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More About This Textbook
Overview
The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Intermediate Algebra 3e. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the textbook. Throughout the text, the authors have integrated many Study Tips and Avoiding Mistakes hints, which are reflective of the comments and instruction presented to students in the classroom. In this way, the text communicates to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition ProblemRecognition Exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the ProblemRecognition exercises is to help students overcome what is sometimes a natural inclination toward applying problemsolving algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the previous edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture or distancelearning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGrawHill’s online homework management system, MathZone.
Product Details
Meet the Author
Julie Miller is from Daytona State College, where she has taught developmental and upperlevel 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 handson 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 MichiganDearborn, 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 fulltime 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.”
Table of Contents
Chapter R Review of Basic Algebraic Concepts
Section R.1 Study Tips
Group Activity: Becoming a Successful Student
Section R.2 Sets of Numbers and Interval Notation
Section R.3 Operations on Real Numbers
Section R.4 Simplifying Algebraic Expressions
Chapter R Summary
Chapter R Review Exercises
Chapter R Test
Chapter 1 Linear Equations and Inequalities in One Variable
Section 1.1 Linear Equations in One Variable
Problem Recognition Exercises: Equations versus Expressions
Section 1.2 Applications of Linear Equations in One Variable
Section 1.3 Applications to Geometry and Literal Equations
Section 1.4 Linear Inequalities in One Variable
Section 1.5 Compound Inequalities
Section 1.6 Absolute Value Equations
Section 1.7 Absolute Value Inequalities
Problem Recognition Exercises: Identifying Equations and Inequalities
Group Activity: Understanding the Symbolism of Mathematics
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
Chapter 2 Linear Equations in Two Variables and Functions
Section 2.1 Linear Equations in Two Variables
Section 2.2 Slope of a Line and Rate of Change
Section 2.3 Equations of a Line
Problem Recognition Exercises: Characteristics of Linear Equations
Section 2.4 Applications of Linear Equations and Modeling
Section 2.5 Introduction to Relations
Section 2.6 Introduction to Functions
Section 2.7 Graphs of Basic Functions
Problem Recognition Exercises: Characteristics of Relations
Group Activity: Deciphering a Coded Message
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Chapters 12 Cumulative Review Exercises
Chapter 3 Systems of Linear Equations and Inequalities
Section 3.1 Solving Systems of Linear Equations by the Graphing Method
Section 3.2 Solving Systems of Linear Equations by the Substitution Method
Section 3.3 Solving Systems of Linear Equations by the Addition Method
Problem Recognition Exercises: Solving Systems of Linear Equations
Section 3.4 Applications of Systems of Linear Equations in Two Variables
Section 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables
Section 3.6 Systems of Linear Equations in Three Variables and Applications
Section 3.7 Solving Systems of Linear Equations by Using Matrices
Group Activity: Creating a Quadratic Model of the Form y = at2 + bt + c
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Chapters 13 Cumulative Review Exercises
Chapter 4 Polynomials
Section 4.1 Properties of Integer Exponents and Scientific Notation
Section 4.2 Addition and Subtraction of Polynomials and Polynomial Functions
Section 4.3 Multiplication of Polynomials
Section 4.4 Division of Polynomials
Problem Recognition Exercises: Operations on Polynomials
Section 4.5 Greatest Common Factor and Factoring by Grouping
Section 4.6 Factoring Trinomials
Section 4.7 Factoring Binomials
Problem Recognition Exercises: Factoring Summary
Section 4.8 Solving Equations by Using the Zero Product Rule
Group Activity: Investigating Pascal’s Triangle
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Chapters 14 Cumulative Review Exercises
Chapter 5 Rational Expressions and Rational Equations
Section 5.1 Rational Expressions and Rational Functions
Section 5.2 Multiplication and Division of Rational Expressions
Section 5.3 Addition and Subtraction of Rational Expressions
Section 5.4 Complex Fractions
Problem Recognition Exercises: Operations on Rational Expressions
Section 5.5 Solving Rational Equationsv Problem Recognition Exercises: Rational Equations vs. Expressions
Section 5.6 Applications of Rational Equations and Proportions
Section 5.7 Variation
Group Activity: Computing the Future Value of an Investment
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Chapters 15 Cumulative Review Exercises
Chapter 6 Radicals and Complex Numbers
Section 6.1 Definition of an nth Root
Section 6.2 Rational Exponents
Section 6.3 Simplifying Radical Expressions
Section 6.4 Addition and Subtraction of Radicals
Section 6.5 Multiplication of Radicals
Problem Recognition Exercises: Simplifying Radical Expressions
Section 6.6 Division of Radicals and Rationalization
Section 6.7 Solving Radical Equations
Section 6.8 Complex Numbers
Group Activity: Margin of Error of Survey Results
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Chapters 16 Cumulative Review Exercises
Chapter 7 Quadratic Equations and Functions
Section 7.1 Square Root Property and Completing the Square
Section 7.2 Quadratic Formula
Section 7.3 Equations in Quadratic Form
Problem Recognition Exercises: Quadratic and Quadratic Type Equations
Section 7.4 Graphs of Quadratic Functions
Section 7.5 Vertex of a Parabola: Applications and Modeling
Section 7.6 Nonlinear Inequalities
Problem Recognition Exercises: Recognizing Equations and Inequalities
Group Activity: Creating a Quadratic Model of the Form y = a(x – h)2 + k
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Chapters 17 Cumulative Review Exercises
Chapter 8 Exponential and Logarithmic Functions and Applications
Section 8.1 Algebra and Composition of Functions
Section 8.2 Inverse Functions
Section 8.3 Exponential Functions
Section 8.4 Logarithmic Functions
Problem Recognition Exercises: Identifying Graphs of Functions
Section 8.5 Properties of Logarithms
Section 8.6 The Irrational Number and Change of Base
Problem Recognition Exercises: Logarithmic and Exponential Forms
Section 8.7 Logarithmic and Exponential Equations and Applications
Group Activity: Creating a Population Model
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Chapters 18 Cumulative Review Exercises
Chapter 9 Conic Sections
Section 9.1 Distance Formula, Midpoint Formula, and Circles
Section 9.2 More on the Parabola
Section 9.3 The Ellipse and Hyperbola
Problem Recognition Exercises: Formulas and Conic Sections
Section 9.4 Nonlinear Systems of Equations in Two Variables
Section 9.5 Nonlinear Inequalities and Systems of Inequalities
Group Activity: Investigating the Graphs of Conic Sections on a Calculator
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Chapters 19 Cumulative Review Exercises
Chapter 10 Binomial Expansions, Sequences, and Series
Section 10.1 Binomial Expansions
Section 10.2 Sequences and Series
Section 10.3 Arithmetic Sequences and Series
Section 10.4 Geometric Sequences and Series
Problem Recognition Exercises: Identifying Arithmetic and Geometric Sequences
Group Activity: Investigating Mean and Standard Deviation
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Chapters 110 Cumulative Review Exercises
Additional Topics Appendix
Section A.1 Determinants and Cramer’s Rule