Intermediate Algebra for College Students

by Angel, Allen R.

• ISBN13: 9780131400597
• ISBN10: 0131400592
• Edition: 6th
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Prentice Hall

Summary

For freshman-level, one- or two- semester courses in Developmental Algebra. The Angel Series continues to offer proven pedagogy sound exercise sets and superior student support. An emphasis on the practical applications of algebra motivates students and encourages them to see algebra as an important part of their daily lives. The student-friendly writing style uses short, clear sentences and easy-to-understand language, and the outstanding pedagogical program makes the material easy to follow and comprehend. The new editions continue to place a strong emphasis on problem solving, incorporating it as a theme throughout the texts. Angel's solid exercise sets are recognized by reviewers as of the highest standard providing a large number of problems, paired exercises, and a broad and increasing range of difficulty.

Table of Contents

Preface	xi
To the Student	xxiv
Basic Concepts	1	(65)
Study Skills for Success in Mathematics, and Using a Calculator	2	(4)
Sets and Other Basic Concepts	6	(12)
Properties of and Operations with Real Numbers	18	(11)
Order of Operations	29	(13)
Exponents	42	(10)
Scientific Notation	52	(14)
Chapter Summary	60	(2)
Chapter Review Exercises	62	(2)
Chapter Practice Test	64	(2)
Equations and Inequalities	66	(81)
Solving Linear Equations	67	(12)
Problem Solving and Using Formulas	79	(11)
Applications of Algebra	90	(14)
Additional Application Problems	104	(11)
Solving Linear Inequalities	115	(14)
Solving Equations and Inequalities Containing Absolute Values	129	(18)
Chapter Summary	140	(1)
Chapter Review Exercises	141	(3)
Chapter Practice Test	144	(1)
Cumulative Review Test	145	(2)
Graphs and Functions	147	(89)
Graphs	148	(15)
Functions	163	(16)
Linear Functions: Graphs and Applications	179	(12)
The Slope-Intercept Form of a Linear Equation	191	(14)
The Point-Slope Form of a Linear Equation	205	(10)
The Algebra of Functions	215	(9)
Graphing Linear Inequalities	224	(12)
Chapter Summary	228	(1)
Chapter Review Exercises	229	(4)
Chapter Practice Test	233	(1)
Cumulative Review Test	234	(2)
Systems of Equations and Inequalities	236	(63)
Solving Systems of Linear Equations in Two Variables	237	(12)
Solving Systems of Linear Equations in Three Variables	249	(7)
Systems of Linear Equations: Applications and Problem Solving	256	(14)
Solving Systems of Equations Using Matrices	270	(9)
Solving Systems of Equations Using Determinants and Cramer's Rule	279	(8)
Solving Systems of Linear Inequalities	287	(12)
Chapter Summary	292	(2)
Chapter Review Exercises	294	(2)
Chapter Practice Test	296	(1)
Cumulative Review Test	297	(2)
Polynomials and Polynomial Functions	299	(86)
Addition and Subtraction of Polynomials	300	(11)
Multiplication of Polynomials	311	(10)
Division of Polynomials and Synthetic Division	321	(11)
Factoring a Monomial from a Polynomial and Factoring by Grouping	332	(8)
Factoring Trinomials	340	(11)
Special Factoring Formulas	351	(8)
A General Review of Factoring	359	(5)
Polynomial Equations	364	(21)
Chapter Summary	377	(1)
Chapter Review Exercises	378	(5)
Chapter Practice Test	383	(1)
Cumulative Review Test	384	(1)
Rational Expressions and Equations	385	(69)
The Domains of Rational Functions and Multiplication and Division of Rational Expressions	386	(10)
Addition and Subtraction of Rational Expressions	396	(12)
Complex Fractions	408	(6)
Solving Rational Equations	414	(13)
Rational Equations: Applications and Problem Solving	427	(11)
Variation	438	(16)
Chapter Summary	447	(1)
Chapter Review Exercises	448	(3)
Chapter Practice Test	451	(1)
Cumulative Review Test	452	(2)
Roots, Radicals, and Complex Numbers	454	(71)
Roots and Radicals	455	(9)
Rational Exponents	464	(9)
Simplifying Radicals	473	(8)
Adding, Subtracting, and Multiplying Radicals	481	(7)
Dividing Radicals	488	(9)
Solving Radical Equations	497	(12)
Complex Numbers	509	(16)
Chapter Summary	518	(1)
Chapter Review Exercises	519	(4)
Chapter Practice Test	523	(1)
Cumulative Review Test	524	(1)
Quadratic Functions	525	(78)
Solving Quadratic Equations by Completing the Square	526	(10)
Solving Quadratic Equations by the Quadratic Formula	536	(13)
Quadratic Equations: Applications and Problem Solving	549	(10)
Writing Equations in Quadratic Form	559	(7)
Graphing Quadratic Functions	566	(19)
Quadratic and Other Inequalities in One Variable	585	(18)
Chapter Summary	596	(1)
Chapter Review Exercises	596	(4)
Chapter Practice Test	600	(1)
Cumulative Review Test	601	(2)
Exponential and Logarithmic Functions	603	(68)
Composite and Inverse Functions	604	(12)
Exponential Functions	616	(10)
Logarithmic Functions	626	(7)
Properties of Logarithms	633	(6)
Common Logarithms	639	(7)
Exponential and Logarithmic Equations	646	(6)
Natural Exponential and Natural Logarithmic Functions	652	(19)
Chapter Summary	664	(1)
Chapter Review Exercises	665	(3)
Chapter Practice Test	668	(1)
Cumulative Review Test	669	(2)
Conic Sections	671	(41)
The Parabola and the Circle	672	(11)
The Ellipse	683	(7)
The Hyperbola	690	(8)
Nonlinear Systems of Equations and Their Applications	698	(14)
Chapter Summary	707	(1)
Chapter Review Exercises	708	(2)
Chapter Practice Test	710	(1)
Cumulative Review Test	710	(2)
Sequences, Series, and the Binomial Theorem	712	(39)
Sequences and Series	713	(8)
Arithmetic Sequences and Series	721	(7)
Geometric Sequences and Series	728	(12)
The Binomial Theorem	740	(11)
Chapter Summary	745	(1)
Chapter Review Exercises	746	(3)
Chapter Practice Test	749	(1)
Cumulative Review Test	749	(2)
Appendix Geometric Formulas	751
Answers	1	(1)
Index	1	(1)
Photo Credits	1

