Test of Mathematics for University Admission (TMUA), Computer Science Aptitudes Test (CSAT), 1x interview
Solving maths problems aloud
Re-reading personal statement and preparing to answer questions on it
Practice tests
Get a good amount of practice tackling challenging maths problems
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), Computer Science Aptitudes Test (CSAT)
Number of interviews: 1
Length of interviews: 30 minutes
Online interview: Yes
My interview consisted of three maths problems asked by a professor. I was given hints while I attempted to solve the problems out loud. I could ask questions when I needed to, but most of it was my own thinking. I felt relaxed because I have done these kinds of maths interviews before in maths competitions, and the questions weren't very daunting.
I re-read my personal statement and brushed up on all of the topics I mentioned in it. In particular, I was ready to answer any questions related to my resume or personal statement.
I did one practice test for each paper.
The interviewers are looking for your thought process—they want to know how you think. Get a good amount of practice tackling challenging maths problems (e.g. try Olympiad problems or AIME problems). Actually, mid-level AIME (American Invitational Mathematics Examination) problems were quite comparable to the ones I received in my interview. If you feel comfortable with that level of maths, then the computer science exams (TMUA, CSAT) and interviews should be fairly straightforward. Of course, this takes a lot of time, and any amount of practice will help. Coming from a background of mathematics competitions helped me massively.