Academic

Course Objectives

Objectives of the various courses are included in the syllabuses for secondary schools prepared by the Curriculum Development Council. Topics to be taught in different teaching groups are designed and reviewed from time to time to meet the needs of individual students.

To enable students to cope confidently with the mathematics needed in their future studies, workplace or daily life in a technological and information-rich society. This course aims at developing students’:

• ability to conceptualize, inquire, reason and communicate mathematically, and to use mathematics to formulate and solve problems in daily life as well as in mathematical contexts;
• ability to manipulate numbers, symbols and other mathematical objects;
• number sense, symbol sense, spatial sense and a sense of measurement as well as the capability in appreciating structures and patterns;
• positive attitude towards mathematics and the capability in appreciating the aesthetic nature and cultural aspect of mathematics.

Major Concerns

1. Enhance teaching and learning effectiveness through sharing
2. Enhance subject-based strategies to uplift students’ learning outcomes

S1 – S3 Curriculum

To enable students to cope confidently with the mathematics needed in their future studies, workplaces or daily life in a technological and information-rich society, this course aims at developing students:

• the ability to conceptualize, inquire, reason and communicate mathematically, and to use mathematics to formulate and solve problems in daily life as well as in mathematical contexts;
• the ability to manipulate numbers, symbols and other mathematical objects;
• the number sense, symbol sense, spatial sense and a sense of measurement as well as the capability in appreciating structures and patterns;
• a positive attitude towards mathematics and the capability in appreciating the aesthetic nature and cultural aspect of mathematics.

S1

• Basic Computation
• Directed Numbers
• Basic Algebra (I)
• Basic Algebra (II)
• Percentages (I)
• Basic Geometry
• Mensuration (I)
• Rectangular Coordinate System (I)
• Angles and Parallel Lines (I)
• Congruence and Similarity (I)
• Numerical Estimation
• Organization and Presentation of Data (I)

S2

• Approximation and Errors
• Operations and Factorization of Polynomials
• Identities
• Algebraic Fractions and Formulae
• Linear Equations in Two Unknowns
• Angles and Parallel Lines (II)
• Organization and Presentation of Data (II)
• Rates, Ratios and Proportions
• Congruence and Similarity (II)
• Polygons
• Pythagoras’ Theorem and Irrational Numbers
• Introduction to Trigonometry
• Mensuration (II)

S3

• More about Factorization
• Laws of Integral Indices
• Percentages (II)
• Linear Inequalities in One Unknown
• Probability
• Measures of Central Tendency
• More About Triangles
• Quadrilaterals
• More About 3-D Figures
• Mensuration (III)
• Trigonometric Relations
• Applications in Trigonometry
• Rectangular Coordinate System (II)

S4 – S6 Compulsory Part

The Compulsory Part serves as a foundation for all students and at the same time provides flexibility to cater for the diverse needs of individual students. Its contents are categorised into Foundation Topics and Non-foundation Topics. The Foundation Topics constitute a coherent set of essential concepts and knowledge while the Non-foundation Topics cover a wider range of content.

The topics in the Compulsory Part emphasise the relevance of mathematics to various human activities. Students are expected to engage in different activities to foster their awareness of the worldwide use of mathematical terminology, notation and strategies to solve problems. Also, to enable students to recognise and appreciate the interconnection between the different parts of mathematics they have learnt at both the junior and senior secondary levels, a “Further Applications” learning unit is incorporated into the Compulsory Part.

This course aims to:

• further develop students’ mathematical knowledge, skills and concepts;
• provide students with mathematical tools for their personal development and future career pathways;
• provide a foundation for students who may further their studies in Mathematics or related areas;
• develop in students the generic skills, and in particular, the capability to use mathematics to solve problems, reason and communicate;
• develop in students interest in and positive attitudes towards mathematics learning;
• develop students’ competence and confidence in dealing with mathematics needed in life; and
• help students to fulfil their potential in mathematics.

S4

• Number Systems
• Equations of Straight Lines
• Quadratic Equations in One Unknown
• Basic Knowledge of Functions
• Quadratic Functions
• More about Polynomials
• Exponential Functions
• Logarithmic Functions
• Rational Functions
• Basic Trigonometry
• Basic Properties of Circles
• More about Basic Properties of Circles

S5

• More about Equations
• Inequalities in One Unknown
• More about Graphs of Functions
• Variations
• Permutations and Combinations
• More about Probability
• Locus
• Equations of Circles
• Applications of Trigonometry in 2-dimentional Problems
• Applications of Trigonometry in 3-dimentional Problems
• Measures of Dispersion

S6

• Arithmetic Sequences
• Geometric Sequences
• Linear Inequalities in Two Unknowns and Linear Programming
• Uses and Abuses of Statistics

S4 – S6 Extension Modules 1 and 2

The Extended Part is designed for students who need more mathematical knowledge and skills for their future studies and careers, and for those whose interests and maturity have been developed to a level that enables them to benefit from further mathematical study in different areas. The Extended Part aims at extending students’ mathematics horizon beyond the Compulsory Part. Students have to handle more complicated problems in the Extended Part than in the Compulsory Part.

Module 1 (Calculus and Statistics) is intended to cater for those students who will be involved in disciplines or careers which demand a wider scope and deeper understanding of mathematics, and for those who would like to learn more mathematical applications at the senior secondary level.

It aims to:

• provide students with skills and concepts beyond the Compulsory Part;
• emphasise applications rather than mathematical rigour with a view to widening students’ perspectives on mathematics; and
• provide students with intuitive concepts of calculus and statistics, related basic skills and useful tools for their future studies and careers.

Extension Module 1: Calculus and Statistics

• Binomial Expansion
• Exponential Functions and Logarithmic Functions
• Limits and Derivatives
• Differentiation
• Application of Differentiation
• Indefinite Integration and its Applications
• Definite Integration and its Applications
• Further Probability
• Probability Distribution, Expectation and Variance
• Discrete Probability Distributions
• Continuous Random Variables and Normal Distribution
• Sampling Distribution and Parameter Estimation

Extension Module 2: Algebra and Calculus

• Mathematical Induction
• Binomial Theorem
• Trigonometry (I)
• Trigonometry (II)
• Limits and the Number e
• Differentiation
• Applications of Differentiation
• Indefinite Integration and its Applications
• Definite Integration
• Applications of Definite Integration
• Matrices and Determinants
• System of Linear Equations
• Introduction of Vectors
• Scalar Products and Vector Products

Continuous Assessment               

• Major Assignments
• Pre-lesson Tasks
• Independent Learning Projects / Presentation
• Quizzes
• Tests
• Uniform Test
• Examination

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