plumiIntegrating exponentials, 1/x and trig functions: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 8.3 Integrating exponentials, 1/x 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 8 questions on Integrating exponentials, 1/x and trig functions, as a list
- June 2023, Paper 1, Q9 (10 marks): d y - . x x 9 The gradient of a curve is given by d e 4 e = - x (a) Show that the x-coordinate of any point on the curve at which the gradient is 3 satisfies th
- June 2023, Paper 3, Q14 (3 marks): =/ 1 13 6 n 5 + 14 Show that the expression given in line 33 simplifies to ln n , as given in . + + r 24 12 n n ( 1 ) + r 1 line 34. [3] 6
- November 2020, Paper 2, Q10 (9 marks): In this question you must show detailed reasoning. The equation of a curve is sin 2 x - . x y = x sin x (a) Use the small angle approximation given in the list
- November 2020, Paper 2, Q14 (8 marks): In this question you must show detailed reasoning. 1 - sin2x cosx. Fig. 14 shows the graphs of y = sin x cos 2x and y = 2 y 1 1 y= –sin2x cosx 2 0.5 x 0 0.5 1 y
- November 2020, Paper 3, Q10 (2 marks): In this question you must show detailed reasoning. y r 1 Show that x x d ln 1 as given in line 37. [2] = r - e
- June 2019, Paper 1, Q15 (12 marks): A model for the motion of a small object falling through a thick fluid can be expressed using the differential equation d = v 9 8 . kv , - d t where v ms 1 - is
- June 2019, Paper 2, Q2 (4 marks): 12 2 Given that y ( x 5 ) , = + y d . (a) Find x [2] d ; 2 11 (b) Hence find 48 x x ( 5 ) d x . [2] +
- June 2018, Paper 1, Q8 (6 marks): 2 can be written as 8 (i) Show that sin 8 x cos x 1 cos x 4 . [3] - y 2 2 (ii) Hence find sin x cos x x d . [3]
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