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Study of STEP past questions based on Year 12 Maths, useful for all STEP papers and other admissions tests, such as MAT and TMUA.

This is an online version of the Summer STEP Course that we hold in the Summer between Year 12 and 13.


If you have your sights set on a mathematics degree at a top university, you are likely to have to take at either the Oxford MAT exam, the Durham TMUA, or the STEP exam next summer.


STEP and other tests require problem solving skills

You will need to display mathematical problem-solving abilities at a level appropriate for Maths undergraduates. Therefore, these papers require extensive preparation and an unshakeable grasp of mathematical fundamentals.

Proof techniques are tested more than at A-level

In this course, we are particularly focused on proof and the logical analysis of questions, which are tested much more severely in MAT, TMUA, and STEP, just as at university.

Since you will be marked in part on your presentation of proofs, we cover questions requiring proof by contradiction, counterexample, induction, and division into cases so that you can see fully explained examples of each type.

Overcoming common sources of error

Two places where students often trip up in their answers are on knowing which manipulations are or are not permitted when dealing with inequalities, and on distinguishing between necessary and sufficient conditions, so we present questions which rely heavily on each. We also expound on the use of symmetry to understand and speed up your approach to some problems.

Topics Covered

  • Learn how to plan for and present all of the most essential kinds of proof
  • Examine the subtlest aspects of manipulating inequalities
  • Perfect your understanding of necessary and sufficient conditions
  • Analyse unfamiliar graphs with symmetry tricks
  • Master the art of dividing problems by cases
Personal Statement
Book free Year 12 Oxbridge Programme Consultation
Book free Year 13 STEP 2/3 Programme Consultation
Book free Year 12/13 Medicine Mastermind Consultation