Skip to content
Try on iPad

Matrices: OCR A‑Level Further Maths questions

Every OCR A-Level Further Maths exam question on CP.3 Matrices, 2018–2025, with its mark scheme and examiner’s report.

Find questions648

648 questions

  1. Q1

    June 2025 · Pure Core 1

    4 marksCP.3 Matrices
    The whole paper ↗
    June 2025 Pure Core 1, question 1: J N 5 0 KK OO. 1 (a) A matrix M is given by M = 0 5 L P Describe the transformation represented by M. [2] (b) Write down the 2 # matrix that represents a rotati

  2. Q5

    June 2025 · Pure Core 1

    8 marksCP.6 Further vectorsCP.3 Matrices
    The whole paper ↗
    June 2025 Pure Core 1, question 5: K O K O K O 5 A vector equation of the plane P is r 4 1 1 OO. = + + KK OO m KK OO n KK 1 3 1 0 - L P L P L P (a) Verify that a cartesian equation of P is x y 2

  3. Q3

    June 2025 · Pure Core 2

    9 marksCP.3 Matrices
    The whole paper ↗
    June 2025 Pure Core 2, question 3: J N J N 1 3 3 3 - = - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = 4 8 1 2 L P L P (a) Find the matrix AB. [1] (b) Verify that det ( AB ) det (

  4. Q4

    June 2025 · AS Pure Core

    6 marksCP.3 Matrices
    The whole paper ↗
    June 2025 AS Pure Core, question 4: Two transformations, TA and TB, are represented by matrices A and B respectively. J N 0 1 KK OO. The matrix A is given by A = 1 0 L P (a) (i) Describe the trans

  5. Q8

    June 2025 · AS Pure Core

    7 marksCP.3 Matrices
    The whole paper ↗
    June 2025 AS Pure Core, question 8: K O 8 Matrix A is given by A a OO where a is a constant and all entries of A are integers. 3 13 6 = KK + a 4 20 9 - - - L P The transformation represented by A

  6. Q3

    June 2024 · Pure Core 1

    8 marksCP.3 Matrices
    The whole paper ↗
    June 2024 Pure Core 1, question 3: K O 3 A transformation T is represented by the matrix N 5 1 0 OO, where a is a constant. = KK 3 6 3 L P (a) Find N2 in terms of a. [3] (b) Find det N in terms o

  7. Q3

    June 2024 · Pure Core 2

    7 marksCP.3 Matrices
    The whole paper ↗
    June 2024 Pure Core 2, question 3: J N J N 4 3 3 5 - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = - = 2 2 0 1 L P L P (a) Find 2A - 4B. [2] (b) Write down the matrix C such that A

  8. Q1

    June 2024 · AS Pure Core

    4 marksCP.3 Matrices
    The whole paper ↗
    June 2024 AS Pure Core, question 1: Use a matrix method to determine the solution of the following simultaneous equations. [4] 2 x 3 y z 1 - + = x 2 y 4 z 40 - - = x 5 6 y z 61 + - =

  9. Q8

    June 2024 · AS Pure Core

    10 marksCP.3 Matrices
    The whole paper ↗
    June 2024 AS Pure Core, question 8: Three transformations, TA, TB and TC, are represented by the matrices A, B and C respectively. J N J N 1 0 1 0 KK OO and B KK OO. You are given that A = = 2 3 0

  10. Q4

    June 2023 · Pure Core 1

    11 marksCP.3 Matrices
    The whole paper ↗
    June 2023 Pure Core 1, question 4: The transformations TA and TB are represented by the matrices A and B respectively, where J N J N 0 1 0 1 - KK OO and B KK OO. A = = 1 0 1 0 L P L P (a) Describ

  11. Q1

    June 2023 · Pure Core 2

    8 marksCP.3 Matrices
    The whole paper ↗
    June 2023 Pure Core 2, question 1: J N 1 0 2 2 - KK OO. 1 (a) The matrix P is given by P = 4 2 2 3 - L P (i) Write down the dimensions of P. [1] (ii) Write down the transpose of P. [1] J N = ^ h,

