Introductory Algebra is typically a 1-semester course that provides a solid foundation in algebraic skills and reasoning for students who have little or no previous experience with the topic.& The goal is to effectively prepare students to transition into Intermediate Algebra.
Table of Contents
R. Prealgebra Preview.
Factors and the Least Common Multiple. Fractions. Decimals and Percents.
1. Real Numbers and Introduction to Algebra.
Tips for Success in Mathematics. Symbols and Sets of Numbers. Introduction to Variable Expressions and Equations. Adding Real Numbers. Subtracting Real Numbers. Multiplying Real Numbers. Dividing Real Numbers. Properties of Real Numbers. Reading Graphs.
2. Equations, Inequalities and Problem Solving.
Simplifying Expressions. The Addition Property of Equality. The Multiplication Property of Equality. Further Solving Linear Equations. An Introduction to Problem Solving. Formulas and Problem Solving. Percent, Ratio, and Proportion. Solving Linear Inequalities.
3. Exponents and Polynomials.
Exponents. Negative Exponents and Scientific Notation. Introduction to Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Special Products. Dividing Polynomials.
4. Factoring Polynomials.
The Greatest Common Factor. Factoring Trinomials of the Form x^2 + bx + c. Factoring Trinomials of the Form ax^2 + bx + c. Factoring Trinomials of the Form ax^2 + bx + ca …Ö 1 by Grouping. Factoring Perfect Square Trinomials and the Difference of Two Squares. Solving Quadratic Equations by Factoring. Quadratic Equations and Problem Solving.
5. Rational Expressions.
Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator. Adding and Subtracting Rational Expressions with Different Denominators. Solving Equations Containing Rational Expressions. Rational Equations and Problem Solving. Simplifying Complex Fractions.
6. Graphing Equations and Inequalities.
The Rectangular Coordinate System. Graphing Linear Equations. Intercepts. Slope. Equations of Lines. Introduction to Functions. Graphing Linear Inequalities in Two Variables.
7. Systems of 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.
8. Roots and Radicals.
Introduction to Radicals. Simplifying Radicals. Adding and Subtracting Radicals. Multiplying and Dividing Radicals. Solving Equations Containing Radicals. Radical Equations and Problem Solving.
9. Quadratic Equations.
Solving Quadratic Equations by the Square Root Property. Solving Quadratic Equations by Completing the Square. Solving Quadratic Equations by the Quadratic Formula. Graphing Quadratic Equations in Two Variables.
Excerpts
About This Book Introductory Algebra,was written to provide asolid foundationin algebra for students who might have had no previous experience in algebra. Specific care was taken to ensure that students have the mostup-to-date relevanttext preparation for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. As suggested by the AMATYC Crossroads Document and the NCTM Standards (plus Addenda), real-life and real-data applications, data interpretation, conceptual understanding, problem solving, writing, cooperative learning, appropriate use of technology, mental .mathematics, number sense, critical thinking, and geometric concepts are emphasized and integrated throughout the book. The many factors that contributed to the success of the first edition have been retained. In preparing the Second Edition, I considered comments and suggestions of colleagues, students, and many users of the prior edition throughout the country. Introductory Algebra,Second Edition is part of a series of texts that can includeBasic College Mathematics,Second Edition;Prealgebra,Third Edition;Intermediate Algebra,Second Edition; and a combined text,Algebra A Combined Approach,Second Edition. Throughout the series pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses. Key Pedagogical Features and Changes in the Second Edition Readability and Connections.I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problem-solving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information. In addition, each section begins with a list of objectives covered in the section. Clear organization of section material based on objectives further enhances readability. Problem-Solving Process.This is formally introduced in Chapter 2 with a four-step process that is integrated throughout the text. The four steps areUnderstand, Translate, Solve,andInterpret.The repeated use of these steps in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' comfort level and confidence in tackling problems. Applications and Connections.Every effort was made to include as many interesting and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. In the Second Edition, the applications have been thoroughly revised and updated, and the number of applications has increased. The applications help to motivate students and strengthen their understanding of mathematics in the real world. They show connections to a wide range of fields including agriculture, allied health, anthropology, art, astronomy, biology, business, chemistry, construction, consumer affairs, earth science, education, entertainment, environmental issues, finance, geography, government, history, medicine, music, nutrition, physics, sports, travel, and weather. Many of the applications are based on recent real data. Sources for data include newspapers, magazines, publicly held companies, government agencies, special-interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included. See the Applications Index on page xx. Practice Problems.Throughout the text, each worked-out example has a parallel Practice Problem plac