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Exploring Intermediate Algebra

Exploring Intermediate Algebra - 04 edition

Exploring Intermediate Algebra - 04 edition

ISBN13: 9780618156962

ISBN10: 0618156968

Exploring Intermediate Algebra by Richard N. Aufmann, Joanne Lockwood and Laurie Boswell - ISBN 9780618156962
Edition: 04
Copyright: 2004
Publisher: Houghton Mifflin Harcourt
International: No
Exploring Intermediate Algebra by Richard N. Aufmann, Joanne Lockwood and Laurie Boswell - ISBN 9780618156962

ISBN13: 9780618156962

ISBN10: 0618156968

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Intended for a first-year level developmental mathematics course in intermediate algebra, Exploring Intermediate Algebra: A Graphing Approach is designed to assist students in making connections between mathematics and its applications. Its goal is to develop a student's mathematical skills through appropriate use of applications and to use technology to establish links between abstract mathematical concepts and visual or concrete representations.

  • The proven Aufmann Interactive Method (AIM) ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains one or more sets of matched-pair examples encouraging students to interact with the text. The first example in each set is completely worked out; the second example, called 'You Try It,' prompts students to practice concepts at the time they are presented in the text. Complete worked-out solutions to these examples in an appendix at the end of the book help students by providing immediate feedback, concept reinforcement, and identification of mistakes to prevent frustration.
  • Technology is integrated throughout the text to assist students in making connections between abstract mathematical concepts and a concrete representation provided by technology. This is one way in which students are encouraged to think about and use multiple representations of a concept. The inclusion of technology also facilitates computation in order to focus on analysis rather than manipulation and enables students to examine concepts that would be too difficult or time consuming if the technology were not available.
  • Calculator Notes throughout offer tips on using the graphing calculator and See Appendix B notes in student text margin refer students to the graphing calculator appendix for detailed TI-83 and TI-83+ keystroke information.
  • AIM for Success, a special preface designed to promote student success, provides students with strategies for using the text and the Aufmann Interactive Method. Suggestions for using this section as a lesson are featured in the Instructor's Resource Manual and the lesson is also available as a PowerPoint presentation.
  • Carefully developed approach to problem solving encourages students to develop their own strategies--such as drawing diagrams or writing out the solution steps in words--as part of their solution to a problem. In each case, model solutions encourage students to "State the goal, devise a strategy, solve the problem, and check your work."
  • To address different learning styles, a unique side-by-side, multiple approach formatpresents worked-out examples in a two-column layout, with both algebraic and graphical solutions (in either order) that help students make the connection between concepts and concrete representations of the math.
  • Applications and real data, selected to motivate an interest in mathematics, require students to use problem-solving strategies along with the skills covered in the section. Applications are taken from many disciplines including agriculture, business, carpentry, chemistry, construction, earth science, education, manufacturing, nutrition, real estate, and sociology. Real data examples and exercises ask students to analyze and solve problems taken from actual situations.
  • For ease of navigation, icons identify writing, data, web, and group exercises. In addition, web, CD, video/DVD, and Student Solutions Manual icons at the beginning of each section refer students to relevant supplements. A transparency icon in the Instructor's Annotated Edition denotes figures in the text with transparency masters.
  • Chapter Openers clearly orient students to the content with a list of sections in the chapter and a photo and caption that refer to a corresponding example, exercise, or exploration.
  • Prep Tests at the beginning of each chapter highlight the prerequisite skills in the upcoming chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the previous section from which the question was taken, encouraging students to review as necessary. Answers to the Prep Test can be found on the same page in Instructor's Annotated Edition. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
  • Point of Interest student margin notes include an interesting and/or historical sidenote to the math presented.
  • Take Note boxes in the student text margin alert students to more complex procedures or remind them to check their work.
  • Each section exercise set includes Topics for Discussion, which ask students to discuss or write about a concept; Applying Concepts, which require analysis or offer challenge problems; Explorations, which expand upon a concept presented in the section and are useful in cooperative learning situations or as extra credit assignments; and Real Data Applications, taken from a variety of disciplines and labeled accordingly, which ask students to analyze and solve real-world problems.
  • End of chapter material designed to promote success includes Chapter Summaries, with referenced Key Terms and Essential Concepts; Chapter Review Exercises; Chapter Tests; and Cumulative Review Exercises.
  • An Instructor's Annotated Edition features Instructor Notes, with teaching ideas, warnings about common student errors, and historical notes. Instructor Notes next to each Example refer teachers to a similar problem in the following exercise set for possible use as an additional in-class example. Suggested Activities (found in the margin) can be used in class to explore concepts, as alternative (discovery) strategies for teaching the concept, or as cooperative learning activities. Suggested Assignments before each exercise set save instructors class preparation time.

