Tables of Contents for Intermediate Algebra for College Students

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Chapter/Section Title

Page #

Page Count

Getting Started: What Do YOU Think?

xiii

Part A Working Together

xiv

Part B Solving Problems

xvi

Part C Making Connections

xviii

CHAPTER 1 Mathematical Models

1-1 Graphical Models

Part A Data and Scatter Plots

Part B Patterns and Relationships

Part C Functions

Part D Making Connections

1-2 Experimental Probability and Simulation

Part A Theoretical and Experimental Probability

Part B Simulation

Part C Making Connections

1-3 Matrices

Part A Matrices and Data Handling

Part B Multiplying Matrices

Part C Making Connections

CHAPTER 1 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

CHAPTER 1 Assessment (Test, Performance Task)

CHAPTER 2 Linear Functions, Equations, and Inequalities

2-1 Linear Functions and Equations

Part A Direct Variation and Linear Functions

Part B Solving Equations

Part C Analyzing Equations of Lines

Part D Making Connections

100

2-2 Fitting Linear Functions to Data

103

Part A Using Equations of Trend Lines

104

Part B The Median-Median Line of Fit

109

Part C Fitting Lines Using Technology

117

Part D Making Connections

122

2-3 Linear Inequalities

127

Part A One-Variable Inequalities

128

Part B Inequalities and Absolute Value

135

Part C Linear Inequalities with Two Variables

142

Part D Making Connections

149

CHAPTER 2 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

152

CHAPTER 2 Assessment (Test, Performance Task)

154

CHAPTER 3 Solving Systems of Linear Equations and Inequalities

156

3-1 Systems of Linear Equations

159

Part A Solving Systems of Equations Graphically

160

Part B Solving Systems of Equations Symbolically

168

Part C Solving Systems Using Matrices

177

Part D Systems with Three Variables

186

Part E Making Connections

194

3-2 Systems of Linear Inequalities

197

Part A Systems of Inequalities

198

Part B Linear Programming Constraints

204

Part C Solving Linear Programming Problems

212

Part D Making Connections

221

CHAPTER 3 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

224

CHAPTER 3 Assessment (Test, Performance Task)

226

CHAPTER 4 Patterns and Structure in Algebra

228

4-1 Analyzing Arithmetic Growth

231

Part A Arithmetic Sequences

232

Part B Arithmetic Series

239

Part C Making Connections

245

4-2 Analyzing Geometric Growth

249

Part A Geometric Sequences

250

Part B Geometric Series

256

Part C Investigating the Concept of a Limit

262

Part D Making Connections

268

4-3 Algebraic Structure and Fractal Geometry

271

Part A Real Numbers and Field Properties

272

Part B Rational and Irrational Numbers

278

Part C Imaginary and Complex Numbers

286

Part D Graphing Complex Numbers

291

Part E Making Connections

297

CHAPTER 4 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

300

CHAPTER 4 Assessment (Test, Performance Task)

303

CHAPTER 5 Quadratic Functions and Relations

304

114

5-1 Quadratic Functions

307

Part A Investigating Quadratic Functions

308

Part B Sketching Parabolas: f(x) = ax(2)

316

Part C Translations: f(x) = a(x-h)(2)+k

323

Part D Completing the Square

330

Part E Making Connections

336

5-2 Solving Quadratic Equations

339

Part A Solving Quadratic Equations Graphically

340

Part B Solving Quadratic Equations by Factoring

348

Part C Using the Quadratic Formula

354

Part D Classifying Solutions

361

Part E Making Connections

368

5-3 Conic Sections

371

Part A Circles

372

Part B Ellipses

380

Part C Hyperbolas

388

Part D Making Connections

396

5-4 Quadratic Systems

399

Part A Quadratic-Linear Systems

400

Part B Quadratic-Quadratic Systems

405

Part C Making Connections

410

CHAPTER 5 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

413

CHAPTER 5 Assessment (Test, Performance Task)

416

CHAPTER 6 Counting and Arranging Discrete Objects

418

6-1 Counting Objects and Permutations

421

Part A Methods of Counting

422

Part B Arrangements and Permutations

428

Part C Making Connections

434

6-2 Combinations and the Binomial Theorem

437

Part A Combinations

438

Part B The Binomial Theorem

443

Part C Making Connections

448

CHAPTER 6 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

452

CHAPTER 6 Assessment (Test, Performance Task)

