# Intermediate Algebra

John Redden, College of the Sequoias

Copyright Year: 2012

ISBN 13: 9781453347485

Publisher: Saylor Foundation

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

All necessary topics are generally well-covered and there is good depth and breadth, with few exceptions which are very specific. It should be noted that there is no index or glossary, which would be helpful to have. I appreciate the way the... read more

All necessary topics are generally well-covered and there is good depth and breadth, with few exceptions which are very specific. It should be noted that there is no index or glossary, which would be helpful to have. I appreciate the way the author frequently illustrates concepts both algebraically and graphically. I would have liked to see applications or contextual problems included in the conic sections unit to give students some insight into how they are useful in the real world. Also, since the concept of functions is so foundational, it would be nice to have included some real world examples of functions where they are introduced in Chapter 2. There are some other sections that could also benefit from including more real-world applications.

Overall, content is accurate, error-free, and unbiased, however; I did find one inaccurate statement regarding absolute value in Chapter 1, namely that absolute value is “always positive.” It’s a minor detail, but nonetheless should be corrected to the effect of “never negative”, or “always positive or zero.” Otherwise, content is very accurate.

There is a good opportunity here to incorporate problems that are more contextually relevant to the everyday lives of students. Less relevant examples related to topics such as investing and chemical mixtures, for instance, could appear less frequently (not removed) and could be juxtaposed with examples more relevant to activities of daily living, like cooking, transportation, sports, or common hobbies. The examples used in the text presently are very standard and are the kind that have been used in many texts for a great many years. Having said that, necessary updates will be very easy to implement, as it is only the contextual problems, examples, and exercises that need updating, not the content itself.

The text is certainly clear overall and I appreciated the predictable structure of each text section, which laid out learning objectives, explanations illustrated by lots of examples, a “key takeaways” summary, and a lengthy set of topic exercises broken down by type, with solutions provided. Explanations and examples are very generally very clear and visually accessible. I would have liked to see key concepts or ideas within a text block underlined or bolded for emphasis. There are only a handful of small specific instances in which phrases stood out to me as needing to be reworded. One example is an objective in Section 1.1 that reads “Define the geometric and algebraic definition of absolute value,” which is redundant. A suggested edit would be “Define absolute value algebraically and geometrically.” Certainly, these instances are few and very minor, and do not really detract from the clarity in any significant way.

The text is very consistent in terms of terminology and framework. All chapters follow the same presentation style and use of terminology is consistent throughout.

This text would be a useful resource regardless of what other materials are being used in the course and lends itself well to courses that are taught in a variety of formats.

The topics are presented in a logical, clear fashion and the examples are well-placed within the discussion of new concepts and problem types. I would suggest that Chapter 6: Solving Equations and Inequalities be renamed, since it specifically covers solving quadratic equations, along with polynomial and rational inequalities. I would also suggest placing this content directly after the chapter on Polynomial and Rational functions, in which solving polynomial equations is discussed, since quadratic equations are a type of polynomial equation.

There are some interface issues; specifically, not all images load properly in the .pdf version of the text, even after several minutes. The video links also did not work for me; I saw a blank box after clicking on any one of the links. Furthermore, there are a few spacing issues, such as one instance in section 1.2 in which there are no spaces between algebraic expressions and their translation to word phrases, which is not such a big deal, but is something to be considered if a revision is to be undertaken.

No grammatical errors were found.

There are no instances of cultural insensitivity or offensiveness; however, there also is not a recognizable effort to provide examples that are inclusive of a variety of races, ethnicities, and backgrounds, which is quite important in today’s world. As one other reviewer noted, names used in application problems are mostly traditional English male names and could easily be changed to further inclusion and reflect diversity. Moving beyond names, application problems that refer to diverse cultures, practices, and ways of life are missing presently and would be a welcome addition.

This book is a solid resource that I would offer to students as a source of support. The explanations are good and most of the examples are well-selected and broken into small steps so that students can easily follow the procedural progression. A few changes are recommended as mentioned above, but overall this is a solid and dependable resource for students and instructors alike.

The text covers all the topics common to an Intermediate Algebra course: Functions, Linear Systems, Radical and Exponential Expressions, Graphing Lines and more. There is a complete table of contents with links to the desired chapter. read more

The text covers all the topics common to an Intermediate Algebra course: Functions, Linear Systems, Radical and Exponential Expressions, Graphing Lines and more. There is a complete table of contents with links to the desired chapter.

The chapters that I reviewed were free of errors.

This text was prepared in 2012. It is in need of some updating. For example, in Chapter 7 in a lesson on Compound Interest, the interest rate for a CD was 5.2%. While 5.2% is more "interesting" than the current 1.1%, it isn't accurate for our present economic conditions. The content and structure of the book makes it adaptable for either a synchronous classroom or asynchronous online course. The course only requires a standard scientific calculator so no expensive additional technology is required.

