Sixth Term Examination Paper (STEP); 1x interview
Interview 1: loosely related problem questions
STEP questions
Past STEP papers
Try to figure out the problems even if you haven't been taught it before
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:
Number of interviews: 1
Length of interviews: 25 min
Online interview: No
My only interview was academic. The interviewer posed a question and we worked through it on paper. He had a series of variations on the same question, so after I answered each version he would pose a new version which was harder. Each version used the same trick at its core, and I was familiar with this trick, so I was easily able to answer every version. The last variation confused me a bit and led to an interesting conversation where I tried my best to come off as curious. The interview was meant to last 25 minutes but we ended up going over to about 40.
I didn't prepare for my interview but I should have. Past STEP papers are a good way to prepare, particularly for the interview test. As far as what material you should know, everything on the STEP is a good starting point, but if you are enthusiastic about Maths then hopefully you will have picked up quite a bit through conversations and your own self study.
For the STEP, I did tons of past papers.
Obviously it's important to be ready to do complex maths.