Mark Dugopolski
Intermediate Algebra
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APPLICATIONS INDEX

1 The Real Numbers

1.1 Sets

1.2 The Real Numbers

1.3 Operations on the Set of Real Numbers

1.4 Evaluating Expressions and the Order of Operations

1.5 Properties of the Real Numbers

1.6 Using the Properties

Chapter 1 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 1 Test

• Critical Thinking

2 Linear Equations and Inequalities in One Variable

2.1 Linear Equations in One Variable

2.2 Formulas and Functions

2.3 Applications

2.4 Inequalities

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

Chapter 2 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 2 Test

• Making Connections: A review of Chapters 1-2

• Critical Thinking

3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope of a Line

3.3 Three Forms for the Equation of a Line

3.4 Linear Inequalities and Their Graphs

3.5 Functions and Relations

Chapter 3 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 3 Test

• Making Connections: a review of Chapters 1-3

• Critical Thinking

4 Systems of Linear Equations

4.1 Solving Systems by Graphing and Substitution

4.2 The Addition Method

4.3 Systems of Linear Equations in Three Variables

4.4 Solving Linear Systems Using Matrices

4.5 Determinants and Cramer’s Rule

4.6 Linear Programming

Chapter 4 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 4 Test

• Making Connections: a review of Chapters 1-4

• Critical Thinking

5 Exponents and Polynomials

5.1 Integral Exponents and Scientific Notation

5.2 The Power Rules

5.3 Polynomials and Polynomial Functions

5.4 Multiplying Binomials

5.5 Factoring Polynomials

5.6 Factoring ax² + bx + c

5.7 Factoring Strategy

5.8 Solving Equations by Factoring

Chapter 5 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 5 Test

• Making Connections: a review of Chapters 1-5

• Critical Thinking

6 Rational Expressions and Functions

6.1 Properties of Rational Expressions and Functions

6.2 Multiplication and Division

6.3 Addition and Subtraction

6.4 Complex Fractions

6.5 Division of Polynomials

6.6 Solving Equations Involving Rational Expressions

6.7 Applications

Chapter 6 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 6 Test

• Making Connections: a review of Chapters 1-6

• Critical Thinking

7 Radicals and Rational Exponents

7.1 Radicals

7.2 Rational Exponents

7.3 Adding, Subtracting, and Multiplying Radicals

7.4 Quotients, Powers, and Rationalizing Denominators

7.5 Solving Equations with Radicals and Exponents

7.6 Complex Numbers

Chapter 7 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 7 Test

• Making Connections: a review of Chapters 1-7

• Critical Thinking

8 Quadratic Equations, Functions, and Inequalities

8.1 Factoring and Completing the Square

8.2 The Quadratic Formula

8.3 More on Quadratic Equations

8.4 Quadratic Functions and Their Graphs

8.5 Quadratic Inequalities

Chapter 8 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 8 Test

• Making Connections: a review of Chapters 1-8

• Critical Thinking

9 Additional Function Topics

9.1 Graphs of Functions and Relations

9.2 Transformations of Graphs

9.3 Combining Functions

9.4 Inverse Functions

9.5 Variation

Chapter 9 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 9 Test

• Making Connections: a review of Chapters 1-9

• Critical Thinking

10 Exponential and Logarithmic Functions

10.1 Exponential Functions and Their Applications

10.2 Logarithmic Functions and Their Applications

10.3 Properties of Logarithms

10.4 Solving Equations and Applications

Chapter 10 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 10 Test

• Making Connections: a review of Chapters 1-10

• Critical Thinking

11 Nonlinear Systems and the Conic Sections

11.1 Nonlinear Systems of Equations

11.2 The Parabola

11.3 The Circle

11.4 The Ellipse and Hyperbola

11.5 Second-Degree Inequalities

Chapter 11 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 11 Test

• Making Connections: a review of Chapters 1-11

• Critical Thinking

12 Sequences and Series (Available online at www.mhhe.com/dugopolski)

12.1 Sequences

12.2 Series

12.3 Arithmetic Sequences and Series

12.4 Geometric Sequences and Series

12.5 Binomial Expansions

Chapter 12 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 12 Test

• Making Connections: a review of Chapters 1-12

• Critical Thinking

Appendix A

Answers to Selected Exercises

