Schaum’s Outline of Intermediate Algebra

391 Pages·2018·31.22 MB·English

by  Ray Steege

Intermediate
Algebra
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Intermediate
Algebra
Third Edition
Ray Steege, MA
Former Professor of Mathematics
Laramie County Community College
Kerry Bailey, MA
Former Professor of Mathematics
Laramie County Community College
Schaum’s Outline Series
New York Chicago San Francisco Athens London Madrid
Mexico City Milan New Delhi Singapore Sydney Toronto
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RAY STEEGE received his BA in mathematics from the University of Wyoming and his MA in mathematics from the University
of Northern Colorado. The first 10 years of his teaching career were at East High School in Cheyenne, Wyoming. He continued his
professional career at Laramie County Community College in Cheyenne, Wyoming, for an additional 25 years prior to his retire-
ment in 1994. Among his many achievements and honors are: past president of the Wyoming Mathematics Association of Two-
Year Colleges, Wyoming Mathematics Coalition Steering Committee member, newsletter editor, and recipient of the Outstanding
Faculty Member of the Physical Science Division award at the college.
KERRY BAILEY received his BA in mathematics from San Diego State University and his MA in mathematics from the Uni-
versity of Colorado. He taught for 37 years at Laramie County Community College in Cheyenne, Wyoming prior to retiring in
2011, though he still teaches an occasional course or two at Maple Woods College in Kansas City, Missouri. Prior to this, he taught
for 10 years at Pikes Peak Community College in Colorado Springs, Colorado. Among his achievements and honors are: Math
Coordinator for the Community College of the Air Force (worldwide) while at PPCC, Wyoming Mathematics Coalition Steering
Committee member, news-letter editor, and recipient of the Outstanding Faculty Member of the Physical Science Division award,
and corecipient of the Outstanding Faculty Member award for the entire college at Laramie County Community College.
Copyright © 2018 by McGraw-Hill Education. All rights reserved. Except as permitted under the United States Copyright Act of
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Preface
The primary purpose of this book is to provide an effective tool for students that will help them understand
and master the basic concepts and techniques of Intermediate Algebra or Algebra II. The book can be useful
to the reader in several ways. It may be used as a valuable supplementary text for the second algebra course
to assist in clarifying and simplifying algebraic concepts and procedures. The book may also be used for
self-study or as the text for a course in Intermediate Algebra or Algebra II. Additionally, it is an excellent
book to review in order to clarify concepts and improve skills prior to enrollment in College Algebra. We
have attempted to provide a treatment of Intermediate Algebra or Algebra II that is more easily understood,
and therefore more useful than most available texts at this level.
The book possesses numerous benefits or strengths. Concepts are introduced and explained at the
student’s level in a thorough, brief manner. The processes employed make the algebra involved as simple and
concrete as possible. Each concept is illustrated completely by one or more solved problems which clarify and
illuminate the relevant ideas. Definitions, properties, and so on, are expressed in clear, concise, understandable
words as well as in mathematical form. Calculator procedures using RPN and Algebraic Entry calculators are
illustrated and employed where it is appropriate. The graphing calculator is used to great advantage in many
instances. A large number of graphs are included to help the student visualize abstract concepts. Step-by-step
procedures accompanied by clarifying statements are employed in many instances. Word problems are often
very difficult for students. We have provided the most detailed step-by-step treatment of word problems avail-
able. Students are led through the process in phases, thereby resulting in manageable steps. The book includes
recommendations to the student for correct, efficient use of mathematics. A concise summary of effective
study skills and suggestions on proven techniques is included. There are 886 solved problems with explana-
tions and step-by-step solutions included. Solved problems are referenced to similar supplementary problems.
