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100+ Free MAT Practice Questions

Pass your MAT — Mathematics Admissions Test (Oxford) exam on the first try — instant access, no signup required.

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An arithmetic progression has first term 5 and common difference 4. The sum of the first 20 terms is:

A
B
C
D
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Key Facts: MAT Exam

2.5 hours

Total test duration

University of Oxford

100 marks

Maximum total score

University of Oxford

25 MCQs

Multiple-choice questions (5 options each)

University of Oxford

2-4 marks

Value of each multiple-choice question

University of Oxford

2 questions

Longer typed-answer questions (15 marks each)

University of Oxford

No calculator

Calculators are not permitted

University of Oxford

Pearson VUE

Computer-based delivery network

University of Oxford

100

Free MAT practice questions here

OpenExamPrep

The Oxford MAT is a 2.5-hour admissions test for maths and computer science. Its multiple-choice section is 25 questions (five options each, worth 2-4 marks) drawn from A-level foundations — algebra, graphs, calculus, logs, sequences, trigonometry, combinatorics and logic — testing depth, not breadth. There is no fixed pass mark; scores are read with the whole application.

Sample MAT Practice Questions

Try these sample questions to test your MAT exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1The quadratic equation x^2 + kx + 9 = 0 has exactly one real root. What are the possible values of k?
A.k = 6 only
B.k = ±6
C.k = ±3
D.k = 9 only
Explanation: A repeated root occurs when the discriminant is zero: k^2 - 4(1)(9) = 0, so k^2 = 36 and k = ±6. Both signs give a perfect square, (x±3)^2 = 0.
2Completing the square, x^2 - 8x + 21 can be written in the form (x - a)^2 + b. What is the minimum value of the expression?
A.5
B.21
C.-16
D.4
Explanation: x^2 - 8x + 21 = (x - 4)^2 - 16 + 21 = (x - 4)^2 + 5. Since (x - 4)^2 ≥ 0, the minimum value is 5, attained at x = 4.
3When the polynomial p(x) = x^3 - 4x^2 + 7x - 5 is divided by (x - 2), the remainder is:
A.1
B.-3
C.5
D.9
Explanation: By the Remainder Theorem the remainder equals p(2). p(2) = 8 - 16 + 14 - 5 = 1.
4Which of the following is a factor of x^3 - 6x^2 + 11x - 6?
A.(x - 1)
B.(x + 1)
C.(x - 4)
D.(x + 2)
Explanation: By the Factor Theorem, (x - a) is a factor if p(a) = 0. p(1) = 1 - 6 + 11 - 6 = 0, so (x - 1) is a factor. (The cubic factorises as (x-1)(x-2)(x-3).)
5The graph of y = f(x) is transformed to y = f(x - 3) + 2. The transformation is best described as:
A.Translation 3 right and 2 up
B.Translation 3 left and 2 up
C.Translation 3 right and 2 down
D.Stretch by factor 3 then shift 2 up
Explanation: Replacing x by (x - 3) translates the graph 3 units in the positive x-direction (right); adding 2 translates it 2 units up. So the combined map is 3 right, 2 up.
6The graph of y = f(x) passes through (4, 9). Which point must lie on the graph of y = f(2x)?
A.(2, 9)
B.(8, 9)
C.(4, 18)
D.(2, 4.5)
Explanation: y = f(2x) is a horizontal stretch by factor 1/2; x-coordinates halve while y-values are unchanged. The point (4, 9) maps to (2, 9).
7How many real solutions does the equation x^3 - 3x = 1 have?
A.3
B.1
C.2
D.0
Explanation: Consider g(x) = x^3 - 3x. Its turning points are at x = ±1 with g(-1) = 2 (local max) and g(1) = -2 (local min). Since 1 lies strictly between -2 and 2, the horizontal line y = 1 crosses the cubic three times.
8The value of log_2(32) + log_2(1/4) is:
A.3
B.5
C.7
D.8
Explanation: log_2(32) = 5 since 2^5 = 32, and log_2(1/4) = -2 since 2^{-2} = 1/4. The sum is 5 + (-2) = 3.
9If 3^x = 7, then x is equal to:
A.log 7 / log 3
B.log 3 / log 7
C.7 / 3
D.log(7/3)
Explanation: Taking logs of both sides: x log 3 = log 7, so x = log 7 / log 3 (equivalently log_3 7). Any consistent base works.
10The expression 2 log x - 3 log y can be written as a single logarithm as:
A.log(x^2 / y^3)
B.log(2x - 3y)
C.log(x^2 y^3)
D.log(x^2) / log(y^3)
Explanation: Using the power law, 2 log x = log x^2 and 3 log y = log y^3. The difference of logs is the log of the quotient: log(x^2/y^3).

