Handbook

Demonstrate understanding of the properties of common functions and their graphs, use composition of functions, and inverse functions; use trigonometric functions to model periodic behaviour.

Represent complex numbers in Cartesian, polar and exponential forms, and on the complex plane.

Perform arithmetic and algebra on complex numbers, including finding powers and complex roots of polynomials.

Demonstrate understanding of the concepts of limit, continuity, differentiable and integrable functions.

Evaluate limits of piecewise functions, and of rational functions at infinity.

Use differentiation rules to find derivatives of implicit and explicit functions.

Apply differentiation techniques to related rates of change problems and optimisation problems.

Use simple integration techniques to find definite and indefinite integrals, including by substitution and partial fractions.

Apply integration techniques to calculate areas, average values, volumes, and centres of mass or moment.

Perform operations with two and three-dimensional vectors, interpret them geometrically, calculate dot products, find vector resolutes, and apply them to motion of a particle.

Solve kinematics problems, and set up and solve problems involving Newton's laws of motion.

Express and explain mathematical techniques and arguments clearly in words.