AS & A Level Mathematics (9709) — October–November 2023, Paper 42

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 · Energy, work and power

A block of mass 15 kg slides down a line of greatest slope of an inclined plane. The top of the plane is at a vertical height of 1.6 m above the level of the bottom of the plane.…

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Question 2 · 5 marks · Forces and equilibrium

The diagram shows a smooth ring R, of mass m kg, threaded on a light inextensible string. A horizontal force of magnitude 2 N acts on R. The ends of the string are attached to…

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Question 3 · 5 marks · Energy, work and power

A block of mass 10 kg is at rest on a rough plane inclined at an angle of 30° to the horizontal. A force of 120 N is applied to the block at an angle of 20° above a line of…

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Question 4 · 7 marks · Forces and equilibrium

A particle P of mass 0.2 kg lies at rest on a rough horizontal plane. A horizontal force of magnitude 1.2 N is applied to P. Given that P is in limiting equilibrium, find the…

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Question 5 · 8 marks · Kinematics of motion in a straight line

A particle A of mass 0.5 kg is projected vertically upwards from horizontal ground with speed 25 m s⁻¹. Find the speed of A when it reaches a height of 20 m above the ground.

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Question 6 · 9 marks · Newton's laws of motion

A railway engine of mass 120000 kg is towing a coach of mass 60000 kg up a straight track inclined at an angle of α to the horizontal where sin α = 0.02. There is a light rigid…

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Question 7 · 12 marks · Kinematics of motion in a straight line

A particle X travels in a straight line. The velocity of X at time t s after leaving a fixed point O is denoted by v m s⁻¹, where v = −0.1t³ + 1.8t² − 6t + 5.6. The acceleration…

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