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Further Maths · AQA 7367 · Paper 3 Mechanics · June 2025

AQA A Level Further Maths Paper 3 Mechanics June 2025 question paper

11 questions

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Figure for question 1

[1 mark]

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The graph shows how a force F newtons varies with displacement x metres.

Figure for question 2

Find the work done by the force as the displacement increases from x = 5 to x = 10

Circle your answer.

10 J 30 J 40 J 80 J

[1 mark]

Answer

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The diagram shows a uniform lamina made from three identical squares.

Figure for question 3

The coordinates of the centre of the mass of the lamina are ( $fraction$ $fraction$

Which one of the following statements is correct?

Circle your answer.

$Question 3, shown as an image$

[1 mark]

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Figure for question 4

(a)

Find the coefficient of restitution between the ball and the surface.

[1 mark]

Answer

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(b)

Figure for question 4

[2 marks]

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Figure for question 5

(a)

Calculate the initial kinetic energy of the ball.

[1 mark]

Answer

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(b)

During the subsequent motion, the ball reaches a maximum height of 6 metres above the horizontal surface.

(b)(i)

Find the maximum gravitational potential energy of the ball, relative to the horizontal surface.

[1 mark]

Answer

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(b)(ii)

Find the minimum speed of the ball during its motion.

[3 marks]

Answer

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(b)(iii)

State one assumption that you have made about the forces acting on the ball.

[1 mark]

Answer

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Figure for question 6

[3 marks]

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Figure for question 7

[3 marks]

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Figure for question 8

(a)

Show that the tension in the string is 2.3 newtons correct to two significant figures.

[3 marks]

Answer

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(b)

Find the speed of the sphere.

[3 marks]

Answer

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Two discs, A and B, are moving on a smooth horizontal surface.

The two discs collide.

$Question 9, shown as an image$

$Question 9, shown as an image$

$Question 9, shown as an image$

(a)

Find the velocity of disc B after the collision.

[3 marks]

Answer

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(b)

Find the magnitude of the impulse exerted on disc A during the collision.

Give your answer to two significant figures.

[3 marks]

Answer

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(c)

The discs are in contact for 0.1 seconds during the collision.

Assume that while the two discs are in contact, the force exerted on disc B by disc A is constant.

Find the force exerted on disc B by disc A during the collision.

Give your answer as a vector.

[2 marks]

Answer

Mark scheme for question 9(c)

A uniform semicircular lamina has radius a

(a)

Show that the centre of mass is a distance $fraction$ from the straight edge of the lamina.

[5 marks]

Answer

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(b)

The lamina is suspended in equilibrium from one end of the straight edge.

Find the acute angle between the straight edge and the vertical.

Give your answer to the nearest degree.

[3 marks]

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Figure for question 11

(a)

Calculate the elastic potential energy of the elastic string when the block is released.

[2 marks]

Answer

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(b)

Find the maximum speed of the block as it moves.

[6 marks]

Answer

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(c)

The model is refined to include air resistance.

Explain how the distance that the block travels before reaching its maximum speed would change.

[2 marks]

Answer

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