plumiSimultaneous equations and planes: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on C.6 Simultaneous equations and planes, 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 7 questions on Simultaneous equations and planes, as a list
- June 2025, Paper 1, Q15 (9 marks): Three planes have equations 2 9 3 3 3 4 x y z x y z t x y z t + − = − + = + + = where t is a constant. The planes meet along a line of intersection. 15 (a) Find
- June 2024, Paper 2, Q14 (10 marks): The matrix M is defined as M = 5 2 1 6 3 2k + 3 2 1 5 where k is a constant. 14 (a) Given that M is a non-singular matrix, find M–1 in terms of k [5 marks] 14 (
- 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 2022, Paper 1, Q7 (9 marks): The matrix M is defined as M = 1 7 −3 3 6 k + 1 1 3 2 2 664 3 775 where k is a constant. 7 (a) (i) Given that M is a non-singular matrix, find M−1 in terms of k
- November 2021, Paper 1, Q12 (14 marks): The matrix A = 1 5 3 4 −2 p 8 5 −11 2 64 3 75 , where p is a constant. 12 (a) Given that A is a non-singular matrix, find A−1 in terms of p. State any restricti
- November 2020, Paper 1, Q7 (7 marks): Three planes have equations (4k + 1)x − 3y + (k − 5)z = 3 (k − 1)x + (3 − k)y + 2z = 1 7x − 3y + 4z = 2 7 (a) The planes do not meet at a unique point. Show tha
- June 2019, Paper 1, Q12 (8 marks): Three planes have equations 4x − 5y + z = 8 3x + 2y − kz = 6 (k − 2)x + ky − 8z = 6 where k is a real constant. The planes do not meet at a unique point. 12 (a)
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