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Past-paper questions pack

Name
Class
Date set
Date due
Score/ 71

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 20 parts, 71 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 3 (Mechanics) · Q6(a) · 1 marks
6. B alpha C (2M) A Figure 4 A uniform rod AB has mass M and length 2a. A particle of mass 2M is attached to the rod at the point C, where AC = 0.5a The rod rests with end A on rough horizontal ground and end B against a vertical wall. The rod lies in a vertical plane which is perpendicular to the wall. The rod is in equilibrium at an angle alpha to the wall, as shown in Figure 4. In an initial model • the vertical wall is modelled as being smooth • the magnitude of the normal reaction of the ground on the rod at A is R • the magnitude of the force exerted on the rod by the wall at B is S Using the model, (a) find R in terms of M and g (1)
2. June 2025 · Paper 3 (Mechanics) · Q6(b) · 3 marks
(b) show that S = Mg tan alpha (3)
3. June 2025 · Paper 3 (Mechanics) · Q6(c) · 1 marks
In a refined model the vertical wall is modelled as being rough • • the magnitude of the normal reaction of the ground on the rod at A is R1 (c) State which is greater, R or R1 , giving a reason for your answer. (1)
4. June 2025 · Paper 3 (Mechanics) · Q6(d) · 6 marks
(3M) B beta C (2M) A Figure 5 A second particle of mass 3M is now attached to the rod at B. The rod again rests with end A on rough horizontal ground and end B against the vertical wall. The rod lies in a vertical plane which is perpendicular to the wall. The rod is now in limiting equilibrium at an angle beta to the wall, as shown in Figure 5. The vertical wall is again modelled as being smooth. The coefficient of friction between the rod and the ground is μ Given that tan beta = 1 (d) use the model to show that μ = 1 (6)
5. June 2024 · Paper 3 (Mechanics) · Q6(a) · 3 marks
6. B C P 1.5a theta A Figure 5 Figure 5 shows a uniform rod AB of mass M and length 2a. • the rod has its end A on rough horizontal ground • the rod rests in equilibrium against a small smooth fixed horizontal peg P • the point C on the rod, where AC = 1.5a, is the point of contact between the rod and the peg the rod is at an angle theta to the ground, where tan theta = 4 • The rod lies in a vertical plane perpendicular to the peg. The magnitude of the normal reaction of the peg on the rod at C is S. (a) Show that S = 2 5 Mg (3)
6. June 2024 · Paper 3 (Mechanics) · Q6(b) · 6 marks
The coefficient of friction between the rod and the ground is μ. Given that the rod is in limiting equilibrium, (b) find the value of μ. (6)
7. June 2023 · Paper 3 (Mechanics) · Q6(b) · 3 marks
The magnitude of the normal reaction of the wall on the rod at B is S. In an initial model, the rod is modelled as being uniform. Use this initial model to answer parts (b), (c) and (d). (b) By taking moments about A, show that S = 1 2 Mg cot theta (3)
8. June 2023 · Paper 3 (Mechanics) · Q6(e) · 1 marks
In a new model, the rod is modelled as being non-uniform, with its centre of mass closer to B than it is to A. A new value for S is calculated using this new model, with tan theta = (e) State whether this new value for S is larger, smaller or equal to the value that S would take using the initial model. Give a reason for your answer. (1)
9. June 2022 · Paper 3 (Mechanics) · Q4(b) · 3 marks
The tension in the string is T (b) Show that T = 2Mg cos theta (3)
10. Oct 2021 · Paper 3 (Mechanics) · Q3(a) · 5 marks
3. B 2a theta A Figure 2 A beam AB has mass m and length 2a. The beam rests in equilibrium with A on rough horizontal ground and with B against a smooth vertical wall. The beam is inclined to the horizontal at an angle theta , as shown in Figure 2. The coefficient of friction between the beam and the ground is μ The beam is modelled as a uniform rod resting in a vertical plane that is perpendicular to the wall. Using the model, (a) show that μ 1 2 cot theta (5)
11. Oct 2021 · Paper 3 (Mechanics) · Q3(b) · 5 marks
A horizontal force of magnitude kmg, where k is a constant, is now applied to the beam at A. This force acts in a direction that is perpendicular to the wall and towards the wall. Given that tan theta = 5 4 , μ = 1 2 and the beam is now in limiting equilibrium, (b) use the model to find the value of k. (5)
