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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 Beginning and Intermediate Algebra 4e. 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 xii
Reference 1
Study Tips 2
Fractions 6
Introduction to Geometry 22
The Set of Real Numbers 41
Sets of Numbers and the Real Number Line 42
Order of Operations 53
Addition of Real Numbers 63
Subtraction of Real Numbers 72
Problem Recognition ExercisesAddition and Subtraction of Signed Numbers 80
Multiplication and Division of Real Numbers 81
Properties of Real Numbers and Simplifying Expressions 92
Summary 105
Review Exercises 109
Test 111
Linear Equations and Inequalities 113
Addition, Subtraction, Multiplication, and Division Properties of Equality 114
Solving Linear Equations 125
Linear Equations: Clearing Fractions and Decimals 134
Applications of Linear Equations: Introduction to Problem Solving 141
Applications Involving Percents 156
Formulas and Applications of Geometry 163
Linear Inequalities 174
Summary 189
Review Exercises 195
Test 198
Cumulative Review Exercises, Chapters 12 199
Graphing Linear Equations in Two Variables 201
Rectangular Coordinate System 202
Linear Equations in Two Variables 213
Slope of a Line 230
SlopeIntercept Form of a Line 245
PointSlope Formula 256
Applications of Linear Equations 265
Summary 276
Review Exercises 280
Test 284
Cumulative Review Exercises, Chapters 13 286
Systems of Linear Equations in Two Variables 289
Solving Systems of Equations by the Graphing Method 290
Solving Systems of Equations by the Substitution Method 302
Solving Systems of Equations by the Addition Method 312
Applications of Linear Equations in Two Variables 323
Summary 334
Review Exercises 337
Test 340
Cumulative Review Exercises, Chapters 14 341
Polynomials and Properties of Exponents 343
Exponents: Multiplying and Dividing Common Bases 344
More Properties of Exponents 354
Definitions of b[superscript 0] and b[superscript n] 359
Scientific Notation 367
Problem Recognition ExercisesProperties of Exponents 376
Addition and Subtraction of Polynomials 376
Multiplication of Polynomials 388
Division of Polynomials 398
Problem Recognition ExercisesOperations on Polynomials 410
Summary 411
Review Exercises 414
Test 417
Cumulative Review Exercises, Chapters 15 418
Factoring Polynomials 421
Greatest Common Factor and Factoring by Grouping 422
Factoring Trinomials of the Form x[superscript 2] + bx + c (Optional) 432
Factoring Trinomials: TriaiandError Method 438
Factoring Trinomials: ACMethod 449
Factoring Binomials 458
General Factoring Summary 466
Solving Equations Using the Zero Product Rule 471
Summary 485
Review Exercises 489
Test 491
Cumulative Review Exercises, Chapters 16 492
Rational Expressions 493
Introduction to Rational Expressions 494
Multiplication and Division of Rational Expressions 504
Least Common Denominator 510
Addition and Subtraction of Rational Expressions 518
Problem Recognition ExercisesOperations on Rational Expressions 528
Complex Fractions 529
Rational Equations 537
Problem Recognition ExercisesComparing Rational Equations and Rational Expressions 547
Applications of Rational Equations and Proportions 548
Summary 561
Review Exercises 566
Test 568
Cumulative Review Exercises, Chapters 17 569
Introduction to Relations and Functions 571
Introduction to Relations 572
Introduction to Functions 580
Graphs of Functions 593
Variation 606
Summary 615
Review Exercises 618
Test 622
Cumulative Review Exercises, Chapters 18 623
Systems of Linear Equations in Three Variables 625
Systems of Linear Equations in Three Variables 626
Applications of Systems of Linear Equations in Three Variables 634
Solving Systems of Linear Equations by Using Matrices 640
Determinants and Cramer's Rule 650
Summary 662
Review Exercises 666
Test 667
Cumulative Review Exercises, Chapters 19 668
More Equations and Inequalities 671
Compound Inequalities 672
Polynomial and Rational Inequalities 681
Absolute Value Equations 693
Absolute Value Inequalities 700
Problem Recognition ExercisesEquations and Inequalities 712
Linear Inequalities in Two Variables 713
Summary 727
Review Exercises 731
Test 735
Cumulative Review Exercises, Chapters 110 736
Radicals and Complex Numbers 739
Definition of an nth Root 740
Rational Exponents 752
Simplifying Radical Expressions 760
Addition and Subtraction of Radicals 767
Multiplication of Radicals 773
Rationalization 781
Problem Recognition ExercisesOperations on Radicals 788
Radical Equations 789
Complex Numbers 800
Summary 811
Review Exercises 816
Test 819
Cumulative Review Exercises, Chapters 111 820
Quadratic Equations and Functions 823
Square Root Property and Completing the Square 824
Quadratic Formula 833
Equations in Quadratic Form 846
Graphs of Quadratic Functions 853
Vertex of a Parabola and Applications 867
Summary 880
Review Exercises 883
Test 886
Cumulative Review Exercises, Chapters 112 888
Exponential and Logarithmic Functions 891
Algebra and Composition of Functions 892
Inverse Functions 900
Exponential Functions 911
Logarithmic Functions 921
Properties of Logarithms 935
The Irrational Number e 944
Problem Recognition ExercisesLogarithmic and Exponential Forms 957
Logarithmic and Exponential Equations 958
Summary 972
Review Exercises 978
Test 982
Cumulative Review Exercises, Chapters 113 984
Conic Sections and Nonlinear Systems 987
Distance Formula and Circles 988
More on the Parabola 997
The Ellipse and Hyperbola 1006
Nonlinear Systems of Equations in Two Variables 1015
Nonlinear Inequalities and Systems of Inequalities 1024
Summary 1033
Review Exercises 1037
Test 1041
Cumulative Review Exercises, Chapters 114 1042
Beginning Algebra Review R1
Set of Real Numbers R1
Linear Equations in One Variable R10
Linear Equations in Two Variables R15
Systems of Linear Equations in Two Variables R25
Polynomials and Properties of Exponents R31
Factoring Polynomials and Solving Quadratic Equations R37
Rational Expressions R42
Additional Topics Appendix Posted in MathZone (www.mathzone.com)
Binomial Expansions
Sequences and Series
Arithmetic and Geometric Sequences and Series
Fundamentals of Counting
Introduction to Probability
Student Answer Appendix SA1