# Intermediate Algebra (softcover)

3^{rd}Edition

ISBN10: 0073384429

ISBN13: 9780073384429

Copyright: 2015

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

# Intermediate Algebra, 3rd Edition

## R Review of Basic Algebraic Concepts

R.1 Study Skills

Group Activity: Becoming a Successful Student

R.2 Sets of Numbers and Interval Notation

R.3 Operations on Real Numbers

R.4 Simplifying Expressions

## 1 Linear Equations and Inequalities in One Variable

1.1 Linear Equations in One Variable

PRE: Equations versus Expressions

1.2 Application of Linear Equations in One Variable

1.3 Applications to Geometry and Literal Equations

1.4 Linear Inequalities in One Variable

1.5 Compound Inequalities

1.6 Absolute Value Equations

1.7 Absolute Value Inequalities

PRE: Identifying Equations and Inequalities Group Activity: Understanding the Symbolism of Mathematics

## 2 Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

2.2 Slope of a Line and Rate of Change

2.3 Equations of a Line

PRE: Characteristics of Linear Equations

2.4 Application of Linear Equations and Modeling

Group Activity: Using Linear Equations to Construct Images

## 3 Relations and Functions

3.1 Relations and Applications

3.2 Introduction to Functions

3.3 Graphs of Basic Functions

PRE: Characteristics of Relations

3.4 Algebra of Functions, Composition, and Applications Group Activity: Deciphering a Coded Message

## 4 Systems of Linear Equations

4.1 Solving Systems of Linear Equations by the Graphing Method

4.2 Solving Systems of Linear Equations by Using the Substitution Method

4.3 Solving Systems of Linear Equations by Using the Addition Method

PRE: Solving Systems of Linear Equations

4.4 Applications of Systems of Linear Equations in Two Variables

4.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

4.6 Systems of Linear Equations in Three Variables and Applications

4.7 Solving Systems of Linear Equations by Using Matrices

Group Activity: Creating a Quadratic Model of the Form y = at^2 +bt + c

## 5 Polynomials

5.1 Properties of Integer Exponents and Scientific Notation

5.2 Addition and Subtraction of Polynomials and Polynomial Functions

5.3 Multiplication of Polynomials

5.4 Division of Polynomaisl

PRE: Operations on Polynomials

5.5 Greatest Common Factor and Factoring by Grouping

5.6 Factoring Trinomials and Perfect Square Trinomials

5.7 Factoring Binomials Including Sum and Difference of Cubes

PRE: Factoring Summary

5.8 Solving Equations and Applications by Factoring Group Activity: Investigating Pascal's Triangle

## 6 Rational Expressions and Rational Equations

6.1 Rational Expressions and Rational Functions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Complex Fractions

PRE: Operations on Rational Expressions

6.5 Solving Rational Equations

PRE: Rational Equations versus Expressions

6.6 Applications of Rational Equations and Proportions

6.7 Variation

Group Activity: Computing the Future Value of an Investment

## 7 Radicals and Complex Numbers

7.1 Definition of an nth-Root

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Addition and Subtraction of Radicals

7.5 Multiplication of Radicals

PRE: Simplifying Radical Expressions

7.6 Division of Radicals and Rationalisation

7.7 Radical Equations and Applications

7.8 Complex Numbers

Group Activity: Margin of Error of Survey Results

## 8 Quadratic Equations, Functions, and Inequalities

8.1 Square Root Property and Completing the Square

8.2 Quadratic Formula and Applications

8.3 Equations in Quadratic Form

PRE: Equations in Quadratic Form

8.4 Graphs of Quadratic Functions

8.5 Vertex of a Parabola: Applications and Modeling

8.6 Polynomials and Rational Inequalities

PRE: Recognizing Equations and Inequalities

Group Activity: Creating a Quadratic Model of the Form y = a(x - h)^2 + k

## 9 Exponential and Logarithmic Functions

9.1 Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

PRE: Identifying Graphs of Functions

9.4 Properties of Logarithms

9.5 The Irrational Number e

PRE: Logarithmic and Exponential Forms

9.6 Exponential Equations and Applications

9.7 Logarithmic Equations and Applications

Group Activity: Creating a Population Model

## 10 Conic Sections

10.1 Distance Formula, Midpoint, and Circles

10.2 More of the Parabola

10.3 The Ellipse and Hyperbola

PRE: Formulas for Conic Sections

10.4 Nonlinear Systems of Equations in Two Variables

10.5 Nonlinear Inequalities and Systems of Inequalities

Group Activity: Investigating the Graphs of Conic Sections on a Calculator

## Additional Topics Appendix

A.1 Binomial Expansions

A.2 Determinants and Cramer's Rule

A.3 Sequences and Series

A.4 Arithmetic and Geometric Sequences and Series

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Molly O'Neill**

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.

**I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.**

**Nancy Hyde**

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.

**I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.**

### Connect

By prompting students to engage with key concepts, while continually adapting to their individual needs, Connect activates learning and empowers students to take control resulting in better grades and increased retention rates. Proven online content integrates seamlessly with our adaptive technology, and helps build student confidence outside of the classroom.

Learn More### Connect Reporting

View complete, at-a-glance reports for individual students or the whole class. Generate powerful data related to student performance across learning outcomes, specific topics, level of difficulty and more. Additionally, you can compare student performance in different sections of the course.

Learn More### LMS Integration

With a single point of access, Connect seamlessly integrates with every learning management system on the market today. Quickly access registration, attendance, assignments, grades, and course resources in real time in one, familiar location.

### Implementation and digital support

We provide self-directed resources, local, on campus training, and live webinar sessions, to get you up and running in a way that works for you, and to help you get the most out of Connect. We maintain a technical support team available to both instructors and students for any questions that might arise while using Connect.

