TMUA · STEP · MAT
Oxbridge maths practice
90 original questions at the level of the Oxford MAT, the TMUA and STEP, each with a full worked solution. Browse them by test, or sit a timed paper.
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- 90
- questions
- 3
- admissions tests
- 75
- minutes, TMUA paper
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Oxford MAT
Multiple choice at the level of the Mathematics Admissions Test: algebra, calculus, sequences, trigonometry and counting.
18 easy · 21 medium · 1 hard MATTMUA
Both papers: applied mathematical knowledge, and logic and proof, including contrapositives, counterexamples and necessary and sufficient conditions.
10 easy · 18 medium · 2 hard TMUA Paper 2 · TMUA Paper 1STEP
Longer problems at STEP 2 and STEP 3 level, each with a single final answer and a full method.
5 easy · 9 medium · 6 hard STEP 2 · STEP 3Common questions
Which test do I need for Oxford or Cambridge mathematics?
Oxford uses the MAT for Mathematics, Computer Science and their joint courses. Cambridge sets STEP as part of conditional offers for Mathematics. The TMUA is required or recommended by several universities for mathematics, economics and computer science courses. Requirements change, so check each course page for your year of entry.
How hard is STEP compared with the MAT and TMUA?
STEP is the hardest of the three: long questions that need sustained reasoning and a written argument, usually taken after an offer. The MAT and TMUA are shortlisting tests with more, shorter questions, where speed and accuracy matter more.
What is on TMUA Paper 2?
Mathematical reasoning: logic, proof, necessary and sufficient conditions, counterexamples and finding the error in an argument, alongside algebra and functions. Many strong students lose marks here simply because they have never practised it.
Are these past paper questions?
No. They are original questions written to the level and style of each test, with full solutions. The setters publish their past papers free, and those are the best practice once the basics are secure.
PDF · Edition 2 · £79
The STEM Admissions Report
Oxford, Cambridge, MIT, Harvard, Stanford, Princeton and Caltech: the tests, the grades, the odds by course, the deadlines, and what the degrees lead to.
Applying for mathematics at Oxford or Cambridge?
The admissions test decides who is interviewed, and the interview decides the offer. I prepare students for both, one to one, with the mathematics taught properly.