  12. Q7

    June 2023 · AS Pure Core

    6 marksCP.3 Matrices
    The whole paper ↗
    June 2023 AS Pure Core, question 7: In this question you must show detailed reasoning. J N a 6 a 3 - - K O Matrix A is given by A a 9 a 4 OO where a is a constant. = + KK a 0 13 1 - - L P Find all

  13. Q9

    June 2023 · AS Pure Core

    10 marksCP.3 Matrices
    The whole paper ↗
    June 2023 AS Pure Core, question 9: K O 9 Matrix R is given by R 0 1 0 OO where a and b are constants. = KK b 0 a L P (a) Find R2 in terms of a and b. [2] ^ h and b ^ h. 2 2 The constants a and b

  14. Q2

    June 2022 · Pure Core 1

    9 marksCP.3 Matrices
    The whole paper ↗
    June 2022 Pure Core 1, question 2: J N 2 2 - KK OO. 2 The matrix A is given by A = 1 3 L P (a) Calculate det A. [1] - . (b) Write down A 1 [1] J N J N (c) Hence solve the equation A x 1 = - KK OO

  15. Q7

    June 2022 · Pure Core 2

    13 marksCP.3 Matrices
    The whole paper ↗
    June 2022 Pure Core 2, question 7: You are given that a is a parameter which can take only real values. J N 2 4 6 - K O The matrix A is given by A 3 10 4 a 9 OO. = - KK - 7 4 4 L P (a) Find an ex

  16. Q2

    June 2022 · AS Pure Core

    7 marksCP.3 Matrices
    The whole paper ↗
    June 2022 AS Pure Core, question 2: J N J N a 1 2 5 - KK OO and B KK OO where a is a constant. 2 Matrices A and B are given by A = - = - 1 3 1 0 L P L P (a) Find the following matrices. • A + B •

  17. Q6

    June 2022 · AS Pure Core

    11 marksCP.3 Matrices
    The whole paper ↗
    June 2022 AS Pure Core, question 6: J N 5 12 1 KK OO. 6 The matrix A is given by A = 13 12 5 - L P You are given that A represents the transformation T which is a reflection in a certain straight

  18. Q9

    November 2021 · Pure Core 1

    5 marksCP.3 Matrices
    The whole paper ↗
    November 2021 Pure Core 1, question 9: J N You are given that the matrix 2 1 KK OO represents a transformation T. 9 1 0 - L P (a) You are given that the line with equation y kx is invariant under T.

  19. Q1

    November 2021 · Pure Core 2

    3 marksCP.3 Matrices
    The whole paper ↗
    November 2021 Pure Core 2, question 1: K O K O 1 Two matrices, A and B, are given by A 2 3 1 OO and B 1 6 4 OO where a is a constant. = KK - = KK - - a 1 1 8 8 1 - - L P L P Find the value of a for w

