AS & A Level Further Mathematics (9231) — October–November 2023, Paper 33

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

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Question 1 · 7 marks · Further Mechanics: momentum and restitution — oblique impact of two smooth spheres

Two uniform smooth spheres A and B of equal radii have masses m and 2m respectively. The two spheres are moving with equal speeds u on a smooth horizontal surface when they…

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Question 2 · 7 marks · Further Mechanics: motion in a straight line with a resistance depending on v (dv/dt equation)

A ball of mass 2 kg is projected vertically downwards with speed 5 m s^-1 through a liquid. At time t s after projection, the velocity of the ball is v m s^-1 and its displacement…

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Question 3 · 8 marks · Further Mechanics: equilibrium of a rigid body — limiting friction and moments

A uniform square lamina of side 2a and weight W is suspended from a light inextensible string attached to the midpoint E of the side AB. The other end of the string is attached to…

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Question 4 · 8 marks · Further Mechanics: elastic strings — Hooke's law, elastic potential energy and energy conservation

A light elastic string has natural length 8a and modulus of elasticity 5mg. A particle P of mass m is attached to the midpoint of the string. The ends of the string are attached…

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Question 5 · 9 marks · Further Mechanics: projectile motion — equation of the trajectory

A particle P is projected with speed u m s^-1 at an angle theta above the horizontal from a point O on a horizontal plane and moves freely under gravity. During its flight P…

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Question 6 · 11 marks · Further Mechanics: circular motion of a rigid system — equal angular speeds

A particle P of mass m is attached to one end of a light inextensible rod of length 3a. An identical particle Q is attached to the other end of the rod. The rod is smoothly…

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