Mathematics

Course summary

Paper 1: Pure Mathematics 1 Proof ● Algebra and functions – indices and surds, quadratics, simultaneous equations, inequalities, functions ● Coordinate geometry in the (x,y) plane – straight lines, the circle ● Sequences and series – binomial expansion ● Trigonometry – simple identities and equations ● Exponentials and logarithms ● Differentiation – first and second derivatives, tangents and normals ● Integration – definite and indefinite integration ● Vectors Paper 2: Pure Mathematics 2 ● Proof ● Algebra and functions – algebraic division, composite and inverse functions, partial fractions ● Coordinate geometry in the (x,y) plane – parametric equations ● Sequences and series – binomial expansion for rational powers, sigma notation, arithmetic and geometric series ● Trigonometry – radian measure, exact values, reciprocal ratios, further identities and equations ● Differentiation – trigonometric functions, product and quotient rules, parametric differentiation ● Integration – area under a curve, substitution and integration by parts, simple first order DE ● Numerical methods – roots of an equation, iterative methods, trapezium rule ● Vectors – three dimensions Paper 3: Statistics and Mechanics Section A: Statistics ● Statistical sampling ● Data presentation and interpretation ● Probability ● Statistical distributions ● Statistical hypothesis testing Section B: Mechanics ● Quantities and units in Mechanics ● Kinematics ● Forces and Newton’s laws ● Moments