plumiMatrices: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on CP.3 Matrices, 2018–2025, with its mark scheme and examiner’s report.
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All 27 questions on Matrices, as a list
- June 2025, Core Pure 1, Q1 (6 marks): M 3 6 0 3 1 2 a a a where a is a constant (a) Determine the values of a for which the matrix M is singular. (3) Given that matrix M is non-singular and
- June 2025, Core Pure 2, Q3 (12 marks): Given A 1 5 0 2 (a) prove by mathematical induction that, for n ∈ An n n 1 5 2 1 0 2 (6) Given B 1 0 0 1 (b) describe fully the singl
- June 2025, Core Pure 2, Q5 (4 marks): Three planes are defined by the following equations 2 3 3 3 2 4 x y z x py z q x y z where p and q are constants. Given that the planes form a sheaf, determine
- June 2025, AS Core Pure, Q3 (6 marks): 1 1 a b M where a and b are real constants and a ≠ b (a) Determine M –1 in terms of a and b (3) Given that M + M –1 = I, where I is the 2 × 2 identity
- June 2025, AS Core Pure, Q4 (10 marks): (i) 2 0 0 1 P (a) Describe fully the single geometrical transformation P represented by the matrix P. (2) (b) State the equation of one invariant line und
- June 2024, Core Pure 2, Q8 (7 marks): A 1 1 1 3 6 0 k k (a) Find, in terms of k, A –1 (4) (b) Determine, in simplest form in terms of k, the coordinates of the point where the follow
- June 2024, AS Core Pure, Q2 (10 marks): With respect to the right-hand rule, a rotation through θ° anticlockwise about the z-axis is represented by the matrix cos sin 0 sin cos 0 0 0 1 θ θ θ
- June 2024, AS Core Pure, Q4 (8 marks): A B 1 2 7 3 2 1 1 4 4 2 1 7 4 10 3 19 3 1 6 k k k k k where k is a constant. (a) Determine the value of the constant c for which AB
- June 2023, Core Pure 1, Q8 (13 marks): A colony of small mammals is being studied. In the study, the mammals are divided into 3 categories N (newborns) 0 to less than 1 month old J (juveniles) 1 to 3
- June 2023, Core Pure 2, Q3 (10 marks): M 2 5 6 k where k is a constant. Given that M 2 + 11M = aI where a is a constant and I is the 2 × 2 identity matrix, (a) (i) determine the value of a (ii
- June 2023, AS Core Pure, Q1 (4 marks): x y z z y z y k 9 3 I where x, y, z and k are constants. Determine the value of x, the value of y and the value of z. (4)
- June 2023, AS Core Pure, Q3 (4 marks): A 0 3 2 1 2 0 1 2 3 2 (a) Describe fully the single geometric transformation A represented by the matrix A. (2) B 1 3 0 3 0 5
- June 2023, AS Core Pure, Q9 (9 marks): (i) P k k k k 3 2 5 7 2 4 where is a constant Show that P is non-singular for all real values of k. (4) (ii) Q 2 1 3 0 The matrix Q represe
- June 2022, Core Pure 1, Q5 (6 marks): M = − a a 2 3 2 3 0 4 2 where a is a constant (a) Show that M is non-singular for all values of a. (2) (b) Determine, in terms of a, M–1 (4)
- June 2022, Core Pure 2, Q2 (8 marks): In this question you must show all stages of your working. A college offers only three courses: Construction, Design and Hospitality. Each student enrols on jus
- June 2022, Core Pure 2, Q3 (11 marks): M = 3 0 1 a where a is a constant (a) Prove by mathematical induction that, for n ∈ M n = 3 2 3 1 0 1 n n a ( ) − (6) Triangle T has
- June 2022, AS Core Pure, Q1 (7 marks): A = 4 1 7 2 5 8 − − B = 2 3 2 1 6 5 − C = − − 5 2 1 4 3 8 6 11 2 Given that I is the 3 × 3 identity matrix, (a) (i) sh
- June 2022, AS Core Pure, Q3 (8 marks): With respect to the right-hand rule, a rotation through θ° anticlockwise about the y-axis is represented by the matrix cos 0 sin 0 1 0 sin 0 cos θ θ θ θ
- November 2021, Core Pure 1, Q1 (6 marks): The transformation P is an enlargement, centre the origin, with scale factor k, where k > 0 The transformation Q is a rotation through angle θ degrees anticlock
- November 2021, Core Pure 1, Q4 (9 marks): (i) A is a 2 by 2 matrix and B is a 2 by 3 matrix. Giving a reason for your answer, explain whether it is possible to evaluate (a) AB (b) A + B (2) (ii) Given t
- November 2021, Core Pure 2, Q2 (5 marks): A = 4 2 5 3 − The matrix A represents the linear transformation M. Prove that, for the linear transformation M, there are no invariant lines. (5)
- November 2020, Core Pure 2, Q6 (14 marks): M = − k 5 7 1 1 1 2 1 1 where k is a constant (a) Given that k ≠ 4, find, in terms of k, the inverse of the matrix M. (4) (b) Find, in terms of
- November 2020, AS Core Pure, Q1 (6 marks): A system of three equations is defined by kx + 3y – z = 3 3x – y + z = –k –16x – ky – kz = k where k is a positive constant. Given that there is no unique solut
- November 2020, AS Core Pure, Q6 (16 marks): (i) A = − 2 4 a a b where a and b are non-zero constants. Given that the matrix A is self-inverse, (a) determine the value of b and the possible value
- June 2019, Core Pure 2, Q7 (11 marks): M = 2 1 1 3 4 3 2 1 − − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ k where k is a constant (a) Find the values of k for which the matrix M has an inverse. (2) (b) Find, in terms of p, the
- June 2018, AS Core Pure, Q1 (5 marks): M = − − − 2 1 3 4 2 1 3 5 2 (a) Find M–1 giving each element in exact form. (2) (b) Solve the simultaneous equations 2x + y – 3z = –4 4x – 2y +
- June 2018, AS Core Pure, Q5 (10 marks): A = − − − 1 2 3 2 3 2 1 2 (a) Describe fully the single geometrical transformation U represented by the matrix A. (3) The transformation V
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