Table of Contents

1. Introduction
   1. Completing the Square for Quadratic Expressions (Harder)
   2. Completing the Square Method in Quadratic Functions
2. Numbers And Algebra
   1. Prime Factors - step by step
   2. Factorization - Visual illustration of divisor pairs
   3. Self Assessment : Quadratic Curve's Properties
   4. Determining the Equation of Straight Lines Given Two Points
   5. Slope Intercept Form of Equation of Straight Line - Quiz
   6. Bar Model for Problems on Ratio Rate Direct Proportion
   7. find LCM and GCD
   8. Self Review of Maps and Scales Problems
   9. Fraction Multiplication
   10. Randomized linear simultaneous equations
   11. Basic Algebra Terms
   12. Distributive Law of Multiplication over Addition ( Pictorial)
   13. Indices Part 4 : Negative Integral Indices
   14. Solve Simple Linear Equations
   15. UCSS Math III 2B.1.5 Example 4
   16. Rational Expressions
   17. Rational Expression Unit Test
   18. "Pass the Paper" Problems- Adding & Subtracting REs
   19. Example 4
   20. Guided Practice Sheets
   21. Anchor Activities
   22. Example 1
   23. Simplify Expressions, More Complicated-Section 1.4
   24. Factoring Quadratic Expressions 3
   25. Multiplication Frame, Algebraic Factorisation.
   26. Factorization of Special Products
   27. Expansion of Linear Factors Using Multiplication Frame
   28. Proportional Thinking using Model-Table-Proportion(Algebra) Representations
   29. Solving Equations where Product of Linear Factors Equals Zero
   30. Map Scales (1)
   31. Map Scales(2)
   32. Binomial Multiplication
   33. Completing the square
   34. Magic machine for function
   35. Equivalent Fractions Puzzel
   36. Story of Rice on Chessboard : - Exponential Doubling
   37. sieve of eratosthenes
   38. Sieve of Eratosthenes
   39. Sieve of Eratosthenes
   40. Function Machine
   41. Percentages: Selling Problems, Profit & Loss
   42. Equivalent Linear Equations
   43. Solving Linear Inequalities (Level 2) Game
   44. Significant Figures Self Directed Quiz
   45. Smallest n such that m × n is a perfect square
   46. Smallest k such that m × k is a perfect cube
   47. Finding the ratio x : y given algebraic equation ax + by = cx + dy
   48. Fraction Division5:　x ÷ a/b (Quotitive)
   49. Speed Time Graph for Self Directed Learning (Customizable)
   50. Distance Time Graph For Self Directed Learning
   51. Graphing on Graph Paper
   52. Solving percents with a bar model
   53. Balance Beam Equations
   54. Solving Proportions
   55. Numberline
   56. Adding and subtracting a negative integer
   57. Graphing Linear Equations in 2 Unknowns
   58. Ordered Pairs, Cartesian Coordinates Self Assessment
   59. Operation of 3 Sets #2
   60. Evaluating unknowns in Linear Equations in Two Variables and Graphing the Equations
   61. Linear Functions : Input Variable x and Output Variable y
   62. Speed, Distance & Time in Motion (RACE CAR)
   63. Distance Between Two Points (Length of Line Segment)
   64. Self Assess Distance Betw Two Points(Length of Line Segment)
   65. Forming Equation of a Straight Line Given Graph of Line
   66. Changes in Inequalities due to Multiplication and Division
   67. Fun With Number Pattern
   68. Representing Numbers on a Number Line
   69. Completing the Square Method in Quadratic Functions
   70. Expand Product of Two Linear Expressions (Area Method)
   71. Solve Simple Linear Equations (Apply Balance Concept)
   72. Algebra balance scales
   73. Equation Balance
   74. Graphing of Polynomial Functions Point by Point
   75. Sorting decimals from least to greatest
   76. Factorization of Quadratic Expressions Aided by Multiplication Frame
   77. Rational Expression Unit Pre-Assessment
   78. Function Machine 2
   79. Problem of movement
   80. Quadratic Formula - Approximate Solutions
   81. Coefficients of a general quadratic function
   82. Expand and Simplify Basic Algebraic Expression with Brackets
