Marge Lial (late) 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, 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. Her interest in archeology led to trips to various digs and ruin sites, producing 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 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.

David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. His hobbies include travel, dancing, bicycling, and hiking.

The table of contents below shows the review topics (bulleted text) that are integrated into the Essentials of College Algebra course. The Integrated Review includes worksheets, videos, and other materials designed to help students master these important topics.

R. Review of Basic Concepts

R.1 Sets

R.2 Real Numbers and Their Properties

R.3 Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Rational Exponents

R.7 Radical Expressions

            Chapter R Test Prep

            Review Exercises

            Test

1. Equations and Inequalities

1.1 Linear Equations

• 1.1 R

• Properties of Real Numbers
• Evaluating Exponential Expressions
• Order of Operations
• Simplifying Expressions
• Operations on Real Numbers

1.2 Applications and Modeling with Linear Equations

• 1.2 R
• Operations with Decimals
• Translating Word Phrases into Algebraic Expressions and Equations
• Formulas and Percent

1.3 Complex Numbers

• 1.3 R
• Radical Notation
• Simplifying Square Root Radicals
• Rationalizing Square Root Denominators
• Addition, Subtraction, and Multiplication of Square Root Radicals
• Product Rule for Exponents
• Zero Exponent Rule
• Negative Exponent Rule
• Add, Subtract, and Multiply Polynomials

1.4 Quadratic Equations

• 1.4 R
• Factoring Out the Greatest Common Factor
• Factoring Trinomials
• Factoring Binomials

            Chapter 1 Quiz (Sections 1.1 - 1.4)

1.5 Applications and Modeling with Quadratic Equations

• 1.5 R
• Factoring Out the Greatest Common Factor
• Factoring Trinomials
• Factoring Binomials

1.6 Other Types of Equations and Applications

• 1.6 R
• Rational Expressions
• Lowest Terms of a Rational Expression
• Operations with Rational Expressions
• Factoring (including by substitution)
• Negative and Rational Exponents
• Simplifying Radicals with Index Greater than 2

1.7 Inequalities

• 1.7 R
• Sets and Set Operations
• Order on the Number Line

1.8 Absolute Value Equations and Inequalities

• 1.8 R
• Definition and Properties of Absolute Value
• Evaluating Absolute Value Expressions

            Chapter 1 Test Prep

            Review Exercises

            Test

2. Graphs and Functions

2.1 Rectangular Coordinates and Graphs

• 2.1. R   Review
• Evaluating Expressions for Given Values

2.2 Circles

• 2.2. R Review
• Squaring a Binomial
• Factoring Perfect Square Trinomials

2.3 Functions

• 2.3. R Review
• Solving for a Specified Variable

2.4 Linear Functions

• 2.4. R Review
• Division Involving Zero

            Chapter 2 Quiz (Sections 2.1 - 2.4)

2.5 Equations of Lines and Linear Models

2.6 Graphs of Basic Functions

2.7 Graphing Techniques

            Chapter 2 Quiz (Sections 2.5 - 2.7)

2.8 Function Operations and Composition

• 2.8. R Review
• Operations with Polynomials
• Operations with Rational Expressions

            Chapter 2 Test Prep

            Review Exercises

            Test

3. Polynomial and Rational Functions.

3.1 Quadratic Functions and Models

• 3.1. R Review
• Squaring a Binomial
• Factoring Perfect Square Trinomials

3.2 Synthetic Division

• 3.2. R Review
• Dividing Polynomials

3.3 Zeros of Polynomial Functions

3.4 Polynomial Functions: Graphs, Applications, and Models

3.5 Rational Functions: Graphs, Applications, and Models

            Chapter 3 Quiz (Sections 3.1 - 3.5)

3.6 Variation

• 3.6. R Review
• Using Geometric Formulas
• Ratio and Proportion

            Chapter 3 Test Prep

            Review Exercises

            Test

4. Inverse, Exponential, and Logarithmic Functions.

4.1 Inverse Functions

• 4.1 R Review
• Simplifying Complex Fractions

4.2 Exponential Functions

4.3 Logarithmic Functions

4.4 Evaluating Logarithms and the Change-of-Base Theorem

            Chapter 4 Quiz (Sections 4.1 - 4.4)

4.5 Exponential and Logarithmic Equations

• 4.5. R Review

            Rules for Rounding

4.6 Applications and Models of Exponential Growth and Decay

            Chapter 4 Test Prep

            Review Exercises

            Test

5. Systems and Matrices

5.1 Systems of Linear Equations

• 5.1. R Review
• Evaluating Expressions for Given Values
• Inverse Property of Multiplication
• Inverse Property of Addition

5.2 Matrix Solution of Linear Systems

5.3 Determinant Solution of Linear Systems

5.4 Partial Fractions

            Chapter 5 Quiz (Sections 5.1 - 5.4)

5.5 Nonlinear Systems of Equations

5.6 Systems of Inequalities and Linear Programming

5.7 Properties of Matrices

5.8 Matrix Inverses

            5.8. R

            Identity and Inverse Properties of Addition and Multiplication of Real Numbers

            Chapter 5 Test Prep

            Review Exercises

            Test

Glossary

Solutions to Selected Exercises

Answers to Selected Exercises

Index of Applications

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