plumiInvariant points and lines: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 3.5 Invariant points and lines, 2018–2025, 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 6 questions on Invariant points and lines, as a list
- 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 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 Further Pure 2, Q2 (8 marks): A linear transformation T : 2 → 2 is represented by the matrix M 5 1 3 k where k is a constant. Given that matrix M has a repeated eigenvalue, (a) de
- 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, 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 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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