Beginning and Intermediate Algebra Book

How Am I Doing? Guide to Math Success (inside front cover)

To the Student

Preface

Acknowledgments

Diagnostic Pretest

CH. 0 - PREALGEBRA REVIEW

0.1 Simplifying Fractions

0.2 Adding and Subtracting Fractions

0.3 Multiplying and Dividing Fractions

How Am I Doing? Sections 0.1—0.3

0.4 Using Decimals

0.5 Percents, Rounding, and Estimating

Chapter 0 Organizer

Chapter 0 Review Problems

How Am I Doing? Chapter 0 Test

CH. 1 - REAL NUMBERS AND VARIABLES

1.1 Adding Real Numbers

1.2 Subtracting Real Numbers

1.3 Multiplying and Dividing Real Numbers

1.4 Exponents

1.5 The Order of Operations

How Am I Doing? Sections 1.1—1.5

1.6 Using the Distributive Property to Simplify Algebraic Expressions

1.7 Combining Like Terms

1.8 Using Substitution to Evaluate Algebraic Expressions and Formulas

1.9 Grouping Symbols

Chapter 1 Organizer

Chapter 1 Review Problems

How Am I Doing? Chapter 1 Test

CH. 2 — EQUATIONS, INEQUALITIES, AND APPLICATIONS

2.1 The Addition Principle of Equality

2.2 The Multiplication Principle of Equality

2.3 Using the Addition and Multiplication Principles Together

2.4 Solving Equations with Fractions

How Am I Doing? Sections 2.1—2.4

2.5 Translating English Phrases into Algebraic Expressions

2.6 Using Equations to Solve Word Problems

2.7 Solving Word Problems Using Geometric Formulas

2.8 Solving Inequalities in One Variable

Chapter 2 Organizer

Chapter 2 Review Problems

How Am I Doing? Chapter 2 Test

Cumulative Test for Chapters 0—2

CH. 3 - GRAPHING AND FUNCTIONS

3.1 The Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 The Slope of a Line

How Am I Doing? Sections 3.1—3.3

3.4 Writing the Equation of a Line

3.5 Graphing Linear Inequalities

3.6 Functions

Chapter 3 Organizer

Chapter 3 Review Problems

How Am I Doing? Chapter 3 Test

Cumulative Test for Chapters 0—3

CH. 4 - SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

4.1 Systems of Linear Equations in Two Variables

4.2 Systems of Linear Equations in Three Variables

How Am I Doing? Sections 4.1—4.2

4.3 Applications of Systems of Linear Equations

4.4 Systems of Linear Inequalities

Chapter 4 Organizer

Chapter 4 Review Problems

How Am I Doing? Chapter 4 Test

Cumulative Test for Chapters 0—4

CH. 5 - EXPONENTS AND POLYNOMIALS

5.1 The Rules of Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Fundamental Polynomial Operations

How Am I Doing? Sections 5.1—5.3

5.4 Multiplying Polynomials

5.5 Multiplication: Special Cases

5.6 Dividing Polynomials

Chapter 5 Organizer

Chapter 5 Review Problems

How Am I Doing? Chapter 5 Test

Cumulative Test for Chapters 0—5

CH. 6 - FACTORING

6.1 Removing a Common Factor

6.2 Factoring by Grouping

6.3 Factoring Trinomials of the Form x² + bx + c

6.4 Factoring Trinomials of the Form ax² + bx + c

How Am I Doing? Sections 6.1—6.4

6.5 Special Cases of Factoring

6.6 A Brief Review of Factoring

6.7 Solving Quadratic Equations by Factoring

Chapter 6 Organizer

Chapter 6 Review Problems

How Am I Doing? Chapter 6 Test

Cumulative Test for Chapters 0—6

CH. 7 - RATIONAL EXPRESSIONS AND EQUATIONS

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions

How Am I Doing? Sections 7.1—7.3

7.4 Simplifying Complex Rational Expressions

7.5 Solving Equations Involving Rational Expressions

7.6 Ratio, Proportion, and Other Applied Problems

Chapter 7 Organizer

Chapter 7 Review Problems

How Am I Doing? Chapter 7 Test

Cumulative Test for Chapters 0—7

CH. 8 - RATIONAL EXPONENTS AND RADICALS

8.1 Rational Exponents

8.2 Radical Expressions and Functions

8.3 Simplifying, Adding, and Subtracting Radicals

8.4 Multiplying and Dividing Radicals

How Am I Doing? Sections 8.1—8.4

8.5 Radical Equations

8.6 Complex Numbers

8.7 Variation

Chapter 8 Organizer

Chapter 8 Review Problems

How Am I Doing? Chapter 8 Test

Cumulative Test for Chapters 0—8

CH. 9 - QUADRATIC EQUATIONS AND INEQUALITIES

9.1 Quadratic Equations

9.2 The Quadratic Formula and Solutions to Quadratic Equations

9.3 Equations that can be Transformed into Quadratic Form

How Am I Doing? Sections 9.1—9.3

9.4 Formulas and Applications

9.5 Quadratic Functions

9.6 Compound Inequalities and Quadratic Inequalities

9.7 Absolute Value Equations and Inequalities

Chapter 9 Organizer

Chapter 9 Review Problems

How Am I Doing? Chapter 9 Test

Cumulative Test for Chapters 0—9

CH. 10 - THE CONIC SECTIONS

10.1 The Distance Formula and the Circle

10.2 The Parabola

10.3 The Ellipse

How Am I Doing? Sections 10.1—10.3

10.4 The Hyperbola

10.5 Nonlinear Systems of Equations

Chapter 10 Organizer

Chapter 10 Review Problems

How Am I Doing? Chapter 10 Test

Cumulative Test for Chapters 0—10

CH. 11 - ADDITIONAL PROPERTIES OF FUNCTIONS

11.1 Function Notation

11.2 General Graphing Procedures for Functions

How Am I Doing? Sections 11.1—11.2

11.3 Algebraic Operations on Functions

11.4 Inverse of a Function

Chapter 11 Organizer

Chapter 11 Review Problems

How Am I Doing? Chapter 11 Test

Cumulative Test for Chapters 0—11

Ch. 12 - LOGARITHMIC AND EXPONENTIAL FUNCTIONS

12.1 The Exponential Function

12.2 The Logarithmic Function

12.3 Properties of Logarithms

How Am I Doing? Sections 12.1—12.3

12.4 Common Logarithms, Natural Logarithms, and Change of Base

12.5 Exponential and Logarithmic Equations

Chapter 12 Organizer

Chapter 12 Review Problems

How Am I Doing? Chapter 12 Test

Cumulative Test for Chapters 0—12

Practice Final Examination

Glossary

Appendix A: Foundations for Intermediate Algebra

A.1 Exponents and the Order of Operations

A.2 Polynomial Operations

A.3 Factoring

Appendix B: Mathematics Blueprint for Problem Solving

Appendix C: Practice with Operations of Whole Numbers

Appendix D: Tables

Appendix E: Determinants and Cramer’s Rule

Appendix F: Solving Systems of Linear Equations Using Matrices

Appendix G: Sets

Solutions to Practice Problems

Answers to Selected Exercises

Applications Index

Index

Photo Credits