Proof

Edexcel Pure 1

A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.

Board and spec code confirmed against Edexcel 9MA0 · registry checked 2026-07-11How this checking works

Edexcel 9MA0 revision notes Edexcel 9MA0 past papers

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.
Where a proof accuracy mark is labelled cso (correct solution only), a slip can lose that final completion mark; question-specific method marks may still be awarded for valid progress.

Where students actually lose marks

In a given-result proof, a cso final accuracy mark needs a complete error-free chain, including brackets. Earlier method marks can still survive where the question-specific scheme awards them.

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

Hard

ORIGINAL · after June 2023 Paper 1 Q14

Prove, using algebra, that

n^3 - n

is divisible by 6 for all integers

n \ge 2

(4)

(Total for Question 1 is 4 marks)

Hard

ORIGINAL · after June 2024 Paper 1 Q15

Prove by contradiction that

\sqrt{2}

is irrational.

(4)

(Total for Question 2 is 4 marks)

Easy

ORIGINAL

A student claims that

n^2 + n + 11

is prime for every positive integer

n

. Disprove this claim.

(2)

(Total for Question 3 is 2 marks)

Medium

ORIGINAL

Prove by exhaustion that the square of any integer is either a multiple of 4 or one more than a multiple of 4.

(3)

(Total for Question 4 is 3 marks)

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

Command words guide

'Show that' vs 'prove' vs 'verify' — what each demands.

Sequences & series

Where 'show that' quadratics most often appear.

Maths flashcards

The four proof methods and their scripts, drilled.

Stuck on proof?

Proof is the purest exam technique on the paper — structure and conclusions, not cleverness. I teach the scripts. Free intro call, then a free first lesson.

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