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More About This Textbook
Overview
Get Better Results with high quality content, exercise sets, and stepbystep pedagogy!
The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Introductory Algebra. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students. Throughout the text, the authors communicate 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. Also included are Problem Recognition Exercises, designed to help students recognize which solution strategies are most appropriate for a given exercise. These types of exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. 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.
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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
Preface x
Reference 1
Study Tips 2
Fractions 3
Decimals and Percents 19
Introduction to Geometry 30
Set of Real Numbers 47
Preview 48
Sets of Numbers and the Real Number Line 49
Order of Operations 61
Addition of Real Numbers 72
Subtraction of Real Numbers 81
Midchapter Review 90
Multiplication and Division of Real Numbers 90
Properties of Real Numbers and Simplifying Expressions 103
Summary 116
Review Exercises 120
Test 123
Linear Equations and Inequalities 125
Preview 126
Addition, Subtraction, Multiplication, and Division Properties of Equality 127
Solving Linear Equations 138
Linear Equations: Clearing Fractions and Decimals 147
Midchapter Review 154
Applications of Linear Equations: Introduction to Problem Solving 155
Applications Involving Percents 167
Formulas and Applications of Geometry 175
Linear Inequalities 186
Summary 203
Review Exercises 209
Test 213
Cumulative Review Exercises Chapters 12 214
Graphing Linear Equations in Two Variables 217
Preview 218
Rectangular Coordinate System 219
Linear Equations in Two Variables 230
Slope of a Line 249
SlopeIntercept Form of a Line 265
Midchapter Review 276
PointSlope Formula 278
Applications of Linear Equations 289
Introduction to Functions 301
Summary 317
Review Exercises 324
Test 330
Cumulative Review Exercises Chapters 13 333
Systems of Linear Equations in Two Variables 335
Preview 336
Solving Systems of Equations by the Graphing Method 337
Solving Systems of Equations by the Substitution Method 349
Solving Systems of Equations by the Addition Method 358
Midchapter Review 369
Applications of Linear Equations in Two Variables 371
Linear Inequalities in Two Variables 381
Summary 393
Review Exercises 398
Test 402
Cumulative Review Exercises Chapters 14 404
Polynomials and Properties of Exponents 407
Preview 408
Exponents: Multiplying and Dividing Common Bases 409
More Properties of Exponents 420
Definitions of b[superscript 0] and b[superscript n] 425
Scientific Notation 434
Midchapter Review 443
Addition and Subtraction of Polynomials 444
Multiplication of Polynomials 456
Division of Polynomials 467
Summary 475
Review Exercises 479
Test 483
Cumulative Review Exercises Chapters 15 484
Factoring Polynomials 487
Preview 488
Greatest Common Factor and Factoring by Grouping 489
Factoring Trinomials: Grouping Method 499
Factoring Trinomials: TrialandError Method 507
Factoring Perfect Square Trinomials and the Difference of Squares 517
Midchapter Review 525
Factoring the Sum and Difference of Cubes and General Factoring Summary 527
Solving Equations Using the Zero Product Rule 536
Summary 550
Review Exercises 553
Test 555
Cumulative Review Exercises Chapters 16 557
Rational Expressions 559
Preview 560
Introduction to Rational Expressions 561
Multiplication and Division of Rational Expressions 572
Least Common Denominator 578
Addition and Subtraction of Rational Expressions 586
Midchapter Review 597
Complex Fractions 598
Rational Equations 605
Applications of Rational Equations and Proportions 616
Direct and Inverse Variation (Optional) 628
Summary 637
Review Exercises 645
Test 648
Cumulative Review Exercises Chapters 17 649
Radicals 653
Preview 654
Introduction to Roots and Radicals 655
Simplifying Radicals 668
Addition and Subtraction of Radicals 678
Multiplication of Radicals 685
Midchapter Review 692
Rationalization 693
Radical Equations 700
Rational Exponents 707
Summary 716
Review Exercises 720
Test 723
Cumulative Review Exercises Chapters 18 725
More Quadratic Equations 729
Preview 730
The Square Root Property and Completing the Square 731
Quadratic Formula 740
9 Midchapter Review 749
Graphing Quadratic Functions 749
Summary 764
Review Exercises 766
Test 769
Cumulative Review Exercises Chapters 19 770