Table of Contents

Table of Contents

1. Fundamental Concepts

Section 1.1 Problem Solving
Section 1.2 Sets
Section 1.3 Evaluating Variable Expressions Using Integers
Section 1.4 Evaluating Variable Expressions Using Rational Numbers
Section 1.5 Simplifying Variable Expressions

2. Introduction to Functions and Relations

Section 2.1 Rectangular Coordinates and Graphs
Section 2.2 Relations and Functions
Section 2.3 Properties of Functions

3. First-Degree Equations and Inequalities

Section 3.1 Solving First-Degree Equations
Section 3.2 Applications of First-Degree Equations
Section 3.3 Applications to Geometry
Section 3.4 Inequalities in One Variable
Section 3.5 Absolute Value Equations and Inequalities

4. Linear Functions

Section 4.1 Slopes and Graphs of Linear Functions
Section 4.2 Finding Equations of Straight Lines
Section 4.3 Linear Regression
Section 4.4 Linear Inequalities in Two Variables

5. Systems of Linear Equations and Inequalities

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method
Section 5.2 Solving Systems of Linear Equations by the Addition Method
Section 5.3 Solving Systems of Linear Equations Using Matrices
Section 5.4 Systems of Linear Inequalities and Linear Programming

6. Polynomials

Section 6.1 Operations on Monomials and Scientific Notation
Section 6.2 Addition and Subtraction of Polynomials
Section 6.3 Multiplication and Division of Polynomials
Section 6.4 Factoring Polynomials
Section 6.5 Special Factoring
Section 6.6 Solving Equations by Factoring

7. Rational Expressions and Equations

Section 7.1 Introduction to Rational Expressions
Section 7.2 Operations on Rational Expressions
Section 7.3 Rational Equations
Section 7.4 Proportions and Similar Triangles
Section 7.5 Variation

8. Radical Expressions and Rational Exponents

Section 8.1 Rational Exponents and Radical Expressions
Section 8.2 Simplifying Radical Expressions
Section 8.3 The Pythagorean Theorem
Section 8.4 Operations on Radical Expressions
Section 8.5 Radical Functions
Section 8.6 Solving Radical Equations
Section 8.7 Complex Numbers

9. Quadratic Functions and Quadratic Inequalities

Section 9.1 Introduction to Quadratic Equations
Section 9.2 Solving Quadratic Equations by Taking Square Roots and by Completing the Square
Section 9.3 Solving Quadratic Equations by Using the Quadratic Formula and by Graphing
Section 9.4 Equations That Are Quadratic in Form
Section 9.5 Quadratic Functions
Section 9.6 Quadratic Inequalities

10. Exponential and Logarithmic Functions

Section 10.1 Algebra of Functions
Section 10.2 Inverse Functions
Section 10.3 Exponential Functions
Section 10.4 Exponential Models and Exponential Regression
Section 10.5 Logarithmic Functions
Section 10.6 Properties of Logarithms
Section 10.7 Exponential and Logarithmic Equations

Additional Topics in Algebra

Section 1 Introduction to Sequences and Series
Section 2 Binomial Expansions
Section 3 Conic Sections

Appendix A. Keystroke Guide for the TI-83 and TI-83 Plus