Test taken: Sixth Term Examination Paper (STEP)
Number of interviews: 2
Time between interviews: 20 minutes
Length of interviews: 25 minutes 
Online interview: No

My interviews consisted entirely of maths problems: no questions about my personal statement and no philosophical questions about maths (so nothing like "Is maths invented or discovered?").

I had quite a lot of questions in each interview - maybe eight or so per interview - which is more than I had expected since some of them were very short (they asked the question and I immediately told them the answer). Others I needed some help with and/or had multiple parts so they took longer - the way it worked is that I was writing my working on paper that the interviewers provided and they looked at my work while I did it, and I also talked through what I was doing. The questions were on a range of maths topics (graph sketching, mechanics, probability, geometry, calculus etc.).

In terms of atmosphere, I was very stressed before my first interview but I calmed down almost as soon as it started. My first two interviewers were both PhD students and they seemed very nice; also the first question they asked me I found quite easy which was a nice start! The second interview went a bit worse in my opinion; I felt a bit tired (it was after 6pm, since I had one of the last interview slots of the day) and the room I was in was very dark. It can't have gone too badly though, seeing as I got an offer (everyone thinks they did worse than they actually did)!

I used a few different websites to look at example interview questions for maths (at both Oxford and Cambridge because the style is very similar); I can't remember any particular examples but you can find a lot online. I also had a mock interview with one of my maths teachers, as well as with a family friend who did maths at Oxford, though to be honest neither of those were hugely helpful; I thought the questions they used were a bit too easy and my maths teacher asked a lot of questions about my personal statement and some more philosophical questions, neither of which I had in my actual interviews.

I didn't prepare for the TMUA (Test of Mathematics for University Admission) that much beyond doing all of the practice and specimen papers (there really weren't many at the time); Cambridge didn't care about my TMUA results.

For STEP I prepared by doing lots and lots of past questions; a maths teacher at my school looked at my work each week and went over it. I found past STEP questions by topic on STEP database (https://stepdatabase.maths.org/database/index.html), which is where I got most of my questions. I also looked at Siklos' STEP booklet though I didn't find it super helpful (http://cuhs.co.uk/wp-content/uploads/2016/03/advpcm.pdf). Finally, I went to a STEP course at UCL (https://www.ucl.ac.uk/maths/study/bscmsci-mathematics/admissions/step-lectures - though they were in person when I did them, not online) which was helpful as well. Some other websites that I used a bit for STEP are: https://www.admissionstesting.org/for-test-takers/step/about-step/ (the official website) https://mathsorchard.weebly.com/step-past-papers.html https://maths.org/step/ https://www.thestudentroom.co.uk/showthread.php?t=448558 (student-written answers to problems from 1987 to 2007)

Talk about what you are doing (it is possible to talk too much though), and don’t be afraid to ask for clarification. Expect to be given a problem that you can’t solve. If you forget something like a formula, don’t worry, they will tell you it (it is not a test of memory). The interviewers are there to help you and want you to do well.

You might be asked to write on a blackboard or on paper. Write big! If you realise you have made a mistake, retrace your steps and try to find it (explaining your thought process). The interviewers might teach you something new and expect you to use it. You can ask “Am I going in the right direction?”; that makes it more of a dialogue. Also, make sure to practice curve sketching because it will almost certainly come up. Practice with lots of graphs, and use www.desmos.com or similar software to check your work afterwards.