A LevelMathsAQAPureRevision NotesProofProofProof by Exhaustion

Proof by Exhaustion (AQA A Level Maths: Pure): Revision Note

Exam code: 7357

Written by: Paul

Reviewed by: Dan Finlay

Updated on 2 July 2026

Proof by exhaustion

What is proof by exhaustion?

Proof by exhaustion is a way to show that the desired result works for every allowed value

How do I prove a result by exhaustion?

Using proof by exhaustion means testing every allowed value not just showing a few examples

Difficulties with proof by exhaustion

In many cases proof by exhaustion is not practical, or possible
- Proving all multiples of 4 are even can’t be shown for every multiple of 4
Aim to minimise the work involved
- Proving a number is prime only requires testing factors up to the square root

Examiner Tips and Tricks

Try a simpler case if you are stuck.
For example, if you are asked to prove that 97 is a prime number you could try thinking about what you would do for smaller primes such as 7 or 11.

Worked Example

Proof by Exhaustion Example_2, A Level & AS Level Pure Maths Revision Notes

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