## Table of Contents

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 4

Part 1 The Questions 5

Chapter 1 Signing on with Signed Numbers 7

The Problems You'll Work On 7

What to Watch Out For 7

Placing Real Numbers on the Number Line 8

Using the Absolute Value Operation 8

Adding Signed Numbers 8

Subtracting Signed Numbers 9

Multiplying and Dividing Signed Numbers 10

Chapter 2 Recognizing Algebraic Properties and Notation 13

The Problems You'll Work On 13

What to Watch Out For 13

Applying Traditional Grouping Symbols 14

Introducing Some Non-Traditional Grouping Symbols 14

Distributing Multiplication over Addition and Subtraction 15

Associating Terms Differently with the Associative Property 15

Rearranging with the Commutative Property 16

Applying More Than One Property to an Expression 16

Chapter 3 Working with Fractions and Decimals 17

The Problems You'll Work On 17

What to Watch Out For 18

Adding and Subtracting Fractions 18

Multiplying Fractions 18

Dividing Fractions 18

Simplifying Complex Fractions 19

Adding and Subtracting Decimals 19

Multiplying Decimals 20

Dividing Decimals 20

Changing Fractions to Decimals 20

Changing Decimals to Fractions 21

Chapter 4 Making Exponential Expressions and Operations More Compatible 23

The Problems You'll Work On 23

What to Watch Out For 23

Multiplying and Dividing Exponentials with the Same Base 24

Raising a Power to a Power 24

Combining Different Operations on Exponentials 25

Changing the Base to Perform an Operation 26

Working with Scientific Notation 26

Chapter 5 Raking in Radicals 29

The Problems You'll Work On 29

What to Watch Out For 29

Simplifying Radical Expressions 30

Rationalizing Denominators 30

Using Fractional Exponents for Radicals 31

Evaluating Expressions with Fractional Exponents 32

Operating on Radicals 32

Operating on Factors with Fractional Exponents 33

Estimating Values of Radicals 33

Chapter 6 Creating More User-Friendly Algebraic Expressions 35

The Problems You'll Work On 35

What to Watch Out For 35

Adding and Subtracting Like Terms 36

Multiplying and Dividing Factors 36

Simplifying Expressions Using the Order of Operations 37

Evaluating Expressions Using the Order of Operations 38

Operating with Factorials 38

Focusing on Function Notation 39

Chapter 7 Multiplying by One or More Terms 41

The Problems You'll Work On 41

What to Watch Out For 41

Distributing One Term Over Sums and Differences 42

Distributing Using Division 42

Multiplying Binomials Using Distributing 42

Multiplying Binomials Using FOIL 43

Distributing Binomials Over Trinomials 43

Squaring Binomials 44

Raising Binomials to the Third Power 44

Using Pascal's Triangle 44

Finding Special Products of Binomials and Trinomials 45

Chapter 8 Dividing Algebraic Expressions 47

The Problems You'll Work On 47

What to Watch Out For 47

Dividing with Monomial Divisors 48

Monomial Divisors and Remainders 48

Using Long Division to Divide with Binomials 49

Dividing with Binomials Using Synthetic Division 50

Dividing with Higher Power Divisors 50

Chapter 9 Factoring Basics 53

The Problems You'll Work On 53

What to Watch Out For 53

Finding Divisors Using Rules of Divisibility 54

Writing Prime Factorizations 54

Factoring Out a GCF 55

Reducing Fractions with a Common GCF 56

Chapter 10 Factoring Binomials 57

The Problems You'll Work On 57

What to Watch Out For 57

Factoring the Difference of Perfect Squares 58

Factoring the Sum or Difference of Two Perfect Cubes 58

Factoring More Than Once 59

Chapter 11 Factoring Quadratic Trinomials 61

The Problems You'll Work On 61

What to Watch Out For 61

Factoring Out the GCF of a Trinomial 62

Factoring Trinomials into the Products of Binomials 62

Factoring Quadratic-Like Expressions 63

Factoring Completely Using More Than One Technique 63

Chapter 12 Other Factoring Techniques 65

The Problems You'll Work On 65

What to Watch Out For 65

Factoring by Grouping 66

Combining Other Factoring Techniques with Grouping 66

Using Multiple Factoring Methods 66

Chapter 13 Solving Linear Equations 69

The Problems You'll Work On 69

What to Watch Out For 69

Solving Linear Equations Using Baste Operations 70

Dealing with Fractions in Linear Equations 71

Chapter 14 Taking on Quadratic Equations 73

