The new edition of BEGINNING & INTERMEDIATE ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The authors have developed a learning plan to help students succeed and transition to the next level in their coursework. Based on their years of experience in developmental education, the accessible approach builds upon the book's known clear writing and engaging style which teaches students to develop problem-solving skills and strategies that they can use in their everyday lives. The authors have developed an acute awareness of students' approach to homework and present a learning plan keyed to Learning Objectives and supported by a comprehensive range of exercise sets that reinforces the material that students have learned setting the stage for their success.
1. REAL NUMBERS AND THEIR BASIC PROPERTIES.
Real Numbers and Their Graphs. Fractions. Exponents and Order of Operations. Adding and Subtracting Real Numbers. Multiplying and Dividing Real Numbers. Algebraic Expressions. Properties of Real Numbers. Projects. Chapter 1 Review. Chapter 1 Test.
2. EQUATIONS AND INEQUALITIES.
Solving Basic Linear Equations in One Variable. Solving More Linear Equations in One Variable. Simplifying Expressions to Solve Linear Equations in One Variable. Formulas. Introduction to Problem Solving. Motion and Mixture Problems. Solving Linear Inequalities in One Variable. Projects. Chapter 2 Review. Chapter 2 Test. Cumulative Review for Chapters 1-2.
3. GRAPHING; WRITING EQUATIONS OF LINES; FUNCTIONS.
The Rectangular Coordinate System. Graphing Linear Equations. Slope of a Line. Point-Slope Form. Slope-Intercept Form. Functions. Solving Linear Inequalities in One or Two Variables. Projects. Chapter 3 Review. Chapter 3 Test.
4. POLYNOMIALS.
Natural-Number Exponents. Zero and Negative-Integer Exponents. Scientific Notation. Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Dividing Polynomials by Monomials. Dividing Polynomials by Polynomials. Synthetic Division. Projects. Chapter 4 Review. Chapter 4 Test. Cumulative Review Exercises for Chapters 1-4.
5. FACTORING POLYNOMIALS.
Factoring Out the Greatest Common Factor; Factoring by Grouping. Factoring the Difference of Two Squares. Factoring Trinomials with a Leading Coefficient of 1. Factoring General Trinomials. Factoring the Sum and Difference of Two Cubes. Summary of Factoring Techniques. Solving Equations by Factoring. Problem Solving. Projects. Chapter 5 Review. Chapter 5 Test.
6. RATIONAL EXPRESSIONS AND EQUATIONS; PROPORTION AND VARIATION.
Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Simplifying Complex Fractions. Solving Equations That Contain Rational Expressions. Solving Applications That Contain Rational Expressions. Proportion and Variation. Projects. Chapter 6 Review. Chapter 6 Test. Cumulative Review Exercises for Chapters 1-6.
7. TRANSITIONING TO INTERMEDIATE ALGEBRA.
Review of Solving Linear Equations and Inequalities in One Variable. Review of Graphing, Slope, and Writing Equations of Lines. Review of Functions. Review of Factoring. Review of Rational Expressions. Solving Equations in One Variable Containing Absolute Values. Solving Inequalities in One Variable Containing an Absolute-Value Term. Projects. Chapter 7 Review. Chapter 7 Test.
8. SOLVING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES.
Solving Systems of Linear Equations by Graphing. Solving Systems of Linear Equations by Substitution and Elimination. Solving Applications of Systems of Linear Equations in Two Variables. Solving Systems of Three Linear Equations in Three Variables. Solving Systems if Linear Equations Using Matrices. Solving Systems of Linear Equations Using Determinants. Solving Systems of Linear Inequalities in Two Variables. Solving Systems Using Linear Programming. Projects. Chapter 8 Review. Chapter 8 Test. Cumulative Review Exercises for Chapters 1-8.
9. RADICALS AND RATIONAL EXPONENTS.
Radical Expressions. Applications of the Pythagorean Theorem and the Distance Formula. Rational Exponents. Simplifying and Combining Rational Expressions. Multiplying and Dividing Radical Expressions. Radical Equations. Complex Numbers. Projects. Chapter 9 Review. Chapter 9 Test.
10. QUADRATIC FUNCTIONS AND INEQUALITIES.
Solving Quadratic Equations Using the Square-Root Property and by Completing the Square. Solving Quadratic Equations by the Quadratic Formula. The Discriminant and Equations That Can be Written in Quadratic Form. Graphs of Quadratic Functions. Graphs of Nonlinear Functions. Quadratic and Other Nonlinear Inequalities. Projects. Chapter 10 Review. Chapter 10 Test. Cumulative Review Exercises for Chapters 1-10.
11. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Algebra and Composition of Functions. Inverse of Functions. Exponential Functions. Base e: Exponential Functions. Logarithmic Functions. Natural Logarithms. Properties of Logarithms. Exponential and Logarithmic Equations. Projects. Chapter 11 Review. Chapter 11 Test. Cumulative Review Exercises for Chapters 1-11.
12. CONIC SECTIONS AND MORE GRAPHING.
The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Systems of Equations and Inequalities Containing One or More Second Degree Terms. Piecewise-Defined Functions and the Greatest Integer Function. Projects. Chapter 12 Review. Chapter 12 Test.
