Elementary Algebra

George Woodbury earned his bachelor’s degree in mathematics from the University of California—Santa Barbara in 1990 and his master’s degree in mathematics from California State University—Northridge, in 1994. He currently teaches at College of the Sequoias in Visalia, CA–just outside of Fresno. He has been honored as an instructor by both his students and his colleagues. Aside from teaching and writing, George served as the department chair of the math/engineering division from 1999—2004. George’s Elementary and Intermediate Algebra, First Edition, was published in 2006.

1. Review of Real Numbers

1.1 Integers, Opposites, and Absolute Value

1.2 Operations with Integers

1.3 Fractions 

1.4 Operations with Fractions 

1.5 Decimals and Percents 

1.6 Representing Data Graphically

1.7 Exponents and Order of Operations 

1.8 Introduction to Algebra

 

2. Linear Equations

2.1 Introduction to Linear Equations

2.2 Solving Linear Equations: A General Strategy

2.3 Problem Solving; Applications of Linear Equations

2.4 Applications Involving Percentages; Ratio and Proportion

2.5 Linear Inequalities

 

3. Graphing Linear Equations

3.1 The Rectangular Coordinate System; Equations in Two Variables

3.2 Graphing Linear Equations and Their Intercepts

3.3 Slope of a Line

3.4 Linear Functions

3.5 Parallel and Perpendicular Lines

3.6 Equations of Lines 

3.7 Linear Inequalities

 

4. Systems of Equations

4.1 Systems of Linear Equations; Solving Systems by Graphing

4.2 Solving Systems of Equations by Using the Substitution Method

4.3 Solving Systems of Equations by Using the Addition Method

4.4 Applications of Systems of Equations

4.5 Systems of Linear Inequalities

 

5. Exponents and Polynomials

5.1 Exponents

5.2 Negative Exponents; Scientific Notation

5.3 Polynomials; Addition and Subtraction of Polynomials

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

 

6. Factoring and Quadratic Equations

6.1 An Introduction to Factoring; The Greatest Common Factor; Factoring by Grouping

6.2 Factoring Trinomials of the Form x2+bx+c

6.3 Factoring Trinomials of the Form ax2+bx+c, where a≠1

6.4 Factoring Special Binomials

6.5 Factoring Polynomials: A General Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Functions

6.8 Applications of Quadratic Equations and Quadratic Functions

 

7. Rational Expressions and Equations

7.1 Rational Expressions and Functions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions That Have the Same Denominator

7.4 Addition and Subtraction of Rational Expressions That Have Different Denominators

7.5 Complex Fractions

7.6 Rational Equations

7.7 Applications of Rational Equations

 

8. Radical Expressions and Equations

8.1 Square Roots and Radical Notation

8.2 Simplifying, Adding, and Subtracting Radical Expressions

8.3 Multiplying and Dividing Radical Expressions

8.4 Radical Equations

8.5 Applications of Radical Equations

8.6 Complex Numbers

8.7 Rational Exponents 

 

9. Quadratic Equations

9.1 Solving Quadratic Equations by Extracting Square Roots; Completing the Square

9.2 The Quadratic Formula

9.3 Applications Using Quadratic Equations

9.4 Graphing Quadratic Equations and Quadratic Functions

 

Appendices

A. Synthetic Division

B. Sample Solutions to Writing in Mathematics Exercises