MAT

The MAT aims to test the depth of mathematical understanding of a student in the fourth term of their A-levels (or equivalent) rather than a breadth of knowledge. It is set with the aim of being approachable by all students, including those without Further Mathematics A-level, and those from other educational systems (e.g. Baccalaureate and Scottish Highers).

It covers:
The syllabus of MAT is based on the first year of A level Maths, and a few topics from the fourth term of A level Maths which will have covered by the time of the test.

Test Information
Candidates should attempt five of the six questions, depending on the degree for which they are applying.
Mathematics / Mathematics & Statistics, Mathematics & Philosophy applicants should attempt questions 1, 2, 3, 4, and 5
Mathematics & Computer Science, Computer Science, Computer Science & Philosophy applicants should attempt questions 1, 2, 3, 5, and 6
Question 1 is multiple choice, and contains 10 parts each worth 4 marks. Marks are given solely for the correct answers. Questions 2-6 are longer questions, each worth 15 marks, and candidates will need to show their working. Part marks are available for the longer questions.

How is the test marked?
The MAT is marked by University of Oxford graduate students. For the multiple-choice questions, there are no marks available for working out. For the long questions, our markers will look carefully at what you've written and give you an appropriate number of marks following an agreed mark scheme.

Do I get marks for working out?
Yes, on questions 2-6 there are marks for working out.

Do I have to use the method in the solutions document (or in the solutions video)?
No- if you follow the instructions in the question and you do correct mathematics, then you should get the marks. Provided you've followed the instructions in the question and it's clear what you're doing, you should get the marks.

Syllabus

Polynomials:

The quadratic formula. Completing the square. Discriminant. Factorisation. Factor Theorem.

Algebra:

Simple simultaneous equations in one or two variables. Solution of simple inequalities. Binomial Theorem with positive whole exponent. Combinations and binomial probabilities.

Differentiation:

Derivative of `x^{a}`, including for fractional exponents. Derivative of `e^{kx}`. Derivative of a sum of functions.
Tangents and normals to graphs. Turning points. Second order derivatives. Maxima and minima. Increasing and decreasing functions. Differentiation from first principles.

Integration:

Indefinite integration as the reverse of differentiation.
Definite integrals and the signed areas they represent. Integration of `x^{a}` (where a /= −1) and sums thereof.

Graphs:

The graphs of quadratics and cubics. Graphs of

`sin x,   cos x,   tan x,   sqrt(x),   ax,   log _{a} x`

Solving equations and inequalities with graphs.

Logarithms and powers:

Laws of logarithms and exponentials.
Solution of the equation `a^{x} = b`.

Transformations:

The relations between the graphs

`y = f (ax)`,   `y = af (x)`,   `y = f (x − a)`,   `y = f (x) + a`,  

and the graph of `y = f (x)`

Geometry:

Co-ordinate geometry and vectors in the plane.
The equations of straight lines and circles. Basic properties of circles. Lengths of arcs of circles.

Trigonometry:

Solution of simple trigonometric equations.
The identities `\ \tan x = \frac{sin^2 x - cos^2 x}{cos x} \,   sin^2 x + cos^2 x = 1,   sin(90^◦ − x) = cos x.`
Periodicity of sine, cosine and tangent. Sine and cosine rules for triangles.

Sequences and series:

Sequences defined iteratively and by formulae. Arithmetic and geometric progressions*. Their sums*. Convergence con- dition for infinite geometric progressions*.
* Part of full A-level Mathematics syllabus.


(Information source- https://www.maths.ox.ac.uk/study-here/undergraduate-study/maths-admissions-test)