Outline
JC-Maths with Mr Downes
- Author:
- Ronan Downes
Table of Contents
S1 \ 01 Basic Computation
S1 \ 02 HCF & LCM
S1 \ 03 Directed Numbers
- Horizontal, vertical and slanted Number Lines.
- Quiz on Number Line
- Addition and Subtraction of Directed Numbers (1)
- Quiz on Addition and Subtraction of Directed Numbers (1)
- Addition and Subtraction of Directed Numbers (2)
- Quiz on Addition and Subtraction of Directed Numbers (2)
- Quiz on Multiplication and Division of Directed Numbers
S1 \ 04 Introduction to Algebra
S1 \ 05 Introduction to Polynomials
S1 \ 06 | Introduction to Geometry
S1 \ 07 Transformations and Symmetries
S1 \ 08 Introduction to Coordinates
- Introduction to Rectangular Coordinates
- Quiz on Rectangular Coordinates (1) 直角坐標測驗1
- Quiz on Rectangular Coordinates (2) 直角坐標測驗2
- Quiz on Points Lying on Vertical or Horizontal Line Segments 水平或鉛垂線段上的點
- Length of Horizontal or Vertical Line Segments 水平或鉛垂線段的長度
- Introduction to Polar Coordinates 極坐標簡介
- Quiz on Polar Coordinates (1) 極坐標測驗1
- Quiz on Polar Coordinates (2) 極坐標測驗2
S1 \ 09 Transformations in Cartesian Plane
S1 \ 10 Percentage(1)
S1 \ 11 Angles associated with Parallel Lines
S1 \ 12 Congruent Triangles
S1 \ 13 Similar Triangles
- Concept of Similarity 相似的概念
- Quiz on Finding Unknowns in Similar Rectangles 求相似長方形中的未知量：測驗
- Quiz on Naming of Congruent & Similar Triangles 全等及相似三角形的命名：測驗
- Conditions for Similarity of Triangles (1) 相似三角形的判別條件(1)
- Conditions for Similarity of Triangles (2) 相似三角形的判別條件(2)
- Conditions for Similarity of Triangles (3) 相似三角形的判別條件(3)
- Summary of Conditions for Similarity of Triangles 相似三角形的判定條件：總結
S1 \ 14 Area & Volume(1)
S1 \ 15 Construction and Interpretation of Simple Diagrams and Graphs
S2 \ 01 Ratios
S2 \ 02 Identities, Factorization
- Equations & Identities 方程與恆等式
- Sum of Squares & Perfect Square 平方和與完全平方
- Quiz on Factorization of Quadratic Polynomials (Table Method) 因式分解一元二次多項式(表格法)：測驗
- Quiz on Factorization of Quadratic Polynomials (Cross Method) 因式分解一元二次多項式(十字相乘法)：測驗
- Difference of Two Squares 平方差 (1)
- Difference of Two Squares 平方差 (2)
- Quiz on Factorization of Difference of Squares | 平方差的因式分解：測驗
- Magical Squaring 兩位數平方速算
S2 \ 03 Simultaneous Linear Equations
S2 \ 04 Approximation & Errors
S2 \ 05 Angles of Triangles & Polygons
- Exterior Angles of Polygons
- Folding an A4 Paper into an Equilateral Triangle 用A4紙摺出等邊三角形
- 尋找等腰三角形 Isosceles Triangle Hunt
- Interior & Exterior Angles of Triangles 三角形內角和及外角
- Quiz on Interior & Exterior Angles of Triangles 三角形內角和及外角：測驗
- Sum of Interior Angles of Polygons 多邊形內角和
- Sum of Exterior Angles of Polygons 多邊形外角和
- 多邊形的外角和
S2 \ 06 Radicals and Pythagoras' Theorem
S2 \ 07 Trigonometry
- Copy of Quiz on Solving Right Triangles (Finding Angles) 解直角三角形：測驗2（求角度）
- Quiz on Solving Right Triangles (Combined) 解直角三角形：合併測驗
- Trigonometric Ratios of Special Angles 特殊角的三角比
- Relations Among Trigonometric Ratios 三角比的關係
- Trigonometric Ratios: Sine 三角比：正弦
- Trigonometric Ratios: Cosine & Tangent 三角比：餘弦和正切
- Quiz on Opposite, Adjacent & Hypotenuse 辨認對邊、鄰邊、斜邊：測驗
- Quiz on Trigonometric Ratios 辨認三角比：測驗
- Quiz on Solving Right Triangles (Finding Side Lengths) 解直角三角形：測驗1（求邊長）
S2 \ 08 Area & Volume(2)
S3 \ 01 Inequalities
S3 \ 02 Law of Integer Exponential | Laws of Indices
S3 \ 03 Continued/More 3D Figures
S3 \ 04 Measures of Central Tendency
S3 \ 05 Special Lines in Triangles
S3 \ 06 Percentage(2)
S3 \ 07 Applications of Trigonometry
S3 \ 08 Coordinate Geometry of a Straight Line
- Copy of Quiz on Mid-point 中點：測驗
- Distance between Two Points 兩點距離
- 兩點距離：測驗 Quiz on Distance between Two Points
- Meaning of Slope 斜率的意義
- Slope 斜率
- Quiz on Slope (1) | 斜率測驗(1)
- Quiz on Slope (2) | 斜率測驗(2)
- Quiz on Slope (3) | 斜率測驗(3)
- Quiz on Slope of Parallel Lines and Perpendicular Lines 平行線和垂直線的斜率：測驗
- Make a Linear Function
- 63=64=65 ?
