plumiProof by deduction and exhaustion: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 1.1 Proof by deduction and exhaustion, 2010–2025, 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 14 questions on Proof by deduction and exhaustion, as a list
- June 2025, Pure 1, Q8 (5 marks): A student was asked to prove that the square of any number can be expressed in the form 5n or 5n ± 1 where n ∈ The start of the student’s proof is shown in th
- June 2025, AS Pure, Q15 (4 marks): “n 3 + 4n is prime for n ∈ ” (I) (a) Determine whether statement (I) is always true, sometimes true or never true. You must fully justify your answer. (2) “n 3
- June 2024, AS Pure, Q14 (4 marks): Prove, using algebra, that n 2 + 5n is even for all n ∈ (4)
- June 2023, Pure 1, Q14 (4 marks): Prove, using algebra, that (n + 1) 3 – n 3 is odd for all n ∈ (4)
- June 2023, AS Pure, Q17 (5 marks): In this question p and q are positive integers with q p > Statement 1: is never a multiple of 5 (a) Show, by means of a counter example, that Statement 1 is not
- June 2022, Pure 1, Q7 (5 marks): (i) Given that p and q are integers such that pq is even use algebra to prove by contradiction that at least one of p or q is even. (3) (ii) Given that x and y
- June 2022, Pure 2, Q11 (4 marks): Prove, using algebra, that n(n 2 + 5) is even for all n . (4)
- June 2022, AS Pure, Q14 (4 marks): (i) A student states “if x2 is greater than 9 then x must be greater than 3” Determine whether or not this statement is true, giving a reason for your answer. (
- November 2021, Pure 1, Q15 (6 marks): (i) Use proof by exhaustion to show that for n ∈ , n 4 (n + 1) 3 > 3 n (2) (ii) Given that m3 + 5 is odd, use proof by contradiction to show, using algebra,
- November 2021, AS Pure, Q10 (5 marks): A student is investigating the following statement about natural numbers. “ n 3 – n is a multiple of 4 ” (a) Prove, using algebra, that the statement is true fo
- November 2020, Pure 2, Q16 (4 marks): Use algebra to prove that the square of any natural number is either a multiple of 3 or one more than a multiple of 3 (4)
- November 2020, AS Pure, Q13 (5 marks): (a) Prove that for all positive values of a and b 4a b b a + 4 (4) (b) Prove, by counter example, that this is not true for all values of a and b. (1)
- June 2019, Pure 1, Q10 (6 marks): (i) Prove that for all n , n2 + 2 is not divisible by 4 (4) (ii) “Given x , the value of µ3x – 28µ is greater than or equal to the value of (x – 9).” State
- June 2019, AS Pure, Q15 (4 marks): Given n `, prove that n3 + 2 is not divisible by 8 (4)
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