AS & A Level Further Mathematics (9231) — October–November 2024, Paper 32

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 · Further Mechanics - circular motion with an elastic string (horizontal circle)

A particle of mass 2 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 100 N. The other end of the string is attached to a…

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Question 2 · 4 marks · Further Mechanics - energy conservation with an elastic spring (vertical motion)

A particle P of mass m is attached to one end of a light elastic spring of natural length a and modulus of elasticity 5mg. The other end of the spring is attached to a fixed point…

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Question 3 · 7 marks · Further Mechanics - oblique impact of smooth spheres (momentum and restitution)

The diagram shows two identical smooth uniform spheres A and B of equal radii and each of mass m. The two spheres are moving on a smooth horizontal surface when they collide with…

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Question 4 · 7 marks · Further Mechanics - equilibrium of a rigid body (rod, string and limiting friction at a wall)

The end A of a uniform rod AB of length 6a and weight W is in contact with a rough vertical wall. One end of a light inextensible string of length 3a is attached to the midpoint C…

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Question 5 · 8 marks · Further Mechanics - projectile motion (equation of the trajectory)

A particle P is projected from a point O on horizontal ground with speed u at an angle theta above the horizontal, where tan theta = 1/3. The particle P moves freely under gravity…

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Question 6 · 10 marks · Further Mechanics - motion in a vertical circle (string, smooth peg, string becoming slack)

A particle P of mass m is attached to one end of a light inextensible string of length a. The other end of the string is attached to a fixed point O. The particle P is held with…

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Question 7 · 11 marks · Further Mechanics - motion in a straight line with variable resistance (v as a function of t)

A particle P of mass m kg is held at rest at a point O and released so that it moves vertically under gravity against a resistive force of magnitude 0.1 m v^2 N, where v m s^-1 is…

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