[Book Cover]

Intermediate Algebra with Applications, 2/e

Linda Exley, DeKalb College
Vince Smith, DeKalb College

Published February, 1994 by Prentice Hall Engineering/Science/Mathematics

Copyright 1994, 640 pp.
Cloth
ISBN 0-13-474552-3


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Summary

A text which students can actually READ and use to learn intermediate algebra — and which instructors can use as a genuinely supportive framework from which to teach algebra — Intermediate Algebra with Applications features an easy-to-read presentation, an emphasis on problem-solving skills, a wealth of well-chosen, illustrative examples, and uniquely structured problem sets.

Features


covers linear equations and inequalities early— and integrates them throughout the text where appropriate. (pp. 125)
explores graphing and functions earlier — so that students will be more adequately prepared for the next course. (pp. 352)
places a greater emphasis on problem solving and mathematical modeling of real-world applications.

  • devotes an entire section to the development of problem solving skills (pp. 157)
  • includes “You Decide” problems at the end of each chapter. These open-ended, extended real-world applications help students develop critical thinking and writing skills. Because these problems have no one correct answer, students are able to hone their problem solving and decision making skills by deciding then supporting their answer with specific evidence (pp. 123)
  • increases the number of word problems throughout
  • revises applications to reflect a more current, realistic context. E.g., section 2.2 refers to real events and celebrities like Florence Griffith-Joiner, Janet Jackson, and Joe Montana
provides Calculator boxes — with help for the use of both scientific and graphing calculators (pp. 64)
begins each chapter with “Connections” — an introductory paragraph which puts the upcoming material in context with other chapters, other disciplines, math history and the real world (pp. 52)
features problem sets uniquely organized into discrete levels of understanding:
  • Warm-Ups — carefully graded and keyed specifically to examples in the section (pp. 87)
  • Practice — mixed, and not referenced to any examples (pp. 88)
  • Challenge — probe natural extensions of the topics (pp. 96)
  • In Your Own Words — test conceptual understanding by requiring a written answer (pp. 96)
highlights “key” problems in red throughout the exercise sets. These are considered to be essential problems which, if assigned, will cover all the section learning objectives. They can be used in class examples, problem assignments, or for review. Answers are provided at the end of the text. (pp. 98)
features “Let's Not Forget” problems at the end of every chapter review problem set. These exercises are cumulative and require students to recall topics covered in previous sections and chapters. (pp. 122)
provides “Be Careful” annotations in the margins — to prominently point out common student errors. (pp. 110)
concludes chapters with a glossary, review of key concepts, and “Checkups” — worked examples stated as problems with specific references. (pp. 119)


Table of Contents
(NOTE: Each chapter concludes with a Chapter Summary, Review Problems, and a Chapter Test.)
    0. Reviewing Sets of Numbers and Geometry.

      Sets. Properties of real numbers. Absolute value. Operations with real numbers. Angles, lines, and plane figures. Perimeter, surface area, area, and volume.

    1. Integer Exponents and Polynomials.

      Integer exponents. Polynomial definition, evaluation, addition, and subtraction. Multiplication of polynomials. Pascal's triangle (optional). Greatest common factor and factoring by grouping. Factoring binomials and trinomials. Summary of factoring. Division of polynomials. Synthetic division (optional).

    2. Using Linear Equations and Inequalities in One Variable.

      Solving linear equations in one variable. Literal equations and formulas. Linear inequalities in one variable. Problem solving. Liner equations as models for applications. Absolute value equations. Boundary numbers and absolute value inequalities.

    3. Rational Expressions.

      Fundamental principle of rational expressions. Multiplication and division. Addition and subtraction. Rational equations and inequalities. Complex fractions.

    4. Radicals and Exponents.

      Roots and radicals. Addition and subtraction of radical expressions. Multiplication of radical expressions. Division of rational expressions and rationalizing. Equations containing square roots. Rational exponents. Complex numbers.

    5. Nonlinear Equations and Inequalities in One Variable.

      Solving quadratic equations and inequalities by factoring. Quadratic equations and inequalities as models for applications. Completing the square. The quadratic formula. Higher-degree equations and inequalities. More rational equations and inequalities. Radical equations.

    6. Graphs and Functions.

      Cartesian coordinate system. Graph of Ax + By = C. Slope. Equations of lines. Functions. Graphs of functions. Variation.

    7. Systems of Equations and Inequalities.

      Systems of equations in two variables. Systems as models for applications. Linear systems of equations in more than two variables. Linear inequalities in two variables. Systems of linear inequalities in two variables. Determinants and Cramer's Rule (optional). Matrix methods (optional).

    8. Exponential and Logarithmic Functions.

      Algebra of functions. Inverse functions. Exponential functions. Logarithmic functions. Properties of logarithms.

    9. Conic Sections.

      The circle. The parabola. The ellipse and the hyperbola. The general second-degree equation in two variables.

    10. Other Topics.

      Sequences. Summation notation. Factorials and binomial coefficients. The binomial theorem. Permutations and combinations.

    Appendix: An Introduction to the Graphing Calculator.
    Answers to Selected Problems.
    Photo Credits.
    Index.


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