2x interviews
Interview 1: subject questions; Interview 2: subject questions
Discussing problems with friends
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The interviewers are there to help
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.
Test taken: none
Number of interviews: 2
Skype interview: no
Time between interviews: 5 hours
Length of first interview: 20 minutes; Length of second interview: 20 minutes
My interviews were both entirely problems-based (we didn't talk about my personal statement at all). I was asked to suggest three topics of interest which they could pose questions on, but they didn't ask me about all of them. In my first interview, they split the time into halves. For the first half, we discussed general probability ideas. These questions were based on A level knowledge and were designed to warm me up and test my intuition for the subject. Next, they introduced to a new idea which was an extension of what I already knew. (This is an extremely common theme in maths and it is the basis of most examples sheets!) They asked me a few questions about this problem, providing help when I needed it. The second half of the interview was similar but on a different topic.
The second interview was again based on A-level knowledge. They preferred to ask me lots of questions on a range of topics. I found this interview enjoyable - perhaps the interviewers were more friendly or perhaps I had developed some more confidence for the second one!
I would highly recommend the NRICH website and looking at STEP I questions. Both of these provide examples of questions at the right level of knowledge (advanced A-level) but also encourage you to think outside the box and to use maths you already know in unusual ways.
A key aspect of my preparation was going to
Although I heard it a million times before my interview, I didn't really believe that the interviewers aren't there to catch you out, but it's true! The interviewers are not there to catch you out. They don't expect you to understand degree-level maths yet, nor are they going to ask you questions which are impossible to answer. They are there to provide key information (such as a definition or a formula) in case you forget. They want to see how you approach hard problems so remember to talk out loud when you're thinking!