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