The Problems You'll Work On 73

What to Watch Out For 73

Applying the Square Root Rule to Quadratic Equations 74

Solving Quadratic Equations Using Factoring 74

Applying the Quadratic Formula to Quadratic Equations 75

Completing the Square to Solve Quadratic Equations 76

Writing Complex Numbers in the Standard a + bi Form 76

Finding Complex Solutions Using the Quadratic Formula 77

Chapter 15 Solving Polynomials with Powers Three AND Higher 79

The Problems You'll Work On 79

What to Watch Out For 79

Applying Descartes's Rule of Signs to Count Real Roots 80

Applying the Rational Root Theorem to List Roots 80

Determining Whether Numbers Are Roots 81

Solving for the Roots of Polynomials 81

Chapter 16 Reining in Radical and Absolute Value Equations 83

The Problems You'll Work On 83

What to Watch Out For 83

Solving Basic Radical Equations 84

Checking for Extraneous Roots 84

Squaring Both Sides of Equations Twice 85

Solving Radicals with Roots Other Than Square Roots 85

Solving Absolute Value Equations 85

Handling Absolute Value Equations with No Solution 86

Chapter 17 Making Inequalities More Fair 87

The Problems You'll Work On 87

What to Watch Out For 87

Performing Operations on Inequalities 88

Writing Inequalities Using Interval Notation 88

Changing interval Notation to Inequality Notation 88

Solving Linear Inequalities 89

Taking on Compound Inequalities 89

Solving Quadratic Inequalities 89

Finding Solutions of Nonlinear Inequalities 90

Rewriting and Solving Absolute Value Inequalities 91

Delving into Complex Inequalities 91

Chapter 18 Using Established Formulas 93

The Problems You'll Work On 93

What to Watch Out For 93

Getting Interested in Interest Problems 94

Heating It Up with Temperature Problems 94

Adding up Natural Numbers 95

Going the Distance with the Distance Formula 95

Getting the Inside Scoop with Sums of Interior Angles 96

Averaging Out the Numbers 97

Summing the Squares of Numbers 97

Finding the Terms of a Sequence 97

Adding the Terms in an Arithmetic Sequence 98

Using the Formula for the Sum of Cubes 98

Compounding the Problems Involving Compound Interest 98

Chapter 19 Using Formulas in Geometric Story Problems 101

The Problems You'll Work On 101

What to Watch Out For 102

Working around the Perimeter of Rectangles 102

Using the Area Formula for a Trapezoid 103

Tackling Area and Perimeter of a Square 103

Solving Problems Using the Perimeter of a Triangle 103

Working with the Area and Perimeter of a Rectangle 104

Using the Formula for the Area of a Hexagon 104

Getting Pythagoras Involved in the Area of a Triangle 104

Making Use of the Volume of a Box 105

Working with the Volume of a Cylinder 105

Changing Radians to Degrees and Degrees to Radians 105

Determining the Height of an Object 106

Working with Heron's Formula for the Area of a Triangle 106

Chapter 20 Tackling Traditional Story Problems 107

The Problems You'll Work On 107

What to Watch Out For 107

Tackling Age Problems 108

Working with Consecutive Integers 109

Getting the Job Done on Work Problems 110

Counting on Quality and Quantity Problems 111

Solving Money Problems 111

Chapter 21 Graphing Basics 113

The Problems You'll Work On 113

What to Watch Out For 113

Plotting Points on the Coordinate System 114

Determining the Quadrant of a Point 115

Finding the Intercepts of a Line 115

Calculating the Slope of a Line from Two Points 116

Determining a Line's Slope from Its Equation 117

Sketching the Graph of a Line from Its Equation 117

Sketching Lines Using Two Points 118

Chapter 22 Using the Algebra of Lines 119

The Problems You'll Work On 119

What to Watch Out For 119

Writing Equations of Lines Using the Slope and a Point 120

Writing the Equation of a Line Using Two Points 120

Dealing with Slopes of Parallel and Perpendicular Lines 121

Finding Equations of Lines Parallel or Perpendicular to One Given 121

Computing the Distance Between Points 121

Determining the Midpoint 122

Chapter 23 Other Graphing Topics 123

The Problems You'll Work On 123

What to Watch Out For 123

Graphing to Find the Intersection of Two Lines 124

Sketching the Graph of a Circle 124

Creating the Graph of a Parabola 125

Transforming the Graph of a Figure 125

Part 2 The Answers 127

Chapter 24 The Answers 129

Index 443