude measures degrees east or west of the prime meridian through Greenwich (0° to 180°). A great circle is any circle on the sphere with the same centre as the Earth: the equator and every meridian are great circles, and the shortest route between two points always follows one.
Two places on the same line of longitude are separated by an angle equal to the difference in their latitudes. With R = 6,371 km, distance = (angle ÷ 360) × 2πR, which works out to 111.2 km for every degree. Two towns at 16°S and 27°S on the same meridian are 11° apart: 11 × 111.2 = 1,223 km. Across the equator, 10°N to 25°S is 35° apart: 3,892 km.
2.4Time zones and UTC
The Earth turns 360° in 24 hours, so 15° of longitude is one hour. Times are quoted as offsets from UTC (Coordinated Universal Time, the time at 0° longitude): places east of Greenwich are ahead, places west are behind.
| City | Zone | When it is 15:00 in Brisbane | Working |
|---|---|---|---|
| Brisbane | UTC+10 | 15:00 | Start here. UTC = 15:00 − 10 h = 05:00 |
| Tokyo | UTC+9 | 14:00 | 05:00 + 9 h, one hour behind Brisbane |
| London (winter) | UTC+0 | 05:00 | The same as UTC |
| New York (winter) | UTC−5 | 00:00, same day | 05:00 − 5 h = midnight |
| Perth | UTC+8 | 13:00 | Two hours behind Brisbane, in the same country |
- From longitude. Two places at 150°E and 30°E differ by 120°, so their solar times differ by 120 ÷ 15 = 8 hours. Real zones follow borders, so always use the stated UTC offset when one is given.
- Flight arrivals. A flight leaves Brisbane (UTC+10) at 10:00 and takes 8 hours to Tokyo (UTC+9). It lands at 18:00 Brisbane time, which is 17:00 in Tokyo. Convert at the end, not the start.
- Daylight saving shifts a zone by +1 in summer: Sydney becomes UTC+11 while Brisbane stays at UTC+10. Questions will tell you when it applies.
Loans, investments and annuities
Every loan, savings plan and pension is the same machine: a balance that grows by a percentage each period and then has a fixed payment added or taken away. Write that as a recurrence relation and you can follow any of them month by month — and see exactly why a car loan costs more than the sticker price.
3.1Compound interest as a recurrence; nominal against effective rates
With k compounding periods a year at a nominal rate r, the rate per period is i = r ÷ k and the balance follows Vn+1 = Vn(1 + i). The nominal rate is the advertised annual figure; the effective annual rate is what you actually earn or pay once compounding within the year is counted: (1 + r/k)k − 1.
| Nominal 6% p.a., compounded… | Rate per period | Effective annual rate |
|---|---|---|
| Yearly (k = 1) | 6% | 6.000% |
| Quarterly (k = 4) | 1.5% | 1.015⁴ − 1 = 6.136% |
| Monthly (k = 12) | 0.5% | 1.005¹² − 1 = 6.168% |
| Daily (k = 365) | 0.01644% | 6.183% |
«8% p.a. compounded quarterly» is really 1.02⁴ − 1 = 8.24% a year. A lender quoting 8.2% compounded yearly is cheaper, even though the number looks bigger.
3.2Reducing-balance loans
A reducing-balance loan charges interest on the balance still owing, then subtracts the repayment: Vn+1 = Vn(1 + i) − R. A $10,000 loan at 6% p.a. compounded monthly (i = 0.005) with repayments of $300 a month:
| Month | Opening balance | Interest at 0.5% | Repayment | Closing balance |
|---|---|---|---|---|
| 1 | $10,000.00 | $50.00 | $300.00 | $9,750.00 |
| 2 | $9,750.00 | $48.75 | $300.00 | $9,498.75 |
| 3 | $9,498.75 | $47.49 | $300.00 | $9,246.24 |
- Recurrence. V₀ = 10000, Vn+1 = 1.005 Vn − 300. Check: 1.005 × 10000 − 300 = 9750 ✓
- Interest falls every month ($50.00, $48.75, $47.49) because the balance falls, so more of each $300 pays off principal.
- How long, how much? Run the recurrence on (a spreadsheet or the calculator’s finance solver): the balance reaches zero during month 37, and the total interest paid is about $967. Paying $400 a month instead clears it in 27 months and saves roughly $270 of interest.
- The trap of a small repayment. If R were only $50, it would exactly cover the first month’s interest and the balance would never fall — an interest-only loan, forever.
3.3Annuities: money in, money out
| Savings annuity (regular deposits) | Retirement annuity (regular withdrawals) | |
|---|---|---|
| Recurrence | An+1 = An(1 + i) + D | An+1 = An(1 + i) − W |
| Example | $500 a month at 6% p.a. monthly, from $0 | $100,000 at 6% p.a. monthly, drawing $1,000 a month |
| Month 1 | 0 × 1.005 + 500 = $500.00 | 100000 × 1.005 − 1000 = $99,500.00 |
| Month 2 | 500 × 1.005 + 500 = $1,002.50 | 99500 × 1.005 − 1000 = $98,997.50 |
| Month 3 | 1002.50 × 1.005 + 500 = $1,507.51 | 98997.50 × 1.005 − 1000 = $98,492.49 |
| Long run | Grows faster and faster: the deposits earn interest on interest | Falls faster and faster: the $500 of interest covers only half the withdrawal |
If the withdrawal equals the interest earned each period, the balance never changes and the payments continue forever. Payment = balance × rate per period. $200,000 invested at 5% p.a. paid yearly funds a perpetuity of 200000 × 0.05 = $10,000 a year. $500,000 at 4% p.a. paid monthly funds 500000 × 0.04 ÷ 12 = $1,666.67 a month. Withdraw a cent more and the balance starts to shrink — slowly, then quickly.
The recurrence relation written out with its starting value; the rate per period stated (0.5%, not 6%); at least one step shown by hand to prove the model; then technology for the long run; then the answer in dollars and cents, in a sentence, with the assumption («assuming the rate does not change») named.
Graphs and networks, and decision mathematics
Year 11 taught you to read a network. Year 12 teaches you to solve one: the cheapest way to connect everything, the shortest route between two points, the tasks a project cannot afford to delay, and the most that can flow through a system of pipes or roads. Each has an algorithm — a recipe that always works — and each is done by hand in the exam.
4.1One network, four questions
The network below has six vertices and nine weighted edges (distances in km). Everything in the next three sections is worked on it.
4.2Euler and Hamiltonian: edges once, or vertices once
| Euler trail / circuit | Hamiltonian path / cycle | |
|---|---|---|
| Uses | Every edge exactly once (vertices may repeat) | Every vertex exactly once (edges may be skipped) |
| Real job | A garbage truck covering every street; a snow plough | A courier visiting every house; a travelling salesperson |
| Test | Circuit: every vertex has even degree. Trail (open): exactly two odd vertices, and it must start at one and end at the other | No simple test — find one by inspection, or explain why none exists |
| In Figure 4.1 | C and E are the only odd vertices, so an Euler trail from C to E exists (no circuit) | A–B–E–F–D–C–A is a Hamiltonian cycle: six vertices, back to the start |
- Euler’s formula for planar graphs: v − e + f = 2, counting the outside region as a face. Figure 4.1 has 6 vertices and 9 edges, so 6 − 9 + f = 2 gives f = 5: the four triangles A-B-C, B-C-D, B-D-E, D-E-F, plus the outside.
- Making a network traversable. Adding one edge between the two odd vertices (C–E) would make every degree even and create an Euler circuit — the one-edge fix examiners like to ask about.
4.3Prim’s algorithm: the minimum spanning tree
A spanning tree connects every vertex with no cycles; the minimum spanning tree is the one with the smallest total weight — the cheapest cable, pipe or road layout that reaches everywhere. Prim’s algorithm: start at any vertex, then repeatedly add the cheapest edge that joins a vertex already in the tree to one that is not.
| Step | Vertices in the tree | Cheapest edge out | Running total |
|---|---|---|---|
| 1 | A | A–C (2) beats A–B (4) | 2 |
| 2 | A, C | C–B (1) | 3 |
| 3 | A, C, B | B–D (6) beats B–E (7) and C–D (8); A–B is skipped — both ends already in | 9 |
| 4 | A, C, B, D | D–E (2) | 11 |
| 5 | A, C, B, D, E | E–F (3) beats D–F (6) | 14 |
4.4Dijkstra’s method: the shortest path
Shortest path from A to F. Label every vertex with the best distance found so far, settle the smallest unsettled label, and update its neighbours. Record where each best distance came from, so the path can be read backwards at the end.
| Settle | B | C | D | E | F |
|---|---|---|---|---|---|
| A (0) | 4 via A | 2 via A | — | — | — |
| C (2) | 3 via C (2 + 1 beats 4) | settled | 10 via C | — | — |
| B (3) | settled | 9 via B (3 + 6 beats 10) | 10 via B | — | |
| D (9) | settled | 10 via B (9 + 2 = 11 does not beat 10) | 15 via D | ||
| E (10) | settled | 13 via E (10 + 3 beats 15) |
Read it backwards: F came via E, E via B, B via C, C via A. The shortest path is A–C–B–E–F, 13 km. Notice it uses B–E, which the minimum spanning tree left out: the cheapest way to connect everything is not the same question as the shortest way between two places.
4.5Critical path analysis
A project is a set of activities with durations and prerequisites. Draw it as an activity network, then scan forward for the earliest each activity can start and backward for the latest it may start without delaying the finish. Activities with no slack form the critical path, whose length is the shortest possible project time.
| Activity | Days | Must follow | Earliest start | Latest start | Float = latest − earliest |
|---|---|---|---|---|---|
| A | 3 | — | 0 | 1 | 1 |
| B | 2 | — | 0 | 0 | 0 — critical |
| C | 4 | A | 3 | 4 | 1 |
| D | 6 | B | 2 | 2 | 0 — critical |
| E | 2 | C and D | 8 | 8 | 0 — critical |
| F | 3 | B | 2 | 7 | 5 |
4.6Maximum flow and the minimum cut
In a flow network each edge has a capacity and the question is how much can travel from the source S to the sink T per unit time. A cut is any line that separates S from T; its capacity is the total of the edges it crosses in the direction from S to T. The maximum flow equals the capacity of the minimum cut.
Two texts, one idea, and a clock.
Year 11 taught you to prove how a single text works. Year 12 raises the stakes three ways: you compare two texts on one concept, you write literature instead of only reading it, and you do the analysis against a clock in the external exam that closes the course. Four topics across QCAA Units 3 and 4.
The mapFour topics, two units
- Unit 3, Topic 1 — Conversations about concepts in texts. How two texts represent one shared concept; the comparative analytical essay: thesis, topic sentences, integrated evidence and comparative signposting; the IA1 essay under exam conditions.
- Unit 3, Topic 2 — Creative responses to literary texts. Transforming a text: a new perspective, a prequel, a shift of genre; voice and narrative choices; intertextuality as a tool; the IA2 imaginative written response.
- Unit 4, Topic 1 — Creative responses to a studied text. Sustained close reading of one short story: symbolism, characterisation, structure and aesthetic features; the IA3 imaginative response that grows out of that reading.
- Unit 4, Topic 2 — Critical responses and the external exam. The analytical essay on a studied literary text: the ten-minute plan, a thesis-driven argument, embedded evidence, evaluating how features shape meaning, timed writing, and what markers complain about.
| Assessment | What it is | Weight |
|---|---|---|
| IA1 — Examination | Analytical essay comparing two texts on a shared concept, written under exam conditions | 25% |
| IA2 — Extended response | Imaginative written response transforming a literary text | 25% |
| IA3 — Extended response | Imaginative written response to the studied literary text | 25% |
| External examination | Analytical essay on a studied literary text, set and marked by the QCAA | 25% |
A B-grade comparison says two texts are similar or different. An A-grade comparison says what the difference reveals: «where the first story treats the house as a body that can be healed, the second treats it as a shell already emptied — so the same flood reads as an injury in one and a verdict in the other». Comparison is not a list of matches. It is an argument about why the two writers made opposite choices.
The seesaw essay — a paragraph on Text A, a paragraph on Text B, and a one-line «in conclusion they are similar» that does no comparing at all. The costume transformation — an imaginative response that changes a character’s name and nothing else, so the marker cannot see any choice being made. The unplanned exam essay — writing from the first minute, discovering the thesis in paragraph three, and running out of time before the conclusion that would have stated it.
Conversations about concepts in texts
Put two texts on the same table and they start talking to each other. Both may be about belonging, or power, or grief — but they will not agree, and the disagreement is where your essay lives.
1.1What a concept is, and what it is not
- A concept is an abstract idea that a text explores: identity, power, belonging, memory, freedom, justice, loss. It is not the plot, and it is not the theme statement. «Belonging» is a concept; «the story shows that belonging is fragile» is one text’s position on that concept.
- Each text builds a representation of the concept — a version of it, made through selection, emphasis and language. Two texts on belonging construct two different belongings.
- The conversation is the relationship between those two representations. Texts can agree, extend, complicate, or flatly contradict one another — and they do it without knowing the other text exists, which is why you have to make the conversation happen.
- Your job in this topic is to state what each text says about the concept, prove it from the language, and then explain what the two positions together reveal that neither shows alone.
| Concept | Questions that open it up | Where the two texts might differ |
|---|---|---|
| Identity | Is it given, chosen, or imposed? Fixed or shifting? Seen from inside or outside? | One text treats identity as something inherited; the other as something performed |
| Power | Who holds it, how is it exercised, and what does it cost the person who holds it? | One shows power as force; the other shows it as the ability to define what counts as normal |
| Belonging | To a place, a group, a family, a past? What is the price of admission? | One makes belonging a comfort; the other makes it a cage |
| Memory | Reliable or reconstructed? Chosen or unavoidable? Individual or shared? | One trusts memory as evidence; the other shows it rewriting itself |
1.2Structuring a comparative essay
- Thesis. One sentence that names the concept, names both texts’ positions on it, and states what the comparison reveals. It must be arguable: «both texts explore belonging» is a topic; «both texts treat belonging as something that must be paid for, but only the second admits the price can be too high» is a thesis.
- Topic sentences that compare. Each opens with an idea and holds both texts in one sentence: «Both writers locate belonging in a building, yet the buildings do opposite work.» A topic sentence that mentions only one text has already lost the paragraph.
- Integrated evidence. Short quotations from both texts, embedded, each followed by what the language does. Aim for two or three quotations per text per paragraph, not one long one.
- Comparative signposting. The connecting words that keep the comparison visible: similarly, likewise, both, whereas, by contrast, conversely, unlike, just as… so too. Use them at the joints where you move between texts.
- The reveal. End each paragraph with what the two positions together show about the concept. This is the sentence markers look for, and the one most students leave out.
1.3Textual features that carry a representation
A representation is built out of features. When you compare two texts you are really comparing the choices that built them, so you need to name those choices at the right level.
| Feature | What to compare | Comparative sentence, as a model |
|---|---|---|
| Point of view | Who narrates, how close we are allowed, what they cannot see | Where the first story keeps us inside the grandson’s head, the second holds the family at a distance, so belonging feels lived in one and observed in the other |
| Setting | How place is made to mean something; what it stands for | Both texts set belonging in a house under threat, but one house is a body and the other is a shell |
| Imagery and symbol | The comparisons each text reaches for, and what they smuggle in | Water is an invited guest in one text and a verdict in the other |
| Structure | Order, framing, repetition, where the text chooses to end | One text ends at the moment of loss; the other ends a year later, which turns loss into something survivable |
| Tone and register | The attitude each text takes; how formal, how ironic | The dry humour of the first refuses the grief the second insists on |
| Dialogue and silence | What characters say, what they avoid, who never speaks | In both, the people who belong least are the ones given the fewest lines |
You will have studied two texts in class. The paper gives you a question about a concept — not a question you have seen — and you write a comparative analytical essay under exam conditions. The marker is checking three things at once: that you know both texts well enough to quote from memory and accurately, that you organise an argument that compares in every paragraph, and that you control the analytical register — present tense, third person, precise naming of features. Prepare six to eight quotations per text that can serve more than one concept, and learn them exactly.
A signpost tells the reader whether the next sentence confirms or complicates what came before. Overuse makes an essay sound mechanical; absence makes it a seesaw. The test: read your paragraph and cover the signposts. If the reader can no longer tell where one text ends and the other begins, the signposts were doing real work. If nothing changes, they were padding.
Creative responses to literary texts
A transformation takes a text you have studied and makes a new one from it: the same world seen by a different pair of eyes, the story before the story, or the story moved into another form. It is the most enjoyable task in the course and the easiest to do badly.
2.1Three kinds of transformation
| Transformation | What it keeps | What it changes | The question it can answer |
|---|---|---|---|
| Shift of perspective | Events, setting, other characters | Who narrates; what is known and what is hidden | What did the original refuse to show us? |
| Prequel | The world and the people | The time; nothing from the original has happened yet | How did they become the people we met? |
| Sequel | The world and the consequences | The time; the original’s ending is now the past | What did the ending actually cost? |
| Genre or form shift | The core situation | The rules the text obeys — a monologue, a poem, a letter, a news report | What does this story look like under different rules? |
2.2Voice: the choice everything else depends on
- Voice is the personality of the narration — diction, sentence rhythm, what the narrator notices and what they refuse to say. A transformation succeeds or fails on whether the new voice is distinct from the original and consistent with itself.
- Build a voice from three decisions: vocabulary (a fisherman and a solicitor do not reach for the same words), sentence habit (short and blunt, or long and qualifying) and attention (what this person cannot help noticing).
- A first-person narrator gives intimacy and a limit: they can only tell what they know, and they can lie. A close third-person narrator gives you a character’s interior while keeping a narrator’s freedom to step back.
- An unreliable narrator is not a confused one. The reader must be able to see, through the narration, what the narrator cannot — which means you plant the evidence they misread.
- Test the voice by removing the names. If two paragraphs by two characters read the same with the names gone, you have written one voice twice.
2.3Narrative choices, deliberately made
| Choice | Options | What each does |
|---|---|---|
| Where to begin | Before the trouble; in the middle of it; after it, looking back | Beginning in the middle creates urgency; beginning after creates reflection and irony |
| Tense | Past; present | Present tense feels immediate and denies the narrator hindsight; past tense allows the narrator to know how it ends |
| Time | Chronological; flashback; a frame story; a single scene | A single scene concentrates meaning; a frame lets two times comment on each other |
| Distance | Inside one head; hovering above; reporting only what can be seen | Distance controls sympathy: the closer we are, the harder it is to judge |
| Ending | Resolved; open; circular (returning to the opening image) | A circular ending makes the reader measure how far the character has come — or not |
2.4Intertextuality as a tool, and the IA2 task
In Year 11 you identified intertextuality in other people’s writing. Now you use it. Your transformation is in conversation with the source, and the reader who knows the source should be able to hear both voices at once.
- Echo deliberately. Repeat an image, a phrase or a structural move from the source and change what it means. A clock that stops in the original and starts in yours is an argument, not a coincidence.
- Fill a silence. The character who never spoke, the year the original skipped, the room we never entered. The best transformations grow from what the source left out.
- Keep the concept. If the source is about belonging, your transformation should still be about belonging — approached from a position the source could not reach.
- Show the seams on purpose. A transformation that could be read as an unrelated story has failed the task, however good it is. The connection must be legible.
An extended piece of imaginative writing that transforms a literary text studied in class, with a short statement of intent explaining the choices you made. The criteria reward three things: that the new text engages with the source (concept, characters, world) rather than just borrowing a name; that the narrative and language choices are deliberate and consistent; and that the writing is controlled at the level of sentence, paragraph and structure. The statement of intent is where you prove the choices were choices: «I moved the story into present tense so the narrator cannot know the flood is coming, which the original narrator did.»
Changing the narrator’s name and retelling the same events in the same order with the same feelings is not a transformation. A shift of perspective must change what the reader knows. If the minor character sees exactly what the original narrator saw, the marker will ask why you bothered.
Close study of one text
Unit 4 asks you to live inside a single literary text for a term: to read it until you know where every image recurs and why the writer stopped where they stopped. The story below was written for this course so that every quotation in this unit is one you can check.
3.1The studied text: The Tide Clock
An original short story, written for this site. Read it twice: once for the story, once for the choices.
i. Morning
The tide clock on Pop’s kitchen wall had stopped at High Water in the year I was born, and nobody had wound it since. «It’s right twice a day,» he said, the first time I asked, «which is more than the weather bureau.» He said it every time after that too, as if the joke were a coin he could keep spending.
I was sixteen that summer and had come to help him pack the house. The council letters had stopped asking. The jetty at the end of his street was missing every third plank now, and the ones that remained had bleached to the grey of driftwood, so that walking out on it felt like stepping along the spine of something that had died a long time ago and was only slowly admitting it.
Pop walked it anyway. Every morning, boots and no line, just to stand at the end.
ii. Noon
We packed the way people argue: politely, and around the actual point. He wrapped forty years of glassware in newspaper from the week he had stopped reading the news. I labelled boxes KITCHEN and SHED and, once, without thinking, HOME, then crossed it out so hard the pen went through.
«The water doesn’t want the house,» he said, when he saw the box. «It just doesn’t know how to want anything else.»
«That’s not how water works, Pop.»
«No,» he agreed, and taped the box shut.
The tide clock stayed on its nail. I had asked, twice, whether it went in KITCHEN. Both times he had answered a different question.
iii. Evening
On the last night the king tide came up the street the way the letters had promised, quietly and without any drama, a dark sheet sliding under the gate as if it had been invited. We watched from the verandah with our feet up on the rail. The jetty was gone entirely; only the posts stood, in a line, like the teeth of a comb.
He took the clock down then. He did not wind it. He turned it over, and on the back, in his own hand, was my mother’s name and the date I was born, and under it, in a newer ink, the date the first letter had come.
«Twice a day,» he said. «Still.»
He gave it to me. And then he went down the steps and stood in the water up to his knees, in the dark, the way he had stood at the end of the jetty every morning, and I understood that he had never once gone out there to fish.
3.2Symbolism: objects that carry the meaning
A symbol is a concrete thing in the text that stands for something larger, and the test of a symbol is that it changes. An object that means the same thing on every page is a prop; one that accumulates meaning as the story moves is doing the story’s work.
| Symbol | First appearance | What it becomes | What it argues |
|---|---|---|---|
| The tide clock | A stopped clock and a repeated joke, «right twice a day» | A record: a birth date on the back, then the date of the first letter, then a gift | Time stopped for Pop at the moment the family was whole; the clock is handed on because the record matters more than the mechanism |
| The jetty | Missing every third plank, «the spine of something that had died» | Gone; only posts «like the teeth of a comb» | Loss happens gradually and then all at once; the body image turns into an object image as the living thing is finished |
| The water | A threat referred to only through letters | A guest: «as if it had been invited» | The flood is not a villain; the story refuses melodrama, and that refusal is the point |
| The boxes | KITCHEN and SHED, the practical labels | HOME, crossed out «so hard the pen went through» | What cannot be packed is the only thing being lost; the violence of the crossing-out is the one moment of open feeling |
3.3Characterisation without statement
- The story never says Pop is grieving. It shows him walking a jetty with no fishing line, answering a different question when asked about the clock, and wrapping glass in newspaper from «the week he had stopped reading the news». Characterisation by action and evasion, not by adjective.
- The narrator is characterised by what she notices and how she jokes: «That’s not how water works, Pop» is affection disguised as correction. Her one unguarded moment is the pen going through the cardboard, and she reports it in the same flat tone as everything else — which is how we know it matters.
- The dialogue is short and evasive: nobody says the true thing. «No,» he agreed, and taped the box shut. The tape does the talking.
- The relationship is built from a repeated joke. A joke told once is a joke; told every time, «as if the joke were a coin he could keep spending», it becomes a way of not saying something — and the simile tells us the currency is running out.
3.4Structure and aesthetic features
| Feature | Where | What it does |
|---|---|---|
| Three-part structure | Morning, Noon, Evening | One day stands for one life; the structure is a tide, rising to the flood the reader has been told to expect |
| Circular ending | The jetty walk in part i returns in part iii | Pop standing in the water «the way he had stood at the end of the jetty» lets the narrator, and the reader, reread the whole story |
| Withheld information | The mother’s name, on the back of the clock | The absence the story has been circling is named once, late, and never explained — the reader supplies the grief |
| Understatement | The flood arrives «quietly and without any drama» | Refusing the expected climax makes the quiet moments — the gift, the knees in the water — carry the weight instead |
| Motif of repetition | «Twice a day» three times | The phrase changes meaning each time: a joke, a habit, and finally «Still» — a refusal to let the record stop |
| Final sentence as revelation | «he had never once gone out there to fish» | Recasts every morning walk as a vigil; the reader’s understanding arrives at the same instant as the narrator’s |
The task is a creative piece that grows out of your close reading — a scene the story withholds (the week the first letter came), a new perspective (Pop’s morning at the end of the jetty), a sequel (the clock on the narrator’s wall, years on). The difference from IA2 is depth: markers expect the piece to use the specific features you have studied — the understatement, the circular structure, the object that changes meaning — and the statement of intent should name them. A response to The Tide Clock that ends in melodrama has misread the text.
The analytical essay, against the clock
The external examination is one analytical essay on a literary text you have studied, written in two hours after fifteen minutes of planning time, and marked by people who have read four hundred essays on the same text. Everything in this topic is about making yours the one they are relieved to read.
4.1Reading the question
- The question names a concept or an aspect (a character, a setting, an idea) and asks how the text represents it or what it invites the reader to think. It is never «describe». Underline the verb and the concept before anything else.
- Most questions contain a proposition you can argue with: «The story presents loss as something that cannot be shared.» You may agree, partly agree, or disagree — but a thesis that qualifies the proposition («only until the final page») is usually stronger than one that simply accepts it.
- The word reader will be in the question or the criteria. Your essay is about what the text does to a reader, and you must say so explicitly, not leave it implied.
4.2The plan, in ten minutes
- Minute 0–2: the question. Circle the concept and the verb. Rewrite the question as a claim you can argue with.
- Minute 2–5: the thesis. Write it in full, as a sentence, on the planning page. If it could be true of any text, it is not a thesis yet.
- Minute 5–9: three ideas, six quotations. Each idea is a way the text builds the representation named in your thesis: one symbol, one structural choice, one feature of voice or characterisation. Under each, two quotations from memory.
- Minute 9–10: the order. Strongest idea last. Draw arrows. Then use the remaining planning time to sharpen the thesis wording.
4.3A model paragraph, annotated
The question: «In The Tide Clock, loss is represented as something that cannot be spoken. Discuss.» The thesis: the story represents loss as unspeakable only until its final page, where an object and an action say what no character could. Here is the second body paragraph, sentence by sentence.
| Sentence | Its job |
|---|---|
| The story’s refusal to speak loss aloud is built most clearly into its dialogue, which is shaped so that every true statement is deflected. | Topic sentence. Names the idea (dialogue), holds the thesis word (loss), and makes a claim the paragraph must prove. |
| When the narrator asks about the tide clock, Pop «answered a different question», and the narration reports the evasion twice without comment, so that the reader learns the family’s grammar of avoidance faster than the narrator admits to. | Evidence and explanation. Short embedded quotation; the technique (reported evasion, withheld comment) is shown rather than announced; the effect on the reader is stated. |
| The one exchange that approaches the subject, «The water doesn’t want the house», is immediately corrected by the narrator’s «That’s not how water works, Pop», a rebuke that is really tenderness, and Pop’s «No» closes the conversation as firmly as he «taped the box shut». | Second piece of evidence, developed. Two quotations in one sentence, the register of the exchange named (rebuke as tenderness), and the physical action read as a metaphor for the silence. |
| The writer positions the reader to hear loss in the gaps between lines rather than in the lines themselves, which is precisely why the final page, where the clock is handed over without a word, can carry so much. | Link. Returns to the thesis (unspeakable until the end), names the reader, and sets up the next paragraph. |
The highest band asks you to evaluate how features shape meaning — to judge, not only describe. Evaluation sounds like this: «the understatement is the story’s most effective choice, because a flood that arrived with drama would let the reader feel the loss on the story’s behalf; its quietness makes the reader do the feeling.» The signal words are most effective, most significant, more than, precisely because. Use them where you mean them.
4.4The marking criteria, in plain words
| Criterion | What the marker is looking for | What the top band looks like |
|---|---|---|
| Knowledge application | How well you know the text and use that knowledge: accurate, well-chosen evidence; understanding of how features build representations; awareness of the reader | Quotations are exact, brief and chosen because they prove the point; the analysis explains how a feature works, and evaluates its effect; the reader’s position is named |
| Organisation and development | Whether the essay is an argument: a thesis, paragraphs that each prove part of it, in an order that builds, with an introduction and conclusion that frame it | The thesis is arguable and answers the question directly; every topic sentence carries it forward; the conclusion adds a final understanding rather than repeating |
| Textual features | Control of the analytical essay as a genre: present tense, third person, precise terminology, embedded quotation, sentence variety, accurate spelling and punctuation | The register never slips into narrative or opinion; terms are used exactly; quotations sit grammatically inside sentences; the writing is fluent enough to disappear |
4.5What markers complain about
| Complaint | What it looks like | The fix |
|---|---|---|
| Answering a different question | A prepared essay on symbolism, whatever the paper asked | The concept in the question appears in the thesis and in every topic sentence |
| Retelling | «Then Pop takes the clock down and gives it to her.» | Every mention of an event is followed by what the choice does to the reader |
| Feature spotting | «The writer uses a simile. This creates imagery.» | Name the feature, quote it, explain its effect, evaluate its importance — four moves, not two |
| The floating quotation | A sentence that is nothing but a quotation | Embed it: the quotation is a phrase inside your own sentence |
| The disappearing reader | An essay that never says who is being positioned, or how | «The reader is positioned to…» at least once per paragraph, and meant each time |
| Tense drift | «Pop walked the jetty and the narrator realises…» | The analytical present, everywhere: the story opens, Pop walks, the writer withholds |
| The missing conclusion | The essay stops at the end of body paragraph three | Plan the time; if it runs short, cut a body paragraph rather than the conclusion |
How a democracy died, and how a world stayed at the brink.
