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CORE |
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TOPIC |
DESCRIPTION |
HRS |
|
1. |
Number and Algebra |
Arithmetic sequences and series; Exponent, logarithms; The binomial
theorem; Induction; Complex numbers; Operations on complex numbers;
De Moivre’s theorem; Conjugate roots |
20 |
|
2. |
Functions and Equations |
Concept of function: domain, range, image, composite and inverse
functions; Function graphing; Transformations; The reciprocal
function; The quadratic function; Complex simultaneous equations;
Linear and quadratic inequalities; Polynomial functions; Exponential
functions; Logarithm functions growth, decay, half life, etc. |
25 |
|
3. |
Circular Functions and Trigonometry |
The circle: radian, length of arc, area of sector; Three basic
Pythagorean identities; Six circular functions and their graphs,
inverse functions and their graphs; Addition, double angle and half
angle formulae, the compound formula with R and ?; Composite
functions; Triangles, sine rule, cosine rule |
25 |
|
4. |
Vector Geometry |
Components of a vector, zero vector, inverse, magnitude, position
vector; Scalar product with properties, perpendicular and parallel
vectors; Angle between vectors; Vector product; Vector equation;
Intersection of lines and planes; Distances in 2D and 3D |
25 |
|
5. |
Matrices and Transformations |
Definition of matrix: row, column and dimension; Operations on
matrices, identity matrix; Singular matrix, Inverse of a square
matrix; Linear transformations; Composition of linear
transformations; Solution of linear equations |
20 |
|
6. |
Statistics |
Population and sample, discrete, continuous data; Presentation of
data; Central tendency; Cumulative frequency, quartiles and
percentiles; Dispersion |
10 |
|
7. |
Probability |
Sample space, probability of an event; Combined events; Conditional
probability, Bayes’ theorem; Venn and tree diagrams; Permutations and
combinations; Discrete probability distributions; Binomial
distribution; Continuous probability distributions; Normal
distribution |
20 |
|
8. |
Calculus |
Limit and convergence; Differentiation from first principles; Types of
differentiation, degrees of derivatives; Graphical behaviour of
functions; Application of first and second derivative; Implicit
differentiation; Indefinite integration; Anti-differentiation;
Further integration; Solution of first order differential equations |
50 |
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Total Teaching Hours |
150 |
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