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DfE statement R14 · Ratio, proportion and rates of change

Gradient as a rate of change

Both tiersEither paper

Gradient as a rate of change is content statement R14 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 3 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: "Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion." (statement R14). 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 R14

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

  • Counting squares for the gradient without reading the scale on each axis.
  • Quoting the rate without its units — the gradient of a cost-against-hours graph is pounds per hour, and the units are usually worth a mark.
  • Reading a curve's steepness at one point as if the whole graph had a single rate of change.

Sample questions (10 of 30)

R14 · Gradient as a rate of changeQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Ratio, proportion and rates of change

R14

Beginner

Four graphs are described below. Each shows one quantity plotted against another. Write down the description of the graph that shows two quantities in direct proportion.

💡 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 another

Questions people ask

Is gradient as a rate of change on Foundation or Higher?

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

Can I use a calculator for gradient as a rate of 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 single most common mistake here?

Counting squares for the gradient without reading the scale on each axis.

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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