A-level · Proof

Proof by deductionExam-style questions

Direct proof — starting from things known to be true and reasoning in valid algebraic steps to the conclusion. Representing the general case (2n, 2n+1, consecutive integers), "show that" manipulations, completing the square for positivity, and always finishing with a clear conclusion.

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
Prove that the difference between the squares of any two consecutive odd numbers is a multiple of $8$ .
Level 5 · 4 marksTry it
2
Prove that if $n$ is odd then $n^2 - 1$ is a multiple of $8$ .
Level 5 · 3 marksTry it