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Introduction / 1

Algebra / 1

1.1 Operations with numbers / 1

1.2 Sequences and series / 3

1.3 Binomial expansion / 10

1.4 Complex number / 11

Module one exercises / 14

2. Functions and equations / 16

2.1 Evaluation and determination / 16

2.2 Discussion of the properties of a function by its graph / 25

2.3 Solving the equations and inequalities by graphing / 40

2.4 Sketching the special functions / 59

2.5 Transforming the functions / 86

2.6 Other forms of the functions or relations / 89

Module two exercises / 96

3. Trigonometry and geometry / 99

3.1 Solutions of triangles and circles / 99

3.2 Trigonometric functions and equations / 109

3.3 Points and vectors / 133

3.4 Angles£¬areas and distances / 139

3.5 Lines and planes / 142

3.6 Intersections and matrices / 146

Module three exercises / 155

Probabilities and statistics / 160

4.1 Statistics / 160

4.2 Regression / 163

4.3 Probability distributions / 167

4.4 Conf idence intervals for means / 174

4.5 Hypothesis test / 177

4.6 The chi-squared distribution / 181

Module four exercises / 185

Calculus / 190

5.1 Equation of the tangent or the normal / 190

5.2 Local extrema and point of inf lection(inf lexion) / 201

5.3 Def inite integral / 206

5.4 Area of the region enclosed / 211

5.5 Volume of revolution about the x-axis or y-axis / 216

5.6 Kinematics / 220

5.7 Related rate of change / 226

5.8 Limits and continuity / 227

5.9 Differential equations / 235

Module f ive exercises / 239

Answers / 243