Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, Algebra II For Dummies, Algebra II Workbook For Dummies, and oodles of other Dummies titles. She was a Professor of Mathematics at Bradley University in Peoria, Illinois, for more than 30??years.

Introduction 1

What You’ll Find 1

How This Workbook Is Organized 2

Part 1: Questions 2

Part 2: Answers 3

Beyond the Book 3

Where to Go for Additional Help 3

Part 1: The Questions 5

Chapter 1: Reviewing Algebra Basics 7

The Problems You’ll Work On 7

What to Watch Out For 7

Multiplying Binomials and Trinomials 8

Using Pascal’s Triangle to Multiply Binomials 8

Solving Linear Equations 9

Solving Linear Equations for Variables 9

Solving Linear Inequalities 10

Making Radical Expressions Simpler 10

Working with Complex Expressions 11

Chapter 2: Solving Quadratic Equations and Nonlinear Inequalities 13

The Problems You’ll Work On 13

What to Watch Out For 13

Applying the Square Root Rule on Quadratic Equations 14

Solving Quadratic Equations Using Factoring 14

Using the Quadratic Formula to Solve Equations 15

Recognizing and Solving Quadratic-Like Equations 16

Completing the Square to Solve Quadratic Equations 17

Combining Methods When Solving Quadratic Equations 17

Solving Quadratic Inequalities Using Number Lines 18

Chapter 3: Solving Radical and Rational Equations 21

The Problems You’ll Work On 21

What to Watch Out For 21

Solving Rational Equations 22

Taking on Radical Equations Involving One Radical Term 23

Solving Radical Equations with Multiple Radical Terms 25

Chapter 4: Graphs and Equations of Lines 27

The Problems You’ll Work On 27

What to Watch Out For 27

Sketching Lines Using a Point and Slope 28

Writing Equations of Lines Given Point and Slope 29

Writing Equations of Lines Given Two Points 30

Finding Equations of Parallel Lines 30

Writing Equations of Perpendicular Lines 31

Chapter 5: Functions 33

The Problems You’ll Work On 33

What to Watch Out For 33

Determining a Function’s Domain and Range 34

Finding Inverses of Functions 34

Recognizing Even and Odd Functions 35

Performing the Composition Operation on Functions 36

Creating a Difference-Quotient and Simplifying 36

Evaluating Piecewise Functions for Particular Inputs 37

Chapter 6: Quadratic Functions and Relations 39

The Problems You’ll Work On 39

What to Watch Out For 39

Determining the Vertex and Intercepts of a Parabola 40

Writing Equations of Parabolas in a Standard Form 40

Sketching Graphs of Parabolas 41

Using Quadratic Equations in Applications 42

Chapter 7: Polynomial Functions and Equations 45

The Problems You’ll Work On 45

What to Watch Out For 45

Recognizing the Intercepts of Polynomials 46

Factoring by Grouping to Solve for Intercepts 46

Applying the Rational Root Theorem to Find Roots 47

Performing Synthetic Division to Factor Polynomials 48

Evaluating Polynomials for Input Values 48

Investigating End-Behavior of Polynomials 49

Sketching the Graphs of Polynomial Functions 50

Chapter 8: Rational Functions 51

The Problems You’ll Work On 51

What to Watch Out For 51

Investigating the Domain of a Rational Function 52

Determining a Function’s Removable Discontinuity 52

Evaluating a Function When x Is Infinitely Large or Small 53

Determining a Function’s Infinite Limit 54

Writing Equations of Asymptotes 54

Adding Oblique Asymptotes to the Mix 55

Sketching the Graphs of Rational Functions 55

Chapter 9: Exponential and Logarithmic Functions 57

The Problems You’ll Work On 57

What to Watch Out For 57

Evaluating Exponential Functions for Input 58

Evaluating Exponential Functions in Base e 58

Sketching the Graphs of Exponential Functions 59

Finding Values of Logarithmic Expressions for Given Input 59

Evaluating Natural Logarithms in Base e 60

