Table of Contents
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
