DfE statement G25 · Geometry and measures
Vector arithmetic and vector proof
Vector arithmetic and vector proof is content statement G25 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. 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: "Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs." (statement G25). 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: "use vectors to construct geometric arguments and proofs". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Treating AB and BA as the same vector. They are negatives of each other.
- Adding vectors head to head rather than head to tail, so the resultant points the wrong way.
- In a vector proof, showing two vectors are multiples of each other and not saying that this makes them parallel — which is the point being proved.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is vector arithmetic and vector proof on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "use vectors to construct geometric arguments and proofs" — are Higher only; the rest is Foundation content.
Can I use a calculator for vector arithmetic and vector proof?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Treating AB and BA as the same vector. They are negatives of each other.
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 Geometry and measures at Foundation or at Higher.