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Algebra : A Combined Approach,9780130674517
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Algebra : A Combined Approach

by
Edition:
2nd
ISBN13:

9780130674517

ISBN10:
0130674516
Format:
Paperback
Pub. Date:
1/1/2003
Publisher(s):
Prentice Hall

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Summary

The engaging Martin-Gay workbook series presents a reader-friendly approach to the concepts of basic math and algebra, giving readers ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the workbooks are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay enhances users' perception of math by exposing them to real-life situations through graphs and applications; and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book includes key topics in algebra such as linear equations and inequalities with one and two variables, systems of equations, polynomial functions and equations, quadratic functions and equations, exponential functions and equations, logarithmic functions an equations, rational and radical expressions, and conic sections. For professionals who wish to brush up on their algebra skills.

Table of Contents

Preface ix
Prealgebra Review
1(1)
Chapter R Pretest
2(1)
Factors and the Least Common Multiple
3(6)
Fractions
9(10)
Decimals and Percents
19
Chapter R Activity: Interpreting Survey Results
28(1)
Chapter R Vocabulary Check
29(1)
Chapter R Highlights
30(3)
Chapter R Review
33(2)
Chapter R Test
35
Real Numbers and Introduction to Algebra
1(80)
Chapter 1 Pretest
2(1)
Tips for Success in Mathematics
3(6)
Symbols and Sets of Numbers
9(12)
Exponents, Order of Operations, and Variable Expressions
21(10)
Adding Real Numbers
31(8)
Subtracting Real Numbers
39(10)
Integrated Review--Operations on Real Numbers
47(2)
Multiplying and Dividing Real Numbers
49(12)
Properties of Real Numbers
61(20)
Chapter 1 Activity: Analyzing Wealth
69(2)
Chapter 1 Vocabulary Check
71(1)
Chapter 1 Highlights
71(4)
Chapter 1 Review
75(4)
Chapter 1 Test
79(2)
Equations, Inequalities, and Problem Solving
81(100)
Chapter 2 Pretest
82(1)
Simplifying Expressions
83(8)
The Addition Property of Equality
91(10)
The Multiplication Property of Equality
101(8)
Further Solving Linear Equations
109(12)
Integrated Review--Solving Linear Equations
119(2)
An Introduction to Problem Solving
121(12)
Formulas and Problem Solving
133(10)
Percent, Ratio, and Proportion
143(12)
Linear Inequalities and Problem Solving
155(26)
Chapter 2 Activity: Investigating Averages
168(1)
Chapter 2 Vocabulary Check
169(1)
Chapter 2 Highlights
169(4)
Chapter 2 Review
173(4)
Chapter 2 Test
177(2)
Cumulative Review
179(2)
Graphing Equations and Inequalities
181(86)
Chapter 3 Pretest
182(1)
Reading Graphs and the Rectangular Coordinate System
183(20)
Graphing Linear Equations
203(12)
Intercepts
215(10)
Slope
225(18)
Integrated Review--Summary on Linear Equations
241(2)
Graphing Linear Inequalities in Two Variables
243(24)
Chapter 3 Activity: Finding a Linear Model
252(1)
Chapter 3 Vocabulary Check
253(1)
Chapter 3 Highlights
253(4)
Chapter 3 Review
257(6)
Chapter 3 Test
263(2)
Cumulative Review
265(2)
Exponents and Polynomials
267(76)
Chapter 4 Pretest
268(1)
Exponents
269(12)
Negative Exponents and Scientific Notation
281(10)
Introduction to Polynomials
291(10)
Adding and Subtracting Polynomials
301(6)
Multiplying Polynomials
307(6)
Special Products
313(8)
Integrated Review--Exponents and Operations on Polynomials
319(2)
Dividing Polynomials
321(22)
Chapter 4 Activity: Modeling with Polynomials
329(2)
Chapter 4 Vocabulary Check
331(1)
Chapter 4 Highlights
331(4)
Chapter 4 Review
335(4)
Chapter 4 Test
339(2)
Cumulative Review
341(2)
Factoring Polynomials
343(70)
Chapter 5 Pretest
344(1)
The Greatest Common Factor
345(8)
Factoring Trinomials of the Form x2 + bx + c
353(6)
Factoring Trinomials of the Form ax2 + bx + c
359(6)
Factoring Trinomials of the Form ax2 + bx + c by Grouping
365(4)
Factoring by Special Products
369(12)
Integrated Review--Choosing a Factoring Strategy
379(2)
Solving Quadratic Equations by Factoring
381(10)
Quadratic Equations and Problem Solving
391(22)
Chapter 5 Activity: Factoring
400(1)
Chapter 5 Vocabulary Check
401(1)
Chapter 5 Highlights
401(4)
Chapter 5 Review
405(4)
Chapter 5 Test
409(2)
Cumulative Review
411(2)
Rational Expressions
413(76)
Chapter 6 Pretest
414(1)
Simplifying Rational Expressions
415(8)
Multiplying and Dividing Rational Expressions
423(10)
Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator
433(8)
Adding and Subtracting Rational Expressions with Different Denominators
