# Intermediate Algebra - 2e

Lynn Marecek, Santa Ana College

Andrea Honeycutt Mathis, Northeast Mississippi Community College

Copyright Year: 2017

Publisher: OpenStax

Language: English

## Formats Available

## Conditions of Use

Attribution

CC BY

## Reviews

This textbook covers all the necessary content for a standard course in Intermediate Algebra. It offers depth in mathematical content, completeness in explanations, a variety of solved examples, practice “Try It” problems, extensive sets of... read more

This textbook covers all the necessary content for a standard course in Intermediate Algebra. It offers depth in mathematical content, completeness in explanations, a variety of solved examples, practice “Try It” problems, extensive sets of exercise problems, chapter reviews, chapter review exercises, and practice tests. All these attributes make it an easy substitute for a more expensive traditional textbook.

Topics presented in Chapters 1 through 11 are sequentially aligned with those found in traditional textbooks: Foundations, Solving Linear Equations, Graphs and Functions, Systems of Linear Equations, Polynomials and Polynomial Functions, Factoring, Rational Expressions and Functions, Roots and Radicals, Quadratic Equations and Functions, Exponential and Logarithmic Functions, and Conics. Chapter 12 goes further by covering Sequences, Series, and the Binomial Theorem.

Each chapter logically scaffolds math content into numbered sections, making it easy to adapt to your course syllabus. The Table of Contents and the Index are effective navigating tools. Moreover, the online text can be searched using key words to locate page numbers and exact exercise problems of interest. It also allows students to highlight sections of the text and to add in their own study notes.

From what I see, the content is accurate, error free, and unbiased. I used the first edition when teaching my Intermediate Algebra course over four semesters, and I had no significant issues concerning content accuracy. In this second edition, the Preface assures us multiple experts have worked to improve mathematical clarity and accuracy from the first edition.

Most content dates to about a decade ago, and 2014 was the most recent year referenced in exercise problems. Prices of homes, cars, and dates of earthquakes are a bit old and should be updated, and more recent current events should be used. In particular, it would be most appropriate to use the Covid pandemic as a topic in Chapter 10 relating to exponential and logarithmic functions.

Clarity of text is appropriate for the audience of this book. Mathematical content is slowly developed from previous material. New jargon and terminology are adequately defined, explained, and illustrated in the example problems and exercises. I analyzed random paragraphs with Microsoft Word’s document editor. The Flesch Reading Ease was 56 (0 = very difficult, 100 = easiest), meaning it was fairly difficulty to read. The Flesch-Kincaid Grade Level was at 9.6, which is appropriate for high school and beginning college students. That said, most of my own students are Hispanic, and they occasionally have difficulty reading because English is their second language. Due to the high Flesch Reading Ease score, I am rating Clarity at a 4, instead of a 5.

Each chapter consistently follows this order: Chapter Outline, Introduction, Chapter Sections, Chapter Review, Key Concepts, Review Exercises, and a Practice Test. Each Section also follows a consistent order: Learning Objectives, Topic Explanations with solved examples, “Try It” practice problems, "How To" instructions, Exercises, Writing Exercises, and a Self-Check. Finally, an Answer Key in the Appendix gives answers to all odd numbered problems. This consistent structure mirrors that found in the more expensive traditional textbooks.

The textbook is extremely modular and readable. There are no large blocks of text without subheadings. At most, there are only 3 or 4 sentences of text separated by subsections or heading titles, making the reading of content more convenient and understandable. Chapters are logically subdivided into sections (5.1, 5.2, 5.3, etc.). Examples are numbered sequentially for the entire chapter but not according to the section. Similarly, exercise problems, review problems and test problems are numbered sequentially for the entire chapter. For example, the Exercises in Section 5.3 begin with problem 178 and end with problem 287. It takes a bit of getting used to, but it’s understandable.

The text is presented in a clear and logical fashion. Both the chapters and chapter contents are presented in the same order found in a traditional textbook.

There are no issues with the hyperlinks within the text, as all seem to work properly and move the user to the desired locations. This is handy for students, especially in the “Be Prepared” readiness quiz problems at the beginning of each section, where students can refer to previously solved problems by clicking on the recommended hyperlinks. In addition, all the odd numbered Exercise problems have direct hyperlinks to the Answer Key. All diagrams, tables, graphs, photographs, images, appear correct without any distortions. When compared to a traditional publisher’s textbook, this OER text is printed with fewer colors and contains minimal images, photographs, and illustrations, making the mathematics stand out as the main point for the reader. I find sometimes that traditional texts often contain too many images, photos, and extra clutter, enough to distract attention away from the math being taught.

