plumiVolumes of revolution: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on E.1 Volumes of revolution, 2019–2025, 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 Volumes of revolution, as a list
- June 2025, AS Paper 1, Q13 (5 marks): The curve C1 is given by the equation xy = m where m is a positive constant. The region R1 is enclosed by curve C1, the x-axis and the lines x = 1 and x = 4 O 1
- June 2024, Paper 2, Q16 (9 marks): The function f is defined by f(x) = ax + 5 x + b where a and b are constants. The graph of y = f(x) has asymptotes x = –2 and y = 3 16 (a) Write down the value
- June 2024, AS Paper 1, Q2 (1 mark): The function f is defined by f(x) = 2x + 3 0 ≤ x ≤ 5 The region R is enclosed by y = f(x), x = 5, the x-axis and the y-axis. The region R is rotated through 2π
- June 2022, Paper 2, Q12 (11 marks): The shaded region shown in the diagram below is bounded by the x-axis, the curve y = f (x) , and the lines x = a and x = b O a b y x y = f(x) The shaded region
- June 2022, AS Paper 1, Q10 (6 marks): The diagram below shows an ellipse E The coordinate axes are the lines of symmetry of E O x y 2 – 2 – 3 3 10 (a) Write down an equation of E [2 marks] 10 (b) Th
- November 2020, Paper 2, Q7 (5 marks): The diagram shows part of the graph of y = cos×1 x 0.2 O 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 – 0.2 – 0.2 0.2 0.4 0.6 0.8 1.0 1.2 x y The finite region enclosed by t
- November 2020, AS Paper 1, Q15 (4 marks): A segment of the line y = kx is rotated about the x-axis to generate a cone with vertex O. The distance of O from the centre of the base of the cone is h. The r
- June 2019, Paper 2, Q8 (9 marks): A parabola P1 has equation y2 = 4ax where a > 0 P1 is translated by the vector b 0 , where b > 0 , to give the parabola P2 8 (a) The line y = mx is a tangent to
- June 2019, AS Paper 1, Q5 (8 marks): A hyperbola H has the equation x2 a2 − y2 4a2 = 1 where a is a positive constant. 5 (a) Write down the equations of the asymptotes of H. [1 mark] 5 (b) Sketch t
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