Unit 3 follows one nation — Germany — from the collapse of 1918 through a fragile republic into dictatorship, genocide and ruin. Unit 4 follows the whole world through the forty-six years in which two superpowers armed for a war they never quite fought. Both units are examined through sources, so the historian's toolkit from Year 11 runs through everything here.
The mapUnits 3 and 4, four topics
- Unit 3, Topic 1 — Weimar Germany, 1918–1933. Defeat and Versailles, a constitution with a trapdoor in it, the year everything broke (1923), the Stresemann recovery, and the Depression that carried the Nazis from twelve seats to the Chancellery.
- Unit 3, Topic 2 — The Nazi dictatorship, 1933–1945. Eighteen months of consolidation, the police state, propaganda, economy and society, the persecution of the Jews to the Holocaust, and war to the collapse of May 1945.
- Unit 4, Topic 1 — The Cold War: origins and early crises, 1945–1962. Yalta and Potsdam, containment, the Berlin blockade, two alliances, Korea, the arms race, the Wall and thirteen days over Cuba.
- Unit 4, Topic 2 — From détente to the end, 1962–1991. Vietnam, détente and SALT, Afghanistan, Reagan and Gorbachev, glasnost and perestroika, 1989, and the dissolution of the Soviet Union — plus the source-analysis toolkit for the external exam.
IA1 — examination: essay in response to historical sources (25 %), on Unit 3. IA2 — independent source investigation (25 %): you choose a question, find and evaluate sources, and write it up. IA3 — investigation: historical essay based on research (25 %), on Unit 4. External examination — short responses to historical sources (25 %), on Unit 4 Topic 2 only. Every one of the four asks you to do the same thing: read a source with its provenance in mind and build a judgement from it.
"The Nazis came to power because of the Depression" is a claim. "The NSDAP held 12 seats in May 1928, 107 in September 1930 after unemployment passed three million, and 230 in July 1932 when it passed six million" is an argument. Every topic below gives you the specific numbers and dates for exactly this reason. Where historians genuinely disagree — casualty totals, how much choice Hindenburg had, who started the Cold War — the text says so, because that contestability is itself examinable.
Weimar Germany: a republic nobody had asked for
Germany's first democracy was born in defeat, blamed for a peace it had not negotiated, wrecked by inflation in its fifth year, rebuilt on American loans, and then hit by the worst depression in modern history. It lasted fourteen years. The question the topic asks is not whether it was doomed — it was not — but why, at each turn, the people who could have saved it chose not to.
1.1Defeat and the birth of the Republic, 1918–1919
By the autumn of 1918 the German army was being driven back on the Western Front and its generals, Hindenburg and Ludendorff, told the Kaiser the war was lost. Sailors at Kiel mutinied on 3 November 1918 rather than sail on a suicide mission; workers' and soldiers' councils spread across the country within days. On 9 November 1918 Kaiser Wilhelm II abdicated and fled to the Netherlands, and the Social Democrat Philipp Scheidemann proclaimed a republic from a balcony of the Reichstag. Friedrich Ebert, leader of the Social Democratic Party (SPD), became head of the provisional government. The armistice was signed on 11 November 1918.
- The Ebert–Groener pact (10 November 1918): the army agreed to support the new government against revolution, and the government agreed to leave the army's officer corps untouched. The Republic thus depended from its first day on an army that did not believe in it.
- The Spartacist uprising, Berlin, January 1919: a communist rising crushed by the army and the Freikorps (volunteer units of demobilised soldiers). Its leaders, Karl Liebknecht and Rosa Luxemburg, were murdered on 15 January 1919. The left never forgave the SPD; the right learned that political murder went unpunished.
- The "stab in the back" (Dolchstoss). Because the army was still on French and Belgian soil when it stopped, and because the generals let civilians sign the armistice, nationalists claimed Germany had been betrayed at home by socialists and Jews — the "November criminals" — rather than beaten in the field. The myth was false and enormously effective.
- Elections to a National Assembly were held on 19 January 1919; it met in the quiet town of Weimar because Berlin was unsafe, which gave the Republic its name.
1.2The Treaty of Versailles, 28 June 1919
Germany was not invited to negotiate. Its delegates were handed the terms in May 1919 and told to sign or face invasion; the National Assembly accepted on 23 June and the treaty was signed in the Hall of Mirrors at Versailles on 28 June 1919 — five years to the day after the assassination at Sarajevo.
| Category | Terms | Why Germans called it the Diktat |
|---|---|---|
| Territory | Alsace-Lorraine to France; the Saar under League of Nations control for 15 years; the "Polish Corridor" to the new Poland, cutting East Prussia off from the rest of Germany; Danzig a free city; all overseas colonies taken; union with Austria forbidden | About 13 per cent of pre-war territory and roughly a tenth of the population were lost; millions of Germans now lived under foreign rule |
| Military | Army capped at 100,000 men, no conscription, no tanks, no air force, no submarines, navy limited to six battleships; the Rhineland demilitarised and occupied by Allied troops for up to 15 years | A great power left, in its own eyes, defenceless |
| Guilt | Article 231: Germany and its allies accepted responsibility for causing all the loss and damage of the war | The "war guilt clause" — the single most hated line, because it was the legal basis for what followed |
| Reparations | Fixed in 1921 at 132 billion gold marks (about £6.6 billion), payable in cash and in goods such as coal | A sum widely believed, then and since, to be beyond Germany's capacity — though historians dispute how far it really was |
Germany recovered economically by 1928 and could have paid. What Versailles did that could not be undone was to attach the new democracy to a national humiliation. Every party of the right ran against the "November criminals" who signed it; even moderates wanted it revised. Notice who benefited from that resentment in 1930–33.
1.3The Weimar constitution and its weaknesses
Adopted on 31 July 1919 and in force from August 1919, the constitution was among the most democratic in the world: all men and women over 20 could vote, there was a bill of rights, and the Reichstag was elected by proportional representation. A President, directly elected for seven years, appointed the Chancellor and commanded the armed forces.
| Feature | Intended to | In practice |
|---|---|---|
| Proportional representation | Give every party a fair share of seats | Produced a Reichstag of many parties and no majorities: every Weimar government was a coalition, and there were 20 cabinets in 14 years |
| Article 48 | Let the President act by emergency decree if public order were threatened | Became the routine way to govern once coalitions failed: from 1930 Chancellors ruled by decree with the President's signature, and the Reichstag was bypassed years before Hitler abolished it |
| Continuity of the state | Keep the country running through the revolution | The army, judges, civil servants and professors of the Empire stayed in office — and most of them despised the Republic. Right-wing political murderers received light sentences; left-wing ones were shot |
| The President | Provide a stable head of state above party | From 1925 the office was held by Paul von Hindenburg, the wartime field marshal, aged 77 on election — a monarchist who never liked the system he presided over |
The Kapp Putsch of March 1920, when Freikorps units seized Berlin and the army refused to fire on them, showed both weaknesses at once: the state could not rely on its own soldiers, and it was saved only by a general strike of Berlin's workers.
1.41923: the year everything broke
- The Ruhr occupation. When Germany fell behind on reparations deliveries, French and Belgian troops occupied the industrial Ruhr on 11 January 1923 to take coal and goods directly. The government called for passive resistance — workers downed tools — and paid their wages by printing money.
- Hyperinflation. The mark, already weak since the war, collapsed. A US dollar bought about 4.2 marks in 1914 and about 4.2 trillion marks in November 1923. Wages were paid twice a day and spent within the hour; savings, pensions and war bonds were wiped out. The middle class that lost everything in 1923 remembered who had been in charge.
- The Munich (Beer Hall) Putsch, 8–9 November 1923. Adolf Hitler, leader of the small Nazi Party (NSDAP), tried to seize power in Bavaria as the first step to marching on Berlin. Police fired on the marchers; sixteen Nazis died. Hitler was tried for treason, used the trial as a platform, and served about nine months of a five-year sentence, during which he dictated Mein Kampf. Lesson learned: power would have to be taken legally.
1.5The Stresemann years, 1924–1929
Gustav Stresemann was Chancellor for only a hundred days (August to November 1923) but Foreign Minister continuously from 1923 until his death on 3 October 1929. His policy was fulfilment: cooperate with the Allies, restore Germany's credit, and get the treaty revised by negotiation rather than defiance.
| Date | Measure | Effect |
|---|---|---|
| Nov 1923 | The Rentenmark | A new currency, backed by land and industry, ended the hyperinflation within weeks; passive resistance in the Ruhr was called off |
| 1924 | The Dawes Plan | Reparations rescheduled and an American loan of 800 million marks arranged; the French left the Ruhr in 1925. US capital then poured in — the recovery was built on short-term American loans |
| 1925 | The Locarno treaties | Germany accepted its western borders with France and Belgium (not its eastern ones); Stresemann shared the Nobel Peace Prize |
| 1926 | Germany joins the League of Nations | Back among the great powers, with a permanent seat on the Council |
| 1929 | The Young Plan | Reparations cut and the payment period extended to 1988; Allied troops to leave the Rhineland in 1930, five years early. Nationalists ran a furious campaign against it, which gave Hitler national publicity |
The "golden years" were real: industrial output passed its 1913 level, Berlin became the cultural capital of Europe, and the Nazis won only 12 seats (2.6 per cent) in the election of May 1928. But Stresemann himself warned that Germany was "dancing on a volcano": the prosperity rested on loans that could be recalled.
1.6The Depression and the rise of the NSDAP
The Wall Street Crash of October 1929 recalled the loans. German banks failed, exports collapsed and factories closed. Registered unemployment rose from about 1.3 million in 1929 to more than three million by 1930 and about six million by early 1932 — roughly one worker in three, with millions more on short time.
- Why the Nazis, and not the communists? The KPD also grew (100 seats by November 1932), and its growth terrified the middle classes, businessmen and farmers — who turned to the one party promising to crush it. The NSDAP was a Volkspartei, a catch-all party: it promised work to the unemployed, order to the frightened, revenge for Versailles to the nationalists, and offered Hitler as the man above all of them.
- Method. Joseph Goebbels ran the most modern campaigns in Europe: aircraft tours ("Hitler over Germany", 1932), mass rallies, posters targeted at particular groups, and the SA (Stormtroopers), about 400,000 strong by 1932, fighting the communists in the streets and making order look like a Nazi promise.
- Government by decree. The last SPD-led coalition collapsed in March 1930. Chancellor Heinrich Brüning (1930–32) governed by Article 48 decrees that cut wages, benefits and prices, deepening the slump; parliamentary democracy was already suspended in practice. In the presidential election of April 1932 Hindenburg beat Hitler 53 per cent to 36.8.
1.730 January 1933: how Hitler was appointed
After the July 1932 election Hitler demanded the Chancellorship and Hindenburg refused, disliking the "Bohemian corporal". Two Chancellors without majorities followed: Franz von Papen (June–November 1932) and General Kurt von Schleicher (December 1932–January 1933). Papen, wanting revenge on Schleicher, persuaded Hindenburg that Hitler could be appointed Chancellor and controlled: Hitler would have only two other Nazis in a cabinet of twelve, and Papen would be Vice-Chancellor. "Within two months," Papen is reported to have said, "we will have pushed Hitler so far into a corner that he'll squeak." Hindenburg appointed Hitler Chancellor on 30 January 1933.
Build the argument in layers, each with a date. Long-term: a republic associated with defeat and Versailles, a constitution that let the Reichstag be bypassed (Article 48), and an army, judiciary and civil service that never accepted it. Medium-term: 1923 destroyed the savings and the loyalty of the middle class; recovery after 1924 was built on American loans. Short-term: the Depression from October 1929 — six million unemployed, government by decree from 1930, a Nazi vote of 37 per cent by July 1932. Immediate: the intrigues of Papen and the decision of Hindenburg in January 1933. Then the contestable bit: historians such as Kershaw stress that Hitler's appointment was a choice made by a small conservative elite, not an inevitability — the Nazi vote was already falling.
The Nazi dictatorship: from Chancellor to Führer to ruin
Hitler took office with a minority cabinet and a President who could dismiss him. Eighteen months later there was no opposition, no free press, no independent courts and no President. How that was done — largely with the appearance of legality — and what the regime then did with total power, are the two halves of this topic.
2.1Consolidating power, 1933–1934
| Date | Step | What it removed |
|---|---|---|
| 27 Feb 1933 | The Reichstag Fire. The parliament building burned; a young Dutch communist, Marinus van der Lubbe, was found inside. The Nazis declared it the signal for a communist uprising | The next day Hindenburg signed the Reichstag Fire Decree suspending freedom of speech, press, assembly and protection from arbitrary arrest — "for the protection of people and state". It was never revoked. Some 4,000 communists were arrested within days |
| 5 Mar 1933 | The last multi-party election, held under intimidation | The NSDAP won 43.9 per cent, still short of a majority; with its Nationalist allies it had one |
| 23 Mar 1933 | The Enabling Act, passed 444 votes to 94 with SA men lining the chamber, the 81 communist deputies excluded and the Centre Party persuaded to vote yes. Only the SPD voted against | The government could make laws without the Reichstag or the President for four years. Every later measure rested on it |
| Apr–July 1933 | Gleichschaltung ("coordination"): state governments replaced by Nazi governors; trade unions abolished on 2 May and replaced by the German Labour Front; the SPD banned in June; on 14 July the NSDAP declared the only legal party | Every independent organisation between the individual and the state |
| 30 June 1934 | The Night of the Long Knives. The SS murdered the leadership of the SA, including its chief Ernst Röhm, along with conservative rivals such as General von Schleicher. At least 85 were killed; estimates run higher | The SA's threat of a "second revolution" that alarmed the army and big business. The army, whose support Hitler needed, thanked him |
| 2 Aug 1934 | Hindenburg died. Hitler merged the offices of President and Chancellor as Führer; every soldier swore a personal oath of loyalty to him | The last person who could legally have dismissed him. A plebiscite approved the change with about 90 per cent |
The pattern to name in an essay: a crisis (real or manufactured), an emergency law that looked legal, then the removal of one more check. Hindenburg's signature, the Centre Party's vote and the army's relief were each given freely. Terror was present throughout — the first concentration camp opened at Dachau in March 1933 — but so was consent.
2.2The police state
- The SS (Schutzstaffel), under Heinrich Himmler, grew from Hitler's bodyguard into a state within the state: it ran the concentration camps, the security police, and eventually the machinery of genocide. Himmler became chief of all German police in 1936.
- The Gestapo (secret state police) had the power to arrest and hold anyone in "protective custody" without trial. It was surprisingly small — historians such as Robert Gellately have shown that most of its cases began with denunciations by ordinary Germans. Fear, not numbers, did the work.
- The SD (security service) reported on public opinion; the People's Court (from 1934) tried political offences with no appeal.
- Concentration camps held communists, socialists, trade unionists, Jehovah's Witnesses, homosexual men, "asocials" and, after 1938, Jews in large numbers. They were places of terror and forced labour; the purpose-built extermination camps of 1941–42 were a different and later thing (section 2.5).
2.3Propaganda and culture
Joseph Goebbels became Minister of Public Enlightenment and Propaganda on 13 March 1933. His aim was not merely to silence opposition but to make the nation want what the regime wanted.
| Medium | Method |
|---|---|
| Radio | Cheap "People's Receivers" (Volksempfänger) put a set in most homes by 1939; loudspeakers in factories and squares carried Hitler's speeches; listening to foreign stations became a crime in wartime |
| Press and books | Editors licensed by the state and told daily what to print; student-led book burnings on 10 May 1933 destroyed works by Jewish, socialist and "un-German" authors |
| Film and spectacle | The Nuremberg rallies each September, filmed by Leni Riefenstahl (Triumph of the Will, 1935); the Berlin Olympics of 1936 presented a peaceful, modern Germany to the world while anti-Jewish signs were temporarily taken down |
| The arts | The Reich Chamber of Culture controlled who could work; modern art was exhibited as "degenerate" in 1937 and then removed from galleries |
| The Führer myth | Hitler was presented as above politics, the embodiment of the nation; Ian Kershaw's argument is that this myth was the regime's single most effective source of consent |
2.4Economy and society
- Unemployment fell from about six million in early 1933 to well under one million by 1938: public works (the Autobahn network), the compulsory Reich Labour Service, conscription from 1935, and above all rearmament. Women and Jews pushed out of jobs were not counted. The recovery was real, and it was the regime's most popular achievement.
- The Four Year Plan of 1936 under Hermann Göring aimed at autarky — self-sufficiency in food and raw materials — and an army ready for war within four years. Synthetic fuel and rubber were subsidised; consumer goods were not.
- Workers lost their unions and the right to strike but gained the German Labour Front's Strength Through Joy (Kraft durch Freude) programme of cheap holidays, concerts and the promised Volkswagen (nobody who paid in received one before the war). Real wages roughly reached 1929 levels by 1938.
- Women were to serve the nation as mothers: marriage loans from 1933 (a quarter written off for each child), the Mother's Cross from 1939, and exclusion from professions — a policy quietly reversed when the war needed their labour.
- Youth. The Hitler Youth and League of German Maidens became the only permitted youth organisations in 1936 and compulsory in 1939; schools taught race theory and rewrote history. Some teenagers rebelled — the Edelweiss Pirates and the Swing Youth — and were punished.
- The churches. A Concordat with the Vatican in July 1933 promised the Catholic Church freedom in return for staying out of politics; the promise was broken. Protestant pastors who resisted Nazification formed the Confessing Church; Martin Niemöller spent 1938–45 in camps.
- The whole was called the Volksgemeinschaft, the "people's community": a nation without class divisions — and without anyone the regime defined as outside it.
2.5The persecution of the Jews, and the Holocaust
Antisemitism was central to Nazi ideology from the start. Germany's roughly 500,000 Jews (under one per cent of the population) were made scapegoats for defeat, inflation and depression. Persecution escalated in stages, each testing what the public and the world would tolerate.
| Date | Measure |
|---|---|
| 1 Apr 1933 | A one-day national boycott of Jewish shops, doctors and lawyers, enforced by the SA |
| 7 Apr 1933 | Jews dismissed from the civil service, and soon from universities, the courts and the press |
| 15 Sept 1935 | The Nuremberg Laws. The Reich Citizenship Law made Jews "subjects" without political rights; the Law for the Protection of German Blood forbade marriage or sexual relations between Jews and "Aryans". Later decrees defined a Jew by grandparents, not belief |
| 9–10 Nov 1938 | Kristallnacht ("the night of broken glass"): after a German diplomat was shot in Paris by a Jewish teenager, the SA and party members burned hundreds of synagogues, smashed some 7,500 Jewish businesses, killed about 91 people and sent about 30,000 Jewish men to concentration camps. The Jewish community was then fined a billion marks for the damage |
| 1939–41 | Emigration was encouraged and then, in October 1941, banned; about half of Germany's Jews had left. After the conquest of Poland in 1939, Jews there were forced into ghettos (Warsaw, Łódź) where tens of thousands died of hunger and disease |
| from 22 June 1941 | With the invasion of the Soviet Union, Einsatzgruppen (SS mobile killing squads) followed the army and shot Jews, Roma and communists in mass graves — more than a million people, including about 33,000 at Babi Yar near Kyiv in two days of September 1941 |
| 20 Jan 1942 | The Wannsee Conference, chaired by Reinhard Heydrich, coordinated the "Final Solution": the deportation of all of Europe's Jews to the East to be worked or gassed to death. The decision had already been taken; Wannsee organised the ministries |
| 1942–45 | The extermination camps in occupied Poland — Chełmno, Bełżec, Sobibór, Treblinka, Majdanek and Auschwitz-Birkenau — murdered people in gas chambers on arrival. About six million Jews were killed in the Holocaust, along with hundreds of thousands of Roma and Sinti, about 70,000 disabled Germans in the earlier "T4" programme, Soviet prisoners of war, political prisoners and others |
The Holocaust is the systematic, state-organised murder of European Jews between 1941 and 1945; the persecution of 1933–39 led to it but was not yet it. Do not write "the Nazis killed six million people in concentration camps": most victims died in purpose-built extermination camps or by shooting, and the total of all victims of Nazi mass murder is far higher than six million. Historians still debate when the decision for total extermination was taken (summer to autumn 1941 is the usual range) and how much was ordered from above versus improvised by officials on the spot — the "intentionalist" and "functionalist" readings. Name that debate when a source question invites it.
2.6War, resistance and collapse
- Foreign policy reversed Versailles step by step, each step unopposed: conscription and an air force announced (1935), the Rhineland remilitarised (March 1936), Austria annexed (March 1938), the Sudetenland ceded at Munich (September 1938), the rest of Czechoslovakia seized (March 1939), the Nazi–Soviet Pact (23 August 1939), and the invasion of Poland on 1 September 1939, which brought Britain and France into war.
- Turning point. The invasion of the Soviet Union on 22 June 1941 and the surrender of the Sixth Army at Stalingrad on 2 February 1943 turned a war of conquest into one of survival. Goebbels' "total war" speech of 18 February 1943 mobilised the whole population; Allied bombing destroyed German cities from 1943.
- Resistance was small and brave: the White Rose students in Munich, whose leaders Hans and Sophie Scholl were executed on 22 February 1943; the Kreisau Circle; and the army officers' bomb plot of 20 July 1944, after which about 5,000 people were executed. There was no popular uprising.
- Collapse. With Soviet troops in Berlin, Hitler killed himself on 30 April 1945. Germany surrendered unconditionally on 8 May 1945, occupied by the four Allied powers, its cities in ruins, having caused a war in which tens of millions died. Unit 4 begins in that rubble.
The Cold War, 1945–1962: from alliance to the brink
In 1945 the United States and the Soviet Union were allies who had just destroyed Hitler together. Within three years they were building rival blocs across a divided Europe; within five, fighting each other by proxy in Korea; within seventeen, thirteen days from nuclear war. The topic asks how, and — the contestable part — whose fault it was.
3.1Yalta, Potsdam and the breakdown of the alliance
| Yalta, 4–11 February 1945 | Potsdam, 17 July–2 August 1945 | |
|---|---|---|
| Who | ||
| Agreed | Germany and Berlin to be divided into four occupation zones; free elections promised in liberated Europe (the Declaration on Liberated Europe); the USSR to join the war against Japan; the United Nations to be founded | The zones confirmed; Germany to be demilitarised, denazified, democratised; reparations taken mainly from each power's own zone; Poland's border moved west to the Oder–Neisse rivers |
| Disputed | Poland: Stalin's installed government versus the exiled one in London. The West accepted a promise of elections that were never freely held | Truman told Stalin of a "new weapon" — the atomic bomb tested on 16 July; Stalin, who knew from spies, shrugged. Hiroshima followed on 6 August |
- By 1947 Soviet-backed communist governments controlled Poland, Romania, Bulgaria and Hungary; Czechoslovakia's elected government fell to a communist coup in February 1948. Stalin saw a belt of friendly states as the minimum security for a country that had lost some 27 million people to a German invasion; the West saw an empire.
- George Kennan's Long Telegram (22 February 1946) argued the USSR was expansionist and could only be met by firm resistance; Churchill's "Iron Curtain" speech at Fulton, Missouri (5 March 1946) said the same in public.
Orthodox (1950s): Soviet expansionism caused the Cold War; the West reacted. Revisionist (1960s–70s, e.g. William Appleman Williams): American economic ambition and the atomic monopoly threatened a Soviet Union that was acting defensively. Post-revisionist (from the 1970s, John Lewis Gaddis): mutual misunderstanding and the security dilemma — each side's defensive moves looked offensive to the other. After the Soviet archives opened in 1991, Gaddis and others moved back toward stressing Stalin's own role. A source question that asks "how useful is this source for explaining the origins of the Cold War" is inviting you to place it in one of these camps.
3.2Containment: the Truman Doctrine and the Marshall Plan
- Containment was Kennan's word: do not try to roll communism back, but hold it where it is until the Soviet system decays. It was American policy for the next forty years.
- The Truman Doctrine, 12 March 1947. Britain could no longer afford to support Greece (fighting a communist insurgency) and Turkey. Truman asked Congress for $400 million and declared that the United States would "support free peoples who are resisting attempted subjugation by armed minorities or by outside pressures". It committed America to a global struggle.
- The Marshall Plan, announced 5 June 1947. Secretary of State George Marshall offered aid to rebuild all of Europe; about $13 billion went to sixteen Western countries between 1948 and 1952. Stalin forbade the Eastern bloc to accept, and answered with Cominform (September 1947) to coordinate communist parties. The plan was economic, but its logic was political: hungry people vote communist.
3.3Germany and Berlin: blockade, two states, two alliances
- The Berlin blockade, 24 June 1948 – 12 May 1949. When the Western powers introduced a new currency in their zones, Stalin cut every road, rail and canal link to West Berlin, expecting the West to withdraw. Instead the Berlin airlift flew in food and coal for eleven months — about 2.3 million tonnes on more than 270,000 flights. Stalin lifted the blockade; the West had won without firing a shot, and Germany's division was sealed.
- Two Germanies. The Federal Republic of Germany (West Germany) was founded on 23 May 1949; the German Democratic Republic (East Germany) on 7 October 1949.
- Two alliances. NATO was founded on 4 April 1949: an attack on one member would be treated as an attack on all. West Germany was admitted in May 1955, and the Soviet Union answered within days with the Warsaw Pact (14 May 1955) binding its Eastern European satellites. Europe now had two armed camps facing each other along the inner German border.
3.4Korea, 1950–1953
Korea had been divided at the 38th parallel in 1945 between a Soviet-backed North and an American-backed South. On 25 June 1950 North Korean forces invaded the South. Because the Soviet delegate was boycotting the UN Security Council, the United Nations authorised a force, overwhelmingly American, under General MacArthur. It drove the North Koreans back almost to the Chinese border; in October 1950 China entered the war with hundreds of thousands of troops and pushed the UN forces south again. Truman sacked MacArthur in April 1951 for demanding the war be widened into China. The front settled near the 38th parallel and an armistice was signed on 27 July 1953. About three million people died, most of them Korean civilians; the border stands where it was.
- Korea turned containment from a European policy into a global and military one: American defence spending tripled under the plan known as NSC-68, and the US built alliances across Asia and the Pacific — including ANZUS with Australia and New Zealand in 1951.
- It set the pattern for proxy war: superpowers fighting through and beside smaller states, never directly.
3.5The arms race
| Date | Development | Significance |
|---|---|---|
| 6 & 9 Aug 1945 | Atomic bombs on Hiroshima and Nagasaki | The American monopoly begins |
| 29 Aug 1949 | First Soviet atomic test | The monopoly ends years earlier than Washington expected, helped by espionage |
| 1952–53 | Hydrogen bombs: US November 1952, USSR August 1953 | Weapons hundreds of times more powerful than Hiroshima |
| 4 Oct 1957 | Sputnik, the first artificial satellite | The rocket that launched it could carry a warhead to America: the intercontinental ballistic missile era, and a panic about a "missile gap" |
| 1960s | Submarine-launched missiles; thousands of warheads on each side | Mutually assured destruction (MAD): neither side could strike first without being destroyed in return — a deterrent that depended on both sides staying rational |
Stalin died on 5 March 1953. His successor Nikita Khrushchev denounced his crimes in 1956 and spoke of "peaceful coexistence" — but also crushed the Hungarian uprising in November 1956 with tanks, killing about 2,500 Hungarians, and the West did nothing. Containment cut both ways: each side accepted the other's sphere.
3.6The Berlin Wall and the Cuban Missile Crisis
- 13 August 1961. With East Germany losing skilled workers through West Berlin at the rate of thousands a week, the East German government, with Khrushchev's approval, sealed the border overnight with barbed wire, then concrete. The Berlin Wall stood for 28 years; at least 140 people died trying to cross it. Kennedy's private reaction: a wall was better than a war.
- Cuba. Fidel Castro's revolution (January 1959) turned toward Moscow after the failed CIA-backed invasion at the Bay of Pigs in April 1961. In 1962 Khrushchev secretly began installing nuclear missiles on the island, ninety miles from Florida.
- The Cuban Missile Crisis, 16–28 October 1962. An American U-2 spy plane photographed the launch sites on 14 October. Kennedy rejected an air strike, announced a naval "quarantine" of Cuba on 22 October, and Soviet ships turned back. On 28 October Khrushchev agreed to remove the missiles in exchange for a public American pledge not to invade Cuba and a secret one to withdraw US missiles from Turkey. It was the closest the world has come to nuclear war.
