What should I revise for my Maths interview?

At Oxford and Cambridge, Mathematics interviews generally consist almost entirely of mathematical problem-solving exercises. It is uncommon for applicants to be asked about their personal statement, motivations for their application, or personal qualities: any such questions are usually ice-breakers and have little bearing on the interviewer's assessment, though you should still be prepared to answer them, just in case! Interviewers want to see how a student can work through a problem - explaining their reasoning aloud - and respond to any hints or suggestions they are given.

Maths interview questions are designed to test applicants’ problem-solving skills and application of knowledge, rather than the extent to which they have memorised core content (though it’s also important for students to make sure that they do know core material well, and have memorised key results and formulae - see below).

Results and Formulae to Memorise

• Circle theorems
  Make sure that you revise circle theorems because they are likely rusty, having not studied them since GCSE!

• Derivatives and integrals of standard trigonometric functions
  It is crucial to have quick recall of these in order to spot when they are going to be useful in solving an integral.

• Standard graphs such as logarithms, exponentials, trigonometric functions, polynomials, and hyperbolic functions (if studied)
  You should be able to work these out effortlessly. You are unlikely to spend much time sketching one of these specific graphs, but they will form the basic building blocks of more challenging graphs, which you're likely to be confronted with.

• Standard trig values
  ‍You should be able to recall these instantly. It will not impress your interviewer if you have to draw a triangle in order to calculate them!

• Fundamentals of probability
  This includes the conditional probability formula, basic probability distributions (e.g. binomial distribution) and the definition of expectation.

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What are the most common topics in a Maths interview?

Interviewers are aware of the order in which content is generally covered at school, and so will usually steer clear of topics that are covered late in Year 13. However, unlike for the MAT and TMUA, it is very common for some second year A Level content to feature prominently. For example, integration by parts and substitution is known to be a common interview topic.

Precise topics will vary widely by college, and even within a college from year to year. However, we have observed that the following topics tend to feature particularly prominently:

• Graph sketching (more than any other topic!)

• Probability problems

• Euclidean geometry, including proofs of standard theorems

• Combinatorics, i.e., counting permutations and choices

• Integration, especially questions requiring a sneaky substitution, or less standard applications of ideas like integration by parts

• Number theory, especially divisibility problems

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Need further guidance?

Visit our YouTube channel to watch some interview question walkthroughs and subscribe for more! Click the thumbnails to watch the video.

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At Vantage Admissions, we offer a comprehensive Interview Preparation Programme for Mathematics. It includes a pre-recorded course of six lessons, each covering a topic that frequently arises in Oxbridge Maths interviews (including those listed above!). We also provide a question bank of real interview questions, complete with detailed solutions, all of which have been asked in interviews in the past two years. Finally, students on the programme take two authentic mock interviews - including one with an active Oxbridge interviewer where available. To learn about our preparation programme, visit our Interview page or book a free consultation today.