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A selection of novel MAT-style long questions to augment and expand on your past-paper practice, complete with solutions.

This course is an online version of the MAT Long Questions Course which is held over October Half Term.


MAT long questions are unlike anything you will see at A-level

They will require practice at logical reasoning, understanding abstract definitions, and writing clear and incisive proofs. These are all skills highly prized by universities and should prove useful beyond these entrance exams, including at interview and in preparing for your career as an undergraduate.

MAT questions also focus on more challenging material

For this reason, we focus on a small number of topics more typical of MAT, including unusual compositions of familiar functions, polynomials of degree greater than 2, and equations that depend on a changeable parameter. We also cover kinds of question that challenge your reasoning skills rather than your knowledge, especially the ability to follow abstract rules, and the ability to count and classify mathematical objects.

You’ll need to learn how to present your thinking

You will learn by practice how to approach abstract questions and argue in a way that the examiner will appreciate, while you can watch our tutor present model solutions detailing how the best candidates are expected to think and write.

What we’ll cover:

  • Sketch and analyse bizarre new functions, or construct them yourself
  • Handle polynomials of any order
  • Master intricate rule-following questions
  • Learn to adjust every parameter and anticipate the consequences
  • Count and classify new abstract objects, possible and impossible
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