  20. Q6

    November 2021 · Pure Core 2

    6 marksCP.3 Matrices
    The whole paper ↗
    November 2021 Pure Core 2, question 6: In this question you must show detailed reasoning. J N 1 2 KK OO. The matrix A is given by A = 0 1 L P (a) Define the transformation represented by A. [1] (b) S
All 35 questions on Matrices, as a list
  1. June 2025, Pure Core 1, Q1 (4 marks): J N 5 0 KK OO. 1 (a) A matrix M is given by M = 0 5 L P Describe the transformation represented by M. [2] (b) Write down the 2 # matrix that represents a rotati
  2. June 2025, Pure Core 1, Q5 (8 marks): K O K O K O 5 A vector equation of the plane P is r 4 1 1 OO. = + + KK OO m KK OO n KK 1 3 1 0 - L P L P L P (a) Verify that a cartesian equation of P is x y 2
  3. June 2025, Pure Core 2, Q3 (9 marks): J N J N 1 3 3 3 - = - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = 4 8 1 2 L P L P (a) Find the matrix AB. [1] (b) Verify that det ( AB ) det (
  4. June 2025, AS Pure Core, Q4 (6 marks): Two transformations, TA and TB, are represented by matrices A and B respectively. J N 0 1 KK OO. The matrix A is given by A = 1 0 L P (a) (i) Describe the trans
  5. June 2025, AS Pure Core, Q8 (7 marks): K O 8 Matrix A is given by A a OO where a is a constant and all entries of A are integers. 3 13 6 = KK + a 4 20 9 - - - L P The transformation represented by A
  6. June 2024, Pure Core 1, Q3 (8 marks): K O 3 A transformation T is represented by the matrix N 5 1 0 OO, where a is a constant. = KK 3 6 3 L P (a) Find N2 in terms of a. [3] (b) Find det N in terms o
  7. June 2024, Pure Core 2, Q3 (7 marks): J N J N 4 3 3 5 - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = - = 2 2 0 1 L P L P (a) Find 2A - 4B. [2] (b) Write down the matrix C such that A
  8. June 2024, AS Pure Core, Q1 (4 marks): Use a matrix method to determine the solution of the following simultaneous equations. [4] 2 x 3 y z 1 - + = x 2 y 4 z 40 - - = x 5 6 y z 61 + - =
  9. June 2024, AS Pure Core, Q8 (10 marks): Three transformations, TA, TB and TC, are represented by the matrices A, B and C respectively. J N J N 1 0 1 0 KK OO and B KK OO. You are given that A = = 2 3 0
  10. June 2023, Pure Core 1, Q4 (11 marks): The transformations TA and TB are represented by the matrices A and B respectively, where J N J N 0 1 0 1 - KK OO and B KK OO. A = = 1 0 1 0 L P L P (a) Describ
  11. June 2023, Pure Core 2, Q1 (8 marks): J N 1 0 2 2 - KK OO. 1 (a) The matrix P is given by P = 4 2 2 3 - L P (i) Write down the dimensions of P. [1] (ii) Write down the transpose of P. [1] J N = ^ h,
  12. June 2023, AS Pure Core, Q7 (6 marks): In this question you must show detailed reasoning. J N a 6 a 3 - - K O Matrix A is given by A a 9 a 4 OO where a is a constant. = + KK a 0 13 1 - - L P Find all
  13. June 2023, AS Pure Core, Q9 (10 marks): K O 9 Matrix R is given by R 0 1 0 OO where a and b are constants. = KK b 0 a L P (a) Find R2 in terms of a and b. [2] ^ h and b ^ h. 2 2 The constants a and b
  14. June 2022, Pure Core 1, Q2 (9 marks): J N 2 2 - KK OO. 2 The matrix A is given by A = 1 3 L P (a) Calculate det A. [1] - . (b) Write down A 1 [1] J N J N (c) Hence solve the equation A x 1 = - KK OO
  15. June 2022, Pure Core 2, Q7 (13 marks): You are given that a is a parameter which can take only real values. J N 2 4 6 - K O The matrix A is given by A 3 10 4 a 9 OO. = - KK - 7 4 4 L P (a) Find an ex
  16. June 2022, AS Pure Core, Q2 (7 marks): J N J N a 1 2 5 - KK OO and B KK OO where a is a constant. 2 Matrices A and B are given by A = - = - 1 3 1 0 L P L P (a) Find the following matrices. • A + B •
  17. June 2022, AS Pure Core, Q6 (11 marks): J N 5 12 1 KK OO. 6 The matrix A is given by A = 13 12 5 - L P You are given that A represents the transformation T which is a reflection in a certain straight
