plumiChain, product and quotient rules: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.07.5 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 2024, Paper 1, Q11 (12 marks): A curve has equation y 5 ln ( 1 cos 2 x ) , where x is in radians. = - (a) State the values of x for which 5 ln ( 1 cos x 2 ) is not defined. [2] - (b) P is the
- June 2024, Paper 2, Q4 (10 marks): - . 1 3 x 4 The diagram shows part of the graph of y xe = y 0.5 x 0 0.5 1 1.5 2 (a) Use the sign change method to determine, correct to 2 decimal places, the ro
- June 2024, Paper 3, Q5 (13 marks): y x O M ^ h 3 2 y x x x The diagram shows the curve with equation 2 ln . The curve has a point of inflection = - at the point M. (a) (i) Show that the x-coordin
- June 2023, Paper 1, Q6 (9 marks): + . ex 2 3 x 6 A curve has equation y = (a) Determine the x-coordinates of any stationary points on the curve. [4] (b) Show that the curve is convex for all val
- June 2022, Paper 3, Q5 (14 marks): In this question you must show detailed reasoning. y x O P x 2 3 - The diagram shows the curve with equation y . The tangent to the curve at the point P = 2 4 x
- November 2021, Paper 1, Q7 (9 marks): 7 The curve y ( x 2 )ln x has one stationary point which is close to x = . 1 = - 2 2 (a) Show that the x-coordinate of this stationary point satisfies the equat
- November 2021, Paper 2, Q1 (4 marks): Differentiate the following with respect to x. x 4 (a) e - [2] x2 (b) + [2] x 1
- November 2021, Paper 3, Q8 (11 marks): y L R P M O x 2 x The diagram shows the curve M with equation y xe - . = (a) Show that M has a point of inflection at the point P where x = . 1 [5] The line L p
- November 2020, Paper 1, Q8 (7 marks): e x 2 8 (a) Differentiate ( 2 3 x ) with respect to x. [3] + 2 e x 2 (b) Hence show that ( 2 3 x ) is increasing for all values of x. [4] +
- November 2020, Paper 2, Q1 (9 marks): (a) Differentiate the following with respect to x. 3 7 (i) ( 2 x ) [2] + 3 (ii) x ln x [3] y (b) Find cos x x 5 d . [2] d = y (c) Find the equation of the curve
- June 2019, Paper 1, Q12 (12 marks): a x 3 2 12 A curve has equation y , where a is a constant greater than 1. = y d 3 2 x (a) Show that 6 xa ln a . [3] = x d 3 passes through the point ( 2 1 , 0).
- June 2019, Paper 2, Q1 (11 marks): (a) Differentiate the following. 2 x (i) + [3] x 2 1 2 - (ii) tan x ( 3 x ) [2] 1 (b) Use the substitution u x - to integrate 1 - . [4] = x 1 x 2 - (c) Integrat
- June 2019, Paper 3, Q4 (14 marks): y P x O 1 r 2 1 The diagram shows the part of the curve y 3 x sin 2 x for which 0 x = G G . r 2 The maximum point on the curve is denoted by P. (a) Show that th
- June 2018, Paper 2, Q6 (13 marks): In this question you must show detailed reasoning. ln x y A curve has equation . = x (i) Find the x-coordinate of the point where the curve crosses the x axis.
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