Proof
A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.
The topic on one screen
- Four methods on the spec: deduction (algebra), exhaustion (check every case), counter-example (kill a claim with one case), contradiction (assume the opposite, break it).
- Algebraic proofs about odd/even: write even = 2m, odd = 2m + 1, expand, then FACTOR the result to exhibit the form — and finish with a conclusion sentence.
- n and n + 1 are consecutive, so n(n + 1) is always even — the workhorse fact for divisibility proofs.
- Contradiction has a fixed script: 'Assume [negation]… then… contradiction. Hence [statement].' The assumption line carries a mark.
- A counter-example needs a specific number and a shown failure — 'it doesn't always work' scores nothing.
- Proofs are marked cso (correct solution only): one algebra slip anywhere and the final mark is gone.
Where students actually lose marks
Given-result ('show that') proofs earn A* marks only with no errors including invisible brackets — expanding (n + 1)3 with a dropped bracket ends the proof even if the final line is right.
June 2023 Paper 1 mark scheme (Q14, cso guidance)
In proof by contradiction the explicit assumption of the negation is a marked step — students who dive into algebra without stating the assumption cap their score.
June 2024 Paper 1 mark scheme (Q15)
Conclusions matter: schemes reserve the final mark for a statement tying the algebra back to the claim ('…which is odd, as required'). Silent algebra loses it.
June 2023 Paper 1 mark scheme (Q14)
Try it — exam-style
Prove, using algebra, that n3 - n is divisible by 6 for all integers n ≥ 2.
Prove by contradiction that √2 is irrational.
A student claims that n2 + n + 11 is prime for every positive integer n. Disprove this claim.
Prove by exhaustion that the square of any integer is either a multiple of 4 or one more than a multiple of 4.
Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.
Get the printable question packfree accountDrill it properly
Stuck on proof?
Proof is the purest exam technique on the paper — structure and conclusions, not cleverness. I teach the scripts, and your first lesson is free.