   83. Plotting graph of a function
   84. Concept of gradient(slope) of a line
   85. Midpoint between two points
   86. Concept of Cartesian coordinates
   87. Solving Simultaneous Linear Inequalities II (Self Directed Practice)
   88. Significant Figures Self Review 2
   89. Solve Simple Linear Equations (II)
   90. Maximum and Minimum Values of Inequalities in variables x and y
   91. Solving Simple Inequalities Game
   92. Copy of Simplifying Algebraic Fractions (Express as a Single fraction)
   93. Linear Equations in Two Variables - Solutions are points on Graph!
   94. Linear Equations in Two Variables - Solutions on the Graph
   95. Factorized Form of Quadratic Function
   96. Factorization involving Special Algebraic Identities (Perfect Squares and Difference of Squares)
   97. Exploration of roots of a quadratic equation (Copy)
   98. Connecting Angle between Two Lines and Trigonometric Ratios
   99. Gradient and Y Intercept of Straight Line & its Equation
   100. Multiplying integers (Copy)
   101. Real Number Classification - Introduction
   102. Place Value for Decimals
   103. Simplifying Combining into Single Algebraic Fraction (Two and Three Terms)
   104. Solve Linear Linear Fractions
   105. Simplifying Algebraic Fractions (Two Terms To be Expressed as Single fraction)
   106. Solving Equation with Expressions on Both Sides and Intersection of Two Graphs
   107. (Self running) Expand and Simplify Basic Algebraic Expression with Brackets
   108. Basic Algebra : Simplifying Expressions (1)
   109. Self Assessment (Record to Google Sheet): Graphs of Quadratic Functions such as +/- (x-p)^2 +q
   110. Shifting Patterns
   111. The Real Number System
   112. Fun with Decimals
   113. Translating between decimal and percentage
   114. Algebric puzzle for (a+b+c)²
   115. Compound Interest 複利息
   116. Compound Interest 複利息 (version with common ratio)
   117. Visualizing Number Patterns with Common Difference
   118. Factorization : Finding the Factor of Distributed Terms
   119. Expansion of Special Products
   120. Combining Simple Algebraic Fractions
   121. Ordering Rational Numbers
   122. Graphing Rational Numbers on a Horizontal Line
   123. Solving Linear Equations involving fractional coefficients and expressions (2)
   124. introduction to LCM
   125. HCF & LCM of Three Numbers by Short Division 以短除法求三個數的HCF和LCM
   126. Solving Linear Equations involving fractional coefficients and expressions (1)
   127. Quadratic Function Machine
   128. Modelling of the Parabolic Shape of the Flower Dome
   129. 複合不等式 Compound inequality (Eng ver)
   130. Representing inequalities on a number line (translated)
   131. Solving Simple Fractional Linear Equation (1)
   132. Real Mastermind
   133. Ordering Rational and Irrational Numbers (Number Sense)
   134. Ordering Irrational Numbers on the Number Line
   135. Rational and Irrational Number Classification
   136. Quadratic Solver Tool
   137. Solving Quadratic Equations by Factorization I (Self Review)
3. Geometry and Measurement
   1. Types of Triangles
   2. Bearings
   3. Angles in Opposite Segments
   4. Angles in the SemiCircle
   5. External Tangents to a Circle
   6. Introduction: Radians
   7. Congruent Triangles 3
   8. Basic Terms in Geometry
   9. Are the triangles congruent?
   10. Congruent Triangles Exploration 1
   11. Example 2
   12. Similar Figures
   13. Congruent Figures Activity
   14. Collinear Points (Definition Prompt)
   15. Triangle Angle Theorems
   16. Geometry Exercise (Basic) Problem 2 : Application of Tangent Radius Property
   17. Geometry Exercise (Basic) Problem 1 : Application of Tangent Radius Property
   18. Area of Parallelograms
   19. Deriving the Area Formula of a Parallelogram
   20. Bearings : Practice with Compass Reference
   21. Area of a Trapezium
   22. Acute Obtuse or Reflex Angles
   23. Angle of Elevation and Depression
   24. 10.2 Angles of elevation and depression(仰角和俯角)
