Arithmetic, Algebra and Simple Trigonometry:

· Revision of number systems and arithmetic operation

· Basic algebra, power laws . Algebraic manipulation, simplification of rational expressions, the Remainder Theorem, algebraic division; Partial fractions

· Solution of linear, quadratic equations and simultaneous linear equations

· Revision of basic trigonometry, trigonometric identities. Double angle formulae and formulae for sin (A+B) etc.

Functions:

· Functions, domain, range, graph sketching, incl. straight line, circle

· Composition of functions. Piecewise defined functions. Odd, even and periodic functions.

· Inverse functions

· The exponential and logarithm functions

· The trigonometric functions and inverse trigonometric functions. Solution of trig equations

· Hyperbolic functions

Sequences and Series:

· Binomial expansions and factorial notation

· Arithmetic sequences and series. Geometric sequences and series

Complex Numbers:

· Definition and use of j and complex conjugate

· Arithmetic operations with complex numbers

· Fundamental Theorem of Algebra

· Modulus and argument of a complex number and their properties. Polar and exponential representations of a complex number . Relationship between trigonometric and hyperbolic functions

· De Moivre’s Theorem

Differentiation:

· Limits

· Definition of a derivative

· Techniques of differentiation such as the product rule, the quotient rule, the chain rule

· Differentiation of a range of functions e.g trigonometric, exponential and logarithmic

· Implicit, parametric and logarithmic differentiation

· Higher derivatives

· Applications of differentiation to equations of the tangent, local maxima, minima and points of inflection, rates of change and related rates of change

· Maclaurin and Taylor series,

· L’Hopitals’ rule

· Newton Raphson method

Integration:

· Indefinite integration as the reverse of differentiation

· Definite integration interpreted as the area under a curve

· Techniques of integration incl. substitution, integration by parts & using partial fractions

· Applications of integration to the area between curves.

· Numerical integration using the Trapezium rule

· Application of integration to curve lengths, surfaces and volumes of revolution, first moments and centroids, second moments and radii of gyration.

Probability and statistics:

· Descriptive statistics: numerical and graphical summaries.

- Basic Probability: elementary laws, random variables, mean and variance.