Intermediate Algebra

Is there anything more beautiful than an #x1C;A#x1D; in Algebra?Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying resources with one goal in mind: giving students all the tools they need to achieve success. #xA0; With this revision, the Lial team has further refined the presentation and exercises throughout the text. They offer several exciting new resources for students that will provide extra help when needed, regardless of the learning environment (classroom, lab, hybrid, online, etc)#x13;new study skills activities in the text, an expanded video program available in MyMathLab and on the Video Resources on DVD, and more!

Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

 

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

 

A native Midwesterner, Terry McGinnis received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series that includes Introductory Algebra, Intermediate Algebra, and Introductory and Intermediate Algebra. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.

 

Study Skills: Using Your Math Textbook

 

1. Review of the Real Number System

1.1 Basic Concepts

1.2 Operations on Real Numbers

1.3 Exponents, Roots, and Order of Operations

1.4 Properties of Real Numbers

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

Study Skills: Reading Your Math Textbook

 

2. Linear Equations, Inequalities, and Applications

2.1 Linear Equations in One Variable

Study Skills: Tackling Your Homework

2.2 Formulas and Percents

2.3 Applications of Linear Equations

Study Skills: Taking Lecture Notes

2.4 Further Applications of Linear Equations

Summary Exercises on Solving Applied Problems

2.5 Linear Inequalities in One Variable

Study Skills: Using Study Cards

2.6 Set Operations and Compound Inequalities

Study Skills: Using Study Cards Revisited

2.7 Absolute Value Equations and Inequalities

Study Skills: Reviewing a Chapter

Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

Chapters 1-2 Cumulative Review Exercises

 

3. Graphs, Linear Equations, and Functions

3.1 The Rectangular Coordinate System

Study Skills: Managing Your Time

3.2 The Slope of a Line

3.3 Linear Equations in Two Variables

Summary Exercises on Slopes and Equations of Lines

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Relations and Functions

3.6 Function Notation and Linear Functions

Study Skills: Taking Math Tests

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

Chapters 1-3 Cumulative Review Exercises

 

4. Systems of Linear Equations

4.1 Systems of Linear Equations in Two Variables

Study Skills: Analyzing Your Test Results

4.2 Systems of Linear Equations in Three Variables

4.3 Applications of Systems of Linear Equations

4.4 Solving Systems of Linear Equations by Matrix Methods

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

Chapters 1-4 Cumulative Review Exercises

 

5. Exponents, Polynomials, and Polynomial Functions

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Polynomial Functions, Graphs, and Composition

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

Chapters 1-5 Cumulative Review Exercises

 

6. Factoring

6.1 Greatest Common Factors and Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring

6.4 A General Approach to Factoring

6.5 Solving Equations by Factoring

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

Chapters 1-6 Cumulative Review Exercises

 

7. Rational Expressions and Functions

7.1 Rational Expressions and Functions; Multiplying and Dividing

7.2 Adding and Subtracting Rational Expressions

7.3 Complex Fractions

7.4 Equations with Rational Expressions and Graphs

Summary Exercises on Rational Expressions and Equations

7.5 Applications of Rational Expressions

7.6 Variation

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

Chapters 1-7 Cumulative Review Exercises

 

8. Roots, Radicals, and Root Functions

8.1 Radical Expressions and Graphs

8.2 Rational Exponents

8.3 Simplifying Radical Expressions

8.4 Adding and Subtracting Radical Expressions

8.5 Multiplying and Dividing Radical Expressions

Summary Exercises on Operations with Radicals and Rational Exponents

8.6 Solving Equations with Radicals

8.7 Complex Numbers

Study Skills: Preparing for Your Math Final Exam

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

Chapters 1-8 Cumulative Review Exercises

 

9. Quadratic Equations, Inequalities, and Functions

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

9.3 Equations Quadratic in Form

Summary Exercises on Solving Quadratic Equations

9.4 Formulas and Further Applications

9.5 Graphs of Quadratic Functions

9.6 More about Parabolas and Their Applications

9.7 Polynomial and Rational Inequalities

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

Chapters 1-9 Cumulative Review Exercises

 

10. Inverse, Exponential, and Logarithmic Functions

10.1 Inverse Functions

10.2 Exponential Functions

10.3 Logarithmic Functions

10.4 Properties of Logarithms

10.5 Common and Natural Logarithms

10.6 Exponential and Logarithmic Equations; Further Applications

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Test

Chapters 1-10 Cumulative Review Exercises

 

11. Nonlinear Functions, Conic Sections, and Nonlinear Systems

11.1 Additional Graphs of Functions

11.2 The Circle and the Ellipse

11.3 The Hyperbola and Functions Defined by Radicals

11.4 Nonlinear Systems of Equations

11.5 Second-Degree Inequalities and Systems of Inequalities

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Chapters 1-11 Cumulative Review Exercises

 

12. Sequences and Series

12.1 Sequences and Series

12.2 Arithmetic Sequences

12.3 Geometric Sequences

12.4 The Binomial Theorem

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Test

Chapter 1-12 Cumulative Review Exercises

 

Appendix A: Determinants and Cramer's Rule

Appendix B: Synthetic Division