Introductory Algebra

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). He has been a rabid 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 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: Your Brain Can Learn Mathematics

 

R. Prealgebra Review

R.1 Fractions

R.2 Decimals and Percents

            Study Skills: Using Your Textbook

 

1. The Real Number System

1.1 Exponents, Order of Operations, and Inequality

            Study Skills: Homework: How, Why, When

1.2 Variables, Expressions, and Equations

            Study Skills: Taking Lecture Notes

1.3 Real Numbers and the Number Line

            Study Skills: Using Study Cards

1.4 Adding Real Numbers

1.5 Subtracting Real Numbers

1.6 Multiplying and Dividing Real Numbers

            Summary Exercises on Operations with Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

            Study Skills: Reviewing a Chapter

            Summary ~ Review Exercises ~ Test

            Study Skills: Preparing for Tests

 

2. Equations, Inequalities, and Applications

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 More on Solving Linear Equations

            Study Skills: Using Study Cards: Revisited

            Summary Exercises on Solving Linear Equations

2.4 An Introduction to Applications of Linear Equations

2.5 Formulas and Additional Applications from Geometry

2.6 Ratio, Proportion, and Percent

            Summary Exercises on Solving Applied Problems

2.7 Solving Linear Inequalities

            Study Skills: Managing Your Time

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

            Study Skills: Taking Tests

 

3. Graphs of Linear Equations and Inequalities in Two Variables

3.1 Reading Graphs; Linear Equations in Two Variables

3.2 Graphing Linear Equations in Two Variables

3.3 Slope of a Line

3.4 Equations of Lines

            Summary Exercises on Graphing Linear Equations

3.5 Graphing Linear Inequalities in Two Variables

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

            Study Skills: Analyzing Your Test Results

 

4. Systems of Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

            Summary Exercises on Solving Systems of Linear Equations

4.4 Applications of Linear Systems

4.5 Solving Systems of Linear Inequalities

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

 

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 The Product Rule and Power Rules for Exponents

5.3 Multiplying Polynomials

5.4 Special Products

5.5 Integer Exponents and the Quotient Rule

            Summary Exercises on the Rules for Exponents

5.6 Dividing a Polynomial by a Monomial

5.7 Dividing a Polynomial by a Polynomial

5.8 An Application of Exponents: Scientific Notation

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

 

6. Factoring and Applications

6.1 Factors; The Greatest Common Factor

6.2 Factoring Trinomials

6.3 Factoring Trinomials by Grouping

6.4 Factoring Trinomials Using FOIL

6.5 Special Factoring Techniques

            Summary Exercises on Factoring

6.6 Solving Quadratic Equations by Factoring

6.7 Applications of Quadratic Equations

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

 

7. Rational Expressions and Applications

7.1 The Fundamental Property of Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

            Study Skills: Making a Mind Map

7.3 Least Common Denominators

7.4 Adding and Subtracting Rational Expressions

7.5 Complex Fractions

7.6 Solving Equations with Rational Expressions

            Summary Exercises on Operations and Equations with Rational Expressions

7.7 Applications of Rational Expressions

7.8 Variation

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

            Study Skills: Preparing for a Final Exam

 

8. Roots and Radicals

8.1 Evaluating Roots

8.2 Multiplying, Dividing, and Simplifying Radicals

8.3 Adding and Subtracting Radicals

8.4 Rationalizing the Denominator

8.5 More Simplifying and Operations with Radicals

            Summary Exercises on Operations with Radicals

8.6 Solving Equations with Radicals

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

 

9. Quadratic Equations

9.1 Solving Quadratic Equations by the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations by the Quadratic Formula

            Summary Exercises on Solving Quadratic Equations

9.4 Graphing Quadratic Equations

9.5 Introduction to Functions

            Summary ~ Review Exercises ~ Test ~ Cumulative Review Exercises

 

Appendix A. Strategies for Problem Solving

Appendix B. Factoring Sums and Differences of Cubes

 

Answers to Selected Exercises

Solutions to Selected Exercises

Index