STPM Mathematics T (also known as Pure Mathematics) Syllabus

(May not be taken with 950 Mathematics S)

Aims
The Mathematics T syllabus aims to develop the understanding of mathematical concepts and their applications, together with the skills in mathematical reasoning and problem solving, so as to enable students to proceed to programmes related to science and technology at institutions of higher learning

CONTENT:

1. Numbers and Sets
   Real numbers
   Exponents and logarithms
   Complex numbers
   Sets
   
   
2. Polynomials
   Polynomials
   Equations and inequalities
   Partial fractions
   
   
3. Sequences and Series
   Sequences
   Series
   Binomial expansions
   
   
4. Matrices
   Matrices
   Inverse matrices
   System of linear equations
   
   
5. Coordinate Geometry
   Cartesian coordinates in a plane
   Straight lines
   Curves
   
   
6. Functions
   Functions and graphs
   Composite functions
   Inverse functions
   Limit and continuity of a function
   
   
7. Differentiation
   Derivative of a function
   Rules for differentiation
   Derivative of a function defined implicitly or parametrically
   Applications of differentiation
   
   
8. Integration
   Integral of a function
   Integration techniques
   Definite integrals
   Applications of integration
   
   
9. Differential Equations
   Differential equations
   First order differential equations with separable variables
   First order homogeneous differential equations
   
   
10. Trigonometry
    Solution of a triangle
    Trigonometric formulae
    Trigonometric equations and inequalities
    
    
11. Deductive Geometry
    Axioms
    Polygons
    Circles
    
    
12. Vectors
    Vectors
    Applications of vectors
    
    
13. Data Description
    Representation of data
    Measures of location
    Measures of dispersion
    
    
14. Probability
    Techniques of counting
    Events and probabilities
    Mutually exclusive events
    Independent and conditional events
    
    
15. Discrete Probability Distributions
    Discrete random variables
    Mathematical expectation
    The binomial distribution
    The Poisson distribution
    
    
16. Continuous Probability Distributions
    Continuous random variable
    Probability density function
    Mathematical expectation
    The normal distribution

Form of Examination
The examination consists of two papers; the duration for each paper is 3 hours. Candidates are required to take both Paper 1 and Paper 2.

Paper 1 (same as Paper 1, Mathematics S) is based on topics 1 to 8 and
Paper 2 is based on topics 9 to 16. Each paper contains 12 compulsory questions of variable mark allocations totaling 100 marks.