I did not proofread the entire text, but the sections I read appear to contain no grammatical errors. I trust the experts who helped review and rewrite this second edition of the text.

I teach at the City Colleges of Chicago, consisting of seven sister colleges located in various ethnic and culturally diverse neighborhoods of Chicago. We pride ourselves in the diversity of our students, staff, and faculty. Although I cannot find anything culturally insensitive or offensive, I have a few suggestions. First, we need more examples related to the inner city and the everyday life encountered in culturally diverse settings. Examples might involve the height of skyscrapers, the number of passengers in a subway car, walking down city blocks to get to school, ingredients used in ethnic foods, etc. Next, images mean a lot to students of color. I’m referring to the photo of two male Caucasian scientists on the title page of Chapter 6, page 575. If one of them would have dark skin, and/or be a female, it would build hope for those students that they too could also become scientists. Finally, in the pdf text there is a small recurring image (emoji) of a Caucasian female teacher at the “HOW TO” lessons. Perhaps, it could be an emoji of someone with darker skin, or a different image altogether, such as an owl. Food for thought.

Anyone teaching with this textbook has access to many free resources on the OpenStax website. Under Instructor Resources, you have access to an LMS course package, the OER Commons Resources where you can find other texts, classroom resources, and more. By the way, OpenStax PowerPoints only show images from the textbook, and you have to fill in explanations on each slide. I must mention that I used Knewton adaptive software when teaching this course which significantly improved student success rates. Knewton aligns closely with OpenStax texts for their math content and classroom worksheets in case you want to give it a try. I highly recommend this text and will use it again.

Comprehensiveness I believe that the author has diligently and successfully incorporated many fruitful well-planned examples and explanations of the various topics that are within the scope of Intermediate Algebra. read more

Comprehensiveness

I believe that the author has diligently and successfully incorporated many fruitful well-planned examples and explanations of the various topics that are within the scope of Intermediate Algebra.

Accuracy

In reviewing this book, I had not noticed any inaccuracies. The only way to really be able to state that a book is accurate is to proof-read the entire book. The chapters and sections I read had no inaccuracies that stood out to me. Based on the percentage of material I had reviewed; I would give this category a rating of five.

Relevance

In the past, I have used at least one book where the applications in the book were based on information 10 years ago. And I would have to make comments to my students about this concerning the situation every time we came across similar situations. For example, speaking of a new car, it might have been stating that someone buys a new car for $7000. In this current year this is not the typical price of a new car. Many of the applications in the book were stuck in time for the year approximately 2010.

But again, I would have to review the entire book line by line to make a very accurate statement on this assessment. As far as I can see the problems are relevant and fairly much accurate in context examples.

Clarity

The author does a great job with clarity. For example, in the online version of the book, a problem will be given for students to try, then there will be a button “see solution” so that students can check for any errors. Another similar problem is given with “Now you try it.” I am sure that students find this to be very helpful in clarifying the topic at hand.

Consistency

The following is a copy of text taken from the “Introduction” to the Chapter2. The mathematical topic of each section is highlighted with an application problem displayed.

Chapter Outline

2.1 Use a General Strategy to Solve Linear Equations

2.2 Use a Problem Solving Strategy

2.3 Solve a Formula for a Specific Variable

2.4 Solve Mixture and Uniform Motion Applications

2.5 Solve Linear Inequalities

2.6 Solve Compound Inequalities

2.7 Solve Absolute Value Inequalities

Imagine being a pilot, but not just any pilot—a drone pilot. Drones, or unmanned aerial vehicles, are devices that can be flown remotely. They contain sensors that can relay information to a command center where the pilot is located. Larger drones can also carry cargo. In the near future, several companies hope to use drones to deliver materials and piloting a drone will become an important career. Law enforcement and the military are using drones rather than send personnel into dangerous situations. Building and piloting a drone requires the ability to program a set of actions, including taking off, turning, and landing. This, in turn, requires the use of linear equations. In this chapter, you will explore linear equations, develop a strategy for solving them, and relate them to real-world situations.

When clicking on hyperlink for 2.1, we see the following:

Learning Objectives

By the end of this section, you will be able to:

• Solve linear equations using a general strategy

• Classify equations

• Solve equations with fraction or decimal coefficients

BE PREPARED 2.1

Before you get started, take this readiness quiz.

Simplify: 32(12x+20).32(12x+20).

If you missed this problem, review Example 1.51.

