Beginning and Intermediate Algebra

This book is a compilation of chapters that discuss the most vital concepts in the field of algebra. It provides in depth knowledge of this field of study. As a part of mathematics, algebra includes the study of groups and fields and their manipulation. It is generally referred to as the backbone of mathematics. Some of the diverse topics covered in this book address the varied branches that fall under this category. The book studies, analyses and upholds the pillars of algebra and its utmost significance in modern times. This textbook is an essential guide for students who are seeking detailed information in this area.

PREFACE ABOUT THIS BOOK

Beginning and Intermediate Algebra, Second Edition, was written to provide a solid foundation in algebra as well as to develop students' problem-solving skills. Specific care has been taken to ensure that students have the most up-to-date and relevant text preparation for their next mathematics course, as well as to help students succeed in nonmathematical courses that require a grasp 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. The basic concepts of graphs and functions are introduced early, and problem solving techniques, real-life and real-data applications, data interpretation, appropriate use of technology, mental mathematics, number sense, critical thinking, decision-making, 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 this edition, I considered the comments and suggestions of colleagues throughout the country, students, and many users of the prior edition. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.

Beginning and Intermediate Algebra, Second Edition, is part of a series of texts that can include Basic College Mathematics and Prealgebra, Third Edition. Also available are Beginning Algebra, Third Edition, Intermediate Algebra, Third Edition, and Intermediate Algebra: A Graphing Approach, 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 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 every day life can help students gradually master both new and old information.

Problem-Solving Process. This is formally introduced in Chapter 2 with a new four-step process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in beginning problems.

Applications and Connections. Every effort was made to include as many accessible, interesting and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. The applications strengthen students' understanding of mathematics in the real world and help to motivate students. They show connections to a wide range of fields including agriculture, astronomy, automotive ownership, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxiv.) Many of the applications are based on recent and interesting real-life data. Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data with and without using the internet are also included.

Helpful Hints. Helpful Hints contain practical advice on applying mathematical concepts. These are found throughout the text and strategically placed where students are most likely to need immediate reinforcement. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 90 and 365.

Visual Reinforcement of Concepts. The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs and circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now approximately 1,000 figures.

Real World Chapter Openers. The new two-page chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the career and the relevance of algebra. For example, look at the opener for Chapter 4. The opening pages also contain a list of section titles, and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.

Student Resource Icons. At the beginning of each section, videotape, tutorial software CD Rom, Student Solutions Manual, and Study Guide icons are displayed. These icons help remind students that these learning aids are available should they choose to use them to review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.

Chapter Highlights. Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to help students understand and retain what they have learned.

Chapter Project. This feature occurs at the end of each chapter, often serving as a chapter wrap-up. For individual or group completion, the multi-part Chapter Project, usually hands-on or data based, allows students to problem solve, make interpretations, and to think and write about algebra.

In addition, a reference to alternative or additional Real World Activities is given. This internet option invites students to find and retrieve real data for use in solving problems. Visit the Real World Activities Website by going to prenhall/martin-gay.

Functional Use of Color and New Design. Elements of this text are highlighted with color or design to make it easier for students to read and study. Special care has been taken to use color within solutions to examples or in the art to help clarify, distinguish, or connect concepts. For example, look at page 301 in Section 5.3. EXERCISE SETS

Each text section ends with an exercise set, usually divided into two parts. Both parts contain graded exercises. The first part is carefully keyed to at least one worked example in the text. Once a student has gained confidence in a skill, the second part contains exercises not keyed to examples. Exercises and examples marked with a video icon have been worked out step-by-step by the author in the videos that accompany this text.

Throughout the text exercises there is an emphasis on data and graphical interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. Similarly, throughout the text there is integration of geometric concepts, such as perimeter and area. Exercises and examples marked with a geometry icon have been identified for convenience.

Each exercise set contains one or more of the following features.

Spotlight on Decision Making. These unique new, specially designed applications help students develop their decision-making and problem-solving abilities, skills useful in mathematics and in life. Appropriately placed before an exercise set begins, students have an opportunity to immediately practice and reinforce basic algebraic concepts found in the accompanying section in relevant, accessible contexts. There is an emphasis on workplace or job-related career situations (such as the decisions of a Meteorologist in Section 3.1, a phychologist in Section 9.6, or a Webmaster in Section 11.4) as well as decision making in general (such as choosing a credit card in Section 6.5 or deciding between two job offers in Section 4.3).

