Objective

1.1 Linear Equations in Two Unknowns and Their Graphs

• Recognize that a linear equation in two unknowns has an infinite number of solutions.
• Plot and explore the graphs of linear equations in two unknowns.

1.2 Simultaneous Linear Equations in Two Unknowns and Their Solutions
A Graphical Method
B Algebraic Methods
C Some Special Simultaneous Linear Equations in Two Unknowns

• Understand the concept of simultaneous linear equations in two unknowns.
• Learn how to solve simultaneous equations in two unknowns by graphical method.
• Learn how to solve simultaneous equations in two unknowns by algebraic methods - the method of substitution and the method of elimination.
• Learn some special simultaneous equations in two unknowns.

Objective

2.1 More about Percentage Increase and Decrease
A Percentage Change
B Successive Percentage Increase
C Successive Percentage Decrease
D Further Applications of Percentages

• Learn the formula for percentage change.
• Apply percentages to solve problems involving successive changes, growth and depreciation.
• Apply percentages to solve further practical problems involving component changes.

2.2 Interest
A Simple Interest
B Compound Interest

• Understand the concepts of simple interest and compound interest.
• Apply percentages to solve problems involving simple interest and compound interest.

2.3 Taxation
A Rates
B Property Tax
C Profits Tax
D Salaries Tax

• Understand different types of taxation in Hong Kong, including rates, property tax, profits tax and salaries tax.

Objective

3.1 Distance between Any Two Points on a Plane

• Understand and apply the distance formula to find the distance between any two points on a plane.

3.2 Slope of a Straight Line
A Slope
B Inclination

• Understand the concept of the slope of a straight line on a coordinate plane.
• Realize and apply the formula of slope.

3.3 Parallel and Perpendicular Lines
A Parallel Lines
B Perpendicular Lines

• Realize the conditions for two straight lines to be parallel or perpendicular on a coordinate plane.
• Use the relationship between the slopes of a pair of parallel lines or perpendicular lines to solve some geometrical problems.

Objective

4.1 Important Lines in a Triangle

• Realize the important lines in a triangle, including angle bisector, median, altitude and perpendicular bisector.
• Use the definition of the important lines in a triangle to perform proofs.

4.2 Relationship among the Lines in a Triangle
A Relationship among the Three Sides of a Triangle
B Centres of a Triangle
C Construction of Centres of a Triangle by Compasses and Straight Edge

• Explore and realize the following relationship among the lines in a triangle:
(a)   Triangle inequality
(b)   The three angle bisectors, medians, altitudes and perpendicular bisectors in a triangle intersect at a point respectively.
• Explore and realize the properties of centres of a triangle, including incentre, centroid, orthocentre and circumcentre.
• Construct the centres of a triangle by compasses and straight edge.

Objective

5.1   Quadrilaterals

• Realize the definition of quadrilaterals and the related terminology and properties.

5.2   Parallelograms
A Properties of Parallelograms
B Identifying Parallelograms

• Investigate the properties of parallelograms.
• Apply the properties of parallelograms to solve problems.
• Realize the conditions for parallelograms, and learn to identify parallelograms.

5.3   Rectangles, Squares, Rhombuses and Trapeziums
A Rectangles
B Squares
C Rhombuses
D Trapeziums

• Realize the properties of some special quadrilaterals, including rectangles, squares, rhombuses and trapeziums.
• Apply the properties of rectangles, squares, rhombuses and trapeziums to solve problems.

5.4   Simple Proofs Related to Parallelograms

• Apply the properties of different kinds of parallelograms to perform simple proofs.

5.5   Mid-point Theorem

• Realize the mid-point theorem and apply it to solve problems.

5.6   Intercept Theorem

• Realize the intercept theorem and apply it to solve problems.

Objective

6.1   Symmetries of Solids
A Reflectional and Rotational Symmetries of Solids
B Symmetries of Regular Polyhedra

• Understand the concepts of reflectional and rotational symmetries of solids.
• Realize the reflectional and rotational symmetries of cubes and regular tetrahedra.
• Explore the reflectional and rotational symmetries of other regular polyhedra.

6.2   Nets of Solids

• Understand and learn to design a net for a solid.
• Realize the relationships among the vertices and the faces of a solid formed by a net.

6.3   2-D Representations of Solids
A Orthographic Views of Solids
B Identifying Solids from their Orthographic Views

• Understand the limitations of a 2-D representation.
• Learn to draw the orthographic views of a solid and understand the related concepts.
• Sketch the solid according to its orthographic views.
• Draw the solid on the isometric grid according to its orthographic views.

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

• Understand the concept of the projection of a point or a line segment on a plane.
• Learn to identify the angle between a line and a plane.
• Learn to identify the angle between two planes.
• Solve practical problems involving lines and planes in a solid.

6.5   More about Solids
A Euler's Formula
B Duality of Regular Polyhedra

• Realize the Euler's formula.
• Explore the duality of regular polyhedra.

Objective

7.1 Pyramids
A Volume of Pyramids
B Total Surface Area of Pyramids

• Learn the names of different parts of a pyramid.
• Learn the properties of right pyramids and regular pyramids.
• Understand and learn how to use formulae to calculate the volume and the total surface area of a pyramid.
• Learn the definition of a frustum of pyramid.

