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Intro Algebra for K-12 Textbooks

by Marvin Bittinger, David Ellenbogen and Barbara Johnson

Cover type: HardbackEdition: 4TH 06

Copyright: 2006

Publisher: Addison-Wesley Longman, Inc.

Published: 2006

International: No

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The goal of Elementary and Intermediate Algebra: Concepts and Applications, 4e is to help today's students learn and retain mathematical concepts by preparing them for the transition from ''skills-oriented'' elementary and intermediate algebra courses to more ''concept-oriented'' college-level mathematics courses, as well as to make the transition from ''skill'' to ''application.'' This edition continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen/Johnson series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. This revision has an even stronger focus on vocabulary and conceptual understanding as well as making the mathematics even more accessible to students. Among the features added are new Concept Reinforcement exercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter.

**Features**

- Connecting the Concepts feature highlights the importance of connecting concepts and invites students to pause and check that they understand the ''big picture.'' This helps ensure that students understand how concepts work together in several sections at once. For example, students are alerted to shifts made from solving equations to writing equivalent expressions. The pacing of this feature helps students increase their comprehension and maximize their retention of key concepts.
- Chapter Openers Each chapter opens with a list of the sections to be covered and a real-life application that includes a testimonial from a person in that field to show how integral mathematics is in solving real problems. Real data is often used in these applications as well as in many other exercises and ''on the job'' examples (like those that students might find in the workforce) to increase student interest.
- Aha! In many exercise sets, students will see an Aha! icon. This icon indicates to students that there is a simpler way to complete the exercise without going through a lengthy computation. It's then up to the student to discover that simpler approach. The Aha! icon is used the first time a new insight can be used on a particular type of exercise. After that first time, it's up to the student to determine if and when that particular insight can be reused.
- Optional Collaborative Corners give students the opportunity to work as a group to solve problems or to perform specially designed activities. There are approximately two Collaborative Corners per chapter, each one appearing after the appropriate exercise set.
- Optional Technology Connections appear throughout each chapter to help students visualize, through the use of technology, a concept that they have just learned. This feature is reinforced in many exercise sets through exercises marked with a graphing calculator icon.
- 5-Step Problem-Solving Process A hallmark feature to all Bittinger Texts, the 5-step problem-solving process is introduced early in the text and then modeled in every application problem throughout the rest of the text, providing students with a foundation for starting and completing the problem-solving process.
- Study Skills These remarks, located in the margins near the start of each section, provide suggestions for successful study habits and can be extended to courses other than algebra. Ranging from ideas for better time management to how to prepare for tests, these comments can be useful to even experience college students.

**Chapter 1 Introduction to Algebraic Expressions**

Introduction to Algebra

The Commutative, Associative, and Distributive Laws

Fraction Notation

Positive and Negative Real Numbers

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Exponential Notation and Order of Operations

Connecting the Concepts

**Chapter 2 Equations, Inequalities, and Problem Solving**

Solving Equations

Using the Principles Together

Connecting the Concepts

Formulas

Applications with Percent

Problem Solving

Solving Inequalities

Solving Applications with Inequalities

**Chapter 3 Introduction to Graphing**

Reading Graphs, Plotting Points, and Scaling Graphs

Graphing Linear Equations

Graphing and Intercepts

Rates

Slope

Slope--Intercept Form

Connecting the Concepts

Point--Slope Form

Connecting the Concepts

**Chapter 4 Polynomials**

Exponents and Their Properties

Polynomials

Addition and Subtraction of Polynomials

Connecting the Concepts

Multiplication of Polynomials

Special Products

Polynomials in Several Variables

Division of Polynomials

Negative Exponents and Scientific Notation

**Chapter 5 Polynomials and Factoring**

Introduction to Factoring

Factoring Trinomials of the Type x2 + bx + c

Factoring Trinomials of the Type ax2 + bx + c

Factoring Perfect-Square Trinomials and Differences of Squares

Factoring Sums or Differences of Cubes

Factoring: A General Strategy

Connecting the Concepts

Solving Quadratic Equations by Factoring

Connecting the Concepts

Solving Applications

**Chapter 6 Rational Expressions and Equations**

Rational Expressions

Multiplication and Division

Addition, Subtraction, and Least Common Denominators

Addition and Subtraction with Unlike Denominators

Complex Rational Expressions

Solving Rational Equations

Connecting the Concepts

Applications Using Rational Equations and Proportions

Formulas and Equations

**Chapter 7 Functions and Graphs**

Introduction to Functions

Domain and Range

Graphs of Functions (including brief review of graphing)

