Intermediate Algebra

Description

A Visual Approach

• Algebraic-Graphical Side-by-Side Solutions give students a direct comparison between these two problem-solving methods. They demonstrate that there is more than one way to obtain a result and illustrate the comparative efficiency and accuracy of the two methods.
• Visualizing the Graph problem sets ask students to match equations and inequalities with their graphs. This helps students to recognize the important characteristics of the equation or inequality and visualize the corresponding attributes of its graph. This feature is animated in MyMathLab^®, enabling the student to visualize concepts on an entirely new level.
• NEW! Chapter Openers pose real-world questions related to the chapter topics. Real data graphs help students analyze these questions and think about the answers.
• NEW! Your Turns offer calculator support at point of use. These simple exercises, designed to provide students with immediate keystroke practice, have been added to the in-text calculator instruction manual. Answers are provided after the exercises.

Emphasis on Conceptual Understanding

• NEW! Try Exercise icons, corresponding to nearly every example, point students to similar problems in the section exercise sets. By solving these problems, students can immediately reinforce their understanding of the mathematical concepts and skills presented in the examples. For easy identification in the exercise sets, the “Try” exercises have a shaded block on the exercise number. Answers to Try Exercises are given at the end of the exercise sets and in the back of the book.
• NEW! Mid-Chapter Reviews give students the opportunity to reinforce their understanding of the mathematical skills and concepts covered in the first half of the chapter before moving on to new material.
• Each Mid-Chapter Review begins with a Brief Summary of the concepts studied in the first part of the chapter, often illustrated with a table or chart.
• Guided Solutions problems with stepped-out solutions include fill-in blanks for students to complete the solution.
• Mixed Review exercises require an understanding of previously learned material to reinforce mastery of skills and concepts.
• NEW! Problem-Solving Steps, called out in the margins adjacent to selected Example Solutions, offer students at-a-glance reinforcement of the problem-solving process.
• The end-of section exercise sets include several special types of problems:
• Concept Reinforcement Exercises (also found in the chapter Study Summary) are True/False questions designed to increase understanding of the concepts rather than merely assess students’ skill at memorizing procedures.
• “Aha!” Exercises discourage rote learning and reward students who “look before they leap” into a problem. The “Aha!” designation is used the first time a new insight can be applied to a particular type of exercise and indicates to the student that there is a simpler way to complete the exercise with less computation.
• TW (Thinking and Writing) Exercises promote conceptual understanding and can also be used for class discussion and group projects.
• Synthesis Exercises help build critical-thinking skills by requiring students to use skills and concepts from the current section along with those from previous sections. These are available in most exercise sets.
• The Connecting the Concepts feature helps students understand the “big picture,” by relating the concept at hand to previously learned and upcoming material.

Additional Support

• Interactive Discoveries invite students to develop analytical and reasoning skills while taking an active role in the learning process. These discoveries can be used as lecture launchers to introduce new topics at the start of a class and quickly guide students through concepts.
• Collaborative Corner exercises, appearing one to three times per chapter, are designed for group work.
• The Study Summary at the end of each chapter has been expanded to provide more comprehensive in-text practice and review. Key Terms and Concepts are paired with worked-out Examples for reference and review and similar Practice Exercises for students to solve.

Preface

1. Basics of Algebra and Graphing

1.1 Some Basics of Algebra

1.2 Operations with Real Numbers

1.3 Equivalent Algebraic Expressions

1.4 Exponential Notation and Scientific Notation

Mid-Chapter Review

1.5 Graphs

1.6 Solving Equations and Formulas

1.7 Introduction to Problem Solving and Models

Summary and Review

Test

2. Functions, Linear Equations, and Models

2.1 Functions

2.2 Linear Functions: Slope, Graphs, and Models

2.3 Another Look at Linear Graphs

2.4 Introduction to Curve Fitting: Point-Slope Form

Mid-Chapter Review

2.5 The Algebra of Functions

Summary and Review

Test

3. Systems of Linear Equations and Problem Solving

3.1 Systems of Equations in Two Variables

3.2 Solving by Substitution or Elimination

3.3 Solving Applications: Systems of Two Equations

Mid-Chapter Review

3.4 Systems of Equations in Three Variables

3.5 Solving Applications: Systems of Three Equations

3.6 Elimination Using Matrices

3.7 Determinants and Cramer’s Rule

3.8 Business and Economics Applications

Summary and Review

Test

Cumulative Review: Chapters 1—3

4. Inequalities

4.1 Inequalities and Applications

4.2 Solving Equations and Inequalities by Graphing

4.3 Intersections, Unions, and Compound Inequalities

4.4 Absolute-Value Equations and Inequalities

Mid-Chapter Review

4.5 Inequalities in Two Variables

Summary and Review

Test

5. Polynomials and Polynomial Functions

5.1 Introduction to Polynomials and Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Polynomial Equations and Factoring