- Consequences. A direct hotline between Washington and Moscow (1963); the Partial Test Ban Treaty (August 1963); and a lesson both sides drew — that crises had to be managed, not won — which is where Unit 4 Topic 2 begins.
The Cold War, 1962–1991: from détente to dissolution
After Cuba the superpowers learned to talk while they armed. The thaw held for a decade, froze again over Afghanistan, and then — in six years under one Soviet leader — the whole structure came down without a shot fired between the two sides. This is the topic the external exam is set on, so it ends with the toolkit for answering it.
4.1Vietnam, briefly
Containment's costliest test. After the French left in 1954, Vietnam was divided at the 17th parallel between a communist North under Ho Chi Minh and an American-backed South. Fearing the "domino theory" — that one country's fall would topple its neighbours — the United States escalated from advisers to war: the Gulf of Tonkin Resolution (August 1964) gave President Johnson a free hand, the first combat troops landed in March 1965, and more than 500,000 Americans were in Vietnam by 1968. The Tet Offensive of January 1968 was a military defeat for the North but a political defeat for Washington: television showed a war the government had said was being won. Nixon withdrew under the Paris Peace Accords of 27 January 1973; Saigon fell on 30 April 1975. About 58,000 Americans and, by most estimates, two to three million Vietnamese died. The war drained American money, confidence and moral authority — and made both superpowers readier to negotiate.
4.2Détente, 1969–1979
Détente ("relaxation") was the deliberate easing of tension through negotiation, trade and arms control. Each side had reasons: the US was exhausted by Vietnam and split with China; the USSR needed Western grain and technology and feared a two-front confrontation after border clashes with China in 1969.
| Date | Agreement | What it did |
|---|---|---|
| 1968 | Nuclear Non-Proliferation Treaty | Signatories without nuclear weapons agreed not to acquire them; the nuclear powers agreed to negotiate disarmament |
| Feb 1972 | Nixon visits Beijing | The US opened relations with communist China, giving Moscow a reason to deal |
| 26 May 1972 | SALT I and the ABM Treaty, signed in Moscow by Nixon and Brezhnev | The first limits on strategic missile launchers (a five-year freeze) and on anti-missile defences — keeping both sides vulnerable, which is what deterrence required |
| 1972 | West Germany's Ostpolitik under Willy Brandt: the Basic Treaty | The two Germanies recognised each other; both joined the UN in 1973 |
| 1 Aug 1975 | Helsinki Accords, signed by 35 states | The West accepted Europe's post-war borders; the Soviet bloc accepted commitments on human rights — which dissidents such as Charter 77 in Czechoslovakia then used against their governments |
| 18 June 1979 | SALT II, signed by Carter and Brezhnev | Set equal ceilings on launchers; never ratified by the US Senate after Afghanistan, though both sides observed it informally |
4.3Afghanistan and the "Second Cold War", 1979–1985
- On 24–27 December 1979 Soviet troops invaded Afghanistan to prop up a failing communist government. The US responded with grain and technology embargoes, a boycott of the Moscow Olympics of 1980, and covert arms to the Afghan mujahideen. The war lasted nine years, killed about 15,000 Soviet soldiers and perhaps a million Afghans, and became the USSR's Vietnam; the last Soviet troops left on 15 February 1989.
- Ronald Reagan (President from January 1981) called the USSR an "evil empire" (8 March 1983), raised defence spending sharply, deployed Pershing II and cruise missiles in Western Europe (November 1983) to match Soviet SS-20s, and announced the Strategic Defense Initiative (SDI, "Star Wars", 23 March 1983), a space-based missile shield that threatened to make Soviet missiles useless.
- Tension peaked in autumn 1983: the Soviets shot down Korean Air Lines flight 007 (1 September), and during the NATO exercise Able Archer in November some in the Soviet leadership feared a real first strike was being prepared. Historians disagree about how close war came; the archives suggest closer than anyone in the West realised at the time.
- The Soviet economy, meanwhile, was stagnating: growth near zero, oil prices collapsing from 1985, a fifth or more of output going to the military, and three elderly leaders dying in office between November 1982 and March 1985.
4.4Gorbachev: glasnost, perestroika and the end of the arms race
Mikhail Gorbachev became General Secretary on 11 March 1985, aged 54, determined to save the Soviet system by reforming it. His two words: glasnost ("openness") — freer speech, honest media, the release of dissidents, public discussion of Stalin's crimes; and perestroika ("restructuring") — limited market reforms and an end to the command economy's worst rigidities. The Chernobyl disaster of 26 April 1986, initially covered up, showed him how badly the old secrecy worked.
| Date | Summit or step | Result |
|---|---|---|
| Nov 1985 | Geneva: Reagan and Gorbachev meet | No agreement, but a personal relationship — and a joint statement that a nuclear war "cannot be won and must never be fought" |
| Oct 1986 | Reykjavik | The two leaders came close to agreeing to abolish all nuclear weapons; the talks broke down over SDI |
| 8 Dec 1987 | INF Treaty, Washington | The first treaty to abolish an entire class of weapons — all intermediate-range missiles — with on-site inspection. About 2,700 missiles destroyed |
| Dec 1988 | Gorbachev at the United Nations | Announced unilateral cuts of 500,000 troops and, in effect, renounced the Brezhnev Doctrine of 1968 that had justified intervening in satellite states. Eastern Europe was on its own |
4.51989, and the dissolution of the Soviet Union
- Poland. Legalised after years of suppression, the trade union Solidarity won almost every seat it contested in semi-free elections on 4 June 1989; by September Poland had its first non-communist prime minister since the 1940s.
- Hungary cut the barbed wire on its Austrian border in May and opened it fully to East Germans on 11 September 1989. Tens of thousands of East Germans "holidayed" in Hungary and drove west.
- East Germany. Weekly demonstrations in Leipzig grew from thousands to hundreds of thousands; Gorbachev, visiting in October, refused to back a crackdown. On the evening of 9 November 1989 a confused announcement about new travel rules brought crowds to the checkpoints, the guards opened the gates, and Berliners climbed onto the Wall that had divided them for 28 years.
- The rest of the bloc fell within weeks: Czechoslovakia's Velvet Revolution in November, Bulgaria's leadership change, and in Romania the only violent end, with Ceauşescu shot on 25 December 1989. At Malta on 2–3 December, Gorbachev and George H. W. Bush declared the Cold War over.
- Germany reunified on 3 October 1990, inside NATO, with Soviet consent. The Warsaw Pact dissolved itself on 1 July 1991.
- The Soviet Union itself. Glasnost let the republics demand independence — Lithuania first, in March 1990 — and perestroika delivered shortages, not prosperity. Hardliners staged a coup on 19–21 August 1991; it collapsed when Boris Yeltsin, President of the Russian republic, defied it from a tank outside the Russian parliament. On 8 December Russia, Ukraine and Belarus declared the Union dissolved; Gorbachev resigned on 25 December 1991 and the Soviet flag came down over the Kremlin. The USSR formally ceased to exist the next day.
The "Reagan victory" school: American rearmament and SDI forced a bankrupt USSR to give up. The "Gorbachev" school (e.g. Archie Brown): the end was chosen by a reformer who refused to use force, and would not have happened under a different General Secretary — China in June 1989 shows what force could still do. Structural explanations: a command economy that could not compete with Western technology and consumer prosperity, and nationalism inside the Soviet empire. People power: Solidarity, Leipzig, the Baltic human chain of August 1989. A good answer weighs these against the specific source in front of it rather than picking a favourite.
4.6The historian's toolkit for the external exam
The external examination gives you a set of sources on this topic and asks short-response questions about them. The vocabulary is the same as Year 11; what changes is that you must now bring the content above to each source. Here is the order of questions to ask, every time.
| Term | The question it answers | Worked on a Cold War source |
|---|---|---|
| Origin | Who made it, when, where, of what type? | A Soviet poster of 1950 showing a smiling worker beneath Stalin: made by the state propaganda apparatus, in the year of Korea, for a Soviet public |
| Purpose | Why was it made, for whom? | To reinforce loyalty and present the USSR as prosperous and peaceful at a moment of confrontation |
| Usefulness | Does it help answer my question? | For "how did the Soviet state present itself in 1950?" — extremely useful. For "what were living standards in 1950?" — almost useless, except as evidence of what the state wanted concealed |
| Reliability | Can it be trusted to be accurate about what it claims? | Not reliable about conditions: its purpose is persuasion and its origin is the party. Say why from the provenance; "it is biased" on its own earns nothing |
| Corroboration | Do independent sources agree? | Compare it with Khrushchev's 1956 secret speech or with post-1991 archival studies; note that two Soviet posters do not corroborate each other because they share an origin |
| Contestability | Do informed historians genuinely disagree? | On the origins of the Cold War (orthodox, revisionist, post-revisionist) and its end (Reagan, Gorbachev, structure, people) — name the school a source belongs to |
Describing instead of judging: the examiner can read the source; they want to know what it is worth. Confusing reliability with usefulness: decide each separately and say which you are doing. Answering a different question: if the question is about the end of the Cold War, a perfect paragraph on Cuba scores nothing. Read the question twice; then apply the seven moves to that question and no other.
Design for someone, for a client, for the planet, for a year that has not happened yet.
Year 11 gave you the process: explore, develop, resolve, and a decision you can defend with evidence. Year 12 runs that process in four harder settings — a real user whose life you do not share, a client with a budget and a market, a product that has to survive its own end of life, and a future nobody can see. It ends with a two-hour design challenge set by the QCAA.
The mapUnits 3 and 4, four topics
- Unit 3, Topic 1 — Designing with empathy. The five-mode human-centred loop; research methods that go deeper than a survey; synthesis into a point-of-view statement; journey maps; turning needs into criteria.
- Unit 3, Topic 2 — Design in industry. Clients, briefs and constraints; markets and value; product, architectural and graphic contexts; industry sketching, prototyping and iteration; presenting a proposal.
- Unit 4, Topic 1 — Redesigning. Life cycle analysis from extraction to end of life; the circular economy; the redesign strategies; evaluating a redesign against sustainability criteria.
- Unit 4, Topic 2 — Designing for the future. Trends, drivers and signals; scenario building; speculative design; the external examination design challenge and how to sketch for an examiner.
| Assessment | What it is | Weight |
|---|---|---|
| IA1 — Examination | Design challenge: respond to an unseen brief under exam conditions, in sketches and annotations | 15% |
| IA2 — Project | A human-centred design project for a client, documented from research to proposal | 25% |
| IA3 — Project | A sustainable redesign project, evaluated against life cycle criteria | 35% |
| External examination | Design challenge set and marked by the QCAA: analyse a brief, generate and evaluate ideas, resolve and communicate one | 25% |
Year 11 asked for a reason attached to evidence. Year 12 asks for a reason attached to evidence and to a person. Not «the handle is 32 mm because that is the ergonomic standard», but «the handle is 32 mm because Joan, who has arthritis, could not close her fingers around the 24 mm sample in the second test, and she is the user the brief names». Every decision in the folio should be traceable to something a user did, said or needed.
Research theatre — a survey of thirty classmates about a product for aged-care residents. The unlabelled sketch — a beautiful drawing with no material, no dimension, no reason, which the examiner has to mark as an idea with no thinking attached. Sustainability by adjective — «eco-friendly bamboo» with no life cycle stage named and no number.
Designing with empathy: the five-mode loop
Human-centred design in Year 11 was a set of commitments. In Year 12 it is a working method with five modes, a research toolkit that goes deeper than asking, and a way of turning what you learned about a person into a criterion you can test.
1.1Empathise, define, ideate, prototype, test
| Mode | The question it answers | What you must have at the end |
|---|---|---|
| Empathise | What does this person actually do, and what does it feel like? | Raw evidence: observation notes, interview transcripts, photographs, a journey map |
| Define | What is the real problem, stated from the user’s side? | A point-of-view statement and design criteria that trace back to the evidence |
| Ideate | How many different ways could this be solved? | Many options, then a shortlist chosen against the criteria |
| Prototype | What is the cheapest thing I can build to find out whether this works? | A rough model that isolates one question |
| Test | What did the user do with it, and what does that tell me? | Recorded behaviour, not opinions, and a decision: keep, change, or go back |
1.2Research methods that go deeper than asking
Year 11 gave you observation, interviews and surveys. These methods find what those miss: the things people do without noticing, the things they will not say, and the way a task feels from inside.
| Method | What it is | What it finds | Run it well |
|---|---|---|---|
| Contextual inquiry | Watching a person do the real task in the real place, asking questions as they go | Workarounds, interruptions, the tools they actually reach for | Be an apprentice, not an examiner: «show me how you…», then shut up and watch |
| Shadowing | Following one person through a whole shift or day | The sequence and rhythm of a job; where time and energy go | Log times. The pain points are usually between tasks, not inside them |
| Diary study | The user records each time the problem happens, over a week or more | Frequency, pattern, and the moments you would never be present for | Make the entry take under a minute: a photo and three words |
| Think-aloud test | The user narrates their thoughts while using a prototype | Where the design confuses, and why, in the user’s own words | Never help. Silence and a wrong move are both data |
| The five whys | Asking «why?» about a stated problem, five times over | The cause beneath the complaint | «The bin is too far» → why do you not walk to it? → because I lose my seat → the problem is seating, not bins |
| Extreme users | Deliberately researching people at the edges: the expert, the first-timer, the person with a disability | Needs the average user has too, but cannot articulate | Design for the edge and the middle usually follows |
A survey of your friends about a product for someone you have never met is not research; it is paperwork. If the brief names aged-care residents, night-shift nurses or Year 1 students, the evidence in your folio must come from those people, or from people who work with them every day. One hour of observation with the right person outweighs a hundred survey responses from the wrong ones.
1.3Synthesis: from a pile of notes to one statement
- Get everything on cards. One observation, quote or fact per card. No conclusions yet.
- Cluster into an affinity diagram. Move cards that seem related together, then name each cluster with a heading written as a sentence: «residents will not ask for help with the remote», not «remotes».
- Turn clusters into insights. An insight is a surprising, useful truth about the user that explains behaviour: «she hides the remote because asking for help feels like admitting she cannot cope».
- Write the point-of-view statement. The formula is [user] needs [need] because [insight]: «Joan, 84, needs to control her television without help because asking makes her feel she is losing her independence.» Note that the need is a verb, not a product: never «needs a bigger remote».
- Generate how-might-we questions from the statement, each opening a different direction: how might we make the controls impossible to get wrong? How might we make asking for help feel normal?
1.4The journey map
1.5From a need to a criterion
A criterion in Year 12 must be traceable: the folio should show the chain from something a user did, through the insight it produced, to the measurable statement the design will be tested against.
| Evidence | Insight | Design criterion |
|---|---|---|
| Joan could not close her fingers around the 24 mm sample; she managed the 32 mm one | Grip diameter, not button size, is what limits her | Every grasped part is 30–36 mm in diameter, and Joan operates all controls unaided on the first attempt |
| Eleven of twelve students queued more than ten minutes to collect a laptop | The desk, not the form, is the bottleneck | A student with an approved request collects a laptop in under 2 minutes without staff involvement |
| Nurses carried the tablet under one arm while pushing a trolley in nine of ten observed corridor trips | Both hands are already busy; the device must survive being carried, not just used | The device attaches to the trolley rail in one motion and stays attached over a 20 mm threshold at walking pace |
Year 11 taught the two opposite skills. In Year 12 you should be able to show the shape in the folio: a wide field of options after ideation (thumbnails, morphological combinations, how-might-we variants), then a visible narrowing — a screen against constraints, a weighted matrix, a shortlist of three, one chosen — with the criteria doing the narrowing, not your taste. An examiner should be able to see where the field was widest and what closed it.
Design in industry: clients, markets and constraints
In industry nobody designs for themselves. There is a client who pays, a user who is not the client, a market that decides whether the thing sells, and a set of constraints that were fixed before you arrived. The skill is to make something good inside all of that, and then to present it so the client says yes.
2.1The client and the brief
A client commissions and pays for the design; the user is the person who will live with it. They are rarely the same person, and when their interests conflict, the folio must say how the conflict was resolved and why. A design brief is the client’s written statement of what they want, and reading it properly is a skill in itself.
| Part of the brief | What it contains | What to do with it |
|---|---|---|
| Context | Who the client is, what they do, why they need this now | Find the problem behind the request: a café asking for «a new sign» may actually have a visibility problem from the road |
| Target user and market | Who it is for, and who it competes with | Research them, not your classmates; map the competitors |
| Requirements | What the design must do | Rewrite as measurable criteria and get the client to agree the weights |
| Constraints | Budget, timeline, materials, standards, site, brand rules, manufacturing method | List them before ideating; any idea that breaks one is dead, however good |
| Deliverables | What the client will receive: concepts, drawings, a prototype, a presentation | Plan backwards from the deliverable date |
| What is missing | Briefs are always incomplete | Write the questions down and ask them at the first meeting; assumptions you make silently are the ones that cost money |
Underline three things in different colours: the user (who), the requirements (must), and the constraints (cannot, within, no more than). Then write one sentence that says what the brief is really asking for. Most exam briefs contain one constraint that rules out the obvious answer — find it before you sketch.
2.2Market, competitors and value
- A target market is the group of buyers the design is aimed at, described by what they need, what they can pay and how they buy — not by age alone. «Parents of primary students who buy school gear online in January» is a target market; «people aged 30–45» is not.
- Competitor analysis places existing products on the two axes the market cares about — price against durability, say — and looks for the empty corner. A design that lands on top of an existing product must beat it; one that lands in an empty corner only has to be wanted.
- A value proposition is one sentence saying what the design does for its user that the alternatives do not: «a school water bottle that survives five years of being dropped, so it is bought once».
- Cost is not price. Cost is what it takes to make; price is what the market will pay; the gap is the margin that keeps the client in business. A design that is beautiful at $60 unit cost in a $40 market has failed the brief.
- Volume changes everything. A tool that costs $9,000 makes each of 10 parts cost $900 and each of 100,000 parts cost nine cents. Ask how many will be made before choosing a manufacturing method.
2.3Three industry contexts
| Product design | Architectural design | Graphic design | |
|---|---|---|---|
| What is designed | Objects that are made and sold: tools, furniture, devices, packaging | Buildings and spaces: houses, shops, public places, interiors | Visual communication: identity, signage, publications, interfaces |
| Typical constraints | Unit cost, manufacturing method, tolerances, safety standards, ergonomics | Site, orientation, building codes, budget per square metre, egress, climate | Brand guidelines, print or screen, legibility at distance, accessibility, budget |
| Deliverables | Concept sketches, CAD, a prototype, technical drawings, a bill of materials | Site plan, floor plans, elevations, sections, a model or render | Concepts, a style guide, final artwork, mock-ups in context |
| Standards that bite | Australian Standards for the product type; anthropometric data | The National Construction Code; local planning rules; AS 1100 drawing | Colour-contrast ratios for accessibility; print specifications; type licensing |
| How it is tested | Drop, load, fatigue and usability tests on prototypes | Walk-throughs of models; daylight and thermal studies; code checks | Legibility at the real viewing distance; comprehension tests; colour-vision checks |
2.4Ideation and sketching, the industry way
- Thumbnails first, and many. Twenty in twenty minutes, none rendered. In industry these stay in the folio as proof that the field was wide.
- Concept sketches develop the three or four survivors: larger, in perspective or an appropriate view, with the construction lines still visible and annotations for material, function and reason.
- Rendered presentation drawings for the client: colour, tone, context, a person for scale. These sell; they do not specify.
- Technical drawings for the maker: orthographic views to scale, dimensioned, toleranced. These specify; they do not sell.
- Annotation conventions. Leader lines to the exact part; the note names the material, the function and the reason; dimensions in millimetres; a question mark for something still to be tested. A sketch with no annotations is an idea with no thinking attached.
2.5Prototyping and iteration under industry pressure
| Term | What it means | Why it matters |
|---|---|---|
| Proof of concept | The roughest build that shows the core idea can work at all | Kills a bad idea for $5 rather than $5,000 |
| Minimum viable product | The simplest version that a real user can actually use, released to learn from | Real use produces evidence that no internal test can |
| Design for manufacture | Changing the design so it can be made by the chosen method at the chosen volume | A part that cannot be moulded, or needs six operations instead of two, is not finished |
| Tolerance | The allowed variation in a dimension, written as ± | Parts that must fit together need tight tolerances; tight tolerances cost money; specify only where fit matters |
| Design freeze | The date after which the design cannot change without cost | Iteration has a deadline in industry; the loop has to close |
| Pilot run | A small production batch to find manufacturing problems before the full run | The first hundred find the faults the first one did not |
2.6Presenting a design proposal
A proposal is a pitch with evidence attached. Year 11 gave you the five parts of a pitch; a Year 12 proposal adds the things a client needs before they can say yes.
| Section | What it contains | The client’s question it answers |
|---|---|---|
| The problem | The brief restated in the user’s terms, with the research evidence | Did you understand what I asked for? |
| The options considered | The shortlist and the matrix that chose between them | Is this the best of what was possible, or the first thing you thought of? |
| The proposed design | Presentation drawings, the prototype, the test results against the criteria | Does it work, and how do you know? |
| Feasibility | Materials, manufacturing method, unit cost at volume, timeline, standards met | Can it actually be made, for what, by when? |
| Risks and next steps | What is still untested, and what you propose to do about it | What could go wrong, and are you hiding anything? |
| The decision | Exactly what you are asking the client to approve | What do you need from me today? |
IA2 is a documented human-centred design project for a client, and the folio is marked on the process as much as the outcome: the research, the synthesis, the breadth of ideation, the evidence that chose the concept, and the proposal. The commonest lost marks are a shortlist with no visible reason for the choice, and a proposal that never returns to the criteria. Present the matrix, present the test results, and say where the design fell short.
Redesigning: the whole life of a product
Every product has a life before it reaches you and a life after you are done with it, and most of the damage happens at the two ends. Sustainable design starts by drawing that whole life, finding the stage that costs most, and redesigning to close the loop.
3.1Life cycle analysis
| Stage | What it costs | Questions to ask |
|---|---|---|
| Extract | Mining, drilling, logging, farming: land, water, energy, habitat | Is the material renewable? Recycled content available? How far did it travel? |
| Process | Turning ore, crude or timber into sheet, pellet, board: usually the most energy-hungry step for metals | Virgin aluminium takes about twenty times the energy of recycled; does the design need virgin? |
| Make | Forming, machining, assembling; offcuts, water, solvents | Can parts nest to cut scrap? Fewer operations? Fewer fasteners? |
| Distribute | Packaging, transport by mass and volume, retail | Does it stack, flat-pack or ship empty? Is the packaging the product’s own waste? |
| Use | Energy, water, consumables, maintenance over the whole service life | How long does it last? Can it be repaired? What does it consume each day? |
| End of life | Collection, sorting, recycling or landfill; toxicity | Can it be separated into single materials with hand tools? Is any part hazardous? |
3.2Linear and circular
| Linear economy | Circular economy | |
|---|---|---|
| The shape | Take, make, use, dispose: a straight line that ends in landfill | Loops that return products, parts and materials to use |
| What counts as waste | Anything the user no longer wants | Nothing, in principle: every output is designed to be an input |
| Business model | Sell as many units as possible; a product that fails early sells a replacement | Sell the service or the outcome; a product that lasts is more profitable, not less |
| Design consequence | Cheap to make, hard to repair, glued and welded, mixed materials | Durable, repairable, modular, mono-material, designed for disassembly |
| The three loops, cheapest first | Reuse and repair keep the product whole. Remanufacture takes it apart and rebuilds it with parts replaced. Recycle destroys the product to recover the material, and spends energy doing it. Design so the highest loop is possible | |
3.3The redesign strategies
| Strategy | What you change | Applied to a school chair | Its trade-off |
|---|---|---|---|
| Dematerialise | Use less material for the same function: thinner sections, ribs instead of solid, fewer parts | A ribbed shell 2.5 mm thick instead of a solid 4 mm one saves 35% of the polymer | Thinner can mean weaker; test it |
| Material substitution | Replace a material with one of lower impact at the dominant stage | Recycled polypropylene shell instead of virgin; a steel frame instead of a mixed alloy | The substitute must meet the same criteria, not just sound better |
| Design for disassembly | Fasteners instead of adhesives; parts separate into single materials with common tools | Four bolts hold the shell to the frame; no glue, no rivets | Bolts cost more than glue and can loosen; specify a locking type |
| Mono-material | Make the whole part from one material so it recycles without sorting | The shell, its glides and its stacking bumpers all in polypropylene | One material rarely does every job best |
| Design for durability and repair | Lengthen the service life; make the wearing parts replaceable | Replaceable floor glides; a frame rated for 15 years of daily use | A longer life must be wanted; fashion can end a product before wear does |
| Modularity | Standard, interchangeable parts across a product family | One frame fits three shell sizes, so a school buys one set of spares | Standard interfaces can constrain the form |
| Product-service system | Sell the use, not the object; the maker keeps ownership and takes it back | The school leases chairs; the maker collects, refurbishes and reissues them | Needs a maker willing to run the return loop |
3.4A worked redesign: the school chair
The brief: a stacking classroom chair. Life cycle analysis shows the dominant stage is make (a solid virgin polymer shell) and, second, end of life (shell glued to frame; landfilled whole). The redesign attacks both.
| Measure | Existing chair | Redesign | Change |
|---|---|---|---|
| Polymer in shell | 1.8 kg virgin PP | 1.2 kg, 60% recycled PP, ribbed | −33% mass; −60% virgin |
| Fastening | Adhesive plus 6 rivets | 4 locking bolts | Separable with one tool |
| Time to separate materials | not possible by hand | 90 seconds | Recyclable at end of life |
| Materials in product | 4 | 2 (PP, steel) | Both loops open |
| Rated service life | 8 years | 15 years, glides replaceable | +88% life |
| Static load test (AS/NZS seating) | Pass | Pass at 2.5 mm ribbed; fail at 2.0 mm | Criterion met at 2.5 mm only |
| Unit cost at 5,000 units | $31 | $34 | +$3; recovered in year 9 |
Every row is a criterion with a number, and one of them is honest about a failure: the 2.0 mm shell did not pass the load test, so the redesign settled on 2.5 mm. The cost went up, and the table says so, then argues that the longer life pays it back. That is what an evaluation against sustainability criteria looks like — not «the new chair is eco-friendly», but a stage named, a measure chosen, a number before and after, and a trade-off admitted.
3.5Evaluating against sustainability criteria
- Write the criteria before redesigning, from the life cycle analysis: one for the dominant stage, one for end of life, one for service life, and the original functional criteria, which still apply. A chair that recycles beautifully and collapses is not a redesign.
- Each criterion needs a measure and a target: mass of virgin material (kg), recycled content (%), time to separate into single materials (s), rated life (years), energy in use (kWh per year), packaging volume (L per unit shipped).
- Beware greenwashing in your own folio: a natural-sounding material is not evidence. Bamboo shipped 9,000 km and bonded with formaldehyde resin can score worse than local recycled steel. Follow the numbers through the stages.
- Report the rebound: a cheaper, lighter product that people buy twice as often may cost more overall. Name it if it applies.
- IA3 is the largest single assessment in the course, and it is marked on this evaluation as much as on the design. Say what was not met, and what the next iteration would change.
Designing for the future, and the external exam
A product designed this year will be used in a world that does not exist yet. Futures thinking is the set of tools for designing into that uncertainty without guessing — and the external examination asks you to do it in two hours, on paper, for a brief you have never seen.
4.1Trends, drivers and signals
- A trend is a direction of change you can already measure: more people living alone; more deliveries per household; hotter summers. Trends are evidence, and you cite the source.
- A driver is the force behind a trend — the reason it is happening: an ageing population, cheaper batteries, a carbon price. A trend can reverse; a driver usually does not. Design for drivers.
- A signal is a small, early example of a possible future — a product, a rule, a behaviour that exists now in one place and may spread. A signal is not proof; it is a question worth asking.
- A megatrend is a large, slow, global shift that will shape decades: urbanisation, climate change, digitisation, an ageing world. Every brief you are given sits inside several.
| STEEP lens | Ask | Driver, for a school furniture brief |
|---|---|---|
| Social | How are people living, learning, working, ageing? | Classrooms are moving from rows to flexible group layouts |
| Technological | What is becoming cheap, small, or possible? | Every student carries a device that needs a flat surface and power |
| Economic | Who has money, and what is it being spent on? | Schools buy on whole-of-life cost, not purchase price |
| Environmental | Climate, resources, regulation on waste and emissions | Procurement rules increasingly require recycled content and take-back |
| Political | Law, standards, public funding, trade | Australian Standards for seating are being revised for heavier loads |
4.2Scenario building
A scenario is a plausible, internally consistent story about one possible future — not a prediction. The standard method takes the two most important uncertainties for the brief and crosses them, producing four futures to design for.
| Classroom furniture, 2040 | Learning stays mostly in the building | Learning is mostly distributed (home, hubs, online) |
|---|---|---|
| Materials remain cheap | «Big school, more of it» — large flexible rooms; furniture bought in volume; durability and stackability dominate | «The kit» — furniture is issued to students, moves between sites; lightness and folding dominate |
| Materials become scarce and costly | «Keep and repair» — schools own furniture for decades; modularity and repairable parts dominate | «Furniture as a service» — nobody owns a chair; leasing, take-back and remanufacture dominate |
- Name the two uncertainties that matter most and could genuinely go either way. If one is really a certainty, it is a driver, not an axis.
