plumiSimultaneous equations and planes: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 3.6 Simultaneous equations and planes, 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 11 questions on Simultaneous equations and planes, as a list
- 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, Q10 (8 marks): The plane Π1 has equation x + y – z = 3 The plane Π2 has equation ax + 3y + 5z = 4 where a is an integer. Given that Π1 is perpendicular to Π2 (a) determine the
- 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, 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, Q5 (12 marks): The line l1 has equation x y z 5 1 4 3 3 5 The plane Π1 has equation 2x + 3y – 2z = 6 (a) Find the point of intersection of l1 and Π1 (2) The line l2 is the ref
- 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, 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
- 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
- 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 +
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