STPM Mathematics T, Mathematics S and Further Mathematics Syllabuses

Please take note that the first eight topics (Paper 1) of Maths T and Maths S are the same. Besides, Maths T and Maths S are mutually exclusive. In other words, a STPM candidate cannot take both subjects at the same time. Maths T is taken by most science stream stuedents whereas Maths S is taken by some art stream students. Meanwhile, Further Maths is taken as the optional fifth subject by some science stream students.

STPM Mathematics T (also known as Pure Mathematics) Syllabus

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
    

STPM Mathematics S (also known as Statistical Mathematics) Syllabus

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. Linear Programming
   
   
10. Network Planning
    
    
11. Data Description
    
    
12. Probability
    
    
13. Probability Distributions
    
    
14. Sampling and Estimation
    
    
15. Correlation and Regression
    
    
16. Time Series and Index Number
    
    

STPM Further Mathematics Syllabus (thanks to Ru7h)
Note: 13 - 16 are statistic topics

1. Logic and Proof
   
   
2. Complex Numbers
   Polar form
   de Moivre's theorem
   Equations
   
   
3. Matrices
   Row & Columns operations
   System of linear equations
   eigenvalues & eigenvectors
   
   
4. Recurrence Relations
   Recurrence relations
   Homogeneous linear recurrence relations
   Non-homogenous linear recurrence relations
   
   
5. Functions
   Inverse trigonometric functions
   Hyperbolic functions
   Inverse hyperbolic functions
   
   
6. Differentiation and Integration
   
   
7. Power Series
   Taylor Polynomials
   Taylor Series
   
   
8. Differential Equations
   
   
9. Number Theory
   Divisibility
   Modular Arithmetic
   
   
10. Graph Theory
    Graphs
    Paths & Cycles
    Matrix Representations
    
    
11. Transformation Geometry
    Transformation
    Matrix Representations
    
    
12. Coordinate Geometry
    Three-Dimensional vectors
    Straight Lines
    Planes
    
    
13. Sampling and Estimation
    Random samples
    Sampling Distributions
    Point Estimates
    Interval Estimates
    
    
14. Hypothesis Testing
    Hypotheses
    Critical Regions
    Tests of Significance
    
    
15. χ² Tests
    χ² distributions
    Tests for goodness of fit
    Tests for Independence
    
    
16. Correlation and Regression
    Scatter Diagrams
    Pearson correlation coefficient
    Linear Regression Lines

Reference : malaysia-students.com