Learn More# Intermediate Algebra, 3rd Edition

## R Review of Basic Algebraic Concepts

R.1 Study Skills

Group Activity: Becoming a Successful Student

R.2 Sets of Numbers and Interval Notation

R.3 Operations on Real Numbers

R.4 Simplifying Expressions

## 1 Linear Equations and Inequalities in One Variable

1.1 Linear Equations in One Variable

PRE: Equations versus Expressions

1.2 Application of Linear Equations in One Variable

1.3 Applications to Geometry and Literal Equations

1.4 Linear Inequalities in One Variable

1.5 Compound Inequalities

1.6 Absolute Value Equations

1.7 Absolute Value Inequalities

PRE: Identifying Equations and Inequalities Group Activity: Understanding the Symbolism of Mathematics

## 2 Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

2.2 Slope of a Line and Rate of Change

2.3 Equations of a Line

PRE: Characteristics of Linear Equations

2.4 Application of Linear Equations and Modeling

Group Activity: Using Linear Equations to Construct Images

## 3 Relations and Functions

3.1 Relations and Applications

3.2 Introduction to Functions

3.3 Graphs of Basic Functions

PRE: Characteristics of Relations

3.4 Algebra of Functions, Composition, and Applications Group Activity: Deciphering a Coded Message

## 4 Systems of Linear Equations

4.1 Solving Systems of Linear Equations by the Graphing Method

4.2 Solving Systems of Linear Equations by Using the Substitution Method

4.3 Solving Systems of Linear Equations by Using the Addition Method

PRE: Solving Systems of Linear Equations

4.4 Applications of Systems of Linear Equations in Two Variables

4.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

4.6 Systems of Linear Equations in Three Variables and Applications

4.7 Solving Systems of Linear Equations by Using Matrices

Group Activity: Creating a Quadratic Model of the Form y = at^2 +bt + c

## 5 Polynomials

5.1 Properties of Integer Exponents and Scientific Notation

5.2 Addition and Subtraction of Polynomials and Polynomial Functions

5.3 Multiplication of Polynomials

5.4 Division of Polynomaisl

PRE: Operations on Polynomials

5.5 Greatest Common Factor and Factoring by Grouping

5.6 Factoring Trinomials and Perfect Square Trinomials

5.7 Factoring Binomials Including Sum and Difference of Cubes

PRE: Factoring Summary

5.8 Solving Equations and Applications by Factoring Group Activity: Investigating Pascal's Triangle

## 6 Rational Expressions and Rational Equations

6.1 Rational Expressions and Rational Functions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Complex Fractions

PRE: Operations on Rational Expressions

6.5 Solving Rational Equations

PRE: Rational Equations versus Expressions

6.6 Applications of Rational Equations and Proportions

6.7 Variation

Group Activity: Computing the Future Value of an Investment

## 7 Radicals and Complex Numbers

7.1 Definition of an nth-Root

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Addition and Subtraction of Radicals

7.5 Multiplication of Radicals

PRE: Simplifying Radical Expressions

7.6 Division of Radicals and Rationalisation

7.7 Radical Equations and Applications

7.8 Complex Numbers

Group Activity: Margin of Error of Survey Results

## 8 Quadratic Equations, Functions, and Inequalities

8.1 Square Root Property and Completing the Square

8.2 Quadratic Formula and Applications

8.3 Equations in Quadratic Form

PRE: Equations in Quadratic Form

8.4 Graphs of Quadratic Functions

8.5 Vertex of a Parabola: Applications and Modeling

8.6 Polynomials and Rational Inequalities

PRE: Recognizing Equations and Inequalities

Group Activity: Creating a Quadratic Model of the Form y = a(x - h)^2 + k

## 9 Exponential and Logarithmic Functions

9.1 Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

PRE: Identifying Graphs of Functions

9.4 Properties of Logarithms

9.5 The Irrational Number e

PRE: Logarithmic and Exponential Forms

9.6 Exponential Equations and Applications

9.7 Logarithmic Equations and Applications

Group Activity: Creating a Population Model

## 10 Conic Sections

10.1 Distance Formula, Midpoint, and Circles

10.2 More of the Parabola

10.3 The Ellipse and Hyperbola

PRE: Formulas for Conic Sections

10.4 Nonlinear Systems of Equations in Two Variables

10.5 Nonlinear Inequalities and Systems of Inequalities

Group Activity: Investigating the Graphs of Conic Sections on a Calculator

## Additional Topics Appendix

A.1 Binomial Expansions

A.2 Determinants and Cramer's Rule

A.3 Sequences and Series

A.4 Arithmetic and Geometric Sequences and Series

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Molly O'Neill**

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.

**I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.**

**Nancy Hyde**

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.

**I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.**

### Connect

By prompting students to engage with key concepts, while continually adapting to their individual needs, Connect activates learning and empowers students to take control resulting in better grades and increased retention rates. Proven online content integrates seamlessly with our adaptive technology, and helps build student confidence outside of the classroom.

Learn More### Connect Reporting

View complete, at-a-glance reports for individual students or the whole class. Generate powerful data related to student performance across learning outcomes, specific topics, level of difficulty and more. Additionally, you can compare student performance in different sections of the course.

Learn More### LMS Integration

With a single point of access, Connect seamlessly integrates with every learning management system on the market today. Quickly access registration, attendance, assignments, grades, and course resources in real time in one, familiar location.

### Implementation and digital support

We provide self-directed resources, local, on campus training, and live webinar sessions, to get you up and running in a way that works for you, and to help you get the most out of Connect. We maintain a technical support team available to both instructors and students for any questions that might arise while using Connect.

Learn More# Related Products

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