Number
Fractions, percentages, negatives and primes — the stuff everything else is built on.
What a fraction actually is
A fraction is just a slice of something. Change the top and bottom numbers and watch the bar — then see how a totally different-looking fraction can be the exact same amount.
Adding & subtracting fractions
You can't add slices of different sizes. So first we re-cut both bars into the same size pieces — then adding is just counting.
Multiplying fractions
"Half of a third" sounds weird until you see it. Shade one fraction across, the other down — the overlap is the answer.
the overlap IS the answer ↑Dividing fractions
"6 ÷ 2" really asks how many 2s fit in 6? Dividing by a fraction asks the same thing — and that's why the answer can get bigger.
Percentages
A percentage is a fraction out of 100. Master the 10% trick and almost every percentage question falls over.
Negative numbers
Stop memorising sign rules — watch them. Adding walks the arrow one way, subtracting walks it back, and a negative flips the direction.
Primes, HCF & LCM
Every whole number is built out of primes, like Lego bricks. Break two numbers down and the HCF and LCM just appear from the shared bricks.
Algebra
Letters aren't scary — they're just numbers wearing a disguise.
Solving equations — the balance
An equation is a set of scales that must stay level. Whatever you do to one side, do to the other — keep stripping things away until x stands alone.
Sequences & the nth term
The nth term is a machine: feed in a position, it spits out a term. Change the machine and watch the whole sequence move.
Straight line graphs: y = mx + c
m is the slope, c is where it cuts the y-axis. Your job: match the red dashed line. You'll learn what m and c do without anyone telling you.
Expanding brackets
(x + a)(x + b) is the area of a rectangle with those side lengths. The four regions inside are exactly the four terms you get when you expand.
Geometry
Shapes, angles and the most famous theorem in maths.
Area & perimeter playground
Formulas with the real numbers substituted in, live, while you stretch the shape. Each grid square is 1 unit.
Angle rules you can drag
Grab a corner and pull. However ugly you make the triangle, the three angles always add to 180°. Always.
go on — try to break itPythagoras (and a peek at trig)
Draw a square on each side of a right-angled triangle. The two small squares exactly fill the big one: a² + b² = c².
Ratio & Proportion
Sharing things out fairly (or deliberately unfairly).
Sharing in a ratio
Ratio questions are bar-model questions in disguise: count the parts, find one part, multiply up. That's the entire topic.
Probability & Statistics
Predicting randomness, and squeezing one number out of many.
Probability — theory vs reality
Theory says what should happen. Spin the spinner and watch reality wobble around the theory — then spin 100 times and watch it settle.
Mean, median, mode & range
Drag the bars up and down. Watch which average flinches and which one shrugs — that's the real difference between them.
Physics
Real simulations, not diagrams — the forces, energy and waves behind GCSE physics, running live in your browser.
Projectile launcher
Angle and speed are the only things you control — gravity does the rest. Find the angle that gives maximum range, then try the same launch on the Moon.
45° is the magic angle. but WHY? launch and compareThe pendulum
Here's the weird part: how far you pull it back barely changes the timing. Only the length (and which planet you're on) sets the period.
F = ma, live
Push a cart with a steady force and it doesn't move at a steady speed — it accelerates. Double the mass and watch the same push do half as much.
Energy never disappears
Drop a ball into a valley and watch height energy trade for speed energy, back and forth, forever — the total bar never changes. Then add friction and see where it really goes.
Waves & the equation v = f λ
Turn the frequency up and the wave doesn't speed up — it squashes. Speed is fixed by the medium, so frequency and wavelength trade off exactly.
interference on: two waves adding point-by-point. find the phase that cancels themBuild an orbit
An orbit is just falling — sideways, fast enough to keep missing. Too slow and you crash. Too fast and you leave forever. Find the speed in between.
this is genuinely how the ISS works. it falls. constantly