Oxford & Cambridge · TMUA, STEP, interviews
Maths admissions coaching.
Preparation for Oxford and Cambridge mathematics applications — the TMUA, STEP, and the interview — with someone who read Mathematics at Oxford and has spent a career doing the thing the interview is really testing: thinking out loud about an unfamiliar problem.
From the 2026 admissions round onwards, Oxford has stopped running the Mathematics Admissions Test. Every applicant to Maths, Computer Science and their joint courses now sits the TMUA instead.
A great deal of preparation material still circulating online — including from established tutoring companies — is written for the MAT. If a provider is still selling “MAT tuition” for Oxford, check carefully what you are buying. Always confirm current requirements on the Oxford Mathematical Institute website for your entry year.
The landscape
What you are actually facing
TMUA
Two papers of 75 minutes, twenty multiple-choice questions each, no calculator, sat at a Pearson VUE test centre in mid-October. Paper 1 is applications of mathematical knowledge; Paper 2 is mathematical reasoning — logic, proof, and spotting invalid arguments.
Required by Oxford, and used by Cambridge and several other universities at application stage.
STEP
Long, deep problems sat in June, normally as a condition of a Cambridge offer (and Warwick and Imperial in some cases). Where TMUA rewards speed and judgement, STEP rewards stamina and the willingness to stay with one problem for forty minutes.
Preparation for STEP is a year-long project, not a term.
The interview
A tutorial in miniature. You are given an unfamiliar problem and asked to think about it aloud, with prompts. Nobody expects you to know the answer. They are watching how you behave when you do not.
This is the most coachable part of the process and the least well prepared for.
Requirements change, and they differ by course, college and entry year. Check the official Oxford and Cambridge pages for the year you are applying in — and do not trust a tutoring site, including this one, over the university.
How I work
No packages. A plan.
Most admissions companies sell a programme: a fixed block of hours, a portal, a headline success rate. I do not think that is the honest shape for this. Here is what I actually do instead.
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A diagnostic on real papers
We sit a past TMUA paper, or a STEP question, under something like real conditions. Then we go through it properly — not marking it, but working out what happened at each point where it went wrong. Was it knowledge, technique, timing, or nerve? Those need completely different responses.
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A plan you could execute without me
You get a written plan: which topics to shore up, which past papers to sit and when, what to read around the subject. Deliberately, this is something you could follow alone. If you want to take it away and do exactly that, good.
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Weekly problems with written feedback
The core of the work. A small set of hard problems each week, marked properly — meaning I write on your solutions about your reasoning, not just whether you arrived at the answer. This is where most of the improvement happens.
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Reasoning and proof, taken seriously
TMUA Paper 2 and the interview both test something school maths barely touches: can you tell a valid argument from a plausible one? We work on proof by contradiction and induction, on necessary versus sufficient conditions, and on finding the flaw in a convincing-looking piece of reasoning.
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Mock interviews, recorded
Unfamiliar problems, thought about aloud, with me prompting the way a tutor would. Recorded so you can watch yourself back — which is uncomfortable and more useful than any amount of advice. We work specifically on what to say when you are stuck, because that is the moment being assessed.
Being straight with you
What coaching can and cannot do
Preparation makes a real difference to admissions test scores and a large difference to interview performance, mostly by removing surprise. Knowing the shape of the thing lets you spend your attention on the mathematics rather than on the format.
What it cannot do is manufacture an offer. Oxford and Cambridge maths are among the most competitive courses in the country, and strong, well-prepared candidates are turned down every year for no reason connected to their preparation.
So I will not quote you a success rate. Any figure a tutoring company gives you is dominated by who they accepted onto the programme in the first place, not by what the programme did. I would rather tell you honestly whether I think the application is realistic, and then work hard on the parts we can actually move.
The preparation is worth doing even if the offer does not come. STEP and TMUA problems are the best mathematics most students will have met, and the habits they build — sitting with a hard problem, arguing rigorously — carry straight into a degree wherever it is taken.
Several excellent maths departments do not use these tests at all. That is worth discussing early.
The best time to begin is the spring of Year 12, giving two terms before the October test. Starting in September is still workable. Starting in October is a different, much narrower conversation, and I will tell you so.
Common questions
Admissions questions
Is the TMUA the same test Cambridge uses?
It is the same test, used differently. Cambridge has used the TMUA at application stage for several courses for some years; Oxford has now adopted it in place of the MAT. Cambridge mathematics offers additionally normally require STEP, sat the following June. Confirm the detail for your course and entry year on the universities’ own pages.
When should we start preparing?
Spring of Year 12 for a comfortable run at an October test. STEP wants longer — ideally from the start of Year 13, and genuinely from Year 12 if Further Maths is being taken.
Can you help with the personal statement?
For maths, yes — specifically the part about what you have read and thought about beyond the syllabus, which is what a maths tutor will pick up on at interview. I will not write it for you, and an admissions tutor can tell.
Do you only work with Oxbridge applicants?
No. Imperial, Warwick, Durham, Bath, St Andrews and others set demanding maths entry requirements, and several use the TMUA or STEP. The preparation overlaps almost entirely.