Secondary Mathematics Scope and Sequence

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New Elementary Mathematics 1

1. Whole Numbers
• System of Numeration
• The Four Operations
• Factors and Multiples
• Prime Numbers and Prime Factorisation
• Highest Common Factor
• Least Common Factor
• Number Patterns
• Variables
• Basic Number Laws
2. Fractions, Decimals and Approximation
• Fractions
• Addition and Subtraction of Fractions
• Multiplication and Division of Fractions
• Decimals
• Approximation
• Conversion Between Fractions and Decimals
• Estimation
3. Arithmetic Problems
• Units of Measure
• Simple Word Problems
• Multi-Step Word Problems
• Estimation in Daily Life Situations
4. Real Numbers
• Negative Numbers
• Addition and Subtraction of Integers
• Multiplication of Integers
• Division of Integers
• Real Numbers
• Order of Calculation
• Mental Calculation
5. Simple Algebraic Expressions
• Algebraic Expressions
• Evaluation of Algebraic Expressions
• Algebraic Terms
• Use of Brackets
• Collecting Like Terms
6. Open Sentences And Equations
• Open Sentences
• Equations
• Equations with Fractional and Decimals Coefficients
• Evaluation of Formulae
• Algebraic Problems
7. Rate, Ratio And Percentage
• Rate and Speed
• Ratio
• Direct and Inverse Proportions
• Percentage
• Applications of Percentages
8. Solving Problems Involving Financial Transactions
• Earnings, Profit and Loss, Commissions and Discounts
• Interest and Hire Purchase
• Taxation and Money Exchange
9. Introducing Geometry
• Line Segment, Line and Angles
• Angle Properties Related to Straight Lines
• Perpendicular and Parallel Lines
• Angle Properties Related to Parallel Lines
10. Polygons
• Triangles
• Angle Properties of a Triangle
• Isosceles and Equilateral Triangles
• Angle Properties of a Polygon
• Quadrilaterals
• Properties of Quadrilaterals
11. Symmetries And Nets Of Solid Figures
• Line Symmetry
• Rotational Symmetry
• Patterns
• Symmetries of Solid Figures
• Nets of Solid Figures
12. Area And Perimeter
• Perimeter and area of Polygon
• Circumference and Area of Circle
• More Problems on Area and Perimeter
13. Volume and Surface Area of Prism and Cylinder
• Cylinder
• Density
• More Problems on Volume and Surface Area
14. Similarity And Congruence
• Similar and Congruent Figures
• Designs and Tessellations
• Scale Drawing

New Elementary Mathematics 2

1. Indices
• Positive Integral Indices
• Zero and Negative Integral Indices
• Indices Involving Variables
• Standard Form
2. Algebraic Manipulations
• Special Algebraic Rules for Calculations
• Expanding Products
• Factorisation
• Addition and Subtraction of Algebraic Fractions
• Multiplication and Division of Algebraic Fractions
• Fractional Equations
• Problems Involving Fractional Equations
3. Literal And Quadratic Equations
• Literal Equations
• Transformation of Formulae
• Quadratic Equations
• Quadratic Factorisation
• Solving Quadratic Equations by Factorisation
• Solving Quadratic Equations by Factorisation
• Word Problems Leading to Quadratic Equations
4. Word Problems
• Problems on Rate, Ratio and Percentage
• Problems Involving Financial Transactions
5. Graphs I
• The Coordinate Plane
• Graphs of Linear Equations in Two Variables
• Simple Applications of Straight Line Graphs
• Travel Guide
• Solving Simultaneous Linear Equations by Graphs
• Quadratic Graphs
6. Simultaneous Linear Equations
• Simple Elimination Method
• Elimination Method
• Substitution Method
• Word Problems Using Simultaneous Equations
7. Inequalities
• Sets of Numbers on the Number Line
• Properties of Order
• Solving Inequalities
8. Congruent and Similar Triangles
• Congruent Triangles
• Similar Triangles
9. Mensuration
• Sectors
• Cones and Pyramids
• Sphere
• Areas of Similar Figures
• Volumes of Similar Solids
10. Pythagoras' Theorem and Trigonometry
• Pythagoras' Theorem
• Indirect Measure
• Trigonometrical Ratios
• Trigonometrical Ratios by Using a Calculator
• Solution of Right-angled Triangles
• Applications of Trigonometrical Ratios to Simple Problems
11. Motion Geometry
• Reflection
• Rotation
• Translation
• Enlargement
• Combination of Transformations
12. Statistics I
• Collection and Presentation of Data
• Reading and Drawing of Bar Graphs
• Reading and Drawing of Pie Charts
• Reading and Drawing of Line Graphs and Pictograms
13. Statistics II
• Frequency Distribution
• Mean, Mode and Median of Frequency Distributions
• Types of Averages
14. More Algebraic Manipulations
• Addition and Subtraction of Polynomials
• Multiplication of Polynomials
• Division of Polynomials (Optional)
• Algebraic Fractions and Fractional Equations
• Algebraic Manipulation
• Manipulation of Expressions

