[Book Cover]

College Mathematics for Technology, 4/e

Cheryl Cleaves, the State Technical Institute of Memphis
Margie Hobbs, the State Technical Institute of Memphis
Paul Dudenhefer, the State Technical Institute of Memphis

Published August, 1997 by Prentice Hall Career & Technology

Copyright 1998, 1008 pp.
Cloth
ISBN 0-13-716614-1


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Summary

“College Mathematics for Technology, Fourth Edition” addresses curriculum and pedagogy standards that are initiatives of the American Mathematical Association of Two-Year Colleges (AMATYC), the National Council of Teachers of Mathematics (NCTM), and the Mathematics Association of America (MAA). The text retains its simple language making it suitable for a wide range of instructional uses.

Features

Each feature is tied to a specific teaching goal as identified by NCTM and SCANS.
to learn to value mathematics.

  • Mathematics in the Workplace includes excerpts and summaries from newspapers, magazines, and journal articles to help students develop a richer appreciation of the usefulness of mathematics in the workplace and in everyday life.
  • Career Applications appear at the end of most chapters. These applications were developed through interviews and market research in the workplace to ensure relevance.
  • An expanded index makes this text an excellent reference text to foster student's life-long learning. Formulas, career applications, and technical terms that are used in examples are indexed along with the mathematical terms. Entries are crossed referenced to make them easy to locate.
to learn to reason mathematically.
  • “Concept Analysis ” will strengthen the students' ability to make generalizations from experimentation and investigation.
  • the text provides this through explanatory comments in the text narrative, examples and in the “Concept Analysis” at the end of each chapter.
  • “Tips and Traps Boxes” draw attention to special cautions and procedures, helping students avoid common errors and misunderstandings.
to communicate mathematically.
  • the authors use both informal language and mathematically precise terminology to enable the students to learn to read and understand the mathematical concepts presented.
  • Concept Analysis” allows the students to formulate mathematical ideas and express them both orally and in writing.
  • The Instructor's Resource Manual contains additional projects that promote mathematical communication among students and teachers.
  • mathematical terms introduced in each chapter are listed at the end of the chapter in the “Words to Know” section.
  • Each section begins with a statement of “Learning Objectives,” which lays out what one should look for and learn in that section.
to become confident of mathematical abilities.
  • Boxes for Rules, Properties and Formulas appear throughout the text to help introduce new procedures and to provide a quick reference for review. To make the procedures as clear as possible, the authors break them down into step-by-step instructions. An example generally follows each rule, property or formula.
  • Self-Study Exercises” with all the answers in the text are designed to help students build confidence in their own mathematical abilities before attempting the “Assignment Exercises” where only the odd answers are provided.
  • Trial Tests” are located at the end of every chapter, and enable students to check their understanding of chapter concepts. Answers are provided to odd-numbered exercises in the back of the text. Solutions are provided to odd-numbered exercises in a separate “Student Solutions Manual”(see supplements).
  • “Chapter Summary” at the end of each chapter (in a grid format) lists each learning objective by section with key points to remember and an example. It's a built-in study guide!
to become math problem-solvers.
  • “Concept Analysis” questions focus on the “why” and “where” of mathematical concepts. They allow the student to formalize his/her understanding of a concept and to connect concepts to other words.
  • when problem-solving is first introduced, a six-step plan is developed for investigating and analyzing the situation presented in the problem to determine what tools to use to solve the problem.
All of the above.
  • Good decisions through teamwork. Projects are designed to promote the various facets of team work. The various projects emphasize computational skills, research skills, critical thinking and/or decision-making skills — all skills highly sought by employers.  AMATYC GOALS:  the AMATYC identifies the following as abilities to be developed by students in college math programs:
number sense.
  • the text emphasizes estimation.
  • whenever calculators are used, students are encouraged to check the answer to ensure it to be reasonable.
  • various reproducible activities are provided in the Instructor's Resource Manual.
symbol sense.
  • properties and formulas are presented in both symbols and words.
  • “Concept Analysis” develops students' ability to write words in math symbols and vise versa.
spacial and geometric sense.
  • geometric concepts are integrated throughout the text so that they are presented with the math concept required to solve problems involving geometry.
  • numerous visual illustrations are provided with word problems.
  • students are asked to devise illustrations from written problems.
function sense.
  • function notation and terminology are presented early in the text and expanded with graphing and formulas and students are encouraged to identify patterns and relationships.
  • reproducible activities are provided in the Instructor's Manual.
probability and statistical sense.
  • text includes an entire chapter on data analysis with emphasis on probability and statistics and the visual representation of data.
Calculator Boxes discuss how to analyze a mathematical procedure and set up a problem for a calculator solution followed by a sample series of keystrokes involved for the procedure.
NEW —“Symbolic Representation”is included just prior to solving linear equations to provide a thorough review of signed numbers and an introduction to variable expressions and translating from words to symbols.
NEW—“Good Decisions Through Teamwork” Every chapter opens with a team project that relates to the content of the chapter. Sufficient details are given to assist the teams in getting organized and to provide direction, however, the projects also have sufficient flexibility for the project to be expanded or to encourage creativity.
NEW—“Mathematics in the Workplace” Several articles that can generate class discussion or projects included throughout the text. These articles represent a wide variety of topics.
NEW—“Career Applications” Career applications for a wide variety of careers are included throughout the text. They are located in the end-of-chapter materials in practically every chapter. Applications include explanations, examples, exercises, and answers. Careers included are electronics, civil engineering, chemical engineering, law enforcement, nursing, horticulture, teaching, and many more.
NEW—Expanded "Tips and Traps," The Tips and Traps feature has been greatly expanded with each instance identified with a title for easier reference.


