plumiCentres of mass by integration: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 6.2 Centres of mass by integration, 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 12 questions on Centres of mass by integration, as a list
- June 2025, Further Mechanics 2, Q2 (7 marks): y = 1 x y x 4 2 O Figure 2 The shaded region shown in Figure 2 is bounded by the curve with equation y = 1 x , the line with equation x = 2 , the line with equa
- June 2025, Further Mechanics 2, Q6 (12 marks): A uniform semicircular lamina has radius r and the midpoint of the diameter of the lamina is at O. The distance of the centre of mass of the lamina from O is d.
- June 2024, Further Mechanics 2, Q4 (12 marks): R O A B y x 4 6 2 2 1 16 36 x y Figure 3 A uniform lamina OAB is in the shape of the region R. Region R lies in the first quadrant and is bounded by the curve w
- June 2024, Further Mechanics 2, Q6 (13 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. y x O 2 6 Figure 4 The shaded
- June 2023, Further Mechanics 2, Q5 (7 marks): 9 3 y = 9 − x2 A B O y x Figure 3 A uniform lamina OAB is modelled by the finite region bounded by the x-axis, the y-axis and the curve with equation y x 9 2, f
- June 2023, Further Mechanics 2, Q7 (13 marks): x2 + y2 = 4a2 2a a x y O 3a m 4a m a m √ Figure 5 Figure 6 The shaded region shown in Figure 5 is bounded by the line with equation x a = and the curve with equ
- June 2022, Further Mechanics 2, Q6 (10 marks): 3 9 y = 1 3 x O x y Figure 4 The shaded region shown in Figure 4 is bounded by the x‑axis, the line with equation x = 9 and the line with equation y = 1 3 x. Th
- November 2021, Further Mechanics 2, Q7 (9 marks): [In this question, you may assume that the centre of mass of a circular arc, radius r, with angle at centre 2α, is a distance sin r α α from the centre.] A B O
- November 2020, Further Mechanics 2, Q2 (10 marks): y x y = 8e−x R ln 2 O ln 5 A C D B Figure 1 Figure 2 A uniform plane figure R, shown shaded in Figure 1, is bounded by the x-axis, the line with equation x = ln
- June 2019, Further Mechanics 2, Q3 (11 marks): Numerical (calculator) integration is not acceptable in this question. O A L x y B Figure 2 The shaded region OAB in Figure 2 is bounded by the x-axis, the line
- June 2019, Further Mechanics 2, Q4 (12 marks): A flagpole, AB, is 4 m long. The flagpole is modelled as a non-uniform rod so that, at a distance x metres from A, the mass per unit length of the flagpole, m k
- June 2019, Further Mechanics 2, Q5 (11 marks): O R x y 2 Figure 4 The region R, shown shaded in Figure 4, is bounded by part of the curve with equation y2 = 2x , the line with equation y = 2 and the y-axis.
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