plumiProof: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P2.1 Proof, 2019–2025, with its mark scheme and examiner’s report.
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All 15 questions on Proof, as a list
- June 2025, AS Pure 2 (P2), Q10 (4 marks): In this question you must show detailed reasoning. Use algebra to prove by exhaustion that, for all positive integers m that are not multiples of 3, the value o
- June 2025 (A), AS Pure 2 (P2), Q1 (3 marks): Given that a, b and c are positive integers such that • c = a 2 – 1 • a + b + c = 20 prove, by exhaustion, that the product abc is always a multiple of 6 You ma
- January 2025, AS Pure 2 (P2), Q8 (5 marks): (i) A student states “If x and y are irrational numbers, x ≠ y, then xy is also irrational.” Show, by counter example, that this statement is not always true. (
- October 2024, AS Pure 2 (P2), Q11 (6 marks): (i) Prove by counter example that the statement “If n is a prime number then 3 n + 2 is also a prime number.” is false. (ii) Use proof by exhaustion to prove th
- June 2024, AS Pure 2 (P2), Q5 (6 marks): In this question you must show detailed reasoning. (a) Given that x and y are positive numbers such that (x – y) 3 > x 3 – y 3 prove that y > x (b) Using a coun
- January 2024, AS Pure 2 (P2), Q8 (6 marks): (i) Use a counter example to show that the following statement is false “n 2 + 3n + 1 is prime for all n ∈ ” (ii) Use algebra to prove by exhaustion that for a
- October 2023, AS Pure 2 (P2), Q1 (3 marks): Given that a, b and c are integers greater than 0 such that • c = 3a + 1 • a + b + c = 15 prove, by exhaustion, that the product abc is always a multiple of 4 Y
- June 2023, AS Pure 2 (P2), Q8 (5 marks): (i) A student writes the following statement: “When a and b are consecutive prime numbers, a 2 + b 2 is never a multiple of 10” Prove by counter example that th
- January 2023, AS Pure 2 (P2), Q10 (4 marks): A student was asked to prove by exhaustion that if n is an integer then 2n2 + n + 1 is not divisible by 3 The start of the student’s proof is shown in the box b
- October 2022, AS Pure 2 (P2), Q1 (3 marks): Given that a, b and c are integers greater than 0 such that • c = b + 2 • a + b + c = 10 Prove, by exhaustion, that the product of a, b and c is always even. Yo
- January 2022, AS Pure 2 (P2), Q10 (5 marks): (i) Prove by counter example that the statement “if p is a prime number then 2p + 1 is also a prime number” is not true. (ii) Use proof by exhaustion to prove t
- October 2021, AS Pure 2 (P2), Q9 (4 marks): (a) Prove that for all positive values of x and y, x y + 2 xy (b) Prove by counter-example that this inequality does not hold when x and y are both negative.
- June 2021, AS Pure 2 (P2), Q3 (5 marks): (i) Prove that for all single digit prime numbers, p, p3 + p is a multiple of 10 (ii) Show, using algebra, that for n ¥ (n + 1)3 – n3 is not a multiple of 3
- January 2021, AS Pure 2 (P2), Q5 (4 marks): (i) Use algebra to prove that for all x 0 3x + 1 2 3x (ii) Show that the following statement is not true. “The sum of three consecutive prime numbers is alw
- June 2019, AS Pure 2 (P2), Q3 (4 marks): (i) Use algebra to prove that for all real values of x (x – 4) 2 . 2x – 9 (ii) Show that the following statement is untrue. 2 n + 1 is a prime number for all va
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