DfE statement R12 · Ratio, proportion and rates of change
Ratio in similar shapes: lengths, areas and volumes
Ratio in similar shapes: lengths, areas and volumes is content statement R12 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: "Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors." (statement R12). 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
- Multiplying an area by the length scale factor. Areas scale by the square of it: scale factor 3 means the area is 9 times bigger.
- Forgetting that volumes scale by the cube, so scale factor 2 multiplies the volume by 8.
- Working back from an area ratio without taking the square root to recover the length scale factor.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is ratio in similar shapes: lengths, areas and volumes on Foundation or Higher?
Both. It is Foundation content, so it can be asked on either tier.
Can I use a calculator for ratio in similar shapes: lengths, areas and volumes?
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?
Multiplying an area by the length scale factor. Areas scale by the square of it: scale factor 3 means the area is 9 times bigger.
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.