AS & A Level Mathematics (9709) — October–November 2023, Paper 41

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

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Question 1 · 3 marks · Energy, work and power (energy method on an inclined plane)

A particle of mass 1.6 kg is projected with a speed of 20 m s^-1 up a line of greatest slope of a smooth plane inclined at α to the horizontal, where tan α = 3/4. Use an energy…

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Question 2 · 5 marks · Forces and equilibrium (equilibrium of a particle under two strings)

A particle of mass 2.4 kg is held in equilibrium by two light inextensible strings, one of which is attached to point A and the other attached to point B. The strings make angles…

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Question 3 · 8 marks · Kinematics of motion in a straight line (velocity-time graph)

The diagram shows the velocity-time graph for the motion of a bus. The bus starts from rest and accelerates uniformly for 8 seconds until it reaches a speed of 12.6 m s^-1. The…

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Question 4 · 9 marks · Newton's laws of motion / friction (deceleration on a rough plane)

Two particles P and Q, of masses 6 kg and 2 kg respectively, lie at rest 12.5 m apart on a rough horizontal plane. The coefficient of friction between each particle and the plane…

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Question 5 · 7 marks · Forces and equilibrium (connected particles over a pulley, limiting friction)

The diagram shows a particle A, of mass 1.2 kg, which lies on a plane inclined at an angle of 40° to the horizontal and a particle B, of mass 1.6 kg, which lies on a plane…

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Question 6 · 9 marks · Energy, work and power (power = driving force × speed)

A car of mass 1300 kg is moving on a straight road. On a horizontal section of the road, the car has a constant speed of 30 m s^-1 and there is a constant force of 650 N resisting…

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Question 7 · 9 marks · Kinematics: use of differentiation and integration

A particle moves in a straight line starting from a point O before coming to instantaneous rest at a point X. At time t s after leaving O, the velocity v m s^-1 of the particle is…

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