FOR THE ENTRANCE TEST IN MATHEMATICS, JOINT DEGREES, AND COMPUTER SCIENCE
Issued January 2018.
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 , including for fractional exponents. Derivative of . 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 (where ) and sums thereof.
Graphs: The graphs of quadratics and cubics. Graphs of Solving equations and inequalities with graphs.
Logarithms and powers: Laws of logarithms and exponentials. Solution of the equation .
Transformations: The relations between the graphs and the graph of .
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 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*.