Table of Contents
    1. Whole Numbers and Decimals.

      Whole Numbers, Decimals, and the Place-Value System. Adding Whole Numbers and Decimals. Subtracting Whole Numbers and Decimals. Multiplying Whole Numbers and Decimals. Dividing Whole Numbers and Decimals. Exponents, Roots, and Powers of 10. Order of Operations.

    2. Integers.

      Natural Numbers, Whole Numbers, and Integers. Addition with Integers. Subtracting Integers. Multiplying Integers. Dividing Integers. Order of Operations.

    3. Fractions and Percents.

      Fraction Terminology. Multiples, Divisibility, and Factor Pairs. Prime and Composite Numbers. Least Common Multiple and Greatest Common Factor. Equivalent Fractions and Decimals. Improper Fractions and Mixed Numbers. Finding Common Denominators and Comparing Fractions and Decimals. Adding Fractions and Mixed Numbers. Subtracting Fractions and Mixed Numbers. Multiplying Fractions and Mixed Numbers. Dividing Fractions and Mixed Numbers. Signed Fractions and Decimals. Calculators with Fraction Key. Finding Number and Percent Equivalents.

    4. Problem Solving with Percents.

      Percentage Proportion. Solving Percentage Problems. Increases and Decreases. Business Applications.

    5. Direct Measure.

      The U.S. Customary System of Measurement. Adding and Subtracting U.S. Customary Measures. Multiplying and Dividing U.S. Customary Measures. Introduction to the Metric System. Metric-U.S. Customary Comparisons. Reading Instruments Used to Measure Length.

    6. Area and Perimeter.

      Squares, Rectangles, and Parallelograms. Area and Circumference of a Circle.

    7. Interpreting and Analyzing Data.

      Reading Circle, Bar, and Line Graphs. Frequency Distributions, Histograms, and Frequency Polygons. Finding Statistical Measures. Counting Techniques and Simple Probabilities.

    8. Symbolic Representation.

      Rational Numbers. Real Numbers. Variable Notation. Function Notation.

    9. Linear Equations.

      Solving Basic Equations. Isolating the Variable in Solving Equations. Applying the Distributive Property in Solving Equations. Strategies for Problem Solving.

    10. Equations with Fractions and Decimals.

      Solving Fractional Equations by Clearing the Denominators. Solving Decimal Equations. Using Proportions to Solve Problems.

    11. Powers and Logarithms.

      Laws of Exponents. Basic Operations with Algebraic Expressions Containing Powers. Powers of 10 and Scientific Notation. Polynomials. Exponential Expressions, Equations, and Formulas. Logarithmic Expressions.

    12. Roots and Radicals.

      Roots and Notation Conventions. Simplifying Square-Root Expressions. Basic Operations with Square-Root Radicals. Complex and Imaginary Numbers. Equations with Squares and Square Roots.

    13. Formulas and Applications.

      Formula Evaluation. Formula Rearrangement. Temperature Formulas. Geometric Formulas. Miscellaneous Technical Formulas.

    14. Products and Factors.

      The Distributive Property and Common Factors. Multiplying Polynomials. Factoring Special Products. Factoring General Trinomials.

    15. Solving Quadratic and Higher-Degree Equations.

      Quadratic Equations. Solving Quadratic Equations Using the Quadratic Formula. Solving Pure Quadratic Equations: ax^2 + c = 0. Solving Incomplete Quadratic Equations: ax^2 + bx = 0. Solving Complete Quadratic Equations by Factoring. Selecting an Appropriate Method for Solving Quadratic Equations. Solving Higher-Degree Equations by Factoring.

    16. Rational Expressions.

      Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Equations with Rational Expressions.

    17. Inequalities and Absolute Values.

      Inequalities and Sets. Solving Simple Linear Inequalities. Compound Inequalities. Solving Quadratic and Rational Inequalities. Equations Containing One Absolute-Value Term. Absolute-Value Inequalities.

    18. Graphical Representation.

      Graphical Representation of Equations. Linear Equations in Two Variables and Function Notation. Graphing Linear Equations with Two Variables. Graphing Linear Inequalities with Two Variables. Graphing Quadratic Equations and Inequalities.

    19. Slope and Distance.

      Slope. Point-Slope Form of an Equation. Slope-Intercept Form of an Equation. Parallel Lines. Perpendicular Lines. Distance and Midpoints.

    20. Systems of Equations and Inequalities.

      Solving Systems of Equations and Inequalities Graphically. Solving Systems of Equations Using the Addition Method. Solving Systems of Equations by the Substitution Method. Problem Solving Using Systems of Equations.

    21. Selected Concepts of Geometry.

      Basic Terminology and Notation. Angle Calculations. Triangles. Polygons. Sectors and Segments of a Circle. Inscribed and Circumscribed Regular Polygons and Circles.

    22. Introduction to Trigonometry.

      Radians and Degrees. Trigonometric Functions. Using a Calculator to Find Trigonometric Values.

    23. Right-Triangle Trigonometry.

      Sine, Cosine, and Tangent Functions. Applied Problems Using Right-Triangle Trigonometry.

    24. Oblique Triangles.

      Vectors. Trigonometric Functions for Any Angle. Law of Sines. Law of Cosines. Area of Triangles.

    Selected Answers to Student Exercise Material.
    Index.


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