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Preface

Preface

Intermediate Algebra was originally authored by Lynn Marecek and Andrea Honeycutt Mathis, and published by OpenStax, Rice University. It is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). The original work is available at openstax.org. This version has been adapted for use in the Universal Open Textbook Initiative.

About Intermediate Algebra

Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester Intermediate Algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

Coverage and Scope

Intermediate Algebra continues the philosophies and pedagogical features of Prealgebra and Elementary Algebra, by Lynn Marecek and MaryAnne Anthony-Smith. By introducing the concepts and vocabulary of algebra in a nurturing, non-threatening environment while also addressing the needs of students with diverse backgrounds and learning styles, the book helps students gain confidence in their ability to succeed in the course and become successful college students.

The material is presented as a sequence of small, and clear steps to conceptual understanding. The order of topics was carefully planned to emphasize the logical progression throughout the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics.

  • Chapter 1: Foundations
     Chapter 1 reviews arithmetic operations with whole numbers, integers, fractions, decimals and real numbers, to give the student a solid base that will support their study of algebra.
  • Chapter 2: Solving Linear Equations and Inequalities
     In Chapter 2, students learn to solve linear equations using the Properties of Equality and a general strategy. They use a problem-solving strategy to solve number, percent, mixture and uniform motion applications. Solving a formula for a specific variable, and also solving both linear and compound inequalities is presented.
  • Chapter 3: Graphs and Functions
     Chapter 3 covers the rectangular coordinate system where students learn to plot graph linear equations in two variables, graph with intercepts, understand slope of a line, use the slope-intercept form of an equation of a line, find the equation of a line, and create graphs of linear inequalities. The chapter also introduces relations and functions as well as graphing of functions.
  • Chapter 4: Systems of Linear Equations
     Chapter 4 covers solving systems of equations by graphing, substitution, and elimination; solving applications with systems of equations, solving mixture applications with systems of equations, and graphing systems of linear inequalities. Systems of equations are also solved using matrices and determinants.
  • Chapter 5: Polynomials and Polynomial Functions
     In Chapter 5, students learn how to add and subtract polynomials, use multiplication properties of exponents, multiply polynomials, use special products, divide monomials and polynomials, and understand integer exponents and scientific notation.
  • Chapter 6: Factoring
     In Chapter 6, students learn the process of factoring expressions and see how factoring is used to solve quadratic equations.
  • Chapter 7: Rational Expressions and Functions
     In Chapter 7, students work with rational expressions, solve rational equations and use them to solve problems in a variety of applications, and solve rational inequalities.
  • Chapter 8: Roots and Radical
     In Chapter 8, students simplify radical expressions, rational exponents, perform operations on radical expressions, and solve radical equations. Radical functions and the complex number system are introduced
  • Chapter 9: Quadratic Equations
     In Chapter 9, students use various methods to solve quadratic equations and equations in quadratic form and learn how to use them in applications. Students will graph quadratic functions using their properties and by transformations.
  • Chapter 10: Exponential and Logarithmic Functions
     In Chapter 10, students find composite and inverse functions, evaluate, graph, and solve both exponential and logarithmic functions.
  • Chapter 11: Conics
     In Chapter 11, the properties and graphs of circles, parabolas, ellipses and hyperbolas are presented. Students also solve applications using the conics and solve systems of nonlinear equations.
  • Chapter 12: Sequences, Series and the Binomial Theorem
     In Chapter 12, students are introduced to sequences, arithmetic sequences, geometric sequences and series and the binomial theorem.

All chapters are broken down into multiple sections, the titles of which can be viewed in the Table of Contents.

Pedagogical Foundation and Features

Examples

Each learning objective is supported by one or more worked examples, which demonstrate the problem-solving approaches that students must master. Typically, we include multiple examples for each learning objective to model different approaches to the same type of problem, or to introduce similar problems of increasing complexity.

All examples follow a simple two- or three-part format. First, we pose a problem or question. Next, we demonstrate the solution, spelling out the steps along the way. Finally (for select examples), we show students how to check the solution. Most examples are written in a two-column format, with explanation on the left and math on the right to mimic the way that instructors "talk through" examples as they write on the board in class.

Be Prepared!

Each section, beginning with Section 2.1, starts with a few "Be Prepared!" exercises so that students can determine if they have mastered the prerequisite skills for the section. Reference is made to specific Examples from previous sections so students who need further review can easily find explanations. Answers to these exercises can be found in the supplemental resources that accompany this title.

