Introductory and Intermediate 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

 

Chapter R: Prealgebra Review

    R.1 Fractions

    R.2 Decimals and Percents

 

1. The Real Number System

1.1 Exponents, Order of Operations, and Inequality

Study Skills: Homework: How, Why, and 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

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

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

Study Skills: Tips for Taking Math Tests

 

3. Graphs of Linear Equations and Inequalities; Functions

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 Linear Equations and Graphs

3.5 Graphing Linear Inequalities in Two Variables

3.6 Introduction to Functions

Study Skills: Analyzing Your Test Results

 

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 of 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 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

 

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

6.6 A General Approach to Factoring

6.7 Solving Quadratic Equations by Factoring

6.8 Applications of Quadratic Equations

Study Skills: Preparing for Your Math Final Exam

 

7. Rational Expressions and Functions

7.1 Rational Expressions and Functions; Multiplying and Dividing

Study Skills: Making a Mind Map

7.2 Adding and Subtracting Rational Expressions

7.3 Complex Functions

7.4 Equations with Rational Expressions and Graphs

Summary Exercises on Rational Expressions and 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 on 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

8.6 Solving Systems of Linear Equations by Matrix Methods

 

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 on 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 on Solving Quadratic Equations

10.5 Formulas and Further 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 Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

11.4 Properties of Logarithms

11.5 Common and Natural Logarithms

11.6 Exponential and Logarithmic Equations; Further 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

Appendix B. Strategies for Problem Solving

Appendix C. Synthetic Division