Free Interview Resources
Free practice questions, preparation advice, and expert insights for Mathematics and Computer Science interviews at Oxford.
Real Mathematics and Computer Science interview questions in the style Oxford asks. Try answering each one aloud before you reveal the hint.
If n² is even, prove that n is even.
Problem-Solving
Hint
Try proving the contrapositive: if n is odd, what can you say about n²?
A staircase has n steps. You can climb either 1 or 2 steps at a time. How many different routes are there?
Problem-Solving
Hint
Split routes by the final move: did the route arrive from step n−1 or step n−2?
You have a sorted list of 1,024 names. What is the maximum number of comparisons binary search needs to decide whether a name is present?
Problem-Solving
Hint
Each comparison halves the remaining search interval.
How many subsets of {1, 2, ..., n} contain no two consecutive integers? Build a recurrence.
Problem-Solving
Hint
Separate subsets that include n from those that do not include n.
Design an algorithm to test whether a string of brackets is balanced. Explain why it works.
Problem-Solving
Hint
Think about what information must be remembered when an opening bracket has not yet been closed.
Tutorial-style interviews with subject-specific problems, often involving unfamiliar material.
Oxford interviews typically take place at the college you applied to. You will usually have two or three interviews of around 20-30 minutes each, sometimes at different colleges if you are pooled. The atmosphere is meant to resemble a tutorial: the interviewer gives you a problem and watches how you reason through it.
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
A recursive algorithm splits a problem into two halves and does linear extra work. Estimate its running time.
midHint
Draw the recursion tree and add the work done at each level.
You toss a fair coin until the first head appears. What is the expected number of tosses?
midHint
Condition on the first toss and set up an equation for the expectation.
Given a connected graph with n vertices and no cycles, how many edges must it have? Justify your answer.
hardHint
Try induction by removing a leaf, or reason about what happens when you add one vertex at a time.
What is the difference between an example, a counterexample, and a proof?
entryHint
Think about what each one can and cannot establish for a universal claim.
What makes an algorithm efficient, and how is that different from being correct?
entryHint
Separate the question of whether the algorithm solves the problem from how its resource use scales.
Why is abstraction useful in computer science?
midHint
Use one example where the same method works for many different kinds of data.
How would you explain the difference between discrete and continuous mathematics to someone choosing this course?
midHint
Give examples from counting, graphs, calculus, and limits rather than only definitions.
Can a computer represent every real number exactly? Why does your answer matter for computation?
hardHint
Think about finite memory, representation, approximation, and error propagation.
You mention a mathematics or computer-science book in your personal statement. Explain one idea from it precisely.
entryHint
Choose one argument, theorem, algorithm, or example instead of summarising the whole book.
Tell us about a programming project you completed. What was the hardest design choice?
entryHint
Describe the problem, one technical decision, and one trade-off you accepted.
Your statement says you enjoy the overlap between mathematics and computer science. Give a concrete example of that overlap.
midHint
Use an example such as proof, logic, graph theory, cryptography, algorithms, or complexity.
Which claim in your personal statement would you now qualify or explain more carefully?
midHint
Show intellectual honesty: identify a simplification and improve it.
Estimate how many comparisons are needed to sort 100 names by hand, and explain the assumptions behind your estimate.
midHint
Compare a simple quadratic method with a divide-and-conquer method.
If two processors share a task, what could make the parallel version slower than the single-processor version?
midHint
Consider communication, setup costs, dependencies, and uneven work division.
Could a computer ever be creative? Give a testable meaning of creative before answering.
hardHint
Define the term first, then separate producing novel outputs from understanding them.
An admissions algorithm rejects more applicants from one school type because of biased historic data. What should the designers do?
midHint
Consider data quality, transparency, validation, appeal routes, and whether the tool should be used at all.
Should a search engine have to explain why it ranks one page above another?
midHint
Balance user trust, gaming the system, commercial secrecy, and public-interest decisions.
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Book Mock Interview →Further Reading
by University of Oxford
Official course information, including UCAS code, duration, entry requirements, admissions test, interview timing, and course-specific admissions statistics.
by UAT-UK
Official information about the Test of Mathematics for University Admission used in the current admissions process.
by University of Oxford Mathematical Institute
Oxford-specific guidance on TMUA and the transition away from MAT for the relevant admissions round.
by University of Oxford Department of Computer Science
Official sample problem material for practising the style of reasoning expected in Computer Science interviews.
by University of Oxford
Official guidance on the interview process, including format and expectations for shortlisted applicants.
by University of Oxford Department of Computer Science
Departmental reading suggestions for applicants who want to build subject knowledge beyond the school syllabus.
by University of Oxford
Oxford's official hub for super-curricular exploration and subject enrichment.
by University of Cambridge Faculty of Mathematics
Problem-solving resource useful for developing the habit of explaining mathematical reasoning, checking cases, and generalising.