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AQA GCSE Maths

Ratio, proportion and rates of change — AQA GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 4 minutes to read.

Ratio

  • Share in a ratio: add the parts, divide the total, multiply back out.
  • Ratio a : b as a fraction of the whole is a/(a+b).
  • Simplify ratios by dividing both sides by the highest common factor.

Proportion and rates

  • Direct proportion: y = kx — doubling one doubles the other.
  • Inverse proportion: y = k/x — doubling one halves the other.
  • Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.

Key terms

Unitary method
Find the value of one unit first, then scale up.
Compound measure
A measure made of two others, like speed or density.
Constant of proportionality
The fixed value k linking two proportional quantities.
Similar shapes
Shapes with the same angles and proportional sides but different sizes.
Scale factor
The number a shape's lengths are multiplied by to create an enlargement.
Best buy
The option offering the lowest price per common unit of measure.

Common exam traps

  • Sharing the total by the number of parts instead of the sum of the parts.
  • Not converting units (minutes to hours) before using speed.
  • Treating an inverse relationship as if it were direct.

Practice questions with answers

  1. 1. Share £120 in the ratio 2 : 3.

    Answer: £48 and £72

    5 parts → £24 each; 2 × 24 and 3 × 24.

  2. 2. A car travels 90 km in 45 minutes. Find the average speed in km/h.

    Answer: 120 km/h

    45 min = 0.75 h; 90 ÷ 0.75.

  3. 3. If y is inversely proportional to x and y = 6 when x = 2, find y when x = 4.

    • • 12
    • • 3
    • • 6
    • • 8

    Answer: 3

    k = 12, so y = 12 ÷ 4.

  4. 4. Simplify the ratio 18 : 24.

    Answer: 3 : 4

    Divide both by 6.

  5. 5. Divide £250 in the ratio 3 : 2.

    Answer: £150 and £100

    Total parts = 5, so each part = £50. 3 × 50 = 150, 2 × 50 = 100.

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