- Write each scenario as a short story from a user’s day, with a name. A scenario nobody can picture is not a scenario.
- Test the design in all four. A concept that works in three and fails in one is worth more than one that is perfect in a single future.
- Look for the robust features — the things every scenario rewards. In the table above, disassembly is rewarded in all four quadrants; that is where the design effort goes.
4.3Speculative design and backcasting
- Speculative design makes objects from a possible future in order to ask a question, not to sell a product: a kitchen appliance that rations water, a school uniform that reports its own repairs. The value is the conversation it starts about whether we want that future.
- Mark speculative work as speculative. A folio that presents a provocation as if it were a proposal has confused two jobs.
- Backcasting starts from a chosen future — «by 2040 every chair we sell comes back to us» — and works backwards to what must be true in 2035, 2030 and next year for it to happen. Forecasting asks what will happen; backcasting asks what has to.
- Futures thinking does not replace the criteria. It changes which criteria matter and how heavily they are weighted. The matrix still decides.
4.4The external examination: the design challenge
The paper gives you a stimulus (images, data, a scenario), a brief with a user and constraints, and a set of tasks that walk through the process in a fixed order. You answer in sketches and annotations as much as in sentences. Everything you have practised in the folio must now happen in about two hours.
| Task | What the examiner marks | Time | What it looks like on the page |
|---|---|---|---|
| Analyse the brief and stimulus | That you found the user, the requirements, the constraints, and the problem behind the request | ~20 min | Underlined brief; a one-sentence problem statement; three to five measurable criteria; the constraint that rules out the obvious |
| Generate ideas | Breadth and difference: genuinely distinct concepts, not one idea in three colours | ~40 min | Six to eight thumbnails, each annotated with what makes it different; two or three developed further |
| Evaluate the ideas | Judgement against the criteria you wrote, with reasons | ~20 min | A quick matrix or a criterion-by-criterion table; a stated choice; what the losing ideas lacked |
| Resolve and communicate | One concept developed to the point where a reader could picture it working, and a justification | ~35 min | A larger annotated sketch with dimensions, materials and reasons; a short paragraph tying it to the user and the criteria |
| Check | — | ~5 min | Every sketch labelled; every criterion referred to at least once; nothing unanswered |
Skipping the analysis and sketching from minute one, so the concept ignores a constraint that was in the brief. Producing three versions of one idea and calling it ideation. Choosing a concept «because it is the best» with no criterion named. And the beautiful unlabelled drawing: an examiner cannot give marks for thinking they cannot see.
4.5Annotated sketching for examiners
- Draw big. One concept per half page for the developed sketch; thumbnails can be small, but their annotations cannot be unreadable.
- Leader lines touch the part. A note floating near a drawing is a guess about what it refers to.
- Material, function, reason. Every note. If you cannot give a reason, you have not made a decision yet — write the question instead.
- Number your criteria and cite them in the notes: «(criterion 2)». It ties the sketch to the analysis you did in the first twenty minutes, and it is exactly what the marking scheme looks for.
- One dimension at least. Height, width, or the one measurement the user’s body dictates. It proves the idea has a size.
The year your code leaves the building.
Four units covering QCAA Digital Solutions Units 3 and 4. Year 11 built solutions that lived on one machine. Year 12 builds solutions that talk to other systems — a browser asking a server, a server asking a database, your app asking someone else's API — and makes you responsible for what happens to the data on the way.
The mapFour units, two QCAA units
- Interactions between users, data and digital systems — Unit 3, Topic 1. Usability and accessibility (WCAG), data structures from arrays to relational tables, SQL with aggregates and multi-table joins, searching and sorting in pseudocode, and validation.
- Real-world problems and solution requirements — Unit 3, Topic 2. The explore–develop–generate–evaluate process, prescribed and self-determined criteria, prototyping a web application in HTML, CSS and JavaScript, testing, and the IA2 project.
- Digital methods for exchanging data — Unit 4, Topic 1. Client–server, HTTP, REST APIs, JSON and XML, encoding, encryption and hashing, TLS, threats and mitigations, and the Australian Privacy Principles.
- Complex digital data exchange problems — Unit 4, Topic 2. Designing a source–transform–sink solution, data integrity and cleaning, working within API limits, the IA3 folio, and the external exam.
Four instruments. IA1 Investigation — technical proposal (20%). IA2 Project — digital solution (25%). IA3 Project — folio (30%). External examination (25%), set and marked by QCAA, assessing Unit 4 with short-response and extended-response items. Three quarters of your result is built during the year from work you can plan; the exam is the quarter you cannot.
Functional versus non-functional requirements, decomposition and abstraction, pseudocode with functions and trace tables, one-to-many relationships and 1NF/2NF, the basic SQL clauses including JOIN, unit/boundary/user testing, and the evaluation paragraph (claim, evidence, judgement, change). All of that is assumed here. If any of it feels shaky, the Year 11 course is one click away.
Users, data and digital systems
Every digital solution is three things meeting: a person with a task, data with a shape, and a system that moves the data around. This unit tightens each of them — interfaces you can defend with a standard, data structures chosen on purpose, SQL that summarises as well as filters, and algorithms you can trace and cost.
1.1Usability and accessibility, with a standard behind them
Usability is how effectively, efficiently and satisfyingly a typical user completes their task. Accessibility is whether people with a disability — low vision, colour-blindness, motor impairment, a screen reader — can complete it at all. The two overlap, but they are marked separately, and only one of them has a published standard you can quote.
The Web Content Accessibility Guidelines (WCAG) organise accessibility under four principles. The initials spell POUR:
| Principle | Meaning | Concrete rule you can test |
|---|---|---|
| Perceivable | Every user can take the content in through at least one sense | Images carry alt text; body text contrast is at least 4.5 : 1 against its background; colour is never the only signal |
| Operable | Every control can be reached and used | Everything works from the keyboard alone (Tab, Enter, Space); touch targets are large enough; nothing flashes |
| Understandable | Content and behaviour are predictable | Labels sit beside their fields; error messages name the field and say how to fix it; the page language is declared |
| Robust | Works with today's and tomorrow's browsers and assistive tools | Valid HTML; semantic elements (button, nav, label) rather than styled divs, so a screen reader knows what things are |
Name the principle, state the rule, show the fix. "The pale grey text on white fails the perceivable principle because its contrast is below 4.5 : 1; changing the text to #3A4941 raises it above 7 : 1." Three parts, one mark each. "Make it more accessible" on its own earns none of them.
1.2Data structures: choose the shape on purpose
| Structure | Shape | Reach an item with | Use it when |
|---|---|---|---|
| Array | A numbered list of values of one type, indexed from 0 | marks[3] | Items are the same kind of thing and order matters |
| Two-dimensional array | An array of arrays — a grid | grid[1][2] is row 1, column 2 | Timetables, game boards, pixel data, seating plans |
| Record | One thing with named fields of different types | ticket.paid | Describing one entity with several attributes |
| Array of records | Many records, in order | tickets[0].paid | Nearly all real data in a program, before it reaches a database |
| Relational table | Rows (records) and columns (attributes), with a primary key | SELECT … WHERE TicketID = 503 | Data that must survive the program ending, be shared, and never contradict itself |
With grid ← [[1, 2, 3], [4, 5, 6]], grid[0] is the whole first row [1, 2, 3], grid[1][2] is 6, and walking every cell takes a nested loop: FOR r FROM 0 TO 1 … FOR c FROM 0 TO 2. Both indexes start at 0, as always.
1.3The worked schema for this course
A school event-booking app. Three tables, and every SQL example below runs against these exact rows — learn them.
| STUDENT | ||
|---|---|---|
| StudentID PK | FirstName | YearLevel |
| 1 | Mia | 12 |
| 2 | Noah | 11 |
| 3 | Zara | 12 |
| 4 | Liam | 10 |
| EVENT | |||
|---|---|---|---|
| EventID PK | Title | Venue | Price |
| 10 | Formal | Hall | 85.00 |
| 11 | Film Night | Library | 5.00 |
| 12 | Careers Expo | Gym | 0.00 |
| TICKET | |||
|---|---|---|---|
| TicketID PK | StudentID FK | EventID FK | Paid |
| 501 | 1 | 10 | TRUE |
| 502 | 1 | 11 | TRUE |
| 503 | 2 | 11 | FALSE |
| 504 | 3 | 10 | TRUE |
| 505 | 4 | 12 | TRUE |
| 506 | 3 | 11 | FALSE |
1.4SQL: aggregates, grouping and three-table joins
Year 11's four clauses filter and sort rows. Year 12 adds aggregate functions that summarise many rows into one number, GROUP BY to summarise per group, and joins across more than two tables. Every query below has been run against the rows in 1.3.
SELECT FirstName FROM Student WHERE YearLevel = 12 ORDER BY FirstName ASC;
-- 2 rows: Mia, Zara
SELECT COUNT(*) FROM Ticket WHERE EventID = 11;
-- 3 (tickets 502, 503 and 506)
SELECT AVG(Price) FROM Event;
-- 30.00 ((85 + 5 + 0) / 3)
SELECT E.Title, COUNT(*) AS Sold
FROM Event E JOIN Ticket T ON E.EventID = T.EventID
GROUP BY E.Title;
-- Formal 2 · Film Night 3 · Careers Expo 1
SELECT S.FirstName, E.Title
FROM Student S
JOIN Ticket T ON S.StudentID = T.StudentID
JOIN Event E ON T.EventID = E.EventID
WHERE T.Paid = FALSE;
-- 2 rows: Noah – Film Night, Zara – Film Night
SELECT SUM(E.Price)
FROM Event E JOIN Ticket T ON E.EventID = T.EventID
WHERE T.Paid = TRUE;
-- 175.00 (85 + 5 + 85 + 0, from tickets 501, 502, 504, 505)
UPDATE Ticket SET Paid = TRUE WHERE TicketID = 503;
-- changes ONE row. Without the WHERE it would mark every ticket paid.
- The five aggregates: COUNT, SUM, AVG, MIN, MAX. An aggregate on its own collapses the whole result to one row; with GROUP BY it produces one row per group.
- Every column in the SELECT that is not inside an aggregate must appear in the GROUP BY. SELECT E.Title, COUNT(*) … GROUP BY E.Title obeys that rule.
- A three-table join is two JOINs in a row. Each ON matches a foreign key to the primary key it refers to; the linking table sits in the middle of the chain.
- Clause order is fixed: SELECT → FROM → JOIN…ON → WHERE → GROUP BY → ORDER BY. WHERE filters rows before grouping.
- INSERT, UPDATE and DELETE change data. Year 11 said "a query only reads"; that is no longer true, and it is why an UPDATE or DELETE without a WHERE clause is the most expensive typo in the subject.
1.5Searching and sorting, in pseudocode
Year 11 compared linear and binary search by cost. Year 12 expects you to write them and to trace them. Pseudocode conventions are unchanged: ← stores, = compares, keywords in capitals, indexes from 0, DIV is whole-number division.
FUNCTION linearSearch(list, target)
FOR i FROM 0 TO LENGTH(list) - 1
IF list[i] = target THEN RETURN i
END FOR
RETURN -1
END FUNCTION
FUNCTION binarySearch(list, target) // list MUST be sorted
lo ← 0
hi ← LENGTH(list) - 1
WHILE lo <= hi
mid ← (lo + hi) DIV 2
IF list[mid] = target THEN RETURN mid
IF list[mid] < target THEN lo ← mid + 1
ELSE hi ← mid - 1
END WHILE
RETURN -1
END FUNCTION
PROCEDURE bubbleSort(list)
FOR pass FROM 1 TO LENGTH(list) - 1
FOR i FROM 0 TO LENGTH(list) - 2
IF list[i] > list[i + 1] THEN swap list[i] and list[i + 1]
END FOR
END FOR
END PROCEDURE
Trace of binarySearch on [3, 8, 12, 17, 23, 31, 44] for target 23:
| Pass | lo | hi | mid = (lo + hi) DIV 2 | list[mid] | Compared with 23 | Next |
|---|---|---|---|---|---|---|
| 1 | 0 | 6 | 3 | 17 | 17 < 23 | lo ← 4 |
| 2 | 4 | 6 | 5 | 31 | 31 > 23 | hi ← 4 |
| 3 | 4 | 4 | 4 | 23 | equal | RETURN 4 |
Three values examined (17, 31, 23) for a list of seven. A linear search for 31 would examine six. One pass of bubbleSort on [5, 2, 9, 1] compares 5–2 (swap), 5–9 (no), 9–1 (swap) and leaves [2, 5, 1, 9]: the largest value has "bubbled" to the end, which is why each later pass can be one shorter.
Bubble sort is the easiest to write and trace; selection sort finds the smallest remaining item and swaps it into place; insertion sort takes each item and slides it back to where it belongs. All three cost about n × n comparisons on n items. In the exam you are asked to trace a given one accurately and to say why a nested-loop sort gets four times slower when the data doubles — not to pick the fastest.
1.6Data validation
Validation is the system checking that input is plausible before it is stored or used. It cannot know whether the input is true — that is verification (a confirmation e-mail, a double entry, a human check).
| Check | Question it asks | Rejects |
|---|---|---|
| Presence | Was anything entered at all? | A blank FirstName |
| Type | Is it the right kind of value? | "twelve" in a numeric YearLevel field |
| Range | Is a number between its limits? | YearLevel 13, when the school runs 7 to 12 |
| Length | Is the text the right number of characters? | A ticket code of 5 characters when every code is 6 |
| Format | Does it match the pattern? | An e-mail address with no @; a code that does not start with T |
| Lookup | Does it exist in the reference list? | EventID 99, which is in no row of EVENT |
FUNCTION isValidCode(code) // format: "T" + 5 characters
IF LENGTH(code) <> 6 THEN RETURN false // length check
IF code[0] <> "T" THEN RETURN false // format check
RETURN true
END FUNCTION
Validate on the client for fast feedback and on the server, because anything sent from a browser can be altered before it arrives. A server that trusts the browser's validation has no validation.
Real-world problems and solution requirements
The IA2 project is a working web application built for a real problem, marked against criteria you partly wrote yourself. This unit is the method: how the four phases of the problem-solving process turn a messy brief into a solution you can test, and how a prototype earns marks before a single feature is finished.
2.1The problem-solving process: explore, develop, generate, evaluate
| Phase | What you do | What you produce |
|---|---|---|
| Explore | Investigate the problem, the users, the existing system, the constraints; elicit and confirm requirements | A problem statement, user needs, functional and non-functional requirements, the criteria |
| Develop | Design the solution on paper: data model, algorithms, user interface, how the parts connect | Relational schema, pseudocode, wireframes and user-flow diagrams, a test plan |
| Generate | Build it — code, database, interface — and refine as you go | A working prototype, then the solution; annotated code; development log |
| Evaluate | Test against the criteria, judge each one, recommend refinements | Test results with evidence, an evaluation, and a list of justified improvements |
The phases are iterative, not a straight line: a test result in Evaluate sends you back to Develop, and a user's reaction to a wireframe in Develop can rewrite a requirement from Explore. In the folio, show the loop — a changed decision with its reason is worth more than a first guess that happened to survive.
2.2Prescribed and self-determined criteria
Criteria are the yardsticks the solution is judged by. Two kinds, and the exam expects you to tell them apart:
| Kind | Comes from | Example, for the event-booking app |
|---|---|---|
| Prescribed criteria | The task, the client, the syllabus — given to you, non-negotiable | "The solution must use a relational database with at least two related tables." "It must be accessible to keyboard-only users." |
| Self-determined criteria | You, from your own exploration of the users and the problem — and you must justify each one | "A student can book a ticket in no more than four taps, because the current paper form takes six steps and is abandoned at lunch." "A double booking of the same student for the same event is refused." |
It must be measurable (a number, a yes/no, a pass/fail), traceable to a requirement or a user need, and written before you build. "The app is easy to use" is not a criterion. "Three first-time users each complete a booking unaided in under 90 seconds" is — and it tells you exactly which test to run in Evaluate.
2.3Prototyping a web application
Year 11 prototyped on paper. Year 12 prototypes in the browser, because the solution is a web application: HTML for structure, CSS for presentation, JavaScript for behaviour. A prototype is deliberately incomplete — it exists to test one thing. This one tests whether a booking form is understandable and validates its input:
<form id="book">
<label for="sid">Student ID</label>
<input id="sid" type="number" min="1" required>
<label for="ev">Event</label>
<select id="ev">
<option value="10">Formal — $85.00</option>
<option value="11">Film Night — $5.00</option>
<option value="12">Careers Expo — free</option>
</select>
<button type="submit">Book ticket</button>
<p id="msg" role="status"></p>
</form>
<script>
const form = document.getElementById("book");
const msg = document.getElementById("msg");
form.addEventListener("submit", function (e) {
e.preventDefault(); // stay on the page
const sid = Number(document.getElementById("sid").value);
if (!Number.isInteger(sid) || sid < 1) { // type + range check
msg.textContent = "Student ID must be a whole number of 1 or more.";
return;
}
msg.textContent = "Booking student " + sid + " for event " +
document.getElementById("ev").value + "…";
// next iteration: send this to the server as a POST request
});
</script>
- Every input has a label joined to it by for and id — a screen reader reads "Student ID" when the field gets focus. That is the WCAG understandable principle, in one attribute.
- The message element has role="status", so assistive tools announce it when its text changes. Visible feedback for everyone, spoken feedback for those who need it.
- The JavaScript does client-side validation and says exactly what is wrong. It does not replace server-side validation — the comment marks where the next iteration goes.
- Structure, presentation and behaviour stay in their own layers. A CSS rule such as input:invalid { border-color: var(--wrong); } adds the visual cue without touching the logic.
2.4Testing and evaluation, at project scale
Year 11's five-column test table still applies, but a project has more kinds of test and the evaluation is against the criteria, not just the requirements.
| Kind | Tests | Example on the booking app |
|---|---|---|
| Unit | One function against a hand-calculated result | isValidCode("T12345") returns true; isValidCode("T1234") returns false |
| Boundary | The edges of every range | Student ID 0, 1, and blank; year level 6, 7, 12, 13 |
| Integration | Two parts working together | Submitting the form really inserts one TICKET row with the right two foreign keys |
| Usability | Real users on real tasks, observed and timed | Three students book a ticket unaided; hesitations and errors recorded |
| Accessibility | Against WCAG rules | Whole booking flow completed with the keyboard only; contrast checked with a tool |
| Security | Hostile input | A Student ID of 1; DROP TABLE Ticket is rejected as not an integer, and the query is parameterised anyway |
- State the criterion and say whether it was prescribed or self-determined.
- Quote the evidence: test ID, input, expected, actual — or the observation from the usability session.
- Judge: met, partly met, or not met, and say what "partly" means in numbers.
- Recommend a refinement tied to that evidence, and estimate its cost.
2.5The IA2 project: what the folio must show
- Explore: the problem, the users, the requirements, and the criteria table with prescribed and self-determined criteria separated and justified.
- Develop: the data model (schema, keys, relationships), the algorithms in pseudocode, the interface designs, the user flow, and the test plan written before coding.
- Generate: the working solution, with annotated code showing where each algorithm and each validation lives, and a log of decisions changed along the way.
- Evaluate: every criterion judged with evidence, refinements recommended, and a short reflection on the process itself.
- The whole thing is judged on communication too: consistent naming, labelled diagrams, and a reader who has never seen your app being able to follow it.
Digital methods for exchanging data
The moment data leaves your program it needs an address, a format, and protection. This unit is how a browser and a server actually talk, what JSON and XML look like on the wire, how encryption and hashing keep the conversation private and honest, and what the law says you may do with what you collect.
3.1Client–server and the HTTP request
| Method | Meaning | Body? | Example |
|---|---|---|---|
| GET | Read a resource; changes nothing | No | GET /api/events/11 |
| POST | Create a new resource | Yes — the new thing, usually JSON | POST /api/tickets with {"studentId":2,"eventId":10} |
| PUT | Replace or update a resource | Yes | PUT /api/tickets/503 with {"paid":true} |
| DELETE | Remove a resource | No | DELETE /api/tickets/506 |
| Status | Means | Whose fault |
|---|---|---|
| 200 OK | Done; the body has what you asked for | — |
| 201 Created | Your POST made a new resource | — |
| 400 Bad Request | The request was malformed or failed validation | Client |
| 401 Unauthorized | No valid token — you have not proved who you are | Client |
| 403 Forbidden | Known who you are; not allowed to do this | Client |
| 404 Not Found | No such resource | Client |
| 429 Too Many Requests | You have hit the rate limit; wait | Client |
| 500 Internal Server Error | The server crashed handling it | Server |
A REST API is a web service organised around resources with URLs, using the HTTP methods for their standard meanings and returning a standard format, usually JSON. Each URL that the API answers is an endpoint. REST is stateless: every request carries everything the server needs, including the token, because the server does not remember the previous request.
3.2JSON and XML, side by side
The same two tickets in both formats. JSON is what almost every modern API returns; XML still carries a great deal of institutional and document data, and the exam can hand you either.
{
"tickets": [
{ "ticketId": 501, "studentId": 1, "eventId": 10, "paid": true },
{ "ticketId": 503, "studentId": 2, "eventId": 11, "paid": false }
]
}
<?xml version="1.0" encoding="UTF-8"?>
<tickets>
<ticket id="501">
<studentId>1</studentId>
<eventId>10</eventId>
<paid>true</paid>
</ticket>
<ticket id="503">
<studentId>2</studentId>
<eventId>11</eventId>
<paid>false</paid>
</ticket>
</tickets>
| JSON | XML | |
|---|---|---|
| Building blocks | Objects { } of key–value pairs, arrays [ ], strings, numbers, true/false, null | Nested elements with opening and closing tags; attributes on the opening tag |
| Rules that bite | Keys and strings in double quotes; no trailing comma; no comments | Every tag closed; one root element; case-sensitive; &, < and > must be escaped in text |
| Types | Numbers and booleans are real types: "paid": true | Everything is text: <paid>true</paid> is a string until you convert it |
| Size and speed | Smaller; parsed natively by JavaScript (JSON.parse) | More verbose; needs an XML parser; supports schemas that validate the structure |
| Read in JavaScript | data.tickets[1].paid → false | Walk the element tree, or convert to an object first |
3.3Data encoding
- Character encoding maps characters to bytes. ASCII covers 128 characters in 7 bits — English letters, digits, punctuation. UTF-8 extends it to every writing system: ASCII characters still take 1 byte, others 2 to 4. A file saved as one encoding and read as another produces the classic "é" garbage, which is why the XML above declares its encoding on line 1.
- Base64 turns any bytes — an image, a PDF — into 64 safe text characters so they can travel inside JSON or a URL. Every 3 bytes become 4 characters, so the data grows by about a third. Base64 is encoding, not encryption: anyone can decode it.
- URL encoding replaces characters that a URL cannot carry: a space becomes %20, an ampersand %26. The query ?title=Film%20Night is "Film Night".
- Encoding is reversible by anyone and protects nothing. That is the job of the next section.
3.4Encryption, hashing and TLS
| Symmetric encryption | Asymmetric encryption | Hashing | |
|---|---|---|---|
| Keys | One shared secret key encrypts and decrypts | A pair: the public key encrypts, only the matching private key decrypts | No key — a fixed function |
| Reversible? | Yes, with the key | Yes, with the private key | No: one-way. You cannot get the input back |
| Typical algorithm | AES (128- or 256-bit key) | RSA | SHA-256 (always 256 bits, 64 hex characters, whatever the input size) |
| Speed | Fast — used for the bulk of the data | Slow — used to exchange the symmetric key and to sign | Fast |
| The problem it solves | Privacy, once both sides have the key | Getting the key to the other side safely, and proving identity | Integrity (has this changed?) and password storage |
| Its weakness | How do you deliver the key without an eavesdropper getting it? | Too slow for large data; you must trust the public key really belongs to the server | Same input always gives the same hash, so common passwords are guessable — hence a salt |
A stored password is hashed with a random salt added first, and the salt is stored beside the hash. At login the system hashes what you typed with the same salt and compares. The password itself is never stored, so a stolen database yields hashes that cannot be reversed — and because every user's salt differs, two people with the password password123 get different hashes, and a pre-computed table of common hashes is useless.
3.5Threats and mitigations
| Threat | How it works | Mitigation |
|---|---|---|
| SQL injection | Input such as 1 OR 1=1 is pasted into a query string and changes its meaning | Parameterised queries: the value is sent separately from the SQL and can never become code; plus validation |
| Cross-site scripting (XSS) | A user submits <script> in a comment; the page shows it to others and it runs in their browsers | Escape everything before it is put on a page (< becomes <); set textContent, not innerHTML |
| Man-in-the-middle | Someone on the same network reads or alters traffic in transit | TLS (HTTPS) everywhere, with a valid certificate |
| Phishing | A fake login page harvests real passwords | Multi-factor authentication, so the password alone is not enough; user education |
| Brute force / credential stuffing | Trying many passwords, or passwords leaked from another site | Rate limiting and lockouts; salted hashes; MFA |
| Denial of service (DoS/DDoS) | Flooding the server with requests so real users cannot get through | Rate limiting, caching, spreading the load across servers |
3.6Privacy: the Australian Privacy Principles
The Privacy Act 1988 (Cth) sets out 13 Australian Privacy Principles (APPs) governing personal information. At syllabus level, these are the ones a design decision turns on:
| Principle | Obligation | Design consequence for the booking app |
|---|---|---|
| APP 1 Open and transparent management | Have a clear, current privacy policy | A privacy page saying what is collected, why, and who sees it |
| APP 3 Collection of solicited personal information | Collect only what is reasonably necessary for a function | No date of birth, no home address — a ticket needs neither |
| APP 5 Notification of collection | Tell people, at or before collection, what you collect and why | A one-line notice on the booking form, not buried in a policy |
| APP 6 Use or disclosure | Use it only for the purpose collected, unless consented or required by law | The ticket list is not passed to a photographer's marketing list |
| APP 11 Security | Protect it from misuse, loss and unauthorised access; destroy or de-identify it when no longer needed | TLS, hashed passwords, access control, and deleting ticket data after the event |
| APP 12 / 13 Access and correction | Let people see and correct their own information | A "my bookings" page with an edit option |
The design habit that satisfies most of these at once: a field you never collected can never leak, never needs securing, and never needs deleting. Data minimisation is a security control and a privacy control in one decision.
Complex digital data exchange problems
Real data arrives from somewhere else, in someone else's shape, with someone else's mistakes in it. This unit is the discipline of moving it safely from a source to where you need it — and it is the unit the external exam is written on.
4.1Designing a data-exchange solution: source, transformation, sink
A worked case. The Bureau of Meteorology's API returns hourly readings as JSON with temperature in tenths of a degree and a timestamp in UTC. Your sink is a READING table with columns Station, LocalTime, TempC. The transformation rules, written so a marker can check them:
- Parse the JSON body into an array of records.
- Convert: TempC ← temp_tenths ÷ 10; LocalTime ← utc + 10 hours (AEST, no daylight saving in Queensland).
- Rename: station_id → Station. Drop the fields the sink does not have.
- De-duplicate: the API sometimes resends the last hour. Keep one row per (Station, LocalTime).
- Validate: TempC between −10 and 55; LocalTime not in the future; Station present in the STATION table.
- Load the valid rows with INSERT; write the rejected rows and their reasons to the log; record how many of each.
4.2Data integrity and cleaning
Data integrity means the data is accurate, consistent and complete over its whole life. The database enforces part of it; the pipeline must do the rest.
| Kind | Rule | Enforced by | Broken example |
|---|---|---|---|
| Entity integrity | Every row has a unique, non-null primary key | The PRIMARY KEY constraint | Two tickets both numbered 503 |
| Referential integrity | Every foreign key points at a row that exists | The FOREIGN KEY constraint | A ticket for EventID 99, which is in no EVENT row |
| Domain integrity | Every value is of the right type and within its allowed set | Column types, CHECK constraints, validation | Paid = "maybe"; Price = −5 |
| Consistency across sources | The same fact means the same thing everywhere | The transformation rules | One source in Celsius, one in tenths of a degree, merged without conversion |
| Cleaning problem | Looks like | Fix, with the decision stated |
|---|---|---|
| Missing values | An empty TempC; "N/A"; 999 used as "no reading" | Reject the row, or store NULL — never a fake number. Say which and why |
| Duplicates | The same reading resent, or the same student typed twice as "Mia" and "mia " | Define what makes two rows the same, then keep one |
| Inconsistent format | Dates as 03/04/2026 and 2026-04-03; names in mixed case; trailing spaces | Normalise to one format on the way in (ISO dates, trimmed, one case) |
| Out-of-range | A temperature of 87 °C; a year level of 0 | Range check; reject and log |
| Wrong type | "5.00" as text where a number is needed | Convert explicitly; reject what will not convert |
4.3Working with APIs: keys, limits and failure
- Most APIs require an API key or token identifying your application, sent in a header. It is a secret: it lives on your server, never in JavaScript sent to a browser, and never in a public repository.
- A rate limit caps how many requests you may make in a period — say 60 per minute. Exceed it and you get 429 Too Many Requests. Design for it: cache responses you have already fetched, request in batches, and wait before retrying rather than hammering.
