plumiSimultaneous equations: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 2.4 Simultaneous equations, 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 10 questions on Simultaneous equations, as a list
- Summer 2025, AS Unit 1, Q4 (10 marks): y x 4 x 6 4. The diagram below shows a sketch of the curve C with equation and the line L y x+ 16 with equation . The curve and the line intersect at t
- Summer 2025, AS Unit 1, Q8 (10 marks): 2 2 4 4 x y x y . 8. A circle C has centre A and equation (a) Find the coordinates of A and the radius of C. [3] y 2 x , intersects the circle C at
- Summer 2024, AS Unit 1, Q16 (10 marks): x kx 4 0 16. (a) Find the range of values of k for which the quadratic equation has no real roots. [4] y x 2 3 x 4 (b) Determine the coordinates of
- Summer 2023, Unit 3, Q13 (7 marks): The curve C1 has parametric equations x = 3p + 1, y = 9p2. 1 3 The curve C2 has parametric equations x = 4q, y = 2q. Find the Cartesian coordinates of the point
- Summer 2023, AS Unit 1, Q7 (13 marks): y 2 x 5 x 12 y mx 14 The curve C has equation and the line L has equation , 0 7 where m is a real constant. a) Given that L is a tangent to C, i) show
- Summer 2022, AS Unit 1, Q5 (9 marks): 5 The curve C1 has equation y = –x2 + 2x + 3 and the curve C2 has equation y = x2 – x – 6. The two curves intersect at the points A and B. a) Determine the coor
- Summer 2022, AS Unit 1, Q7 (11 marks): 7 A circle C has centre A and equation x2 + y2 – 4x – 6y = 3. a) Find the coordinates of A and the radius of C. [3] The line L with equation y = x + 5 intersect
- Summer 2022, AS Unit 1, Q15 (8 marks): 5 Solve the simultaneous equations ⎛ ⎞ ( ) − loga x2y2 ( ) + loga 9 3loga x2y ⎠⎟= loga 36 , ⎝⎜ x2y2 ( ) = 0 . loga y − loga x + 3 [8]
- Summer 2019, AS Unit 1, Q9 (12 marks): 9 The points A(–2, 4) and B(6, 10) are such that AB is the diameter of a circle. a) Show that the centre of the circle has coordinates (2, 7). [1] The equation
- Summer 2018, AS Unit 1, Q6 (10 marks): 6 y L B C A x O The sketch shows the curve C with equation y = 14 + 5x – x2 and line L with equation y = x + 2. The line intersects the curve at the points A an
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