Connecting the Concepts

The Algebra of Functions

Variation and Problem Solving

**Chapter 8 Systems of Equations and Problem Solving**

Systems of Equations in Two Variables

Solving by Substitution or Elimination

Connecting the Concepts

Solving Applications: Systems of Two Equations

Systems of Equations in Three Variables

Connecting the Concepts

Solving Applications: Systems of Three Equations

Elimination Using Matrices

Determinants and Cramer's Rule

Business and Economics Applications

**Chapter 9 Inequalities and Problem Solving**

Interval Notation and Problem Solving

Intersections, Unions, and Compound Inequalities

Absolute-Value Equations and Inequalities

Inequalities in Two Variables

Connecting the Concepts

Applications Using Linear Programming

**Chapter 10 Exponents and Radicals**

Radical Expressions and Functions

Rational Numbers as Exponents

Multiplying Radical Expressions

Dividing Radical Expressions

Expressions Containing Several Radical Terms

Solving Radical Equations

Connecting the Concepts

Geometric Applications

The Complex Numbers

**Chapter 11 Quadratic Functions and Equations**

Quadratic Equations

The Quadratic Formula

Applications Involving Quadratic Equations

Studying Solutions of Quadratic Equations

Equations Reducible to Quadratic

Quadratic Functions and Their Graphs

Connecting the Concepts

More About Graphing Quadratic Functions

Problem Solving and Quadratic Functions

Polynomial and Rational Inequalities

**Chapter 12 Exponential and Logarithmic Functions**

Composite and Inverse Functions

Exponential Functions

Connecting the Concepts

Logarithmic Functions

Properties of Logarithmic Functions

Common and Natural Logarithms

Solving Exponential and Logarithmic Equations

Applications of Exponential and Logarithmic Functions

**Chapter 13 Conic Sections**

Conic Sections: Parabolas and Circles

Conic Sections: Ellipses

Conic Sections: Hyperbolas

Connecting the Concepts

Nonlinear Systems of Equations

**Chapter 14 Sequences, Series, and The Binomial Theorem**

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

The Binomial Theorem

Connecting the Concepts

**Chapter R Elementary Algebra Review**

Introduction to Algebraic Expressions

Equations, Inequalities, and Problem Solving

Introduction to Graphing

Polynomials

Polynomials and Factoring Rational Expressions and Equations

Appendix A: Sets

Appendix B: Synthetic Division

Table 1: Fractional and Decimal Equivalents

Table 2: Squares and Square Roots

Table 3: Geometric Formulas

Answers

Glossary

Index

Index of Applications

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Summary

The goal of Elementary and Intermediate Algebra: Concepts and Applications, 4e is to help today's students learn and retain mathematical concepts by preparing them for the transition from ''skills-oriented'' elementary and intermediate algebra courses to more ''concept-oriented'' college-level mathematics courses, as well as to make the transition from ''skill'' to ''application.'' This edition continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen/Johnson series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. This revision has an even stronger focus on vocabulary and conceptual understanding as well as making the mathematics even more accessible to students. Among the features added are new Concept Reinforcement exercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter.