S3 \ 09 Probability | Introduction to Probability
S3 \ 10 Quadrilaterals
S3 \ 11 Area and Volume(3)
- Trisecting the Cube into 3 Pyramids
- Building Pyramids 建造角錐體
- Relationship between Volume and Surface Area of a Sphere
- Cone Anatomy
- Curved Surface Area of a Cone 圓錐的曲面面積
- Building Cones 建造圓錐體
- Surface Area of a Sphere (Mnemonic) 球體的表面面積（記憶法）
- Quiz on Formula about Area and Volume 面積及體積公式：測驗
- Frustum | 平截頭體
- Ratio of Areas and Volumes of Similar Figures 相似圖形的面積比和體積比
S4 \ 01 Measures of Dispersion
- Quartiles and Box Plot (one data set) 四分位數與框線圖（一組數據）
- Quartiles and Box Plot (two data sets) 四分位數與框線圖（比較兩組數據）
- Quiz on Quartiles and Box Plot 四分位數與框線圖：測驗
- Matching Histograms to Boxplots 配對組織圖和框線圖
- Standard Deviation (one data set) 標準差（一組數據）
- Standard Deviation (two data sets) 標準差（比較兩組數據）
- 標準差：測驗
- Standard Deviation of a Large Set of Data 大量數據的標準差
- Standard Score 標準分
S4 \ 02 Equation of Straight Lines
- Graphs of Linear Equations in Two Unknowns
- Equation of Straight Lines 直線的方程
- Steps in Finding Equation of Straight Lines 求直線方程的步驟
- Quiz on Equation of Straight Lines 直線的方程：測驗
- Reading Slopes from Equation of Straight Lines 由直線方程讀取斜率
- Comparing Equations of Two Straight Lines 比較兩條直線的方程
- Equations of Parallel Lines and Perpendicular Lines 平行線和垂直線方程
S4 \ 03 Trajectory | Loci
S4 \ 04 Equation of Circles
S4 \ 05 Basic Properties of Circles
- Basic Terms about Circles 圓的基本用語
- Arcs and Angles at Centre/ Circumference 弧、圓心角與圓周角
- Inscribed Angle Theorem (V1)
- Inscribed Angle Theorem Dance: Take 2!
- Spotlight 探射燈
- Right Triangles in a Circle 圓內的直角三角形
- Angle at Centre & Angle at Circumference: Proof 圓心角與圓周角：証明
- Cyclic Quadrilaterals (IAT: Corollary 3)
- Quiz on Angles in a Circle 圓內的角：測驗
- Cyclic Quadrilaterals and Concyclic Points 圓內接四邊形與共圓點
- Tangent of a Circle 圓的切線
- Tangent to Circle at a Point 由圓周上的點作切線
- Tangents to Circle from External Point 由外點引切線
- Angle in Alternate Segment 內錯弓形的圓周角
- Opposite Angles of Cyclic Quadrilaterals (with tangent-chord angles)
- Relationships among 3 Circle Theorems 三個圓定理的關係
- Amazing Circles (1)
- Amazing Circles (2)
S4 \ 06 Introduction to Functions
S4 \ 07 Quadratic Equations & Quadratic Functions
- Quiz on Quadratic Formula 二次公式：測驗
- Quiz on Discriminant 判別式：測驗
- Quadratic Function Calculator 二次函數計算器
- General Form of Quadratic Functions 二次函數的圖像：一般式
- General Form of Quadratic Functions(2) 二次函數的圖像：一般式(2)
- Quiz on Features of Quadratic Graphs 二次函數圖像的特徵：測驗
- Vertex Form of Quadratic Functions 二次函數的圖像：頂點式
- Vertex Form of Quadratic Functions(2) 二次函數的圖像：頂點式(2)
- Quiz on Signs of Coefficients of Quadratic Functions 二次函數係數的正負號：測驗
- 配方法 Completing the Square
- Different Forms of Quadratic Functions 二次函數的不同形式
- Quiz on Vertex Form of Quadratic Functions 二次函數的頂點式：測驗
- Life Examples of Quadratic Functions 生活中的二次函數
S4 \ 08 continued polynomials | More about Polynomials
S4 \ 09 Variations
S5 \ 01 Continued/more Inequalities |
S5 \ 02 Exponential and Logarithmic Functions
S5 \ 03 Arithmetic and geometric sequence
S5 \ 04 Continued Trigonometry
S5 \ 05 Continued Trigonometry Application
- Sine Formula 正弦公式
- Proof without words: Cosine Rule (餘弦公式)
- Using Sine & Cosine Formulae 運用正弦和餘弦公式
- Solving Triangles (SSA case) 解任意三角形(SSA情況)
- Area Formulas for Triangles 三角形面積公式
- Heron's Formula 希羅公式
- HKDSE Sample Paper I #18
- HKDSE Practice Paper I #18
- HKDSE 2012 Paper I #18
- HKDSE 2013 Paper I #18
- HKDSE 2014 Paper I #17
- HKDSE 2015 Paper I #19
- HKDSE 2016 Paper I #19
- HKDSE 2017 Paper I #19
- HKDSE 2018 Paper I #17
- HKDSE 2019 Paper I #18
- HKDSE 2020 Paper I #19
- A Formula for Finding Angle between Two Planes 計算兩平面之交角的公式
- Folding Aeroplane (HKCEE 1999 )
S5 \ 06 Linear Inequalities in Two Unknowns
S6 \ 01 Permutations & Combinations
S6 \ 02 Continued Probability
S6 \ 03 Function Transformations
S6 \ 04 Complex Numbers
S6 \ 05 Travel Graph