This mini-lesson covers the Ratio, proportion & rates of change strand of AQA GCSE Maths (8300): ratio, direct & inverse proportion, percentages & compound interest, the speed / density / pressure formulae, and growth & decay.
These games test recall of facts, formulae and methods — not full multi-step working. Answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
To divide a quantity in a ratio, add the parts to find the total number of parts, then find one part:
Share £416 in the ratio 5 : 3.
Total parts = 5 + 3 = 8, so one part = 416 ÷ 8 = £52
Shares: 5 × 52 = £260 and 3 × 52 = £156 (check: 260 + 156 = 416 ✓)
Always check your shares add back to the original total — a quick way to catch arithmetic slips.
Two quantities are in direct proportion when one is a fixed multiple of the other — double one, you double the other. Use the unitary method: find the value of one, then scale up.
5 pens cost £3.50. How much do 8 pens cost?
One pen: 3.50 ÷ 5 = £0.70
Eight pens: 0.70 × 8 = £5.60
Tip: "y varies directly as x" means y = kx for a constant k. Find k from the first pair, then use it.
In inverse proportion, as one quantity goes up, the other goes down — their product stays constant.
3 painters take 8 days. How long for 4 painters (same rate)?
Total work = 3 × 8 = 24 painter-days.
With 4 painters: 24 ÷ 4 = 6 days
Direction check: more painters should take fewer days. If your answer went up, you've used direct proportion by mistake.
The quickest way to increase or decrease is a multiplier:
A sofa costs £360 after a 20% discount. Original price?
£360 is 80% of the original → multiplier = 0.80
original = 360 ÷ 0.80 = £450
The classic trap: reverse percentage is not "just add the 20% back". You must divide by the multiplier to undo the change.
With compound interest the change is applied repeatedly, each year on the new total. Use the multiplier raised to a power:
£1000 invested at 5% compound interest for 3 years.
Multiplier = 1.05 → 1000 × 1.05³
1.05³ = 1.157625 → £1157.63 (2 d.p.)
Depreciation / decay works the same way but with a decrease multiplier — a car losing 15% per year uses ×0.85 each year.
These are compound measures — a rate of one quantity per another. Learn the formula triangles:
Watch the units: speed in km/h needs distance in km and time in hours. Convert minutes to hours first (30 min = 0.5 h).
Tap a quantity on the left, then its correct formula on the right.
A multiplier above 1 increases an amount; a multiplier below 1 decreases it. Tap a multiplier, then the box it belongs in.
Ratio: one part = total ÷ (sum of parts), then scale up.
Direct proportion: unitary method — find one, then multiply.
Inverse proportion: product stays constant (xy = k); more → less.
Percentages: multipliers; reverse percentage = ÷ multiplier.
Compound interest & decay: P × (multiplier)ⁿ.
Compound measures: speed = d ÷ t, density = m ÷ V, pressure = F ÷ A.
You've covered every Ratio, Proportion & Rates of Change sub-topic in AQA 8300. Press Finish to see your score.
You've worked through Ratio, Proportion & Rates of Change for AQA GCSE Maths (8300). 🎉
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