__STPM Mathematics T (also known as Pure Mathematics) Syllabus__

- Numbers and Sets

Real numbers

Exponents and logarithms

Complex numbers

Sets

- Polynomials

Polynomials

Equations and inequalities

Partial fractions

- Sequences and Series

Sequences

Series

Binomial expansions

- Matrices

Matrices

Inverse matrices

System of linear equations

- Coordinate Geometry

Cartesian coordinates in a plane

Straight lines

Curves

- Functions

Functions and graphs

Composite functions

Inverse functions

Limit and continuity of a function

- Differentiation

Derivative of a function

Rules for differentiation

Derivative of a function defined implicitly or parametrically

Applications of differentiation

- Integration

Integral of a function

Integration techniques

Definite integrals

Applications of integration

- Differential Equations

Differential equations

First order differential equations with separable variables

First order homogeneous differential equations

- Trigonometry

Solution of a triangle

Trigonometric formulae

Trigonometric equations and inequalities

- Deductive Geometry

Axioms

Polygons

Circles

- Vectors

Vectors

Applications of vectors

- Data Description

Representation of data

Measures of location

Measures of dispersion

- Probability

Techniques of counting

Events and probabilities

Mutually exclusive events

Independent and conditional events

- Discrete Probability Distributions

Discrete random variables

Mathematical expectation

The binomial distribution

The Poisson distribution

- Continuous Probability Distributions

Continuous random variable

Probability density function

Mathematical expectation

The normal distribution

__STPM Mathematics S (also known as Statistical Mathematics) Syllabus__

- Numbers and Sets

Real numbers

Exponents and logarithms

Complex numbers

Sets

- Polynomials

Polynomials

Equations and inequalities

Partial fractions

- Sequences and Series

Sequences

Series

Binomial expansions

- Matrices

Matrices

Inverse matrices

System of linear equations

- Coordinate Geometry

Cartesian coordinates in a plane

Straight lines

Curves

- Functions

Functions and graphs

Composite functions

Inverse functions

Limit and continuity of a function

- Differentiation

Derivative of a function

Rules for differentiation

Derivative of a function defined implicitly or parametrically

Applications of differentiation

- Integration

Integral of a function

Integration techniques

Definite integrals

Applications of integration

- Linear Programming

- Network Planning

- Data Description

- Probability

- Probability Distributions

- Sampling and Estimation

- Correlation and Regression

- Time Series and Index Number

__STPM Further Mathematics Syllabus__(thanks to Ru7h)

Note: 13 - 16 are statistic topics

- Logic and Proof

- Complex Numbers

Polar form

de Moivre's theorem

Equations

- Matrices

Row & Columns operations

System of linear equations

eigenvalues & eigenvectors

- Recurrence Relations

Recurrence relations

Homogeneous linear recurrence relations

Non-homogenous linear recurrence relations

- Functions

Inverse trigonometric functions

Hyperbolic functions

Inverse hyperbolic functions

- Differentiation and Integration

- Power Series

Taylor Polynomials

Taylor Series

- Differential Equations

- Number Theory

Divisibility

Modular Arithmetic

- Graph Theory

Graphs

Paths & Cycles

Matrix Representations

- Transformation Geometry

Transformation

Matrix Representations

- Coordinate Geometry

Three-Dimensional vectors

Straight Lines

Planes

- Sampling and Estimation

Random samples

Sampling Distributions

Point Estimates

Interval Estimates

- Hypothesis Testing

Hypotheses

Critical Regions

Tests of Significance

- χ² Tests

χ² distributions

Tests for goodness of fit

Tests for Independence

- Correlation and Regression

Scatter Diagrams

Pearson correlation coefficient

Linear Regression Lines