Intermediate Algebra with Applications, 2/e
Linda Exley, DeKalb College
Vince Smith, DeKalb College
Published February, 1994 by Prentice Hall Engineering/Science/Mathematics
Copyright 1994, 640 pp.
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A text which students can actually READ and use to learn intermediate
algebra and which instructors can use as a genuinely supportive
framework from which to teach algebra Intermediate Algebra
with Applications features an easy-to-read presentation, an emphasis
on problem-solving skills, a wealth of well-chosen, illustrative examples,
and uniquely structured problem sets.
covers linear equations and inequalities early and
integrates them throughout the text where appropriate. (pp. 125)
explores graphing and functions earlier
so that students will be more adequately prepared for
the next course. (pp. 352)
places a greater emphasis on problem solving
and mathematical modeling of real-world applications.
provides Calculator boxes with
help for the use of both scientific and graphing calculators (pp. 64)
- devotes an entire section to the development of
problem solving skills (pp. 157)
- includes You Decide problems at the end
of each chapter. These open-ended, extended real-world applications
help students develop critical thinking and writing skills. Because
these problems have no one correct answer, students are able to hone
their problem solving and decision making skills by deciding then
supporting their answer with specific evidence (pp. 123)
- increases the number of word problems throughout
- revises applications to reflect a more current,
realistic context. E.g., section 2.2 refers to real events and celebrities
like Florence Griffith-Joiner, Janet Jackson, and Joe Montana
begins each chapter with Connections
an introductory paragraph which puts the upcoming material in context
with other chapters, other disciplines, math history and the real
world (pp. 52)
features problem sets uniquely organized into discrete
levels of understanding:
highlights key problems in red throughout
the exercise sets. These are considered to be essential problems which,
if assigned, will cover all the section learning objectives. They
can be used in class examples, problem assignments, or for review.
Answers are provided at the end of the text. (pp. 98)
- Warm-Ups carefully graded and keyed specifically
to examples in the section (pp. 87)
- Practice mixed, and not referenced to any
examples (pp. 88)
- Challenge probe natural extensions of the
topics (pp. 96)
- In Your Own Words test conceptual understanding
by requiring a written answer (pp. 96)
features Let's Not Forget problems at the
end of every chapter review problem set. These exercises are cumulative
and require students to recall topics covered in previous sections
and chapters. (pp. 122)
provides Be Careful annotations in the margins
to prominently point out common student errors. (pp. 110)
concludes chapters with a glossary, review of key concepts,
and Checkups worked examples stated as problems
with specific references. (pp. 119)
(NOTE: Each chapter concludes with a Chapter Summary, Review Problems, and a Chapter Test.)
0. Reviewing Sets of Numbers and Geometry.
Sets. Properties of real numbers. Absolute value. Operations
with real numbers. Angles, lines, and plane figures. Perimeter, surface
area, area, and volume.
1. Integer Exponents and Polynomials.
Integer exponents. Polynomial definition, evaluation, addition, and
subtraction. Multiplication of polynomials. Pascal's triangle (optional).
Greatest common factor and factoring by grouping. Factoring binomials and
trinomials. Summary of factoring. Division of polynomials. Synthetic division
2. Using Linear Equations and Inequalities in One Variable.
Solving linear equations in one variable. Literal equations and
formulas. Linear inequalities in one variable. Problem solving. Liner
equations as models for applications. Absolute value equations. Boundary
numbers and absolute value inequalities.
3. Rational Expressions.
Fundamental principle of rational expressions. Multiplication
and division. Addition and subtraction. Rational equations and inequalities.
4. Radicals and Exponents.
Roots and radicals. Addition and subtraction of radical
expressions. Multiplication of radical expressions. Division of rational
expressions and rationalizing. Equations containing square roots. Rational
exponents. Complex numbers.
5. Nonlinear Equations and Inequalities in One Variable.
Solving quadratic equations and inequalities by factoring. Quadratic
equations and inequalities as models for applications. Completing the square.
The quadratic formula. Higher-degree equations and inequalities. More
rational equations and inequalities. Radical equations.
6. Graphs and Functions.
Cartesian coordinate system. Graph of Ax + By = C. Slope.
Equations of lines. Functions. Graphs of functions. Variation.
7. Systems of Equations and Inequalities.
Systems of equations in two variables. Systems as models for
applications. Linear systems of equations in more than two variables. Linear
inequalities in two variables. Systems of linear inequalities in two
variables. Determinants and Cramer's Rule (optional). Matrix methods
8. Exponential and Logarithmic Functions.
Algebra of functions. Inverse functions. Exponential functions.
Logarithmic functions. Properties of logarithms.
9. Conic Sections.
The circle. The parabola. The ellipse and the hyperbola. The general
second-degree equation in two variables.
10. Other Topics.
Sequences. Summation notation. Factorials and binomial coefficients.
The binomial theorem. Permutations and combinations.
Appendix: An Introduction to the Graphing Calculator.
Answers to Selected Problems.