Test of Mathematics for University Admission (TMUA), Sixth Term Examination Paper (STEP), 2x 25 minute interviews
Interview 1: working through maths problems on a whiteboard Interview 2: talking throughs maths problems with the interviewer
Mock interviews and practice questions
Untimed practice questions, then timed exam papers
Think out loud and explain your ideas as you go
Remember this advice isn't official. There is no guarantee it will reflect your experience because university applications can change between years. Check the official Cambridge and Oxford websites for more accurate information on this year's application format and the required tests.
Also, someone else's experience may not reflect your own. Most interviews are more like conversations than tests and like, any conversation, they are quite interactive.
Test taken: Test of Mathematics for University Admission (TMUA), Sixth Term Examination Paper (STEP)
Number of interviews: 2
Time between interviews: 2hrs
Length of interviews: 25 minutes
Online interview: Yes
I was asked a mix of topics in both interviews, they were all maths questions - nothing on personal statements or discussions. There were some stats and mechanics questions so don't just revise pure content. The first interview was more independent so I wrote on a whiteboard, talking through it and then showing my working/answer as I went, and the interviewer asked me follow-up questions when I reached the correct answer. The second interview was more interactive and me and the interviewer talked an equal amount to get through the lines of working while they wrote it on the screen.
I think I had 3 main questions in each interview but some of them would have smaller questions at the end, e.g. "could you check the answer seems reasonable using this example value" or "for what other values of n would this method work". They gave me a few hints when I was struggling so try to use this to make progress but it's ok to say you're not sure if it's totally out of your depth. They asked me a question from further mechanics (which I had technically studied but wasn't revising for exams so I didn't know much at all) and I suggested a potential method but said I wasn't sure how to implement it and they said it was ok and we moved onto another question which i could do.
The most useful thing was
Practice questions (untimed), then timed exam papers close to the exam
They care about your thought process and ability to pick up on their hints to make progress, so the most important thing is to think out loud and explain your working or ideas as you go. Don't worry if you need to pause to think a bit, the pause will seem much shorter to them than it will to you. Try to follow the guidance they provide and use their hints rather than getting stuck on one fixed method