Index

APPLICATIONS INDEX

1 The Real Numbers

1.1 Sets

1.2 The Real Numbers

1.3 Operations on the Set of Real Numbers

1.4 Evaluating Expressions and the Order of Operations

1.5 Properties of the Real Numbers

1.6 Using the Properties

Chapter 1 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 1 Test

• Critical Thinking

2 Linear Equations and Inequalities in One Variable

2.1 Linear Equations in One Variable

2.2 Formulas and Functions

2.3 Applications

2.4 Inequalities

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

Chapter 2 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 2 Test

• Making Connections: A review of Chapters 1-2

• Critical Thinking

3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope of a Line

3.3 Three Forms for the Equation of a Line

3.4 Linear Inequalities and Their Graphs

3.5 Functions and Relations

Chapter 3 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 3 Test

• Making Connections: a review of Chapters 1-3

• Critical Thinking

4 Systems of Linear Equations

4.1 Solving Systems by Graphing and Substitution

4.2 The Addition Method

4.3 Systems of Linear Equations in Three Variables

4.4 Solving Linear Systems Using Matrices

4.5 Determinants and Cramer’s Rule

4.6 Linear Programming

Chapter 4 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 4 Test

• Making Connections: a review of Chapters 1-4

• Critical Thinking

5 Exponents and Polynomials

5.1 Integral Exponents and Scientific Notation

5.2 The Power Rules

5.3 Polynomials and Polynomial Functions

5.4 Multiplying Binomials

5.5 Factoring Polynomials

5.6 Factoring ax² + bx + c

5.7 Factoring Strategy

5.8 Solving Equations by Factoring

Chapter 5 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 5 Test

• Making Connections: a review of Chapters 1-5

• Critical Thinking

6 Rational Expressions and Functions

6.1 Properties of Rational Expressions and Functions

6.2 Multiplication and Division

6.3 Addition and Subtraction

6.4 Complex Fractions

6.5 Division of Polynomials

6.6 Solving Equations Involving Rational Expressions

6.7 Applications

Chapter 6 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 6 Test

• Making Connections: a review of Chapters 1-6

• Critical Thinking

7 Radicals and Rational Exponents

7.1 Radicals

7.2 Rational Exponents

7.3 Adding, Subtracting, and Multiplying Radicals

7.4 Quotients, Powers, and Rationalizing Denominators

7.5 Solving Equations with Radicals and Exponents

7.6 Complex Numbers

Chapter 7 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 7 Test

• Making Connections: a review of Chapters 1-7

• Critical Thinking

8 Quadratic Equations, Functions, and Inequalities

8.1 Factoring and Completing the Square

8.2 The Quadratic Formula

8.3 More on Quadratic Equations

8.4 Quadratic Functions and Their Graphs

8.5 Quadratic Inequalities

Chapter 8 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 8 Test

• Making Connections: a review of Chapters 1-8

• Critical Thinking

9 Additional Function Topics

9.1 Graphs of Functions and Relations

9.2 Transformations of Graphs

9.3 Combining Functions

9.4 Inverse Functions

9.5 Variation

Chapter 9 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 9 Test

• Making Connections: a review of Chapters 1-9

• Critical Thinking

10 Exponential and Logarithmic Functions

10.1 Exponential Functions and Their Applications

10.2 Logarithmic Functions and Their Applications

10.3 Properties of Logarithms

10.4 Solving Equations and Applications

Chapter 10 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 10 Test

• Making Connections: a review of Chapters 1-10

• Critical Thinking

11 Nonlinear Systems and the Conic Sections

11.1 Nonlinear Systems of Equations

11.2 The Parabola

11.3 The Circle

11.4 The Ellipse and Hyperbola

11.5 Second-Degree Inequalities

Chapter 11 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 11 Test

• Making Connections: a review of Chapters 1-11

• Critical Thinking

12 Sequences and Series (Available online at www.mhhe.com/dugopolski)

12.1 Sequences

12.2 Series

12.3 Arithmetic Sequences and Series

12.4 Geometric Sequences and Series

12.5 Binomial Expansions

Chapter 12 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 12 Test

• Making Connections: a review of Chapters 1-12

• Critical Thinking

Appendix A

Answers to Selected Exercises

Index

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