My interview was at the start of December. I arrived at the Porter's Lodge quite early in the afternoon and was given a map and directions to the pre-test interview room, Hall and the JCR.After signing in, I was allowed to roam freely within the college and explore a little. I didn't go to the JCR but I was told that there were many Trinity students there to welcome you and chat to. After having lunch in Hall, I went to the pre-interview test room to take an informal one-hour'test'consisting of several maths questions. There were two questions that involved a bit of physics, but most purely tested mathematical ability. After the test, I took my working and went straight to the interview room. I had one interview with two college fellowslasting approximately one hour, although we actually went a bit over, which I guess was a good sign!

The interview was literally just a discussion about the questions that I attempted in the pre-interview test - nothing else was asked, since all they care about is your academic ability! We started with the questions that I found quite straightforward and then progressed to the trickier ones. Most of the questions can be done with A level maths knowledge - some required a bit of further maths - but they were all non-standard questions that require you to apply your knowledge in new ways. They really push you until you get stuck, so that they can give you hints and see how well you respond to them. I ended up having to sketch some tricky functions.

Trinity College has specimen pre-interview tests on their website (https://www.trin.cam.ac.uk/undergraduate/courses/mathematics/) - do these to get used to the style of question but remember that the questions themselves will be different in the real test. I also found past MAT papers (the entrance test for maths at Oxford, can be readily found online) and past UKMT Maths Challenge/Maths Olympiad papers very useful to getting used to thinking more creatively and applying your knowledge in 'weird' questions.

I also had a few mock interviewsat school, which were very useful, especially because I got to practise saying my ideas and thoughts out loud, which is very important in the real interview!

Reading maths books is not that useful, in my opinion, since the interview and test are more about how you think, rather than what you know. By all means read some if you've got the time, but I would say that doing practice questions definitely takes priority.

Remember that the interviewers want to hear your ideas - that's the most important thing when applying for maths. Even if you're not sure what to do, don't be afraid to tell them what ideas you have - even if you think your ideas won't work, they really appreciate it when you have the confidence to say them out loud and try them out regardless. Don't worry if you can't do many questions, and definitely don't worry if you get stuck, because that's meant to happen!