plumiQuadratics and the discriminant: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 2.3 Quadratics and the discriminant, 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 Quadratics and the discriminant, as a list
- Summer 2025, Unit 3, Q3 (6 marks): cos Given that θ is small, find an estimate for the solution of the equation 0 8 3. . 1 sin 2 [6]
- Summer 2025, AS Unit 1, Q5 (6 marks): x kx k 3 0 5. Find the range of values of k for which the quadratic equation has two distinct real roots. [6]
- Summer 2025, AS Unit 1, Q11 (9 marks): f x ( ) x 3 9 x 2 28 x 4 . 11. The function f is defined by f x is an increasing function. ( ) (a) Show that [4] y = f x . ( ) (b) Two straight lines, b
- Summer 2024, AS Unit 1, Q8 (4 marks): x 10 x 5 x 8. Prove that for all real values of x. [4] !
- Summer 2024, AS Unit 1, Q10 (6 marks): 10. Water is being emptied out of a sink. The depth of water, y cm, at time t seconds, may be modelled by y t 2 14 t 49 0 X t X 7. (a) Find the value of t
- 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 2024, AS Unit 1, Q18 (12 marks): A circle C has centre (–3, –1) and radius 5. Show that the equation of C can be written 18. (a) 2 2 6 2 5 0 x y x y as . [2] (b) (i) Find the equation
- 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, Unit 3, Q12 (13 marks): 2 The diagram below shows a sketch of the graph of y = f (x), where ( ) = 2x2 +12x +10. f x The graph intersects the x-axis at the points (p, 0), (q, 0) and the
- Summer 2022, AS Unit 1, Q9 (4 marks): Find the range of values of k for which the quadratic equation x2 + 2kx + 8k = 0 has 0 9 no real roots. [4]
- Summer 2019, AS Unit 1, Q2 (7 marks): 2 Find all the values of k for which the equation x2 + 2kx + 9k = – 4x has two distinct real roots. [7]
- Summer 2019, AS Unit 1, Q15 (4 marks): Prove that f(x) = x3 – 6x2 + 13x – 7 is an increasing function. 1 5 [4]
- Summer 2018, AS Unit 1, Q12 (5 marks): 2 Find the values of m for which the equation 4x2 + 8x – 8 = m(4x – 3) has real roots. [5]
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