DfE statement R10 · Ratio, proportion and rates of change
Direct and inverse proportion
Direct and inverse proportion is content statement R10 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: "Solve problems involving direct and inverse proportion, including graphical and algebraic representations." (statement R10). 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. 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
- Handling inverse proportion as if it were direct: doubling one quantity should halve the other, not double it.
- Using the unitary method but multiplying where you should divide when finding the value of one unit.
- Assuming 'more workers, less time' is a direct relationship because both numbers change together.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is direct and inverse proportion on Foundation or Higher?
Both. It is Foundation content, so it can be asked on either tier.
Can I use a calculator for 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?
Handling inverse proportion as if it were direct: doubling one quantity should halve the other, not double it.
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.