7.2 Circular Cones
A Volume of Right Circular Cones
B Total Surface Area of Right Circular Cones

• Learn the names of different parts of a cylinder.
• Understand and learn how to use formulae to calculate the volume and the total surface area of a cylinder.

7.3 Spheres
A Volume of Spheres
B Surface Area of Spheres

• Learn the names of different parts of a sphere.
• Understand and learn how to use formulae to calculate the volume and the surface area of a sphere.

7.4 Formulae for Lengths, Areas and Volumes

• Learn how to distinguish the formulae for lengths, areas and volumes.

7.5 Similar Figures

• Explore the relationship between lengths and areas of similar plane figures.
• Explore the relationship between lengths, areas and volumes of similar solids.
• Understand and learn how to use the relationship between lengths, areas and volumes of similar figures to do calculation.

Objective

8.1 Trigonometric Ratios of Special Angles

• Explore the exact trigonometric ratios of the special angles 30°, 45° and 60°.

8.2 Finding Trigonometric Ratios by Constructing Right-Angled Triangles

• Learn how to construct a right-angled triangle from a given trigonometric ratio, so as to find the other two trigonometric ratios.

8.3 Trigonometric Identities
A Basic Trigonometric Identities
B Trigonometric Ratios of Complementary Angles
C Proof of Simple Trigonometric Identities

• Explore the basic trigonometric identities, and use them to simplify expressions.
• Learn how to use trigonometric identities to find the other two trigonometric ratios from a given trigonometric ratio.
• Explore the trigonometric identities for complementary angles, and use them to simplify expressions.
• Learn how to use trigonometric identities to solve trigonometric equations.
• Learn how to prove simple trigonometric identities.

Objective

9.1 Simple Practical Applications of Trigonometry

• Learn how to apply trigonometric ratios to solve simple problems

9.2 Applications of Trigonometry to Rectilinear Figures

• Learn how to apply trigonometric ratios to solve problems on rectilinear figures.

9.3 Gradients
A Gradient of a Road
B Finding Gradient from a Map

• Learn the concept of gradient of a road.
• Learn how to find gradients from a map.
• Learn how to solve daily-life problems on gradients.

9.4 Angles of Elevation and Depression

• Learn the concepts of angles of elevation and depression.
• Learn how to solve problems on angles of elevation and depression

9.5 Bearings
A Simple Bearings
B Problems Involving Bearings

• Learn the concepts of two kinds of bearings, which are true bearing and compass bearing.
• Learn how to solve problems on bearings.

Objective

10.1 Point of Division
A Mid-point
B Internal Point of Division (NF)

• Learn the mid-point formula.
• Learn the section formula for internal division.

10.2 Using Analytic Approach to Prove Results Relating to Rectilinear Figures (NF)

• Learn to use the analytic approach to prove results relating to rectilinear figures.
• Learn to choose between the analytic approach and the deductive approach in performing proofs.

Objective

11.1 Introduction to General Tendency

• Learn the concept of central tendency.
• Learn that averages are used to reflect the central tendency of data sets.

11.2 Arithmetic Means
A Arithmetic Means of Ungrouped Data
B Arithmetic Means of Grouped Data

• Learn the definition of arithmetic mean and its applications.
• Learn to find arithmetic means of ungrouped data from frequency distribution tables.
• Learn to find arithmetic means of grouped data from frequency distribution tables.

11.3 Medians
A Medians of Ungrouped Data
B Medians of Grouped Data

• Learn the definition of median and its applications.
• Learn to find medians of data from frequency distribution tables.
• Review how to find medians of data from cumulative frequency polygons/curves.

11.4 Modes and Modal Classes
A Introduction to Modes
B Modal Classes of Grouped Data

• Learn the definition of mode/modal class and its applications.
• Learn to find modal classes of grouped data from frequency distribution tables.

11.5 Comparing Different Types of Averages
A Measuring the Central Tendency with Different Averages
B Comparing Two Sets of Data with Different Types of Averages

• Compare the characteristics of different averages.
• Learn to choose the appropriate averages in different situations to reflect the central tendency.
• Understand the limitations of using only one average to compare two different groups of data.

11.6 Misuses of Averages

• Understand the consequences of the misuses of averages.
• Understand how business people may use averages to mislead customers.
• Learn to determine whether the averages used to reflect central tendency are appropriate

11.7 Further Investigations on Averages

• Learn the effects on the averages when the data sets are modified.

11.8 Weighted Mean

• Learn the definition of weighted mean.
• Learn to find the weighted means of data sets.

Objective

12.1 Probability

• Learn the basic concept of probability and the definitions of related terms.
• Learn the nature of probability.
• Know the application and calculation of probability in daily life.

12.2 Further Problems on Probability
A Listing Possible Outcomes by Tree Diagrams or in Tables
B Geometric Probability

• Learn to use tree diagrams and tables to solve further problems on probability.
• Learn to use the counting principle to find the total number of possible outcomes.
• Learn the idea of geometric probability.

12.3 Experimental Probability

• Learn that the probability introduced previously is the theoretical probability.
• Learn the meaning of experimental probability and how to find it.
• Understand the difference and relationship between theoretical probability and experimental probability.

12.4 Expected Value