plumiSimultaneous equations and planes: OCR A‑Level Further Maths questions
OCR 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 7 questions on Simultaneous equations and planes, as a list
- June 2025, Pure Core 1, Q5 (8 marks): K O K O K O 5 A vector equation of the plane P is r 4 1 1 OO. = + + KK OO m KK OO n KK 1 3 1 0 - L P L P L P (a) Verify that a cartesian equation of P is x y 2
- June 2024, AS Pure Core, Q1 (4 marks): Use a matrix method to determine the solution of the following simultaneous equations. [4] 2 x 3 y z 1 - + = x 2 y 4 z 40 - - = x 5 6 y z 61 + - =
- June 2022, Pure Core 2, Q7 (13 marks): You are given that a is a parameter which can take only real values. J N 2 4 6 - K O The matrix A is given by A 3 10 4 a 9 OO. = - KK - 7 4 4 L P (a) Find an ex
- June 2022, AS Pure Core, Q2 (7 marks): J N J N a 1 2 5 - KK OO and B KK OO where a is a constant. 2 Matrices A and B are given by A = - = - 1 3 1 0 L P L P (a) Find the following matrices. • A + B •
- November 2021, AS Pure Core, Q8 (6 marks): K O 8 The matrix A is given by A 1 t 6 t OO . = KK - 2 2 t 2 2 t 1 - - L P (a) Find, in fully factorised form, an expression for det A in terms of t. [3] (b) St
- November 2020, AS Pure Core, Q4 (6 marks): You are given the system of equations 2 a x 2 y 1 - = 2 x b y 3 + = where a and b are real numbers. (a) Use a matrix method to find x and y in terms of a and b.
- June 2019, Pure Core 1, Q10 (11 marks): K O 10 You are given the matrix A where A 0 a 2 . = KK OO 4 5 1 L P (a) Find, in terms of a, the determinant of A, simplifying your answer. [2] (b) Hence find t
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