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Elayn Martin-Gay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful. Martin-Gay also strives to provide the highest level of instructor and adjunct support. Real Numbers, Algebraic Expressions, Equations, Graphs, Functions, Inequalities, Systems of Equations, Exponents, Polynomial Functions, Rational Equations, Rational Exponents, Radicals, Complex Numbers, Quadratic Equations, Exponential & Logorihmic Functions, Conic Sections, and Sequences and Series. For all readers interested in algebra, and for all readers interested in learning or revisiting essential skills in intermediate algebra through the use of lively, up-to-date applications.
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This text provides a solid foundation in algebra with the exceptional pedagogy, clear and well-constructed writing style, superb problem-solving strategies, and other qualities that have made the Martin-Gay series so successful. Intermediate Algebra: A Graphing Approach features incorporation of AMATYC and NCTM standards--reflected in an increased emphasis on visualization graphing, and data analysis. Also featured are current, relevant and realistic applications of math and its function in the world today.From the Inside Flap:
PREFACE ABOUT THIS BOOK
Intermediate Algebra: A Graphing Approach, 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. We 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, mental mathematics, number sense, critical thinking, decision making, and geometric concepts are emphasized and integrated throughout the book. This text makes reference to the use of graphing technology to help students better understand important mathematical connections.
The many factors that contributed to the success of the first edition have been retained. In preparing this edition, we considered the comments and suggestions of colleagues throughout the country, students, and 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.
Intermediate Algebra: A Graphing Approach, Second Edition is part of a series of texts that can include Basic College Mathematics, Prealgebra, Third Edition, and Beginning Algebra, Third Edition. Also available are Beginning and Intermediate Algebra, Second Edition, a combined algebra text and Intermediate Algebra, Third 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 THIRD EDITION
Readability and Connections. We 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.
Problem Solving Process. This is formally introduced in Chapter 1 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. When solving problems, students are encouraged to use technology when applicable during this problem-solving process and/or when checking a solution. For instance, with technology, a graph can be generated quickly and accurately in order to enhance the problem-solving process.
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 them. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, 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 xxi.) Many of the applications are based on recent and interesting real-life data. For instance, see Section 2.4, exercise 76, Section 4.3, exercise 44 , or Section 5.3 exercise 85, for a variety of ways real data is used. 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.
Discover the Concept. These explorations, integrated appropriately throughout the text, are often for use with graphing calculators or computer graphing utilities. They promote student involvement and interaction with the text as students are reading. This feature helps students recognize patterns or discover a concept on their own immediately before the concept is formally introduced.
Helpful Hints. Helpful Hints, formerly Reminders, 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 129 and 348.
Technology Note. Generally found in the margin, technology notes contain specific suggestions for problem solving with technology. They also contain notes on extra features students might find available on their graphing utilities.
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 mufti-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 site 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 555 in Section 8.5. 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.
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 2.1, a phychologist in Section 7.6, or a Webmaster in Section 9.4) as well as decision making in general (such as choosing a long-distance telephone plan in Section 4.3 or choosing an online service in Section 5.4 or deciding between two job offers in Section 11.1).
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.
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 5,000 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 THE 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. For example, look at Sections 2.4, 2.6, or 8.2. Some sections have internal re-organization to better clarify and enhance the presentation.
Increased Integration of Geometry Concepts. In addition to the traditional topics in 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 student's 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 back cover provides a quick reference of geometric formulas.
Real Numbers and Algebraic Expressions. Chapter 1 now begins with Tips for Success in Mathematics (Section 1.0). 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 Chapter 1, an emphasis is placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 2. 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 2. 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 importance of a function is continuously reinforced by not treating it as a single, stand-alone topic but by constantly integrating functions in appropriate sections of this text.
Increased Attention to Problem Solving. Building on the strengths of the prior edition, a special emphasis and strong commitment are given to contemporary, accessible, and practical applications of algebra. Real data was drawn from a variety of sources including internet sources, magazines, newspapers, government publications, and reference books. Unique Spotlight on Decision Making exer...
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