plumiProof by deduction and exhaustion: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on A.1 Proof by deduction and exhaustion, 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 deduction and exhaustion, as a list
- June 2024, Paper 1, Q13 (6 marks): (a) It is given that P(x) = 4x3 + 8x2 + 11x + 4 Use the factor theorem to show that (2x + 1) is a factor of P(x) [2 marks] 13 (b) Express P(x) in the form P(x)
- June 2022, Paper 2, Q6 (5 marks): (a) Asif notices that 242 = 576 and 2 + 4 = 6 gives the last digit of 576 He checks two more examples: 272 = 729 292 = 841 2 + 7 = 9 2 + 9 = 11 Last digit 9 Las
- November 2021, Paper 1, Q13 (8 marks): (a) Given that P(x) = 125x3 + 150x2 + 55x + 6 use the factor theorem to prove that (5x + 1) is a factor of P(x). [2 marks] 13 (b) Factorise P(x) completely. [3
- November 2021, Paper 2, Q8 (6 marks): Kai is proving that n3 − n is a multiple of 3 for all positive integer values of n. Kai begins a proof by exhaustion. Step 1 n3 − n = n(n2 − 1) Step 2 When n =
- November 2020, Paper 1, Q5 (2 marks): Prove that, for integer values of n such that 0 × n < 4 2n+2 > 3n [2 marks]
- June 2019, Paper 3, Q6 (4 marks): The three sides of a right-angled triangle have lengths a, b and c, where a, b, c 2 Z b c a 6 (a) State an example where a, b and c are all even. [1 mark] 6 (b)
- June 2018, Paper 2, Q1 (1 mark): Which of these statements is correct? Tick one box. [1 mark] x = 2 ) x2 = 4 x2 = 4 ) x = 2 x2 = 4 , x = 2 x2 = 4 ) x = −2
- June 2018, Paper 2, Q5 (2 marks): Prove that 23 is a prime number. [2 marks]
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