Beginning and Intermediate Algebra / Edition 3

Beginning and Intermediate Algebra / Edition 3

by Julie Miller, Molly O'Neill, Nancy Hyde

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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

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Get Better Results with high quality content, exercise sets, and step-by-step 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 distance-learning; 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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McGraw-Hill Companies, The
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Meet the Author

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.

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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 Exercises-Addition 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 1-2     199
Graphing Linear Equations in Two Variables     201
Rectangular Coordinate System     202
Linear Equations in Two Variables     213
Slope of a Line     230
Slope-Intercept Form of a Line     245
Point-Slope Formula     256
Applications of Linear Equations     265
Summary     276
Review Exercises     280
Test     284
Cumulative Review Exercises, Chapters 1-3     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 1-4     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 Exercises-Properties of Exponents     376
Addition and Subtraction of Polynomials     376
Multiplication of Polynomials     388
Division of Polynomials     398
Problem Recognition Exercises-Operations on Polynomials     410
Summary     411
Review Exercises     414
Test     417
Cumulative Review Exercises, Chapters 1-5     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: Triai-and-Error Method     438
Factoring Trinomials: AC-Method     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 1-6     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 Exercises-Operations on Rational Expressions     528
Complex Fractions     529
Rational Equations     537
Problem Recognition Exercises-Comparing Rational Equations and Rational Expressions     547
Applications of Rational Equations and Proportions     548
Summary     561
Review Exercises     566
Test     568
Cumulative Review Exercises, Chapters 1-7     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 1-8     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 1-9     668
More Equations and Inequalities     671
Compound Inequalities     672
Polynomial and Rational Inequalities     681
Absolute Value Equations     693
Absolute Value Inequalities     700
Problem Recognition Exercises-Equations and Inequalities     712
Linear Inequalities in Two Variables     713
Summary     727
Review Exercises     731
Test     735
Cumulative Review Exercises, Chapters 1-10     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 Exercises-Operations on Radicals     788
Radical Equations     789
Complex Numbers     800
Summary     811
Review Exercises     816
Test     819
Cumulative Review Exercises, Chapters 1-11      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 1-12     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 Exercises-Logarithmic and Exponential Forms     957
Logarithmic and Exponential Equations     958
Summary     972
Review Exercises     978
Test     982
Cumulative Review Exercises, Chapters 1-13     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 1-14     1042
Beginning Algebra Review     R-1
Set of Real Numbers     R-1
Linear Equations in One Variable     R-10
Linear Equations in Two Variables     R-15
Systems of Linear Equations in Two Variables     R-25
Polynomials and Properties of Exponents     R-31
Factoring Polynomials and Solving Quadratic Equations     R-37
Rational Expressions     R-42
Additional Topics Appendix Posted in MathZone (
Binomial Expansions
Sequences and Series
Arithmetic and Geometric Sequences and Series
Fundamentals of Counting
Introduction to Probability
Student Answer Appendix     SA-1

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