**Features**

- Connecting the Concepts feature highlights the importance of connecting concepts and invites students to pause and check that they understand the ''big picture.'' This helps ensure that students understand how concepts work together in several sections at once. For example, students are alerted to shifts made from solving equations to writing equivalent expressions. The pacing of this feature helps students increase their comprehension and maximize their retention of key concepts.
- Chapter Openers Each chapter opens with a list of the sections to be covered and a real-life application that includes a testimonial from a person in that field to show how integral mathematics is in solving real problems. Real data is often used in these applications as well as in many other exercises and ''on the job'' examples (like those that students might find in the workforce) to increase student interest.
- Aha! In many exercise sets, students will see an Aha! icon. This icon indicates to students that there is a simpler way to complete the exercise without going through a lengthy computation. It's then up to the student to discover that simpler approach. The Aha! icon is used the first time a new insight can be used on a particular type of exercise. After that first time, it's up to the student to determine if and when that particular insight can be reused.
- Optional Collaborative Corners give students the opportunity to work as a group to solve problems or to perform specially designed activities. There are approximately two Collaborative Corners per chapter, each one appearing after the appropriate exercise set.
- Optional Technology Connections appear throughout each chapter to help students visualize, through the use of technology, a concept that they have just learned. This feature is reinforced in many exercise sets through exercises marked with a graphing calculator icon.
- 5-Step Problem-Solving Process A hallmark feature to all Bittinger Texts, the 5-step problem-solving process is introduced early in the text and then modeled in every application problem throughout the rest of the text, providing students with a foundation for starting and completing the problem-solving process.
- Study Skills These remarks, located in the margins near the start of each section, provide suggestions for successful study habits and can be extended to courses other than algebra. Ranging from ideas for better time management to how to prepare for tests, these comments can be useful to even experience college students.

Table of Contents

**Chapter 1 Introduction to Algebraic Expressions**

Introduction to Algebra

The Commutative, Associative, and Distributive Laws

Fraction Notation

Positive and Negative Real Numbers

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Exponential Notation and Order of Operations

Connecting the Concepts

**Chapter 2 Equations, Inequalities, and Problem Solving**

Solving Equations

Using the Principles Together

Connecting the Concepts

Formulas

Applications with Percent

Problem Solving

Solving Inequalities

Solving Applications with Inequalities

**Chapter 3 Introduction to Graphing**

Reading Graphs, Plotting Points, and Scaling Graphs

Graphing Linear Equations

Graphing and Intercepts

Rates

Slope

Slope--Intercept Form

Connecting the Concepts

Point--Slope Form

Connecting the Concepts

**Chapter 4 Polynomials**

Exponents and Their Properties

Polynomials

Addition and Subtraction of Polynomials

Connecting the Concepts

Multiplication of Polynomials

Special Products

Polynomials in Several Variables

Division of Polynomials

Negative Exponents and Scientific Notation

**Chapter 5 Polynomials and Factoring**

Introduction to Factoring

Factoring Trinomials of the Type x2 + bx + c

Factoring Trinomials of the Type ax2 + bx + c

Factoring Perfect-Square Trinomials and Differences of Squares

Factoring Sums or Differences of Cubes

Factoring: A General Strategy

Connecting the Concepts

Solving Quadratic Equations by Factoring

Connecting the Concepts

Solving Applications

**Chapter 6 Rational Expressions and Equations**

Rational Expressions

Multiplication and Division

Addition, Subtraction, and Least Common Denominators

Addition and Subtraction with Unlike Denominators

Complex Rational Expressions

Solving Rational Equations

Connecting the Concepts

Applications Using Rational Equations and Proportions

Formulas and Equations

**Chapter 7 Functions and Graphs**

Introduction to Functions

Domain and Range

Graphs of Functions (including brief review of graphing)

