This provides an introduction to mathematics at A-level standard which include the topics:

  • Basic algebra: different types of numbers (natural numbers, integers, rational numbers and real numbers), inequalities, factorials and modulus.
  • Functions and graphs: definition of functions, composition of numbers, inverse functions and their graphical representations.
  • Linear Equations: definitions of lines in the plane, their equations and graphical representation, gradients, normals, intersection of lines and shortest distance from a point to a line.
  • Quadratic equations: their definition, their graphs, factorisation, completing the square(vertex form), solving the quadratic equation, finding the maximum and minimum of quadratics, intersection of quadratic equations with lines and other quadratics, quadratics in other guises, polynomials, roots, odd/even functions and circles.
  • Limits: Definition of a limit of a sequence, the number e, algebra of limits for sequences, limits of functions, algebra of limits for functions, continuity, one sided limits and intermediate limits.
  • Differential Calculus: Definition of a tangent, definition of a derivative, higher derivatives, differentiation of sums, products, quotients and compositions(chain rule), L’Hopital’s rule, MacLaurin series, stationary points and maxima/minima.
  • Trigonometry: Right angled triangles, Pythagoras’ theorem, definition of sin,cos and tan, radians, properties of trig functions,their derivatives, values of trig functions for certain angles, periodicity, double angle fomulae, trig identities and solving trigonometric functions.
  • Exponentials and logarithms: Their definitions, their graphs, their derivatives, their MacLaurin series, and general exponentials and logarithms.
  • Complex numbers: Definition of i, a complex number, the argand diagram, the complex plane, polar representation of a complex number, argument of a complex number, Eulers formula (exponential representation of a complex number) and De Movoire’s theorem.

The total mark for the course will be 10% coursework and 90% unseen exam at the end of the year.

Lecture notes cheat sheet

Week Question sheets Solutions
Week 1 Sheet 1 Week 1 solutions
Week 2 Sheet 2 Week 2 Solutions
Week 3 Sheet 3 Week 3 Solutions
Week 4 Sheet 4 Week 4 Solutions
Week 5 Sheet 5 Week 5 Solutions
Week 6 Sheet 6 Week 6 Solutions
Week 7 Sheet 7 Week 7 Solutions
Week 8 Sheet 8 Week 8 Solutions

Last years exam paper. Unfortunately the exam solutions can only be obtained from Bonita Carbo from the maths office on floor 6.