AS & A Level Further Mathematics (9231) — October–November 2024, Paper 33

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

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Question 1 · 5 marks · Further Mechanics: projectile motion — equation of the trajectory

A particle P is projected with speed u m s^-1 at an angle tan^-1 2 above the horizontal from a point O on a horizontal plane and moves freely under gravity. When P has travelled a…

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Question 2 · 5 marks · Further Mechanics: circular motion in a vertical plane — energy conservation and tension in a string

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 at the…

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Question 3 · 8 marks · Further Mechanics: elastic strings — Hooke's law, elastic potential energy and energy conservation

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

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Question 4 · 7 marks · Further Mechanics: centre of mass of a composite (uniform solid of revolution) body

An object is formed by removing a cylinder of radius (2/3)a and height kh (k < 1) from a uniform solid cylinder of radius a and height h. The vertical axes of symmetry of the two…

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Question 5 · 7 marks · Further Mechanics: linear motion — first-order differential equation, separation of variables

A particle P of mass 2 kg moving on a horizontal straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The only horizontal force…

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Question 6 · 8 marks · Further Mechanics: circular motion — conical arrangement of two connected particles, vertical equilibrium

A particle P of mass 0.05 kg is attached to one end of a light inextensible string of length 1 m. The other end of the string is attached to a fixed point O. A particle Q of mass…

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Question 7 · 10 marks · Further Mechanics: projectiles and oblique impact with a smooth plane (Newton's experimental law)

A particle P is projected with speed u at an angle tan^-1(4/3) above the horizontal from a point O on a horizontal plane and moves freely under gravity. When P is moving…

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