A Level Maths: Proof Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- GCSE Maths Algebra — comfortable manipulation of expressions, factorisation, and algebraic identities supports deductive proofs
- Indices — useful for proofs involving powers and divisibility
A Level Maths proof teaches you to construct watertight mathematical arguments. Rather than just computing answers, proof questions ask you to demonstrate that a statement is true for every case it claims to cover. It is a small topic by mark count but a hugely valuable one — the rigorous thinking it develops pays off across the whole A Level, especially on the harder reasoning questions.
At A Level you meet four proof techniques. Proof by deduction builds a chain of logical implications from known truths to the result you want, often using algebra (for example, proving that the sum of two odd numbers is even by writing them as $2m+1$ and $2n+1$). Proof by exhaustion checks every case in a finite collection. Disproof by counter-example disproves a 'for all' claim by finding a single case where it fails. Proof by contradiction — covered later in Proof By Contradiction — assumes the opposite of what you want to prove and derives a contradiction. You also use set and interval notation to write conclusions precisely.
Proof is part of the Pure Maths strand of A Level Maths and is essential revision content for all UK exam boards including AQA, Edexcel, OCR, and OCR MEI.
Watch out for…
A few things to be careful with: showing a statement holds for one or two values is verification, not proof — a proof needs to cover every case the claim makes; 'show that' is usually less formal than 'prove that', which demands full rigour; write arguments forwards from given assumptions to the result, not backwards from the answer; and a single counter-example is enough to disprove a universal claim — you do not need to find a 'typical' one.