DfE statement R13 · Ratio, proportion and rates of change
Equations of direct and inverse proportion
Equations of direct and inverse proportion is content statement R13 of the DfE GCSE mathematics subject content, in the ratio, proportion and rates of change area. It is on both tiers, with a Higher-only part, 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: "Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations that describe direct and inverse proportion." (statement R13). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "construct and". Everything else in the statement is Foundation content.
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
- Writing y ∝ 1/x as y = kx. Inverse proportion gives y = k/x.
- Skipping the step that finds k from the given pair of values, and answering with the proportion statement instead of a number.
- For y ∝ x², applying k to x and then squaring, rather than squaring x and then multiplying by k.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is equations of direct and inverse proportion on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "construct and" — are Higher only; the rest is Foundation content.
Can I use a calculator for equations of direct and inverse proportion?
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?
Writing y ∝ 1/x as y = kx. Inverse proportion gives y = k/x.
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.