AS & A Level Further Mathematics (9231) — October–November 2024, Paper 31

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

Start with Question 1 →
Question 1 · 5 marks · Projectile motion (equation of 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…

Answer this question and get it marked →
Question 2 · 5 marks · Circular motion in a vertical plane (energy conservation and Newton's second law along the radius)

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…

Answer this question and get it marked →
Question 3 · 8 marks · Elastic strings and springs (Hooke's law, elastic potential energy, 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…

Answer this question and get it marked →
Question 4 · 7 marks · Centre of mass of a composite rigid body (uniform bodies)

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…

Answer this question and get it marked →
Question 5 · 7 marks · Linear motion under a variable force (separable differential equation)

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…

Answer this question and get it marked →
Question 6 · 8 marks · Circular motion (conical pendulum with 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…

Answer this question and get it marked →
Question 7 · 10 marks · Projectile motion and oblique impact with a fixed smooth plane (restitution)

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…

Answer this question and get it marked →

← October–November 2024 Paper 32 · October–November 2024 Paper 23 →

← All AS & A Level Further Mathematics (9231) past papers