This mini-lesson covers the Ratio, Proportion & Rates of Change strand of OCR GCSE Maths (J560): sharing in a ratio, direct & inverse proportion, percentages & compound interest, the rate formulae for speed, density & pressure, and growth & decay.
Work through each screen, answer the questions as you go (most are calculations) and collect ⭐ stars. Press Start when you're ready.
A ratio like 3 : 5 splits an amount into parts. Add the numbers to find the total number of parts, divide the amount by that total to find one part, then multiply up for each share.
Share £240 between Amy and Ben in the ratio 3 : 5.
Total parts = 3 + 5 = 8, so one part = 240 ÷ 8 = £30
Amy = 3 × 30 = £90 · Ben = 5 × 30 = £150
Check: the shares must add back to the total: 90 + 150 = 240 ✓. If they don't, you've divided by the wrong number of parts.
Two quantities are in direct proportion when doubling one doubles the other — they scale up together. The safest method is the unitary method: find the value of one, then multiply up.
5 pens cost £3.50. Find the cost of 8 pens.
One pen = 3.50 ÷ 5 = £0.70
8 pens = 0.70 × 8 = £5.60
Watch out: don't add or subtract to adjust the count — proportion is multiplicative. Always scale down to one first, then scale back up.
When the numbers aren't whole multiples, a small table keeps proportion tidy. Find the value of one unit, then multiply by however many you need.
Sense check: 7 books should weigh a bit less than double 4 books (1800 g). 1575 g sits sensibly below that.
A rate tells you how much of one quantity there is per unit of another. Speed is a rate of distance per unit time:
A car travels 150 km in 2.5 hours. Find its average speed.
speed = distance ÷ time = 150 ÷ 2.5 = 60 km/h
The same triangle idea works for other compound rates. Density is mass per unit volume; pressure is force per unit area:
A block has mass 240 g and volume 30 cm³. Find its density.
density = mass ÷ volume = 240 ÷ 30 = 8 g/cm³
A force of 200 N acts on an area of 4 m².
pressure = force ÷ area = 200 ÷ 4 = 50 Pa
Units matter: read the compound unit backwards — g/cm³ literally means "grams divided by cm³", which tells you the formula.
Tap a quantity on the left, then the formula on the right that works it out. Recall check: do you know each rate formula?
A percentage change is fastest with a multiplier. Increase means "add on"; decrease means "keep the rest":
Key idea: a decrease multiplier is less than 1; an increase multiplier is more than 1. Multipliers let you chain changes together (that's the basis of compound interest).
When a change happens again and again on the new amount each time, you apply the multiplier repeatedly — that's a power. This is compound interest (growth) or depreciation (decay).
£2000 is invested at 10% compound interest per year for 2 years.
multiplier = 1.10, so final = 2000 × 1.10²
= 2000 × 1.21 = £2420
Compound ≠ simple: simple interest would add 10% of £2000 = £200 each year (£2400 total). Compound earns interest on the interest, so it's a little more (£2420). Higher questions often push this over more years.
In inverse proportion, as one quantity goes up the other goes down — but their product stays constant. More workers means fewer days, yet the total work is fixed.
6 workers take 10 days to build a wall. How long would 4 workers take (working at the same rate)?
Total work = 6 × 10 = 60 worker-days (constant)
4 workers: days = 60 ÷ 4 = 15 days
Spot inverse vs direct: in direct proportion both grow together; in inverse proportion one shrinks as the other grows. Fewer workers → more days, so the answer must be bigger than 10, not smaller.
A multiplier above 1 increases an amount; a multiplier below 1 decreases it. Tap a multiplier, then tap the box it belongs in.
Ratio: add the parts, find one part, multiply up for each share; the shares add back to the total.
Direct proportion: unitary method — find the value of one, then scale up.
Rates: speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area. Read the compound unit to recall the formula.
Percentages: use multipliers — increase > 1, decrease < 1.
Compound interest & decay: final = start × (multiplier)ⁿ.
Inverse proportion: the product stays constant (workers × days = total work); more of one means less of the other.
You've covered the Ratio, Proportion & Rates of Change strand of OCR GCSE Maths (J560) — Foundation content plus the Higher-tier compound interest and inverse proportion. Press Finish to see your score.
You've worked through Ratio, Proportion & Rates of Change for OCR GCSE Maths (J560). 🎉
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