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Further matrices and complex numbers: OCR MEI A‑Level Further Maths questions

Every OCR MEI A-Level Further Maths exam question on FP.8 Further matrices and complex numbers, 2018–2025, with its mark scheme and examiner’s report.

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847 questions

  1. Q5

    June 2025 · Extra Pure

    14 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    June 2025 Extra Pure, question 5: In this question you must show detailed reasoning. J N a b 0 K O 2 2 The matrix A is given by b a 0 OO where a and b are constants with a b = and a 1 1 . KK - +

  2. Q4

    June 2024 · Extra Pure

    15 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    June 2024 Extra Pure, question 4: K O 4 The matrix P is given by P = - 6 12 12 OO. KK 2 4 8 - L P 3 2 (a) Show that the characteristic equation of P is 21 126 216 0 . [3] - m + m - m + = You are

  3. Q5

    June 2023 · Extra Pure

    15 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    June 2023 Extra Pure, question 5: J N a 0 KK OO where a is a constant and a 5 The matrix P is given by P ! . 3 = 2 3 L P 1 r radians, (a) Given that the acute angle between the directions of the

  4. Q2

    June 2022 · Extra Pure

    12 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    June 2022 Extra Pure, question 2: K O 2 The matrix A is given by A 1 2 4 . = - KK OO 3 6 2 L P (a) In this question you must show detailed reasoning. 3 2 Show that the characteristic equation of

  5. Q3

    November 2021 · Extra Pure

    14 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    November 2021 Extra Pure, question 3: K O 3 The matrix A is given by A 0 2 2 OO. = KK 1 3 4 L P (a) Determine the characteristic equation of A. [3] (b) Hence verify that the eigenvalues of A are 1,

  6. Q1

    November 2020 · Extra Pure

    5 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    November 2020 Extra Pure, question 1: J N 0 2 KK OO. 1 The matrix A is given by A = 3 1 - L P Find • the eigenvalues of A, • an eigenvector associated with each eigenvalue. [5]

  7. Q5

    November 2020 · Extra Pure

    8 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    November 2020 Extra Pure, question 5: In this question you must show detailed reasoning. J N 1 2 2 - - K O J N 1 3 3 3 K O K O 2 1 2 The matrix A is given by and the vector e is given by OO. You are

  8. Q1

    June 2019 · Extra Pure

    5 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    June 2019 Extra Pure, question 1: J N 0 6 . 0 8 . KK OO. 1 The matrix A is 0 8 . 0 6 . - L P (a) Given that A represents a reflection, write down the eigenvalues of A. [1] (b) Hence find the eig

  9. Q3

    June 2019 · Extra Pure

    8 marksFP.8 Further matrices and complex numbers
    The whole paper ↗
    June 2019 Extra Pure, question 3: K O 3 The matrix A is 0 1 25 OO. - - KK 3 5 1 - - L P Use the Cayley-Hamilton theorem to find A−1. [8]
All 9 questions on Further matrices and complex numbers, as a list
  1. June 2025, Extra Pure, Q5 (14 marks): In this question you must show detailed reasoning. J N a b 0 K O 2 2 The matrix A is given by b a 0 OO where a and b are constants with a b = and a 1 1 . KK - +
  2. June 2024, Extra Pure, Q4 (15 marks): K O 4 The matrix P is given by P = - 6 12 12 OO. KK 2 4 8 - L P 3 2 (a) Show that the characteristic equation of P is 21 126 216 0 . [3] - m + m - m + = You are
  3. June 2023, Extra Pure, Q5 (15 marks): J N a 0 KK OO where a is a constant and a 5 The matrix P is given by P ! . 3 = 2 3 L P 1 r radians, (a) Given that the acute angle between the directions of the
  4. June 2022, Extra Pure, Q2 (12 marks): K O 2 The matrix A is given by A 1 2 4 . = - KK OO 3 6 2 L P (a) In this question you must show detailed reasoning. 3 2 Show that the characteristic equation of
  5. November 2021, Extra Pure, Q3 (14 marks): K O 3 The matrix A is given by A 0 2 2 OO. = KK 1 3 4 L P (a) Determine the characteristic equation of A. [3] (b) Hence verify that the eigenvalues of A are 1,
  6. November 2020, Extra Pure, Q1 (5 marks): J N 0 2 KK OO. 1 The matrix A is given by A = 3 1 - L P Find • the eigenvalues of A, • an eigenvector associated with each eigenvalue. [5]
  7. November 2020, Extra Pure, Q5 (8 marks): In this question you must show detailed reasoning. J N 1 2 2 - - K O J N 1 3 3 3 K O K O 2 1 2 The matrix A is given by and the vector e is given by OO. You are
  8. June 2019, Extra Pure, Q1 (5 marks): J N 0 6 . 0 8 . KK OO. 1 The matrix A is 0 8 . 0 6 . - L P (a) Given that A represents a reflection, write down the eigenvalues of A. [1] (b) Hence find the eig
  9. June 2019, Extra Pure, Q3 (8 marks): K O 3 The matrix A is 0 1 25 OO. - - KK 3 5 1 - - L P Use the Cayley-Hamilton theorem to find A−1. [8]

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