*About This Book iii* *About the Authors v*

*Acknowledgments vii*

**SECTION 1: INTEGERS, VARIABLES, AND EXPRESSIONS 1**

1.1: Using the Order of Operations 2

1.2: Simplifying Expressions That Have Grouping Symbols 4

1.3: Simplifying Expressions with Nested Grouping Symbols 6

1.4: Using Positive Exponents and Bases Correctly 8

1.5: Simplifying Expressions with Grouping Symbols and Exponents 10

1.6: Evaluating Expressions 12

1.7: Writing Expressions 14

1.8: Writing Expressions Involving Grouping Symbols 16

1.9: Identifying Patterns by Considering All of the Numbers 18

1.10: Writing Prime Factorization 20

1.11: Finding the Greatest Common Factor 22

1.12: Finding the Least CommonMultiple 24

1.13: Classifying Counting Numbers, Whole Numbers, and Integers 26

1.14: Finding Absolute Values and Opposites 28

1.15: Adding Integers with Different Signs 30

1.16: Subtracting Integers 32

1.17: Multiplying Two Integers 34

1.18: MultiplyingMore Than Two Integers 36

1.19: Using Integers as Bases 38

1.20: Dividing Integers 40

1.21: Finding Absolute Values of Expressions 42

1.22: Finding Square Roots of Square Numbers 44

**SECTION 2: RATIONAL NUMBERS 47**

2.1: Classifying Counting Numbers, Whole Numbers, Integers, and Rational Numbers 48

2.2: Simplifying Fractions 50

2.3: RewritingMixed Numbers as Improper Fractions 52

2.4: Comparing Rational Numbers 54

2.5: Expressing Rational Numbers as Decimals 56

2.6: Expressing Terminating Decimals as Fractions or Mixed Numbers 58

2.7: Expressing Repeating Decimals as Fractions or Mixed Numbers 60

2.8: Adding Rational Numbers 62

2.9: Subtracting Rational Numbers 64

2.10: Multiplying and Dividing Rational Numbers 66

2.11: Expressing Large Numbers in Scientific Notation 68

2.12: Evaluating Rational Expressions 70

2.13: Writing Ratios Correctly 72

2.14: Writing and Solving Proportions 74

2.15: Expressing Fractions as Percents 76

2.16: Expressing Percents as Fractions 78

2.17: Solving Percent Problems 80

2.18: Finding the Percent of Increase or Decrease 82

2.19: Converting from One Unit of Measurement to Another Using theMultiplication Property of One 84

**SECTION 3: EQUATIONS AND INEQUALITIES 87**

3.1: Writing Equations 88

3.2: Solving Equations by Adding or Subtracting 90

3.3: Solving Equations byMultiplying or Dividing 92

3.4: Solving Two-Step Equations with the Variable on One Side 94

3.5: Solving Equations Using the Distributive Property 96

3.6: Solving Equations with Variables on Both Sides 98

3.7: Solving Equations with Variables on Both Sides, Including Identities and Equations That Have No Solution 100

3.8: Solving Absolute Value Equations 102

3.9: Solving Absolute Value Equations That Have Two Solutions, One Solution, or No Solution 104

3.10: Classifying Inequalities as True or False 106

3.11: Writing Inequalities 108

3.12: Solving Inequalities with Variables on One Side 110

3.13: Rewriting Combined Inequalities as One Inequality 112

3.14: Solving Combined Inequalities—Conjunctions 114

3.15: Solving Combined Inequalities—Disjunctions 116

3.16: Solving Absolute Value Inequalities 118

3.17: Solving Systems of Equations Using the Substitution Method 120

3.18: Solving Systems of Equations Using the Addition-or-SubtractionMethod 122

3.19: Solving Systems of Equations Using Multiplication with the Addition-or-SubtractionMethod 124

3.20: Solving Systems of Equations Using a Variety of Methods 126

3.21: Solving Systems of Equations That Have One Solution, No Solution, or an Infinite Number of Solutions 128

3.22: Using Matrices—Addition, Subtraction, and Scalar Multiplication 130

3.23: Identifying Conditions forMultiplying TwoMatrices 132

3.24: Multiplying TwoMatrices 134

**SECTION 4: GRAPHS OF POINTS AND LINES 137**

4.1: Graphing on a Number Line 138

4.2: Graphing Conjunctions 140

4.3: Graphing Disjunctions 142

4.4: Graphing Ordered Pairs on the Coordinate Plane 144

4.5: Completing T-Tables 146

4.6: Finding the Slope of a Line, Given Two Points on the Line 148

4.7: Identifying the Slope and *Y*-Intercept from an Equation . . 150

4.8: Using Equations to Find the Slopes of Lines 152

4.9: Identifying Parallel and Perpendicular Lines, Given an Equation 154

4.10: Using the *X*-Intercept and the *Y*-Intercept to Graph a Linear Equation 156

