Beginning and Intermediate Algebra

Miller/O'Neill/Hyde continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate 2e. 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, helping to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition, Problem-Recognition Exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises, is to help students overcome what is sometimes a natural inclination toward applying problem-sovling 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 first 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 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. For even more support, students have access to a wealth of supplements, including McGraw-Hill’s online homework management system, MathZone.

Table of Contents:
Chapter R: Reference R.1Study Tips R.2Fractions R.3Introduction to Geometry Chapter 1: The Set of Real Numbers 1.1 Sets of Numbers and the Real Number Line 1.2 Order of Operations 1.3 Addition of Real Numbers 1.4 Subtraction of Real Numbers Problem Recognition Exercises – Addition and Subtraction of Signed Numbers 1.5 Multiplication and Division of Real Numbers 1.6Properties of Real Numbers and Simplifying Expressions Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Test Chapter 2: Linear Equations and Inequalities 2.1Addition, Subtraction, Multiplication, and Division Properties of Equality 2.2Solving Linear Equations 2.3Linear Equations: Clearing Fractions and Decimals 2.4Applications of Linear Equations: Introduction to Problem Solving 2.5Applications Involving Percents 2.6Formulas and Applications of Geometry 2.7Linear Inequalities Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Test Cumulative Review Exercises Chapters 1 – 2 Chapter 3: Graphing Linear Equations in Two Variables 3.1Rectangular Coordinate System 3.2Linear Equations in Two Variables 3.3Slope of a Line 3.4Slope-Intercept Form of a Line 3.5Point-Slope Formula 3.6Applications of Linear Equations Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Test Cumulative Review Exercises Chapters 1 – 3 Chapter 4: Systems of Linear Equations in Two Variables 4.1 Solving Systems of Equations by the Graphing Method 4.2 Solving Systems of Equations by the Substitution Method 4.3 Solving Systems of Equations by the Addition Method 4.4Applications of Linear Equations in Two Variables Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Test Cumulative Review Exercises Chapters 1 – 4 Chapter 5: Polynomials and Properties of Exponents 5.1Exponents: Multiplying and Dividing Common Bases 5.2More Properties of Exponents 5.3Definitions of b0 and b-n 5.4 Scientific NotationProblem Recognition Exercises – Properties of Exponents 5.5Addition and Subtraction of Polynomials 5.6Multiplication of Polynomials 5.7 Division of Polynomials Problem Recognition Exercises – Operations on Polynomial Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Test Cumulative Review Exercises, Chapters 1-5 Chapter 6: Factoring Polynomials 6.1Greatest Common Factor and Factoring by Grouping 6.2Factoring Trinomials of the form x2 + bx + c (Optional) 6.3Factoring Trinomials: Trial-and-Error Method 6.4Factoring Trinomials: AC-Method 6.5Factoring Binomials 6.6 General Factoring Summary 6.7Solving Equations by Using the Zero Product Rule Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Test Cumulative Review Exercises Chapters 1 – 6 Chapter 7: Rational Expressions 7.1Introduction to Rational Expressions 7.2Multiplication and Division of Rational Expressions 7.3Least Common Denominator 7.4Addition and Subtraction of Rational Expressions Problem Recognition Exercises - Operations on Rational Expressions 7.5Complex Fractions 7.6Rational EquationsProblem Recognition Exercises – Comparing Rational Equations and Rational Expressions 7.7Applications of Rational Equations, Ratios and Proportions 7.8 Variation (Optional) Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Test Cumulative Review Exercises Chapters 1 – 7 Chapter 8: Introduction to Relations and Functions 8.1Introduction to Relations 8.2Introduction to Functions 8.3Graphs of Functions 8.4Variation Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Test Cumulative Review Exercises, Chapters 1 – 8 Chapter 9: Systems of Linear Equations in Three Variables 9.1Systems of Linear Equations in Three Variables 9.2Applications of Systems of Linear Equations in Three Variables 9.3Solving systems of Linear Equations Using Matrices 9.4Determinants and Cramer’s Rule Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Test Cumulative Review Exercises, Chapters 1 – 9 Chapter 10: More Equations and Inequalities 10.1Compound Inequalities 10.2Polynomial and Rational Inequalities 10.3Absolute Value Equations 10.4Absolute Value Inequalities Problem Recognition Exercises – Equations and Inequalities 10.5Linear Inequalities in Two Variables Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Test Cumulative Review Exercises, Chapters 1 – 10 Chapter 11: Radicals and Complex Numbers 11.1Definition of an nth-Root 11.2Rational Exponents 11.3Simplifying Radical Expressions 11.4Addition and Subtraction of Radicals 11.5Multiplication of Radicals 11.6Rationalization Problem Recognition Exercises – Operations on Radicals 11.7Radical Equations 11.8Complex Numbers Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Test Cumulative Review Exercises, Chapters 1 – 11 Chapter 12: Quadratic Equations and Functions 12.1Square Root Property and Completing the Square 12.2Quadratic Formula 12.3Equations in Quadratic Form 12.4 Graphs of Quadratic Functions 12.5 Vertex of a Parabola and Applications Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Test Cumulative Review Exercises, Chapters 1 – 12 Chapter 13: Exponential and Logarithmic Functions 13.1Algebra and Composition of Functions 13.2Inverse Functions 13.3Exponential Functions 13.4Logarithmic Functions 13.5Properties of Logarithms 13.6The Irrational Number, e Problem Recognition Exercises - Logarithmic and Exponential Forms 13.7 Logarithmic and Exponential Equations Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Test Cumulative Review Exercises, Chapters 1 – 13 Chapter 14:Conic Sections and Nonlinear Systems 14.1Distance Formulas and Circles 14.2More on the Parabola 14.3The Ellipse and Hyperbola 14.4Nonlinear Systems of Equations in Two Variables 14.5Nonlinear Inequalities and Systems of Inequalities Chapter 14 Summary Chapter 14 Review Exercises Chapter 14 Test Cumulative Review Exercises, Chapters 1 – 14 Beginning Algebra Review: Review ASet of Real Numbers Review BLinear Equations in One Variable Review CLinear Equations in Two Variables Review DSystems of Linear Equations in Two Variables Review EPolynomials and Properties of Exponents Review FFactoring Polynomials and Solving Quadratic Equations Review G Rational Expressions Appendix A.1Binomial Expansions A.2Sequences and Series A.3 Arithmetic and Geometric Sequences and Series Student Answer Appendix

About 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 Id 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 masters 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.