plumiDifferentiating exponentials, logs and trig functions: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.07.4 Differentiating exponentials, logs and trig functions, 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 9 questions on Differentiating exponentials, logs and trig functions, as a list
- June 2025, Paper 1, Q10 (12 marks): ex e x 2 1 10 The graph of y can be transformed to the graph of y - by a stretch parallel to the = = x-axis followed by a translation. (a) (i) State the scale f
- 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 2023, Paper 1, Q9 (6 marks): Conservationists are studying how the number of bees in a wildflower meadow varies according to the number of wildflower plants. The study takes place over a se
- June 2023, Paper 2, Q5 (12 marks): In this question you must show detailed reasoning. The function f is defined by f( ) x cos x 3 sin x with domain 0 x 2 r. = + G G (a) Solve the following equati
- 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 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
- November 2020, Paper 3, Q4 (11 marks): 4 A curve has equation y 2 ln ( k 3 x ) x 3 x , where k is a positive constant. = - + - (a) Given that the curve has a point of inflection where x = 1, show tha
- 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
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