The Learning objectives are stated for the section as well as a mini-preparedness check.

This pedagogical format is used consistently for each chapter and section.

Modularity

With each chapter being broken into six or seven sections per chapter, by the very nature has modularity. Modularity is demonstrated also in the examples I have given above on Consistency.

Organization

The content is very well organized in a pyramid structure. Once in a while in a couple of other books I have had my students complete one section before the other section, breaking the organization of the sections. But in this book I am very satisfied with the organization

Interface

There are no navigation problems distortions of images of charts and any other display features that I could see that could distract the students. If there are interface issues, they were ones that I had not seen.

Grammatical

I have taken a graduate course in Grammar and am very keenly sensitive to spotting grammatical errors. I did not find any errors in the sections of the book that I previewed. ( I hope that you will not find any grammatical errors within this review that I am writing!)

Language is never stagnant and is always fluid.. As a result, there are allowances and changes in grammatical rules that grammartitions will make due to this fluidity of language.

Cultural Within the text, I have not noticed anything, explicitly or implicitly stated, or characterized, that is culturally insensitive or offensive in any way. In today’s society, I believe that the majority of educators are trained and are very keenly aware of being culturally respectful. There is no excuse today not to be culturally respectful. Just as in the classroom we must be on our best behavior to demonstrate cultural awareness and respect, we would expect that most books do not have a problem with this dimension of education.. My thoughts and hopes are that the books would not be published by companies unless they are culturally respectful.

Other comments

I could not easily see where I could find examples of computerized homework. I have written to Rice University requesting information about this. Rice responded in a timely fashion that the books do not offer computerized homework, but that there are a few third-party vendors who may offer this. I researched this. Could not find much. Disappointed.

This text provides ample material to cover an Intermediate Algebra course as well as supplemental material for remediation or extension. read more

This text provides ample material to cover an Intermediate Algebra course as well as supplemental material for remediation or extension.

I found no more errors (few) than I would find in a commercially available text.

The on-line text is continually updated and so remains quite current. There is a lag for the printed versions.

The language was clear and concise and the examples thoroughly explained.

There were no shifts in style, nomenclature or terminology.

The text carved the material into a granularity adequate to support most teaching style.

The organization is similar to most algebra textbooks. (Why wouldn't it be?)

I used the text in a remote fashion and found no glitches. It actually was a quite good visual aid.

I saw no grammatical errors.

The text was as blandly neutral as possible.

I just finished using the text in an entirely remote fashion. I found it quite useful (all the students had a "copy" right from the beginning) and I look forward to employing it this fall in a face to face class.

Each chapter opens up with a real-life application, outlines the objectives, contains lots of practice problems, key terms and concepts, a review section, and a practice test. read more

Each chapter opens up with a real-life application, outlines the objectives, contains lots of practice problems, key terms and concepts, a review section, and a practice test.

The content flows well and is clear with no errors and unbiased.

The content matter in this book will not be obsolete within a short period of time. The material can be easily rearranged and implemented to suit different instructor needs.

The text is definitely written with the student in mind. For example, the authors use lots of graphs and tables to help students understand different concepts.

The entire book is writtenly consistently from chapter to chapter. New terms are highlighted at the end of each chapter. The terms are used consistently throughout the book.

The text is well designed and organized. Each section begins with objectives and a mini quiz of previously learned topics. This connects previously learned topics to the new or current topics.

The topics in the text are presented in a logical and clear fashion. The examples and practice problems are developed from easy to difficult.

The text is easy to navigate and is free of significant interface issues . The images, graphs, and charts display very well and are not distracting or confusing to the reader.

I did not come across any grammatical errors.

I did not find any instances of cultural insensitive or offensive content in the text.

I found this book very instructor and student friendly. The two things I really like about this book are the pictures at the beginning of each chapter and the mini quizzes before each section. The pictures highlight a real-life application for the topics of that chapter and provide relevancy of what is learned to real life careers. The mini quizzes review previous topics for mastery and connection to the new topics.

The Intermediate Algebra textbook covers 12 topics: Foundations that include all operations with real numbers, Solving Linear Equations and inequalities, Graphs and Functions, Systems of Linear Equations, including matrices, Polynomials,... read more

The Intermediate Algebra textbook covers 12 topics: Foundations that include all operations with real numbers, Solving Linear Equations and inequalities, Graphs and Functions, Systems of Linear Equations, including matrices, Polynomials, Factoring, including special products, Rational expressions, Roots and Radicals, Quadratic equations, Exponential and Logarithmic Functions, Conics, Sequences, Series and more. The textbook is well structured. It is designed for one-semester Algebra course. No need of supplemental materials. There are plenty of examples and problems, including real life problems that could be used for class work and homework.

