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
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
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