Free Interview Resources
Free practice questions, preparation advice, and expert insights for Mathematics and Statistics interviews at Oxford.
Real Mathematics and Statistics interview questions in the style Oxford asks. Try answering each one aloud before you reveal the hint.
As a ladder slides down a wall, determine the path traced by the midpoint of the ladder.
Problem-Solving
Hint
Model the floor and wall as coordinate axes and use the fixed length of the ladder.
Find a recurrence for the number of ways to tile a 2 by n rectangle using 2 by 1 dominoes, then explain why it has that form.
Problem-Solving
Hint
Count the cases according to what happens at one end of the rectangle.
The cube of a linear expression has the expansion below. Find p.
Problem-Solving
Hint
Compare the constant term and the coefficient of x cubed before using the x-squared term.
A cubic has the factor x+2. Use that information to identify its complete factorisation.
Problem-Solving
Hint
Substitute x = -2 to determine the missing constant, then factor the remaining quadratic.
Find the length cut off by the normal to the curve at x = 1.
Problem-Solving
Hint
Differentiate to get the tangent gradient, then use the negative reciprocal for the normal.
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
Evaluate the sum for the alternating sequence defined below.
entryHint
Work out the first few values and look for a short repeating cycle.
Find the total enclosed area between a parabola, the x-axis, and two vertical lines.
midHint
Split the integral at the roots, because area below the x-axis contributes positively.
A mixture is formed from three paints in a fixed ratio; two red-paint percentages and the final percentage are known. Find the missing percentage.
entryHint
Use a weighted average equation, not an unweighted average.
Find the largest angle in the given interval satisfying the trigonometric equation.
midHint
Reduce the equation to a standard sine or cosine condition, then remember the doubled angle.
Evaluate the definite integral below.
midHint
Expand the square first so that each term is a simple power of x.
Differentiate the function below.
entryHint
Rewrite the fourth root as a fractional power before simplifying.
Use the club membership information to find the probability that a randomly chosen member is a woman who plays tennis.
midHint
Draw a two-way table for gender and sport, then fill entries from the given proportions.
A circle is translated, reflected, and enlarged. Determine the final equation.
midHint
Track the centre and radius separately; transformations affect them in different ways.
How many solutions does the equation have in the stated interval?
hardHint
Consider symmetry and intervals between vertical asymptotes; a sketch can be more useful than algebra alone.
Find the largest angle, in radians, satisfying the equation in the given interval.
midHint
Use the identity linking sine squared and cosine squared to reduce the equation.
Five urns make statements about the number of balls they contain. Exactly one statement is true. Determine which urn has the true statement.
hardHint
Test possible common numbers of balls and count how many statements would be true in each case.
For the statement below, count the counterexamples in the specified range.
midHint
Separate the true statement about primes from the false converse, and list candidates systematically.
For the recursively defined sequence of functions, find a closed form for the finite sum.
hardHint
Compute the first few functions to see the coefficient pattern before summing.
You wrote about probability in your personal statement. Explain one example where independence is a modelling assumption rather than a fact.
midHint
Choose a concrete example, then say what evidence would make the assumption plausible or implausible.
Choose a mathematical result you mentioned in your application and explain why the proof matters more than numerical examples.
midHint
Start with an example, then identify the step that turns examples into a general argument.
You say you enjoy statistics. Describe a situation where a statistically significant pattern might still be misleading.
midHint
Think about confounding, sampling bias, or a mismatch between correlation and causation.
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Free Oxford-hosted problem-solving livestreams that model mathematical discussion.
Useful for admissions-test style trigonometry and problem-solving strategy; now best treated as enrichment alongside TMUA preparation.
Works through an interview-style mathematics question with live discussion.
Good for recurrence thinking and explaining patterns, both common in mathematics interviews.
All videos are the property of their respective creators.
Further Reading
by Lara Alcock
Official Oxford recommended bridging material for the transition from school to proof-based university mathematics.
by Richard Earl
Written by an Oxford mathematician and well suited to building proof and problem-solving fluency.
by Kevin Houston
A practical bridge into definitions, proof, and university-style mathematical habits.
by Martin Liebeck
Useful for applicants who want a taste of abstraction beyond A-level syllabuses.
by George Pólya
A classic problem-solving text listed in Oxford's recommended popular mathematics reading.
by University of Oxford Mathematical Institute
Oxford's current free programme focuses on TMUA, interviews, and problem-solving strategy for 2027-entry applicants.
by UAT-UK
Official historic TMUA papers; UAT-UK says the content specification and question style are unchanged despite the move to computer-based testing.
by Pearson VUE / UAT-UK
Helps applicants practise the live test-player format and navigation.
by University of Oxford Mathematical Institute
Weekly Oxford livestreams and maths content for supercurricular development.
by University of Oxford Mathematical Institute
Department-linked practice for strengthening pre-course and admissions-relevant foundations.