Maths @ Pembroke, Cambridge in 2021

Interview format

1x interview, Sixth Term Examination Paper (STEP)

Interview content

1 interview in 2 parts - short questions, then a longer problem

Best preparation

Practice talking through maths problems and thinking aloud

Test preparation

STEP Assignments, past papers, keeping track of topics and techniques

Final thoughts

Don't be afraid to take a bit of time to think, but equally go ahead and say the ideas you're having!

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.

Interview Format

Test taken: Sixth Term Examination Paper (STEP)
Number of interviews: 1
Online interview: Yes

What happened in your interview? How did you feel?

My interview was virtual, so I logged in a few minutes early, got put into a waiting room, and then went through to the interviewers. As it was a maths interview, they didn't talk about my personal statement at all, or really me personally! I found that quite reassuring because I feel much more comfortable doing maths than having to sell myself as a good mathematician.

There were two parts to the interview; the first part was a lot of short questions. None of them were particularly difficult topics, they were just applied in a slightly weirder way than usual; so rather than your typical distance-speed-time questions, it was more abstract, for example. I think I talked a lot and very quickly during this bit, because I was nervous, but the interviewers understood this and it didn't seem to bother them.

The second part of the interview was one longer idea. The premise was to teach me a new method for figuring something out, and see how quickly I picked it up. This is the bit I thought went terribly! My interviewer kept prompting me to find a way to answer a specific bit, and with each suggestion I came up with, he said I was overcomplicating it! I felt quite embarrassed when I finally worked out what the actual solution was, and thought that I might have damaged my chances by taking so long to work it out, but in the end, it was ok, because they really just want to see how you think, not how you solve this one super specific question.

How did you prepare for your interviews?

I think an important thing for maths students is to not stress too much about the interview; they give out lots of offers because they know that STEP is a better test of your mathematical ability than an interview.

The biggest difference between doing maths in an interview and doing maths normally is that in an interview, you have to speak everything you're thinking aloud, and this can be really difficult to teach yourself to do. To build on this skill, practice is most important; find someone to sit in front of, find a question that is brand new to you (a longer MAT question might be a good idea), and just work through it, explaining all your thoughts. I found I was basically just saying constant words, and even though many of my ideas went nowhere, it shows the interviewer that you have a wide range of knowledge to draw upon, that you have good instincts, and that you can tell when you should stop pursuing a certain idea.

Even if you can't find someone to practice with (a teacher of maths is ideal, because they can guide you if you get stuck, like the interviewers will, or even better a maths teacher who you're not very familiar with, but I tried with my mum's friend!), even just trying with yourself aloud is better than nothing.

If you took a test, how did you prepare?

I started in Year 12, and tried to do a little and often. Of course, I stressed myself out all the time thinking I wasn't doing as much as I should, but especially in Year 12 or early Year 13, you don't need to overload yourself with practice.

I started by doing the STEP Assignments, and I found they were really helpful in teaching me how to think in the way STEP questions are required. However, by about halfway through, I gave up doing a lot of the warm-up, preparation and warm-down questions unless they were themselves STEP questions, as I didn't think they helped me all that much. By the time I was getting through the STEP 2 assignments, I began to know what topics I liked and didn't like, and began to skip the occasional question in modules I didn't enjoy and wasn't very good at. It was at this point I started a spreadsheet detailing all the questions I had done, which worked as a great motivator for me (ooh I just hit 100, for example), and meant I didn't accidentally do the same problem twice. It was getting closer to the actual exams when I moved from STEP 2 modules to STEP 3, and then I just picked random questions from the STEP database by deciding, ok, now I'm gonna do complex numbers, and tomorrow I'll do DEs, etc.

A lot of the time I wouldn't do it time-pressured, but if I knew I had a solid 45 mins, say, I would try and do it non-stop and see how long it took me. I also made sure to save plenty of whole papers, and when it was getting very close to June, I would start doing them under timed conditions, and, very importantly, learning how to pick which 6 questions of the 12 to complete. I always tried to look at solutions online, or even better, mark schemes, so I wasn't teaching myself wrong answers. Throughout it all, I also made a list of useful techniques or familiar tricks in questions, so I could come back to it if I was really struggling with a question.

What advice would you give to future applicants?

I would probably try to remember that the interviews aren't here to find the bad candidates and kick them out, but find the good candidates to make an offer. Instead of thinking that everything you say has to be perfect, just remember on the whole that you will show the best side of yourself if you try not to stress too much (obviously easier said than done!) Don't be afraid to take a bit of time to think about a question they've asked, or to ask for clarification or a hint, but equally, go ahead and say the ideas you're having, even if you're not certain they will necessarily lead you to the right answer - they will prefer a candidate with lots of decent but not perfect ideas to a candidate who says nothing!