Objective

1.1 Different Types of Angles
A Adjacent Angles on a Straight Line
B Angles at a Point
C Vertically Opposite Angles

• Recognize different types of angles such as adjacent angles on a straight line, angles at a point and vertically opposite angles.
• By using the properties of these angles, find unknowns in simple figures.

1.2 Angles and Lines
A Transversal
B Angles Associated with Parallel Lines
C Identifying Parallel Lines

• Recognize the angles associated with intersecting lines such as corresponding angles, alternate angles and interior angles on the same side.
• Explore the angle properties associated with parallel lines, and use them to find unknowns in simple figures.
• Understand the conditions for two lines to be parallel.

1.3 Angles and Sides of a Triangle
A Angle Sum of a Triangle and Exterior Angle of a Triangle
B Properties of Isosceles Triangles and Equilateral Triangles
C Identifying Isosceles Triangles and Equilateral Triangles

• Revise the property of angle sum of a triangle and use it to find unknowns in simple figures.
• Explore the property of exterior angle of a triangle and use it to find unknowns in simple figures.
• Explore the properties of isosceles triangles and equilateral triangles, and use them to find unknowns in simple figures.
• Understand the conditions for a triangle to be isosceles or equilateral.

1.4 Angles of a Polygon
A Sum of Interior Angles of a Polygon
B Sum of Exterior Angles of a Polygon

• Explore the property of the sum of interior angles of a polygon and use it to find unknowns in simple figures.
• Explore the property of the sum of exterior angles of a polygon and use it to find unknowns in simple figures.

1.5 Tessellation

• Explore which regular polygons can tessellate.

1.6 Construction of Regular Polygons (NF)
A Construction of Regular Polygons Using ruler and Protractor
B Construction of Special Regular Polygons Using Straight Edge and Compasses

• Construct regular polygons using ruler and protractor.
• Construct some special regular polygons using straight edge and compasses.

Objective

2.1 Basic Concept of Deductive Reasoning

• Realize the shortcomings of making judgment by intuition. Hence, lead students to learn the importance of deductive reasoning in studying mathematics.

2.2 Deductive Geometry
A Euclid and 'Elements'
B Definition, Proposition, Axiom and Theorem

• Learn the story about Euclid, his book 'Elements' and his learning attitude.
• Understand the meaning of definition, proposition, axiom and theorem, and their relations.

2.3 Simple Proofs about Angles Related with Lines and Triangles
A Steps of Proof
B Examples of Simple Proofs

• Learn how to present simple proofs about angles related with lines and triangles.

2.4 Simple Proofs about Triangles
A Congruent Triangles
B Isosceles Triangles
C Similar Triangles

• Understand and use the conditions for congruent triangles to perform simple proofs.
• Understand and use the properties and conditions of isosceles triangles to perform simple proofs.
• Understand and use the conditions for similar triangles to perform simple proofs.

Objective

5.1 Factorization of Simple Algebraic Expressions

• Learn to factorize simple algebraic expressions by taking out common factors.

5.2 Manipulation of Simple Algebraic Fractions
A Multiplication and Division of Algebraic Fractions
B Addition and Subtraction of Algebraic Fractions

• Learn to manipulate simple algebraic fractions.

5.3 Formulae and their Manipulations
A Formula and Substitution
B Change of Subject

• Understand the meaning of formulae.
• Learn to use the method of substitution to find unknowns in a formula.
• Learn how to change the subject of a formula.

Objective

6.1 Meaning of Identities

• Understand the difference between equations and identities.
• Learn how to find the unknown constants in an identity.

6.2 Some Important Algebraic Identities
A Difference of Two Squares
B Perfect Square

• Learn the identity of the difference of two squares.
• Learn the identities of the perfect square.
• Use the above identities to expand expressions or find the values of expressions.

Objective

7.1 Factorization by Grouping Terms Method

• Learn to factorize simple algebraic expressions by the grouping terms method.

7.2 Factorization by Using Identities
A Using Identity of Difference of Two Squares
B Using Identities of Perfect Square
C Using Identities of Sum and Difference of Two Cubes (NF)

• Learn to factorize by using the identity of the difference of two squares.
• Learn to factorize by using the identities of the perfect square.
• Learn to factorize by using the identities of the sum and difference of two cubes.

7.3 Factorization by Cross-method
A Quadratic Polynomials in One Variable x2+qx+r
B Quadratic Polynomials in One Variable px2+qx+r
C Quadratic Polynomials in Two Variables

• Learn to factorize quadratic polynomials in one variable x2+qx+r by the cross-method.
• Learn to factorize quadratic polynomials in one variable px2+qx+r by the cross-method.
• Learn to factorize quadratic polynomials in two variables by the cross-method.

Objective

3.1 Significant Figures and Approximate Values
A Meaning of Significant Figures
B Significant Figures and Rounding Off

• Understand the meaning of significant figures and the skills of rounding off numbers.

3.2 Errors
A Absolute Error
B Maximum Absolute Error
C Relative Error
D Percentage Error

• Understand and calculate different types of errors such as absolute error, maximum absolute error, relative error and percentage error.

Objective

4.1 Rate

• Learn the concept of rate.

4.2 Ratio
A Basic Concept of Ratio
B Continued Ratio

• Learn the concept of ratio and continued ratio.
• Learn the properties of ratio and continued ratio.

4.3 Applications of Ratios
A Equal Ratios
B Similar Figures
C Scale

• Learn the applications of equal ratios on similar figures and scale.

