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 Basic 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
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