No tests. One general interview (15 mins) followed by two academic ones (25 mins each). Two interviewers each. Some breaks in between. Advice is to scout out the locations of the rooms beforehand to avoid being late.

In the general interview with two tutors, they introduced me to the procedures of the three interviews and made me feel at ease. At first there was a general question which I answered as well as changing the topic to something I really wanted to talk about, making a point about my passion in maths using a useful mathematical curiosity I’ve studied. It was a very general question so I used an example to switch the focus to something I wanted to talk about. Here, it is important to be yourself. If you’re applying to Cambridge then hopefully you’re genuinely interested in the subject, so you don’t need to be trained to answer general questions. The tutor kept asking questions on the topic I switched to, probing my understanding about it, but was finally impressed as he thought I could successfully explain that same topic to a kid. Also a tutor picked up on a small point I made in my personal statement and asked a related question (not asking me to explain a maths concept). Then they asked me to explain an elementary maths concept.

In the first academic interview with the Director of Studies of Pure Maths (and a PhD student), they opened by introducing me to the format of the interview (basically doing maths), and that they don’t expect me to have seen the kind of questions here. They started by asking me to explain a calculus concept. Then I sketched graphs related to an arbitrary given graph (without given equation). The last question was about a maths concept that they do not expect a high schooler to know or have seen. Then they gave me a few mathematical constructs and asked me to determine, according to the given rules, whether they do or do not satisfy the given condition.

In my second academic interview with the Director of Studies of Applied maths (plus a PhD student) I was first asked to sketch an implicitly defined graph. I went down a wrong path but I was quickly given a hint to rearrange the equation to an explicit form. Then there was a question requiring some logical reasoning. I tried to rush slightly and it backfired. Then we did a probability question in an abstract form. I was then asked to conjecture a general-case solution for a more general question. Finally, there was a question of the same style as the last question in the first academic interview, only this time there were more rules to check. It is important to have an intuitive image of the mathematical construct at hand, and to brainstorm ways in which it can broken (disproof) or why it cannot be broken (casework leading to proof).

Some BMO (British Mathematical Olympiad) Experience. STEP questions, graph sketching. Mock interviews “Say what you think/write.” Interest in advanced maths.

Nah!