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Intermediate Algebra

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Overview

The focus of this series by Hutchison and Hoelzle is to make students proficient in algebra while becoming better problem solvers. To accomplish this goal,the authors emphasize conceptual understanding. They ask students to think critically,to explore and explain concepts in writing,and to extend their understanding through group activities. The environmental essays that open each chapter connect algebra to real world problem solving and can be used to stimulate class discussions and promote collaborative learning. Functions and graphing are introduced early (Chapter Three) and are then integrated throughout the rest of the text. This approach allows for visual interpretation of the mathematical concepts,which in turn encourages students to develop an intuitive understanding of equations and their graphs. Also by introducing these topics early,students become familiar and comfortable with concepts that are critical to their success in future math courses. Intermediate Algebra includes marginal notes and examples that indicate how technology can enhance the study of algebra through exploration,visualization,and geometric interpretation. These examples fall at the end of section discussions and may be omitted if a graphing tool is not being used. The text is written in a clear,concise style with numerous examples which are connected by thoughtful transitions that either reinforce the student's understanding of the previous concepts or prepare them for the next example. Each example is followed by a "Check Yourself' exercise that facilitates the student's active involvement in the learning process.
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Product Details

  • ISBN-13: 9780070626027
  • Publisher: McGraw-Hill Higher Education
  • Publication date: 8/1/1994
  • Pages: 639

Meet the Author

Don began teaching in a preschool while he was an undergraduate. He subsequently

taught children with disabilities, adults with disabilities, high school mathematics, and

college mathematics. Although each position offered different challenges, it was always

breaking a challenging lesson into teachable components that he most enjoyed.

It was at Clackamas Community College that he found his professional niche. The community

college allowed him to focus on teaching within a department that constantly

challenged faculty and students to expect more. Under the guidance of Jim Streeter,

Don learned to present his approach to teaching in the form of a textbook. Don has also

been an active member of many professional organizations. He has been president of

ORMATYC, AMATYC committee chair, and ACM curriculum committee member. He

has presented at AMATYC, ORMATYC, AACC, MAA, ICTCM, and a variety of other

conferences.

Above all, he encourages you to be involved, whether as a teacher or as a learner.

Whether discussing curricula at a professional meeting or homework in a cafeteria, it is

the process of communicating an idea that helps one to clarify it.

Stefan began teaching math and science in New York City middle schools. He also taught

math at the University of Oregon, Southeast Missouri State University, and York County

Technical College. Currently, Stefan is a member of the mathematics faculty at Clackamas

Community College where he has found a niche, delighting in the CCC faculty, staff, and

students. Stefan’s own education includes the University of Michigan (BGS, 1988), Brooklyn

College (CUNY), and the University of Oregon (MS, 1996).

Stefan is currently serving on the AMATYC Executive Board as the organization’s Northwest

Vice President. He has also been involved with ORMATYC, NEMATYC, NCTM, and the

State of Oregon Math Chairs group, as well as other local organizations. He has applied his

knowledge of math to various fi elds, using statistics, technology, and web design. More personally,

Stefan and his wife, Peggy, try to spend time enjoying the wonders of Oregon and

the Pacifi c Northwest. Their activities include scuba diving, self-defense training, and hiking.

Barry has enjoyed teaching mathematics to a wide variety of students over the years. He

began in the fi eld of adult basic education and moved into the teaching of high school

mathematics in 1977. He taught high school math for 11 years, at which point he served

as a K-12 mathematics specialist for his county. This work allowed him the opportunity to

help promote the emerging NCTM standards in his region.

In 1990, Barry began the next portion of his career, having been hired to teach at Clackamas

Community College. He maintains a strong interest in the appropriate use of technology

and visual models in the learning of mathematics.

Throughout the past 32 years, Barry has played an active role in professional organizations.

As a member of OCTM, he contributed several articles and activities to the group’s journal.

He has presented at AMATYC, OCTM, NCTM, ORMATYC, and ICTCM conferences. Barry

also served 4 years as an offi cer of ORMATYC and participated on an AMATYC committee

to provide feedback to revisions of NCTM’s standards.

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Table of Contents

1 The Real Numbers
1.1 The Set of Real Numbers
1.2 Operations and Properties
1.3 Inequalities and Absolute Values
1.4 Algebraic Expressions
1.5 Properties of Exponents and Scientific Notation

2 Linear Equations and Inequalities
2.1 Solutions of Linear Equations in One Variable
2.2 Literal Equations and Formulas
2.3 Applications and Problem Solving
2.4 Linear Inequalities
2.5 Absolute Value Equations and Inequalities

3 Graphs of Linear Relations and Functions
3.1 Graphing Linear Equations
3.2 An Introduction to Functions
3.3 The Slope of a Line
3.4 Forms of Linear Equations
3.5 Graphing Absolute Value Functions and Linear Inequalities

4 Systems of Linear Relations
4.1 Systems of Linear Equations in Two Variables
4.2 Systems of Linear Equations in Three Variables
4.3 Solving Systems of Equations Using Matrices
4.4 Graphing Systems of Linear Inequalities

5 Polynomials and Polynomial Functions
5.1 Addition and Subtraction of Polynomials
5.2 Multiplication of Polynomials
5.3 Division of Polynomials
5.4 Common Factors and Factoring by Grouping
5.5 Factoring Special Binomials
5.6 Factoring Trinomials: Trial and Error
5.7 Factoring Trinomials: The ac Method
5.8 Strategies in Factoring
5.9 Solving Quadratic Equations by Factoring

6 Rational Expressions and Functions
6.1 Simplification of Rational Expressions and Functions
6.2 Multiplication and Division of Rational Expressions
6.3 Addition and Subtraction of Rational Expressions
6.4 Complex Fractions
6.5 Solving Rational Equations
6.6 Variation

7 Radical and Radical Exponents
7.1 Roots and Radicals
7.2 Simplification of Radical Expressions
7.3 Operations on Radical Expressions
7.4 Solving Radical Equations
7.5 Geometric and Other Applications
7.6 Rational Exponents
7.7 Complex Numbers

8 Quadratic Equations, Functions, and Inequalities
8.1 Graphing Factorable Quadratic Functions
8.2 Solving Quadratic Equations by Completing the Square
8.3 Solving Quadratic Equations by Using the Quadratic Formula
8.4 Solving Equations that are Quadratic in Form
8.5 Quadratic Inequalities and Rational Inequalities

9 Conic Sections
9.1 Parabolas
9.2 Circles
9.3 Ellipses and Hyperbolas
9.4 Nonlinear Systems

10 Additional Properties of Functions
10.1 Algebra of Functions
10.2 Composition of Functions
10.3 Inverse Relations and Functions

11 Exponential and Logarithmic Functions
11.1 Exponential Functions
11.2 Logarithmic Functions
11.3 Properties of Logarithms
11.4 Solving Logarithmic and Exponential Equations

Appendix: Determinants and Cramer’s Rule
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