Try It
A dark grey right-pointing chevron symbol is centered within a white square, framed by a soft, light blue gradient border. This icon typically represents 'next,' 'forward,' or 'expand'.

Try it The Try It feature includes a pair of exercises that immediately follow an Example, providing the student with an immediate opportunity to solve a similar problem with an easy reference to the example. In the PDF and the Web View version of the text, answers to the Try It exercises are located in the Answer Key

How To
An avatar of a person with a neutral expression, next to a speech bubble containing three ellipses, suggesting thought, a pending response, or a message being typed.

How To Examples use a three column format to demonstrate how to solve an example with a certain procedure. The first column states the formal step, the second column is in words as the teacher would explain the process, and then the third column is the actual math. A How To procedure box follows each of these How To examples and summarizes the series of steps from the example. These procedure boxes provide an easy reference for students.

Media
A teal-colored play button icon, depicted as a right-pointing triangle, centered within a white square with a soft, blurred teal border. It signifies the start of video or audio playback.

Media The "Media" icon appears at the conclusion of each section, just prior to the Self Check. This icon marks a list of links to online videos that reinforce the concepts and skills introduced in the section.

Self Check

The Self Check includes the learning objectives for the section so that students can self-assess their mastery and make concrete plans to improve.

Art Program

Intermediate Algebra contains many figures and illustrations. Art throughout the text adheres to a clear, understated style, drawing the eye to the most important information in each figure while minimizing visual distractions.

This figure shows three x y-coordinate planes. The first plane shows two lines which intersect at one point. Under the graph it says,

Section Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. Exercise sets are named Practice Makes Perfect to encourage completion of homework assignments.

  • Exercises correlate to the learning objectives. This facilitates assignment of personalized study plans based on individual student needs.
  • Exercises are carefully sequenced to promote building of skills.
  • Values for constants and coefficients were chosen to practice and reinforce arithmetic facts.
  • Even and odd-numbered exercises are paired.
  • Exercises parallel and extend the text examples and use the same instructions as the examples to help students easily recognize the connection.
  • Applications are drawn from many everyday experiences, as well as those traditionally found in college math texts.
  • Everyday Math highlights practical situations using the concepts from that particular section
  • Writing Exercises are included in every exercise set to encourage conceptual understanding, critical thinking, and literacy.

Chapter Review Features

Each chapter concludes with a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

  • Key Terms provide a formal definition for each bold-faced term in the chapter.
  • Key Concepts summarize the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.
  • Chapter Review Exercises include practice problems that recall the most important concepts from each section.
  • Practice Test includes additional problems assessing the most important learning objectives from the chapter.
  • Answer Key includes the answers to all Try It exercises and every other exercise from the Section Exercises, Chapter Review Exercises, and Practice Test.

Answers to Questions in the Book

Answers to Examples and Be Prepared! questions are provided just below the question in the book. All Try It answers are provided in the Answer Key. Odd-numbered Section Exercises, Review Exercises, and Practice Test questions are provided to students in the Answer Key. Even-numbered answers are provided only to instructors in the Instructor Answer Guide via the Instructor Resources page.

Additional Resources

Instructor resources for this book include manipulative mathematics worksheets, an answer guide to section review exercises, and a Getting Started Guide. These are available through the OpenStax instructor resources page for this book. Instructors can also find and share community-created teaching materials at oercommons.org/hubs/OpenStax.

About the Authors

Senior Contributing Authors

Lynn Marecek, Santa Ana College

Andrea Honeycutt Mathis, Northeast Mississippi Community College

Reviewers

Shaun Ault, Valdosta State University
 Brandie Biddy, Cecil College
 Kimberlyn Brooks, Cuyahoga Community College
 Michael Cohen, Hofstra University
 Robert Diaz, Fullerton College
 Dianne Hendrickson, Becker College
 Linda Hunt, Shawnee State University
 Stephanie Krehl, Mid-South Community College
 Yixia Lu, South Suburban College
 Teresa Richards, Butte-Glenn College
 Christian Roldán- Johnson, College of Lake County Community College
 Yvonne Sandoval, El Camino College
 Gowribalan Vamadeva, University of Cincinnati Blue Ash College
 Kim Watts, North Lake college
 Libby Watts, Tidewater Community College
 Matthew Watts, Tidewater Community College