Mathematics


S.1 Curriculum

Chapter 0    Basic Mathematics

Section

0.1  Fundamental Arithmetic
       A. Numbers
       B. The Four Basic Arithmetic Operations (+, –, ´, ¸)

0.2  Multiples and Factors
       A. Multiples and L.C.M.
       B. Factors and H.C.F.
       C. Prime Numbers and Prime Factors

0.3  Fractions
       A. Introduction
       B. Equal Fractions
       C. Arithmetic Operations on Fractions

Chapter 1    Directed Numbers and the Number Line

Section

1.1  Concept of Directed Numbers

1.2  The Number Line

1.3  Addition and Subtraction of Directed Numbers
       A. By Using the Number Line
       B. By Removing Brackets

1.4  Multiplication and Division of Directed Numbers
       A. Multiplication of Directed Numbers
       B. Division of Directed Numbers
       C. Mixed Operations of Directed Numbers

Chapter 2    Introduction to Algebra

Section

2.1  Algebraic Language
       A. Using Letters to Represent Unknown Values
       B. Algebraic Expressions
       C. Operations and Notations in Algebra

2.2  Method of Substitution and Formulas
       A. Method of Substitution
       B. Formulas

2.3  Number Patterns
       A. Introduction to Sequences
       B. Some Common Sequences
       C. General Term of a Sequence

Chapter 3    Algebraic Equations in One Unknown

Section

3.1  Algebraic Equations
       A. Introduction to Algebraic Equations
       B. Basic Techniques for Solving Algebraic Equations

3.2  More about Solving Equations
       A. Combining Terms with the Same Unknown
       B. Removing Brackets
       C. Eliminating Denominators

3.3  Applications of Algebraic Equations

3.4  Literal Equations (Enrichment)

Chapter 4    Percentages (I)

Section

4.1  Simple Problems on Percentages
       A. Finding the Percentage of a Part
       B. Finding a Part from the Percentage
       C. Finding the Whole from the Percentage and the Part

4.2  Percentage Increase and Percentage Decrease
       A. Percentage Increase
       B. Percentage Decrease

4.3  Profit and Loss
       A. Profit
       B. Loss
       C. Discount

Chapter 5    Estimation in Numbers and Measurement

Section

5.1  Introduction to Estimation
       A. Concept of Estimation
       B. Reasons for Estimation

5.2  Numerical Estimation Strategies
       A. Reformulation Strategy
       B. Compensation Strategy
       C. Translation Strategy
       D. More about Estimation

5.3  Measurement
       A. Approximate Nature of Measurement
       B. Choosing an Appropriate Measuring Tool
       C. Choosing an Appropriate Unit for Measurement
       D. Choosing an Appropriate Degree of Accuracy for Measurement

5.4  Estimation Strategies in Measurement
       A. Benchmark Strategy
       B. Decomposition - recomposition Strategy
       C. Estimation of p

5.5  Methods of Reducing Errors in Measurement

Chapter 6    Introduction to Geometry

Section

6.1  The Three Elements of Geometry
       A. Points
       B. Lines
       C. Surfaces

6.2  Angles
       A. Concept of Angles
       B. Types of Angle
       C. Measurement and Construction of Angles

6.3  Lines on a Plane

6.4  Plane Figures
       A. Triangles
       B. Polygons
       C. Circles

6.5  Construction of Figures
       A. Construction of Parallel Lines and Perpendicular Lines
       B. Construction of Circles and Line Segments

6.6  Three-Dimensional Figures
       A. Introduction to Solids
       B. Polyhedra

6.7  Cross-sections of Solids

6.8  2-D Representations of Simple Solids
       A. Sketching Solids
       B. Drawing Solids on Grid Paper (Enrichment)

Chapter 7    Symmetry and Transformation

Section

7.1  Symmetry
       A. Reflectional Symmetry
       B. Rotational Symmetry

7.2  Transformation
       A. Translation
       B. Reflection
       C. Rotation
       D. Enlargement / Reduction

7.3  Designing Tile Patterns (Enrichment)

Chapter 8    Areas and Volumes (I)

Section

8.1  Areas of Simple Polygons

8.2  Prisms
       A. Review on Volume
       B. Volumes of Prisms
       C. Total Surface Areas of Prisms

Chapter 9    Congruence and Similarity

Section

9.1  Congruence

9.2  Congruent Triangles and their Properties

9.3  Construction of Triangles

9.4  Conditions for Congruent Triangles

9.5  Similarity

9.6  Similar Triangles and their Properties

9.7  Conditions for Similar Triangles

Chapter 10    Introduction to Coordinates

Section

10.1  Introduction to Ordered Pairs

10.2  Rectangular Coordinate System

10.3  Distance between Two Points

10.4  Areas of Plane Figures

10.5  Transformations of Points on the Coordinate Plane
          A. Translation
          B. Reflection
          C. Rotation about the Origin

10.6  Polar Coordinate System

Chapter 11    Angles related to Lines

Section

11.1  Angles related to Intersecting Lines
          A. Adjacent Angles on a Straight Line
          B. Angles at a Point
          C. Vertically Opposite Angles

11.2  Angles related to Parallel Lines
          A. Angles Formed by a Transversal and Two Lines
          B. Angles Formed by a Transversal and Parallel Lines

11.3  Identifying Parallel Lines

Chapter 12    Manipulation of Simple Polynomials

Section

12.1  Laws of Positive Integral Indices

12.2  Monomials

12.3  Polynomials
          A. Basic Concept of Polynomials
          B. Like Terms and Unlike Terms
          C. Arrangement of Terms
          D. Value of a Polynomial

12.4  Addition and Subtraction of Polynomials

12.5  Multiplication of Polynomials
          A. Distributive Law of Multiplication
          B. Multiplication of Binomials and Polynomials

Chapter 13    Introduction to Various Stages of Statistics

Section

13.1  Introduction to Statistics

13.2  Collection of Data

13.3  Classification of Data

13.4  Organization of Data

Chapter 14    Simple Statistical Diagrams and Graphs (I)

Section

14.1  Simple Statistical Diagrams
          A. Bar Charts
          B. Broken-Line Graphs
          C. Pie Charts

14.2  Stem-and-Leaf Diagrams
          A. Stem-and-Leaf Diagrams
          B. Back-to-Back Stem-and-Leaf Diagrams

14.3  Histograms
          A. Grouping of Continuous Data
          B. Drawing Histograms

14.4  Scatter Diagrams

14.5  Constructing Statistical Diagrams with Computer Software