AS & A Level Mathematics (9709) — May–June 2025, 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 · 4 marks · Forces and equilibrium / Newton's laws of motion

A block of mass 12 kg is being pulled by a rope up a rough plane. The plane is inclined at an angle of 20° above the horizontal. The rope pulling the block is parallel to a line…

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Question 2 · 4 marks · Forces and equilibrium / resolution of forces

Three coplanar forces of magnitudes P N, 5 N and 10 N act at a point O, as shown in the diagram. The resultant of the three forces has magnitude Q N and acts in a direction…

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Question 3 · 7 marks · Kinematics of motion in a straight line

The diagram shows the velocity-time graph of the motion of a cyclist. The graph consists of three straight line segments. The cyclist passes a point O with speed 3 m s^-1 and then…

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Question 4 · 6 marks · Work, energy and power

A lorry of mass 18 000 kg is travelling along a straight road. On a horizontal section of the road, the power of the lorry's engine is constant. There is a constant resistance to…

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Question 5 · 7 marks · Momentum / energy, work and power

When a particle P of mass m kg has speed u m s^-1, its momentum is 4 N s and its kinetic energy is 16 J. Find the value of m and the value of u. [3]

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Question 6 · 9 marks · Newton's laws of motion / connected particles

Two particles, P and Q, of masses 0.3 kg and 0.6 kg respectively, are attached to the ends of a light inextensible string. The string passes over a smooth pulley fixed at a point…

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Question 7 · 13 marks · Kinematics: use of differentiation and integration

A particle X moves along a straight track, starting from a point O at time t = 0. The displacement of X from O at time t s is s m, where s = 3t^(3/2) − 6t. Find the time at which…

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