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DfE statement R9 · Ratio, proportion and rates of change

Percentages and percentage change

Both tiersEither paper

Percentages and percentage change is content statement R9 of the DfE GCSE mathematics subject content, in the ratio, proportion and rates of change area. It is on both tiers, and it appears on both the calculator and the non-calculator papers. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics." (statement R9). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement R9

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This turns up on both the non-calculator and the calculator papers, so practise it both ways — the written method for Paper 1 and the efficient calculator route for Papers 2 and 3.

Common mistakes

  • Reverse percentages by subtraction: given £84 after a 20% rise, taking 20% off £84. Divide by 1.2 instead, giving £70.
  • Adding successive percentage changes: 10% then 10% is not 20%, because the second is applied to a larger amount.
  • Using the new value as the denominator for a percentage change. The denominator is always the original.
  • Applying compound interest when the question says simple interest, or the reverse.

Formulae for this statement

Compound interest, growth and decayFinal = P × (1 + r/100)ⁿBe able to derive this

Sample questions (10 of 30)

R9 · Percentages and percentage changeQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Ratio, proportion and rates of change

R9

Beginner

Write 0.25 as a percentage.

💡 Hints:
Foundation worksheetHigher worksheetFoundation ratio, proportion and rates of change practiceHigher ratio, proportion and rates of change practice

Nearby statements

R1Converting between standard and compound unitsR2Scale factors, scale diagrams and mapsR3One quantity as a fraction of anotherR4Ratio notation and simplest formR5Dividing in a ratioR6Multiplicative relationships as ratios or fractionsR7Proportion as equality of ratiosR8Ratios, fractions and linear functionsR10Direct and inverse proportionR11Compound units: speed, density, pressureR12Ratio in similar shapes: lengths, areas and volumesR13Equations of direct and inverse proportionpart HigherR14Gradient as a rate of changeR15Instantaneous rate of change: gradients of curvesHigher only

Questions people ask

Is percentages and percentage change on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for percentages and percentage change?

It depends on the paper. Paper 1 is non-calculator; Papers 2 and 3 allow one, and this topic is asked on both kinds.

What is the multiplier for a percentage change?

For an increase of p%, multiply by 1 + p/100; for a decrease, by 1 − p/100. A 15% rise is × 1.15, a 15% fall is × 0.85. Multipliers make repeated changes easy — three years of 15% growth is × 1.15³ — and they are also what makes reverse percentages a division rather than a subtraction.

What is the single most common mistake here?

Reverse percentages by subtraction: given £84 after a 20% rise, taking 20% off £84. Divide by 1.2 instead, giving £70.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Ratio, proportion and rates of change at Foundation or at Higher.

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