[Book Cover]

Intermediate Algebra, 2/e

K. Elayn Martin-Gay, University of New Orleans, Lakefront

Published December, 1996 by Prentice Hall Engineering/Science/Mathematics

Copyright 1997, 760 pp.
Cloth
ISBN 0-13-242462-2


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Summary

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. The Second Edition features a greater incorporation of AMATYC and NCTM standards—reflected in an increased emphasis on visualization and graphing, carefully revised problems, and more data analysis. Also featured are current, relevant and realistic applications of math and its function in the world today.

Features


Accessible Presentation.

  • Writing style is clear and direct.
  • Many clear explanations are provided.
  • Pedagogy is ample and accessible.
Treatment of graphing and scientific calculators is integrated in separate boxes and noted in exercise sets (one icon for graphing calculators, another for scientific). Instructors can pick and choose when and how they want to integrate technology into their course.
Mental Math boxes ask students to employ analytical skills and solve problems intuitively. They can be incorporated as in-class oral exercises or as preludes to exercise sets.
Definitions are clearly explained, both visually (definitions are summarized and highlighted by color) and by worked example. Ideal for visual learners, and/or for those who learn best by example.
Conceptual Exercises, identified by an icon, ask students to verbalize solutions, increasing students' “writing in mathematics” skills.
  • Also help develop pattern recognition.
Cumulative Reviews in every chapter include worked examples from previous chapters. Students can find the answers in an appendix, as well as a reference to where the problem first appeared so that a complete solution is available.
  • Similar Skill Reviews are featured at the end of every section.
Geometry concepts and applications are incorporated where appropriate.
NEWUnique chapter openers feature vignettes and related photographs demonstrating real-life applications of mathematics. Vignettes are summarized at ends of chapters with boxes stressing problem- solving and critical thinking skills.
  • Can be used as collaborative activities.
Group Activities at the end of chapters emphasize critical thinking and problem solving.
NEWA six-step problem-solving framework is woven consistently throughout. Students are asked to:
  • 1) Understand
  • 2) Assign
  • 3) Illustrate
  • 4) Translate into a model (equation)
  • 5) Complete
  • 6) Interpret—a variety of realistic problems.
NEWAn increased emphasis on data interpretation; real data is integrated throughout. With the emphasis on interpreting data via graphs, students reinforce what they've learned visually and see math's tangibility.
NEW—Basic concepts of functions are introduced early and intuitively. Students are gently eased into the concept of a function in Chapter 3, the concept of function is revisited as appropriate throughout the text.
NEWExercise sets have been carefully reviewed and revised to include more real data. The sets are graded in level of difficulty, and feature more conceptual and current data from environmental science, allied health, astronomy, business and other disciplines.
  • USA Today and other well-known sources are used.
NEWReminders (formerly Helpful Hints) alert students to trouble areas and provide encouragement and suggestions to avoid common errors.


Table of Contents
(NOTE: Each chapter ends with highlights, review, test and cumulative review.)
    1. Real Numbers and Algebraic Expressions.

      Algebraic Expressions and Sets of Numbers. Properties of Real Numbers. Operations on Real Numbers. Order of Operations and Algebraic Expressions.

    2. Equations, Inequalities and Problem Solving.

      Linear Equations in One Variable. An Introduction to Problem Solving. Formulas and Problem Solving. Linear Inequalities and Problem Solving. Compound Inequalities. Absolute Value Equations. Absolute Value Inequalities.

    3. Graphs and Functions.

      Graphing Equations. Introduction to Functions. Graphing Linear Functions. The Slope of a Line. Equations of Lines. Graphing Linear Inequalities.

    4. Systems of Equations.

      Solving Systems of Linear Equations in Two Variables. Solving Systems of Linear Equations in Three Variables. Systems of Linear Equations and Problem Solving. Solving Systems of Equations by Matrices. Solving Systems of Equations by Determinants.

    5. Exponents, Polynomials, and Polynomial Functions.

      Exponents and Scientific Notation. More Work with Exponents and Scientific Notation. Polynomials and Polynomial Functions. Multiplying Polynomials. The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials. Factoring by Special Products and Factoring Strategies. Solving Equations by Factoring and Problem Solving. An Introduction to Graphing Polynomial Functions.

    6. Rational Expressions.

      Rational Functions and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Simplifying Complex Fractions. Dividing Polynomials. Synthetic Division and the Remainder Theorem. Solving Equations Containing Rational Expressions. Rational Equations and Problem Solving. Variation and Problem Solving.

    7. Rational Exponents, Radicals, and Complex Numbers.

      Rational and Radical Functions. Rational Exponents. Simplifying Radicals Expressions. Adding, Subtracting, and Multiplying Radicals. Rationalizing Numerators and Denominators of Radical Expressions. Radical Equations and Problem Solving. Complex Numbers.

    8. Quadratic Equations and Functions.

      Solving Quadratic Equations by Completing the Square. Solving Quadratic Equations by the Quadratic Formula. Solving Equations by Using Quadratic Methods. Nonlinear Inequalities in One Variable. Quadratic Functions and Their Graphs. Further Graphing of Quadratic Functions.

    9. Conic Sections.

      The Parabola and the Circle. The Ellipse and the Hyperbola. Solving Nonlinear Systems of Equations. Nonlinear Inequalities and Systems of Inequalities.

    10. Exponential and Logarithmic Functions.

      Exponential Functions. Composite and Inverse Functions. Logarithmic Functions. Properties of Logarithms. Common Logarithms, Natural Logarithms, and Change of Base. Exponential and Logarithmic Equations and Applications.

    11. Sequences, Series and the Binomial Theorem.

      Sequences. Arithmetic and Geometric Sequences. Series. Partial Sums of Arithmetic and Geometric Sequences. The Binomial Theorem.

    Appendix.

      A. Operations on Decimals. B. Reviews of Angles, Lines and Special Triangles. C. Review of Geometric Figures. D. Table of Squares and Square Roots. E. Intro Graphing and Calculators. F. Answers to Selected Exercises.


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