A Level Maths
A Level Maths Proof Exam Questions
Free A Level Maths exam questions on Proof, with full model answers. Covers deduction, exhaustion, counterexample.
Proof exam questions
1 question pack of real past exam questions with its mark scheme. Answer every question without notes, then mark your answers line by line against the mark scheme.
About A Level Maths Proof
Proof is part of Pure Maths in A Level Maths. These questions suit AQA, Edexcel, OCR A, OCR B (MEI), WJEC, Edexcel International and CCEA A Level Maths students. Answer the pack without notes, then mark every line against the model answers and redo the questions you dropped marks on.
What you need to know
- Proof by deduction Start from known facts and reach the result logically.
- Proof by exhaustion Check every possible case.
- Disproof by counterexample One example that breaks the claim is enough.
Common mistakes in Proof
- Using examples as a proof.
- Missing a case in exhaustion.
Try two Proof exam-style questions
1. Prove that the square of any odd number is odd. (3 marks)
Show the mark scheme answer
(2n + 1)² = 4n² + 4n + 1 = 2(2n² + 2n) + 1, which is odd
2. Disprove: n² + n + 41 is prime for all positive integers n. (2 marks)
Show the mark scheme answer
n = 40 gives 1681 = 41², not prime
Proof FAQs
Which exam boards include Proof?
These questions suit AQA, Edexcel, OCR A, OCR B (MEI), WJEC, Edexcel International and CCEA A Level Maths.
Is Proof pure, mechanics or statistics?
Proof is part of Pure Maths.
How should I use these Proof questions?
Answer every question without notes, then check each line against the model answers and redo any you got wrong.
