plumiCentres of mass: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on FM.6 Centres of mass, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 AS Further Mechanics 2, question 3: [In this question you may quote, without proof, the formula for the distance of the centre of mass of a circular arc from its centre.] A B D C 1.5a 2a Figure 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/8fm0-26-jun25-03-qp.webp)
![June 2023 Further Mechanics 2, question 3: [In this question you may quote, without proof, the formula for the distance of the centre of mass of a uniform circular arc from its centre.] C B O A r r r Fig](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4c-jun23-03-qp.webp)
All 37 questions on Centres of mass, as a list
- June 2025, Further Mechanics 2, Q1 (7 marks): A B D C E 2a 2a 2a Figure 1 A uniform rod is cut into six pieces. The pieces are used to form the framework ABCDE shown in Figure 1. • All the pieces of the fra
- 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, Q4 (9 marks): A 6a B 9a C F 9a E 6a D 3a Figure 5 The uniform rectangular lamina ACDF shown in Figure 5 has AC = FD = 15a and AF = CD = 3a . The point B on AC is such that AB
- 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 2025, AS Further Mechanics 2, Q1 (8 marks): 4a D C A M E B 3a 3a Figure 1 A uniform plane lamina, shown shaded in Figure 1, is formed by removing an isosceles triangle ABE from a rectangle ABCD. • The mid
- June 2025, AS Further Mechanics 2, Q3 (9 marks): [In this question you may quote, without proof, the formula for the distance of the centre of mass of a circular arc from its centre.] A B D C 1.5a 2a Figure 2
- June 2024, Further Mechanics 2, Q2 (7 marks): A B C D E 4a 4a Figure 1 A uniform rod of length 28a is cut into seven identical rods each of length 4a. These rods are joined together to form the rigid framew
- 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 2024, AS Further Mechanics 2, Q1 (7 marks): A 4a B 2a C 4a F E D Figure 1 A uniform rod of length 24a is cut into seven pieces which are used to form the framework ABCDEF shown in Figure 1. It is given th
- June 2024, AS Further Mechanics 2, Q4 (12 marks): A a D E 6a 6a B 3a 2a G F C Figure 3 The uniform triangular lamina ABC has AB perpendicular to AC, AB = 9a and AC = 6a. The point D on AB is such that AD = a. T
- June 2023, Further Mechanics 2, Q1 (6 marks): Three particles of masses 3m, 4m and km are positioned at the points with coordinates (2a, 3a), (a, 5a) and (2μa, μa) respectively, where k and μ are constants.
- June 2023, Further Mechanics 2, Q3 (9 marks): [In this question you may quote, without proof, the formula for the distance of the centre of mass of a uniform circular arc from its centre.] C B O A r r r Fig
- 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 2023, AS Further Mechanics 2, Q1 (9 marks): Three particles of masses 4m, 2m and km are placed at the points with coordinates (–3, –1), (6, 1) and (–1, 5) respectively. Given that the centre of mass of th
- June 2023, AS Further Mechanics 2, Q4 (14 marks): 18a 12a 18a 6a A M B E D C Figure 1 A uniform triangular lamina ABC is isosceles, with AC = BC. The midpoint of AB is M. The length of AB is 18a and the length
- June 2022, Further Mechanics 2, Q1 (6 marks): Three particles of masses 2m, 3m and km are placed at the points with coordinates (3a, 2a), (a, –4a) and (–3a, 4a) respectively. The centre of mass of the three
- June 2022, Further Mechanics 2, Q3 (7 marks): A 3a 3a 3a 4a 4a 5a 4a 5a 5a D E F B C Figure 1 Nine uniform rods are joined together to form the rigid framework ABCDEFA, with AB = BC = DF = 3a, BF = CD = DE
- June 2022, Further Mechanics 2, Q5 (11 marks): A 3a 3a 3a 3a D E F B O C Figure 3 The uniform plane lamina shown in Figure 3 is formed from two squares, ABCO and ODEF, and a sector ODC of a circle with centr
- 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
- June 2022, AS Further Mechanics 2, Q1 (7 marks): A B C D F E a 3a a Figure 1 A uniform plane lamina is in the shape of an isosceles trapezium ABCDEF, as shown shaded in Figure 1. • BCEF is a square • AB = CD =
- June 2022, AS Further Mechanics 2, Q2 (12 marks): A B C D O E 2a a Figure 2 Uniform wire is used to form the framework shown in Figure 2. In the framework • ABCD is a rectangle with AD = 2a and DC = a • BEC is
- November 2021, Further Mechanics 2, Q1 (8 marks): A a 4a O E D C B 2a 2a Figure 1 A letter P from a shop sign is modelled as a uniform plane lamina which consists of a rectangular lamina, OABDE, joined to a sem
- November 2021, Further Mechanics 2, Q3 (6 marks): 2a O a Figure 2 A uniform solid hemisphere H has radius 2a. A solid hemisphere of radius a is removed from the hemisphere H to form a bowl. The plane faces of t
- 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, Q1 (7 marks): Three particles of masses 3m, 4m and 2m are placed at the points (−2, 2) , (3, 1) and ( p, p) respectively. The value of p is such that the distance of the cent
- 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
- November 2020, Further Mechanics 2, Q4 (9 marks): O r 4 3 r Figure 3 A uniform solid cylinder of base radius r and height 4 3 r has the same density as a uniform solid hemisphere of radius r. The plane face of
- November 2020, AS Further Mechanics 2, Q1 (15 marks): A D C B a 2a Figure 1 Figure 1 shows a uniform rectangular lamina ABCD with AB = 2a and AD = a The mass of the lamina is 6m. A particle of mass 2m is attached t
- 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.
- June 2019, AS Further Mechanics 2, Q1 (9 marks): A B C D Figure 1 Five identical uniform rods are joined together to form the rigid framework ABCD shown in Figure 1. Each rod has weight W and length 4a. The po
- June 2019, AS Further Mechanics 2, Q4 (10 marks): C B F A B A E D E D C 6a 4a Triangular lamina Folded lamina 6a 3a 9a Figure 2 The uniform triangular lamina ABCDE is such that angle CEA = ° 90 , CE a 9 and EA
- June 2018, AS Further Mechanics 2, Q1 (7 marks): 12a A C B 5a 13a Figure 1 A thin uniform rod, of total length 30a and mass M, is bent to form a frame. The frame is in the shape of a triangle ABC, where AB = 1
- June 2018, AS Further Mechanics 2, Q3 (11 marks): E a a C D F 2a B 2a A Figure 2 The lamina L, shown in Figure 2, consists of a uniform square lamina ABDF and two uniform triangular laminas BDC and FDE. The squ
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