plumiChain, product and quotient rules: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on G.5 Chain, product and quotient rules, 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 14 questions on Chain, product and quotient rules, as a list
- June 2025, Paper 2, Q10 (13 marks): A curve C has equation y = xk ln x for x > 0 where k is a positive integer. 10 (a) Show that dy dx = xk–1 [A + k ln x] where A is a constant to be found. [4 mar
- June 2024, Paper 1, Q6 (2 marks): Use the chain rule to find dy dx when y = (x3 + 5x)7 [2 marks]
- June 2024, Paper 2, Q5 (3 marks): Given that y = x3 sin x find dy dx [3 marks]
- June 2022, Paper 1, Q5 (3 marks): Find an equation of the tangent to the curve y = (x × 2)4 at the point where x = 0 [3 marks]
- June 2022, Paper 1, Q15 (16 marks): (a) Given that y = cosecy 15 (a) (i) Express y in terms of siny. [1 mark] 15 (a) (ii) Hence, prove that dy dy = × cosecy cot y [3 marks] 15 (a) (iii) Show that
- June 2022, Paper 2, Q17 (7 marks): A particle is moving such that its position vector, r metres, at time t seconds, is given by r = et cos t i + et sin t j Show that the magnitude of the accelera
- June 2022, Paper 3, Q10 (13 marks): The function f is defined by f (x) = x2 + 10 2x + 5 where f has its maximum possible domain. The curve y = f (x) intersects the line y = x at the points P and Q
- November 2021, Paper 1, Q10 (8 marks): (a) Given that y = tanx use the quotient rule to show that dy dx = sec2 x [3 marks] 10 (b) The region enclosed by the curve y = tan2 x and the horizontal line,
- November 2021, Paper 2, Q10 (11 marks): The function h is defined by h(x) = x p x − 3 where h has its maximum possible domain. 10 (a) Find the domain of h. Give your answer using set notation. [3 mark
- November 2020, Paper 1, Q14 (9 marks): The function f is defined by f (x) = 3x x p × 1 where x ≥ 0 14 (a) f (x) = 0 has a single solution at the point x = a By considering a suitable change of sign,
- June 2019, Paper 1, Q13 (7 marks): A curve, C, has equation y = e3x−5 x2 Show that C has exactly one stationary point. Fully justify your answer. [7 marks]
- June 2019, Paper 1, Q16 (16 marks): (a) y = e−x( sinx + cos x) Find dy dx Simplify your answer. [3 marks] 16 (b) Hence, show that ( e−x sinx dx = ae−x( sinx + cos x) + c where a is a rational numb
- June 2018, Paper 1, Q13 (10 marks): A company is designing a logo. The logo is a circle of radius 4 inches with an inscribed rectangle. The rectangle must be as large as possible. The company mode
- June 2018, Paper 3, Q6 (13 marks): A function f is defined by f (x) = x 2x − 2 p 6 (a) State the maximum possible domain of f. [2 marks] 6 (b) Use the quotient rule to show that f 0(x) = x − 2 (2
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