New Elem Mathematics 3A (Chp 1-7)

1. Computation and Manipulation
• Indices
• Evaluation of Algebraic Expressions
• Algebraic Fractions
2. Equations
• Equations and Formulae
• Quadratic Equations
• Solving Equations by Formula
• Problems Leading to Quadratic Equation
3. Inequalities
• Solving Inequalities
• Problems Involving Inequalities
• Approximation
4. Coordinate Geometry
• Length and Midpoint of a Line Segment
• Gradient of a Straight Line
• Equation of a Straight Line
5. Functions and Variations
• Functions
• Graphs of a Function
• Inverse Functions
• Direct and Inverse Variation
6. Graphs
• Gradient of a Graph
• Solving Simultaneous Equations by Graphs
• More Problems on Graphs
7. Trigonometry and Bearings
• Trigonometrical ratios of an Obtuse Angle
• Cosine Rule
• Sine Rule
• Bearings
• Trigonometrical Problems Involving Bearings
• Trigonometrical Problems in Three Dimension

New Elem Mathematics 3B (Chp 8-14)

8. Symmetry Properties of a Circle
• Useful Geometrical Properties
• Symmetry Properties of a Circle
9. Angle Properties of a Circle
• Angle Properties of a Circle
• More Angle Properties of a Circle
10. Sets
• The Idea of a Set
• Intersection and Union of Sets
11. More About Sets
• The Universal Set
• Using Venn Diagrams to Solve Problems
12. Rate of Change and Area
• Rate of Change
• Areas under Graphs
13. Transformations
• Reflection
• Rotation
• Translation
• Enlargement
• Shear
• Stretching
• Combination of Transformation
14. Statistics
• Presenting Grouped Data
• Calculation of the Mean
• Histogram for Grouped Data
• Cumulative Frequency
• Percentiles, Quartiles and the Interquartile Range
• More Problems on Cumulative Frequency

New Elem Mathematics 4A (Chp 1-4)

1. Loci
• Locus as a Set of Points
• Geometrical Properties Related to Loci
2. Equations
• Vectors as Directed Line Segments
• Position Vectors and Column Vectors
• More Vector Problems
3. Transformations
• Reflection, Rotation and Translation
• Enlargement, Shear and Stretch
• Combination of Transformations
4. Probability
• Meaning of Probability
• More About Probability
• Combined Events
5. Revision (4B is an overall review of New Elementary Math from 1A through 4A)
• Arithmetic
• Algebra
• Geometry
• Mensuration
• Trigonometry and bearings
• Loci
• Vectors
• Graphs
• Transformations
• Statistics and Probability
• Assessment Paper Set A
• Assessment Paper Set B
• Assessment Paper Set C