441(8)
Solving Equations Containing Rational Expressions
449(10)
Integrated Review--Summary on Rational Expressions
457(2)
Rational Equations and Problem Solving
459(10)
Simplifying Complex Fractions
469(20)
Chapter 6 Activity: Analyzing a Table
476(1)
Chapter 6 Vocabulary Check
477(1)
Chapter 6 Highlights
477(4)
Chapter 6 Review
481(4)
Chapter 6 Test
485(2)
Cumulative Review
487(2)
Graphs and Functions
489(70)
Chapter 7 Pretest
490(1)
The Slope-Intercept Form
491(8)
More Equations of Lines
499(12)
Integrated Review--Linear Equations in Two Variables
509(2)
Introduction to Functions
511(14)
Polynomial and Rational Functions
525(8)
Variation and Problem Solving
533(26)
Chapter 7 Activity: Measuring Slope
544(1)
Chapter 7 Vocabulary Check
545(1)
Chapter 7 Highlights
545(4)
Chapter 7 Review
549(4)
Chapter 7 Test
553(4)
Cumulative Review
557(2)
Systems of Equations and Inequalities
559
Chapter 8 Pretest
560(1)
Solving Systems of Linear Equations by Graphing
561(12)
Solving Systems of Linear Equations by Substitution
573(8)
Solving Systems of Linear Equations by Addition
581(10)
Integrated Review--Systems of Linear Equations
589(2)
Systems of Linear Equations and Problem Solving
591(16)
Solving Systems of Linear Equations in Three Variables
607(12)
Solving Systems of Equations Using Matrices
619(6)
Systems of Linear Inequalities
625
Chapter 8 Activity: Analyzing the Courses of Ships
632(1)
Chapter 8 Vocabulary Check
633(1)
Chapter 8 Highlights
633(6)
Chapter 8 Review
639(6)
Chapter 8 Test
645(4)
Cumulative Review
649
Rational Exponents, Radicals, and Complex Numbers
65(670)
Chapter 9 Pretest
652(1)
Radical Expressions and Functions
653(10)
Rational Exponents
663(8)
Simplifying Radical Expressions
671(8)
Adding, Subtracting, and Multiplying Radical Expressions
679(8)
Rationalizing Numerators and Denominators of Radical Expressions
687(12)
Integrated Review--Radicals and Rational Exponents
697(2)
Radical Equations and Problem Solving
699(12)
Complex Numbers
711(24)
Chapter 9 Activity: Calculating the Length and Period of a Pendulum
720(1)
Chapter 9 Vocabulary Check
721(1)
Chapter 9 Highlights
721(4)
Chapter 9 Review
725(6)
Chapter 9 Test
731(2)
Cumulative Review
733(2)
Quadratic Equations and Functions
735(84)
Chapter 10 Pretest
736(1)
Solving Quadratic Equations by Completing the Square
737(12)
Solving Quadratic Equations by Using the Quadratic Formula
749(12)
Solving Equations by Using Quadratic Methods
761(14)
Integrated Review--Summary on Solving Quadratic Equations
773(2)
Nonlinear Inequalities in One Variable
775(8)
Quadratic Functions and Their Graphs
783(12)
Further Graphing of Quadratic Functions
795(24)
Chapter 10 Activity: Recognizing Linear and Quadratic Models
806(1)
Chapter 10 Vocabulary Check
807(1)
Chapter 10 Highlights
807(4)
Chapter 10 Review
811(4)
Chapter 10 Test
815(2)
Cumulative Review
817(2)
Exponential and Logarithmic Functions
819(82)
Chapter 11 Pretest
820(1)
The Algebra of Functions
821(6)
Inverse Functions
827(10)
Exponential Functions
837(10)
Logarithmic Functions
847(10)
Properties of Logarithms
857(10)
Integrated Review--Functions and Properties of Logarithms
865(2)
Common Logarithms, Natural Logarithms, and Change of Base
867(8)
Exponential and Logarithmic Equations and Problem Solving
875(26)
Chapter 11 Activity: Modeling Temperature
884(1)
Chapter 11 Vocabulary Check
885(1)
Chapter 11 Highlights
885(4)
Chapter 11 Review
889(6)
Chapter 11 Test
895(4)
Cumulative Review
899(2)
Conic Sections
901(66)
Chapter 11 Pretest
902(1)
The Parabola and the Circle
903(16)
The Ellipse and the Hyperbola
919(12)
Integrated Review--Graphing Conic Sections
929(2)
Graphing Nonlinear Functions
931(6)
Solving Nonlinear Systems of Equations
937(6)
Nonlinear Inequalities and Systems of Inequalities
943(24)
Chapter 12 Activity: Modeling Conic Sections
950(1)
Chapter 12 Vocabulary Check
951(1)
Chapter 12 Highlights
951(4)
Chapter 12 Review
955(6)
Chapter 12 Test
961(4)
Cumulative Review
965(2)
Appendix A Transition Review: Exponents, Polynomials, and Factoring Strategies 967(6)
Appendix B Transition Review: Solving Linear and Quadratic Equations 973(6)
Appendix C An Introduction to Using a Graphing Utility 979(6)
Appendix D Sets and Compound Inequalities 985(6)
Appendix E Absolute Value Equations and Inequalities 991(10)
Appendix F Determinants and Cramer's Rule 1001(8)
Appendix G Review of Geometric Figures 1009(2)
Appendix H Review of Angles, Lines, and Special Triangles 1011
Answers to Selected Exercises A1
Solutions to Selected Exercises A55
Index I1
Photo Credits 114

