Understanding Intermediate Algebra A Course for College Students (with CD-ROM, Make the Grade, and InfoTrac)

by Hirsch, Lewis R.; Goodman, Arthur

• ISBN13: 9780534432232
• ISBN10: 0534432239
• Edition: CD
• Format: Hardcover
• Copyright: 2001-12-12
• Publisher: Brooks Cole

Summary

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples - both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

Table of Contents

1. THE FUNDAMENTAL CONCEPTS

Basic Definitions: The Real Numbers and the Real Number Line

Operations with Real Numbers

Algebraic Expressions

Translating Phrases and Sentences into Algebraic Form

First-Degree Equations and Inequalities

Chapter Summary, Review Exercises, and Practice Test

2. EQUATIONS AND INEQUALITITES

Equations as Mathematical Models

First-Degree Equations and Applications

First-Degree Inequalities and Applications

Absolute-Value Equations and Inequalities

Chapter Summary, Review Exercises, and Practice Test

3. GRAPHING STRAIGHT LINES AND FUNCTIONS

The Rectangular Coordinate System and Graphing Straight Lines

Graphs and Equations

Relations and Functions: Basic Concepts

Function Notation

Interpreting Graphs

Chapter Summary, Review Exercises, and Practice Test

Cumulative Review and Practice Test: Chapters 1-3. 4

EQUATIONS OF A LINE AND LINEAR SYSTEMS IN TWO VARIABLES

Straight Lines and Slope

Equations of a Line and Linear Functions as Mathematical Models

Linear Systems in Two Variables

Graphing Linear Inequalities in Two Variables

Chapter Summary, Review Exercises, and Practice Test

5. POLYNOMIAL EXPRESSIONS AND FUNCTIONS

Polynomial Functions as Mathematical Models

Polynomials: Sums, Differences, and Products

General Forms and Special Products

Factoring out the Greatest Common Factor

Factoring Trinomials

Solving Polynomial Equations by Factoring

Polynomial Division

Chapter Summary, Review Exercises, and Practice Test

6. RATIONAL EXPRESSIONS AND FUNCTIONS

Rational Functions

Equivalent Fractions

Multiplication and Division of Rational Expressions

Sums and Differences of Rational Expressions

Mixed Operations and Complex Fractions

Fractional Equations and Inequalities

Literal Equations

Applications: Rational Functions and Equations as Mathematical Models

Chapter Summary, Review Exercises, and Practice Test

Cumulative Review and Practice Test: Chapters 4-6. 7

EXPONENTS AND RADICALS

Natural Number and Integer Exponents

Scientific Notation

Rational Exponents and Radical Notation

Simplifying Radical Expressions

Adding and Subtracting Radical Expressions

Multiplying and Dividing Radical Expressions

Radical Functions and Equations

Complex Numbers

Chapter Summary, Review Exercises, and Practice Test

8. QUADRATIC FUNCTIONS AND EQUATIONS

Quadratic Functions as Mathematical Models

Solving Quadratic Equations: The Factoring and Square Root Methods

Solving Quadratic Equations: Completing the Square

Solving Quadratic Equations: The Quadratic Formula

Equations Reducible to Quadratic Form (and More Radical Equations)

Graphing Quadratic Functions

Quadratic and Rational Inequalities

The Distance Formula: Circles

Chapter Summary, Review Exercises, and Practice Test

9. MORE ON FUNCTIONS

More on Function Notation: Split Functions

Composition and the Algebra of Functions

Types of Functions

Inverse Functions

Variation

Chapter Summary, Review Exercises, and Practice Test

Cumulative Review And Practice Test: Chapters 7-9. 10

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Exponential Functions

Logarithms and Logarithmic Functions

Properties of Logarithms

Common Logarithms, Natural Logarithms, and Change of Base

Exponential and Logarithmic Equations

Applications: Exponential and Logarithmic Functions as Mathematical Models

Chapter Summary, Review Exercises, and Practice Test

11. MORE SYSTEMS OF EQUATIONS AND SYSTEMS OF INEQUALITITIES

3x3 Linear Systems

Solving Linear Systems Using Augmented Matrices

The Algebra of Matrices

Solving Linear Systems Using Matrix Inverses

Determinants and Cramer's Rule

Systems of Linear Inequalities

Nonlinear Systems of Equations

Chapter Summary, Review Exercises, and Practice Test

Cumulative Review And Practice Test: Chapters 10-11. Appendix A: Sets

Appendix B: The Conic Sections

Answers to Selected Exercises and Chapter Tests

Index