Bob Miller's Calc for the Clueless: Precalc

Bob Miller's PreCalc for the Clueless, Third Edition,is jam-packed with tips, techniques, and surefire strategies to help students understand and advance in this challenging subject. In this third edition, new features include: Recent changes in the precalculus pedagogy implemented over the past seven years New sections explaining the fundamentals of algebra and trigonometry A new chapter on induction All the math needed for the new SAT Sample problems for every technique and topic

Bob Miller was a lecturer in mathematics at City College of New York for more than 30 years. His principal goal is to make the study of mathematics both easier and enjoyable for students.

Acknowledgments

ix

To the Student

x

Lines, the Straight Kind

1

(8)

Standard Form

1

(8)

Quadratic Equations

9

(6)

Solving a Quadratic (or Higher) by Factoring

9

(2)

The Quadratic Formula

11

(4)

Inequalities, Linear and Quadratic

15

(8)

Linear Inequalities

15

(1)

Quadratic Inequalities

16

(7)

Absolute Value

23

(4)

Exponents---Negative, Fractional

27

(6)

Geometric Formulas and Facts You Must Know

33

(4)

Squares, Rectangles, Boxes, and Cubes

33

(1)

Circles

34

(1)

Other Shapes

34

(3)

Distances, Midpoints, Circles, and Parabolas

37

(4)

Distances

37

(1)

Midpoints

37

(1)

Circles

38

(1)

Parabolas

38

(3)

Functions

41

(16)

Functional Notation

42

(9)

Finding the Ranges and Domains and Sketches of Functions (Beginning)

46

(5)

Composite Functions

51

(2)

Inverse Functions

53

(4)

Linear Systems and More About y = x2

57

(14)

Equations in Twos and Threes

57

(1)

Two Equations in Two Unknowns

57

(6)

Graphing

57

(1)

Algebra: Substitution

58

(2)

Algebra: Elimination

60

(2)

Relating the Graph to the Algebra

62

(1)

Three Equations in Three Unknowns

63

(4)

Graphing a Point in 3D

64

(1)

What Would It Look Like?

65

(2)

y = x2, y = x3, and a Little More

67

(4)

Trigonometry

71

(38)

Angles

71

(2)

Basic Definitions

73

(1)

Multiples of 30°, 45°, 60°, and 90°

74

(3)

Curve Sketching

77

(6)

Identities

83

(4)

Attacking Identities

85

(2)

Trig Equations

87

(5)

Domains and Ranges of the Trig Functions

92

(1)

Double Angles, Half Angles, Sum and Difference of Two Angles

92

(8)

Inverse Trig Functions

100

(4)

Right-Angle Trig

103

(1)

The Law of Sines

104

(3)

Two Angles and a Side

105

(1)

Two Sides and an Angle Opposite One of Those Sides

105

(2)

The Law of Cosines

107

(2)

Curve Sketching

109

(14)

Polynomials

109

(4)

Rational Functions

113

(10)

Vertical Asymptotes

114

(1)

Horizontal Asymptotes

115

(8)

Modern Logarithms

123

(8)

Parabolas II, Ellipses, and Hyperbolas

131

(22)

Systems of Nonlinear Equations

144

(9)

Writing Functions of x, the Algebraic Part of Calculus Word Problems

153

(12)

The Binomial Theorem

165

(4)

The Theory of Equations

169

(8)

Theorem 1: The Fundamental Theorem of Algebra

170

(1)

Theorem 2: Number of Roots

170

(1)

Theorem 3: The Remainder Theorem

170

(1)

Theorem 4: The Factor Theorem

170

(1)

Theorem 5: The Rational Root Theorem

171

(1)

Theorem 6: The Upper and Lower Bounds for Roots Theorem

172

(1)

Theorem 7: Descartes' Rule of Signs

173

(2)

What to Do If Nothing Else Works

175

(2)

Finite Induction

177

(4)

Progressions

181

(10)

Arithmetic Progressions

181

(4)

Finite Geometric Progressions

185

(2)

Infinite Geometric Progressions

187

(4)

Limits

191

(8)

Finite Limits

191

(5)

Limits Going to Infinity

196

(3)

APPENDIX Synthetic Division and Sets

199

(4)

Synthetic Division

199

(1)

Sets

200

(3)

Index

203

(3)

About Bob Miller . . . In His Own Words

206

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Bob Miller's Calc for the Clueless: Precalc

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Author Biography

Table of Contents

Supplemental Materials