GCSE Maths: Ratio, Proportion & Rates Revision

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If 6 workers take 8 hours to paint a wall, how long would 12 workers take (assuming they work at the same rate)?

Ratio, Proportion & Rates is a core part of GCSE Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Exponentialy = kbˣ — fixed % growth per step

Inverse proportiony × x = constant

GradientSteepness — rate of change on a graph

TangentLine touching a curve giving instantaneous rate

Area under curveTotal change — useful for speed/time

IterationRepeated calculation to converge

RatioComparison of two quantities, e.g. 3:5

Direct proportiony = kx — doubles when x doubles

SpeedDistance ÷ time

DensityMass ÷ volume

PressureForce ÷ area

MultiplierDecimal used for fast % change

Compound interestInterest on the new balance each time

DepreciationLoss in value over time

What your exam board covers

Where Ratio, Proportion & Rates sits in each exam board's specification. Tap a board to see what it lists.

AQARatio, proportion and rates of changeSpec 8300

Ratio
Proportion
Rates of change and compound measures
Growth and decay

Source: AQA GCSE Mathematics (8300) specification — Subject content, accessed 23 June 2026.

EdexcelRatio, proportion and rates of changeSpec 1MA1

Ratio and proportion
Compound measures and rates of change

Source: Pearson Edexcel GCSE (9–1) Mathematics (1MA1) specification, accessed 23 June 2026.

Eduqas/WJECRatio, proportion and rates of changeSpec C300QS

Ratio and proportion
Rates of change and compound measures
Direct and inverse proportion

Source: Eduqas GCSE Mathematics specification, accessed 9 July 2026.

OCRRatio, proportion and rates of changeSpec J560

Calculations with ratio
Direct and inverse proportion
Discrete growth and decay

Source: OCR GCSE (9–1) Mathematics (J560) specification, accessed 23 June 2026.

Learn Ratio, Proportion & Rates step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board:

Other boards:CCEA Cambridge IGCSE Edexcel IGCSE

Common mistakes to avoid

Questions where students often pick the tempting wrong answer — make sure you know the right one:

If 6 workers take 8 hours to paint a wall, how long would 12 workers take (assuming they work at the same rate)?✗ 16 hours, because doubling the workers doubles everything including the time. ✓ 4 hours — this is inverse proportion: double the workers, halve the time.

In a school the ratio of boys to girls is 3:2. There are 30 boys. How many girls are there?✗ There are 27 girls because the ratio 3:2 means subtracting 3 - 2 = 1 from 30 and adding to make 2 girls' part. ✓ 20 — each part of the ratio represents 10 pupils, so girls = 2 x 10.

If 5 pens cost £3.50, how much do 7 pens cost?✗ £5.50, by adding £2 to £3.50 because there are 2 more pens. ✓ £4.90 — find the unit cost (£0.70 per pen), then multiply by 7.

Share 60 in the ratio 2 : 3.✗ 30 and 30, by splitting 60 in half because there are two numbers in the ratio. ✓ 24 and 36 — 5 parts in total, each part is 12, so 2 x 12 = 24 and 3 x 12 = 36.

What is the difference between simple and compound interest?✗ Simple and compound interest give the same total — compound just uses a different formula. ✓ Simple interest is calculated only on the original amount; compound interest is calculated on the original amount plus accumulated interest.

Practise Ratio, Proportion & Rates — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie ▶ Reveal Race ▶ Connections Grid ▶ Falling Words ▶ Word Web

See all 22 games in the Revision Arcade →

Ratio, Proportion & Rates

Key concepts

What your exam board covers

Common mistakes to avoid

Practise Ratio, Proportion & Rates — free games

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