   25. Angle of elevation and depression
   26. Angle of elevation - light house1
   27. Angle of Elevation & Angle of Depression 仰角和俯角
   28. Converse of Pythagoras Theorem : Self Assessment
   29. Lines representing equations of the form x = a and y = c
   30. Mathematical Modelling of Filling of Circular Water Tank
   31. Angle between line AB and radius of the circle (Tangent Radius)
   32. Perpendicular lines and their Gradients
   33. 3D Sphere, Hemisphere Volume and Total Surface Areas
   34. Cone Volume and Total Surface Area
   35. Total Surface Area & Volume of Cylinder (with net shown)
   36. Self Review Mensuration of Hemispherical Bowl
   37. Self Review Mensuration of Composite Cylinder & Hemisphere
   38. Self Review Mensuration of Composite Hemisphere & Cone
   39. Are the triangles congruent?
   40. Arc Length 1
   41. Pythagorean Triple Generator
   42. Indices (Positive Integer Index) : Introduction
   43. Relationship between Arc Length, Area of Sector, Radius and Angle (in degrees)
   44. Exploring the Converse of Pythagoras Theorem
   45. Shortest Distance between a Point and a Line (in Angle Bisector)
   46. Deriving area of trapezium by using a parallelogram
   47. Parallelogram Investigation - Area
   48. Quiz on Solving Right Triangles (Combined) 解直角三角形：合併測驗
   49. Net of cone
   50. Net of pyramid
   51. Net of prism
   52. Net of cylinder
   53. Different nets of cube
   54. Different nets of rectangular prism(cuboid)
   55. Area of kite
   56. Geometric properties of a quadrilateral
   57. Investigation - Corresponding angles, alternate angles and interior angles
   58. Let's Build Prisms
   59. Investigating - Ratios of Sides in a Right Angled Triangle Triangle
   60. Proof Without Words
   61. Pythagoras Theorem (Proof with Calculations)
   62. Pythagoras
   63. MCAS Pythagorean Theorem Self-Test
   64. Leiter an der Wand
   65. Pythagoras Theorem Revision & Practical Applications
   66. Spiral of Pythagoras
   67. Missing Side Lengths
   68. Quiz: Pythagorean Theorem (2A)
   69. More Trouble with Triangles
   70. Cavalieri's Principle (祖暅原理)
   71. Volume of a Pyramid - Cavalieri's Principle
   72. Deplacement, velocity and acceleration in the same visual
4. Statistics and Probability
   1. Tree Diagrams
   2. Permutation Braid, 4 Unique Objects
   3. Mean Median Mode -Tabulated Data with Visual Mode Example 2
   4. Boxplot Game
   5. Dot Plot Interactive
   6. AQR Section 16: Matching a Pie Chart to a Dot Plot
   7. AQR Section 17: Calculating Summary Statistics
   8. AQR Section 17: Dot Plot and Box-and-Whisker Plot
   9. Visualizing Statistical Information
   10. 3 Dice
   11. Probability: Selecting Balls
   12. Computing Simple Probabilities from Tables
   13. Experimental probability
   14. rolling a dice
   15. Example 1
   16. flipping a coin
   17. Probability with Area
   18. dotplot
   19. Mean and Median Practice
   20. measures of center
   21. Averages (Mean, Median, Mode)
   22. AQR Section 17: Mean but Sensitive
   23. Data Visualization
   24. Standard Deviation Investigation
   25. AQR Quick Question 17.3: Mean, Median, and Midrange
   26. Probability
   27. Probability and Tree Diagram
   28. Probability trees
   29. rolling two dice-1
   30. Introduction to Probability ---- The Rolling of a Die
   31. Mean, Median, Mode, and Range
   32. Outlier Influence
   33. UCSS Math II 4.3.2 Example 1
   34. UCSS Math II 4.3.1 Example 3
   35. UCSS Math II 4.3.1 Example 2
   36. Stem and Leaf Plot Template
   37. Interactive Dot Diagram(with Illustration of Mean, Median)
   38. Comparing Histogram, Dot and Stem & Leaf Diagrams
   39. Big Tree Diagram
   40. Displaying grouped data as individual values and as frequency histogram
5. Past Examination Resources
   1. Past Years' Examination O Level Math and Additional Math Compilations