plumiDifferentiating powers of x: AQA Level 2 Further Maths questions
Every AQA Level 2 Further Maths exam question on 4.3 Differentiating powers of x, 2021–2025, with its mark scheme and examiner’s report.
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All 17 questions on Differentiating powers of x, as a list
- June 2025, Paper 1, Q20 (4 marks): y = 3 3 x – 5x2 + 28x + 11 Show that y is an increasing function for all values of x.
- June 2025, Paper 2, Q5 (3 marks): The equation of a curve is y = x5 + px4 where p is a constant. When x = –1 the gradient of the curve is –3 Work out the value of p. p =
- June 2024, Paper 1, Q5 (3 marks): y = + x x x 3 7 4 4 Work out d d y x d d y x =
- June 2024, Paper 2, Q3 (3 marks): The equation of a curve is y = x4 – 3kx2 where k is a constant. When x = 2 the rate of change of y with respect to x is 23 Work out the value of k. k =
- June 2024, Paper 2, Q8 (3 marks): y = 2 1 x2 + x4 3 4 Work out d d y x 2 2 Give your answer in the form a + bxn where a, b and n are integers. Answer
- June 2023, Paper 1, Q11 (3 marks): y = 1 12 x4 + 3x2 + 4 Work out the positive value of x for which y x 2 2 d d = 55 x =
- June 2023, Paper 2, Q5 (3 marks): y = 0.5x4 Work out the value of x for which the rate of change of y with respect to x is 6.75 x =
- June 2023, Paper 2, Q17 (4 marks): The function h is given by h(x) = ax(3x2 – 2) + 5x where a is a positive constant. h is an increasing function for all values of x. Work out the possible values
- June 2022, Paper 1, Q6 (3 marks): = + y x x x − 4 3 3 2 2 Work out y x d d y x d d =
- June 2022, Paper 2, Q8 (4 marks): A curve has equation y = x3 – 5x2 At two points on the curve, the rate of change of y with respect to x is 4 8 (a) Work out an equation, in terms of x, to repre
- June 2022, Paper 2, Q12 (5 marks): Work out the gradient of the curve y = + x x x − 3 2 12 8 3 4 at the point where x = –1 You must show your working. Answer
- November 2021, Paper 1, Q2 (3 marks): y = x(2x4 – 7x3) Work out an expression for the rate of change of y with respect to x. Answer
- November 2021, Paper 2, Q13 (4 marks): P is the point on the curve y = ax3 + 10x2 where x = 2 The gradient of the normal to the curve at P is – 1 4 Work out the value of a. Answer
- November 2021, Paper 2, Q18 (5 marks): y = 12x + x 3 Show that y has a minimum value when x = 0.5
- Specimen, Paper 1, Q5 (3 marks): y x x = − 10 2 3 2 Work out d d y x Answer
- Specimen, Paper 1, Q19 (4 marks): f(x) = 2x3 – 12x2 + 25x – 11 Use differentiation to show that f(x) is an increasing function for all values of x.
- Specimen, Paper 2, Q10 (5 marks): y = 9 8 4 6 2 x x x + Work out the value of d d y x 2 2 when x = 0.5 Answer
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