plumiIntegrating powers of x: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 8.1 Integrating powers of x, 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 10 questions on Integrating powers of x, as a list
- June 2025, AS Paper 1, Q9 (5 marks): a k in the form x 1 3 5 p q 9 (a) Write the expression x x x [1] 3 . + + 2 2 a k. The curve passes through the point (1, –2). d y 1 3 5 (b) A curve has gradient
- June 2024, AS Paper 1, Q12 (10 marks): The diagram shows the graph of ( ) f x k x ( p x )( q ) where k , p and q are constants. The graph = - - passes through the points (–1, 0), (0, –4) and (2, 0).
- June 2023, Paper 1, Q3 (3 marks): ^ h y 2 4 - 3 Find x x x d x . [3]
- June 2023, Paper 2, Q11 (6 marks): In this question you must show detailed reasoning. d is directly proportional to the square root of x. y The variables x and y are such that x d d = . y When x
- June 2022, AS Paper 1, Q6 (8 marks): d y 2 6 x x The curve passes through the The gradient of a curve is given by the equation 6 20 6 . = - + d x point (2, 6). (a) Find the equation of the curve. [
- November 2021, AS Paper 1, Q7 (6 marks): The diagram shows part of a curve which passes through the point (1, 0). y x O 1 d y 8 The gradient of the curve is given by 6 x . = + d x 3 x Determine whether
- November 2021, AS Paper 2, Q4 (4 marks): J N 6 y 2 + KK OO 4 Find 9 x d x . [4] x L P
- June 2019, Paper 3, Q14 (4 marks): h / 2 2 14 (a) Express lim ( h y ) y as an integral. [1] - d y 0 " d 0 2 2 (b) Hence show that V r h , as given in line 41. [3] = r 3
- June 2019, AS Paper 2, Q7 (8 marks): c 11 d m y 3 7 (a) Find x x x [5] 15 . + 3 x c 11 m 8 y 3 11 (b) Show that x x x a , where a is a positive integer to be determined. [3] 15 d 2 + = # 3 x 0
- June 2018, Paper 2, Q7 (4 marks): c 6 m y 7 x x [4] Find 4 d . - 3 x 5 Answer all the questions
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