Below is some general advice on preparing for interview. The AMSP are running free online mock interviews which state-educated students applying to Oxford or Cambridge can apply for here.
Preparing for interview is quite different to preparing for other types of admissions test, as students need to work on their verbal communication skills in the context of mathematical problem solving. Often, students' experience of explaining a solution is confined to explaining something they already understand on the A Level syllabus to their peers, but at interview the problems will be challenging and students may not be able to solve them straight away. Keeping a clear head, and combining clear, concise verbal communication with a strong problem solving foundation is the key to success at interview.
There is often confusion amongst students about what Oxbridge interviews consist of. In simple terms, the interviewers will give you problems to solve one at a time, and watch how you go about solving them. You will be expected to explain your reasoning verbally, and in the (expected) situation where you cannot immediately solve the problem, talk through your ideas for making the problem more tractable as you attempt them.Â
Please note:
Interview questions are not of uniform difficulty, and it is nigh impossible for a student to tell if their interview is going well. If a question seems too easy, by all means scrutinise your work as you proceed (e.g. checking for potential divisions by zero) but do not assume that you are wrong just because it seems easy. The interviewers may expect most interviewees to solve that problem quickly and move on. If a question seems far too hard, and the interviewer gives you an easier version of the question instead, don't assume they have concluded you are a weak problem solver on the basis of you not solving the hard problem straight away. It may be that the interviewers expect to break down the problem in this way for all interviewees, but give everybody a chance to solve the hard version first.
Interview questions are highly variable in style. Whilst it is good to practise core skills such as sketching, differentiating, and integrating a wide range of unusual functions, do not get too attached to the idea that one particular skill will be tested at interview. Your time is much better spent getting comfortable with the sensation of working on unfamiliar maths where you aren't sure where it is going to go.
The following are all key components to interview preparation:
(Content) Plenty of problem solving practice. You aren't going to succeed at verbally explaining solutions to unfamiliar problems in a high pressure situation if your mathematical problem solving skills aren't up to scratch. This is good news - it means any preparation you are doing for an admissions test (e.g. MAT, STEP or TMUA) will also help you prepare for interview.
(Get used to vocalising) Practice talking through your problem solving process. I used to explain my solutions to a desk lamp.
(Get used to being observed) Give somebody else a couple of problems to ask you and work through it with them watching. If they can understand the maths, great, but this is worth doing with somebody without a maths background just to get you used to somebody observing you.
(Technology) In the run up to interview, ensure that you understand the platform that you will be required to interview on. If you will be using a tablet, familiarise yourself with the application you will use to write your solutions in the interview. Prepare a backup plan in case your technology fails. If you will be using pen and paper, make sure you have a pen thick enough to easily show up on camera and get used to writing with it. If possible, figure out a webcam arrangement that will allow the interviewer to see the paper you are writing on in real time so you don't have to keep stopping to hold it up. If this involves using a second device with a microphone, ensure the microphone and speakers on the second device are switched off to prevent feedback.
In the interview itself, keep the following in mind.
The interviewers will not speak as much during your problem solving process as a teacher would. If it seems like the interviewers are being unusually quiet, do not be put off or start questioning yourself. Keep going!
If there is a technical problem, the interviewers will stop the clock and give you time to continue the interview once the issues are resolved. If that technical problem cannot be straightforwardly resolved, the interview will be rescheduled. Interviewers will not hold technical issues against you, and it is important to do your best to remain calm and trust in the procedure if they do arise.