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Contents 1

Ⅰ．Elementary Knowledge 1

1．Some mathematical symbols and notations 1

2．Fractions 6

3．Decimals 6

4．Some geometric figures and their terminology 7

Ⅱ．Inequalities 16

1．Intervals;Absolute value 16

2．Definition 17

3．Inequalities in two variables 22

4．Absolute inequalities 27

5．Applications of inequalities——Maxima and minima 32

Ⅲ．The Remainder Theorem;Synthetic Division 40

1．The remainder theorem 40

2．Synthetic division 42

Ⅳ．Indeterminate Coefficients;Partial Fractions 48

1．Indeterminate coefficients 48

2．Partial fractions 53

Ⅴ．Mathematical Induction;Binomial Theorem 61

1．Mathematical induction 61

2．Binomial theorem 64

Ⅵ．Trigonometric Functions of Compound and MultipleAngles 69

1．Functions of compound angles 69

2．Functions of multiple angles 72

Ⅶ．Transformations of Sums and Products 79

1．Transformation of sums or differences into products 79

2．Transformation of products into sums or differences 83

Ⅷ．The Straight Line 88

1．Coordinates 88

2．Directed line segments 89

4．Symmetry 90

3．Intercepts 90

5．Distance formula 91

6．Division of a line at a given ratio 93

7．Area of a triangle 97

8．Inclination and slope 100

9．Necessary and sufficient condition for two straight lines to be parallel or perpendicular 101

10．Equation of a straight line 102

11．To transform the equation of a straight line from general form into normal form 109

12．Distance from a point to a straight line 109

13．Angular bisector 112

14．Angle between two straight lines 114

15．Concurrent lines 116

Ⅸ．Conic Sections 121

1．The circle 122

2．The ellipse 129

3．The hyperbola 132

4．The parabola 137

5．Directrices of an ellipse and a hyperbola 140

6．Tangents to conic sections 141

Ⅹ．Parametric Equations 152

1．To transform parametric equations into equations involving x and y 152

2．Parametric equations of curves 153

3．Graphs of parametric equations 160

Ⅺ．Polar Coordinates 163

1．Polar coordinates 163

2．Connection between Cartesian and polar coordinate systems 164

3．Polar equations of curves 164

4．Sketching graphs of curves 172

Appendix Ⅰ 179

Answers to Problems 179

Appendix Ⅱ 188

Vocabulary 188