plumiQuadratics and the discriminant: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on B.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 10 questions on Quadratics and the discriminant, as a list
- June 2025, Paper 1, Q9 (10 marks): (a) A geometric series, S, has second term 60 The common ratio of S is 0.2 Find the exact value of the sum of the first five terms of S [4 marks] 9 (b) A differ
- June 2024, Paper 3, Q2 (1 mark): The quadratic equation 4x2 + bx + 9 = 0 has one repeated real root. Find b Circle your answer. [1 mark] b = 0 b = ±12 b = ±13 b = ±36
- June 2023, Paper 1, Q6 (5 marks): Show that the equation 2 log10 x = log10 4 + log10 (x + 8) has exactly one solution. Fully justify your answer. [5 marks]
- June 2023, Paper 3, Q6 (9 marks): (a) Sketch the curve with equation y = x2(2x + a) where a > 0 [3 marks] O y x 6 (b) The polynomial p(x) is given by p(x) = x2(2x + a) + 36 6 (b) (i) It is given
- June 2022, Paper 1, Q11 (10 marks): The polynomial p(x) is given by p(x) = x3 + (b + 2)x2 + 2(b + 2)x + 8 where b is a constant. 11 (a) Use the factor theorem to prove that (x + 2) is a factor of
- November 2021, Paper 2, Q1 (1 mark): Four possible sketches of y = ax2 + bx + c are shown below. Given b2 − 4ac = 0 and a, b and c are non-zero constants, which sketch is the only one that could po
- November 2020, Paper 3, Q4 (7 marks): p(x) = 4x3 − 15x2 − 48x − 36 4 (a) Use the factor theorem to prove that x − 6 is a factor of p(x). [2 marks] 4 (b) (i) Prove that the graph of y = p(x) intersec
- November 2020, Paper 3, Q7 (7 marks): (a) Using nCr = n! r!(n − r)! show that nC2 = n(n − 1) 2 [2 marks] 7 (b) (i) Show that the equation 2 × nC4 = 51 × nC2 simplifies to n2 − 5n − 300 = 0 [3 marks]
- June 2019, Paper 1, Q15 (10 marks): (a) At time t hours after a high tide, the height, h metres, of the tide and the velocity, v knots, of the tidal flow can be modelled using the parametric equat
- June 2018, Paper 2, Q4 (6 marks): A curve, C, has equation y = x2 − 6x + k , where k is a constant. The equation x2 − 6x + k = 0 has two distinct positive roots. 4 (a) Sketch C on the axes below
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