plumiInvariant points and lines: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on C.5 Invariant points and lines, 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 8 questions on Invariant points and lines, as a list
- June 2025, Paper 1, Q12 (13 marks): (a) Find the eigenvalues and corresponding eigenvectors of the matrix = 19 3 1 3 11 20 M [5 marks] 12 (b) State, with a reason, the Cartesian equati
- June 2024, Paper 2, Q10 (4 marks): The matrix C is defined by C = 3 2 –4 5 Prove that the transformation represented by C has no invariant lines of the form y = kx [4 marks]
- 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, Q3 (1 mark): The matrix A = 1 2 0 1 represents a transformation. Which one of the points below is an invariant point under this transformation? Circle your answer. [1 mark]
- 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 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
- November 2021, AS Paper 1, Q4 (1 mark): The point (2, −1) is invariant under the transformation represented by the matrix N Which of the following matrices could be N? Circle your answer. [1 mark] 4 6
- June 2019, AS Paper 1, Q12 (12 marks): The matrix A is given by A = 1 2 0 3 12 (a) Prove by induction that, for all integers n ≤ 1, An = 1 3n − 1 0 3n [4 marks] 12 (b) Find all invariant lines under
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