- Every call can fail: the network drops, the server returns 500, the format changes. A pipeline that assumes success is a pipeline that silently loads nothing. Check the status code, handle the failure, log it.
- Read the documentation for units and formats before writing a single transformation. "temp_tenths" was in the docs; guessing would have loaded 235 °C.
- Give attribution and respect the terms of use. Data is licensed, like images.
// Fetch one page of readings; retry once on a rate limit
async function fetchReadings(station) {
const url = "https://api.example.gov.au/readings?station=" + station;
let res = await fetch(url, { headers: { "Authorization": "Bearer " + KEY } });
if (res.status === 429) { // rate limited: wait, then retry once
await new Promise(ok => setTimeout(ok, 60000));
res = await fetch(url, { headers: { "Authorization": "Bearer " + KEY } });
}
if (!res.ok) { log("fetch failed", station, res.status); return []; }
const data = await res.json(); // JSON body → JavaScript object
return data.readings; // an array of records
}
4.4The IA3 project: the folio
- IA3 is worth 30% — the largest single instrument. It is a data-exchange solution built through the same explore–develop–generate–evaluate process as IA2, but the problem is about moving data between systems, and the folio must show why each design decision was made.
- Explore: the source system and its format, the sink and its needs, the users, the privacy and security obligations, the criteria.
- Develop: the pipeline diagram (like figure 4.1, for your data), the transformation rules in pseudocode, the validation rules, the schema of the sink, the security design (where the keys live, what is encrypted, what is hashed).
- Generate: the working exchange — code that fetches, transforms, validates and loads, with a log.
- Evaluate: the criteria judged with evidence, including counts — rows received, rows rejected and why, rows loaded — and the impacts: on users, on privacy, on the organisation.
4.5The external examination
Worth 25%, set by QCAA, on Unit 4. It has short-response items (a definition, a calculation, a query, a short justification) and extended-response items that give you a scenario — a data source, a format, a sink, a threat — and ask you to design or evaluate the exchange.
Read the scenario twice and list what is given: the source format, the sink's shape, the constraints. Draw the pipeline. Then write in the phase order: what the transformation must do (named rules), what validation is needed (named checks, with what happens on failure), how the data is protected in transit and at rest (name the mechanism, not just "encryption"), and which privacy principle each decision satisfies. Every claim gets a reason. The markers' scheme rewards specific, justified statements — "use TLS so that a token cannot be read on shared Wi-Fi" — and gives nothing for "make it secure".
REST API · endpoint · JSON · XML · encoding · symmetric encryption · asymmetric encryption · hash and salt · data integrity · rate limit. If any of them takes you more than one sentence, go back to the section that defines it.
Now the structure has to stand up.
Four units covering QCAA Engineering Units 3 and 4. Year 11 gave you the tools — stress, moments, equilibrium, gear ratios. Year 12 points them at whole systems: a loaded beam and what is happening inside it, a truss member by member, a material chosen by the numbers, a gearbox designed backwards from the torque it must deliver, and a machine that corrects itself.
The mapUnits 3 and 4, four topics
- Unit 3, Topic 1 — Civil structures. Dead, live and wind loads; reactions on beams with several loads and distributed loads; trusses by the method of joints; shear force and bending moment diagrams; columns and buckling.
- Unit 3, Topic 2 — Materials science. Stress, strain and extension; ductile against brittle stress–strain curves; hardness, toughness and fatigue; choosing a material with a selection matrix; designing a member with a factor of safety.
- Unit 4, Topic 1 — Mechanical machines. Mechanical advantage, velocity ratio and efficiency; compound gear trains, torque and power; screws and screw jacks; linkages and cams; energy and power in machines.
- Unit 4, Topic 2 — Control and emerging technologies. Open- and closed-loop control, sensors and actuators, block diagrams and feedback, an automated system case study, and technique for the external examination.
Four instruments of equal weight. IA1 Project — folio (25%). IA2 Examination (25%). IA3 Project — folio (25%). External examination (25%), set and marked by QCAA: problem-solving with given data, where the working, the units and the significant figures are marked as well as the answer.
σ = F ÷ A with 1 MPa = 1 N/mm²; ε = ΔL ÷ L₀; E = σ ÷ ε; W = mg; components F cos θ and F sin θ; M = F × d; ΣF = 0 and ΣM = 0; reactions on a simply supported beam with one load; lever classes; gear ratio = driven ÷ driver; P = 2πNT ÷ 60; efficiency; factor of safety; the failure modes. Assumed here, not re-taught.
Civil structures: what is happening inside the beam
Year 11 found the reactions and stopped. A structural engineer keeps going: what force is each member of the truss carrying, and is it pushed or pulled? At which point along the beam is the bending greatest, and by how much? The two diagrams that answer that second question are the centre of this topic.
1.1Loads: dead, live, and wind
| Load | What it is | Examples | How it is treated |
|---|---|---|---|
| Dead load | The permanent weight of the structure itself and everything fixed to it | Slabs, beams, roof sheeting, fixed partitions, cladding | Known accurately from drawings and material densities; always present |
| Live load (imposed) | Whatever the structure carries that can change | People, furniture, stored goods, vehicles, a crowd in a grandstand | Taken from AS/NZS 1170.1 by building use; the worst credible arrangement is designed for |
| Wind and environmental | Loads from the environment acting on the structure | Wind pressure and suction, snow, earthquake, flood, thermal expansion | From AS/NZS 1170.2 (wind) and related parts; depends on region, height and exposure |
A point load acts at one place (a column landing on a beam). A uniformly distributed load (UDL) is spread evenly along a length, in kN per metre — a slab's weight on the beam under it. For finding reactions, a UDL of w kN/m over L metres is replaced by a single force of w × L acting at its midpoint.
1.2Reactions with several loads
A 6 m beam carries a uniformly distributed load of 2 kN/m along its whole length. Total load = 2 × 6 = 12 kN, acting at mid-span (3 m from A). By symmetry, R(A) = R(B) = 6 kN. The maximum bending moment for a UDL on a simply supported span is wL² ÷ 8 = 2 × 36 ÷ 8 = 9 kN·m, at mid-span. Compare: the same 12 kN as a single point load at mid-span would give PL ÷ 4 = 12 × 6 ÷ 4 = 18 kN·m — twice as much. Spreading a load out halves its worst bending, which is why slabs sit on beams and not on posts.
1.3Trusses by the method of joints
A truss is a frame of straight members joined at pins, loaded only at the joints. Each member then carries a force along its own length — pure tension or pure compression, no bending. The method of joints finds those forces one joint at a time: at every pin, ΣFx = 0 and ΣFy = 0, two equations, so start at a joint with no more than two unknown members.
- Find the reactions for the whole truss first, exactly as for a beam.
- Pick a joint with at most two unknown members. A support joint usually qualifies.
- Draw that joint's free-body diagram: the known forces, and every member force drawn as tension (away from the joint).
- Resolve: ΣFx = 0 and ΣFy = 0. Two equations, two unknowns.
- Move to the next joint, carrying the forces you now know. A member in compression pushes on both its joints.
- Check at the last joint: everything should balance with nothing left to solve.
1.4Shear force and bending moment diagrams
Reactions tell you what the supports do. To size the beam you need what happens inside it, at every point along its length. Two quantities describe that:
- Shear force V at a section is the net vertical force on one side of it — the tendency of the beam to be cut across. Convention used here: working from the left, an upward force makes V positive.
- Bending moment M at a section is the net moment of everything on one side of it about that section — the tendency of the beam to bend. Sagging (the middle drooping) is positive.
- The two are linked: where V is zero, M is at a maximum. The gradient of the M diagram at any point equals V there.
The beam must be strong enough for the largest bending moment, 16 kN·m, which occurs under the load — not at the middle. Moving that load to mid-span gives PL ÷ 4 = 12 × 6 ÷ 4 = 18 kN·m, the worst position. The largest shear, 8 kN, is at support A. A deep I-section resists bending because it puts material far from the centre; the web resists the shear. Both diagrams are therefore read before a section is chosen.
1.5Columns and buckling, in words
- A short, stocky column fails by crushing when the stress reaches the material's compressive strength. A long, slender one fails by buckling — bowing sideways — at a load that can be far lower, while the stress is still well inside the elastic region.
- The buckling load falls with the square of the effective length: make a column twice as long and it carries about a quarter of the load. That is why long struts are braced at mid-height — bracing halves the effective length and roughly quadruples the capacity.
- It rises with the material's stiffness E, not its strength, and with how far the section's material sits from its centre. A hollow tube out-buckles a solid rod of the same mass; an I-section beats a flat bar.
- End conditions matter: fixed ends resist rotation and raise the buckling load; pinned ends lower it.
- Buckling is sudden and gives no warning — so slender compression members get larger factors of safety than ties.
Materials science: choosing by the numbers
Year 11 defined the properties. Year 12 uses them to make decisions: how much a tie will stretch, whether a material will warn you before it fails, how a part survives a million load cycles, which of four candidate materials wins for a footbridge, and how big a member must be to carry its load with a margin.
2.1Stress, strain and extension
Three equations, chained: σ = F ÷ A, ε = σ ÷ E, ΔL = ε × L₀. Combined, the extension of a member under load is ΔL = F × L₀ ÷ (A × E). Keep F in newtons, A in mm², L in mm and E in MPa (N/mm²) and the extension comes out in millimetres.
| Worked: an aluminium tie | Working | Result |
|---|---|---|
| Area 250 mm², load 35 kN. Stress? | σ = 35 000 ÷ 250 | 140 MPa |
| E for aluminium alloy = 70 GPa = 70 000 MPa. Strain? | ε = 140 ÷ 70 000 | 0.002 (0.2%) |
| Original length 1.5 m = 1500 mm. Extension? | ΔL = 0.002 × 1500 | 3 mm |
| Same tie in steel (E = 200 GPa). Extension? | ΔL = (140 ÷ 200 000) × 1500 | 1.05 mm — steel is nearly three times stiffer |
| A 16 mm steel rod (A = π × 16² ÷ 4 = 201 mm²) carrying 30 kN. Stress? | σ = 30 000 ÷ 201 | 149 MPa — below mild steel's 250 MPa yield |
Notice what the aluminium answer means for a structure: a 1.5 m tie stretching 3 mm is fine for a shed and unacceptable for a machine frame holding a bearing in line. Stiffness, not strength, often governs the choice — a part can be nowhere near yielding and still deflect too much to do its job.
2.2Ductile against brittle
| Ductile | Brittle | |
|---|---|---|
| Before fracture | Yields, then large plastic deformation; necks | Almost none — fails at the end of the straight line |
| Fracture surface | Cup-and-cone, dull, fibrous | Flat, bright, crystalline |
| Toughness | High — large area under the curve | Low — small area |
| Sensitivity to flaws | Low: a small scratch is blunted by yielding | High: a scratch or notch starts the crack |
| Examples | Mild steel, copper, aluminium, most polymers when warm | Cast iron, glass, ceramics, concrete in tension, many polymers when cold |
| Design consequence | Use for members that must not fail without warning — beams, ties, bolts | Use only in compression, or with reinforcement, or with a large factor of safety |
2.3Hardness, toughness and fatigue at senior level
- Hardness (surface resistance to indentation) and toughness (energy to fracture) still trade against each other. Heat-treating a steel to harden the surface of a gear tooth against wear is done case-hardening: a hard skin over a tough core, so the tooth resists scratching yet does not shatter under a shock. One part, two microstructures, chosen on purpose.
- Fatigue is failure under repeated loading at stresses below yield. An S–N curve plots the stress amplitude S against the number of cycles N to failure: the higher the stress, the fewer cycles survive. Steels show an endurance limit — a stress below which they last indefinitely, roughly 40–50% of the UTS. Aluminium alloys have no endurance limit: at any stress they eventually fail, which is why aircraft structures are given finite lives and inspection schedules.
- Fatigue cracks start at stress raisers: sharp internal corners, holes, keyways, weld toes, surface scratches, corrosion pits. Design against fatigue is mostly geometry — generous fillet radii, polished surfaces, no sudden changes of section — plus keeping the stress amplitude under the endurance limit.
- A fatigue fracture surface tells its own story: smooth "beach marks" where the crack grew cycle by cycle, then a rough final region where the remaining section snapped. Investigators read failures from these.
2.4Selecting a material for a structure
A selection matrix turns an argument into arithmetic: list the criteria, weight them by importance, score each candidate, multiply and add. Worked for the main beams of a 20 m pedestrian footbridge in a coastal town:
| Criterion (weight) | Structural steel | Aluminium alloy | Glulam timber | Reinforced concrete |
|---|---|---|---|---|
| Strength-to-weight (3) | 4 × 3 = 12 | 5 × 3 = 15 | 3 × 3 = 9 | 2 × 3 = 6 |
| Stiffness — deflection under a crowd (3) | 5 × 3 = 15 | 3 × 3 = 9 | 3 × 3 = 9 | 4 × 3 = 12 |
| Corrosion resistance, salt air (2) | 2 × 2 = 4 | 5 × 2 = 10 | 3 × 2 = 6 | 3 × 2 = 6 |
| Cost, supplied and installed (2) | 4 × 2 = 8 | 2 × 2 = 4 | 4 × 2 = 8 | 3 × 2 = 6 |
| Embodied energy and end of life (1) | 3 × 1 = 3 | 2 × 1 = 2 | 5 × 1 = 5 | 2 × 1 = 2 |
| Total (max 55) | 42 | 40 | 37 | 32 |
- Steel wins on stiffness and cost, but its corrosion score is what the coastal site punishes — the decision then depends on whether galvanising or a paint system (an added cost and a maintenance schedule) is acceptable. The matrix does not end the argument; it shows exactly where the argument is.
- The weights are the client's priorities, decided before scoring. Changing them afterwards to get the answer you wanted is the classic folio error, and markers look for it.
- A criterion can also be a gate: a material that fails a must-have (say, non-combustible) is eliminated before scoring, however well it would score elsewhere.
2.5Designing a member with a factor of safety
Year 11 calculated a factor of safety. Year 12 designs with one: choose the material, apply the factor to get an allowable stress, and size the member so its working stress stays under it.
| Worked: a mild-steel tie for 60 kN | Working | Result |
|---|---|---|
| Yield strength 250 MPa, required FoS 2 on yield. Allowable stress? | 250 ÷ 2 | 125 MPa |
| Minimum cross-sectional area? | A = F ÷ σ = 60 000 ÷ 125 | 480 mm² |
| Diameter of a round bar with that area? | d = √(4A ÷ π) = √(1920 ÷ 3.1416) = √611.2 | 24.7 mm → specify 25 mm |
| Actual FoS with the 25 mm bar (A = 491 mm²)? | σ = 60 000 ÷ 491 = 122 MPa; FoS = 250 ÷ 122 | 2.05 — just over the required 2 |
The calculated 24.7 mm is a minimum. Rounding down to 24 mm would give an area of 452 mm², a stress of 133 MPa and a factor of safety of 1.88 — below what was specified. Always round a required size up to the next available stock size, then recalculate the actual factor of safety and state it. That last line is where the mark is.
- Apply the factor to yield for ductile materials (permanent deformation is the failure) and to the ultimate strength for brittle ones (there is no yield to use). Say which you used.
- Typical values: 1.5–2 for well-known static loads on ductile materials; 3–4 where loads are uncertain or shock; 4 or more for brittle materials, buckling, and anything whose failure would injure people.
- A factor of safety covers what the calculation could not know. It does not excuse a wrong calculation.
Mechanical machines: designed from the output backwards
Year 11 asked what a machine does. Year 12 asks what machine you need: given the torque a conveyor must deliver and the motor you can buy, what gear train joins them? Given a 20 kN car and a person's arm, what screw jack lifts it? The answers come from three ratios and one conservation law.
3.1Mechanical advantage, velocity ratio and efficiency
| Quantity | Definition | What it depends on |
|---|---|---|
| Mechanical advantage MA | load ÷ effort | Measured on the real machine; friction reduces it |
| Velocity ratio VR | distance moved by effort ÷ distance moved by load, in the same time | Geometry only — arm lengths, tooth counts, rope sections, thread lead. Friction cannot change it |
| Efficiency η | useful work out ÷ work in × 100% = MA ÷ VR × 100% | Friction, and nothing else. For an ideal machine MA = VR and η = 100% |
Worked: an effort of 250 N moves 2 m while the 1000 N load rises 0.4 m. VR = 2 ÷ 0.4 = 5. MA = 1000 ÷ 250 = 4. Efficiency = 4 ÷ 5 × 100 = 80%. Check with work: in = 250 × 2 = 500 J, out = 1000 × 0.4 = 400 J, 400 ÷ 500 = 80% — the same number by both routes, as it must be.
3.2Levers and pulleys, one step further
- Levers and pulleys keep the Year 11 rules. What is added is compounding: two class 1 levers in series multiply their advantages, exactly as gear stages do. A pair of bolt cutters is two lever pairs — handle to pivot 6 : 1, then jaw link 4 : 1 — for an overall ideal MA of 24. Hand force 150 N becomes 3.6 kN at the blade.
- A pulley system's VR is the number of rope sections supporting the moving block; its MA is what you measure. A 4-section block and tackle with 85% efficiency has MA = 0.85 × 4 = 3.4, so lifting 1200 N takes 1200 ÷ 3.4 = 353 N of effort, and 4 m of rope per metre of lift.
- Both are reversible: let go and the load runs back down. Machines with a low efficiency, like a screw jack, are often self-locking — friction holds the load when the effort is removed. Inefficiency, in that one case, is the feature you are paying for.
3.3Compound gear trains, torque and power
| Worked: a conveyor drive | Working | Result |
|---|---|---|
| A 2 kW motor runs at 1500 rpm. Its torque? Rearrange P = 2πNT ÷ 60. | T = 60P ÷ (2πN) = 120 000 ÷ (2π × 1500) = 120 000 ÷ 9425 | 12.7 N·m |
| Through the 7.5 : 1 train above, ideal output torque? | 12.7 × 7.5 | 95.5 N·m at 200 rpm |
| With the gearbox 90% efficient? | 95.5 × 0.90 | 86 N·m; output power 1.8 kW |
| The conveyor needs 120 N·m. Ratio required from this motor at 90%? | 120 ÷ (12.7 × 0.90) = 120 ÷ 11.4 | 10.5 : 1 — so 7.5 is not enough; add a stage or choose a bigger motor |
3.4Screws and the screw jack
A screw thread is an inclined plane wrapped around a cylinder. One turn of the effort moves the load forward by one lead (the pitch, for a single-start thread). If the effort is applied at a handle of radius R, it travels 2πR per turn, so VR = 2πR ÷ lead.
| Worked: a screw jack lifting a 20 kN car | Working | Result |
|---|---|---|
| Handle radius 300 mm, thread lead 5 mm. VR? | 2π × 300 ÷ 5 = 1885 ÷ 5 | 377 |
| Efficiency 30% (screws are friction-heavy). MA? | 0.30 × 377 | 113 |
| Effort needed at the handle? | 20 000 ÷ 113 | 177 N — one arm |
| Handle travel to lift the car 100 mm? | 100 × 377 | 37.7 m of handle movement, 20 turns |
The 30% efficiency looks terrible and is the point: below about 50% a screw is self-locking, so the car stays up when you let go. A ball screw in a machine tool runs at 90% efficiency and must be braked, because it will back-drive under load.
3.5Linkages and cams
| Mechanism | Converts | Where you meet it |
|---|---|---|
| Four-bar linkage | One rotation or swing into another, with the coupler tracing a designed path | Windscreen wipers, bicycle rear suspension, excavator arms, the human knee joint |
| Crank and slider | Rotation into reciprocating straight-line motion, or back | Piston engines and pumps — the crankshaft and connecting rod |
| Cam and follower | Rotation into a precisely timed rise, dwell and fall of the follower | Engine valves; the profile is the timing, drawn on a displacement diagram |
| Rack and pinion | Rotation into linear motion at constant ratio: one pinion turn moves the rack by one pitch circumference | Car steering, sliding gates, lathe carriages |
| Worm and wheel | Rotation at right angles with a very large reduction; usually self-locking | Winches, tuning pegs, hoists that must not run back |
| Ratchet and pawl | Allows rotation in one direction only | Socket wrenches, bicycle freewheels, cable ties |
A cam's displacement diagram plots follower height against cam angle over one revolution: a rise, a dwell (the flat, where nothing moves) and a fall. Read the diagram and you can build the cam; read the cam and you can predict the timing. A worm and wheel with a single-start worm driving a 40-tooth wheel has a ratio of 40 : 1 in a single stage — the worm behaves as a one-tooth gear.
3.6Energy and power in machines
- Work W = F × d, in joules. Power P = W ÷ t, in watts. Lifting is work against gravity: W = m g h.
- Worked: a hoist lifts 500 kg through 12 m in 20 s. W = 500 × 9.8 × 12 = 58 800 J. Useful power = 58 800 ÷ 20 = 2940 W. If the hoist is 75% efficient, the motor must supply 2940 ÷ 0.75 = 3920 W — choose a 4 kW motor. The missing 980 W is heat in the gearbox and brake.
- Energy is stored on the way: kinetic KE = ½ m v², gravitational potential PE = m g h. A flywheel stores KE to smooth a piston engine; a counterweight stores PE so a lift motor only ever moves the difference between car and weight.
- No machine gains energy. Every chain of stages multiplies its efficiencies: a 90% gearbox driving an 85% belt drive delivers 0.90 × 0.85 = 76.5% of the motor's power to the load.
Control systems: machines that correct themselves
A machine that measures its own output and adjusts is doing something no lever can: closing the loop. This topic is the vocabulary and the block diagram of control, one automated system worked end to end, and the exam technique that turns correct engineering into full marks.
4.1Open-loop and closed-loop control
| Open loop | Closed loop | |
|---|---|---|
| What it does | Runs the actuator according to the input, with no idea what actually happened | Measures the output, compares it with the setpoint and acts on the difference |
| Needs | A controller and an actuator | Also a sensor and a feedback path to a comparator |
| Examples | A toaster on a timer; a garden sprinkler on a clock; a microwave; a conveyor set to one speed | A thermostat; cruise control; a cistern float valve; a drone holding altitude; a 3D printer's heated bed |
| Strength | Simple, cheap, cannot oscillate | Copes with disturbances — a cold day, a hill, a leak |
| Weakness | Blind: the toast burns if the bread is thin, the lawn floods if it rains | More parts; a bad sensor gives a confident wrong answer; can overshoot and oscillate if tuned badly |
4.2Sensors and actuators
A sensor converts a physical quantity into a signal the controller can read. An actuator converts the controller's signal into a physical action. The controller is the decision in between — a thermostat's bimetal strip, a microcontroller's program, a PLC in a factory.
| Sensors (measure) | Quantity | Actuators (act) | Action |
|---|---|---|---|
| Thermistor, thermocouple | Temperature | DC motor, stepper motor | Rotation — continuous or in exact steps |
| Limit switch, reed switch | Position reached, yes or no | Solenoid | A short linear push or pull; opens a valve or latch |
| Potentiometer, encoder | Angle or position, continuously | Pneumatic or hydraulic cylinder | Linear force — pneumatic for speed, hydraulic for very large forces |
| Light-dependent resistor, photodiode | Light level | Servo motor | Rotation to a commanded angle, with its own internal feedback |
| Strain gauge, load cell | Force, weight | Relay, heater, lamp | Switching a large current from a small signal |
| Ultrasonic, infrared | Distance | Pump, fan | Moving fluid or air |
4.3The block diagram and feedback
- On–off control: the actuator is fully on when the error is positive, fully off when negative. Simple, but the output hunts around the setpoint; a deadband (switch on at 26 °C, off at 24 °C) stops the vent motor chattering.
- Proportional control: the action is in proportion to the error — the vent opens a little for a small error and wide for a large one. Smoother, but with a small steady error left over; more advanced controllers add terms to remove it.
- Lag is the enemy: if the sensor is far from the vent, the air it measures changes long after the vent moves, and the controller over-corrects. Sensor placement is a design decision, not an afterthought.
- Every automated system needs a fail-safe state: what happens when the sensor fails or power drops. For a greenhouse in Queensland, the vent should fail open.
4.4Case study: an automated greenhouse
- Requirement. Keep the air between 22 and 28 °C and the soil moisture above 40%, unattended for a week, on a site with mains power and occasional outages.
- Sensors. Two thermistors (one at plant height, one near the roof, averaged, so neither a sunny patch nor the vent draught misleads the controller); a capacitive soil-moisture probe in each bed.
- Actuators. A 12 V linear actuator on the roof vent (rack-and-pinion drive); a solenoid valve on the irrigation line; a 24 V fan as a second stage if the vent alone cannot hold 28 °C.
- Controller. A microcontroller reading every sensor every 30 s. Temperature: proportional control of the vent, fan on above 28. Moisture: on–off with a deadband (water at 40%, stop at 55%) and a maximum run time so a failed probe cannot flood the bed.
- Fail-safe. The vent actuator is spring-return, so it opens when power is lost; the valve is normally closed, so it shuts. Both defaults chosen because overheating and flooding are the two ways to lose the crop.
- Evaluation. Logged data over a week: temperature held within 22–28 for 97% of the time; the 3% was a 40 °C afternoon where the fan stage ran flat out. The recommendation is shade cloth, not a bigger fan: cheaper and no power.
An industrial robot is a set of closed loops — one per joint, an encoder feeding back each angle — under a controller that plans the path. A 3D printer closes loops on bed and nozzle temperature and runs its axes open-loop on stepper motors, which is why a skipped step ruins a print. Internet-of-things sensors move the feedback path onto a network: the loop still needs to close, and now lag includes the network. A drone holding altitude is a barometer, an accelerometer and four motors in a loop that closes hundreds of times a second. New hardware, the same diagram.
4.5Technique for the external examination
The exam gives you data and expects a defended answer. Markers award working, units and rounding separately from the final number, so a correct answer with no method loses most of its marks and a wrong answer with sound method keeps most of them.
- List what is given, with units, and convert at the start: kN to N, mm to m or m to mm, rpm stays rpm. Write g = 9.8 m s⁻² if you use it.
- Draw the free-body diagram, the joint, or the block diagram. A labelled sketch is marked.
- Write the equation in symbols first (ΣMA = 0; σ = F ÷ A; T = 60P ÷ 2πN), then substitute numbers with their units.
- Keep full precision through the working; round only the final answer.
- Significant figures: give the answer to the precision of the least precise data, usually 3 s.f. 12.732 N·m becomes 12.7 N·m; 176.8 N becomes 177 N. Never 12.73205.
- State the answer with its unit and a one-line sense check: "9.6 kN at A, larger than B because the heavier load is nearer A".
- For "explain" and "justify" items, the pattern is claim → reason → consequence: "Use a roller at B because the deck expands in summer, so the support cannot be pushed over."
A 2 kW motor turns at 1500 rpm. Find its torque.
Given: P = 2000 W, N = 1500 rpm. P = 2πNT ÷ 60, so T = 60P ÷ (2πN) = (60 × 2000) ÷ (2π × 1500) = 120 000 ÷ 9424.8 = 12.73 N·m. T = 12.7 N·m (3 s.f.). Sense check: small motor, modest torque — a gearbox will be needed for any conveyor.
Build it, ship it, hand it over.
Four units covering QCAA Information & Communication Technology Units 3 and 4. Year 11 taught you how the machine, the network and the file formats work. Year 12 is about producing things for other people: a website that works on a phone, images and animation that are built properly, video that plays everywhere, and a project that a real client signs off on.
The mapFour units, four modules
- Web design and development — Unit 3. HTML structure, CSS and the box model, responsive layout with media queries, accessibility and usability you can actually check, planning a small site for a client, and testing it across devices.
- Digital imaging and animation — Unit 3. Bit depth and colour modes, layers and masks, master files versus exports, and the principles of animation: keyframes, timing, spacing and easing, from a storyboard to a rendered clip.
- Audio and video production — Unit 4. Frame rate, resolution, bit depth and sample rate; the editing workflow; codecs and containers; exporting for the web; and the copyright rules that apply to music and footage.
- Working with clients: the ICT project cycle — Unit 4. Brief, scope, milestones, documentation, user testing, evaluation, presenting to a client — and exactly how the four Applied assessments are judged.
There is no external exam. Over Units 3 and 4 you complete four assessment instruments — projects (a product plus its documentation) and extended responses — and your teacher marks them against the syllabus standards. A result of C or better across the four units contributes 4 credits towards your QCE. The mock exam on this site is practice for the knowledge those instruments draw on, not a copy of one.
Web design and development
A web page is three separate things pretending to be one: HTML says what each part is, CSS says how it looks, and the browser lays it out for whatever screen it is on. Keep the three apart and a site is easy to change; mix them and every edit breaks something else.
1.1What a page is made of: HTML structure
HTML is a set of elements, each an opening tag, some content and a closing tag. The browser does not care about your spacing or line breaks; it cares that every element is closed and correctly nested. This is a complete, valid page:
<!DOCTYPE html>
<html lang="en-AU">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Riverside Netball Club</title>
<link rel="stylesheet" href="styles.css">
</head>
<body>
<header>
<h1>Riverside Netball Club</h1>
</header>
<nav aria-label="Main">
<a href="index.html">Home</a>
<a href="fixtures.html">Fixtures</a>
<a href="contact.html">Contact</a>
</nav>
<main>
<h2>This week's fixtures</h2>
<p>Saturday 9 am at the Riverside courts.</p>
<img src="courts.jpg" alt="The four outdoor courts at Riverside, seen from the clubhouse">
</main>
<footer>
<p>© 2026 Riverside Netball Club</p>
</footer>
</body>
</html>
- <!DOCTYPE html> tells the browser to use modern standards mode. Leave it out and old, inconsistent layout rules apply.
