plumiQuadratics and the discriminant: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 2.3 Quadratics and the discriminant, 2010–2025, 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 33 questions on Quadratics and the discriminant, as a list
- June 2025, Pure 1, Q4 (5 marks): Given that • f(x) = 2x 3 + 3x 2 – 16x + 16 • f(–4) = 0 (a) write f(x) in the form (x + a) Q(x) where a is a constant and Q(x) is a quadratic expression. (3) (b)
- June 2025, Pure 2, Q11 (11 marks): A company is trying to determine the most profitable selling price for a new toy. Given that • if the selling price of each toy is £30, the company expects to s
- June 2025, Statistics, Q6 (11 marks): The discrete random variable R takes even integer values from 2 to 2n inclusive. The probability distribution of R is given by P 2, 4, 6, … , 2 r R r r n k wher
- June 2025, AS Pure, Q7 (10 marks): P x O Figure 3 A company makes a particular type of chair. The annual profit made by the company is modelled by the equation P = –x 2 + 260x – 16 450 where P is
- June 2025, AS Pure, Q9 (3 marks): An equation x 2 – 3 px + 5 q + 4 = 0 where p and q are constants, has equal roots. Show that q = 1 20 (3 p + 4)(3 p – 4) (3)
- June 2024, Pure 1, Q8 (11 marks): The functions f and g are defined by f(x) 2 4 3 5 9 , 2 9 2 x x x x x g(x) (a) Find fg(2) (2) (b) Find g –1 (3) (c) (i) Find gf(x), giving your answer as a simp
- June 2024, Pure 1, Q15 (6 marks): (i) Show that k 2 – 4k + 5 is positive for all real values of k. (2) (ii) A student was asked to prove by contradiction that “There are no positive integers x a
- June 2024, Pure 2, Q9 (7 marks): O B(20, 0.8) A(0, 2) H (m) x (m) Figure 3 The graph in Figure 3 shows the path of a small ball. The ball travels in a vertical plane above horizontal ground. Th
- June 2024, Pure 2, Q15 (12 marks): The curve C has equation ( ) x y x y 3 2 3 3 2 (a) Find an expression for d d y x in terms of x and y. (5) The point P(1, 0) lies on C. (b) Show that the normal
- June 2023, Pure 1, Q2 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f(x) = 4x 3 + 5x 2 – 10x + 4a
- June 2023, Pure 1, Q10 (9 marks): A circle C has equation x 2 + y 2 + 6kx – 2ky + 7 = 0 where k is a constant. (a) Find in terms of k, (i) the coordinates of the centre of C (ii) the radius of C
- June 2023, Pure 1, Q13 (7 marks): On a roller coaster ride, passengers travel in carriages around a track. On the ride, carriages complete multiple circuits of the track such that • the maximum
- June 2023, AS Pure, Q2 (4 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Using the substitution u x = or otherw
- June 2022, Pure 2, Q12 (6 marks): The function f is defined by f(x) = e3 2 4 x x k + where k is a positive constant. (a) Show that fʹ(x) = (12x 2 − 8x + 3k) g(x) where g(x) is a function to be f
- June 2022, Pure 2, Q16 (12 marks): y l P C O x Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 2 tan t + 1 y = 2 sec 2 t + 3 − 4 π t 3 π The line l is the normal
- June 2022, AS Pure, Q2 (7 marks): f(x) = 2x3 + 5x2 + 2x + 15 (a) Use the factor theorem to show that (x + 3) is a factor of f(x). (2) (b) Find the constants a, b and c such that f(x) = (x + 3)(a
- November 2021, Pure 1, Q2 (4 marks): Given that f (x) = x2 − 4x + 5 x ∈ (a) express f (x) in the form (x + a)2 + b where a and b are integers to be found. (2) The curve with equation y = f (x) •
- November 2021, Pure 1, Q3 (6 marks): The sequence u1, u2, u3, … is defined by un + 1 = k − 24 un u1 = 2 where k is an integer. Given that u1 + 2u2 + u3 = 0 (a) show that 3k 2 − 58k + 240 = 0 (3) (b
- November 2021, Pure 1, Q7 (9 marks): The circle C has equation x2 + y2 − 10x + 4y + 11 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C, giving your answer as a simpl
- November 2021, Pure 1, Q12 (9 marks): H x O 3 Figure 3 Figure 3 is a graph of the trajectory of a golf ball after the ball has been hit until it first hits the ground. The vertical height, H metres,
- November 2021, AS Pure, Q6 (6 marks): In this question you should show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Using algebra, find all solution
- November 2021, AS Pure, Q14 (10 marks): A curve C has equation y = f(x) where f(x) = –3x 2 + 12x + 8 (a) Write f(x) in the form a(x + b) 2 + c where a, b and c are constants to be found. (3) The curve
- November 2020, Pure 1, Q7 (5 marks): y x O l C R 25 (−2, 13) Figure 1 Figure 1 shows a sketch of a curve C with equation y = f (x) and a straight line l. The curve C meets l at the points (−2, 13)
- November 2020, Pure 2, Q14 (7 marks): A circle C with radius r ● lies only in the 1st quadrant ● touches the x-axis and touches the y-axis The line l has equation 2x + y = 12 (a) Show that the x coo
- November 2020, AS Pure, Q7 (8 marks): Given that k is a positive constant and 5 2 3 4 1 x x k + = ∫ d (a) show that 3k + 5 k – 12 = 0 (4) (b) Hence, using algebra, find any values of k suc
- June 2019, Pure 1, Q5 (10 marks): f(x) = 2x2 + 4x + 9 x (a) Write f(x) in the form a(x + b)2 + c, where a, b and c are integers to be found. (3) (b) Sketch the curve with equation y = f(x) sho
- June 2019, Pure 2, Q6 (10 marks): y O x Figure 4 Figure 4 shows a sketch of the graph of y J [࣠) , where g( ) ( ) x x x x x = − + − ⎧ ⎨ ⎩ 2 1 4 7 2 2 2 - (a) Find the value of gg(0). (2) (b)
- June 2019, AS Pure, Q2 (8 marks): Find, using algebra, all real solutions to the equation (i) 16a2 = 2 a (4) (ii) b4 + 7b2 – 18 = 0 (4)
- June 2019, AS Pure, Q7 (8 marks): The curve C has equation y = k x 2 + 1 x \, x 0 where k is a constant. (a) Sketch C stating the equation of the horizontal asymptote. (3) The line l has equ
- June 2019, AS Pure, Q9 (6 marks): A company started mining tin in Riverdale on 1st January 2019. A model to find the total mass of tin that will be mined by the company in Riverdale is given by
- June 2018, Pure 1, Q14 (10 marks): A curve C has parametric equations x = 3 + 2 sin t, y = 4 + 2 cos 2t, 0 t < 2π (a) Show that all points on C satisfy y = 6 − (x − 3)2 (2) (b) (i) Sketch the c
- June 2018, Pure 2, Q6 (6 marks): f (x) = −3x3 + 8x2 − 9x + 10, x ∈ (a) (i) Calculate f (2) (ii) Write f (x) as a product of two algebraic factors. (3) Using the answer to (a)(ii), (b) prove t
- June 2018, Pure 2, Q8 (7 marks): H x O Figure 1 Figure 1 is a graph showing the trajectory of a rugby ball. The height of the ball above the ground, H metres, has been plotted against the horiz
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