Oxford and Cambridge maths interviews

What is a maths interview like?

Oxford’s mathematics department says candidates generally have one or two interviews at their first-choice college and at least one at another, each lasting about 25 minutes and largely mathematical, all by video call. It lists the kinds of thing you might do: sketch a curve, solve a problem while talking us through how you are thinking, or take a definition you have not met and work out some of its consequences. Maths is one of the subjects where Oxford asks for a touchscreen and a stylus, so that you can write on a shared online whiteboard.

Cambridge’s colleges run their own interviews within the university’s main interview period, 7 to 18 December 2026, and most applicants have one or two interviews lasting 35 minutes to an hour in total. Some colleges set a short written test first: Trinity, for example, says applicants it interviews sit a written test immediately before an interview of about 40 to 45 minutes with two of its mathematics teaching staff. The college’s own page says what it does.

What are the tutors looking for?

Oxford’s department lists three things: a capacity to absorb and use new ideas, the ability to think and work independently, and perseverance and enthusiasm. Its course page puts the aim as an applicant’s potential to think imaginatively, deeply and in a structured way about the patterns of mathematics, and the department’s interview page is blunter: they are trying to see how you think when you do mathematics.

So the interview is not a test of how much you have covered. Being stuck is normal, and what matters is what you do next: try a small case, draw a picture, say what you would need to know, and use the hint when it comes. A tutor would rather watch you get halfway with good reasoning than see an answer you cannot explain.

Problems the universities have published

Oxford publishes sample questions from its own tutors. One, from a Christ Church tutor, asks you to imagine a ladder leaning against a wall with its middle rung painted a different colour, and to say what shape that rung traces out as the ladder slides to the floor. The tutor explains that it tests whether you can strip away the unimportant information and represent what is going on with mathematics; sketches are fine to start with, but you need something you can generalise, and the answer is a quarter circle centred where the floor meets the wall.

Another, from a Worcester College tutor, asks how many ways there are to cover a 2 by n grid with 2 by 1 tiles. You are expected to try small cases first (the answers for n from 1 to 4 are 1, 2, 3 and 5), spot the pattern, which is the Fibonacci sequence, and then explain why it appears, before moving on to 3 by n grids. The tutor says its knowledge content is no more than GCSE but that it is hard enough to test the strongest applicants.

At Cambridge, Trinity publishes specimen versions of its pre-interview test on its mathematics page. They are short problems of the kind you would be asked to talk about afterwards, such as how many of the numbers from 1 to 6000 are not multiples of 2, 3 or 5, or the probability that a coin picked at random from a pile, one of which has heads on both sides, comes up heads a ninth time after eight heads in a row.

Tests and written work for 2027 entry

Both universities use the TMUA (Test of Mathematics for University Admission), sat between 12 and 16 October 2026; Oxford says the MAT is not taking place this admissions round and all its maths applicants take the TMUA instead. Neither asks for written work. Cambridge also uses STEP, which it says is part of almost all its conditional offers for mathematics: if you apply in October 2026 you should expect to sit it in June 2027.

The table gives the dates the universities have published for this cycle. Oxford says shortlisted applicants usually hear between the middle of November and early December, and its decisions come on 12 January 2027.

How to prepare

Do problems out loud. Work through the published sample questions, the TMUA and STEP past papers and anything else just beyond your A level course, saying each step as you go, ideally to somebody who will interrupt. Practise curve sketching from first principles, without a calculator: where the function is zero, what happens as x gets large or small, where it is undefined, where it turns.

Get used to the equipment too: an online whiteboard and a stylus feel different from paper, and Oxford suggests practising with them beforehand. Watch Oxford’s demonstration interview videos, and reread anything in your personal statement you might be asked about.

With an account, cookie’s Interview prep runs a mock Oxford or Cambridge interview in this subject with an AI interviewer. It writes problems in the style of the universities’ published examples, not real interview questions, gives a hint when you go quiet and writes a report at the end. It uses credits, and it is for practising beforehand: Cambridge says using AI during an interview is prohibited.