Free · MAT · TMUA · STEP
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.
Start a timed paper Browse all 90
- 90
- questions
- 3
- admissions tests
- 75
- minutes, TMUA paper
Try it: pick an answer.
Pick a topic
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 3How the timed practice works
- Pick a testTen MAT multiple-choice questions in 50 minutes, a 20-question TMUA paper in 75, or four STEP problems in an hour.
- Work without a calculatorOne question at a time, as in the real tests. STEP answers accept exact forms such as pi/4 or ln(2)/2.
- Study the methodEvery question comes back with a full worked solution. For STEP, the method is the point: the answer only tells you whether you found it.
How to use them
These tests reward seeing structure more than grinding. When a question looks like a long computation, look first for the shortcut: a substitution, a symmetry, a telescoping sum, a counterexample. The solutions here show that route rather than the brute-force one.
Once these feel comfortable, move to the setters' own past papers, published free by Oxford and Cambridge. For how examiners read a MAT answer, see reading a MAT question the way an examiner does.
Common 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.
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.