plumiProof: Edexcel A‑Level Maths questions
Every Edexcel A-Level Maths exam question on P.1 Proof, 2019–2025, with its mark scheme and examiner’s report.
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All 17 questions on Proof, 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, Pure 1, Q15 (6 marks): (i) Show that k 2 – 4k + 5 is positive for all real values of k. (2) (ii) A student was asked to prove by contradiction that “There are no positive integers x a
- 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, Pure 2, Q15 (3 marks): A student attempts to answer the following question: Given that x is an obtuse angle, use algebra to prove by contradiction that sin x – cos x 1 The student s
- 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 1, Q16 (4 marks): Prove by contradiction that there are no positive integers p and q such that 4 p2 − q2 = 25 (4)
- 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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