Beginning Algebra, 2/e
K. Elayn Martin-Gay, University of New Orleans, Lakefront
Published August, 1996 by Prentice Hall Engineering/Science/Mathematics
Copyright 1997, 678 pp.
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This book offers a sound mathematics presentation, useful pedagogy,
and a superb problem-solving framework to thoroughly prepare students
for a second or intermediate algebra course. The Second Edition features
a greater incorporation of AMATYC and NCTM standards, reflected in
an increased emphasis on visualization and graphing, carefully revised
problems and exercises, and more data analysis.
A six-step problem-solving approach is woven consistently
throughout. Students are asked to:
4) Translate into a model (or equation)
6) Interpret a variety of realistic problems.
Problems feature real-world topics and are applied
to a variety of disciplines.
Cumulative Reviews in every chapter after Chapter
1 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.
Mental Math boxes ask students to employ analytical
skills and solve problems intuitively. They can be incorporated in-class
as oral exercises or as preludes to exercise sets.
- Writing style is clear and direct.
- Many clear explanations are provided.
Conceptual Exercises, identified by an icon, ask students
to verbalize solutions, increasing students' writing in mathematics
NEWAn increased emphasis on data interpretation;
real data is integrated throughout, beginning with an introduction
to bar graphs in Section 1.1. With the emphasis on interpreting data
via graphs, students reinforce what they've learned visually and see
- Also help develop pattern recognition.
NEWExercise sets have been carefully reviewed
and revised to include real data. The sets are graded in level
of difficulty, and feature more conceptual and current real-world
- The ability to interpret data through reading graphs
is developed gradually (graphs are presented informally in Ch. 1,
then formally in Sec. 1.9); students become comfortable with reading
graphs before moving on to the rectangular coordinate system and other
NEWHighlights at the end of each chapter contain
key definitions, concepts and examples to help students retain what
they have learned.
Treatment of graphing and scientific calculators is
integrated in separate boxes and noted in exercise sets (one icon
for graphing calculators, another for scientific). Instructors can
pick and choose when and how they want to integrate technology into
NEWGraphing is introduced earlier and developed
in-depth in more than one chapter (In line with AMATYC and NCTM standards).
An early introduction to graphing helps students see the math.
An emphasis on visualization through graphing is integrated; by Chapter
7, students are ready to master functions and equations of lines.
- Sources include USA Today and other well-known
NEWCollaborative 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 activity
designed for students to work together.
- Chapter 3 now contains graphing linear equations and
inequalities, slopes, and intercepts.
- Chapters 4, 5 and 6 allow students to use newly learned
graphing techniques in exercise sets.
NEWSkills Practice exercises integrated
throughout help mathematically challenged students make connections
between math, other courses, and the real world.
(NOTE: Each chapter ends with a group activity, highlights,
review, test, and cumulative review.)
1. Review of Real Numbers.
Symbols and Sets of Numbers. Fractions. Exponents and Order
of Operations. Introduction to Variable Expressions and Equations.
Adding Real Numbers. Subtracting Real Numbers. Multiplying and Dividing
Real Numbers. Properties of Real Numbers. Reading Graphs.
2. Equation, Inequalities, and Problem Solving.
Simplifying Algebraic Expressions. The Addition Property
of Equality. The Multiplication Property of Equality. Solving Linear
Equations. An Introduction to Problem Solving. Formulas and Problem
Solving. Percent and Problem Solving. Further Problem Solving. Solving
The Rectangular Coordinate System. Graphing Linear Equations.
Intercepts. Slope. Graphing Linear Inequalities.
4. Exponents and Polynomials.
Exponents. Adding and Subtracting Polynomials. Multiplying
Polynomials. Special Products. Negative Exponents and Scientific Notation.
Division of Polynomials.
5. Factoring Polynomials.
The Greatest Common Factor and Factoring by Grouping. Factoring
Trinomials of the Form x^2 + bx + c. Factoring
Trinomials of the Form ax^2 + bx + c. Factoring
Binomials. Choosing a Factoring Strategy. Solving Quadratic Equations
by Factoring. Quadratic Equations and Problem Solving.
6. Rational Expressions.
Simplifying Rational Expressions. Multiplying and Dividing
Rational Expressions. Adding and Subtracting Rational Expressions
with Common Denominators and Least Common Denominators. Adding and
Subtracting Rational Expressions with Unlike Denominators. Simplifying
Complex Fractions. Solving Equations Containing Rational Expressions. Ratio
and Proportion. Rational Equations and Problem Solving.
7. Further Graphing.
The Slope-Intercept Form. The Point-Slope Form. Graphing
Nonlinear Equations. An Introduction to Functions.
8. Solving Systems of Linear Equations.
Solving Systems of Linear Equations by Graphing. Solving
Systems of Linear Equations by Substitution. Solving Systems of Linear
Equations by Addition. Systems of Linear Equations and Problem Solving.
Systems of Linear Inequalities.
9. Roots and Radicals.
Introduction to Radicals. Simplifying Radicals. Adding and
Subtracting Radical Expressions. Multiplying and Dividing Radical
Expressions. Solving Equations Containing Radicals. Radical Equations
and Problem Solving. Rational Exponents.
10. Solving Quadratic Equations.
Solving Quadratic Equations by the Square Root Method. Solving
Quadratic Equations by Completing the Square. Solving Quadratic Equations
by the Quadratic Formula. Summary of Methods for Solving Quadratic
Equations. Complex Solutions to Quadratic Equations. Graphing Quadratic
Operations on Decimals. Review of Angles, Lines, and Special
Triangles. Review of Geometric Figures. Mean, Median, and Mode. Table
of Squares and Square Roots. Answers to Selected Exercises.