Advance Math (Form V)

TOPIC SUB-TOPICS
1.0 CALCULATING DEVICES 1.1 Scientific calculators
1.2 Computer packages
2.0 SETS 2.1 Operations on sets
2.2 Simplification of set expressions
2.3 Number of elements of a set
3.0 LOGIC 3.1 Statements
3.2 Logical connectives
3.3 Laws of algebra of proposition
3.4 Validity of argument
3.5 Electrical networks
4.0 COORDINATE GEOMETRY 4.1 Rectangular Cartesian coordinate
4.2 Ratio theorem
4.3 Circle
6.0 SERIES 6.1 Sequences
6.2 Series
6.3 Proof by mathematical induction
6.4 Roots of a polynomial function
6.5 Remainder theorem
6.6 Inequalities
6.7 Matrices
6.8 Binomial theorem
6.9 Partial fractions
TOPIC SUB-TOPICS
7.0 TRIGONOMETRY 7.1 Trigonometric ratios
7.2 Trigonometric identities
7.3 Compound angle formula
7.4 Double angle formula
7.5 Multiple angle formula
7.6 Factor formulae
7.7 Radians and small angles
7.8 Trigonometric functions
7.9 Inverse trigonometric functions
8.0 LINEAR PROGRAMMING 8.1 Linear programming problems formulation
8.2 Graphical solution
9.0 DIFFERENTIATION 9.1 Limits and continuity
9.2 Differentiation of a function
9.3 Application of differentiation
9.4 Taylor’s series and Maclaurin’s series
9.5 Introduction to partial derivatives
10.0 INTEGRATION 10.1 Anti-derivatives
10.2 Integration of functions
10.3 Application of integration

Advance Mathematics (Form VI)

TOPIC SUB-TOPICS
11.0 COORDINATE GEOMETRY II 11.1 Conic section
11.2 The parabola
11.3 The ellipse
11.4 The hyperbola
11.5 Polar coordinates
12.0 VECTORS 12.1 Vectors representation
12.2 Dot product
12.3 Cross product
12.4 Vector differentiation and integration
13.0 HYPERBOLIC FUNCTIONS 13.1 Hyperbolic cosine and sine
13.2 Derivative of hyperbolic functions
13.3 Integration of hyperbolic functions
14.0 STATISTICS 14.1 Measure of central tendency
14.2 Measure of dispersion
15.0 PROBABILITY 15.1 Counting techniques for the sample space
15.2 Probability axioms and theorems
15.3 Properties of probability
15.4 Conditional probability
15.5 Probability distributions
15.6 Some special probability distributions
16.0 COMPLEX NUMBERS 16.1 Complex numbers and their operations
16.2 De Moivre’s theorem
17.0 DIFFERENTIAL EQUATIONS 17.1 Introduction to differential equations
17.2 Solution to a differential equation
17.3 First-order differential equations
17.4 Second-order differential equations
18.0 NUMERICAL METHODS 18.1 Errors
18.2 Roots by iterative methods
18.3 Numerical integration