About the MAT Exam

The Mathematics Admissions Test (MAT) is the entrance test set by the University of Oxford for applicants to Mathematics, Mathematics & Statistics, Mathematics & Philosophy, Mathematics & Computer Science, and Computer Science, and was also used by Imperial College London and the University of Warwick. Sat in late October/early November, the MAT runs 2 hours 30 minutes and is now delivered by computer at Pearson VUE test centres. It contains 25 multiple-choice questions (each worth 2, 3 or 4 marks, five options apiece) and two longer typed-answer questions worth 15 marks each, for a total of 100 marks. The syllabus is based on first-year A-level Maths plus a few early-Year-13 topics, testing depth of understanding rather than breadth.

Questions

100 scored questions

Time Limit

2 hours 30 minutes

Passing Score

No fixed pass mark — scored out of 100 and read alongside the application; competitive Oxford applicants typically score 50-80+

Exam Fee

Free at school/college test centres in some regions; commercial Pearson VUE centres may charge a sitting fee (typically £75-£100) (University of Oxford (delivered by Pearson VUE))

MAT Exam Content Outline

25%

Algebra & Polynomials

Quadratic formula and completing the square, discriminant and nature of roots, factorisation, factor and remainder theorems, simultaneous equations, and solving quadratic and polynomial inequalities

20%

Graphs, Transformations & Sketching

Sketching quadratics and cubics, modulus and reciprocal graphs, the transformations f(x-a), f(ax), af(x) and f(x)+a, reflections, symmetry of even/odd functions, asymptotes and counting intersections

20%

Differentiation & Integration

Differentiating x^a and e^kx, chain rule basics, first principles, tangents and normals, turning points and the second-derivative test, increasing/decreasing functions, definite integrals and areas under and between curves

20%

Logarithms, Powers & Sequences

Laws of logarithms and indices, solving a^x = b, fractional and negative exponents, arithmetic and geometric progressions, their sums, and the |r| < 1 convergence condition for infinite series

15%

Trigonometry, Geometry, Combinatorics & Logic

Trig identities and equations, periodicity, sine and cosine rules, coordinate geometry of lines and circles, arcs and vectors, combinations and binomial probability, and proof reasoning (contrapositive, contradiction, counterexamples)

How to Pass the MAT Exam

What You Need to Know

  • Passing score: No fixed pass mark — scored out of 100 and read alongside the application; competitive Oxford applicants typically score 50-80+
  • Exam length: 100 questions
  • Time limit: 2 hours 30 minutes
  • Exam fee: Free at school/college test centres in some regions; commercial Pearson VUE centres may charge a sitting fee (typically £75-£100)

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

MAT Study Tips from Top Performers

1Work through every official MAT past paper from 2010 onward, marking with the published solutions and reading the examiner reports for common pitfalls
2Drill the no-calculator skill: practise exact surds, logs and trig values so arithmetic never costs you a multiple-choice mark
3For graph-sketching questions, quickly note intercepts, turning points and end behaviour rather than plotting points one by one
4Use elimination and value-testing on multiple-choice items — substituting a sample number or checking limiting cases often reveals the answer faster than full algebra
5Master the four graph transformations and the difference between f(ax), af(x), f(x-a) and f(x)+a, a recurring MAT theme
6Time yourself: budget roughly the marks-in-minutes split so the 25 multiple-choice questions leave enough time for the two long questions

Frequently Asked Questions

Is the MAT still used in 2026?

Oxford ran the MAT through the 2025 admissions cycle (for 2026 entry) as a computer-based test at Pearson VUE centres. From the 2026 admissions cycle onwards Oxford is moving to the TMUA, so check the current Oxford Mathematical Institute page for the test required for your year. The mathematical content overlaps heavily, so MAT-style multiple-choice practice remains excellent preparation.

How is the MAT structured?

The MAT lasts 2 hours 30 minutes and is marked out of 100. It has 27 questions: 25 multiple-choice questions (each with five options, worth 2, 3 or 4 marks) and two longer questions worth 15 marks each that require typed working and justification.

What syllabus does the MAT cover?

The MAT syllabus is based on the first year of A-level Maths plus a few early Year-13 topics: polynomials, graphs and transformations, logarithms and powers, sequences and series, basic differentiation and integration, trigonometry, coordinate geometry, and combinations with binomial probability. Further Maths is not required.

Is there a pass mark for the MAT?

No. The MAT has no fixed pass mark; the score out of 100 is one part of a holistic Oxford application alongside grades, personal statement and interview. Score thresholds for interview shortlisting vary year to year and by course, but strong applicants typically score in the 50-80+ range.

Can I use a calculator in the MAT?

No. The MAT must be sat without a calculator. Questions are designed so that exact reasoning and algebraic manipulation, not arithmetic, lead to the answer, which is why mental and on-paper technique matters.

How should I approach the multiple-choice section?

Each multiple-choice question has exactly one correct option among five and rewards efficient reasoning — sketching a graph, testing values, eliminating impossible options, or spotting structure. There is no penalty for wrong answers, so attempt every question and use estimation or sketching to rule out distractors quickly.