AS & A Level Mathematics (9709) — October–November 2024, Paper 43

7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 4 marks · Work, energy and power (work–energy principle with a resistance force)

An athlete has mass m kg. The athlete runs along a horizontal road against a constant resistance force of magnitude 24 N. The total work done by the athlete in increasing his…

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Question 2 · 6 marks · Forces and equilibrium (resolving coplanar forces; the equilibrant)

Coplanar forces of magnitudes 16 N, 12 N, 24 N and 8 N act at a point in the directions shown in the diagram. Taking the point as the origin with the 24 N force directed along the…

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Question 3 · 6 marks · Work, energy and power (power and driving force on an incline)

A car of mass 1600 kg travels up a slope inclined at an angle of sin⁻¹0.08 to the horizontal, against a constant resistance of magnitude 240 N. It is given that the car travels at…

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Question 4 · 6 marks · Momentum (conservation of momentum; loss of kinetic energy in a collision)

Two particles, A and B, of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and A is moving towards B with speed 8 m s⁻¹. After A and B…

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Question 5 · 8 marks · Forces and equilibrium (limiting friction with an inclined pull)

A particle of mass 12 kg is pulled across a rough horizontal plane by a light inextensible string at 30° above the plane with tension T N. The coefficient of friction between the…

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Question 6 · 10 marks · Kinematics (velocity by integration of variable acceleration)

A particle starts from rest at t = 0 and accelerates at 0.6t m s⁻² for 4 s, reaching a speed of V m s⁻¹. Show that V = 4.8. [1]

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Question 7 · 10 marks · Newton's laws (connected particles over a smooth pulley)

Two particles A and B, of masses 3 kg and 5 kg, are connected by a light inextensible string over a fixed smooth pulley, hanging with vertical string parts. A is 1 m above a…

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