plumiDifferentiating powers of x: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.07.2 Differentiating 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 8 questions on Differentiating powers of x, as a list
- June 2025, AS Paper 2, Q4 (10 marks): 2 4 The cubic polynomial x 2 kx 4 x + , where k is a constant, is denoted by ( )x k f . - + It is given that f ( ) 2 16 . l = (a) Show that k = 3. [4] For the r
- June 2024, Paper 2, Q1 (4 marks): Differentiate the following with respect to x. 2 4 (a) 3 x [2] - 2 x (b) 4 x - 9 [2]
- June 2023, Paper 3, Q3 (8 marks): 3 The cubic polynomial ( ) f x is defined by ( )x f x px + , where p and q are constants. q = + (a) (i) Given that f 2 ( ) 13 , find the value of p. [2] l = (ii
- June 2022, AS Paper 2, Q5 (7 marks): y x O 1 ( , 1 ) - 2 The diagram shows a curve C for which y is inversely proportional to x. The curve passes through a k. 1 the point ,1 - 2 (a) (i) Determine t
- November 2021, AS Paper 1, Q2 (4 marks): The number of people, n, living in a small town is changing over time. In an attempt to predict the future growth of the town, a researcher uses the following m
- 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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