MAT syllabus

Syllabus for the entrance test in Mathematics, Joint Degrees, and Computer Science

Issued January 2018. This is an HTML version of the MAT 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 $a\neq -1$) and sums thereof.

Graphs: The graphs of quadratics and cubics. Graphs of
\begin{equation*}
\sin x, \quad \cos x, \quad \tan x, \quad \sqrt{x}, \quad a^x ,\quad \log_a x.
\end{equation*}
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
\begin{equation*}
y = f (ax),\quad y = af (x),\quad y = f (x - a), \quad y = f (x) + a
\end{equation*}
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
\begin{equation*}
\tan x = \frac{\sin x}{\cos x} ,\quad \sin^2 x + \cos^2 x = 1, \quad \sin\left(90^\circ - x\right) = \cos x.
\end{equation*}
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 condition for infinite geometric progressions*.

* Part of full A-level Mathematics syllabus.