《英语数学》

Contents1

Ⅰ．Elementary Knowledge1

1．Some mathematical symbols and notations1

2．Fractions6

3．Decimals6

4．Some geometric figures and their terminology7

Ⅱ．Inequalities16

1．Intervals;Absolute value16

2．Definition17

3．Inequalities in two variables22

4．Absolute inequalities27

5．Applications of inequalities——Maxima and minima32

Ⅲ．The Remainder Theorem;Synthetic Division40

1．The remainder theorem40

2．Synthetic division42

Ⅳ．Indeterminate Coefficients;Partial Fractions48

1．Indeterminate coefficients48

2．Partial fractions53

Ⅴ．Mathematical Induction;Binomial Theorem61

1．Mathematical induction61

2．Binomial theorem64

Ⅵ．Trigonometric Functions of Compound and MultipleAngles69

1．Functions of compound angles69

2．Functions of multiple angles72

Ⅶ．Transformations of Sums and Products79

1．Transformation of sums or differences into products79

2．Transformation of products into sums or differences83

Ⅷ．The Straight Line88

1．Coordinates88

2．Directed line segments89

4．Symmetry90

3．Intercepts90

5．Distance formula91

6．Division of a line at a given ratio93

7．Area of a triangle97

8．Inclination and slope100

9．Necessary and sufficient condition for two straight lines to be parallel or perpendicular101

10．Equation of a straight line102

11．To transform the equation of a straight line from general form into normal form109

12．Distance from a point to a straight line109

13．Angular bisector112

14．Angle between two straight lines114

15．Concurrent lines116

Ⅸ．Conic Sections121

1．The circle122

2．The ellipse129

3．The hyperbola132

4．The parabola137

5．Directrices of an ellipse and a hyperbola140

6．Tangents to conic sections141

Ⅹ．Parametric Equations152

1．To transform parametric equations into equations involving x and y152

2．Parametric equations of curves153

3．Graphs of parametric equations160

Ⅺ．Polar Coordinates163

1．Polar coordinates163

2．Connection between Cartesian and polar coordinate systems164

3．Polar equations of curves164

4．Sketching graphs of curves172

Appendix Ⅰ179

Answers to Problems179

Appendix Ⅱ188

Vocabulary188