Preface

About Your Guide to Intermediate Algebra

This text is disseminated via the Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org(opens in new window)) and like the hundreds of other texts available within this powerful platform, it is freely available for reading, printing and "consuming." Most, but not all, pages in the library have licenses that may allow individuals to make changes, save, and print this book. Carefully consult the applicable license(s) before pursuing such effects.  This particular text was created through remixing two texts available through creative commons licenses -- OpenStax Intermediate Algebra and David Arnold's Intermediate Algebra -- as well as the addition of certain sections as needed.

Instructors can adopt existing LibreTexts texts or Remix them to quickly build course-specific resources to meet the needs of their students. Unlike traditional textbooks, LibreTexts’ web based origins allow powerful integration of advanced features and new technologies to support learning. 

Pedagogical Philosophy and Structure

One of the biggest goals behind this text was to help students increase their confidence in their ability to learn and understand the concepts necessary to be successful in future courses.  We note that more often than not, intermediate algebra is not a terminal course for students, so it is critical that not only do they leave the course with a solid foundation in the concepts necessary to be successful, but also that they have the confidence to explore and wrestle with the concepts they will see in future math courses. 

With this in mind, each learning objective and concept has multiple examples associated to it that increase in complexity, and the exercises for each section correspond directly to objectives and examples in that section.  Moreover, the answers to ALL exercises are contained just below each exercise, so as to encourage students to check their own work after each problem and gauge their own understanding as they practice.

We believe in approaching concepts in multiple ways to help students gain a variety of perspectives and problem solving techniques.  Because of this, heavy emphasis is also placed on visual understanding of each concept, with the structure of the text being centered on the graphs of different types of functions that students may encounter.  

Learning Objectives

Since the goal of this text is designed to present material tailored to the needs of intermediate algebra students, heavy emphasis is placed on core student learning objectives, or SLO's.  Since this text was created with a course offered at a Kansas university in mind, our SLO's are heavily based on those required in the state of Kansas, but should be universal enough to be easily adapted or further remixed for use at other universities.

Our SLO's and corresponding sections are as follows:

1. Demonstrate the ability to perform arithmetic and algebraic manipulation by
   1. Factoring expressions completely using various techniques  (Section 1.2)
   2. Performing addition, subtraction, multiplication, and division on rational expressions  (Section 1.2)
   3. Simplifying compound fractions  (Section 1.2)
   4. