There was a pre-interview test consisting of 10 questions that we sat for an hour, followed by one hour long interview with two interviewers, one a fellow and one a PhD student. The questions were meant to be challenging, but covered a wide range of material to make sure that everyone could find something they felt comfortable attempting. The interviewers then used the questions as a springboard for discussion - they tended to focus on the ones you attempted in the time before the interview but couldn't solve, and try and help you to work through them, a bit like a mock supervision.

I enjoyed the fact that we had some time to think about the questions before the interview and prepare - it meant that you had a much better idea about what would be asked during the interview by the time you got there and there were fewer stressful surprises. The Trinity College website contains some example interview tests which are really useful for preparation and definitely worth looking at.

Working through the example tests provided on the Trinity website, as well as discussing some other practice interview questions in an interview preparation class run by a teacher for some of the students at school.

It's worth getting some sort of practise speaking about maths before the interview, either in a mock interview if you can find someone to do that for you, or just explaining your thought process aloud to yourself. Having to explain to someone else how you are going about approaching a problem when you are stuck is a key part of the interview, but it's not a skill you really get to practise much elsewhere.