Intermediate Algebra: A Graphing Approach, 1/e

K. Elayn Martin-Gay, University of New Orleans
Margaret Greene, Florida Community College, Jacksonville

Published March, 1997 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-281495-1

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Intermediate Algebra-Mathematics

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.

Graphing calculators are introduced in chapter 1, first as a calculating tool and then in chapter 2 as a graphing utility.
Graphing Utility exercises are fully integrated throughout the text.
“Discover the Concept”—These explorations are integrated appropriately throughout to promote student involvement and interaction with the text and graphing utility to help reinforce concepts, interpret graphs, recognize patterns and motivate discovery-based learning.
An 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.
Exercise sets include real data. The sets are graded in level of difficulty, and feature conceptual and current data from environmental science, allied health, astronomy, business and other disciplines.
Functions are introduced early and intuitively. Students are introduced to functions in Chapter 2.
Technology Notes refer students to possible keystrokes and other differences among different graphing calculator models. Notes are also used to clarify information about graphs.
Mental Math boxes ask students to employ analytical skills and solve problems intuitively and without a pencil. They can be incorporated as in-class oral exercises or as preludes to exercise sets.
Conceptual Exercises, identified by an icon, ask students to answer questions combining two or more concepts or to verbalize solutions, increasing students' “writing in mathematics” skills.
A 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.
Accessible Presentation:
• writing style is clear and direct.
• many explanations are provided.
• pedagogy is ample and accessible.
Definitions are explained, both visually (definitions are summarized and highlighted by color) and by worked example or exploration. Ideal for visual learners, and/or for those who learn best by doing.
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.
• Skill Reviews are featured at the end of every section.
Reminders alert students to trouble areas and provide encouragement and suggestions to avoid common errors.
• USA Today and other well-known sources are used.
Geometry concepts and applications are incorporated where appropriate.
Collaborative Projects are introduced in the chapter opener. At the end of each chapter concepts covered in the chapter opener are incorporated into a discovery-based group activity designed for students to work together using technology to manipulate data.

1. Review of Real Numbers and Algebraic Expressions.

Real Numbers. Properties of Real Numbers. Operations on Real Numbers. Order of Operations and Algebraic Expressions. Group Activity: Analyzing Newspaper Circulation

2. Basic Concepts of Algebra.

Solving Linear Equations Algebraically. Introduction to Modeling with Tables. An Introduction to Problem Solving. Formulas and Problem Solving. Interpreting Data and Reading Bar, Line, and Circle Graphs. Group Activity: Comparison of Volumes.

3. Introduction to Graphs and Functions.

Introduction to Graphing and Graphing Utilities. Graphing Equations. Introduction to Functions. Graphing Linear Functions. The Slope of a Line. Equations of Lines. Solving Linear Equations Graphically. Group Activity: Modeling Japanese Automobile Imports.

4. Inequalities and Absolute Value.

Solving Linear Inequalities Algebraically and Graphically. Compound Inequalities. Absolute Value Equations. Absolute Value Inequalities. Graphing Linear Inequalities in Two Variables. Group Activity: Analyzing a Budget.

5. 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. Group Activity: Locating Lightning Strikes.

6. 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 Polynomial Equations Algebraically and Graphically. Group Activity: Finding the Largest Area.

7. 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. Solving Equations Containing Rational Expressions. Rational Equations and Problem Solving. Variation and Problem Solving. Group Activity: Modeling Electricity Production.

8. Rational Exponents, Radicals, and Complex Numbers.

Solving Quadratic Equations by Completing the Square. Solving Quadratic Equations by the Quadratic Formula. Solving Equations Using Quadratic Methods. Non-linear Inequalities in One Variable. Quadratic Functions and their Graphs. Further Graphing of Quadratic Functions. Interpreting Data: Recognizing Linear and Quadratic Models. Group Activity: Modeling the Position of a Freely Falling Object.

10. Conic Sections.

The Parabola and the Circle. The Ellipse and the Hyperbola. Solving Nonlinear Systems of Equations. Nonlinear Inequalities and Systems of Inequalities. Group Activity: Modeling Conic Sections.

11. 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. Group Activity: Modeling Temperature.

12. Sequences, Series, and the Binomial Theorem.

Sequences. Arithmetic and Geometric Sequences. Series. Partial Sums of Arithmetic and Geometric Sequences. The Binomial Theorem. Group Activity: Modeling College Tuition.

Appendices.
Index.
Photo Credits.