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Unit 1 Algebraic Expression 1

Lesson 1 Multiplication,Addition and Subtraction 1

Lesson 2 Expansion of Two Brackets 4

Lesson 3 Squares and Harder Expansions 6

Lesson 4 Yang Huei s Triangle 8

Unit 2 Factorising 12

Lesson 1 Factorising Quadratic Expressions 12

Lesson 2 Harder Factorising 15

Lesson 3 Factor Theorem 18

Lesson 4 The Factors of a3-b3 and a3+b3 20

Lesson 1 Simplification of Fractions 23

Unit 3 Fractions and Roots 23

Lesson 2 Addition,Subtraction and Division 26

Lesson 3 Surds(I) 30

Lesson 4 Surds(II) 33

Unit 4 Indices,Logarithms and Eqnations 37

Lesson 1 Indices 37

Lesson 2 Logarithms(I) 41

Lesson 3 Logarithms(II) 45

Lesson 4 Simple Equation 49

Unit 5 Equation 52

Lesson 1 Solution of the Quadratic Equations 52

Lesson 2 Properties of the Roots of a Quadratic Equation 56

Lesson 3 Solution of the Linear Equations 60

Lesson 4 Disguised Quadratic Equations 63

Unit 6 Mapping and Function 66

Lesson 1 Concept of a Function 68

Lesson 2 Characteristics of a Function 72

Lesson 3 Solving Absolute Value Inequalities and Quadratic Inequalities 76

Lesson 4 Powerful and Colorful Man in the History of Mathematics 79

Unit 7 Related Functions 81

Lesson 1 Exponential Functions 81

Lesson 2 Logarithmic Functions 86

Lesson 3 Quadratic Functions 89

Lesson 4 Achilles Can Never Overtake the Tortoise 91

Unit 8 Trigonometric Formulas 93

Lesson 1 Radian Measurement of Angles 94

Lesson 2 Trigonometric Functions of Any Angle 99

Lesson 3 Addition Laws 102

Lesson 4 Double-Angle and Half-Angle Identities 107

Unit 9 Graphs and Characteristics of a Trigonometric Function 110

Lesson 1 Graphing Sine and Cosine Functions 111

Lesson 2 The Graph of the Function y=Asin(ωx+φ) 115

Lesson 3 The Characteristics of Tangent Function 120

Lesson 4 Sine and Cosine Rules 124

Unit 10 The Appliance of the Function 127

Lesson 1 Solving Practical Problems 127

Lesson 2 Using of the Trigonometry 130

Lesson 3 Maths History-a Story of Euler 134

Lesson 4 A Test of the Function 135

Lesson 1 Some Necessary Definitions and Designations 138

Unit 11 Vectors(I) 138

Lesson 2 The Sum of Vectors(I) 142

Lesson 3 The Sum of Vectors(II) 146

Lesson 4 Multiplication of a Vector by a Scalar 150

Unit 12 Vectors(II) 154

Lesson 1 The Condition of Complanarity of Vectors 154

Lesson 2 Scalar Product of Vectors 158

Lesson 3 Use the XOY System to Denote Vectors in Plane 162

Lesson 4 The Condition of Collinear Vectors and Orthogonal Vectors 166

Unit 13 Complex Number 170

Lesson 1 Definition of a Complex Number 170

Lesson 2 Properties of the Operations of Addition and Multiplication 173

Lesson 3 Trigonometric Form 177

Lesson 4 Multiplication and Division of Complex Number 181

Unit 14 The Probability(I) 185

Lesson 1 Permutations 185

Lesson 2 Combinations 189

Lesson 3 About Probability 192

Lesson 4 More Examples of Experiments 195

Unit 15 The Probability(II) 199

Lesson 1 Definition of Probalility 199

Lesson 2 Examples of Probability 203

Lesson 3 Find the Probability of an Event 207

Lesson 4 Examples of Computing the Probabilities 210

Lesson 1 Limits(I) 214

Unit 16 Limits 214

Lesson 2 Limits(II) 218

Lesson 3 Definition of Limit 220

Lesson 4 Theorems on Limits 224

Unit 17 The Definition of Derivative and Its Geometric Interpretation 229

Lesson 1 The Definition of the Derivative 229

Lesson 2 Differentiating Constants and axn 233

Lesson 3 Geometric Interpretation of the Derivative 236

Lesson 4 The Equation of Tangents and Normals 239

Unit 18 Continuity and Limits of Sequences 242

Lesson 1 Continuity and One-sided Limits 242

Lesson 2 Limits at Infinity and Infinits Limits 246

Lesson 3 Limits of Two Important Functions 249

Lesson 4 Limits of Sequences 251

Unit 19 Theorems on Differentiation 254

Lesson 1 Theorems on Differentiation of Function 254

Lesson 2 The Chain Rule-the Derivative of Function of Functions 258

Lesson 3 Intervals of the Function 261

Lesson 4 Stationary Values 264

Unit 20 Integration 267

Lesson 1 Differentiation Reversed 267

Lesson 2 Using Integration to Find an Area 270

Lesson 3 The Integration of Sinx and Cosx 274

Lesson 4 The Derivative of f(x)=Inx and f(x)=ex 277

Appendix I Keys 280

Appendix II Vocabulary 298

Appendix III Reference Books 313