## Sunday, 31 May 2009

## Thursday, 21 May 2009

### Chapter 1 : Numbers and sets

1. Numbers and sets

1.1 Real numbers

1.2 Exponents and logarithms

1.3 Complex numbers

1.4 Sets

Explanatory notes

Candidates should be able to

(a) understand the real number system;

(b) carry out elementary operations on real numbers;

(c) use the properties of real numbers;

(d) use the notation for intervals of real numbers;

(e) use the notation |x| and its properties;

(f) understand integral and rational exponents;

(g) understand the relationship between logarithms and exponents;

(h) carry out change of base for logarithms;

(i) use the laws of exponents and laws of logarithms;

(j) use the results: for a

1.1 Real numbers

1.2 Exponents and logarithms

1.3 Complex numbers

1.4 Sets

Explanatory notes

Candidates should be able to

(a) understand the real number system;

(b) carry out elementary operations on real numbers;

(c) use the properties of real numbers;

(d) use the notation for intervals of real numbers;

(e) use the notation |x| and its properties;

(f) understand integral and rational exponents;

(g) understand the relationship between logarithms and exponents;

(h) carry out change of base for logarithms;

(i) use the laws of exponents and laws of logarithms;

(j) use the results: for a

**1, and and,,and**

(k) solve equations and inequality of involving exponents and logarithms;

(l) understand the meaning of the real part, imaginary part, and conjugate of a complex number;

(m) find the modulus and argument of a complex number;

(n) represent complex numbers geometrically by means of an Argand diagram;

(o) use the condition for the equality of two complex numbers;

(p) carry out elementary operations on complex numbers expressed in Cartesian form;

(q) understand the concept of a set and set notation;

(r) carry out operations on sets;

(s) use the laws of the algebra of sets;

(k) solve equations and inequality of involving exponents and logarithms;

(l) understand the meaning of the real part, imaginary part, and conjugate of a complex number;

(m) find the modulus and argument of a complex number;

(n) represent complex numbers geometrically by means of an Argand diagram;

(o) use the condition for the equality of two complex numbers;

(p) carry out elementary operations on complex numbers expressed in Cartesian form;

(q) understand the concept of a set and set notation;

(r) carry out operations on sets;

(s) use the laws of the algebra of sets;

**
**

## Wednesday, 20 May 2009

### STPM Mathematics S (also known as Statistical Mathematics) Syllabus

(May not be taken with 954 Mathematics T or 956 Further Mathematics T)

**Aims**

The Mathematics S 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 social sciences and management at institutions of higher learning.

CONTENT:

- 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

**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 T) 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 totalling 100 marks.

**
**

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