- lang="en-AU" sets the language for spell-checking, hyphenation and the voice a screen reader chooses. The charset line stops accented characters turning into rubbish.
- <head> holds things about the page — the title shown in the tab, the stylesheet link, the viewport setting. Nothing in it is drawn on the page.
- An <a href> is a link. A relative address such as fixtures.html points to a file next to this one; an absolute address such as https://example.org/ works from anywhere. Use relative links inside your own site, so the whole folder can be moved or uploaded without every link breaking.
- Every <img> needs an alt attribute: a description if the image carries meaning, and alt="" (empty) if it is purely decorative.
1.2CSS: selectors and the box model
A CSS rule is a selector (which elements), then declarations of property: value. The stylesheet lives in its own file, linked once from every page, so one change restyles the whole site.
/* styles.css */
body {
font-family: Arial, Helvetica, sans-serif;
font-size: 18px;
line-height: 1.5;
margin: 0;
color: #1B1B1B;
background: #FFFFFF;
}
header {
background: #1E5B45; /* club green */
color: #FFFFFF;
padding: 16px 24px;
}
nav a {
display: inline-block;
padding: 12px 16px; /* a big enough touch target */
color: #1E5B45;
text-decoration: none;
}
nav a:hover, nav a:focus { text-decoration: underline; }
.card {
border: 1px solid #CCCCCC;
border-radius: 8px;
padding: 16px;
margin: 0 0 16px;
}
img { max-width: 100%; height: auto; }
| Selector | Matches | Example |
|---|---|---|
Element — p | Every element of that type | p { margin: 0 0 12px; } |
Class — .card | Anything given class="card", as many times as you like | Reusable components: cards, buttons, alerts |
ID — #booking | The one element with id="booking" — an id must be unique on the page | A jump-link target; rarely needed for styling |
Descendant — nav a | Links that are inside the nav, and nowhere else | Styling the menu without touching links in the text |
State — a:hover, a:focus | The element while the mouse is over it, or while it has keyboard focus | Always style focus as well as hover: keyboard users need to see where they are |
Every element is a box built from four layers: the content, the padding inside the border, the border, and the margin outside it that keeps neighbours away. By default width sets only the content, so a 300 px box with 16 px padding and a 1 px border is really 334 px wide. Most stylesheets start with * { box-sizing: border-box; } so that width means the whole visible box — which is what everyone assumes it means anyway.
1.3Responsive layout
Most of your visitors will arrive on a phone. A responsive site is one set of HTML that rearranges itself for the screen it is on. Three things make it work, and they are all in the code above and below: the viewport meta tag (otherwise a phone pretends to be 980 px wide and shrinks the page), fluid images (max-width: 100%), and a media query that switches the layout at a chosen width.
/* Mobile first: one column, nothing to do */
.columns { display: grid; gap: 16px; }
/* At 700px and wider, three equal columns */
@media (min-width: 700px) {
.columns { grid-template-columns: repeat(3, minmax(0, 1fr)); }
}
- The width at which the layout switches is a breakpoint. Choose it where your content stops fitting, not from a list of phone models — there are hundreds of screen sizes and next year's are different.
- Use relative units where you can: percentages and
remscale with the screen and the user's font setting; a fixedwidth: 960pxis exactly what breaks on a phone. - The commonest responsive fault: a wide table, a long unbroken address, or a fixed-width image forces a horizontal scroll at phone width. Test at 375 px and look for it.
1.4Accessibility and usability you can check
Accessibility means people with a disability can use the site — and it is a legal expectation in Australia, not a nicety. The checks below come from the international web accessibility guidelines, in plain words. Each one is testable, which is what makes it a mark.
| Check | Rule | How to test it |
|---|---|---|
| Contrast | Body text at least 4.5:1 against its background; large headings at least 3:1 | Paste the two colours into a contrast checker; light grey on white fails |
| Images | Meaningful images have descriptive alt text; decorative ones have alt="" | Turn images off, or read the page with a screen reader; is anything lost? |
| Headings | One h1; levels in order, never skipping from h1 to h4 for the look | List the headings alone — do they make sense as an outline? |
| Keyboard | Everything reachable with Tab and Enter, in a sensible order, with a visible focus ring | Unplug the mouse and use the site |
| Forms | Every input has a <label> tied to it; errors say what went wrong and where | Click the label text: the cursor should land in the field |
| Links | Link text says where it goes: "View the fixtures", never "click here" | Read only the links out loud — do they make sense alone? |
| Colour | Never the only way meaning is shown — "required fields are in red" fails | View the page in greyscale |
| Touch | Buttons and links big enough for a finger, roughly 44 × 44 px, with space between them | Use it on a phone with a thumb |
| Video | Captions for speech; a transcript for audio | Watch it muted — can you follow it? |
Usability is the wider question of whether anyone can get things done without effort: the menu is in the same place on every page, the most wanted thing (fixtures, opening hours, a phone number) is one tap from the home page, pages load in a couple of seconds on mobile data, and the text is written for the reader, not the club committee. Accessibility fixes usually improve usability for everyone — captions help in a noisy bus, and big touch targets help everybody with cold hands.
1.5Planning a small site for a client, and testing it
- Purpose and audience first. What must a visitor be able to do? For a sports club: find fixtures, find the venue, contact someone, join. Every page earns its place by serving one of those.
- Site map. A simple tree of pages: Home, Fixtures, About, Contact. Five to seven pages is plenty; a page nobody will maintain is a page that will be wrong by next season.
- Content before layout. Get the real text, images and the logo from the client early. Placeholder text hides problems: a real fixture table is wider than "lorem ipsum" ever is.
- Wireframes. Boxes and labels, no colour, one per page type, drawn for phone and desktop. The client can say "the phone number should be higher" now, cheaply.
- Build from a shared stylesheet and a shared template, so every page matches. Validate the HTML with the W3C validator — an unclosed tag renders differently in different browsers.
- Test across devices. A real phone and a real tablet, not only the browser's device emulator; at least two browsers; a slow connection; keyboard only; a screen reader for at least one page. Record every fault in a test log: what, where, on which device, fixed on which date.
An Applied project is marked on the documentation as much as the site. "I used a media query at 700 px" earns little. "The fixture table stopped fitting below about 700 px on the iPad in portrait, so I set the breakpoint there and the table becomes a scrolling block" earns the mark, because it links the decision to the evidence.
Digital imaging and animation
Year 11 settled raster versus vector and JPEG versus PNG. This unit goes inside the file: what a pixel actually stores, how layers and masks let you edit without destroying anything, which file is the master and which is a copy — and then how a sequence of images becomes movement that feels alive.
2.1Pixels, bit depth and colour modes
A raster image is a grid of pixels, and each pixel is a number. Bit depth is how many bits store that number, which fixes how many different values it can hold: 2bits. Eight bits give 28 = 256 values. Three channels of eight bits give 224 = 16,777,216 colours — "16.7 million colour" or "24-bit" RGB.
| Colour mode | Per pixel | Can show | Used for |
|---|---|---|---|
| Bitmap (1-bit) | 1 bit | 2 values: black or white | Line art for a laser cutter; fax; tiny files |
| Greyscale | 8 bits | 256 shades of grey | Black-and-white photography, masks |
| Indexed colour | 8 bits | 256 colours chosen from a palette stored in the file | GIF and PNG-8: flat logos and icons, small files |
| RGB, 8 bits per channel | 24 bits | 16.7 million colours | Everything for screens: photographs, web images |
| RGB with alpha | 32 bits | 16.7 million colours plus 256 levels of transparency | PNG-24 with a transparent background; layers in an editor |
| RGB, 16 bits per channel | 48 bits | Billions of colours — smoother edits, no banding in skies | The master file while editing, before exporting to 8-bit |
| CMYK | 32 bits | Four ink channels | Only for commercial print; convert at the very end |
- The alpha channel is a fourth number per pixel: how opaque it is. Without it a logo cannot sit on a coloured background without a white box around it. JPEG has no alpha channel; PNG and WebP do.
- Uncompressed size still follows the Year 11 arithmetic: pixels × bytes per pixel. A 3000 × 2000 photo at 3 bytes per pixel is 18,000,000 bytes, 18 MB, before any compression.
- Banding — visible steps in a smooth gradient — is what 8-bit editing produces when you push brightness or colour a long way. Edit in 16-bit, export in 8-bit.
2.2Layers, masks and non-destructive editing
| Tool | What it does | Destructive or not? |
|---|---|---|
| Eraser | Deletes pixels from the layer | Destructive — use a mask instead |
| Layer mask | Hides or shows parts of a layer with black, white and grey | Non-destructive — repaint the mask any time |
| Adjustment layer | Brightness, levels, hue and saturation applied to all layers below | Non-destructive — the settings stay editable |
| Image > Adjust applied directly | The same change baked into the pixels | Destructive — only undo can reverse it, and only today |
| Opacity and blend mode | How a layer combines with those below: 50% opacity, multiply, screen | Non-destructive |
| Resize the image | Resamples every pixel | Destructive — and enlarging invents detail that was never there. Keep the full-size master |
| Selection (marquee, lasso, magic wand, pen) | Chooses which pixels an operation affects | Neither — a selection is a choice, not an edit. Turn it into a mask to keep it |
2.3Master files and exports
- The master is the layered, full-resolution, 16-bit file in the editor's own format — PSD, XCF, .afphoto. It is never uploaded anywhere and never overwritten by an export.
- Every delivered image is an export from the master: flattened, resized to the size actually needed, converted to 8-bit, and compressed for its destination. Need a change? Edit the master and export again.
- Web: JPEG for photographs at quality 70–85 (above that the file grows fast and the eye sees nothing); PNG-24 where transparency or sharp edges matter; WebP does both jobs at smaller sizes and every current browser supports it; SVG for anything that began as vector.
- Print: TIFF or a print-ready PDF at 300 ppi, converted to CMYK only if the printer asks for it.
- Size for the destination: a 4000-pixel photo displayed 800 pixels wide downloads twenty-five times more data than it shows. Export at the size it will be seen, or at twice that for high-density screens.
"The client wants the edited team photo for the website and for a printed A3 poster. What do you supply and why?" Two exports from one master: a JPEG at about 1600 px wide, quality 80, for the web page; and a 300 ppi TIFF or PDF at full resolution for the printer. Never the master itself, and never a re-saved JPEG of a JPEG.
2.4Principles of animation
Animation is a sequence of still frames shown fast enough that the eye reads movement: 24 frames per second for film, 25 for Australian television, and often 12 drawn frames shown twice each ("on twos") for hand-drawn work. Five seconds at 24 fps is 5 × 24 = 120 frames. Nobody draws them all.
| Principle | Meaning | What it looks like |
|---|---|---|
| Keyframes | The frames that define a movement: where it starts, where it ends, the extreme poses in between | You set the ball at the top of its bounce and at the floor; the software fills the rest |
| In-betweens (tweening) | The frames between keyframes — drawn by an assistant in the old days, calculated by the software now | Position, size, rotation and opacity can all be tweened |
| Timing | How many frames a movement takes | A door closing in 6 frames slams; in 30 frames it drifts |
| Spacing | How the in-betweens are distributed between the keyframes | Even spacing reads as mechanical; bunched at the ends reads as weight |
| Easing | Spacing done for you: ease-in starts slowly, ease-out slows into the stop, ease-in-out does both | Almost every real movement eases; only machines move linearly |
| Squash and stretch | Things deform as they move and stop, keeping the same volume | A ball flattens on the floor and stretches as it leaves |
| Anticipation | A small movement in the opposite direction before the main one | A crouch before a jump; a wind-up before a throw |
| Follow-through | Parts keep moving after the body stops | Hair, a cape, a ponytail settling a few frames late |
| Arcs | Natural movement follows curves, not straight lines | A thrown ball, a turning head, a swinging arm |
2.5Storyboarding and the animation pipeline
A storyboard is the animation drawn as a comic before anything moves: one panel per shot, in order. It is the cheapest place to find out that a scene does not work, and it is the document the client approves before you spend a week animating.
| Each storyboard panel records | Why |
|---|---|
| Shot number and a rough sketch of the frame | So everyone can refer to "shot 4" and know what it looks like |
| Action — what moves, and how | Arrows on the sketch for movement; a sentence underneath |
| Camera — wide, close-up, pan, zoom | Framing decides what has to be drawn and what does not |
| Sound — dialogue, music cue, effect | Timing is often set by the sound, so it must be planned with the picture |
| Duration in seconds, or frames | Adds up to the running time, and to the frame count you must produce |
- Brief and script. What the client needs, for whom, how long, where it will be shown.
- Storyboard. Every shot as a panel with action, camera, sound and duration. Client approves it.
- Animatic. The storyboard panels cut to the soundtrack at their planned durations — a rough moving version. This is where timing problems show, while they are still cheap to fix.
- Assets. Characters, backgrounds and props built as layered, reusable files (vector where possible, so they scale).
- Keyframes, then in-betweens. Set the extreme poses first, then let the software tween, then adjust the easing until the movement feels right.
- Render, review, revise. Export a test at the delivery frame rate and resolution, review it against the storyboard and the brief, fix, and export the final master.
Audio and video production
Video is the biggest file most people ever make, and it has to play on a phone over mobile data. Everything in this unit — the capture settings, the edit, the codec, the export — is a trade between quality and size, and every trade has a number attached that you can be asked to calculate.
3.1Capturing video: frame rate, resolution, bit depth
| Setting | Common values | What it decides |
|---|---|---|
| Frame rate (frames per second, fps) | 24 — cinema; 25 — Australian television and most local work; 30 — common online and in North America; 50 / 60 — sport, fast motion, and footage to be slowed down | How smooth motion looks, and how many frames you store: 10 seconds at 25 fps is 250 frames. Mixing frame rates in one edit causes stutter — choose one and shoot everything at it |
| Resolution | 720p 1280 × 720; 1080p (Full HD) 1920 × 1080; 4K UHD 3840 × 2160 | Detail, and file size — 4K has four times the pixels of 1080p. Shoot 4K only if you will deliver 4K or want room to crop |
| Aspect ratio | 16:9 landscape for TV and YouTube; 9:16 portrait for phone-first social video; 1:1 square | Which way you hold the camera. Cropping landscape to portrait later throws away two-thirds of the frame |
| Bit depth | 8-bit: 256 levels per colour channel; 10-bit: 1024 levels per channel | Smoothness of gradients and how far colour can be corrected before it bands. 10-bit for anything that will be graded heavily |
| Shutter speed | About double the frame rate: 1/50 s at 25 fps | Natural motion blur. A much faster shutter makes movement look staccato |
3.2Capturing audio: sample rate and bit depth
- Sound is captured by measuring the signal thousands of times a second. The sample rate is how many measurements per second: 44,100 Hz (44.1 kHz) for CD audio, 48,000 Hz for anything going with video. The rate must be at least twice the highest frequency you want to keep, and human hearing tops out around 20 kHz — which is where 44.1 kHz comes from.
- Bit depth is the precision of each measurement: 16-bit for delivery (CD quality), 24-bit for recording, because it leaves headroom so quiet passages are not lost in noise.
- Uncompressed size = sample rate × bit depth × channels × seconds. Stereo CD quality is 44,100 × 16 × 2 = 1,411,200 bits per second — about 176 kB per second, or roughly 10.6 MB per minute. That is why delivered audio is compressed.
- Clipping is the one audio fault that cannot be fixed later: a signal louder than the maximum (0 dBFS) is simply cut flat. Record with peaks around −12 to −6 dBFS and raise the level in the edit.
- Get the microphone close. A lapel (lavalier) mic on the speaker or a shotgun mic just out of frame beats the camera's own microphone every time, because the room's echo and the traffic outside are quieter relative to the voice. Record 20 seconds of room tone — the room's silence — to patch gaps in the edit.
3.3The editing workflow
- Ingest and back up first. Copy the card to the edit drive and to a second drive before you touch anything — the 3-2-1 rule from Year 11, applied to footage that cannot be re-shot.
- Name and organise. Folders per shoot day; clips renamed with scene and take. An edit with 200 clips called MVI_0417 is an edit you cannot find anything in.
- Proxies. The editor makes small copies of 4K clips to edit smoothly, then swaps the originals back in for export. The quality of the final export is unaffected.
- J-cuts and L-cuts. Audio from the next shot starts before its picture (J), or the current shot's audio runs on under the next picture (L). It is the difference between a conversation and a slideshow.
3.4Compression, codecs and containers
| Codec | Kind | Notes |
|---|---|---|
| H.264 (AVC) | Video, lossy | The universal delivery codec: every phone, browser and TV decodes it. Default for the web |
| H.265 (HEVC) | Video, lossy | About half the file size of H.264 at the same quality, but older devices and some browsers cannot play it |
| VP9 / AV1 | Video, lossy | Open codecs used by streaming platforms; AV1 is the most efficient but slow to encode |
| ProRes / DNxHD | Video, lightly compressed | Editing and master formats: huge files, every frame stored whole, so they cut and grade cleanly |
| AAC | Audio, lossy | The audio partner of H.264 in MP4; 128–256 kbit/s is transparent for most listeners |
| MP3 | Audio, lossy | Older, less efficient than AAC at the same bit rate, but plays on anything |
| WAV | Audio, uncompressed | The recording and master format; 10.6 MB per stereo minute at CD quality |
| FLAC | Audio, lossless | About half the size of WAV with nothing lost; for archiving, not for the web |
- Delivery codecs are lossy and inter-frame: a full picture (a keyframe, or I-frame) is stored every second or two, and the frames between store only what changed. A talking head compresses brilliantly; confetti and fast pans do not, and they turn blocky at the same bit rate.
- Bit rate is the size per second, and it is the one number that sets the file size: size = bit rate × duration. Eight megabits per second for 60 seconds is 480 megabits, and 480 ÷ 8 = 60 megabytes. Bits, not bytes: the small b matters.
- Re-encoding a lossy file is like re-saving a JPEG: the loss accumulates. Export web copies from the master, never from a previous export.
3.5Exporting for the web
| Export | Settings | Why |
|---|---|---|
| Master | ProRes or high-bit-rate H.264 (50 Mbit/s or more), full resolution, original frame rate, uncompressed or 320 kbit/s audio | Kept, backed up, never uploaded; every future copy comes from it |
| Web / YouTube | MP4, H.264, 1080p, 8–12 Mbit/s (higher for 50/60 fps), AAC 192 kbit/s, same frame rate as the shoot | Plays everywhere; the platform re-encodes it anyway, so starting from a clean high-quality upload matters more than a tiny file |
| Social, phone-first | MP4, H.264, 1080 × 1920 portrait, 6–8 Mbit/s, captions burned in or attached | Most social video is watched muted on a phone held upright |
| Embedded on the client's site | MP4 at a modest bit rate, or better, host it on a video platform and embed the player | A 60 MB file on a small site's hosting is slow and expensive; the platform handles the streaming |
- Always watch the export from start to finish on the target device before delivering it. Dropped frames, a missing audio channel and a wrong aspect ratio all show up in the first minute of watching and never in the export dialog.
- Supply captions (a .srt file or burned in) and a thumbnail image. Both are accessibility and usability, and both are marks.
- Name deliverables so the client can tell them apart: clubpromo_v3_1080p_web.mp4, not final.mp4.
3.6Copyright and licensing for sound and footage
- A piece of recorded music carries two copyrights: the composition (the song) and the sound recording (this performance of it). Using a commercial track in a video needs permission for both, and "we are only a school club" is not a permission.
- Australian law has fair dealing, not American "fair use": specific purposes only — research or study, criticism or review, parody or satire, news reporting. A club promo video is none of them.
- Schools have a statutory licence covering music used in class. It does not cover uploading the result to YouTube or a public website.
- Creative Commons works for video exactly as it does for images: BY needs credit in the video and its description; NC rules out anything that promotes a paid service, including a club that charges fees; ND rules out trimming or fading the track, which is a derivative. CC0 and purpose-built royalty-free libraries are the safe sources; "royalty-free" still has a licence to read.
- People in your footage: a release form for anyone identifiable, and a parent's or guardian's signature for anyone under 18. Filming in a public place is generally lawful; publishing a stranger's face in an advertisement is a different matter.
- Moral rights belong to the creator even after they sell the copyright: to be credited, and not to have the work treated in a derogatory way. Credit the composer and the videographer by name.
Working with clients: the ICT project cycle
A good product delivered late, to the wrong brief, without documentation, is a failed project. This unit is the process that stops that happening — and it is also, almost line for line, what the markers of an Applied project are looking for.
4.1The brief and the scope
A brief is the client's statement of what they need. It is almost never complete, and the first job is to turn it into one by asking questions. Write the answers down and get the client to agree to them: that agreed document is the scope.
| The scope states | Example, for the netball club website |
|---|---|
| Client and purpose | Riverside Netball Club; to publish fixtures and attract new junior players |
| Audience | Parents of 8–14 year olds, mostly on phones; current members checking fixtures on Saturday morning |
| Deliverables | A five-page responsive website, a logo file set, a one-page guide to updating the fixtures |
| Constraints | No budget for hosting beyond a free tier; must use the existing logo and colours; live by 1 March |
| Content supplied by the client | Fixtures, photographs with releases, committee contact details — by a stated date |
| Success criteria | Measurable: loads in under 3 seconds on 4G; fixtures reachable in one tap from the home page; passes the accessibility checklist; the secretary can update fixtures unaided |
| Out of scope | Online registration and payment; a members-only area — written down so nobody assumes them later |
"While you're at it, could it also…" is the sentence that sinks projects. The answer is not "no" — it is "that's a change to the scope; here is what it adds to the time, and here is what we would drop or delay to fit it." A written scope is what makes that conversation possible. Without one, every extra is your fault for not having read the client's mind.
4.2Planning: milestones, schedule and documentation
- A milestone is a checkpoint with a date and a deliverable the client can see: "wireframes approved — 10 Feb"; "all content received — 17 Feb"; "test version live — 24 Feb". Milestones are how you find out you are late while there is still time to do something about it.
- The schedule lists the tasks between milestones, how long each should take, and who does it. Add contingency: things you have never done before take longer than you think, always.
- The change log records what changed, when, and why, with a version number. When the client asks "why did the menu move?" the answer is in the log, dated, with their own request beside it.
- The asset register lists every file that is not yours — photos, fonts, icons, music — with its source, licence and the attribution required. It is the document that keeps you out of trouble.
4.3User testing
- Decide what to test from the success criteria: "can a parent find Saturday's fixture on a phone?" Write it as a task for the user, not a question about their opinion.
- Recruit people like the audience — a parent, a player, the secretary — not your friends who watched you build it. Five users find most of the serious problems.
- Watch, do not help. Give the task, then say nothing. The moment you say "it's under Fixtures" you have learned nothing, because you will not be there for the real users.
- Record what they did, where they hesitated, what they said, and whether they finished. Screen recording on the phone is ideal.
- Rate each fault by severity: stops the task; slows it; cosmetic. Fix in that order.
- Fix and retest the serious ones with new users. A fix that seems obvious to you is a new thing to test, not a thing that is now done.
Testing on devices is separate from testing with users and needs both: the site must work on the school iPad, an old Android phone and a desktop in two browsers, and it must be usable by the people it is for. A test log records each case, the device, what happened, and the fix.
4.4Evaluating, and presenting to the client
- Evaluation is judging the product against the success criteria written in the scope, with evidence: the load time measured, the accessibility checks passed, the user tests completed. "The client was happy" is a feeling; "6 of 6 test users found the fixtures in under 15 seconds" is an evaluation.
- Be honest about what did not work and what you would change. In an Applied subject, a clear account of a shortfall and its fix scores higher than a claim that everything went perfectly — markers can tell.
- Presenting: start with what they asked for (the scope), show the product doing exactly that on a phone, explain the two or three decisions that mattered and why, state the limits plainly, then hand over. Keep it under fifteen minutes and rehearse it once out loud.
- The hand-over pack: the files, where they are hosted, every login (changed to the client's own password on the day), the asset register, and a short plain-English guide to the one thing they will need to do themselves — updating the fixtures. Then a sign-off: a dated acceptance that the deliverables were received.
4.5How the four Applied assessments are judged
Over Units 3 and 4 you complete four assessment instruments: typically projects (a product with its supporting documentation) and extended responses (a written or multimodal response to a scenario). Each is marked against three objectives, which are simpler than their names suggest:
| Objective | In plain words | What it looks like in your work |
|---|---|---|
| Knowing and understanding | Do you know the facts and terms, and can you explain how things work? | Correctly using and explaining: codec, breakpoint, alt text, keyframe, bit rate, licence — and the concepts behind them |
| Analysing and applying | Can you take a real brief, work out what it needs, and choose the right tools and methods for it, with reasons? | The scope and plan; the justified choices — why this breakpoint, why H.264, why a mask instead of the eraser; the test plan |
| Producing and evaluating | Can you make the thing well, and then judge honestly how well it meets the brief? | The product itself, working on the target devices; the test log and the evaluation against the success criteria |
- Results are reported as a grade from A to E on each instrument and for the subject. A C or better across the four units earns 4 credits towards the QCE.
- There is no external exam, which means the documentation is the exam. A brilliant site with no scope, no test log and no evaluation cannot score on two of the three objectives, whatever it looks like.
- Everything on this site's mock exam is the "knowing and understanding" that the other two objectives are built on. Learn it so that in the project you can spend your time on the choices and the making.
A cabinet that closes with a click, twenty times over.
Year 11 was about timber and the joint. Year 12 is the cabinet shop: carcases in sheet material, doors that hang straight, drawers that run true, a sprayed finish that does not run, and the cutting list, job sheet and quality checks that let you build the same unit twenty times — the way a kitchen is actually made.
The mapTwo units, four topics
- Unit 3, Topic 1 — Cabinetmaking: carcase construction. Sheet materials against solid timber, the carcase joints (dowel, biscuit, housing, rebate, knock-down fittings), squaring and clamping, and edge treatment.
- Unit 3, Topic 2 — Doors, drawers and hardware. Drawer construction and runners, overlay and inset doors, concealed hinges and how they adjust, handles, and installing hardware from the manufacturer's specification.
- Unit 4, Topic 1 — Furniture finishing. Surface preparation and the grit sequence, stains, oils, lacquers and water-based coatings, spray against brush, drying and curing, finish defects and their fixes, and finishing safety.
- Unit 4, Topic 2 — Industry practice. Reading a cutting list and a job sheet, estimating material and time, batch production, quality checks, and workplace health and safety around dust, noise, machine guarding and isolation.
Four instruments across Units 3–4 — two projects (a furniture item with its planning folio) and two practical demonstrations (a set task under supervision) — graded A–E, with no external exam. A C or better contributes 4 QCE points. Written marks reward select and justify: “16 mm melamine board on a dowelled carcase, because it is pre-finished, stable in a kitchen's humidity and the dowels give alignment as well as strength” — not just “melamine”.
Cabinetmaking: carcase construction
A carcase is the box: two sides, a top or top rails, a bottom, a back, and whatever shelves and dividers it needs. Almost every kitchen, wardrobe and bookcase is a carcase in sheet material, and the whole trade rests on cutting the panels to size, joining them square, and hiding the edges.
1.1Sheet material or solid timber?
| Material | What it is | Strengths | Weaknesses | Used for |
|---|---|---|---|---|
| Melamine board (MFC) | Particleboard with a melamine-resin paper face bonded both sides | Pre-finished, wipe-clean, stable, cheap, fully square sheets 2400×1200 (16 and 18 mm) | Chips on the cut edge unless scored; swells if water gets into the core; poor screw-holding in the edge | Kitchen and wardrobe carcases — the industry standard |
| MDF | Wood fibres and resin pressed into a dense, uniform board | Smooth face for paint, machines to a crisp profile, no grain to move | Heavy; edges soak up paint; fine dust is a respiratory hazard; swells badly when wet (use MR MDF in wet areas) | Painted doors and panels, routed profiles, drawer fronts |
| Plywood | Thin veneers glued at 90° to each other, an odd number of plies | Strong for its weight in both directions, holds screws well, stable, takes a clear finish (birch, hoop pine) | Dearer; voids in cheap grades; the edge shows the plies unless lipped or celebrated | Drawer boxes, backs, shelves that carry weight, exposed “plywood look” furniture |
| Solid timber | Boards from the tree, dressed and jointed | Repairable, beautiful, strong along the grain, ages well | Moves with humidity across the grain; must be dried, jointed and allowed to move; expensive | Face frames, door frames, tops, legs, anything shaped |
Sheet material is stable; solid timber moves across the grain — a 600 mm-wide solid top can change 5 mm between a wet summer and a dry winter. A carcase mixes them safely only when the solid part is free to move: a solid top is fixed with slotted holes or buttons, never glued down all round to a sheet carcase. Ignore this and the top splits or the carcase racks.