The content is clear, error-free and culturally unbiased.

The Textbook covers standard Algebra topics which are cohesive. Each topic is build upon previously taught material. The content and examples are up to date.

The textbook is student-friendly. There are some excellent explanations about working with integers and fractions, a lot of tables and graphs to help students understand different types of functions and how the graph changes when the function is changed

The textbook is internally consistent. The new terminology and notations are given at the end of each chapter and once introduced are properly used in the following chapters.

The Chapters, the different sections and the learning objectives are very clear. There are small quizzes at the beginning of each chapter to prepare the students for the new topic. The text can be easily reorganized for meeting some specific need or requirements.

The topics are organized logically and start with the easiest one. The examples in each topic are also arranged from easy to more challenging.

The text is free of interface issues. The images are clear and well organized.

I have not found grammatical errors.

The text is culturally relevant.

I would recommend the textbook to have two options: teacher’s book and student’s book or a textbook in the way it is now and an additional practice workbook with chapter tests included. This is a well-done, student-friendly textbook, that I can recommend for Developmental Math courses.

This is a great textbook for Intermediate Algebra or College Algebra course. This textbook includes covers standard topics such as linear functions/equation, graphs and functions, systems of linear equations, polynomials, rational functions, roots... read more

This is a great textbook for Intermediate Algebra or College Algebra course. This textbook includes covers standard topics such as linear functions/equation, graphs and functions, systems of linear equations, polynomials, rational functions, roots and radicals, quadratic functions/equations, exponential and logarithmic functions, conics, and sequences and series. All of topics are self-contained and instructors do not have to provide supplements.

However, instructors, who plan to cover trigonometric functions, may need to provide extra materials.

The author made a great effort in this aspect and the examples, homework problems and the solutions I read are error-free.

The content of algebra should remain the same for a long while, therefore, the book is very suitable for what are taught .As most openstax math books, the book provides very useful youtube link at end of each session, which is very appropriate for the learning habit of current students.

The author made a tremendous effort to make mathematical contents accessible to students. The first chapter Foundations provides a reference. There are lots of tables to compare similar terminologies which students may be easily confused. For example, on page 690, a table is provided to help students to understand rational expression and rational functions.

The whole book is organized in a very consistent format from chapter to chapter, and from section to section. Moreover, consistent terminology and notations are used throughout the whole book.

The book is well designed and facilitates instructors' teaching and students' learning. Each section starts with clearly stated learning objects, followed by Be Prepared! with exercises and the similar examples in previous sections, which helps students to review what they need for the current section. I have to mention, students can just click examples in blue to locate them.

The order of the topics is presented in a logical way and all examples and problems are ordered from easy to more challenging.

The links for chapters, sections and even specific examples which allow users to jump specific locations work well. Colors and headings really help reader to sort out information.

I did not spot grammar errors.

I did not spot any culturally insensitive or offensive instance.

I have adopted this as a textbook for one semester. From my experience and students' feedback, it is a user-friendly and comprehensive textbook. I will still use it in the future.

## Table of Contents

- 1 Foundations
- 2 Solving Linear Equations
- 3 Graphs and Functions
- 4 Systems of Linear Equations
- 5 Polynomials and Polynomial Functions
- 6 Factoring
- 7 Rational Expressions and Functions
- 8 Roots and Radicals
- 9 Quadratic Equations and Functions
- 10 Exponential and Logarithmic Functions
- 11 Conics
- 12 Sequences, Series and Binomial Theorem

## Ancillary Material

## About the Book

*Intermediate Algebra 2e* 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. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses.

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.

## About the Contributors

### Authors

**Lynn Marecek **has been teaching mathematics at Santa Ana College for many years has focused her career on meeting the needs of developmental math students. At Santa Ana College, she has been awarded the Distinguished Faculty Award, Innovation Award, and the Curriculum Development Award four times. She is a Coordinator of the Freshman Experience Program, the Department Facilitator for Redesign, and a member of the Student Success and Equity Committee, and the Basic Skills Initiative Task Force.

She is the coauthor with MaryAnne Anthony-Smith of Strategies for Success: Study Skills for the College Math Student, Prealgebra published by OpenStax and Elementary Algebra published by OpenStax.

**Andrea Honeycutt Mathis, **Northeast Mississippi Community College