plumiTransformations with matrices: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on C.3 Transformations with matrices, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 23 questions on Transformations with matrices, as a list
- June 2025, Paper 2, Q2 (1 mark): The quadrilateral Q1 has an area of 5 cm2 The matrix − 4 1 2 1 represents the transformation T The transformation T acts on Q1 to give the quadrilat
- June 2025, Paper 2, Q13 (10 marks): The matrix M is defined by − = 1 3 3 1 M 13 (a) The matrix M represents an anticlockwise rotation about the origin through an angle θ, where 0 ≤
- June 2025, AS Paper 1, Q10 (8 marks): The 3× 3 matrix M represents a reflection in the plane z = 0 The point A has position vector 2 5 4 The point A′ is the image of A under the reflection represent
- June 2025, AS Paper 1, Q11 (9 marks): The 2 × 2 matrix A represents an anticlockwise rotation of 150° about the origin. 11 (a) Find matrix A Write each element in its simplest exact form. [2 marks]
- June 2024, Paper 1, Q12 (10 marks): The line L1 has equation r = 4 2 1 + λ 1 3 –1 The transformation T is represented by the matrix 2 1 0 3 4 6 –5 2 –3 The transformation T transforms the line L1
- June 2024, Paper 2, Q12 (5 marks): The transformation S is represented by the matrix M = 1 –6 2 7 The transformation T is a reflection in the line y = x√ 3 and is represented by the matrix N The
- June 2024, AS Paper 1, Q14 (10 marks): The matrix M represents the transformation T, and is given by M = 3 –1 –2 6 14 (a) The point A has coordinates (4, –5) Find the coordinates of the image of A un
- June 2023, Paper 1, Q10 (12 marks): The matrix M is defined as M = 2 −1 1 −1 −1 −2 1 2 c 2 64 3 75 where c is a real number. 10 (a) The linear transformation T is represented by the matrix M Show
- June 2023, Paper 2, Q5 (5 marks): Josh and Zoe are solving the following mathematics problem: The curve C1 has equation x2 16 − y2 9 = 1 The matrix M = 0 1 1 0 " # maps C1 onto C2 Find the equat
- June 2023, AS Paper 1, Q9 (11 marks): The matrix M represents the transformation T and is given by M = [ 3p + 1 p + 2 12 ] p2 – 3 9 (a) In the case when p = 0 show that the image of the point (4, 5)
- June 2022, Paper 1, Q9 (14 marks): Roberto is solving this mathematics problem: The curve C1 has polar equation r2 = 9 sin 2y for all possible values of y Find the area enclosed by C1 Roberto’s s
- June 2022, Paper 2, Q11 (9 marks): (a) Find the eigenvalues and corresponding eigenvectors of the matrix M = 5 2 −3 2 −3 2 13 2 2 64 3 75 [5 marks] 11 (b) (i) Describe how the directions of the i
- June 2022, Paper 2, Q13 (16 marks): (a) The matrix A represents a reflection in the line y = mx , where m is a constant. Show that A = 1 m2 + 1 1 − m2 2m 2m m2 − 1 " # You may use the result in th
- June 2022, AS Paper 1, Q3 (1 mark): Which of the following transformations is represented by the matrix 1 0 0 0 −1 0 0 0 1 2 64 3 75 ? Tick (3) one box. [1 mark] Rotation of 180° about the x-axis
- November 2021, Paper 1, Q13 (3 marks): The transformation S is represented by the matrix 3 0 0 1 The transformation T is a translation by the vector 0 −5 Kamla transforms the graphs of various functi
- November 2021, Paper 2, Q11 (9 marks): The Cartesian equation of the line L1 is x + 1 3 = −y + 5 2 = 2z + 5 3 The Cartesian equation of the line L2 is 2x − 1 2 = y − 14 m = z + 12 p The non-singular
- November 2021, AS Paper 1, Q3 (1 mark): The matrix M represents a rotation about the x-axis. M = 1 0 0 0 a 3 p 2 0 b − 1 2 2 666664 3 777775 Which of the following pairs of values is correct? Tick (3)
- November 2020, Paper 1, Q2 (1 mark): Which one of the matrices below represents a rotation of 90° about the x-axis? Circle your answer. [1 mark] 1 0 0 0 1 0 0 0 −1 2 64 3 75 −1 0 0 0 1 0 0 0 1 2 64
- November 2020, Paper 2, Q8 (9 marks): (a) Factorise 2a + b + x x + b x2 + b2 0 a ×a2 a + b b b2 as fully as possible. [6 marks] 8 (b) The matrix M is defined by M = 13 + x x + 3 x2 + 9 0 5 ×25 8 3 9
- November 2020, Paper 2, Q9 (7 marks): The matrix C = a ×b b a , where a and b are positive real numbers, and C2 = p3 2 × 1 2 1 2 p3 2 2 6664 3 7775 Use C to show that cos p 12 can be written in the
- November 2020, AS Paper 1, Q6 (2 marks): Anna has been asked to describe the transformation given by the matrix 1 0 0 0 − 3 p 2 − 1 2 0 1 2 − 3 p 2 2 66664 3 77775 She writes her answer as follows: The
- June 2019, Paper 1, Q7 (4 marks): Three non-singular square matrices, A, B and R are such that AR = B The matrix R represents a rotation about the z-axis through an angle y and B = − cos y sin y
- June 2019, Paper 1, Q9 (9 marks): (a) Solve the equation z3 = 2 p − 6 p i , giving your answers in the form reiy where r > 0 and 0 × y < 2p [5 marks] 9 (b) The transformation represented by the
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