Mental Mathematics. These problems are found at the beginning of many exercise sets. They are mental warm-ups that reinforce concepts found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselves but also their number sense and estimation ability.

Writing Exercises. These exercises now found in almost every exercise set are marked with a pencil icon. They require students to assimilate information and provide a written response to explain concepts or justify their thinking. Guidelines recommended by the American Mathematical Association of Two Year Colleges (AMATYC) and other professional groups recommend incorporating writing in mathematics courses to reinforce concepts. Writing opportunities also occur within features such as Spotlight on Decision Making and Chapter Projects.

Data and Graphical Interpretation. Throughout the text there is an emphasis on data interpretation in exercises via tables, bar charts, line graphs, or circle graphs. The ability to interpret data and read and create a variety of graphs is developed gradually so students become comfortable with it.

Calculator Explorations and Exercises. These optional explorations offer guided instruction, through examples and exercises, on the proper use of scientific and graphing calculators or computer graphing utilities as tools in the mathematical problem-solving process. Placed appropriately throughout the text, these explorations reinforce concepts or motivate discovery learning.

Additional exercises building on the skills developed in the Explorations may be found in exercise sets throughout the text and are marked with the icon for scientific calculator use or with the icon for graphing calculator use.

Review Exercises. These exercises occur in each exercise set (except for those in Chapter 1). These problems are keyed to earlier sections and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the links between earlier topics and later material.

A Look Ahead. These exercises occur at the end of some exercise sets. This section contains examples and problems similar to those found in a subsequent algebra course. "A Look Ahead" is presented as a natural extension of the material and contains an example followed by advanced exercises.

In addition to the approximately 7000 exercises within sections, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, and Cumulative Reviews.

Vocabulary Checks. Vocabulary checks, new to this edition, provide an opportunity for students to become more familiar with the use of mathematical terms as they strengthen their verbal skills.

Chapter Review and Chapter Test. The end of each chapter contains a review of topics introduced in the chapter. The review problems are keyed to sections. The chapter test is not keyed to sections.

Cumulative Review. Each chapter after the first contains a cumulative review of all chapters beginning with the first up through the chapter at hand. Each problem contained in the cumulative review is actually an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete worked-out solution, with explanation, can do so by turning to the appropriate example in the text. KEY CONTENT FEATURES IN TIDE SECOND EDITION

Overview. This new edition retains many of the factors that have contributed to its success. Even so, every section of the text was carefully re-examined. Throughout the new edition you will find numerous new applications, examples, and many real-life applications and exercises. Some sections have internal re-organization to better clarify and enhance the presentation.

Table of Content Changes in the Second Edition. The second edition includes a new Chapter 8, Transitions to Intermediate Algebra. Although intermediate algebra topics are woven into earlier chapters where appropriate, the purpose of this chapter is to help students make the transition from beginning algebra to intermediate algebra. For example, Chapter 8 contains types of equations and inequalities normally found in intermediate algebra, such as absolute value equations and inequalities, system of equations in three variables as well as matrices and determinants.

By moving these intermediate algebra topics to Chapter 8, Chapters 2 and 3 were combined to form a new Chapter 2, Equations, Inequalities, and Problem Solving. As a result, graphing is now covered in Chapter 3, Graphs and Functions. A new Section 3.1 is devoted to introducing the rectangular coordinate system and creating scatter diagrams from real data. Functions are introduced in Section 3.3 and continually revisited to help students fully understand and see the importance of this topic. For example, see Sections 3.4, 5.3, 6.8, and 7.1 just to name a few.

Increased Integration of Geometry Concepts. In addition to the traditional topics in beginning algebra courses, this text contains a strong emphasis on problem solving, and geometric concepts are integrated throughout. The geometry concepts presented are those most important to a students' understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with the geometry icon. Also, geometric figures, a review of angles, lines, and special triangles, are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.

Real Numbers and Algebraic Expressions. Chapter 1 now begins with Tips for Success in Mathematics (Section 1.1). Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. New applications and real data enhance the chapter.

Early and Intuitive Introduction to Graphs and Functions. As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis are placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 3. This edition offers more real data and conceptual type applications and further strengthens the introduction to slope.

Once students are comfortable with graphing equations, functions are introduced in Chapter 3. The concept of function is illustrated in numerous ways to ensure student understanding: by listing ordered pairs of data, showing rectangular coordinate system graphs, visually representing set correspondences, and including numerous real-data and conceptual examples. The ...