Excerpts

About This Book Algebra A Combined Approach,Second Edition is intended for a two semester course in introductory and intermediate algebra. It was written to provide asolid foundationin algebra for students who might have had no previous experience in algebra. Specific care was taken to ensure that students have the mostup-to-date relevanttext preparation for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. As suggested by the AMATYC Crossroads Document and the NCTM Standards (plus Addenda), real-life and real-data applications, data interpretation, conceptual understanding, problem solving, writing, cooperative learning, appropriate use of technology, mental .mathematics, number sense, critical thinking, and geometric concepts are emphasized and integrated throughout the book. The many factors that contributed to the success of the first edition have been retained. In preparing the Second Edition, I considered comments and suggestions of colleagues, students, and many users of the prior edition throughout the country. Algebra A Combined Approach,Second Edition is part of a series of texts that can includeBasic College Mathematics,Second Edition;Prealgebra,Third Edition;Introductory Algebra,Second Edition; andIntermediate Algebra,Second Edition. Throughout the series pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses. Key Pedagogical Features and Changes in the Second Edition Readability and Connections.I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problem-solving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information. In addition, each section begins with a list of objectives covered in the section. Clear organization of section material based on objectives further enhances readability. Problem-Solving Process.This is formally introduced in Chapter 2 with a four-step process that is integrated throughout the text. The four steps areUnderstand, Translate, Solve,andInterpret.The repeated use of these steps in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' comfort level and confidence in tackling problems. Applications and Connections.Every effort was made to include as many interesting and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. In the Second Edition, the applications have been thoroughly revised and updated, and the number of applications has increased. The applications help to motivate students and strengthen their understanding of mathematics in the real world. They show connections to a wide range of fields including agriculture, allied health, anthropology, art, astronomy, biology, business, chemistry, construction, consumer affairs, earth science, education, entertainment, environmental issues, finance, geography, government, history, medicine, music, nutrition, physics, sports, travel, and weather. Many of the applications are based on recent real data. Sources for data include newspapers, magazines, publicly held companies, government agencies, special-interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included. See the Applications Index on page xx. Practice Problem


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