1.2The carcase joints
| Joint | How it is made | Strength comes from | Best for |
|---|---|---|---|
| Dowel | 8 mm fluted dowels into matching holes bored with a jig or a line borer, glued | The dowels in shear, plus the glued face; the dowels also align the panels | Carcase corners and rails in MFC — the production standard |
| Biscuit | A biscuit joiner cuts a slot in each face; a compressed beech biscuit swells in the glue | Alignment more than strength; the glued face does the work | Edge-to-edge panels, face frames, quick carcases |
| Housing (dado) | A groove across a panel, the width of the shelf, one third the thickness deep | The shelf sits in the groove: it cannot sag out, and the shoulder carries the load | Fixed shelves and dividers |
| Rebate | A step cut along an edge | The panel sits in the step, hidden and located | Backs, and corners where a lipped edge is wanted |
| Knock-down (KD) fittings | Cam-and-dowel, confirmat screws, or corner blocks — no glue | Mechanical; can be taken apart and reassembled | Flat-pack, site assembly, anything that must move house |
| Pocket screws | Angled holes bored with a jig; screws pull the joint tight | The screw; fast, no clamps | Face frames, hidden fixings, jigs |
1.3Squaring and clamping
- Dry-fit first. Assemble without glue, check every joint closes, then take it apart and glue — PVA gives you about 10 minutes of open time, which is not enough to discover a problem.
- Measure the diagonals. A rectangle is square only when both diagonals are equal. If they differ, rack the carcase towards the longer diagonal until they match, then fix the back.
- Sash clamps across the joints, on the centre line of the panel, with softwood blocks under the shoes; tighten until the glue squeezes out in a fine line, not until it crushes. Too much pressure bows the panel and starves the joint.
- The back squares the box. A back panel cut square and fixed into its rebate on all four edges locks the carcase; until it is on, the carcase is a parallelogram waiting to happen.
- Clean squeeze-out with a damp cloth while wet; dried PVA under a stain shows as a pale patch.
1.4Edge treatment
A cut edge of sheet material shows the core. Edge banding hides it: pre-glued melamine or PVC tape (0.4–2 mm) is applied with heat — an iron or an edge bander — then trimmed flush with a trimmer and the arris softened; ABS/PVC 2 mm on a kitchen door gives a durable radiused edge; a solid timber lipping glued on and planed flush is the furniture-grade answer, and the only one that can be shaped. Where the edge is a joint (a dowelled corner) it is not banded — the mating panel covers it — so the cutting list marks which edges are visible.
Doors, drawers and hardware
The carcase is judged by what moves on it. A door with an even 2 mm gap all round and a drawer that runs out silent and stops soft say “professional” louder than any joint — and both come from reading the hardware manufacturer's specification and drilling to it, exactly.
2.1Drawer construction
| Runner | Fixing | Clearance | Extension and load | Where |
|---|---|---|---|---|
| Side-mount ball-bearing | One half on the cabinet side, one on the drawer side | 12.7 mm (½″) each side — box = opening − 26 | Full extension, 35–45 kg, soft-close versions | Workshops, offices, budget kitchens; the runner is visible |
| Under-mount (concealed) | Under the drawer box, clipped at the front, hooked at the back | Per the maker's table: box width, side thickness, bottom recess, rear notch | Full extension, soft-close, 30–70 kg | Quality kitchens and furniture; nothing shows |
| Metal drawer system | Metal sides ARE the runner; you supply only the bottom and back | Set by the system | Soft-close, very high load | Production kitchens |
| Timber runner (traditional) | A hardwood strip the drawer side rides on, waxed | 1–2 mm each side, fitted by hand | Three-quarter extension, no soft-close | Fine furniture, reproduction, repair |
2.2Doors: overlay and inset
An overlay door sits in front of the carcase and covers its edges; a full-overlay door covers the whole side (the standard in frameless kitchens: door = carcase width − 4 mm, so two doors on one cabinet leave 2 mm gaps); a half-overlay covers half a shared side where two cabinets sit side by side. An inset door sits inside the opening, flush with the carcase face, with an even 1.5–2 mm gap all round — the furniture-maker's door, and the one that shows every error, because there is no overlap to hide it. The choice sets the hinge: overlay, half-overlay and inset are three different hinge arms on the same cup.
2.3The concealed hinge
- Bore to the spec: the 35 mm cup hole is centred 21.5–22.5 mm in from the door edge (the maker's K or C dimension), 12.5 mm deep. Too close to the edge and the cup breaks through; too far and the door binds on the carcase as it opens.
- Hinge count by height: two hinges up to about 900 mm, three to 1500, four to 2000. Weight adds hinges too: a heavy solid door gets one more.
- Opening angle is a hinge choice: 95–110° standard, 155–170° for corner cabinets and where a drawer behind must pull past the open door.
- Soft-close is built into the hinge or added as a clip-on damper; push-to-open replaces the handle with a catch and needs a non-sprung hinge.
- Handles: mark from a template or jig at the same height on every door — a common rule is the handle on the stile, at the top of a base door and the bottom of a wall door; drill from the face with a backing block so the back does not break out. A handle screw is M4; hole centres are 96, 128, 160 or 192 mm.
2.4Installing from the specification
Every runner and hinge ships with a drilling pattern: hole positions from the front edge and the bottom of the cabinet, screw sizes, and the clearance the box or door needs. That sheet, not memory, is the source of truth — a runner mounted 1 mm out of parallel binds, and a door bored 2 mm too deep splits. The trade uses jigs for exactly this: a drilling template for the hinge cup and plate, a runner jig that sets the height and holds the runner while you screw. Set up once, check on the first door, and every door after that hangs the same.
Furniture finishing
The finish is what the customer touches, and it is unforgiving: every scratch you did not sand out, every drip of glue, every speck of dust in the booth is now sealed under a coat of lacquer where it will stay. Ninety per cent of a good finish is what happens before the first coat.
3.1Surface preparation and the grit sequence
- Repair first: fill nail holes and dents with a matching filler (or steam a dent out of solid timber with a damp cloth and an iron); remove every trace of glue — scrape, do not sand, because sanding spreads it.
- Sand in sequence: 120 to remove machine marks, 150, 180, then 240 for a clear finish. Each grit removes the scratches of the one before; skipping a grit leaves the coarser scratches, which the stain will find. Sand with the grain by hand for the last pass; a random-orbit sander leaves swirls that show under stain.
- Raise the grain before a water-based finish: wipe with a damp cloth, let it dry, sand lightly with the last grit. Otherwise the first coat raises it and the surface feels like sandpaper.
- Dust off with compressed air and a tack cloth, and let the air in the booth settle before spraying.
- Break the arrises — a stroke of 240 along every sharp edge — because a finish will not hold on a knife edge and the first knock chips it.
3.2The finishes, in a cabinet shop
| Finish | What it is | Applied by | Dry / recoat / cure | Choose it for | Beware |
|---|---|---|---|---|---|
| Stain | Colour only, no protection: pigment or dye in water, spirit or oil | Rag, brush or spray, wiped back | Water 2 h, spirit 30 min; always top-coated | Matching timbers, colouring cheap species | Blotches on pine and other soft, uneven woods — use a conditioner or a gel stain |
| Oil (Danish, hard-wax) | Penetrating oil that cures in the fibres; hard-wax oils add a thin film | Rag, several thin coats, wiped off | Touch-dry 6–12 h, recoat 24 h, full cure 2–4 weeks | Tables and solid timber; repairable by rubbing on more | Little protection from water rings early; oily rags self-ignite — lay them flat to dry or soak in water |
| Nitrocellulose / pre-cat lacquer | Solvent-based film; pre-catalysed cures harder | Spray only | Dust-free 10 min, recoat 30–60 min, cure 7 days | Production cabinets: fast, sandable between coats, good build | Flammable solvent, strong fumes — booth and respirator; blushes (goes white) in humid air |
| Two-pack polyurethane (2K) | Resin plus a hardener, mixed by ratio; cures chemically | Spray | Recoat 4–6 h, cure 24 h hard, 7 days full | Kitchen doors, benchtops, high wear and moisture | Isocyanate hardener: air-fed or organic-vapour respirator, gloves, booth; pot life 2–4 h then it sets in the gun |
| Water-based polyurethane / acrylic | Resin dispersed in water; low odour, low VOC | Brush, roller or spray | Dry 30 min, recoat 2 h, cure 7 days | Schools, homes, low-VOC jobs; clear, non-yellowing | Raises the grain; runs and sags easily when sprayed thick; shows brush marks |
| Polish / wax | Shellac or paste wax | Rag, pad | Minutes | Antiques, restoration, a final sheen over oil | Almost no protection; water and heat mark it |
Dry (or touch-dry) means the solvent or water has left and the surface can be handled. Cured means the film has finished hardening chemically — days to weeks later. A lacquered door is dry in an hour and can be sanded and recoated; it should not be stacked face to face or have a hot cup on it for a week. Stacking uncured doors is the commonest way a kitchen gets ruined between the shop and the site.
3.3Spray or brush?
Brush for water-based and oil finishes on small work, repairs and edges: cheap, no booth, but slower and it leaves marks on large flat panels. Spray for every production finish: an even, thin, fast coat over a whole door in seconds — but it needs a booth with extraction, a respirator, a compressor or turbine, and gun settings that suit the coating. The industry gun is HVLP (high volume, low pressure): more of the paint lands on the job and less becomes overspray. Thin the coating to the maker's viscosity, set the fan to a vertical ellipse for a horizontal pass, hold the gun 150–200 mm off the surface and square to it, move at a steady walking pace, overlap each pass by half, and keep the gun moving before the trigger is pulled and after it is released. Two thin coats beat one thick one every time.
3.4Defects and their fixes
| Defect | Looks like | Cause | Fix |
|---|---|---|---|
| Runs and sags | Drips or curtains on a vertical face | Coat too thick, gun too close or too slow, coating too thin | Let it cure fully, sand flat, recoat thinner |
| Orange peel | A dimpled, peel-textured surface | Coating too thick (viscosity), gun too far away, pressure too low, drying too fast | Thin correctly, raise pressure, move closer; sand and recoat |
| Blushing | A milky white cloud in lacquer | Moisture trapped as the solvent flashes off in humid air | Spray a retarder thinner over it, or wait for a dry day and recoat |
| Fish eyes | Small craters the finish pulls away from | Silicone or wax contamination — polish, hand cream, lubricant spray | Strip and clean with wax-and-grease remover; add a fish-eye eliminator |
| Dust nibs | Small bumps in the film | Dust in the booth or on the job, settling into the wet coat | Clean the booth, tack cloth, let the air settle; denib with 400 and recoat |
| Blotchy stain | Dark and light patches | Uneven absorption in pine, cherry, birch; end grain drinks more | Pre-conditioner, gel stain, or a toner in the top coat |
| Pinholes / bubbles | Tiny holes in the film | Air in the grain of open-pored timber, or shaking the tin | Grain-fill first; stir, never shake; thinner coats |
3.5Finishing safety
- VOCs and solvent vapour: the booth's extraction runs before, during and after spraying; an organic-vapour respirator with the right cartridge (A1/A2), changed on schedule; no ignition sources — lacquer vapour is heavier than air and flammable.
- Isocyanates (2K hardeners) sensitise the lungs: once you are sensitised you cannot work with them again. Air-fed respirator or a fitted organic-vapour mask, nitrile gloves, coveralls, and never spray 2K outside a booth.
- Read the SDS for every product, and store solvents in a flammables cabinet.
- Oily rags: linseed and Danish oil rags generate heat as they cure and can catch fire in a bin. Lay them flat outdoors to dry, or put them in water.
- Dust from sanding a cured finish is a fine, resin-loaded dust: extraction on the sander and a P2 mask.
Industry practice
A kitchen is thirty carcases, sixty doors and twenty drawers, promised for a Tuesday. It is made from a cutting list that must be right the first time, a job sheet that says who does what, checks that catch the mistake at the first unit and not the thirtieth, and a workshop where the machines are guarded and the dust is under control.
4.1Reading a cutting list
The cutting list is generated from the drawings: every panel, its finished size (length × width × thickness), material, quantity, which edges get banded, and the part code written on the panel. Length is conventionally along the grain or the pattern direction, and a marker checks that the sizes make a carcase that actually closes: for a 600 mm-wide, 720 mm-high base unit in 16 mm board, the sides are 720 high, the bottom is 600 − 32 = 568 wide, and the back is cut to the rebate.
| Code | Part | Qty | Length | Width | Thk | Material | Edges banded |
|---|---|---|---|---|---|---|---|
| B600-S | Side | 2 | 720 | 560 | 16 | White MFC | Front (1 long) |
| B600-B | Bottom | 1 | 568 | 560 | 16 | White MFC | Front (1 long) |
| B600-R | Top rail | 2 | 568 | 100 | 16 | White MFC | None |
| B600-K | Back | 1 | 704 | 584 | 6 | White HMR ply | None |
| B600-D | Door | 1 | 716 | 596 | 18 | Painted MDF | All four (2 mm ABS) |
- Optimise the sheets: nesting software (or a pencil) lays the parts on 2400×1200 sheets to waste least, allowing the saw's kerf (about 3 mm) between parts. Yield of 80–85% is good; the offcuts are recorded, not thrown out.
- Estimating: sheets = parts nested and rounded up; edge tape in metres from the “edges banded” column; hardware counted per unit; labour from the job-sheet times; then consumables (glue, screws, finish) and a margin. Time is where estimates fail: allow for set-up and for the first unit taking twice as long as the tenth.
4.2The job sheet and batch production
The job sheet follows the job through the shop: the customer and job number, the drawings and cutting list attached, the operations in order with the machine, the person, the time allowed and the sign-off — cut → edge → bore → assemble → hardware → finish → final check → pack. In batch production the whole kitchen's panels go through the saw, then all of them through the edge bander, then all through the boring machine, so each machine is set up once. The thirty carcases are then assembled on one jig, and the hardware fitted with one drilling template — identical, and each faster than the last.
4.3Quality checks
| Stage | Check | Tolerance / standard | Tool |
|---|---|---|---|
| After the saw | Panel size and squareness; chip-free cut edge | ±0.5 mm; diagonals equal | Tape, square, a sample panel measured fully (first-off) |
| After edging | Tape bonded, trimmed flush, no glue line showing | No lift when flexed; arris even | Fingernail and eye |
| After boring | Hole positions match the hardware spec | ±0.3 mm; test-fit one hinge and runner | Vernier; the hardware itself |
| After assembly | Carcase square, joints closed, back fixed | Diagonals within 1 mm | Tape across diagonals |
| After hardware | Door gaps even, drawers run and close soft, handles aligned | Gaps 2 mm ±0.5; handles level to 1 mm | Feeler or 2 mm packer; level; eye at arm's length |
| After finishing | Colour matches the sample; no runs, nibs, blush or holidays | Against the approved sample, in daylight | Eye, hand, sample board |
| Before packing | Every part on the list present and labelled; protective wrap on faces | Checklist signed | Job sheet |
Measure the first panel, carcase and door fully. If the first is right the set-up is right; then check a sample — every fifth or tenth — and the last. A fault found at unit one costs a panel; found at unit thirty it costs the kitchen and the Tuesday.
4.4Workplace health and safety in the cabinet shop
| Hazard | Why it matters | Controls, highest first |
|---|---|---|
| Wood dust (especially MDF and hardwoods) | Fine dust is a carcinogen and a sensitiser; MDF dust carries formaldehyde resin | Extraction on every machine and sander (engineering); enclosed booths; P2 respirator; vacuum, never sweep or blow down |
| Noise (panel saw, thicknesser, router, edge bander) | Above the 85 dB(A) eight-hour standard; the damage is cumulative and permanent | Quieter tooling and enclosures; rostering; earmuffs or plugs rated for the machine |
| Machine guarding | Saw blades, cutter blocks and router bits remove fingers in a quarter-second | Riving knife and crown guard on the saw; guards fixed or interlocked; push sticks; never freehand on the router table without a fence and guard |
| Isolation | Changing a blade or clearing a jam on a live machine | Lock-out, tag-out: isolate, lock, test, then work; the lock comes off only by the hand that put it on |
| Manual handling | A 2400×1200×18 MDF sheet weighs about 40 kg | Sheet trolleys, panel lifters, two-person lifts, vacuum lifters on the saw |
| Chemicals | Solvents, 2K hardeners, adhesives | SDS for each, flammables cabinet, booth extraction, correct respirator and gloves |
Two projects: a furniture item to a brief with its folio — drawings, cutting list, job sheet, risk assessment, and an evaluation against the specification. Two practical demonstrations: a set task (a carcase joint, a hung door, a sprayed panel) under supervision in a fixed time, marked on accuracy and safe practice. The verbs are the same across the Applied subjects: describe and explain; organise and interpret; select and apply; produce; evaluate. Show the first attempt and what changed. Graded A–E; a C or better contributes 4 QCE points.
Drawings that get built, and get built right.
Year 11 taught the language: line types, third angle, pictorials and the parametric workflow. Units 3 and 4 use it on the two kinds of drawing the industry actually pays for — mechanical drawings of parts that must fit together, and building drawings a house is put up from — and then close the loop from a 3D model to a released, revision-controlled sheet.
The mapTwo units, four topics
- Unit 3, Topic 1 — Mechanical drafting: assemblies and sections. Assembly and detail drawings, balloons and parts lists, and the full family of sectional views — full, half, offset, revolved, removed and broken-out — with the hatching rules and the parts that are never sectioned.
- Unit 3, Topic 2 — Dimensioning, tolerances and fits. Datum dimensioning, the tolerance forms, limits, clearance and interference fits worked at the extremes, surface-finish symbols with Ra values, and how threads and fasteners are represented.
- Unit 4, Topic 1 — Building and construction drafting. The set of house drawings — site plan, floor plan, elevations, sections, details — at 1:100 and 1:50, the wall, door and window symbols, dimensioning a plan and reading a set.
- Unit 4, Topic 2 — 3D CAD modelling and documentation. Feature-based modelling and the feature tree, constraints and assemblies, generating the 2D drawing from the model, title blocks and revision control, PDF and DXF output, and how the four Applied assessments are judged.
Industrial Graphics Skills is an Applied subject: there is no external exam. Across Units 3 and 4 you complete four assessment instruments — projects (a folio of drawings and the process behind them) and practical demonstrations (drawing to a brief under supervision). Each is graded A–E against the syllabus standards, and your exit result is the pattern across all four. A result of C or better contributes 4 QCE points. The mock exam on this site is practice for the knowledge those instruments test; it is not the shape of an exam you will sit.
AS 1100 line types, third-angle layout, the basic dimensioning rules, scale arithmetic, isometric and oblique, and sketch → constrain → extrude are all assumed here. The Year 11 course is one click away if any of it feels shaky.
Mechanical drafting: assemblies and sections
A machine is never one part. The drawing set that builds it has a detail drawing for each part and an assembly drawing showing how they go together — and because the interesting bits of an assembly are inside it, most assembly drawings are sections.
1.1Third angle, in one paragraph
A reminder only: Australian drawings are in third-angle projection, each view placed on the side you looked from — top view above the front view, right side view to its right — and the truncated-cone symbol in the title block says so. Top and front views share width, front and side share height, top and side share depth. Everything in this unit sits on top of that.
1.2Detail drawings and assembly drawings
| Drawing | Shows | Carries | Who uses it |
|---|---|---|---|
| Detail drawing | One part, alone, in as many views as it needs | Every dimension, tolerance, surface finish, material and heat-treatment note needed to make that part | The machinist or fabricator making the part |
| Assembly drawing (general assembly, GA) | All the parts in their working positions, usually sectioned | Balloons, a parts list, overall and interface dimensions only — no manufacturing dimensions | The fitter assembling it, the buyer ordering it, the person servicing it |
| Sub-assembly drawing | A group of parts that is built up first, then fitted as a unit | Balloons and its own parts list; it appears as one item on the GA | The assembly line, in stages |
| Exploded assembly | The parts pulled apart along their assembly axes, pictorially | Balloons and a parts list — the assembly sequence is the drawing | Instruction sheets, service manuals, catalogues |
- A balloon is a circle about 10 mm across on a leader, carrying the item number. Under AS 1100 the leader ends in an arrowhead where it meets an outline and in a dot where it lands on a surface. Balloons are arranged in neat rows or columns, never scattered.
- The parts list sits above the title block (numbered upwards from it) or on its own sheet, one row per item: item, quantity, description, material, drawing number or standard. A bought part is called up by its standard — “M8 × 40 hex bolt, AS 1110, zinc plated” — not drawn in detail.
- Dimension the assembly for assembly and installation only: overall size, mounting-hole positions, the interfaces to other machines, and any adjustment. Every manufacturing dimension belongs on the detail drawing, once. A dimension in two places is a disagreement waiting to happen.
1.3Sections of an assembly: the hatching rules
Shafts, bolts, nuts, studs, rivets, keys, pins, washers, ribs, webs and spokes are drawn whole in a section when the cutting plane runs along their length. Hatching them would suggest they had been cut lengthways and hide their shape — a hatched bolt looks like a hole. The rule flips when the plane cuts across them: a shaft cut crosswise is a circle of hatching, because that really is cut material. Thin parts such as gaskets and sheet-metal washers are too thin to hatch and are blacked in solid instead.
1.4The family of sections
| Section | What the plane does | Use it when |
|---|---|---|
| Full section | Passes straight through; everything in front of it is removed | Internal detail runs the whole way through |
| Half section | Cuts one quarter away, up to the centre line; half the view is outside, half inside | The part is symmetrical — hidden lines are left off the uncut half |
| Offset section | Steps at right angles to pass through features that do not lie on one line; the view is drawn as if the plane were flat, with no line where it changes direction | Several holes or slots in a row that one straight plane would miss |
| Revolved section | The cross-section of a bar, rib, spoke or arm is turned 90° and drawn on the view itself | Showing the shape of a section without another view — a hand-wheel spoke, a rib |
| Removed section | The same, but drawn away from the view, labelled SECTION B–B, often at a larger scale | The section would clutter the view, or needs enlarging |
| Broken-out (local) section | A small area is broken away with a thin freehand line to show one internal feature | One hole or one keyway in a part that is otherwise fine as an outside view |
| Aligned section | A feature on an angle — a hole on a bolt circle, an angled spoke — is rotated into the cutting plane before projecting | Parts with features on angles: odd numbers of holes, three-spoke wheels |
- The cutting plane line is a thick chain line with arrows at its ends pointing the way you look, and letters naming the section; in an offset section the plane line shows every step, but the section view does not. A section is titled to match its letters.
- Hatching is thin, at 45°, evenly spaced — about 3 mm apart on an A3 sheet. Where 45° would run parallel to a main outline, tilt it to 30° or 60° instead. Very large areas may be hatched only around their edge.
- Hatching never crosses a dimension figure or note: leave a gap in the hatch around any text that must sit on it.
Dimensioning, tolerances and fits
No part can be made to an exact size, so a drawing does not ask for one. It asks for a size and how far the maker is allowed to miss it — and where two parts meet, those two allowances together decide whether the shaft slides, locates or has to be pressed in.
2.1A detail drawing, dimensioned from datums
- Size dimensions say how big a feature is; location dimensions say where it is. A hole needs both: its diameter and the two coordinates of its centre.
- Parallel (datum) dimensioning: every dimension measured from the datum, so each carries only its own error. Chain dimensioning: each starts where the last ended, so errors add along the chain — three dimensions at ±0.1 can put the far end out by ±0.3. Running dimensioning is datum dimensioning drawn compactly, one line with an origin circle and the figures stacked along it. Choose by function: the dimension that must be right is the one that is given directly.
- A dimension in brackets, (60), is a reference or auxiliary dimension — given for information, not inspected, because it follows from other dimensions. Never close a chain with a toleranced dimension; make the least important link the reference.
- Do not dimension to hidden lines; section the part instead. Dimension a hole on the view where it is a circle, and a countersink or counterbore with a note.
2.2Tolerances and limits
| Form | Written as | Limits | Tolerance (band width) |
|---|---|---|---|
| Bilateral | 50 ± 0.1 | 49.9 – 50.1 | 0.2 |
| Unequal bilateral | 18 +0.05 / −0.02 | 17.98 – 18.05 | 0.07 |
| Unilateral | 30 +0.03 / 0 | 30.00 – 30.03 | 0.03 |
| Limit dimensions | 29.98 over 29.95 | 29.95 – 29.98 | 0.03 |
| General tolerance note | UNLESS OTHERWISE STATED ±0.2 | Applies to every dimension with no tolerance of its own | 0.4 |
Halving a tolerance does not halve the difficulty — it can multiply it. A tighter band means a slower machine, a better one, more inspection and more scrap. A good drawing puts a tight tolerance only on the features that mate with something, and lets the general note cover the rest. “Why is this hole H7 and that one ±0.2?” is answered with one word: function.
2.3Limits and fits: work the extremes
Where a shaft goes into a hole, the two tolerance bands together make the fit. Prove which fit it is by testing the two extreme combinations: largest hole with smallest shaft (the loosest case) and smallest hole with largest shaft (the tightest case).
| Fit | Definition | Loosest case | Tightest case | Feels like | ISO example |
|---|---|---|---|---|---|
| Clearance | The shaft is always smaller than the hole | Largest hole − smallest shaft = max clearance | Smallest hole − largest shaft = min clearance, still positive | Slides or rotates freely — a shaft in a bush | H7/g6 |
| Transition | The bands overlap | A small clearance | A small interference | Locates accurately; light taps to assemble — a dowel, a locating spigot | H7/k6 |
| Interference | The shaft is always larger than the hole | Largest hole − smallest shaft = min interference | Smallest hole − largest shaft = max interference | Pressed or shrunk together; permanent — a bush in a housing, a bearing on a shaft | H7/p6 |
- Worked: clearance. Hole 30.00–30.03, shaft 29.95–29.98. Max clearance = 30.03 − 29.95 = 0.08. Min clearance = 30.00 − 29.98 = 0.02. Both positive → a clearance fit under every combination.
- Worked: interference. Hole 40.00–40.02, shaft 40.03–40.05. Even the largest hole (40.02) is smaller than the smallest shaft (40.03): min interference = 40.03 − 40.02 = 0.01; max interference = 40.05 − 40.00 = 0.05. It must be pressed.
- The ISO shorthand. A capital letter is a hole, lower case a shaft; the letter fixes where the band sits relative to the nominal size and the number (the grade, IT5 fine to IT11 coarse) fixes how wide it is. Australia uses the hole-basis system: the hole is always H (its lower limit is the nominal size) and the shaft letter chooses the fit — g clearance, k transition, p interference. One reamer for the hole, and the fit is set on the lathe.
2.4Surface finish, threads and fasteners
| Ra (µm) | Process that gives it | Specified for |
|---|---|---|
| 12.5 | Sawn, flame cut, rough machined | Surfaces nothing touches |
| 6.3 | Ordinary turning or milling | General machined faces |
| 3.2 | Fine turning or milling | Mating faces, gasket faces |
| 1.6 | Fine machining, reaming | Running fits, sealing surfaces |
| 0.8 and finer | Grinding, honing, lapping | Bearing journals, precision slides |
- The surface-texture symbol is the tick in Figure 2.1, with the Ra value written beside it. Add a bar across the top when material must be removed by machining, and a circle in the vee when it must not be (an as-cast or as-rolled surface is required). A symbol in the title block with “all over” sets the default; individual faces override it.
- Threads are represented, not drawn. An external thread shows the major diameter as thick lines and the minor diameter as a thin line, with a thin line across for the thread run-out; end-on, a thin circle open for about a quarter of its circumference marks the minor diameter. An internal (tapped) thread is the reverse: the drilled hole (minor diameter) is thick, the major diameter is the thin three-quarter circle, and in section the hatching runs up to the thick line.
- The thread callout does the specifying: M8 × 1.25 is an ISO metric thread, 8 mm major diameter, 1.25 mm pitch (the coarse pitch, so “M8” alone means the same). A tolerance class such as 6H (internal) or 6g (external) may follow; a depth follows for a blind hole.
- Fasteners are drawn simplified — a hexagon head is two views of a hexagon with the chamfer curves approximated by arcs — or, in CAD, dropped in from a standards library. They are never sectioned, and they are called up in the parts list by size and standard, not drawn in detail.
Building and construction drafting
A house is built from a set of drawings, each answering one question — where on the block, what is the layout, what does it look like from outside, and how is it put together. The same AS 1100 grammar applies, but the scales, the symbols and the units of thinking change.
