Introductory and Intermediate Algebra

Marge Lial (late) became interested in math at an early age–it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology; trips to various digs and ruin sites 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. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed.   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.

R. Prealgebra Review

R.1 Fractions

R.2 Decimals and Percents

            Study Skills: Using Your Math Textbook

            Study Skills: Reading Your Math Textbook

 

1. The Real Number System

1.1 Exponents, Order of Operations, and Inequality

            Study Skills: Taking Lecture Notes

1.2 Variables, Expressions, and Equations

            Study Skills: Tackling Your Homework

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 Performing Operations with Real Numbers

1.7 Properties of Real Numbers

            Study Skills: Reviewing a Chapter

1.8 Simplifying Expressions

            Study Skills: Taking Math Tests

 

2. Equations, Inequalities, and Applications

2.1 The Addition Property of Equality

            Study Skills: Managing Your Time

2.2 The Multiplication Property of Equality

            Study Skills: Analyzing Your Test Results

2.3 More on Solving Linear Equations

            Study Skills: Using Study Cards Revisited

            Summary Exercises Applying Methods for 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 Applying Problem-Solving Techniques

2.7 Solving Linear Inequalities

 

3. Graphs of Linear Equations and Inequalities in Two Variables; Functions

3.1 Linear Equations in Two Variables; The Rectangular Coordinate System

            Study Skills: Preparing for Your Math Final

3.2 Graphing Linear Equations in Two Variables

3.3 The Slope of a Line

3.4 Writing and Graphing Equations of Lines

            Summary Exercises Applying Graphing and Equation-Writing Techniques for Lines

3.5 Graphing Linear Inequalities in Two Variables

3.6 Introduction to Relations and Functions

3.7 Function Notation and Linear Functions

 

4. Systems of Linear 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 Applying Techniques for Solving Systems of Linear Equations

4.4 Applications of Linear Systems

4.5 Solving Systems of Linear Inequalities

 

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 Applying 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

 

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 by Using the FOIL Method

6.5 Special Factoring Techniques

6.6 A General Approach to Factoring

6.7 Solving Quadratic Equations by Factoring

6.8 Applications of Quadratic Equations

 

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 Simplifying Rational Expressions vs Solving Rational Equations

7.5 Applications of Rational Expressions

7.6 Variation

 

8. Equations, Inequalities, and Systems Revisited

8.1 Review of Solving Linear Equations and Inequalities

8.2 Set Operations and Compound Inequalities

8.3 Absolute Value Equations and Inequalities

            Summary Exercises Solving Linear and Absolute Value Equations and Inequalities

8.4 Review of Systems of Linear Equations in Two Variables

8.5 Systems of Linear Equations in Three Variables; Applications

 

9. Roots, Radicals, and Root Functions

9.1 Radical Expressions and Graphs

9.2 Rational Exponents

9.3 Simplifying Radical Expressions

9.4 Adding and Subtracting Radical Expressions

9.5 Multiplying and Dividing Radical Expressions

            Summary Exercises Performing Operations with Radicals and Rational Exponents

9.6 Solving Equations with Radicals

9.7 Complex Numbers

 

10. Quadratic Equations, Inequalities, and Functions

10.1 Solving Quadratic Equations by the Square Root Property

10.2 Solving Quadratic Equations by Completing the Square

10.3 Solving Quadratic Equations by the Quadratic Formula

10.4 Equations Quadratic in Form

            Summary Exercises Applying Methods for Solving Quadratic Equations

10.5 Formulas and Applications

10.6 Graphs of Quadratic Functions

10.7 More about Parabolas and Their Applications

10.8 Polynomial and Rational Inequalities

 

11. Inverse, Exponential, and Logarithmic Functions

11.1 Operations on Functions and Composition

11.2 Inverse Functions

11.3 Exponential Functions

11.4 Logarithmic Functions

11.5 Properties of Logarithms

11.6 Common and Natural Logarithms

11.7 Exponential and Logarithmic Equations and Their Applications

 

12. Nonlinear Functions, Conic Sections, and Nonlinear Systems

12.1 Additional Graphs of Functions; Operations and Composition

12.2 The Circle and the Ellipse

12.3 The Hyperbola and Other Functions Defined by Radicals

12.4 Nonlinear Systems of Equations

12.5 Second-Degree Inequalities and Systems of Inequalities

 
Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra)
Appendix B: Solving Systems of Linear Equations by Matrix Methods
Appendix C: Synthetic Division
Answers to Selected Exercises
Solutions to Selected Exercises
Index