Sixth Term Examination Paper (STEP), 2x interviews
Interview 1: pure maths questions, including explaining definitions and theorem Interview 2: questions about personal statement, then applied maths questions
Practice doing timed maths questions and explaining thought process out loud
Going over textbooks, memorising formulae, doing past papers then going over weak areas
Explain your thought process out loud
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: Sixth Term Examination Paper (STEP)
Number of interviews: 2
Time between interviews: 5-10 minutes
Length of interviews: 15-20 minutes
Online interview: Yes
In the first interview, the interviewer went straight into asking questions about mathematics without asking me anything. I was not very shocked and just got straight into answering those questions, there were about 4 questions related to explaining definitions and theorem, I explained my thought process out loud and indicated clearly which part I was stuck at to interact with the interviewer.
In the second interview, the interviewer asked me questions about my personal statement, and I answered questions about the internship which I'd written about in my personal statement. They also asked me more about my hobbies, likes and dislikes and my personal opinion about graphic calculators. After half the time, they asked me mathematics questions again. This time the maths questions were more related to geometry and mechanics than pure mathematics in the first interview. I also explained how I would solve those problems step by step to the interviewer
I re-read my entire application paper to see which part of mathematics knowledge I claimed I knew about and reread those because the interviewer may take an interest in one of those. I practiced answering mathematics exercises on the spot with a time limit and explaining my thought process out loud to my friends. If they understood my answer step by step, it was a success and if it was not I practiced until my explanation was clear and concise. The questions I used for practice were taken from STEPs 2 and 3.
I reread all of my mathematics A level textbooks (Maths, Further Maths, Mechanics, Probability and Statistics) and memorised all formulae to avoid mistakes when doing the test. I did very many past papers (all of the STEP 2 and STEP 3 past papers from the year 2000 to the year 2022). After finishing those past papers, I marked them and rechecked all of the mistakes I made. I reread the knowledge section that I lost points on and did some additional exercises in the book to be more familiar with them.
I would definitely read more STEP questions to prepare myself for the content. You really need to explain your thought process out loud, be very concise and straight to the point to the interviewer. If you need time to collect your thought, use a lot of filler words such as 'uhm, this means that, this implies that, therefore, this leads to,... yes, I think that,...' but when you are stuck say you are stuck. Don't be too quiet, remember to interact and engage with the interviewer to gather their interest.