5.4 Trinomials of the Type x² + bx + c

5.5 Trinomials of the Type ax² + bx + c

5.6 Perfect-Square Trinomials and Differences of Squares

5.7 Sums or Differences of Cubes

Mid-Chapter Review

5.8 Applications of Polynomial Equations

Summary and Review

Test

6. Rational Expressions, Equations, and Functions

6.1 Rational Expressions and Functions: Multiplying and Dividing

6.2 Rational Expressions and Functions: Adding and Subtracting

6.3 Complex Rational Expressions

Mid-Chapter Review

6.4 Rational Equations

6.5 Applications Using Rational Equations

6.6 Division of Polynomials

6.7 Synthetic Division

6.8 Formulas, Applications, and Variation

Summary and Review

Test

Cumulative Review: Chapters 1—6

7. Exponents and Radical Functions

7.1 Radical Expressions, Functions, and Models

7.2 Rational Numbers as Exponents

7.3 Multiplying Radical Expressions

7.4 Dividing Radical Expressions

7.5 Expressions Containing Several Radical Terms

Mid-Chapter Review

7.6 Solving Radical Equations

7.7 The Distance Formula, the Midpoint Formula, and Other Applications

7.8 The Complex Numbers

Summary and Review

Test

8. Quadratic Functions and Equations

8.1 Quadratic Equations

8.2 The Quadratic Formula

8.3 Studying Solutions of Quadratic Equations

8.4 Studying Solutions of Quadratic Equations

8.5 Equations Reducible to Quadratic

Mid-Chapter Review

8.6 Quadratic Functions and Their Graphs

8.7 More About Graphing Quadratic Functions

8.8 Problem Solving and Quadratic Functions

8.9 Polynomial Inequalities and Rational Inequalities

Summary and Review

Test

9. Exponential Functions and Logarithmic Functions

9.1 Composite Functions and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithmic Functions

Mid-Chapter Review

9.5 Natural Logarithms and Changing Bases

9.6 Solving Exponential and Logarithmic Equations

9.7 Applications of Exponential and Logarithmic Functions

Summary and Review

Test

Cumulative Review: Chapters 1—9

10. Conic Sections

10.1 Conic Sections: Parabolas and Circles

10.2 Conic Sections: Ellipses

10.3 Conic Sections: Hyperbolas

Mid-Chapter Review

10.4 Nonlinear Systems of Equations

Summary and Review

Test

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

Mid-Chapter Review

11.4 The Binomial Theorem

Summary and Review

Test

Cumulative Review: Chapters 1-11

Answers

Glossary

Photo Credits

Index

Index of Applications

The Bittinger Graphs and Models Series helps students “see the math” and learn algebra by making connections between mathematical concepts and their real-world applications. The authors use a variety of tools and techniques—including side-by-side algebraic and graphical solutions and graphing calculators, when appropriate—to engage and motivate all types of learners. Abundant applications, many of which use real data, provide a context for learning and understanding the math.

The Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques—including graphing calculators, multiple approaches to problem solving, and interactive features—to engage and motivate all types of learners.

New and Updated Features

• Mid-Chapter Reviews give students the opportunity to reinforce their understanding of the mathematical skills and concepts covered in the first half of the chapter before moving on to new material.
• Each Mid-Chapter Review begins with a Brief Summary of the concepts studied in the first part of the chapter, often illustrated with a table or chart.
• Guided Solutions problems with stepped-out solutions include fill-in blanks for students to complete the solution.
• Mixed Review exercises require an understanding of previously learned material to reinforce mastery of skills and concepts.
• The Study Summary at the end of each chapter has been expanded to provide more comprehensive in-text practice and review. Key Terms and Concepts are paired with worked-out Examples for reference and review and similar Practice Exercises for students to solve.
• Try Exercise icons, corresponding to nearly every example, point students to similar problems in the section exercise sets. By solving these problems, students can immediately reinforce their understanding of the mathematical concepts and skills presented in the examples. For easy identification in the exercise sets, the “Try” exercises have a shaded block on the exercise number. Answers to Try Exercises are given at the end of the exercise sets and in the back of the book.
• Problem-Solving Steps, called out in the margins adjacent to selected Example Solutions, offer students at-a-glance reinforcement of the problem-solving process.
• Your Turns offer calculator support at point of use. These simple exercises, designed to provide students with immediate keystroke practice, have been added to the in-text calculator instruction manual. Answers are provided after the exercises.
• Chapter Openers pose real-world questions related to the chapter topics. Real data graphs help students analyze these questions and think about the answers.

Content Changes

• Every exercise set has been carefully reviewed and revised to improve grading and pairing. Over 25% of the exercises are new, ensuring the right kind of practice for today’s students.
• Coverage of the Distance and Mid-Point Formulas has been added to Section 7.7.
• Solutions of quadratic equations (Section 8.3) are now covered before applications of quadratic equations (Section 8.4).
• All real data has been updated.

New to the Supplements Package

• Mini Lectures, now available in the Instructor’s Resource Manual, include learning objectives, teaching tips, and key examples for use in the classroom for each section of the text.
• Enhancements to MyMathLab include the following:
• Increased exercise coverage provides more practice options for students.
• New math games help students practice math skills in a fun, interactive environment.
• Premade homework assignments will be available for each section of the text. In additional to the section-level premade assignments, the Bittinger MyMathLab courses will also include premade mid-chapter review assignments for each chapter.
• Interactive Translating for Success matching activities help students learn to associate word problems (through translation) with their appropriate mathematical equations. These activities are now assignable.
• Interactive Visualizing for Success activities ask students to match equations and inequalities with their graphs, allowing them to recognize the important characteristics of the equation and visualize the corresponding attributes of its graph. These activities are now assignable.
• The English/Spanish Audio Glossary allows students to see key mathematical terms and hear their definitions in either English or Spanish.

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled “Baseball and Mathematics.” His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael’s College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor’s degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.

Barbara Johnson has a B.S. in mathematics from Bob Jones University and a M.S. in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she recently earned a black belt in karate.

Additional information

Dimensions	1.65 × 8.90 × 11.20 in
Imprint	Pearson
Format	gen
ISBN-13	09780321725554
ISBN-10	0321725557
Author	Barbara L. Johnson, Marvin L. Bittinger, David J. Ellenbogen
Subjects	mathematics, higher education, Developmental Math, Intermediate Algebra