CURRICULUM
The contents of the Additional Mathematics curriculum are arranged into two learning packages. They are the Core Package and the Elective Package. The Core Package is compulsory for all students and consists of five components, that is:
   • Geometry;
   • Algebra;
   • Calculus;
   • Trigonometry; and
   • Statistics.

The Elective Package consists of two packages, that is:
   • Science and Technology Application; and
   • Social Science Application.

Students need to choose only one Elective Package according to their inclination in their future field. Those who are inclined towards science and technology are encouraged to choose Science and Technology Application Package while those who are inclined towards commerce, literature and economy are encouraged to choose Social Science Application Package.

 

CORE PACKAGE
The Core Package consists of five learning components.
 »   Geometric Component
G1. Coordinate Geometry
1. Distance between two points.
2. Division of line segment.
3. Area of polygon.
4. Equation of straight line.
5. Parallel and perpendicular lines.
6. Equation of locus involving distance between two points.

G2. Vector
1. Introduction to vector and its properties.
2. Addition and subtraction of vectors.
3. Expressing a vector as a combination of other linear vectors.
4. Vectors in the Cartesian plane.
 
 »   Algebraic Component
A1. Functions
1. Relation.
2. Functions.
3. Composite functions.
4. Inverse functions.

A2. Quadratic Equations
1. Quadratic equation and its roots.
2. Solving quadratic equations.
3. Conditions for quadratic equations to have
   • Two different roots
   • Two equal roots
   • No roots.

A3. Quadratic Functions
1. Quadratic function and its graph.
2. Maximum and minimum values of quadratic functions.
3. Sketch graphs of quadratic functions.
4. Quadratic inequalities.

A4. Simultaneous Equations
1. Simultaneous equations in two unknowns; one linear equation and one non-linear equation.

A5. Indices and Logarithms
1. Indices and laws of indices.
2. Logarithms and laws of logarithms.
3. Change the base of logarithms.
4. Equations involving indices and logarithms.

A6. Progressions
1. Arithmetic progressions.
2. Geometric progressions.

A7. Linear Law
1. Line of best fit.
2. Application to non-linear functions.
 
 »   Calculus Component
C1. Differentiation
1. Gradients of curves and differentiation.
2. Differentiation of axn; (n is an integer), differentiation of the sum of algebraic functions; tangents and normals to curves.
3. Differentiation of the products and quotients of algebraic functions; differentiation of composite functions.
4. Application to minimum and maximum values, rates of change, small changes and approximations.
5. Second derivative.

C2. Integration
1. Integration as an inverse of differentiation.
2. Integration of axn (n is an integer, but n ≠ -1).
3. Integration by substitution.
4. Definite integrals.
5. Integration as a sum; area and volume.
 
 »   Trigonometric Component
T1. Circular Measure
1. Radian.
2. Length of arc of a circle.
3. Area of sectors.

T2. Trigonometric Functions
1. Positive and negative angles in degrees and radians.
2. Six trigonometric functions of any angle.
3. Graphs of sine, cosine and tangent functions.
4. Basic Identities:
    sin2A + cos2A = 1, sec2A = 1 + tan2A, cosec2A = 1 + cot2A

5. Addition formulae and double angle formulae:
    sin(A±B). cos(A±B), tan(A±B), sin 2A, cos 2A, tan 2A
 
 »   Statistic Component
S1. Statistics
1. Measures of central tendency : mean, mode and median.
2. Measures of dispersion : range, interquartile range, variance and standard deviation.

S2. Permutations and Combinations
1. Permutations.
2. Combinations.

S3. Probability
1. Probability of an event.
2. Probability of mutually exclusive events.
3. Probability of independent events.

S4. Probability Distributions
1. Discrete probability distribution and binomial distribution.
2. Continuous probability distribution and normal distribution.
 
 

 

ELECTIVE PACKAGE
The Elective Package consists of two application packages. Students choose only one application package.
 »   For Science and Technology
AST1. Solutions of triangles
1. Sine rule.
2. Cosine rule.
3. Area of triangles.

AST2. Motion along a straight line
1. Displacement.
2. Velocity.
3. Acceleration.
 
 »   For Social Science
ASS1. Index Number
1. Index number.
2. Composite index.

ASS2. Linear Programming
1. Graphs of linear inequalities.
2. Solving linear programming problems.