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Proof by Exhaustion (OCR AS Maths A): Revision Note

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OCR Maths A: PureAQA Maths: PureEdexcel Maths: Pure

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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

    Proof by Exhaustion Notes Diagram_2, A Level & AS Level Pure Maths Revision Notes

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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    Paul

    Author: Paul

    Expertise: Maths Content Creator (Previous)

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.