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
$n$ is a whole number. Write down an expression for the next whole number after $n$ .
Level 1 · 1 markTry it
2
$n$ is a whole number. Explain why $2n + 1$ is always odd.
Level 1 · 1 markTry it