plumiSuspension and toppling: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 6.3 Suspension and toppling, 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 20 questions on Suspension and toppling, 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 2025, Mechanics Minor, Q4 (14 marks): A block of mass m kg rests on a rough plane inclined at an angle a to the horizontal. The coefficient of friction between the block and the plane is n. At first
- June 2025, AS Mechanics A, Q5 (9 marks): Fig 5.1 shows a uniform triangular lamina OAB where O is the origin of the coordinate system in which the points A and B have coordinates (30, 0) and (90, 50) 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 2024, AS Mechanics A, Q6 (10 marks): A uniform lamina OABC is in the shape of a trapezium where O is the origin of the coordinate system in which the points A, B and C have coordinates (12, 0), ( a
- 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, Mechanics Minor, Q2 (8 marks): The diagram below shows the cross-section through the centre of mass of a uniform block of weight W N, resting on a slope inclined at an angle a to the horizont
- June 2022, Mechanics Minor, Q6 (13 marks): Fig. 6.1 shows a light rod ABC, of length 60 cm, where B is the midpoint of AC. Particles of masses 3.5 kg, 1.4 kg and 2.1 kg are attached to A, B and C respect
- 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 Minor, Q5 (16 marks): Fig. 5.1 shows a solid L-shaped ornament, of uniform density. The ornament is 3 cm thick. The x, y and z axes are shown, along with the dimensions of the orname
- November 2021, AS Mechanics A, Q6 (9 marks): Fig. 6.1 shows a cross-section through a block of mass 5 kg which is on top of a trolley of mass 11 kg. The trolley is on top of a smooth horizontal surface. Th
- November 2021, AS Mechanics A, Q7 (10 marks): The vertices of a uniform triangular lamina, which is in the x-y plane, are at the origin and the points (20, 60) and (100, 0). (a) Determine the coordinates of
- 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
- November 2020, Mechanics Minor, Q1 (6 marks): A uniform solid rectangular prism has cross-section with width w cm and height 24 cm. Another uniform solid prism has cross-section in the shape of an isosceles
- November 2020, AS Mechanics A, Q6 (10 marks): Fig. 6.1 shows a solid uniform prism OABCDEFG. The Ox, Oy and Oz axes are also shown. The cross-section of the prism is a trapezium. Fig. 6.2 shows the face OAB
- June 2019, Mechanics Major, Q4 (6 marks): 5a A B F 4a C a E D Fig. 4 Fig. 4 shows a uniform lamina ABCDE such that ABDE is a rectangle and BCD is an isosceles triangle. AB 5 a , AE 4 a and CD . The poin
- June 2019, Mechanics Minor, Q6 (12 marks): A uniform solid cylinder, L, has base radius 5 cm, height 24 cm and mass 5 kg. L is placed on a rough plane inclined at an angle a to the horizontal, as shown i
- June 2019, AS Mechanics A, Q4 (9 marks): A shovel consists of a blade and handle, as shown in Fig. 4.1 and Fig. 4.2. The dimensions shown in the figures are in metres. The blade is modelled as a unifor
- 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
- June 2018, AS Mechanics A, Q4 (9 marks): A uniform lamina ABDE is in the shape of an equilateral triangle ABC of side 12 cm from which an equilateral triangle of side 6 cm has been removed from corner
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