Symbols are the basic building blocks of mathematics. After you have studied mathematics at advanced level for a while you will come to appreciate that certain symbols tend to mean certain things. For example x and y are used to represent variables, whereas a and b are used to stand for constants. Greek symbols are commonly used too.

Simplifying algebraic fractions and multiplying, dividing, adding and subtracting these expressions. Definitions of functions, including domain and range, composite functions and inverse functions. Combinations of transformations of graphs, including the modulus functions y=|f(x)| and y = f(|x|). Solving modulus equations.

Understand and use the functions secant, cosecant and cotangent and their graphs. Use various trigonometrical identities, including double angle formulae, addition formulae and equivalent forms for a cos x + b sin x.

Learn about the exponential function e^x and its graph and the logarithmic function ln x and its graph. Learn how to solve equations using these functions.

How to locate roots of equations f(x)=0 by considering change of sign of f(x). How to find approximate solutions to equations by iterative methods including recurrence relations.

How to differentiate products, quotients and functions of functions and all the remaining standard functions: trigonometrical (sin, cos, tan, cot, cosec, sec), logarithmic and exponential. How to solve problems of gradient that require differentiation of combinations of these rules and functions.