GCSE · Algebraic proof

Expressing generality — the language of proofExam-style questions

Why testing examples proves nothing, how 2n, 2n + 1 and n, n + 1, n + 2 encode "any even", "any odd" and "consecutive", and when one counterexample settles everything.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Prove that the sum of any three consecutive integers is a multiple of 3.
Level 3 · 2 marksTry it
2
$n$ is an integer.

(a) Write down an expression, in terms of $n$ , for any even number.

(b) Explain why $2n + 1$ is an odd number for every integer $n$ .
Level 3 · 2 marksTry it
3
Prove that the sum of any odd number and any even number is odd.
Level 3 · 3 marksTry it