12. Oct 2020 · Paper 3 (Mechanics) · Q4(a) · 3 marks
4. B C 6a 4a alpha A Figure 1 A ladder AB has mass M and length 6a. The end A of the ladder is on rough horizontal ground. The ladder rests against a fixed smooth horizontal rail at the point C. The point C is at a vertical height 4a above the ground. The vertical plane containing AB is perpendicular to the rail. The ladder is inclined to the horizontal at an angle alpha , where sin alpha = 4 5 , as shown in Figure 1. The coefficient of friction between the ladder and the ground is μ. The ladder rests in limiting equilibrium. The ladder is modelled as a uniform rod. Using the model, Mg (a) show that the magnitude of the force exerted on the ladder by the rail at C is 9 (3)
13. Oct 2020 · Paper 3 (Mechanics) · Q4(b) · 7 marks
(b) Hence, or otherwise, find the value of μ. (7)
14. June 2019 · Paper 3 (Mechanics) · Q4(a) · 1 marks
4, 3m7 B se 5m _—-— —|A q j q df NN . ~ ie .a Figure 2 A ramp, AB, of length 8m and mass 20kg, rests in equilibrium with the end 4 on rough horizontal ground. The ramp rests on a smooth solid cylindrical drum which is partly under the ground. The drum is fixed with its axis at the same horizontal level as A. The point of contact between the ramp and the drum is C, where AC = 5m, as shown in Figure 2. The ramp is resting in a vertical plane which is perpendicular to the axis of the drum, 7 at an angle @ to the horizontal, where tan = 7A The ramp is modelled as a uniform rod. (a) Explain why the reaction from the drum on the ramp at point C acts in a direction which is perpendicular to the ramp. (1)
15. June 2019 · Paper 3 (Mechanics) · Q4(b) · 9 marks
(b) Find the magnitude of the resultant force acting on the ramp at A. (9)
16. June 2019 · Paper 3 (Mechanics) · Q4(c) · 1 marks
The ramp is still in equilibrium in the position shown in Figure 2 but the ramp is not now modelled as being uniform. Given that the centre of mass of the ramp is assumed to be closer to A than to B, (c) state how this would affect the magnitude of the normal reaction between the ramp and the drum at C. 1(1)
17. June 2018 · Paper 3 · Q9(a) · 3 marks
9. C x alpha P A B 2a Figure 3 A plank, AB, of mass M and length 2a, rests with its end A against a rough vertical wall. The plank is held in a horizontal position by a rope. One end of the rope is attached to the plank at B and the other end is attached to the wall at the point C, which is vertically above A. A small block of mass 3M is placed on the plank at the point P, where AP = x. The plank is in equilibrium in a vertical plane which is perpendicular to the wall. The angle between the rope and the plank is alpha , where tan alpha = 3 4 , as shown in Figure 3. The plank is modelled as a uniform rod, the block is modelled as a particle and the rope is modelled as a light inextensible string. (a) Using the model, show that the tension in the rope is 5 Mg ( x + a ) a (3)
18. June 2018 · Paper 3 · Q9(b) · 2 marks
The magnitude of the horizontal component of the force exerted on the plank at A by the wall is 2 Mg. (b) Find x in terms of a. (2)
19. June 2018 · Paper 3 · Q9(c) · 5 marks
The force exerted on the plank at A by the wall acts in a direction which makes an angle beta with the horizontal. (c) Find the value of tan beta (5)
20. June 2018 · Paper 3 · Q9(d) · 3 marks
The rope will break if the tension in it exceeds 5 Mg. (d) Explain how this will restrict the possible positions of P. You must justify your answer carefully. (3)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · Paper 3 (Mechanics) · Q6
Mark scheme June 2025 Paper 3 (Mechanics) Q6(d)
June 2024 · Paper 3 (Mechanics) · Q6
Mark scheme June 2024 Paper 3 (Mechanics) Q6(b)
June 2023 · Paper 3 (Mechanics) · Q6
Mark scheme June 2023 Paper 3 (Mechanics) Q6(e)
June 2022 · Paper 3 (Mechanics) · Q4
Mark scheme June 2022 Paper 3 (Mechanics) Q4(b)
Oct 2021 · Paper 3 (Mechanics) · Q3
Mark scheme Oct 2021 Paper 3 (Mechanics) Q3(b)
Oct 2020 · Paper 3 (Mechanics) · Q4
Mark scheme Oct 2020 Paper 3 (Mechanics) Q4(b)
June 2019 · Paper 3 (Mechanics) · Q4
Mark scheme June 2019 Paper 3 (Mechanics) Q4(c)
June 2018 · Paper 3 · Q9
Mark scheme June 2018 Paper 3 Q9(d)