plumiIntegration by parts: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.08.7 Integration by parts, 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 Integration by parts, as a list
- June 2025, Paper 2, Q8 (5 marks): In this question you must show detailed reasoning. 1 y Use integration by parts to find the exact value of 2 ln ( 3 2 x ) d x . [5] - 0
- 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 2022, Paper 1, Q11 (9 marks): d y 2 3 x ln x 11 The gradient function of a curve is given by d . = x 3 y e The curve passes through the point (e, 1). 3 = y (a) Find the equation of this curv
- 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, Q10 (11 marks): y x 1 2 O a k, for 1 The diagram shows the curve y sin x 1 1 x 2 . = - G G 2 a k 2 y 1 (a) Use rectangles of width 0.25 to find upper and lower bounds for sin x
- November 2020, Paper 3, Q5 (12 marks): y P R C x O 1 6 The diagram shows the curve C with parametric equations 3 - , where t 3 2 t x , y t e 2 0 . = = t The maximum point on C is denoted by P. (a) De
- June 2019, Paper 1, Q11 (10 marks): y x O The diagram shows part of the curve y ln ( x 4 ) . = - y (a) Use integration by parts to show that ln ( x 4 ) d x ( x 4 ) ln x 4 x c . [5] - = - - - + (b)
- 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
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