Connecting the Concepts

The Algebra of Functions

Variation and Problem Solving

**Chapter 8 Systems of Equations and Problem Solving**

Systems of Equations in Two Variables

Solving by Substitution or Elimination

Connecting the Concepts

Solving Applications: Systems of Two Equations

Systems of Equations in Three Variables

Connecting the Concepts

Solving Applications: Systems of Three Equations

Elimination Using Matrices

Determinants and Cramer's Rule

Business and Economics Applications

**Chapter 9 Inequalities and Problem Solving**

Interval Notation and Problem Solving

Intersections, Unions, and Compound Inequalities

Absolute-Value Equations and Inequalities

Inequalities in Two Variables

Connecting the Concepts

Applications Using Linear Programming

**Chapter 10 Exponents and Radicals**

Radical Expressions and Functions

Rational Numbers as Exponents

Multiplying Radical Expressions

Dividing Radical Expressions

Expressions Containing Several Radical Terms

Solving Radical Equations

Connecting the Concepts

Geometric Applications

The Complex Numbers

**Chapter 11 Quadratic Functions and Equations**

Quadratic Equations

The Quadratic Formula

Applications Involving Quadratic Equations

Studying Solutions of Quadratic Equations

Equations Reducible to Quadratic

Quadratic Functions and Their Graphs

Connecting the Concepts

More About Graphing Quadratic Functions

Problem Solving and Quadratic Functions

Polynomial and Rational Inequalities

**Chapter 12 Exponential and Logarithmic Functions**

Composite and Inverse Functions

Exponential Functions

Connecting the Concepts

Logarithmic Functions

Properties of Logarithmic Functions

Common and Natural Logarithms

Solving Exponential and Logarithmic Equations

Applications of Exponential and Logarithmic Functions

**Chapter 13 Conic Sections**

Conic Sections: Parabolas and Circles

Conic Sections: Ellipses

Conic Sections: Hyperbolas

Connecting the Concepts

Nonlinear Systems of Equations

**Chapter 14 Sequences, Series, and The Binomial Theorem**

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

The Binomial Theorem

Connecting the Concepts

**Chapter R Elementary Algebra Review**

Introduction to Algebraic Expressions

Equations, Inequalities, and Problem Solving

Introduction to Graphing

Polynomials

Polynomials and Factoring Rational Expressions and Equations

Appendix A: Sets

Appendix B: Synthetic Division

Table 1: Fractional and Decimal Equivalents

Table 2: Squares and Square Roots

Table 3: Geometric Formulas

Answers

Glossary

Index

Index of Applications

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2006

International: No

Published: 2006

International: No

The goal of Elementary and Intermediate Algebra: Concepts and Applications, 4e is to help today's students learn and retain mathematical concepts by preparing them for the transition from ''skills-oriented'' elementary and intermediate algebra courses to more ''concept-oriented'' college-level mathematics courses, as well as to make the transition from ''skill'' to ''application.'' This edition continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen/Johnson series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. This revision has an even stronger focus on vocabulary and conceptual understanding as well as making the mathematics even more accessible to students. Among the features added are new Concept Reinforcement exercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter.

**Features**

- Connecting the Concepts feature highlights the importance of connecting concepts and invites students to pause and check that they understand the ''big picture.'' This helps ensure that students understand how concepts work together in several sections at once. For example, students are alerted to shifts made from solving equations to writing equivalent expressions. The pacing of this feature helps students increase their comprehension and maximize their retention of key concepts.
- Chapter Openers Each chapter opens with a list of the sections to be covered and a real-life application that includes a testimonial from a person in that field to show how integral mathematics is in solving real problems. Real data is often used in these applications as well as in many other exercises and ''on the job'' examples (like those that students might find in the workforce) to increase student interest.
- Aha! In many exercise sets, students will see an Aha! icon. This icon indicates to students that there is a simpler way to complete the exercise without going through a lengthy computation. It's then up to the student to discover that simpler approach. The Aha! icon is used the first time a new insight can be used on a particular type of exercise. After that first time, it's up to the student to determine if and when that particular insight can be reused.
- Optional Collaborative Corners give students the opportunity to work as a group to solve problems or to perform specially designed activities. There are approximately two Collaborative Corners per chapter, each one appearing after the appropriate exercise set.
- Optional Technology Connections appear throughout each chapter to help students visualize, through the use of technology, a concept that they have just learned. This feature is reinforced in many exercise sets through exercises marked with a graphing calculator icon.
- 5-Step Problem-Solving Process A hallmark feature to all Bittinger Texts, the 5-step problem-solving process is introduced early in the text and then modeled in every application problem throughout the rest of the text, providing students with a foundation for starting and completing the problem-solving process.
- Study Skills These remarks, located in the margins near the start of each section, provide suggestions for successful study habits and can be extended to courses other than algebra. Ranging from ideas for better time management to how to prepare for tests, these comments can be useful to even experience college students.

