Revision – 1

Algebra 

Arithmetic and Geometric Sequence and Series

Exponents and Logarithms

Binomial theorem and expansion

Revision – 2

Functions and Equations

Domain, range, odd, even, composite, identify and inverse, one to one and many to one functions

Inverse functions including domain restriction, self-inverse functions

Key features of graphs such as maximum, minimum, intercepts, horizontal and vertical asymptotes, and symmetry,  considering its domain and range and sketching the graphs.

The graphs of the functions y =|f(x)| and y = f(|x|)

The graph of 1/f(x)  given the graph of y = f(x)

Transformation of graphs; translations; stretches; reflections in the axes

The graph of the inverse function as a reflection in y = x

Revision – 3

Trigonometry 

Length of an arc; area of a sector

The unit circle

Trigonometric identities and problem-solving

Compound angle and double angle identities.

Composite functions of the form f(x) = a sin (b(x + c)) + d

Algebraic and graphical methods of solving trigonometric equations.

Revision – 4

Vectors

Unit vectors, Position vectors, Parallel vectors

The scalar product of vectors and its properties

The angle between vectors, parallel and perpendicular vectors

Vector equation of a straight line in 3 – D, applications to kinematics, the point of intersection and angle between two lines.

Coincident, parallel, Intersecting and skew lines, Distinguishing between these cases.

Revision – 5

Statistics & Probability

Mutually exclusive Events

Conditional Probability

Concept of discrete and continuous random variables and their probability distributions

Probability density functions

Expected value ( mean), Mode, median,   

variance and standard deviation and it applications

Binomial Distributions

Normal distribution

Revision – 6

Calculus

Differentiation by first principles

Rate of change

Tangent and normals

Sketching graphs and its derivatives

Optimization problems

Graphical behaviors of functions and point of inflections

Integrating composite functions

Area and volume.