plumiIntegrating powers of x: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.08.1 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 9 questions on Integrating powers of x, as a list
- June 2024, AS Paper 1, Q6 (7 marks): A curve has the following properties: d y • The gradient of the curve is given by d 2 x . =- x • The curve passes through the point ( , 4 13 ) . - Determine the
- June 2023, Paper 1, Q3 (7 marks): 3 (a) Given that ( ) f x x 2 x , use differentiation from first principles to show that f ( )x 2 x 2 . l = + = + [4] d = y (b) The gradient of a curve is given
- June 2022, Paper 2, Q3 (10 marks): 3 (a) Amaya and Ben integrated ( 1 )x , with respect to x, using different methods, as follows. + 3 x ( 1 ) + y 2 1 2 1 3 Amaya: ( 1 x ) d x c x x x c + = + = +
- June 2022, AS Paper 1, Q5 (8 marks): d y 2 5 The gradient of a curve is given by d x 3 x . The curve passes through the point (6, 20). = - x (a) Determine the equation of the curve. [4] p 1y (b) He
- November 2021, AS Paper 2, Q6 (6 marks): y d 2 6 A curve C has an equation which satisfies x 3 x + , for all values of x. 2 = 2 d (a) It is given that C has a single stationary point. Determine the nat
- 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, AS Paper 1, Q1 (6 marks): d c 5 m. 3 1 (a) Find x x 3 x [3] - + d 2 x c 2 d m y 2 (b) Find 6 x x . [3] - 3 x
- June 2019, AS Paper 1, Q1 (8 marks): 1 It is given that ( )x f 3 x . = - 3 x Find (a) f l ( )x , [3] (b) f ll ( )x , [2] y (c) f ( )x d x . [3]
- June 2018, AS Paper 1, Q4 (9 marks): 4 (i) It is given that y x 3 x . = + d . y (a) Find x [2] d (b) Find the values of x for which y is increasing. [2] ^ h y (ii) Find 3 4 x d x . [5] -
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