Introductory Algebra

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers. My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students. Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics. I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students. Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra. I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.

Introductory Algebra, 3rd Edition
RReference
R.1Study Tips
R.2Fractions
R.3Decimals and Percents
R.4Introduction to Geometry
1The Set of Real Numbers
1.1Introduction to Algebra and the Set of Real Numbers
1.2Exponents, Square Roots, and the Order of Operations
1.3Addition of Real Numbers
1.4Subtraction of Real Numbers
PRE: Addition and Subtraction of Real Numbers
1.5Multiplication and Division of Real Numbers
1.6Properties of Real Numbers and Simplifying Expressions
Group Activity: Evaluating Formulas Using a Calculator
2Linear Equations and Inequalities
2.1Addition, Subtraction, Multiplication, and Division Properties of Equality
2.2Solving Linear Equations
2.3Linear Equations: Clearing Fractions and Decimals
PRE: Equations and Expressions
2.4Applications of Linear Equations:Introduction to Problem Solving
2.5Applications Involving Percents
2.6Literal Equations and Applications of Geometry
2.7Mixture Applications and Uniform Motion
2.8Linear Inequalities
Group Activity: Computing Body Mass Index (BMI)
3Graphing Linear Equations in Two Variables
3.1Rectangular Coordinate System
3.2Linear Equations in Two Variables
3.3Slope of a Line and Rate of Change
3.4Slope-Intercept Form of a Linear Equation
PRE: Linear Equations in Two Variables3.5Point-Slope Formula
3.6Applications of Linear Equations and Modeling
Group Activity: Modeling a Linear Equation
4Systems of Linear Equations in Two Variables
4.1Solving Systems of Equations by the Graphing Method
4.2Solving Systems of Equations by the Substitution Method
4.3Solving Systems of Equations by the Addition Method
PRE: Systems of Equations
4.4Applications of Linear Inequalities in Two Variables
4.5Linear Inequalities and Systems of Inequalities in Two Variables
Group Activity: Creating Linear Models from Data
5Polynomials and Properties of Exponents
5.1Multiplying and Dividing Expressions with Common Bases
5.2More Properties of Exponents
5.3Definitions of b^0 and b^-n
PRE: Properties of Exponents
5.4Scientific Notation
5.5Addition and Subtraction of Polynomials
5.6Multiplication of Polynomials and Special Products
5.7Division of Polynomials
PRE: Operations on Polynomials
Group Activity: The Pythagorean Theorem and a Geometric 'Proof'
6Factoring Polynomials
6.1Greatest Common Factor and Factoring by Grouping
6.2Factoring Trinomials of the Form x^2 + bx + c
6.3Factoring Trinomials: Trial and Error Method
6.4Factoring Trinomials: A-C Method
6.5Difference of Squares and Perfect Square Trinomials
6.6Sum and Difference of Cubes
PRE: Factoring Strategy
6.7Solving Equations Using the Zero Product Rule
PRE: Polynomial Expressions versus PolynomialEquations
6.8Applications of Quadratic Equations
Group Activity: Building a Factoring Test
7Rational Expressions and Equations
7.1Introduction to Rational Expressions
7.2Multiplication and Division of Rational Expressions
7.3Least Common Denominator
7.4Addition and Subtraction of Rational Expressions
PRE: Operations on Rational Expressions
7.5Complex Fractions
7.6Rational Equations
PRE: Comparing Rational Equations and Rational Expressions
7.7Applications of Rational Equations and Proportions7.8Variation
Group Activity: Computing Monthly Mortgage Payments
8Radicals
8.1Introduction to Roots and Radicals
8.2Simplifying Radicals
8.3Addition and Subtraction of Radicals
8.4Multiplication of Radicals
8.5Division of Radicals and Rationalisation
PRE: Operations on Radicals
8.6Radicals Equations
8.7Rational Exponents
Group Activity: Calculating Standard Deviation
9More Quadratic Equations
9.1The Square Root Property
9.2Completing the Square
9.3Quadratic Formula
PRE: Solving Different Types of Equations
9.4Graphing Quadratic Equations
9.5Introduction to Functions
Group Activity: Maximising Volume
Additional Topics Appendix
A.1Converting Units of Measurement