# Intermediate Algebra: Concepts and Applications, 11th edition

Published by Pearson (March 17, 2023) © 2024

**Marvin L. Bittinger**Indiana University Purdue University Indianapolis**David J. Ellenbogen**Community College of Vermont**Barbara L. Johnson**Indiana University Indianapolis

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## MyLab

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For courses in Intermediate Algebra.

### Understanding and applying concepts

**Intermediate Algebra: Concepts and Applications** prepares students to transition from skills-based math to the more concept-oriented math they'll need for college courses. The authors' approach fosters the critical-thinking skills needed to achieve this: the ability to reason mathematically, communicate mathematically, and identify/solve mathematical problems.

The **11th Edition** features carefully reviewed and revised exposition, examples and exercises. Abundant new features include more resources for review and preparation, while maintaining the strong emphasis on critical thinking and making connections between concepts.

### Hallmark features of this title

**Connecting the Concepts**gives students the opportunity to tie together concepts from multiple sections or chapters and includes the all-important mixed practice.**Exploring the Concept**activities ask students to dive deeper into a key concept.**Algebraic-Graphical Connections,****Translating for Success**and**Visualizing for Success**draw connections between math from multiple perspectives.**Exercises**foster skills and greater conceptual understanding, including**“Aha!”****exercises**that develop student insight on solving certain problem types,**“Synthesis” exercises**that ask them to combine skills from earlier sections, and**“Writing” exercises**that require critical thinking to explain concepts.**Mid-Chapter Reviews and end-of-chapter resources**provide reinforcement for review and retention.

### New and updated features of this title

**A new Just-in-Time Review chapter**at the start of the text reviews prerequisite topics from previous courses. It includes material on fractions, decimals, percent, unit conversion and more.**New Essential Review**offers just-in-time review of earlier material needed for current topics and is integrated at the start of objectives as appropriate.**Updated Skill Maintenance**(formerly Skill Review) appears in every section beginning with Section 1.2.**New Guided Solution Exercises**with fill-in blanks have been added to selected margin exercises in nearly every section, giving students a guided, interactive format to reinforce skills.**Updated Chapter Opener Applications with infographics**use current data and applications to present math in context. Many new spotlights focus on real people sharing how they use math in their careers.**Updated, optional Technology Connections**in each chapter help students use a graphing calculator. Exercises are included frequently, and additional exercises are marked with a graphing calculator icon to provide more practice. Calculator screenshots have been updated to reflect the TI-84+ CE.**Introduction to Matrices**is added to Chapter 3 (Systems of Linear Equations and Problem Solving) to introduce matrix notation as well as matrix operations.

### Features of MyLab Math for the 11th Edition

**New GeoGebra exercises**: Gradable GeoGebra graphing exercises enable students to interact directly with the graph in a manner that reflects how students would graph on paper.**Updated To-the-Point Objective videos**for every section in the text are presented in a modern format. They are updated based on updates made in the text, and are also available to view and assign as shorter, objective-level videos.- In select videos, an Interactive
**Your Turn Video Check**pauses for the student to work an exercise, input their answer, and learn through the video if they were correct and why or why not.

- In select videos, an Interactive
**New Just-in-Time Review Videos**offer a concise presentation of the foundational topics covered in the Just-in-Time modules at the front of the text. These basic skills are referenced as needed throughout the main text, providing a refresh on topics like fractions or decimals at point-of-use.**Interactive Animations**complement the Exploring the Concepts feature in the text, giving students a hands-on opportunity to manipulate graphs and cement their understanding.**Skill Builder**can now be required by the instructor. Skill Builder is an in-homework adaptive practice experience; students who get an exercise incorrect are taken to a personalized practice experience, including prerequisites, to help them succeed on their homework.

**J. Just-in-Time Review**- J.1 The Factors of a Number
- J.2 Prime Factorizations
- J.3 Multiplying and Dividing with Fraction Notation
- J.4 Adding and Subtracting with Fraction Notation
- J.5 Converting between Percent Notation and Decimal Notation
- J.6 Unit Conversion
- J.7 Order for the Real Numbers
- J.8 Graphing Inequalities on the Number Line
- J.9 Exponential Notation
- J.10 Order of Operations
- J.11 Evaluating Algebraic Expressions
- J.12 Equivalent Fraction Expressions
- J.13 Combining Like Terms
- J.14 Removing Parentheses and Combining Like Terms

**1. Algebra and Problem Solving**- 1.1 Some Basics of Algebra
- 1.2 Operations and Properties of Real Numbers
- 1.3 Solving Equations
- Mid-Chapter Review
- 1.4 Introduction to Problem Solving
- 1.5 Formulas, Models, and Geometry
- Connecting the Concepts
- 1.6 Properties of Exponents
- Exploring the Concept
- 1.7 Scientific Notation
- Translating for Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 1
- Test: Chapter 1

**2. Graphs, Functions, and Linear Equations**- 2.1 Graphs
- 2.2 Functions
- 2.3 Linear Functions: Slope, Graphs, and Models
- Exploring the Concept
- 2.4 Another Look at Linear Graphs
- Algebraic Graphical Connection
- Mid-Chapter Review
- 2.5 Equations of Lines and Modeling
- Connecting the Concepts
- 2.6 The Algebra of Functions
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 2
- Test: Chapter 2
- Cumulative Review: Chapters 1-2

