1.0  Review

1.1  The Real Number System
       A. Integers
       B. Rational Numbers
       C. Irrational Numbers
       D. Real Numbers

1.2  Complex Numbers
       A. Needs to Extend the Real Numbers
       B. Imaginary Numbers
       C. Complex Numbers
       D. Hierarchy of Number Systems

2.0  Review

2.1  Equations of Straight Lines
       A. Two-point Form
       B. Point-slope Form
       C. Slope-intercept Form
       D. Intercept Form
       E. Equations of Special Straight Lines

2.2  Number of Points of Intersection of Two Straight Lines

3.0  Review

3.1  Solving Quadratic Equations by the Factor Method

3.2  Solving Quadratic Equations by the Graphical Method

3.3  Solving Quadratic Equations by the Quadratic Formula

3.4  Relations between the Discriminant and the Nature of Roots

3.5  Practical Problems Leading to Quadratic Equations

3.6  Forming Quadratic Equations

3.7  Relations between Roots and Coefficients
       A. Sum and Product of Two Roots
       B. Use the Relations between Roots and Coefficients to Form Quadratic Equations

4.1  Basic Concept of Functions

4.2  Representations of Functions
       A. Tabular Method
       B. Algebraic Method
       C. Graphical Method

4.3  Notation of a Function: f(x)
       A. Notation of Functions
       B. Values of Functions
       C. Domains and Co-domains of Functions
       D. Four Arithmetic Operations on Functions

5.0  Review

5.1  Features of the Graphs of Quadratic Functions
       A. The Graph of y=ax2
       B. The Graph of y=ax2+bx+c

5.2  Finding the Maximum or Minimum Values of Quadratic Functions by the Algebraic Method
       A. Completing the Square
       B. Exploring the Properties of Quadratic Functions Using the Method of Completing the Square
       C. Solving Application Problems Using the Method of Completing the Square

6.0  Review

6.1  Division of Polynomials

6.2  Remainder Theorem
       A. Polynomial: Definition and Fuction Notation
       B. Remainder Theorem and Its Deduction

6.3  Factor Theorem
       A. Factor Theorem
       B. Use the Factor Theorem to Factorize  Polynomials

8.0  Review

8.1  Rational Indices
       A. The Root of a number
       B. Rational Indices
       C. Laws of Rational Indices

8.2  Exponential Functions
       A. Exponential Functions and Their Graphs
       B. Applications of Exponential Functions

9.1  Meaning of Logarithms
       A. Definition of Logarithms
       B. Properties of Logarithms
       C. Find the Values of Logarithms Using a Calculator

9.2  Logarithmic Functions and Their Graphs

9.3  Exponential Equations and Logarithmic Equations
       A. Exponential Equations
       B. Logarithmic Equations

9.4  Applications of Logarithms
       A. Richter Scale
       B. Intensity Level of Sound
       C. History of Logarithmic Tables and Slide Rules

10.0  Review

10.1  Highest Common Factor and Least Common Multiple
          A. Highest Common Factor (H.C.F.)
          B. Least Common Multiple (L.C.M.)

10.2  Addition and Subtraction of Rational Functions
          A. Rational Functions
          B. Addition and Subtraction of Rational Functions

10.3  Multiplication and Division of Rational Functions

11.0  Review

11.1  Basic Knowledge about Circles
          A. Basic Concepts of a Circle
          B. Special Circles

11.2  Properties of Chords of a Circle
          A. Perpendiculars to Chords
          B. Equal Chords
          C. Circle Passing through Three Non-collinear Points

11.3  Angle Properties of a Circle
          A. Angles at the Centre and Angles at the Circumference
          B. Angles in the Same Segment

11.4  Relationships among Angles, Arcs and Chords
          A. Equal Relations among Angles, Arcs and Chords
          B. Proportion Relations between Angles and Arcs

12.1  Properties of Cyclic Quadrilaterals
          A. Opposite Angles of Cyclic Quadrilaterals
          B. Exterior Angles of Cyclic Quadrilateral

12.2  Tests for Cyclic Quadrilaterals

12.3  Tangents to Circles
          A. Basic Properties of Tangents to Circles
          B. Tangents from an External Point
          C. Common Tangent

12.4  Angles in the Alternate Segments

12.5  Geometric Proofs on Circles
          A. Geometric Proofs from Induction to Deduction
          B. Proofs that Relate Properties of Circles

13.0  Review

13.1  Trigonometric Ratios of Any Angle
          A. Angles of Rotation and Quadrants
          B. Definitions of Trigonometric Ratios of Any Angle
          C. Signs of Trigonometric  Ratios
          D. Patterns of the Values of Trigonometric Ratios
          E. Finding Trigonometric Ratios of Any Angle Using a Calculator

13.2  Trigonometric Identities
          A. Relations among Trigonometric Ratios of the Same Angle
          B. Simplifying Trigonometric Ratios of n·90°±θ to Those of θ

13.3  Graphs of Trigonometric Functions
          A. The Graph of y = sin x
          B. The Graph of y = cos x
          C. The Graph of y = tan x

13.4  Trigonometric Equations
          A. Finding the Corresponding Angles from Given Trigonometric Ratios
          B. Solving Simple Trigonometric Equations
          C. Solving Other Trigonometric Equations