plumiProof by contradiction: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on A.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 8 questions on Proof by contradiction, as a list
- June 2025, Paper 3, Q12 (3 marks): Given that the real numbers a, b, and c are such that a × b = c Use proof by contradiction to show that if c is irrational then at least one of a or b is irrati
- June 2024, Paper 2, Q11 (6 marks): (a) A student states that 3 is the smallest value of k in the interval 3 < k < 4 Explain the error in the student’s statement. [1 mark] 11 (b) The student’s tea
- June 2023, Paper 2, Q10 (6 marks): (a) Expand and simplify (a − b)2 [1 mark] 10 (b) Peter thinks that the sum of any rational number and its reciprocal is always greater than 2 Peter checks two e
- June 2022, Paper 3, Q9 (6 marks): Assume that a and b are integers such that a2 − 4b − 2 = 0 9 (a) Prove that a is even. [2 marks] 9 (b) Hence, prove that 2b + 1 is even and explain why this is
- November 2021, Paper 1, Q4 (1 mark): Millie is attempting to use proof by contradiction to show that the result of multiplying an irrational number by a non-zero rational number is always an irrati
- November 2020, Paper 2, Q7 (7 marks): a and b are two positive irrational numbers. The sum of a and b is rational. The product of a and b is rational. Caroline is trying to prove 1 a + 1 b is ration
- June 2019, Paper 1, Q9 (5 marks): Prove that the sum of a rational number and an irrational number is always irrational. [5 marks]
- June 2018, Paper 3, Q10 (7 marks): Prove by contradiction that 2 3p is an irrational number. [7 marks]
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