There are 1,100 supplementary problems with answers included for student practice. Problems are arranged
in an easy to more difficult order.
The book covers the concepts typically found in the second algebra course including: fundamental con-
cepts; polynomials; rational expressions; first- and second-degree equations and inequalities; exponents, roots,
and radicals; systems of equations and inequalities; relations and functions; exponential and logarithmic func-
tions; sequences, series, and the binomial theorem. The terms and notation employed are those commonly used
by other authors.
We thank Mr. Stephen Koch for planting the seed that grew into the final product. Our sincere appreciation
goes to those people at McGraw-Hill who played a part in the development of the work. Special thanks go to
Diane Grayson, Surbhi Mittal, and Maureen Dennehy for their special help with the Third Edition.
Finally, and most importantly, for their encouragement, tolerance, and never-ending support, we thank our
families: Ray’s wife Marge; and Kerry’s wife Jan and children Matt, Sara, and Abby.
Ray Steege
Kerry Bailey
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Contents
INTRODUCTION Study Skills 1
CHAPTER 1 Fundamental Concepts 7
1.1 Definitions 7
1.2 Axioms of Equality and Order 9
1.3  Properties of Real Numbers 11
1.4  Operations with Real Numbers 12
1.5  Order of Operations 14
1.6  Evaluation by Calculator 15
1.7  Translating Phrases and Statements into Algebraic Form 18
Solved Problems 20
Supplementary Problems 33
CHAPTER 2 Polynomials 42
2.1 Definitions 42
2.2 Sums and Differences 43
2.3 Products 44
2.4 Factoring 46
2.5 Division 50
Solved Problems 54
Supplementary Problems 68
CHAPTER 3 Rational Expressions 74
3.1 Basic Properties 74
3.2 Products and Quotients 76
3.3 Sums and Differences 77
3.4 Mixed Operations and Complex Fractions 78
Solved Problems 79
Supplementary Problems 87
CHAPTER 4 First-Degree Equations and Inequalities 91
4.1 Solving First-Degree Equations 91
4.2 Graphs of First-Degree Equations 93
4.3 Formulas and Literal Equations 95
4.4 Applications 96
vii
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viii Contents
4.5 Solving First-Degree Inequalities 96
4.6 Graphs of First-Degree Inequalities 97
4.7 Applications Involving Inequalities 98
4.8 Absolute-Value Equations and Inequalities 98
Solved Problems 101
Supplementary Problems 129
CHAPTER 5 Exponents, Roots, and Radicals 140
5.1 Zero and Negative-Integer Exponents 140
5.2 Scientific Notation 141
5.3 Rational Exponents and Roots 143
5.4 Simplifying Radicals 145
5.5 Operations on Radical Expressions 146
5.6 Complex Numbers 147
Solved Problems 150
Supplementary Problems 167
CHAPTER 6 Second-Degree Equations and Inequalities 172
6.1 Solving by Factoring and Square Root Methods 172
6.2 Completing the Square and the Quadratic Formula 173
6.3 Equations Involving Radicals 175
6.4 Quadratic Form Equations 175
6.5 Applications 175
6.6 Graphs of Second-Degree Equations 176
6.7 Quadratic and Rational Inequalities 177
Solved Problems 179
Supplementary Problems 210
CHAPTER 7 Systems of Equations and Inequalities 217
7.1 Linear Systems in Two Variables 217
7.2 Linear Systems in Three Variables 220
7.3 Determinants and Cramer’s Rule 221
7.4 Matrix Methods 223
7.5 Nonlinear Systems 224
7.6 Systems of Inequalities 225
Solved Problems 225
Supplementary Problems 252
CHAPTER 8 Relations and Functions 256
8.1 Basic Concepts 256
8.2 Function Notation and the Algebra of Functions 257
8.3 Distance and Slope Formulas 258
8.4 Linear Equation Forms 260
8.5 Types of Functions 262
8.6 Variation 264
8.7 Inverse Relations and Functions 265
Solved Problems 266
Supplementary Problems 283
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Contents ix
CHAPTER 9 Exponential and Logarithmic Functions 291
9.1 Exponential Functions 291
9.2 Logarithmic Functions 291
9.3 Properties of Logarithms 292
9.4 Exponential and Logarithmic Equations 293
9.5 Applications 293
Solved Problems 294
Supplementary Problems 312
CHAPTER 10 Sequences, Series, and the Binomial Theorem 318
10.1 Sequences 318
10.2 Series 319
10.3 The Binomial Theorem 321
Solved Problems 323
Supplementary Problems 329
Chapter Quizzes 332
Chapter Quizzes Answers 354
Final Exam 361
Final Exam Answers 365
APPENDIX A The Frentheway Method Proof 367
APPENDIX B Alternate Method for Factoring x2±bx±c 369
APPENDIX C Study Tips from the Authors 371
INDEX 373
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