**Chapter 1 Introduction to Algebraic Expressions**

Introduction to Algebra

The Commutative, Associative, and Distributive Laws

Fraction Notation

Positive and Negative Real Numbers

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Exponential Notation and Order of Operations

Connecting the Concepts

**Chapter 2 Equations, Inequalities, and Problem Solving**

Solving Equations

Using the Principles Together

Connecting the Concepts

Formulas

Applications with Percent

Problem Solving

Solving Inequalities

Solving Applications with Inequalities

**Chapter 3 Introduction to Graphing**

Reading Graphs, Plotting Points, and Scaling Graphs

Graphing Linear Equations

Graphing and Intercepts

Rates

Slope

Slope--Intercept Form

Connecting the Concepts

Point--Slope Form

Connecting the Concepts

**Chapter 4 Polynomials**

Exponents and Their Properties

Polynomials

Addition and Subtraction of Polynomials

Connecting the Concepts

Multiplication of Polynomials

Special Products

Polynomials in Several Variables

Division of Polynomials

Negative Exponents and Scientific Notation

**Chapter 5 Polynomials and Factoring**

Introduction to Factoring

Factoring Trinomials of the Type x2 + bx + c

Factoring Trinomials of the Type ax2 + bx + c

Factoring Perfect-Square Trinomials and Differences of Squares

Factoring Sums or Differences of Cubes

Factoring: A General Strategy

Connecting the Concepts

Solving Quadratic Equations by Factoring

Connecting the Concepts

Solving Applications

**Chapter 6 Rational Expressions and Equations**

Rational Expressions

Multiplication and Division

Addition, Subtraction, and Least Common Denominators

Addition and Subtraction with Unlike Denominators

Complex Rational Expressions

Solving Rational Equations

Connecting the Concepts

Applications Using Rational Equations and Proportions

Formulas and Equations

**Chapter 7 Functions and Graphs**

Introduction to Functions

Domain and Range

Graphs of Functions (including brief review of graphing)

Connecting the Concepts

The Algebra of Functions

Variation and Problem Solving

**Chapter 8 Systems of Equations and Problem Solving**

Systems of Equations in Two Variables

Solving by Substitution or Elimination

Connecting the Concepts

Solving Applications: Systems of Two Equations

Systems of Equations in Three Variables

Connecting the Concepts

Solving Applications: Systems of Three Equations

Elimination Using Matrices

Determinants and Cramer's Rule

Business and Economics Applications

**Chapter 9 Inequalities and Problem Solving**

Interval Notation and Problem Solving

Intersections, Unions, and Compound Inequalities

Absolute-Value Equations and Inequalities

Inequalities in Two Variables

Connecting the Concepts

Applications Using Linear Programming

**Chapter 10 Exponents and Radicals**

Radical Expressions and Functions

Rational Numbers as Exponents

Multiplying Radical Expressions

Dividing Radical Expressions

Expressions Containing Several Radical Terms

Solving Radical Equations

Connecting the Concepts

Geometric Applications

The Complex Numbers

**Chapter 11 Quadratic Functions and Equations**

Quadratic Equations

The Quadratic Formula

Applications Involving Quadratic Equations

Studying Solutions of Quadratic Equations

Equations Reducible to Quadratic

Quadratic Functions and Their Graphs

Connecting the Concepts

More About Graphing Quadratic Functions

Problem Solving and Quadratic Functions

Polynomial and Rational Inequalities

**Chapter 12 Exponential and Logarithmic Functions**

Composite and Inverse Functions

Exponential Functions

Connecting the Concepts

Logarithmic Functions

Properties of Logarithmic Functions

Common and Natural Logarithms

Solving Exponential and Logarithmic Equations

Applications of Exponential and Logarithmic Functions

**Chapter 13 Conic Sections**

Conic Sections: Parabolas and Circles

Conic Sections: Ellipses

Conic Sections: Hyperbolas

Connecting the Concepts

Nonlinear Systems of Equations

**Chapter 14 Sequences, Series, and The Binomial Theorem**

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

The Binomial Theorem

Connecting the Concepts

**Chapter R Elementary Algebra Review**

Introduction to Algebraic Expressions

Equations, Inequalities, and Problem Solving

Introduction to Graphing

Polynomials

Polynomials and Factoring Rational Expressions and Equations

Appendix A: Sets

Appendix B: Synthetic Division

Table 1: Fractional and Decimal Equivalents

Table 2: Squares and Square Roots

Table 3: Geometric Formulas

Answers

Glossary

Index

Index of Applications