Excerpts

This book was written for college students who have successfully completed a first course in elementary algebra. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear explanations, and many detailed, worked-out examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text. Features of the Text Full-Color Format.Color is used pedagogically in the following ways: Important definitions and procedures are color screened. Color screening or color type is used to make other important items stand out. Artwork is enhanced and clarified with use of multiple colors. The full-color format allows for easy identification of important features by students. The full-color format makes the text more appealing and interesting to students. Readability.One of the most important features of the text is its readability. The book is very readable, even for those with weak reading skills. Short, clear sentences are used and more easily recognized, and easy-to-understand language is used whenever possible. Accuracy.Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typographical errors and have checked all the answers. Connections.Many of our students do not thoroughly grasp new concepts the first time they are presented. In this text, we encourage students to make connections. That is, we introduce a concept, then later in the text briefly reintroduce it and build upon it. Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Important concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumulative Review Tests. Chapter Opening Application.Each chapter begins with a real-life application related to the material covered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem. A Look Ahead.This feature at the beginning of each chapter gives students a preview of the chapter. This feature also indicates where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book and the connection to real-world situations. The Use of Icons.At the beginning of each chapter and of each section, a variety of icons are illustrated. These icons are provided to tell students where they may be able to get extra help if needed. There are icons for theStudent's Solution Manual;theStudent's Study Guide;CDs and videotapes; Math Pro 4/5 Software;thePrentice Hall Tutor Center;and theAngel Website.Each of these items will be discussed shortly. Keyed Section Objectives.Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with red numbers such as 1. Problem Solving.George Polya's five-step problem-solving procedure is discussed in Section 1.2. Throughout the book problem solving and Polya's problem-solving procedure are emphasized. Practical Applications.Practical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students. Detailed; Worked-Out Examples.A wealth of examples have been worked o