plumiCentres of mass by integration: OCR MEI A‑Level Further Maths questions
OCR MEI 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 10 questions on Centres of mass by integration, as a list
- June 2025, Mechanics Major, Q9 (10 marks): y 1 y cos x R = 0 x 1 r 2 The diagram shows the shaded region R bounded by the curve y cos x , the x-axis and the = y-axis. The region R is rotated through 2r r
- June 2024, Mechanics Major, Q7 (9 marks): 2 7 The region bounded by the curve y x 3 x + , the positive x-axis and the positive y-axis is 4 = - occupied by a uniform lamina L. The vertices of L are O, A
- June 2023, Mechanics Major, Q8 (8 marks): y (4, 4) y 3 x 4 = + 2 R k x O The diagram shows the shaded region R bounded by the curve y 3 x + , the x-axis, the y-axis, 4 = and the straight line that passe
- June 2022, Mechanics Major, Q9 (11 marks): [In this question you may use the facts that for a uniform solid right circular cone of height h and 1 1 above the base on the line from the 2 base radius r the
- June 2022, AS Mechanics B, Q3 (10 marks): 3 Fig. 3.1 shows the curve with equation y x 3 . The region R, shown shaded, is bounded by = + the curve, the x-axis, the y-axis and the line x 2 . A uniform so
- November 2021, Mechanics Major, Q4 (6 marks): In this question you must show detailed reasoning. y 4 y 3 x = ,13 ^ h 2 y 4 x = - x 0 2 2 The diagram shows parts of the curves y 3 x and y 4 x , which interse
- November 2021, AS Mechanics B, Q3 (8 marks): In this question you must show detailed reasoning. 1 # [In this question you may use the formula: Volume of cone base area # height.] = 3 The region between the
- November 2020, Mechanics Major, Q8 (13 marks): [In this question, you may use the fact that the volume of a right circular cone of base radius r and 1 2 height h is r h . ] r 3 (a) By using integration, show
- June 2019, Mechanics Major, Q7 (8 marks): In this question you must show detailed reasoning. y y 2 ln x = 3 ln2 R x 0 Fig. 7 2 Fig. 7 shows the curve with equation y ln x . The region R, shown shaded in
- June 2019, AS Mechanics B, Q5 (12 marks): 5 Fig. 5 shows the curve with equation y x 4 x + . 2 =- + The curve intersects the x-axis at P and Q. The region bounded by the curve, the x-axis, the y-axis an
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