**3. Systems of Linear Equations and Problem Solving**- 3.1 Systems of Equations in Two Variables Algebraic Graphical Connection
- 3.2 Solving by Substitution or Elimination Connecting the Concepts
- 3.3 Solving Applications: Systems of Two Equations Exploring the Concept
- 3.4 Systems of Equations in Three Variables Mid-Chapter Review
- 3.5 Solving Applications: Systems of Three Equations
- 3.6 Matrices
- 3.7 Elimination Using Matrices
- 3.8 Determinants and Cramer's Rule
- 3.9 Business and Economics Applications
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 3
- Test: Chapter 3
- Cumulative Review: Chapters 1-3

**4. Inequalities and Problem Solving**- 4.1 Inequalities and Applications
- 4.2 Intersections, Unions, and Compound Inequalities
- 4.3 Absolute-Value Equations and Inequalities
- Exploring the Concept
- Mid-Chapter Review
- 4.4 Inequalities in Two Variables
- Connecting the Concepts
- 4.5 Applications Using Linear Programming
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 4
- Test: Chapter 4
- Cumulative Review: Chapters 1-4

**5. Polynomials and Polynomial Functions**- 5.1 Introduction to Polynomials and Polynomial Functions
- 5.2 Multiplication of Polynomials
- Algebraic Graphical Connection
- 5.3 Common Factors and Factoring by Grouping
- 5.4 Factoring Trinomials
- Mid-Chapter Review
- 5.5 Factoring Perfect-Square Trinomials and Differences of Squares
- 5.6 Factoring Sums or Differences of Cubes
- 5.7 Factoring: A General Strategy
- 5.8 Applications of Polynomial Equations
- Exploring the Concept
- Connecting the Concepts
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 5
- Test: Chapter 5
- Cumulative Review: Chapters 1-5

**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
- 6.4 Rational Equations
- Algebraic Graphical Connection
- Connecting the Concepts
- Mid-Chapter Review
- 6.5 Solving Applications Using Rational Equations
- 6.6 Division of Polynomials
- 6.7 Synthetic Division and the Remainder Theorem
- 6.8 Formulas, Applications, and Variation
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 6
- Test: Chapter 6
- Cumulative Review: Chapters 1-6

**7. Exponents and Radicals**- 7.1 Radical Expressions and Functions
- 7.2 Rational Numbers as Exponents
- 7.3 Multiplying Radical Expressions
- 7.4 Dividing Radical Expressions
- 7.5 Expressions Containing Several Radical Terms
- Connecting the Concepts
- Mid-Chapter Review
- 7.6 Solving Radical Equations
- 7.7 The Distance Formula, the Midpoint Formula, and Other Applications
- 7.8 The Complex Numbers
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 7
- Test: Chapter 7
- Cumulative Review: Chapters 1-7<

**8. Quadratic Functions and Equations**- 8.1 Quadratic Equations
- Algebraic Graphical Connection
- 8.2 The Quadratic Formula
- Connecting the Concepts
- 8.3 Studying Solutions of Quadratic Equations
- 8.4 Applications Involving 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
- Algebraic Graphical Connection
- 8.8 Problem Solving and Quadratic Functions
- 8.9 Polynomial Inequalities and Rational Inequalities
- Algebraic Graphical Connection
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 8
- Test: Chapter 8
- Cumulative Review: Chapters 1-8

**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 Common Logarithms and Natural Logarithms
- 9.6 Solving Exponential Equations and Logarithmic Equations
- Connecting the Concepts
- 9.7 Applications of Exponential Functions and Logarithmic Functions
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 9
- Test: Chapter 9
- 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
- Connecting the Concepts
- Mid-Chapter Review
- 10.4 Nonlinear Systems of Equations
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 10
- Test: Chapter 10
- Cumulative Review: Chapters 1-10

**11. Sequences, Series, and the Binomial Theorem**- 11.1 Sequences and Series
- 11.2 Arithmetic Sequences and Series
- 11.3 Geometric Sequences and Series
- Connecting the Concepts
- Mid-Chapter Review
- 11.4 The Binomial Theorem
- Visualizing For Success
- Collaborative Activity
- Decision-Making Connection
- Study Summary
- Review Exercises: Chapter 9
- Test: Chapter 9
- Cumulative Review: Chapters 1-9

##### Answers

##### Glossary

##### Subject Index

##### Index of Applications

### About our authors

**Marvin Bittinger **has taught math at the university level for more than 38 years, and he is now professor emeritus of mathematics education at Indiana University - Purdue University. Professor Bittinger has authored numerous textbooks 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. His hobbies include hiking in Utah, baseball, golf and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, particularly in apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 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 2 sons, Monroe and Zachary.

**Barbara Johnson **has taught math at the college and high school level for nearly 40 years. She is currently a lecturer in the Department of Mathematical Sciences at Indiana University - Purdue University Indianapolis, where she also serves as coordinator for the Mathematics for Elementary Teachers course sequence. She received her BS in mathematics from Bob Jones University, her MS in mathematics from Clemson University, and her PhD in Educational Studies from Ball State University. Dr. Johnson's research focuses on affect in mathematics education. Her other interests include gardening, karate and hiking. She lives in central Indiana with her husband Jeff, and has 5 children and 3 grandchildren.

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