3.1The set of drawings
| Sheet | What it is | Usual scale | What you find on it |
|---|---|---|---|
| Site plan | The block seen from above, with the house on it | 1:200 or 1:500 | Boundaries with their lengths, the north point, setbacks from each boundary, contours or spot levels, existing trees and buildings, the driveway and crossover, services, the lot and plan number |
| Floor plan | A horizontal section cut about 1.2 m above the floor, looking down | 1:100 | Walls with their thickness, doors with swing arcs, windows, room names and sizes, fixtures, dimension strings, the section-line marks |
| Elevations | Each outside face, square-on | 1:100 | Named by the direction the face looks: the North Elevation faces north. Roof pitch, window and door positions, finished floor level, ceiling height, external materials, the natural ground line |
| Section | A vertical cut through the building | 1:50 or 1:100 | Footings and slab, wall frame, ceiling and roof structure, heights — floor to ceiling 2400 or 2700 — and how the parts are fixed |
| Details | Enlargements of one junction | 1:20, 1:10, 1:5 | Eaves, window head and sill, slab edge, stair — every layer named |
| Services plans | Electrical, plumbing and drainage laid over the floor plan | 1:100 | Power points, lights and switches; sanitary drainage with fall |
3.2Reading a floor plan
| Symbol | Drawn as | Notes |
|---|---|---|
| Door | A thin line for the leaf, open at 90°, with a quarter-circle swing arc | Standard leaf widths 720, 820, 920; a sliding door is two overlapping lines with an arrow |
| Window | Three thin lines in a brick-veneer wall, two in a stud wall; a code (W1, W2) refers to the window schedule | The schedule gives the size, type and glazing — never write them on the plan |
| Stairs | Treads as parallel lines with an arrow marked UP, and a break line where the stair passes above the cut | Number of risers noted |
| Fixtures | Outline symbols for the WC, basin, bath, shower, sink, stove and hot-water unit | Placed to scale so clearances can be checked |
| Section marks | A thick line with arrows and letters (A–A) across the plan, exactly as on a mechanical drawing | The section sheet carries the matching title |
| North point | An arrow marked N, on the site plan and every plan | Orientation decides sun, shade and which elevation is which |
3.3Scale and dimensioning on a plan
- At 1:100, 1 mm on paper is 100 mm on site: 10 mm = 1 m. A 4200 wall is 42 mm long. At 1:50, 20 mm = 1 m, so the same wall is 84 mm. At 1:20 a detail is drawn five times larger than at 1:100. The number written is always the real size, in millimetres, with no unit.
- Plans are dimensioned in strings: an outer string for the overall length, an inner string for the wall-to-wall room sizes and the wall thicknesses, and a third for openings. The strings must add up — the overall equals the sum of the pieces — and a marker will check.
- Dimensions on a plan run to the face of the structure — the stud or the brickwork — not to plaster or cladding, because that is what the builder sets out. A note says which.
- Levels are given as heights above a datum: FFL (finished floor level), ceiling height, and RL (reduced level) on the site plan. Elevations and sections carry them; plans do not.
- Reading a set: start at the drawing register on the cover sheet, check every sheet carries the same revision, find the north point, then walk the house — site plan for position, floor plan for layout, the section for heights, the details for how each junction is built. A note on one sheet applies to the whole set unless it says otherwise.
3D CAD modelling and documentation
In Year 11 you built a part from a sketch. Year 12 asks what the model is for: a history of features you can edit, an assembly you can test, and a drawing sheet that is generated from it, checked, numbered and released — then changed under revision control when the design changes.
4.1Features and the feature tree
| Feature | What it does | Needs |
|---|---|---|
| Extrude | Pushes a closed sketch profile straight out to a distance, adding or cutting material | A closed, fully defined sketch and a distance (or “through all”, “to face”) |
| Revolve | Spins a profile about an axis to make a turned shape — a shaft, a pulley, a bottle | A profile that does not cross its axis, and the axis |
| Hole | A drilled, counterbored, countersunk or tapped hole from a standards table | A point on a face; the size comes from the thread or bolt standard |
| Fillet | Rounds an edge to a radius; inside fillets also relieve stress | An edge and a radius — and it should come late in the tree |
| Chamfer | Bevels an edge at a distance and angle; makes parts easier to assemble | An edge, a distance, an angle |
| Shell | Hollows a solid to a wall thickness, removing chosen faces | A thickness; used for boxes, housings, mouldings |
| Pattern / mirror | Repeats a feature in a line, a grid or around an axis; mirror copies it across a plane | The seed feature, a count and spacing (or an angle) |
4.2Assemblies
- An assembly file references the part files; it does not copy them. Edit the part and every assembly that uses it updates — and rename or move the part file and the assembly cannot find it. Folder discipline is part of the subject.
- A free part has six degrees of freedom: three slides and three rotations. Mates (or joints) remove them: coincident face-to-face removes one slide and two rotations; concentric on two cylinders leaves only a slide and a spin; a revolute joint leaves one rotation. The first part is grounded so everything else locates against it.
- Run the interference check before the drawing: two parts occupying the same space is a design error the drawing will faithfully reproduce. Check the mass properties too — the model knows the volume and, given a material, the weight.
- A CAD exploded view is generated from the assembly and stays associative; balloons and the parts list are then placed on it from the same data that built it.
4.3From model to released drawing
- Model the part from constrained sketches and features, and check it: mass properties, and interference if it is in an assembly.
- Open a drawing sheet from the template — A3 or A4, the frame and title block already on it, third-angle symbol included.
- Place the base view (the front view, the one that shows the most) and project the others from it; the software puts them in third angle and keeps them aligned.
- Add section and detail views where the base views hide something: the cutting plane is drawn on the parent view and the section is generated, hatched, and titled to match.
- Dimension from datums, retrieving the model's sketch dimensions where they are the right ones and adding the rest; apply tolerances, surface-finish symbols and notes.
- Balloon and list an assembly: the parts list is filled from the part properties (description, material, quantity) — type it into the parts, not into the sheet.
- Complete the title block: title, drawing number, scale, sheet number, who drew and who checked, the date, the projection symbol, and revision A.
- Check, then export: PDF for viewing, quoting and the workshop wall; DXF of the flat profile for the laser or plasma; STEP if another CAD system needs the solid.
| Control | Rule | Why |
|---|---|---|
| Drawing number | Unique, never reused, and the same on the model, the sheet and the file name | A number is the only thing that survives a phone call, an email and a photocopy |
| Revision | A, B, C… in the title block and a revision table saying what changed, who did it and when; a change cloud on the sheet marks the change | The workshop must be able to tell which sheet is current and what is different about it |
| Checked by | Someone who did not draw it signs the block | Errors are cheapest before material is cut |
| Sheet scale and “DO NOT SCALE” | The scale in the block is for the sheet size named; a note says do not measure the drawing | A PDF printed “fit to page” on A4 is no longer 1:2 — only the written dimensions are true |
| Superseded copies | Old revisions are withdrawn from the workshop and marked SUPERSEDED | A part made to the wrong revision fits nothing |
Plotting is printing at a stated scale on a stated sheet size, with line weights applied by a plot style so thick outlines and thin dimensions print as the standard says. PDF preserves that appearance for viewing and printing and is what the quote is priced from. DXF throws away the sheet and keeps the flat geometry, in real millimetres, for a cutting machine — export the profile at 1:1, on one layer, with no dimensions, and check the cutter's operator has allowed for the kerf. STEP carries the solid to a different CAD system; STL carries a triangulated surface to a 3D printer. The native file stays with you, because it is the only one that can still be edited.
4.4How the four Applied assessments are judged
- Two projects: a folio of drawings for a brief — a mechanical set in Unit 3, a building set in Unit 4 — with the sketches, research and decisions that led to them. Marked on how completely and correctly the set communicates the design: standards applied, views chosen well, every needed dimension present and none duplicated.
- Two practical demonstrations: producing drawings to a set task under supervision, usually in CAD, in a fixed time. Marked on accuracy against the standard, and on speed only insofar as the set is finished.
- The standards use verbs. Describe and explain the conventions and processes; organise information and interpret drawings; select and apply the right techniques and standards; produce drawings; evaluate your own work against the brief and the standard. A folio that shows the evaluation — what was wrong in the first draft and what changed — scores higher than a perfect sheet with no history.
- Four instruments, graded A–E, no external exam. A C or better across the course contributes 4 QCE points.
From a drawing to a batch of parts, on time and in tolerance.
Year 11 taught you what metal is and how to measure it. Year 12 asks you to make with it: cut and weld a frame, turn a shaft on the lathe at the right speed, fold a sheet-metal box that comes out the size the drawing says, and then do it ten times over — identically, safely, and with the paperwork a real workshop runs on.
The mapTwo units, four topics
- Unit 3, Topic 1 — Metal fabrication: cutting and joining. Marking out, cutting bar and plate (hacksaw, cold saw, angle grinder, plasma), MIG and arc welding settings and weld types, brazing, weld defects and their causes, and the fume, UV and fire hazards of hot work.
- Unit 3, Topic 2 — Machining: lathe and mill. The parts of a centre lathe, facing, turning, drilling and knurling, cutting speed and the spindle-speed calculation, milling basics, and measuring the result against its tolerance.
- Unit 4, Topic 1 — Sheet metal and jigs. Developments and bend allowance, the pan brake and the box, seams and hems, pop and solid riveting, and the jigs and fixtures that make the second part identical to the first.
- Unit 4, Topic 2 — Manufacturing practice. Production planning and job cards, batch production, go/no-go gauges and inspection, machine maintenance, and workplace health and safety as a system: isolation, guarding, housekeeping and Safety Data Sheets.
Four instruments across Units 3–4 — two projects (a fabricated product with its planning folio) and two practical demonstrations (a set task under supervision in a fixed time) — graded A–E, with no external exam. A C or better contributes 4 QCE points. Written marks come from the same habit as Year 11: select and justify. “MIG at 19 V and 6 m/min wire, because 3 mm mild steel needs enough heat to fuse the root but not so much that it burns through” earns marks; “use MIG” does not.
Metal fabrication: cutting and joining
Fabrication is the sequence mark out → cut → fit → join → finish, and most of the quality is decided in the first two steps. A frame that is square at the tack stage stays square; one that is a millimetre out at the cut cannot be welded straight.
1.1Marking out and cutting
Mark out from one datum edge with a scriber and an engineer's square, and centre-punch every hole before it goes near a drill. Add the kerf — the width of metal the cut removes — on the waste side of the line: about 1 mm for a hacksaw or cold saw, 2–3 mm for an angle-grinder cutting disc, 1–2 mm for plasma. Cut to the waste side and file, or grind, back to the line.
| Process | Suits | Edge it leaves | Chief hazard |
|---|---|---|---|
| Hacksaw | Bar and tube to about 50 mm; the three-tooth rule for blade choice | Square, slightly rough; needs filing | Blade breakage; cut on the forward stroke only |
| Cold saw / drop saw | Repeat cuts of bar, tube and angle, square or mitred | Clean and square, ready to weld | Guarding and clamping; hot offcuts |
| Angle grinder, cutting disc | Plate, bolts, rough cuts anywhere | Rough, heat-marked, wide kerf | Disc burst, sparks igniting rags and fumes, kickback; guard on, both hands, disc rated for the speed |
| Guillotine | Sheet and thin plate in straight cuts | Straight, slight burr on the underside | Finger guard and back-gauge; never reach under the blade |
| Plasma cutter | Any conductive metal, plate to 20 mm+, curves and holes | Slight bevel and dross to grind off | Arc UV, fume, electric shock; earth clamp on the work |
| Oxy-acetylene | Thick mild steel only (it burns the iron) | Wide kerf, heat-affected, needs dressing | Flashback, cylinder handling, fire |
1.2The welding processes
A weld melts the parent metals and (usually) a filler into one pool that freezes as a single piece. What differs between processes is where the filler comes from and how the pool is shielded from the air — because molten steel that touches oxygen and nitrogen makes a porous, brittle weld.
| Process | Filler and shield | Best for | Settings you choose |
|---|---|---|---|
| MIG / GMAW | A continuously fed wire is the filler; a shielding gas (argon–CO2 mix for steel) flows from the nozzle | Mild steel 1–10 mm, fast, easy to learn; most school and production welding | Voltage (arc heat and bead width), wire feed speed (amps and deposition), gas flow about 12–15 L/min, stick-out about 10 mm |
| MMAW / arc (stick) | A flux-coated rod is the filler; the burning flux makes the shielding gas and a slag blanket | Thicker steel, outdoor and repair work where wind would blow MIG gas away | Amps for the rod diameter (about 40 A per millimetre of rod), polarity, arc length equal to the rod diameter |
| TIG / GTAW | A non-consumable tungsten makes the arc; filler rod fed by hand; argon shield | Stainless, aluminium, thin material, where the weld must look perfect | Amps by foot pedal, AC for aluminium, tungsten type and grind |
1.3Setting up, and reading the weld
- MIG settings scale with thickness. A rough start for mild steel with 0.9 mm wire: 1.6 mm plate about 16 V / 3 m/min; 3 mm about 19 V / 6 m/min; 6 mm about 22 V / 9 m/min. Then listen: a steady frying-bacon crackle is right; loud popping means the wire speed is too high for the voltage; a hissing, wandering arc means too much voltage.
- Arc rod amps come from the rod: a 2.5 mm general-purpose rod runs at about 80–100 A, a 3.2 mm rod at about 110–130 A. Hold the arc length about equal to the rod diameter; too long and the shield fails, too short and the rod sticks.
- Tack first, weld second. Tack the whole frame, check it is square across the diagonals, then weld in a sequence that balances the shrinkage — opposite corners, not one side then the other — because a weld pulls the metal towards itself as it cools.
- Travel speed and angle: push or drag at about 10–15° from vertical, moving steadily enough that the bead is about twice the wire diameter wide and sits slightly convex. Too fast leaves a thin, ropey bead; too slow piles up metal and burns through thin plate.
| Defect | What it looks like | Usual cause | Fix |
|---|---|---|---|
| Porosity | Pinholes on or in the bead | Shielding gas failing: draught, low flow, blocked nozzle, dirty or oily plate, damp rods | Screen the draught, check flow and nozzle, clean the joint, dry the rods |
| Undercut | A groove melted into the parent plate beside the bead | Too much heat, arc too long, travel too fast, wrong angle | Lower voltage/amps, shorten the arc, slow down |
| Lack of fusion | Bead sitting on top of the plate, easily lifted | Too little heat, travel too fast, dirty plate, no vee on thick plate | More heat, slower, clean and prepare the joint |
| Burn-through | A hole where the weld should be | Too much heat for the thickness, travel too slow, gap too wide | Lower settings, faster travel, close the gap, backing bar |
| Spatter | Balls of metal stuck around the weld | Wire speed too high for the voltage, long stick-out, dirty plate | Balance the settings, shorten stick-out, anti-spatter spray |
| Slag inclusion (arc) | Dull patches of slag trapped inside the weld | Slag not chipped and brushed off between passes | Clean every pass completely before the next |
| Distortion | The job pulls out of square as it cools | Welding one side fully before the other; too much heat | Tack, balance the sequence, clamp, weld in short runs |
1.4Brazing, and the hazards of hot work
Brazing joins metal without melting the parent: a bronze or silver filler melts above 450 °C, is drawn into a close-fitting joint by capillary action, and bonds to the clean, fluxed surfaces. It is the choice for joining dissimilar metals (steel to brass, copper tube), for thin tube that welding would burn through, and for bicycle-frame-style lugged joints. The joint must be clean, fluxed and a close fit — about 0.05–0.15 mm gap — and the work is heated, not the filler, until the rod melts on touching it.
Arc UV burns skin and eyes (“arc eye” hours later): helmet of the right shade (10–13 for MIG/arc), leather or cotton sleeves, screens for bystanders. Fume — especially from galvanised, painted or stainless steel — needs extraction at the source, and a P2 respirator where extraction is poor. Fire: sparks travel metres; clear rags, solvents and cardboard, keep an extinguisher and a fire watch for 30 minutes after grinding or welding near anything combustible. Electric shock: dry gloves, good earth clamp on the work, never change a rod with bare wet hands. Burns: everything you just welded is still 300 °C and looks exactly like cold steel — chalk it HOT, and use tongs.
Machining: lathe and mill
A machine tool removes metal in a controlled way, so that the result matches a drawing to a hundredth of a millimetre. The lathe turns the work; the mill turns the cutter. Everything else — speed, feed, depth of cut — is arithmetic you can do before you touch the switch.
2.1The centre lathe
| Operation | Tool moves | Makes | Watch for |
|---|---|---|---|
| Facing | Across the end, on the cross slide | A flat, square end face | Tool exactly at centre height, or a pip is left in the middle |
| Turning (parallel) | Along the bed, on the carriage | A cylinder to a set diameter | Roughing cuts, then a light finishing cut; measure before the last cut |
| Taper turning | Along the compound slide set to the angle | A cone — a chamfer, a centre, a tapered spigot | The angle is half the included angle |
| Drilling | Drill in the tailstock fed into the turning work | A hole exactly on the axis | Centre drill first, or the drill wanders |
| Boring | A boring bar along the bed inside a hole | An accurate, larger, true hole | Bar deflection: shortest bar that reaches |
| Knurling | Hardened wheels pressed in, low speed, lots of oil | A grip pattern on a handle | It forms the metal, not cuts it; heavy pressure, slow |
| Parting | A thin blade straight in on the cross slide | Cuts the finished part off | Slow speed, blade square, plenty of oil; chatter means it is not rigid |
2.2Cutting speed and the spindle-speed calculation
Every tool material has a cutting speed (Vc) at which it cuts a given metal well — the speed of the metal surface past the cutting edge, in metres per minute. A high-speed-steel (HSS) tool in mild steel runs about 30 m/min; in aluminium about 90–120 m/min; in brass about 60 m/min; carbide tooling about three times faster. The lathe, though, is set in revolutions per minute, and one revolution of a big bar moves more surface past the tool than one revolution of a thin one. The conversion is the formula you will be asked for:
N is the spindle speed in rpm, Vc the cutting speed in m/min, d the diameter in mm. The 1000 turns metres into millimetres; π × d is the circumference — how far one revolution takes the surface.
Worked: HSS tool, mild steel (30 m/min), 40 mm bar. N = 1000 × 30 ÷ (π × 40) = 30 000 ÷ 125.66 = 239 rpm — choose the nearest lower speed the gearbox offers, about 230. Worked: same tool, aluminium (100 m/min), 20 mm bar: 100 000 ÷ 62.83 = 1592 rpm. On the mill, d is the cutter diameter, because it is the cutter that turns: a 10 mm HSS end mill in mild steel runs at 30 000 ÷ 31.42 = 955 rpm.
- Halve the diameter, double the speed. Drilling a 5 mm hole needs twice the rpm of a 10 mm hole in the same metal — which is why small drills scream and big drills crawl.
- Feed is how far the tool advances per revolution (mm/rev): about 0.1–0.2 for finishing, 0.3–0.5 for roughing. Depth of cut is how much comes off the radius per pass; the diameter drops by twice that.
- Coolant (soluble oil) carries heat away, lubricates and flushes swarf; use it on steel. Aluminium and brass often cut dry or with a dab of kerosene.
- Chatter — a rattling cut and a rippled finish — means something is not rigid: too much tool overhang, work too far from the chuck, a blunt tool, or too high a speed. Fix the rigidity, not the speed, first.
2.3The milling machine
On a mill the cutter rotates and the work, clamped in a machine vice on the table, is fed under it on three hand-wheel axes (X along, Y across, Z up). An end mill cuts on its end and sides for slots, steps and pockets; a face mill or fly cutter skims a large flat surface; a slitting saw cuts a narrow slot. Feed the work against the cutter's rotation (conventional milling) on a manual machine — climb milling, feeding with the rotation, gives a better finish but grabs the table on a machine with any backlash. Set the vice square to the table with a dial indicator before any cut that must be parallel.
2.4Measuring the result
Rough-turn to about 0.5 mm over size, stop, measure with the micrometer (0.01 mm), set the cross-slide dial for the remaining cut (remembering it takes off the radius), and take the finishing cut. A vernier caliper reads to 0.02 mm and is fine for lengths and rough diameters; a micrometer is for any diameter with a tolerance. Check a turned diameter in two places along its length — if they differ, the work is tapering because the tailstock is offset or the tool is deflecting. A part that measures inside its limits is accepted; one outside is rework if it is still oversize, scrap if it is under.
Sheet metal and jigs
Sheet metal is drawn flat, cut flat and then folded into a shape — so the whole skill is working out the flat pattern, the development, that folds up to the right size. And because a real job is never one box but twenty, the second skill is the jig: the fixture that makes number twenty identical to number one.
3.1Developments and bend allowance
When sheet is bent, the outside of the bend stretches and the inside compresses; somewhere between them a layer, the neutral axis, keeps its length. The flat pattern is the sum of the flat faces plus the length of the neutral axis around each bend — the bend allowance. Ignore it and a folded box comes out short on every side.
BA = (π ÷ 2) × (r + k × t), where r is the inside bend radius, t the sheet thickness and k the K-factor — where the neutral axis sits as a fraction of the thickness, about 0.33 for a tight bend and up to 0.5 for a large-radius one. Use k = 0.4 unless told otherwise.
Worked: 1.2 mm sheet, inside radius 1 mm, k = 0.4, one 90° bend. BA = 1.571 × (1 + 0.48) = 1.571 × 1.48 = 2.32 mm. A bracket with two 50 mm outside legs, measured to the outside of the bend, has flat faces of 50 − (r + t) = 47.8 mm each, so the blank is 47.8 + 2.32 + 47.8 = 97.9 mm long — not 100.
3.2Folding, seams and hems
- The pan brake (folder) clamps the sheet under a beam and swings the bending leaf up; segmented fingers let you fold a box whose sides are already up. The bend radius is set by the nose of the clamping beam — at least one sheet thickness, or the outside cracks.
- Fold order matters: plan it so every fold can still be reached; fold the short flanges before the long sides on a tray.
- A safe edge or hem is the sheet folded back on itself 180°: it stiffens the edge and removes the cut edge that would slice a hand. A wired edge rolls the sheet around a wire for a rigid rim.
- A grooved seam interlocks two hems and is hammered flat: a mechanical joint with no heat, standard for ductwork. A lap seam is simply overlapped and riveted, soldered or spot-welded.
- Pop (blind) rivets need access to one side only: drill a hole the rivet's size, insert, squeeze the tool until the mandrel snaps. A solid rivet is set with a hammer and a rivet set from the other side and is stronger. Spacing about 3 to 4 diameters apart, at least 1.5 diameters from the edge.
- Spot welding clamps the sheets between two copper electrodes and passes a heavy current for a fraction of a second: fast, clean, no filler, but only for overlapping thin steel.
3.3Jigs and fixtures
A fixture holds the work in a fixed position for an operation — a welding table with stops that locate every frame member the same way. A jig holds the work and guides the tool — a drilling jig with hardened bushes puts every hole in the same place without marking out. Both exist for one reason: the first part takes skill and time; the fiftieth must take neither. Design rules: locate from the same datum the drawing dimensions from; clamp against a solid stop, never against a clamp; make it impossible to load the part the wrong way round (a fool-proof or poka-yoke feature); keep swarf from building up under the part; and prove it on the first piece with a full inspection before running the batch.
Manufacturing practice
A workshop that makes one thing well is a hobby. A workshop that makes the same thing fifty times, on the day it promised, with every one inside tolerance and nobody hurt, is a business — and it runs on planning, inspection, maintenance and a safety system, not on skill alone.
4.1Production planning and the job card
Planning turns a drawing into a job card (or route sheet): the ordered list of operations, the machine and tooling for each, the time allowed, and the check that ends it. Read the drawing, list every operation, put them in an order that makes sense — cut before drill, drill before weld, weld before paint — and work out the materials from a cutting list that adds the kerf and a little waste to every length.
| Op | Operation | Machine / tool | Set-up | Time (min) | Check |
|---|---|---|---|---|---|
| 10 | Cut 4 × 40×40×3 SHS to 500 | Cold saw | Length stop at 500 + kerf | 8 | Length ±1, square |
| 20 | Drill 2 × Ø10 each leg | Pedestal drill, jig J-12 | Jig on table, 900 rpm | 6 | Go/no-go plug, position by jig |
| 30 | Tack and weld frame | MIG, fixture F-4 | 19 V, 6 m/min, gas 14 L/min | 15 | Diagonals equal ±2, welds visual |
| 40 | Dress welds, deburr | Angle grinder, file | Flap disc 80 grit | 5 | No sharp edges |
| 50 | Degrease and prime | Spray booth | Zinc-rich primer | 6 | Full coverage, no runs |
- Batch production does every part at operation 10, then every part at 20: one set-up per operation instead of one per part. It is faster and more consistent than one-off work, and it is why jigs, fixtures and length stops pay for themselves.
- Estimating: materials from the cutting list at the supplier's stock lengths (6 m for most steel sections — nest the cuts to waste least); consumables (wire, gas, discs); labour at the job-card times plus set-up; then a margin. A quote that forgets set-up time loses money on every job.
- First-off inspection: the first part of a batch is fully measured against the drawing before the rest are run. If it is right, the set-up is right; if it is wrong, only one part is scrap.
4.2Quality control
Quality control is checking parts against the drawing; quality assurance is running the process so that they come out right without checking every one. In a batch, the fast tool is the go/no-go gauge: for a Ø10 H9 hole (10.00–10.036), the GO plug is 10.00 and must enter; the NO-GO plug is 10.036 and must not. No numbers to read, no judgement — pass or fail in two seconds. The same idea gives gap gauges for shafts and length stops for cuts. Full measurement with the micrometer is kept for the first-off and for a sample (every tenth part) after it. Every rejected part is tagged and quarantined, and the cause found before the batch continues.
4.3Maintenance
Machines are maintained on a schedule, not when they break: daily — clean swarf, check guards and stops, oil the slides; weekly — check belts, coolant level and concentration, dress the grinding wheel; monthly or by hours — gearbox oil, way lubrication, spindle bearings, calibration of measuring tools against a standard. A machine with a fault is tagged out of service and the fault is reported, never worked around. Keep the record: the log of what was done and when is what tells you a bearing is failing before it seizes.
4.4Workplace health and safety as a system
| System | What it is | The rule that matters |
|---|---|---|
| Isolation (lock-out, tag-out) | Switching a machine off and locking the isolator before working on it | The person who fits the lock is the only one who removes it; test that the machine will not start before putting hands in |
| Guarding | Fixed guards on belts and gears; interlocked guards that stop the machine when opened; adjustable guards on saws and grinders | A guard that is off or bypassed is a reportable fault; the machine does not run without it |
| Housekeeping | Clear floors, swarf bins emptied, offcuts racked, oil spills cleaned at once, tools returned to the shadow board | Most workshop injuries are slips, trips and cuts from mess — not machines |
| Safety Data Sheets | The SDS for every chemical (cutting fluid, degreaser, paint, gas) kept where the chemical is used | Read the SDS before first use: PPE, ventilation, first aid, spill and disposal |
| Induction and sign-off | Nobody operates a machine until inducted and signed off on that machine | Competence is recorded, not assumed |
| Incident reporting | Every injury and every near-miss recorded and investigated | A near-miss is a free lesson; an unreported one repeats with worse luck |
Two projects: a fabricated product made to a brief with its folio — drawing, cutting list, job card, risk assessment, and an evaluation of the result against the specification. Two practical demonstrations: a set task (a weld test, a turned component, a folded box) under supervision in a fixed time, marked on accuracy and safe practice. The standards use verbs: describe and explain processes; organise and interpret drawings and information; select and apply the right materials, tools and techniques; produce the product; evaluate it against the brief. A folio that shows the first attempt, what was wrong and what changed scores higher than a clean product with no history. Graded A–E; a C or better contributes 4 QCE points.
Practice zone
Two ways to test yourself before the real thing: a spoken quiz that asks a question, times you, then gives the answer — and a mixed drill that pulls questions from every unit at once.
9.1Quiz me out loud
Turn Voice on in the top bar and the question is read to you. Say your answer out loud before the timer runs out — saying it, rather than thinking it, is what shows you whether you actually know it. Then the answer appears and you mark yourself honestly.
9.2Mixed drill
Ten questions pulled at random from every unit of this course, re-shuffled every time you press reset. If you can hit ten out of ten twice in a row, you are ready.
Mock exam — Year 8 Biology
A full practice paper under exam conditions. When you finish you get a mark out of 100, an A–E grade, a breakdown of which topics let you down, and the worked answer to every question you missed.
Glossary & cheat sheet
Every term the exam can ask you to define, in the words you should use. Press the speaker on any entry to hear it read out.
1. Cell theory, all three parts. 2. Which three organelles are plant-only. 3. Cell → tissue → organ → organ system → organism. 4. The path of blood through the heart, chamber by chamber. 5. The word equation for aerobic respiration. 6. The four alveolus adaptations.
CreditsWhere the diagrams come from
The anatomical plates are free-licensed artwork from Wikimedia Commons, reused here with their original labels removed and Year 8 labels added. The explanatory figures — the microscope, surface area to volume, the organisation ladder, specialised cells, diffusion, double circulation, the mechanism of breathing and the systems map — are drawn for this site.
| Plate | Author | Licence |
|---|---|---|
| Animal cell | LadyofHats (Mariana Ruiz) | Public domain |
| Plant cell | LadyofHats, derivative by Vivelefrat | Public domain |
| Digestive system | Mariana Ruiz & Jmarchn | Public domain |
| Respiratory system | LadyofHats & Jmarchn | Public domain |
| Urinary system | Arcadian, derivative by Thstehle | Public domain |
| The heart | Wapcaplet | CC BY-SA 3.0 |
| Blood vessels | Kelvinsong | CC BY-SA 3.0 |
All plates were downloaded from commons.wikimedia.org. The two CC BY-SA plates are adapted here (labels replaced) and that adaptation is shared under the same licence. Map outlines come from Natural Earth (1:110m countries, public domain), simplified and drawn by this site. Country flags are Wikimedia Commons renderings, all public domain except the flag of Oman (Open Government Licence, Oman).