  18. November 2021, Pure Core 1, Q9 (5 marks): J N You are given that the matrix 2 1 KK OO represents a transformation T. 9 1 0 - L P (a) You are given that the line with equation y kx is invariant under T.
  19. November 2021, Pure Core 2, Q1 (3 marks): K O K O 1 Two matrices, A and B, are given by A 2 3 1 OO and B 1 6 4 OO where a is a constant. = KK - = KK - - a 1 1 8 8 1 - - L P L P Find the value of a for w
  20. November 2021, Pure Core 2, Q6 (6 marks): In this question you must show detailed reasoning. J N 1 2 KK OO. The matrix A is given by A = 0 1 L P (a) Define the transformation represented by A. [1] (b) S
  21. November 2021, Pure Core 2, Q9 (6 marks): J N 2 3 KK OO. 9 The matrix A is given by A = 0 2 L P (a) By considering A, A2, A3 and A4 make a conjecture about the form of the matrix An in terms of n for n
  22. November 2021, AS Pure Core, Q5 (8 marks): J N K O - 1 0 = - 13 13 KK OO and B K O 5 Matrices A and B are given by A . = 12 5 0 1 KK OO L P 13 13 L P (a) Use A and B to disprove the proposition: “Matrix
  23. November 2021, AS Pure Core, Q8 (6 marks): K O 8 The matrix A is given by A 1 t 6 t OO . = KK - 2 2 t 2 2 t 1 - - L P (a) Find, in fully factorised form, an expression for det A in terms of t. [3] (b) St
  24. November 2020, Pure Core 1, Q3 (5 marks): K O 3 You are given the matrix A 0 0 1 . = KK OO 0 1 0 - L P A4 (a) Find . [1] (b) Describe the transformation that A represents. [2] The matrix B represents a
  25. November 2020, Pure Core 2, Q7 (6 marks): 6 . 2 4 . KK OO. 7 The matrix A is given by A = - 0 8 . 1 8 . L P (a) Find det A. [1] The matrix A represents a stretch parallel to one of the coordinate axes f
  26. November 2020, AS Pure Core, Q2 (10 marks): P, Q and T are three transformations in 2-D. P is a reflection in the x-axis. A is the matrix that represents P. (a) Write down the matrix A. [1] J N J N Q is a
  27. November 2020, AS Pure Core, Q4 (6 marks): You are given the system of equations 2 a x 2 y 1 - = 2 x b y 3 + = where a and b are real numbers. (a) Use a matrix method to find x and y in terms of a and b.
  28. June 2019, Pure Core 1, Q10 (11 marks): K O 10 You are given the matrix A where A 0 a 2 . = KK OO 4 5 1 L P (a) Find, in terms of a, the determinant of A, simplifying your answer. [2] (b) Hence find t
  29. June 2019, Pure Core 2, Q4 (5 marks): A 2-D transformation T is a shear which leaves the y-axis invariant and which transforms the object point (2, 1) to the image point (2, 9). A is the matrix whic
  30. June 2019, AS Pure Core, Q2 (4 marks): f 1 k 0 p and ^ h where k is a constant. 2 Matrices P and Q are given by P Q ( 1 k ) 1 = - = + - 2 1 3 Exactly one of statements A and B is true. Statement A: P
  31. June 2019, AS Pure Core, Q6 (5 marks): f x 1 4 p. + - 6 A transformation T is represented by the matrix T where T = 2 2 3 2 x x 5 - + A quadrilateral Q, whose area is 12 units, is transformed by T to
  32. June 2019, AS Pure Core, Q7 (7 marks): f p. 7 A transformation A is represented by the matrix A where A 7 x 6 1 = - - 5 5 x 2 x - The tetrahedron H has vertices at O, P, Q and R. The volume of H is 6
  33. June 2018, AS Pure Core, Q4 (7 marks): f p. 4 The matrix A is given by A 1 1 1 = - 2 2 a (i) Show that detA = 6 - 3a. [2] (ii) State the value of a for which A is singular. [1] (iii) Given that A is
  34. June 2018, AS Pure Core, Q6 (7 marks): f t 6 p and f 2 t 4 p where t is a constant. 6 The matrices A and B are given by A B = = t 2 t 2 - - (i) Show that A B . [2] = (ii) Verify that AB A B . [3] = (
  35. June 2018, AS Pure Core, Q8 (13 marks): The 2 # 2 matrix A represents a transformation T which has the following properties. • The image of the point (0, 1) is the point (3, 4). • An object shape whos

Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every OCR A-Level Further Maths paper.

Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.