13. MISCELLANEOUS TOPICS.
The Binomial Theorem. The nth Term of a Binomial Expansion. Arithmetic Sequences. Geometric Sequences. Infinite Geometric Sequences. Permutations and Combinations. Probability.
APPENDIX I MEASUREMENT CONVERSIONS.
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Rosemary Karr
Rosemary Karr graduated from Eastern Kentucky University (EKU) in 1976 with a B.S. in Mathematics, attained her M.A. at EKU in Mathematics Education in 1981, and earned her Ph.D. from the University of North Texas in 1996. After two years teaching high school mathematics, she joined the faculty at Eastern Kentucky University, where she earned tenure as Assistant Professor of Mathematics. A professor of mathematics at Collin [[COUNTY COMMUNITY]] College in Plano Texas since 1990, Prof. Karr has written more than ten solutions manuals, presented numerous papers and been an active member in several educational associations (including President of the National Association for Developmental Education). She has been honored several times by Collin [[COUNTY COMMUNITY]] College, and has received such national recognitions as U.S. Professor of the Year (2007), Minnie Stevens Piper Professor (2008), and CLADEA fellow (2012).
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Marilyn Massey
Marilyn Massey teaches mathematics at Collin College in McKinney, Texas. She has been President of the Texas Association for Developmental Education, featured on the list of Who's Who among America's Teachers and received an Excellence in Teaching Award from the National Conference for College Teaching and Learning. Professor Massey has presented at numerous state and national conferences; her article “Service-Learning Projects in Data Interpretation” was one of two included from community college instructors for the Mathematical Association of America's publication, Mathematics in Service to the Community. She earned her Bachelor's degree in Secondary Education from the University of North Texas and Master's Degree in the Art of Teaching Mathematics from the University of Texas at Dallas.
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R. David Gustafson
R. David Gustafson is professor emeritus of mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA; INTERMEDIATE ALGEBRA; BEGINNING AND INTERMEDIATE ALGEBRA; BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH; and the Tussy/Gustafson and Tussy/Gustafson/Koenig Developmental Mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in the American Mathematical Association of Two-Year Colleges (AMATYC) as a Midwest vice president. He has also served as president of IMACC, AMATYC's Illinois affiliate. Professor Gustafson earned a master of arts from Rockford College in Illinois as well as a master of science from Northern Illinois University.
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NEW! Reach for Success highlights study skills and is featured at the beginning and end of each chapter. This feature is designed as an activity to help the student prepare for a successful semester.
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NEW! The Warm Ups have been significantly revised to include skills needed for the development of section concepts.
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NEW! Self Checks are now included with each Example so that students can check reading comprehension.
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NEW! A tear-out Basic Calculator Keystroke Guide for the Casio 9750GII has been provided, in addition to the existing TI-83 and TI-84 guide, to assist students with their calculator functionality and to serve as a quick reference.
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NEW! Additional Teaching Tips have been included at the request of reviewers.
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The design incorporates a tabular structure identifying features that guide students through the textbook, providing for increased readability.
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Chapter Openers showcase the many career paths available in the world of mathematics and include a brief overview of each career, as well as job outlook, growth and annual earnings potential statistics from the U.S. Department of Labor.
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Reach for Success highlights study skills and is featured at the beginning and end of each chapter. This feature is designed as an activity to help the student prepare for a successful semester.
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Learning Objectives at the beginning of each section are mapped to content, as well as to exercises in the Guided Practice section, helping students identify specific concepts that may need reinforcement, and helping instructors tie problems to objectives and their own learning outcomes.
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Section vocabulary feature help students speak the language of mathematics. Not only are vocabulary words identified at the beginning of each section, these words are also bolded within the section. Exercises include questions on the vocabulary words, and a glossary has been developed to facilitate the students' reference to these words.
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Getting Ready questions appear at the beginning of each section, linking past concepts to the upcoming material.
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Examples are worked out in each chapter, highlighting the concept being discussed. “Notes” in many of the text's examples, give students insight into the process adopted when approaching a problem and working toward a solution. Each Example also ends with a Self Check problem, so that students may immediately apply concepts.
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The Now Try This feature at the end of each section focuses on developing transitional group-work exercises and increase conceptual understanding through active classroom participation. These problems can be worked independently or in small groups and transition to exercises in the following section.
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The Exercise Sets at the end of each section help transition students through progressively more difficult homework problems. Students are initially asked to work quick, simple problems on their own, proceed to working exercises keyed to examples, and finally complete application and critical thinking questions on their own. These sets include a variety of problem types, including “Warm Ups,” “Review,” “Vocabulary and Concept,” “Guided Practice,” “Additional Practice,” “Applications,” “Writing about Math,” and “Something to Think About.”
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Chapter-ending Projects encourage in-depth exploration and a review of key concepts.
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The Chapter Review grid presents the material cleanly and simply, giving students an efficient means of reviewing material.
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Chapter Tests allow students to pinpoint their strengths and challenges with the material.
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Cumulative Reviews follow the end of chapter material for every even-numbered chapter, and keep students' skills current before moving on to the next topic.
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Everyday Connections boxes invite students to see how the material is relevant to their lives. These have been updated to more accurately reflect a topic of the selected chapter.
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Perspectives highlight important mathematicians and connect students to discoveries of the past and their importance to the present.
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