plumiSimultaneous equations and planes: OCR MEI A‑Level Further Maths questions
OCR MEI 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 13 questions on Simultaneous equations and planes, as a list
- June 2025, AS Core Pure, Q4 (8 marks): K O 4 (a) The transformation T is represented by the matrix M 2 1 0 OO. = KK 1 2 1 - L P A shape S1 is mapped to a shape S2 by the transformation T. Show that v
- June 2024, Core Pure, Q15 (10 marks): Three planes have equations x ky 3 z = , 1 + + 3 x 4 y 2 z = , 3 + + x 3 y z =- , k + - where k is a constant. (a) Show that the planes meet at a point except f
- June 2024, AS Core Pure, Q7 (6 marks): Three planes have equations x 2 y 3 z 0 , + - = x 3 y 2 z 0 , - + - = x 2 y k z k , - + = where k is a constant. (a) For the case k = 0, the origin lies on all
- June 2023, Core Pure, Q14 (13 marks): Three planes have equations kx - z 2 , = x ky 2 z = , 1 - + + 2 kx 2 y 3 z 0 , + + = where k is a constant. (a) By considering a suitable determinant, show that
- June 2023, AS Core Pure, Q8 (6 marks): The equations of three planes are 2 x y 3 z 3 , + + = 3 x y 2 z 2 , - - = 4 x 3 y 7 z k , - + + = where k is a constant. (a) By considering a suitable determina
- June 2022, AS Core Pure, Q1 (6 marks): (a) (i) Write the following simultaneous equations as a matrix equation. x y 2 z 7 + + = 2 x 4 y 3 z 5 - - =- [1] 5 x 3 y 5 z 13 - + + = (ii) Hence solve the eq
- November 2021, Core Pure, Q15 (6 marks): The equations of three planes are 4 x ky 7 z 4 , - + + = x 2 y 5 z l , - + = 2 x 3 y z 2 . + + = Given that the planes form a sheaf, determine the values of k a
- November 2021, AS Core Pure, Q3 (7 marks): Three planes have the following equations. 2 x 3 y z 3 , - + =- x 4 y 2 z 1 , - + = 3 x 2 y 3 z 14 . - - + = (a) (i) Write the system of equations in matrix for
- November 2020, Core Pure, Q15 (17 marks): (a) Show that the three planes with equations x y z 3 12 + m + = - x y z 2 5 11 + + = - x y z 2 2 9 - + = - where m is a constant, meet at a unique point except
- November 2020, AS Core Pure, Q9 (7 marks): Three planes have equations kx y 2 z 0 + - = 2 x 3 y 6 z 5 + - = - 3 x 2 y 5 z 1 - + = where k is a constant. Investigate the arrangement of the planes for each
- June 2019, Core Pure, Q14 (13 marks): Three planes have equations x ay 2 - + = 2 x 3 y z 3 + + =- x by z c + + = where a, b and c are constants. (a) In the case where the planes do not intersect at
- June 2019, AS Core Pure, Q4 (8 marks): K O (a) Find M -1, where M 4 1 1 2 OO. [1] = - KK 2 1 2 - L P (b) Hence find, in terms of the constant k, the point of intersection of the planes x 2 y 3 z 19 ,
- June 2018, AS Core Pure, Q10 (8 marks): Three planes have equations -x + 2y + z = 0 2x - y - z = 0 x + y = a where a is a constant. (i) Investigate the arrangement of the planes: • when a 0 ; = • when
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