The book is well written in a easy to follow format. All the steps for the sample problems are shown. Students can clearly see how the steps follow from one another. When you scroll over a vocabulary word, the definition appears. The book is primarily in black and white for easy reading. Red and blue are used to highlight steps or in parenthetical notes.

Each chapter follows the same progression of topics and style of presentation with a clear objective, new content, examples and practice exercises. All the chapters I reviewed were of consistent quality of content.

The chapters can be rearranged or omitted entirely.

The objective for each lesson is clearly stated at the beginning. The KEY TAKEAWAYS provide a helpful summary of what was covered in the section. I appreciate the inclusion of DISCUSSION BOARD questions in the practice sets. The odd answers are included after the exercises, but I was unable to locate the even solutions. Each chapter includes a review and a practice exam. The sections and chapters flow smoothly from each another, building on previous knowledge.

I was able to navigate the textbook easily, but I was unable to access the embedded videos. (404 not found; this page is not available)

I did not find any grammatical errors.

In 2020 we are more aware of inclusion and a desire for students to see themselves in the course. The names chosen for the people in the application problems were primarily Joe, Billy and John with an occasional Mary, Raul or Omar. There needs to be more references to women and minorities. There are references to famous mathematicians, but they are all primarily white males. I realize that the choice of historical figures is relative to the topic, but perhaps there are modern mathematicians who have added to the classical theory.

In general this is a well developed textbook that is adaptable to different modalities. It is organized in a manner to promote success for the Developmental Mathematics student with its clear objectives and many examples and practice exercises. However, it could use some minor updates to make it more relevant in 2020.

The textbook covers all of the chosen topics very well. read more

The textbook covers all of the chosen topics very well.

All of the problems I checked were correct and well presented.

It is hard to be outdated in general math problems and the application exercises will stand the test of time. It is written using traditional notation as well as textual notation allowing for easier emailing. This helps a great deal so students don't need extra technology to use the book effectively. I will use and reuse the book as long as I am assigned courses that align with the objectives.

It is well written. Some of the presentation of the math work and problems might confuse some students but overall ok.

I did love how ALL the steps were included in examples and exercise answers when there were multi-tiered problems. Students will clearly see how one step flowed to another.

Consistency is well done.

Chapters can be rearranged and skipped as needed without compromising the upcoming lessons. The book is very malleable as well. This book can fit many different Instructors' needs.

I loved having objectives. It is easy using given objectives to plans lessons to meet course objectives and have students know immediately what is expected in that lesson. I have had expensive textbooks that didn't have written objectives.

The organization is similar to his other book Elementary Algebra and I like the sequence in both.

The author also sets students up for success with an eased in and early approach to concepts that are the foundation of future lessons (square root simplification for one).

Embedded videos are nice but the reinforcement of the necessity of hand working math problems is clear.

I had no issues.

I saw no grammatical issues, but I am also better at math than grammar.

I saw no cultural relevance concerns.

Key Takeaways and Tips charts are so helpful to students and instructors. If student questions interrupt an instructor's flow these extras will help ensure no point goes unmentioned. The Try This! option gives immediate extra exercises too. As I mentioned, listed objectives are so useful. Students need to know what they are expected to learn from any given lesson. This book helps increase student success by having multiple application problems from the get go so students can become comfortable with word problems--well as comfortable as developmental math students usually become. Also, exercise summaries have problems split by topic so students can easily find which examples of problems they need to work on. And there are a ton of homework problems for both the students and the instructor. this is a nice book that can easily be adapted to fit many needs. I appreciate all the effort John Redden put into this textbook--especially as an OER book. If you are new to OER, give John Redden a try. I suspect he will make you a fan.

## Table of Contents

- Chapter 1: Algebra Fundamentals
- Chapter 2: Graphing Functions and Inequalities
- Chapter 3: Solving Linear Systems
- Chapter 4: Polynomial and Rational Functions
- Chapter 5: Radical Functions and Equations
- Chapter 6: Solving Equations and Inequalities
- Chapter 7: Exponential and Logarithmic Functions
- Chapter 8: Conic Sections
- Chapter 9: Sequences, Series, and the Binomial Theorem

## Ancillary Material

## About the Book

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines.

Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines.

Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged.

*Intermediate Algebra* is written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success.

A more modernized element, embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. Therefore, this text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today.

The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.

## About the Contributors

### Author

**John Redden **earned his bachelor’s and master’s degree at California State University of Northridge. Before this he earned an associate’s degree at Glendale Community College and is now a professor of mathematics at the College of the Sequoias located in Visalia, California. With over a decade of experience working with students to develop their algebra skills, he knows just where students struggle and how to present complex techniques in more understandable ways. His student friendly and common sense approach carries over to his writing of Elementary Algebra and various other open source learning resources.