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Identities and algebraic proof: Edexcel GCSE Maths questions

Every Edexcel GCSE Maths exam question on A6 Identities and algebraic proof, 2017–2025, with its mark scheme and examiner’s report.

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997 questions

  1. Q10

    June 2025 · Paper 1H

    3 marksA6 Identities and algebraic proof
    The whole paper ↗
    June 2025 Paper 1H, question 10: Prove that the difference in the squares of two consecutive even numbers is always a multiple of 4

  2. Q14

    November 2024 · Paper 3H

    3 marksN10 Fractions, decimals and recurring decimalsA6 Identities and algebraic proof
    The whole paper ↗
    November 2024 Paper 3H, question 14: Prove algebraically that 0.46 495

  3. Q13

    November 2023 · Paper 2H

    3 marksN10 Fractions, decimals and recurring decimalsA6 Identities and algebraic proof
    The whole paper ↗
    November 2023 Paper 2H, question 13: Prove algebraically that 0.07. 23. can be written as 241 3330

  4. Q13

    June 2023 · Paper 3H

    3 marksA6 Identities and algebraic proofA24 Special sequences
    The whole paper ↗
    June 2023 Paper 3H, question 13: An expression for the nth term of the sequence of triangular numbers is n n + 1 ( ) 2 Prove that the sum of any two consecutive triangular numbers is a square n

  5. Q15

    June 2023 · Paper 3H

    3 marksA4 Simplifying, expanding and factorisingA6 Identities and algebraic proof
    The whole paper ↗
    June 2023 Paper 3H, question 15: (a) Factorise a 2 – b 2 40 – 1 is the product of two consecutive odd numbers. (b) Show that 2

  6. Q20

    June 2023 · Paper 3H

    3 marksN10 Fractions, decimals and recurring decimalsA6 Identities and algebraic proof
    The whole paper ↗
    June 2023 Paper 3H, question 20: Prove algebraically that 0.12∙ 3∙ can be written as 61 495

  7. Q16

    November 2022 · Paper 1H

    4 marksA6 Identities and algebraic proof
    The whole paper ↗
    November 2022 Paper 1H, question 16: (a) Prove that (2m + 1)2 − (2n – 1)2 = 4(m + n)(m − n + 1) Sophia says that the result in part (a) shows that the difference of the squares of any two odd numbe

  8. Q15

    November 2019 · Paper 3H

    3 marksA6 Identities and algebraic proof
    The whole paper ↗
    November 2019 Paper 3H, question 15: Prove algebraically that the sum of the squares of any two consecutive even numbers is always a multiple of 4

  9. Q13

    June 2019 · Paper 1H

    2 marksA6 Identities and algebraic proof
    The whole paper ↗
    June 2019 Paper 1H, question 13: Given that n can be any integer such that n 1, prove that n2 – n is never an odd number.

  10. Q15

    November 2018 · Paper 3H

    3 marksA6 Identities and algebraic proof
    The whole paper ↗
    November 2018 Paper 3H, question 15: Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8

  11. Q12

    June 2018 · Paper 1H

    4 marksA6 Identities and algebraic proof
    The whole paper ↗
    June 2018 Paper 1H, question 12: Prove that the square of an odd number is always 1 more than a multiple of 4

  12. Q17

    November 2017 · Paper 1H

    2 marksA6 Identities and algebraic proof
    The whole paper ↗
    November 2017 Paper 1H, question 17: n is an integer. Prove algebraically that the sum of 1 2 n(n + 1) and 1 2 (n + 1)(n + 2) is always a square number.

  13. Q16

    June 2017 · Paper 1H

    4 marksA6 Identities and algebraic proof
    The whole paper ↗
    June 2017 Paper 1H, question 16: n is an integer greater than 1 Prove algebraically that n2 – 2 – (n – 2)2 is always an even number.
All 13 questions on Identities and algebraic proof, as a list
  1. June 2025, Paper 1H, Q10 (3 marks): Prove that the difference in the squares of two consecutive even numbers is always a multiple of 4
  2. November 2024, Paper 3H, Q14 (3 marks): Prove algebraically that 0.46 495
  3. November 2023, Paper 2H, Q13 (3 marks): Prove algebraically that 0.07. 23. can be written as 241 3330
  4. June 2023, Paper 3H, Q13 (3 marks): An expression for the nth term of the sequence of triangular numbers is n n + 1 ( ) 2 Prove that the sum of any two consecutive triangular numbers is a square n
  5. June 2023, Paper 3H, Q15 (3 marks): (a) Factorise a 2 – b 2 40 – 1 is the product of two consecutive odd numbers. (b) Show that 2
  6. June 2023, Paper 3H, Q20 (3 marks): Prove algebraically that 0.12∙ 3∙ can be written as 61 495
  7. November 2022, Paper 1H, Q16 (4 marks): (a) Prove that (2m + 1)2 − (2n – 1)2 = 4(m + n)(m − n + 1) Sophia says that the result in part (a) shows that the difference of the squares of any two odd numbe
  8. November 2019, Paper 3H, Q15 (3 marks): Prove algebraically that the sum of the squares of any two consecutive even numbers is always a multiple of 4
  9. June 2019, Paper 1H, Q13 (2 marks): Given that n can be any integer such that n 1, prove that n2 – n is never an odd number.
  10. November 2018, Paper 3H, Q15 (3 marks): Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8
  11. June 2018, Paper 1H, Q12 (4 marks): Prove that the square of an odd number is always 1 more than a multiple of 4
  12. November 2017, Paper 1H, Q17 (2 marks): n is an integer. Prove algebraically that the sum of 1 2 n(n + 1) and 1 2 (n + 1)(n + 2) is always a square number.
  13. June 2017, Paper 1H, Q16 (4 marks): n is an integer greater than 1 Prove algebraically that n2 – 2 – (n – 2)2 is always an even number.

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