454

CHAPTER 7 Investigating Roots and Powers

456

7-1 Variation and Integral Exponent Powers

459

Part A Inverse, Combined, and Joint Variation

460

Part B Positive Integer Exponents

467

Part C Properties of Exponents and Powers

474

Part D Making Connections

481

7-2 Roots, Radicals, and Rational Exponents

485

Part A Rational Exponents

486

Part B Real-Number Exponents and Modeling

492

Part C Solving Radical Equations

498

Part D Other Radical Equations

503

Part E Making Connections

509

7-3 Combining Functions

513

Part A Operations with Functions

514

Part B Composite Functions

520

Part C Inverse Relations and Functions

525

Part D Making Connections

531

CHAPTER 7 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

535

CHAPTER 7 Assessment (Test, Performance Task)

537

CHAPTER 8 Polynomials and Polynomial Functions

538

8-1 Polynomial Functions and Their Graphs

541

Part A Graphing Polynomial Functions

542

Part B Maximums and Minimums

548

Part C Zeros of a Function

555

Part D Making Connections

561

8-2 The Fundamental Theorem of Algebra

565

Part A Solving Polynomial Equations by Graphing

566

Part B Factors and Roots of Polynomials

570

Part C The Fundamental Theorem

577

Part D Making Connections

582

8-3 Rational Expressions and Functions

585

Part A Rational Expressions

586

Part B Adding and Subtracting Rational Expressions

592

Part C Rational Functions

598

Part D Solving Rational Equations

603

Part E Making Connections

608

CHAPTER 8 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

611

CHAPTER 8 Assessment (Test, Performance Task)

614

CHAPTER 9 Exponential and Logarithmic Functions

616

9-1 Exponential Patterns and Graphs

619

Part A Exploring Exponential Functions

620

Part B Exponential Growth and Decay

627

Part C Modeling Exponential Growth and Decay

634

Part D The Number e

640

Part E Making Connections

646

9-2 Logarithmic Functions

649

Part A Defining Logarithmic Functions

650

Part B Solving Exponential Equations

657

Part C Properties of Logarithms

663

Part D Making Connections

670

CHAPTER 9 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

673

CHAPTER 9 Assessment (Test, Performance Task)

674

CHAPTER 10 Trigonometry

676

10-1 Trigonometric Ratios

679

Part A Triangle Trigonometry

680

Part B Radian Measure and Special Angles

688

Part C Arc Length and Sector Area

693

Part D Extended Trigonometric Values

700

Part E Making Connections

706

10-2 Laws of Cosines and Sines

709

Part A Law of Cosines

710

Part B Law of Sines and Triangle Areas

717

Part C Making Connections

725

10-3 Trigonometric Functions

729

Part A Period and Amplitude

730

Part B Trigonometric Translations

738

Part C Making Connections

744

CHAPTER 10 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

747

CHAPTER 10 Assessment (Test, Performance Task)

750

CHAPTER 11 Advanced Techniques for Chance and Data

752

11-1 Compound Events

755

Part A The Probability of A or B

756

Part B Independent and Dependent Events

762

Part C Conditional Probability

769

Part D Making Connections

775

11-2 Sampling Methods

779

Part A Biased and Unbiased Sampling

780

Part B The Normal Distribution

787

Part C Making Connections

794

CHAPTER 11 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

797

CHAPTER 11 Assessment (Test, Performance Task)

799

CHAPTER 12 Discrete Mathematics and Models

800

12-1 Graph Theory

803

Part A Euler's Formula and Graphs

804

Part B Paths and Circuits

810

Part C Optimization and Trees

817

Part D Making Connections

824

12-2 Recursion

829

Part A Recursive Sequences

830

Part B Probability Matrices

836

Part C Making Connections

843

CHAPTER 12 Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)

846

CHAPTER 12 Assessment (Test, Performance Task)

848

REFERENCE CENTER

850

Enrichment

850

Calculating Inverse Matrices

850

Solving Systems Using Augmented Matrices

852

Synthetic Division

853

Complex Rational Expressions

854

Trigonometric Inverse Functions

855

Trigonometric Inverse Relations and Equations

856

Trigonometric Properties and Identities

858

Measures of Central Tendency

860

Standard Deviation

861

Z-Scores

862

Hypothesis Testing of Means

864

Residuals and Linear Regression

866

Choosing a Mathematical Model

868

Inequalities from Polynomial, Square Root, and Rational Equations

870

Inequalities from Exponential and Logarithmic Equations

872

Spiral Review

874

Measurement Conversion Factors

898

Symbols

899

Random Numbers

900

Standard Normal Distribution

901

Geometric Formulas

902

Algebraic Properties

903

Algebraic Formulas

904

Glossary

906

Selected Answers

920

Credits

952

Index

954