Test taken: TMUA (Test of Mathematics for University Admission) 
Number of interviews: 2
Online interview: Yes

I had two interviews, each with two interviewers (although one usually did most of the talking). In the first interview they asked me a little about my personal statement and some of the programs I'd talked about writing then moved on to a question. I had no idea how to start it, but they gave some pointers and let me work through it. I was anxious and made lots of silly mistakes with the interviewers not seeming to have much of a reaction so it was hard to gauge how well it was going, particularly with being online. I didn't end up getting very far with the question and left feeling like it hadn't gone very well.

I think an important part of that interview was making sure I showed what I was thinking and doing to the interviewers which was tricky online, but you don't need to be familiar with a tablet or something of the sort if you do end up doing things online, holding up a piece of paper to the camera worked alright for me but it's something you might want to check if you do any mock interviews what works for you.

The second interview seemed to go much better. There was less talk about my personal statement and more, shorter questions. It was much more relaxed and the problems seemed easier to tackle.  The types of things that are rumoured to happen like strange questions that require niche knowledge (or simply asking to impress them and waiting for a response, which was one I heard rumoured) don't happen. The question may seem strange at first but that's usually just the headline, the interviewers will often then give you hints on where to start if it's not clear or you seem to be struggling. I was asked questions based on logic and maths, sort of lateral thinking puzzles more than straight maths, but all something that could be worked through to get to the solution rather than some strange trick you either see or you don't. TEDed riddles on YouTube are a good example of the sort of problems I mean.

In other colleges, I've heard the questions could be more maths-related, but usually they don't have much tie to A-level content and are more about how you think than what you can remember or have been taught. If a question seems to be on a topic you haven't covered in school yet or uses notation you don't understand, it is worth saying as they may be able to help you or switch to a different question. 

I was lucky enough to have a few mock interviews run by my school which I used to prepare and read over my personal statement and the projects I included there. The most useful thing I found from that was reminding myself how the code I wrote for the projects I mentioned worked and the structure of it. The mock interviews were useful for getting used to working through problems aloud and generally being more comfortable in the setting.

The other thing that can be useful is looking online for past interview questions and giving a couple a go, but beware the interviewers can give you significantly more help than the questions do, and if you can't get to the answer don't worry! Doing the questions was mostly useful as a sort of warm up getting used to the trickier problems and muddling through, although doing questions by yourself and spending a while thinking how to get started tends not to be the style of interviews. While working out how to translate the question into something you can solve is a useful exercise, it's exactly that kind of thing they may tell you fairly quickly in the actual interview.

My main revision was TMUA (Test of Mathematics for University Admission) past paper questions; doing past questions really helps you prepare for what sort of questions are going to come up and the types of tricks they like to make you use. One of the main issues I found initially was thinking a question was unapproachable so ignoring it, but after I learnt the type of language they use in the questions it became easier and was something I could manage. Comparing your score in past papers against how many got in with that score for that year can be a useful indicator of how well you are doing, but there is a lot more to the application and what they consider than just your TMUA result so if you're not in a group with a high percentage don't be completely discouraged.

The key thing (as you may have already heard) is to show your enthusiasm. Showing that you enjoy working on the question and taking their hints or corrections in stride while making many mistakes and never reaching an answer is better than beating yourself up about every error and getting anxious but getting to the correct solution. However, the interviewers are aware that you are likely very stressed and may not be quite as open to enjoying the content as you usually would. They also want to see that the drive for the subject comes from you, even if you've only picked up the subject recently, showing that you are eager to learn new things about it is really valuable, much more so than being able to say you are following in your parent's footsteps or something of the sort. I expected the questions I was asked to be much more maths-based than they were, turning out to be more logic puzzles than maths questions.