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A-level Further Maths Solutions

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Your preparation for the A-level Further Maths exams should include working through past papers systematically. There will inevitably be questions you find difficult — or ones you’d like longer solutions for than the mark scheme provides.

Post a message below with the year, question number or a link, and we’ll create a worked solution thread on that question. You can ask as many questions as you wish.

Recommended revision checklist
  • New linear format past papers — including unit tests and sample assessment material. Do every question at least once.
    Edexcel AQA OCR A OCR B (MEI)
  • Legacy (modular) past papers — highly relevant for the new linear format. Key modules: FP1, FP2, FP3, M2, M3, S3, D1, D2.
  • All specimen papers — especially useful for topics with limited new-format past papers.

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A-level Further Maths Practice Questions & Solutions (8)

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Dr. Korte 19 May 2026
Try this further maths question on coupled differential equations
Dr. Korte 19 May 2026
Try this question on differential equations about dissolving salt in water. It has a useful 2-step method for forming the differential equation.
Dr. Korte 19 May 2026
Try this question on invariant lines
Dr. Korte 19 May 2026
Try this polars question
Dr. Korte 19 May 2026
Try this FM transformations question
Dr. Korte 19 May 2026
Try this FM vectors question
Dr. Korte 19 May 2026
My cat Geoffry has a mass of 4 kg and is sitting on rough ground near a sledge of mass 8 kg. The sledge is on a large area of smooth horizontal ice.

Initially, the sledge is at rest and Jeoffry jumps and lands on it with a horizontal velocity of 2.25 m s^-1 parallel to the runners of the sledge. On landing, Jeoffry grips the sledge with his claws so that he does not move relative to the sledge in the subsequent motion.

(i) Show that the sledge with Jeoffry on it moves off with a speed of 0.75 m s^-1.

With the sledge and Jeoffry moving at 0.75 m s^-1, the sledge collides directly with a stationary stone of mass 3 kg. The stone may move freely over the ice. The coefficient of restitution in the collision is 4/15.

(ii) Calculate the velocity of the sledge and Jeoffry immediately after the collision.

In a new situation, Jeoffry is initially sitting at rest on the sledge when it is stationary on the ice. He then walks from the back to the front of the sledge.

(iii) Giving a brief reason for your answer, describe what happens to the sledge during his walk. [2]

Jeoffry is again sitting on the sledge when it is stationary on the ice. He jumps off and, after he has lost contact with the sledge, has a horizontal speed relative to the sledge of 3 m s^-1.

(iv) Determine the speed of the sledge after Jeoffry loses contact with it.
Dr. Korte 14 May 2026
Try this sheaf question