plumiDisproof by counter-example: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 1.2 Disproof by counter-example, 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 6 questions on Disproof by counter-example, as a list
- 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 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, 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, 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, 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 2018, Pure 2, Q3 (5 marks): (a) “If m and n are irrational numbers, where m ≠ n, then mn is also irrational.” Disprove this statement by means of a counter example. (2) (b) (i) Sketch the
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