Further Mathematics

Course summary

Paper 1: Further Pure Mathematics 1 Proof ● Complex numbers – modulus and argument, conjugates, Argand diagrams, simple loci ● Matrices – add, subtract and multiply, transformations, determinants, inverse matrices ● Further algebra and functions – roots of polynomials, series formulae ● Further calculus – volumes of revolution ● Further vectors – equation of a straight line and plane, scalar product Paper 2: Further Pure Mathematics 2 Complex numbers – de Moivre’s theorem, exponential form, complex roots ● Further algebra and functions – method of differences, Maclaurin series ● Further calculus – improper integrals, mean value of a function, inverse trigonometric functions ● Polar coordinates ● Hyperbolic functions ● Differential equations – first and second order, simple harmonic motion, damped harmonic motion Paper 3: Further Statistics Linear regression ● Discrete distributions ● Continuous distributions ● Correlation ● Hypothesis testing ● Chi squared tests Paper 4: Further Mechanics ● Momentum and impulse ● Collisions ● Centres of mass ● Work and energy ● Elastic strings and springs