GCSE · Algebraic proof

Proving divisibility resultsExam-style questions

The expand–collect–factorise engine: to prove "always a multiple of k", exhibit the expression as k × (whole number) — and say so.

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

DifficultyAll Level 3 Level 4 Level 5

1
Prove that the product of any two consecutive even numbers is a multiple of $8$ . (4 marks)
Level 4 · 4 marksTry it
2
Prove that $(n + 3)^2 - (n - 1)^2$ is a multiple of $8$ for all integer values of $n$ . (3 marks)
Level 4 · 3 marksTry it
3
Prove that the difference between the squares of any two consecutive odd numbers is a multiple of $8$ . [4]
Level 4 · 4 marksTry it
4
Prove that the sum of any three consecutive odd numbers is a multiple of 3.
Level 4 · 3 marksTry it
5
Prove that $(3n + 1)(n + 2) - n(3n + 7) = 2$ for all values of $n$ .
Level 4 · 3 marksTry it

2 more questions on proving divisibility results

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