Algebra : A Combined Approach

by Martin-Gay, K. Elayn

• ISBN13: 9780130674517
• ISBN10: 0130674516
• Edition: 2nd
• Format: Paperback
• Copyright: 2003-01-01
• Publisher: Pearson College Div

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