Sketching the Graphs of Log Functions 61

Rewriting a Log Function as Its Exponential Inverse 61

Changing Exponential Functions to Logarithmic Inverses 62

Solving Exponential Equations 62

Solving Logarithmic Equations 63

Chapter 10: Conic Sections 65

The Problems You’ll Work On 65

What to Watch Out For 66

Rewriting Equations of Parabolas in Standard Form 66

Determining a Vertex, Focus, Directrix, and Axis of Symmetry 67

Sketching the Graph of a Parabola 67

Rewriting a Circle’s Equation in Standard Form 68

Identifying the Center and Radius of a Circle 68

Sketching the Graph of a Circle 69

Writing an Ellipse’s Equation in Standard Form 69

Identifying the Center, the Foci, and Axis Endpoints 70

Sketching the Graphs of Ellipses 70

Writing the Equation of a Hyperbola in Standard Form 71

Finding the Center, Foci, and Asymptotes of Hyperbolas 71

Sketching the Graphs of Hyperbolas 72

Chapter 11: Systems of Linear Equations 73

The Problems You’ll Work On 73

What to Watch Out For 73

Solving Systems of Two Linear Equations 74

Performing Row Operations on Linear Equations 74

Solving Systems of Equations with Row Echelon Form 75

Using Reduced Row Echelon Form to Solve Systems 76

Solving Systems of Linear Equations 76

Decomposing Fractions Using Systems of Equations 77

Chapter 12: Systems of Nonlinear Equations and Inequalities 79

The Problems You’ll Work On 79

What to Watch Out For 79

Determining Intersections of Parabolas and Lines 80

Finding Where Two Parabolas Meet 80

Solving for Intersections of Conics 81

Finding the Intersections of Exponential Functions 82

Using Graphing to Solve Systems of Inequalities 83

Chapter 13: Working with Complex Numbers 85

The Problems You’ll Work On 85

What to Watch Out For 85

Rewriting Powers of i as i, –i, 1, or –1 86

Operating on and Simplifying Complex Expressions 86

Multiplying and Simplifying Complex Numbers 87

Using Conjugates to Divide Complex Numbers 88

Solving for Complex Solutions in Quadratic Equations 89

Chapter 14: Matrices 91

The Problems You’ll Work On 91

What to Watch Out For 92

Determining the Dimension and Type of Matrix 92

Adding and Subtracting Matrices 92

Performing Scalar Multiplication on Matrices 93

Multiplying Matrices 93

Determining Inverses of Square Matrices 94

Dividing Matrices Using Inverses 94

Using Matrices to Solve Systems of Equations 95

Chapter 15: Sequences and Series 97

The Problems You’ll Work On 97

What to Watch Out For 97

Writing Terms of a Sequence Given a Rule 98

Finding a General Term for an Arithmetic Sequence 98

Writing a General Term for a Geometric Sequence 98

Recognizing Patterns in Sequences 99

Creating Recursively Defined Sequences 99

Writing More Terms of Special Sequences 99

Finding the Sum of the Terms in a Series 100

Summing Arithmetic Series 100

Determining the Sum of a Geometric Series 101

Computing the Sum of a Special Series 102

Using a Special Formula for the Sum of an Infinite Series 102

Chapter 16: Sets 103

The Problems You’ll Work On 103

What to Watch Out For 103

Creating the Elements of a Set from a Description 104

Performing Set Operations 104

Operating on Sets of Special Numbers 105

Using Venn Diagrams to Solve Problems Involving Sets 106

Enlisting Venn Diagrams to Solve Applications 107

Chapter 17: Counting Techniques and Probability 109

The Problems You’ll Work On 109

What to Watch Out For 110

Solving Problems Using the Multiplication Property 110

Counting How Many Using Permutations 111

Incorporating Combinations in Counting Problems 112

Performing a Binomial Expansion 113

Solving Probability Problems Using Counting Techniques 113

Part 2: The Answers 117

Chapter 18: The Answers 119

Index 499

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