4.11: Using Slope-Intercept Form to Graph the Equation of a Line 158

4.12: Graphing Linear Inequalities in the Coordinate Plane 160

4.13: Writing a Linear Equation, Given Two Points 162

4.14: Finding the Equation of the Line of Best Fit 164

4.15: Using theMidpoint Formula 166

4.16: Using the Distance Formula to Find the Distance Between Two Points 168

4.17: Graphing Systems of Linear Equations When Lines Intersect 170

4.18: Graphing Systems of Linear Equations if Lines Intersect, Are Parallel, or Coincide 172

**SECTION 5: MONOMIALS AND POLYNOMIALS 175**

5.1: ApplyingMonomial Vocabulary Accurately 176

5.2: Identifying Similar Terms 178

5.3: Adding Polynomials 180

5.4: Subtracting Polynomials 182

5.5: MultiplyingMonomials 184

5.6: Using Powers ofMonomials 186

5.7: Multiplying a Polynomial by aMonomial 188

5.8: Multiplying Two Binomials 190

5.9: Multiplying Two Polynomials 192

5.10: DividingMonomials 194

5.11: Dividing Polynomials 196

5.12: Finding the Greatest Common Factor of Two or More Monomials 198

5.13: Factoring Polynomials by Finding the Greatest Monomial Factor 200

5.14: Factoring the Difference of Squares 202

5.15: Factoring Trinomials if the Last TermIs Positive 204

5.16: Factoring Trinomials if the Last TermIs Negative 206

5.17: Factoring by Grouping 208

5.18: Factoring Trinomials if the Leading Coefficient Is an Integer Greater Than 1 210

5.19: Factoring the Sums and Differences of Cubes 212

5.20: Solving Quadratic Equations by Factoring 214

5.21: Solving Quadratic Equations by Finding Square Roots 216

5.22: Solving Quadratic Equations Using the Quadratic Formula 218

5.23: Using the Discriminant 220

**SECTION 6: RATIONAL EXPRESSIONS 223**

6.1: Using Zero and Negative Numbers as Exponents 224

6.2: Using the Properties of Exponents That Apply to Division 226

6.3: Using the Properties of Exponents That Apply to Multiplication and Division 228

6.4: Identifying Restrictions on the Variable 230

6.5: Simplifying Algebraic Fractions 232

6.6: Adding and Subtracting Algebraic Fractions with Like Denominators 234

6.7: Finding the Least CommonMultiple of Polynomials 236

6.8: Writing Equivalent Algebraic Fractions 238

6.9: Adding and Subtracting Algebraic Fractions with Unlike Denominators 240

6.10: Multiplying and Dividing Algebraic Fractions 242

6.11: Solving Proportions 244

6.12: Solving Equations That Have Fractional Coefficients 246

6.13: Solving Fractional Equations 248

**SECTION 7: IRRATIONAL AND COMPLEX NUMBERS 251**

7.1: Simplifying Radicals 252

7.2: Multiplying Radicals 254

7.3: Rationalizing the Denominator 256

7.4: Dividing Radicals 258

7.5: Adding and Subtracting Radicals 260

7.6: Multiplying Two Binomials Containing Radicals 262

7.7: Using Conjugates to Simplify Radical Expressions 264

7.8: Simplifying Square Roots of Negative Numbers 266

7.9: Multiplying Imaginary Numbers 268

7.10: Simplifying ComplexNumbers 270

**SECTION 8: FUNCTIONS 273**

8.1: Determining if a Relation Is a Function 274

8.2: Finding the Domain of a Function 276

8.3: Finding the Range of a Function 278

8.4: Using the Vertical Line Test 280

8.5: Describing Reflections of the Graph of a Function 282

8.6: Describing Vertical Shifts of the Graph of a Function 284

8.7: Describing Horizontal and Vertical Shifts of the Graph of a Function 286

8.8: Describing Dilations of the Graph of a Function 288

8.9: Finding the Composite of Two Functions 290

8.10: Finding the Inverse of a Function 292

8.11: Evaluating the Greatest Integer Function 294

8.12: Identifying Direct and Indirect Variation 296

8.13: Describing the Graph of the Quadratic Function 298

8.14: Using Rational Numbers as Exponents 300

8.15: Using Irrational Numbers as Exponents 302

8.16: Solving Exponential Equations 304

8.17: Using the Compound Interest Formula 306

8.18: Solving Radical Equations 308

8.19: Writing Logarithmic Equations as Exponential Equations 310

8.20: Solving Logarithmic Equations 312

8.21: Using the Properties of Logarithms 314

*Common Core State Standards for Mathematics 316*