Objective

8.1 Basic Concept of Inequalities
A What Are Inequalities?
B Solutions of Inequalities and their Graphical Representations
C Basic Properties of Inequalities

• Learn the inequalities and the inequality signs.
• Understand the law of trigonometry.
• Learn how to represent the solutions of inequalities graphically.
• Learn the basic properties of inequalities.

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

• Introduce the meaning of linear inequalities in one unknown.
• Learn the techniques of solving linear inequalities in one unknown.                
• Learn how to apply inequalities to solve simple problems.

Objective

9.1 Laws of Positive Integral Indices

• Learn the five laws of indices with positive integral indices.

9.2 Zero and Negative Integral Indices

• Understand the meanings of zero and negative integral indices.

9.3 Simple Equations with Unknown Indices

• Learn how to solve simple equations with unknown indices.

9.4 Scientific Notation
A Meaning of Scientific Notation
B Applications of Scientific Notation

• Introduce the meaning of scientific notation.
• Use scientific notation to express and evaluate extremely large or small numbers.

9.5 Different Numeral Systems
A Denary System
B Binary System
C Hexadecimal System
D Conversions between Denary System and Other Numeral Systems

• Learn the denary system and the place values in denary numbers.
• Learn the binary system and the place values in binary numbers.
• Learn the hexadecimal system and the place values in hexadecimal numbers.
• Learn the conversions between the denary system and other numeral systems.

Objective

 10.1 Rational Numbers

• Introduce the definition of rational numbers.

10.2 Square Roots and Surds
A Square Roots
B       and Surds

• Introduce the meanings of square roots and surds.

10.3 Irrational Numbers

• Introduce the meaning of irrational numbers.
• Learn to represent irrational numbers on a number line.

10.4 Manipulation of Surds
A Properties of Surds
B Rationalization of Denominators
C Surd in its Simplest Form
D Addition, Subtraction and Multiplication of Surds

• Learn the properties of surds.
• Learn how to rationalize fractions
• Learn how to express surds in their simplest forms.
• Learn the addition, subtraction and multiplication of surds.

Objective

11.1 Pythagoras' Theorem and its Proofs
A Pythagoras' Theorem
B Proofs of Pythagoras' Theorem
C Surds and Irrational Numbers
D Converse of Pythagoras' Theorem

• Learn Pythagoras' theorem.
• Admire different proofs of Pythagoras' theorem (including the method used in proving 'Kou–ku theorem').
• Introduce the discovery of surds and irrational numbers.
• Learn the story about the First Mathematical Crisis.
• Learn the converse of Pythagoras' theorem.

11.2 Applications of Pythagoras' Theorem and its Converse

• Use Pythagoras' theorem and its converse to solve problems in real-life.

Objective

12.1 Circles
A Circumference of Circles
B Area of Circles

• Review the formula for calculating the circumferences of circles.           
• Explore the formula for calculating the areas of circles. 
• Apply the formulae to calculate the circumferences and areas of circles.

12.2 Arcs and Sectors
A Length of Arcs
B Area of Sectors

• Introduce arcs and angles at the centre.
• Learn the formula for calculating arc lengths.
• Introduce sectors and the angle of the sector.
• Learn the formula for calculating the areas of sectors.

12.3 Cylinders
A Volume of Cylinders
B Total Surface Area of Cylinders

• Understand and use formulae to calculate the volumes and total surface areas of cylinders.

Objective

13.1 Introduction to Trigonometric Ratios

• Introduce the trigonometric ratios.

13.2 Sine Ratio
A Concept of Sine Ratio
B Finding Sine Ratio Using Calculators
C Using Sine Ratio to Find Unknowns in Right-Angled Triangles

• Learn the concept of sine ratio of acute angle θ.
• Find sine ratio by using calculators and θ from a given value of sin θ.
• Use sine ratio to solve right-angled triangles.

13.3 Cosine Ratio
A Concept of Cosine Ratio
B Finding Cosine Ratio Using Calculators
C Using Cosine Ratio to Find Unknowns in Right-Angled Triangles

• Learn the concept of cosine ratio of acute angle θ.
• Find cosine ratio by using calculators and θ from a given value of cos θ.
• Use cosine ratio to solve right-angled triangles.

13.4 Tangent Ratio
A Concept of Tangent Ratio
B Finding Tangent Ratio Using Calculators
C Using Tangent Ratio to Find Unknowns in Right-Angled Triangles

• Learn the concept of tangent ratio of acute angle θ.
• Find tangent ratio by using calculators and θ from a given value of tan θ.
• Use tangent ratio to solve right-angled triangles.

13.5 Simple Applications of Trigonometric Ratios
A Solving Problems Involving Plane Figures
B Solving Real-life Problems

• Use trigonometric ratios to solve simple problems involving plane figures and real-life problems.

13.6 Trigonometric Ratios on a Unit Circle

• Learn how to use the relation between x-, y-coordinates of points on a unit circle and the acute angle θ on a coordinate plane to define trigonometric ratios.
• Explore the relation between the size of θ and the value of trigonometric ratios.

Objective

14.1 Frequency Distribution and its Graphical Representation
A Review on Histograms
B Frequency Polygons and Curves
C Cumulative Frequency Polygons and Curves

• Review on how to construct a histogram.
• Learn frequency polygons and frequency curves.
• Learn cumulative frequency polygons and cumulative frequency curves.
• Learn how to obtain percentiles, quartiles and medians from cumulative frequency polygons or cumulative frequency curves.

14.2 Choosing an Appropriate Diagram to Present Data

• Learn to choose an appropriate diagram according to the nature of the data and the characteristics of the diagram.

14.3 Abuses of Statistical Diagrams

• Understand that some people intend to use wrong presentations in order to mislead readers to have a wrong perception on the information presented from the diagram.