Mathematics


S.3 Curriculum

Chapter 1   Linear Inequalities in One Unknown

Section

1.1 Basic Concept of Inequalities
       A. What are Inequalities?
       B. Solutions of Inequalities
       C. Graphical Representations of the Solutions of Inequalities

1.2 Basic Properties of Inequalities

1.3 Linear Inequalities in One Unknown
       A. Solving Linear Inequalities in One Unknown
       B. Using Inequalities to Solve Simple Problems

Chapter 2   Percentages (II)

Section

2.1 More about Percentage Increase and Decrease
       A. Percentage Changes
       B. Successive Percentage Changes
       C. Percentage Changes in Different Parts

2.2 Increase or Decrease at a Constant Rate
       A. Increase at a Constant Rate
       B. Decrease at a Constant Rate

2.3 Interest
       A. Simple Interest
       B. Compound Interest

2.4 Taxation
       A. Rates
       B. Property Tax
       C. Salaries Tax

Chapter 3   Special Lines and Centres in a Triangle

Section

3.1 Important Lines in a Triangle

3.2 Relationship among the Three Sides of a Triangle (Non-foundation)

3.3 Centres of a Triangle
       A. Properties of the Centres of a Triangle
       B. Construction of Centres of a Triangle Using Compasses and Straight Edge
       (Non-foundation)

Chapter 4   Quadrilaterals

Section

4.1 Quadrilaterals

4.2 Parallelograms
       A. Properties of Parallelograms
       B. Identifying Parallelograms (Non-foundation)

4.3 Rectangles, Squares, Rhombuses, Trapeziums and Kites
       A. Rectangles
       B. Squares
       C. Rhombuses
       D. Trapeziums
       E. Kites

4.4 Simple Proofs related to Parallelograms (Non-foundation)

4.5 Mid-point Theorem (Non-foundation)

4.6 Intercept Theorem (Non-foundation)

Chapter 5   More about 3-D Figures

Section

5.1 Symmetries of Solids
       A. Reflectional and Rotational Symmetries of Solids
       B. Symmetries of Regular Polyhedra (Enrichment: Other Regular Polyhedra)

5.2 Nets of Solids

5.3 2-D Representations of Solids
       A. Orthographic Views of Solids
       B. Identifying Solids from their Orthographic Views
(Enrichment: Drawing Solids on Isometric Grid)

5.4 Points, Lines and Planes in Solids
       A. Relationships between Lines and Planes
       B. Relationships between Two Planes

5.5 More about Solids
       A. Euler’s Formula
       B. Duality of Regular Polyhedra

Chapter 6   Measures of Central Tendency

Section

6.1 Introduction to Central Tendency

6.2 Arithmetic Means
       A. Arithmetic Means of Ungrouped Data
       B. Arithmetic Means of Grouped Data

6.3 Medians
       A. Medians of Ungrouped Data
       B. Medians of Grouped Data

6.4 Modes and Modal Classes
       A. Introduction to Modes
       B. Modal Classes of Grouped Data

6.5 Comparing Different Types of Average
       A. Choosing the most Appropriate Measure of Central Tendency
       B. Comparing Two Sets of Data with Different Types of Average

6.6 Misuses of Averages and the Consequences of Misues
       A. Misuses of Averages
       B. Consequences of Misusing Averages

6.7 Further Investigations on Averages (Non-foundation)

6.8 Weighted Mean

Chapter 7   Areas and Volumes (III)

Section

7.1 Pyramids
       A. Volumes of Pyramids
       B. Total Surface Areas of Pyramids

7.2 Circular Cones
       A. Volumes of Right Circular Cones
       B. Total Surface Areas of Right Circular Cones

7.3 Spheres
       A. Volumes of Spheres
       B. Surface Areas of Sheres

7.4 Formulas for Lengths, Areas and Volumes

7.5 Similar Shapes
       A. Similar Plane Figures
       B. Similar Solids

Chapter 8   Coordinate Geometry of Straight Lines

Section

8.1 Distance between Any Two Points on a Plane

8.2 Slope of a Straight Line
       A. Slope
       B. Inclination

8.3 Parallel and Perpendicular Lines
       A. Parallel Lines
       B. Perpendicular Lines

8.4 Point of Division
       A. Mid-point
       B. Internal Point of Division

8.5 Using Analytic Approach to Prove Results Relating to Rectilinear Figures

Chapter 9   Trigonometric Relations

Section

9.1 Trigonometric Ratios of Special Angles

9.2 Finding Trigonometric Ratios by Constructing Right-Angled Triangles

9.3 Trigonometric Identities
       A. Basic Trigonometric Identities
       B. Trigonometric Ratios of Complementary Angles
       C. Proofs of Simple Trigonometric Identities

Chapter 10   Application of Trigonometry

Section

10.1 Gradients
       A. Gradient of a Road
       B. Finding Gradient from a Map

10.2 Angles of Elevation and Depression

10.3 Bearings
       A. Simple Bearings
       B. Problems Involving Bearings

10.4 Applications of Trigonometric to Rectilinear Figures

Chapter 11   Introduction of Probability

Section

11.1 Probability
       A. The Meaning of Probability
       B. Possible Outcomes
       C. Calculation of Probabilities
       D. Impossible Events and Certain Events

11.2 Further Problems on Probability
       A. Listing Possible Outcomes by Tree Diagrams
       B. Geometric Probability

11.3 Experimental Probability

11.4 Expected Value