Chain, product and quotient rules: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on 7.5 Chain, product and quotient rules, 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.

All 19 questions on Chain, product and quotient rules, as a list

June 2025, Pure 1, Q9 (9 marks): O T t v Figure 2 A racing car is driven along a straight road. Figure 2 shows a graph of the speed of the car as it travels along the road. The car starts from
June 2025, Pure 2, Q5 (7 marks): The curve C has parametric equations x t 1 2 y = 5(t + 2) 4 t ∈  The point P with x coordinate –3 lies on C. (a) Find the y coordinate of P. (2) (b) Find a Car
June 2025, Pure 2, Q15 (13 marks): R y x P Q O –1 1 Figure 5 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 5 sho
June 2024, Pure 1, Q5 (6 marks): The function f is defined by f(x) = 2 2 3 4 x x x (a) Show that f′(x) = ax bx c x 2 2 2 4 where a, b and c are constants to be found. (3) (b) Hence, using a
June 2024, Pure 2, Q6 (7 marks): O y = f(x) y = g(x) x y Figure 1 Figure 1 shows a sketch of the curves with equations y = f(x) and y = g(x) where f(x) = e 4x2 – 1 x > 0 g(x) = 8 ln x x > 0 (a)
June 2023, Pure 1, Q15 (13 marks): A curve has equation y = f(x), where f(x) = 7 2 3 x x x e e − x > ln 2 3 (a) Show that f′(x) = 7 2 2 3 3 3 2 e e 2(e x x x x Ax B ( ( ) ) ) where A and B are co
June 2022, Pure 1, Q8 (8 marks): v t T O Figure 2 A car stops at two sets of traffic lights. Figure 2 shows a graph of the speed of the car, v ms−1, as it travels between the two sets of traffi
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
November 2021, Pure 1, Q4 (9 marks): The curve with equation y = f (x) where f (x) = x2 + ln (2x2 − 4x + 5) has a single turning point at x = α (a) Show that α is a solution of the equation 2x3 − 4
November 2021, Pure 1, Q14 (4 marks): Given that y = x x − + 4 2 x > 0 show that d d y x = A x 1 x > 0 where A is a constant to be found. (4)
November 2020, Pure 1, Q9 (9 marks): y x O C Figure 2 Figure 2 shows a sketch of the curve C with equation y = f (x) where f (x) = 4(x2 − 2)e−2x x   (a) Show that f ʹ(x) = 8(2 + x − x2)e−2x (3) (
November 2020, Pure 2, Q13 (6 marks): The function g is defined by g (x) = 3 7 2 ln( ) ln( ) x x − − x > 0 x ≠ k where k is a constant. (a) Deduce the value of k. (1) (b) Prove that gʹ (x) > 0 for a
June 2019, Pure 1, Q3 (5 marks): y x x x x = + + ≠− 5 10 1 1 2 2 ( ) (a) Show that d d y x A x n = + ( )1 where A and n are constants to be found. (4) (b) Hence deduce the range of values for x
June 2019, Pure 1, Q12 (10 marks): f(x) = 10e±௘x sin x, x . 0 (a) Show that the x coordinates of the turning points of the curve with equation y = f(x) satisfy the equation tan x = 4 (4) y O
June 2019, Pure 1, Q14 (7 marks): The curve C, in the standard Cartesian plane, is defined by the equation x = 4 sin 2\ 4 4 π π y − < < The curve C passes through the origin O (a) Find th
June 2018, Pure 1, Q5 (5 marks): Given that 3sin 2sin 2cos θ y θ θ = + 3 4 4 π π θ − < < show that d d 1 sin 2 y A θ θ = + 3 4 4 π π θ − < < where A is a rational constant to be found. (5)
June 2018, Pure 2, Q11 (7 marks): 1 11 6 3 1 2 3 1 2 2 + − − − ≡ + − + − x x x x A B x C x ( )( ) ( ) ( ) (a) Find the values of the constants A, B and C. (4) f (x) = 1 11 6 3 1 2 2 + − − − x x
June 2018, Pure 2, Q13 (10 marks): y x O R C P(e, e) l Figure 2 Figure 2 shows a sketch of part of the curve C with equation y = x ln x, x > 0 The line l is the normal to C at the point P(e, e) T
June 2018, Pure 2, Q14 (10 marks): A scientist is studying a population of mice on an island. The number of mice, N, in the population, t months after the start of the study, is modelled by the e

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