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
Copyright 1997, 816 pp.
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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 standardsreflected 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
Discover the ConceptThese 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
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
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
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) interpreta variety of realistic problems.
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.
- writing style is clear and direct.
- many explanations are provided.
- pedagogy is ample and accessible.
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.
Reminders alert students to trouble areas and provide
encouragement and suggestions to avoid common errors.
- Skill Reviews are featured at the end of every
Geometry concepts and applications are incorporated
- USA Today and other well-known sources are used.
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
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
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
8. Rational Exponents, Radicals, and Complex Numbers.
Radicals and Radical Functions. Rational Exponents.
Simplifying Radical Expressions. Adding, Subtracting, and
Multiplying Radicals. Rationalizing Numerators and Denominators
of Radical Expressions. Radical Equations and Problem Solving.
Complex Numbers. Group Activity: Calculating the Length and Period
of a Pendulum.
9. Quadratic Equations and Functions.
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
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
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.