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.

Start practising Read the lesson

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
3
$n$ is an integer.

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

(b) Write down expressions for the next two odd numbers after $2n + 1$ .
Level 2 · 2 marksTry it
4
Prove that the sum of any three consecutive integers is a multiple of 3.
Level 3 · 2 marksTry it
5
$n$ 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

7 more questions on expressing generality — the language of proof

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free