Contents

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Chapter R Reference 1

R.1 Study Tips 2

Group Activity: Becoming a Successful Student 4

R.2 Fractions 6

R.3 Decimals and Percents 20

R.4 Introduction to Geometry 29

Chapter 1 The Set of Real Numbers 45

1.1 Introduction to Algebra and the Set of Real Numbers 46

1.2 Exponents, Square Roots, and the Order of Operations 59

1.3 Addition of Real Numbers 69

1.4 Subtraction of Real Numbers 77

Problem Recognition Exercises: Addition and Subtraction of Real Numbers 85

1.5 Multiplication and Division of Real Numbers 85

Problem Recognition Exercises: Adding, Subtracting, Multiplying and Dividing Real Numbers 96

1.6 Properties of Real Numbers and Simplifying Expressions 97

Group Activity: Evaluating Formulas Using a Calculator 110

Chapter 1 Summary 111Chapter 1 Review Exercises 115Chapter 1 Test 117

Chapter 2 Linear Equations and Inequalities 119

2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 1202.2 Solving Linear Equations 131

2.3 Linear Equations: Clearing Fractions and Decimals 140Problem Recognition Exercises: Equations and Expressions 146

2.4 Applications of Linear Equations: Introduction to Problem Solving 1472.5 Applications Involving Percents 157

2.6 Literal Equations and Applications of Geometry 1642.7 Mixture Applications and Uniform Motion 173

2.8 Linear Inequalities 182Group Activity: Computing Body Mass Index (BMI) 197Chapter 2 Summary 198Chapter 2 Review Exercises 204Chapter 2 Test 207Chapters 1–2 Cumulative Review Exercises 208

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Chapter 3 Graphing Linear Equations in Two Variables 211

3.1 Rectangular Coordinate System 2123.2 Linear Equations in Two Variables 221

3.3 Slope of a Line and Rate of Change 2363.4 Slope-Intercept Form of a Linear Equation 250

Problem Recognition Exercises: Linear Equations in Two Variables 2603.5 Point-Slope Formula 2613.6 Applications of Linear Equations and Modeling 269

Group Activity: Modeling a Linear Equation 277Chapter 3 Summary 278Chapter 3 Review Exercises 283Chapter 3 Test 287Chapters 1–3 Cumulative Review Exercises 289

Chapter 4 Systems of Linear Equations in Two Variables 291

4.1 Solving Systems of Equations by the Graphing Method 2924.2 Solving Systems of Equations by the Substitution Method 3024.3 Solving Systems of Equations by the Addition Method 312

Problem Recognition Exercises: Systems of Equations 3214.4 Applications of Systems of Equations 3224.5 Linear Inequalities and Systems of Inequalities in Two Variables 331

Group Activity: Creating Linear Models from Data 342Chapter 4 Summary 344Chapter 4 Review Exercises 349Chapter 4 Test 353Chapters 1–4 Cumulative Review Exercises 354

Chapter 5 Polynomials and Properties of Exponents 357

5.1 Multiplying and Dividing Expressions with Common Bases 358

5.2 More Properties of Exponents 368

5.3 Definitions of b0 and b�n 373

Problem Recognition Exercises: Properties of Exponents 381

5.4 Scientific Notation 382

5.5 Addition and Subtraction of Polynomials 388

5.6 Multiplication of Polynomials and Special Products 397

5.7 Division of Polynomials 406

Problem Recognition Exercises: Operations on Polynomials 414

Group Activity: The Pythagorean Theorem and a Geometric “Proof” 415

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Chapter 5 Summary 416

Chapter 5 Review Exercises 419

Chapter 5 Test 422

Chapters 1–5 Cumulative Review Exercises 423

Chapter 6 Factoring Polynomials 425

6.1 Greatest Common Factor and Factoring by Grouping 426

6.2 Factoring Trinomials of the Form x2 � bx � c 435

6.3 Factoring Trinomials: Trial-and-Error Method 441

6.4 Factoring Trinomials: AC-Method 450

6.5 Difference of Squares and Perfect Square Trinomials 456

6.6 Sum and Difference of Cubes 463

Problem Recognition Exercises: Factoring Strategy 469

6.7 Solving Equations Using the Zero Product Rule 471

Problem Recognition Exercises: Polynomial Expressions versus Polynomial Equations 477

6.8 Applications of Quadratic Equations 478

Group Activity: Building a Factoring Test 485

Chapter 6 Summary 486

Chapter 6 Review Exercises 491

Chapter 6 Test 493

Chapters 1–6 Cumulative Review Exercises 494

Chapter 7 Rational Expressions and Equations 495

7.1 Introduction to Rational Expressions 496

7.2 Multiplication and Division of Rational Expressions 506

7.3 Least Common Denominator 512

7.4 Addition and Subtraction of Rational Expressions 519

Problem Recognition Exercises: Operations on Rational Expressions 528

7.5 Complex Fractions 529

7.6 Rational Equations 536

Problem Recognition Exercises: Comparing Rational Equations and Rational Expressions 545

7.7 Applications of Rational Equations and Proportions 546

7.8 Variation 557

Group Activity: Computing Monthly Mortgage Payments 565

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Chapter 7 Summary 566

Chapter 7 Review Exercises 571

Chapter 7 Test 574

Chapters 1–7 Cumulative Review Exercises 575

Chapter 8 Radicals 577

8.1 Introduction to Roots and Radicals 578

8.2 Simplifying Radicals 588

8.3 Addition and Subtraction of Radicals 596

8.4 Multiplication of Radicals 602

8.5 Division of Radicals and Rationalization 608

Problem Recognition Exercises: Operations on Radicals 617

8.6 Radical Equations 618

8.7 Rational Exponents 624

Group Activity: Calculating Standard Deviation 631

Chapter 8 Summary 632

Chapter 8 Review Exercises 636

Chapter 8 Test 639

Chapters 1–8 Cumulative Review Exercises 640

Chapter 9 More Quadratic Equations 643

9.1 The Square Root Property 644

9.2 Completing the Square 649

9.3 Quadratic Formula 655

Problem Recognition Exercises: Solving Different Types of Equations 663

9.4 Graphing Quadratic Equations 664

9.5 Introduction to Functions 674

Group Activity: Maximizing Volume 687

Chapter 9 Summary 688

Chapter 9 Review Exercises 692

Chapter 9 Test 694

Chapters 1–9 Cumulative Review Exercises 696

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Additional Topics Appendix A-1

A.1 Converting Units of Measurement A–1

Student Answer Appendix SA–1

Credits C–1

Index I–1

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