plumiProof by contradiction: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.01.3 Proof by contradiction, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 4 questions on Proof by contradiction, as a list
- June 2025, Paper 1, Q11 (7 marks): A student is attempting to prove that 5 is irrational. The first three lines of their proof are shown below. a Line 1 Assume that 5 is rational, so it can be wr
- June 2023, Paper 2, Q7 (5 marks): 7 A student wishes to prove that, for all positive integers a and b, a 4 b 2 . ! - 2 (a) Prove that a & [2] 4 b 2 a is even. - = 2 (b) Hence or otherwise prove
- November 2020, Paper 1, Q4 (3 marks): Prove by contradiction that there is no greatest multiple of 5. [3]
- June 2018, Paper 2, Q5 (6 marks): Charlie claims to have proved the following statement. “The sum of a square number and a prime number cannot be a square number.” (i) Give an example to show th
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