DfE statement R15 · Ratio, proportion and rates of change
Instantaneous rate of change: gradients of curves
Instantaneous rate of change: gradients of curves is content statement R15 of the DfE GCSE mathematics subject content, in the ratio, proportion and rates of change area. It is Higher tier only, 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 at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts." (statement R15). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.
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
- Giving the gradient of a chord when the instantaneous rate of change — the gradient of the tangent — was asked for.
- Drawing the tangent so it cuts the curve, or touching it at a point other than the one named.
- Losing the negative sign on a curve that is falling, and reporting a decreasing rate as positive.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is instantaneous rate of change: gradients of curves on Foundation or Higher?
Higher only. Foundation papers do not ask for it.
Can I use a calculator for instantaneous rate of change: gradients of curves?
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?
Giving the gradient of a chord when the instantaneous rate of change — the gradient of the tangent — was asked for.
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.