What should I revise for my Oxbridge interview?

While the term ‘interview’ may bring to mind job interview questions about personal qualities and experience, the interviews conducted by Oxford and Cambridge are almost entirely designed to simulate the small group teaching used to teach their undergraduate students, called tutorials at the former and supervisions at the latter. This is the best way to assess applicants’ suitability for the course and provides an opportunity for the interviewers to carefully inspect students’ style of thought and see how they think through difficult, unfamiliar problems. For this reason, candidates should expect the interviews to be dominated by problem solving exercises, although it’s important to be prepared to answer questions about anything they have written on their personal statement, and to convey their enthusiasm and reason for choosing the subject.

Mathematics

Mathematics interviews generally consist almost entirely of mathematical problem solving exercises. These questions are designed to test candidates’ problem solving skills 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). Interviewers are aware of the order in which content is generally covered in school, and so will usually steer clear of topics which are covered late in Year 13. However, unlike for the MAT and TMUA, it is very common for some second year A Level content such as integration by parts and substitution to feature prominently.

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 including divisibility problems

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Computer Science

Computer Science interviews tend to emphasise mathematical problem solving rather than overly technical computer science knowledge. This is because applicants have very different levels of experience studying computer science, and mathematics problems provide an excellent setting in which to assess thinking skills. The topics covered are similar to mathematics; however, computer science questions do often place more emphasis on:

• Recursion

• Game theory

• Probability

• Number theory

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Integration is often emphasised a little less than in Mathematics interviews.

Something which we have observed in the past two years is that questions involving pseudocode have become more common. In these questions, students are presented with a piece of code in an informal programming language, and need to identify what it does, and how it could be modified to achieve certain tasks. Suitable practice questions can be quite difficult to come by, but such problems are included as part of the Vantage Interview Course.

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Economics

Just as for computer science, economics interviews (especially at Cambridge) will often include an element of mathematical problem solving, as this provides a neutral setting in which to test applicants’ thinking skills. Most colleges will have one interview which is geared more heavily towards such problems, and will resemble a mathematics interview, except that typically probability and simple game theory are emphasised more heavily than for mathematics. There will generally then be another interview which will involve more subject-specific discussion.

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Crucially, interview questions use ideas which are often not covered in school and are unique to interviews. Even thorough past paper practice for exams such as the MAT or TMUA may not provide adequate interview preparation (though it can be a good starting point). However, interview questions are not publicly released, so tricks, techniques and even specific questions are frequently seen to recur between years. The Vantage Interview Course includes 80 genuine interview questions, all of which have been asked at interviews in the past three years.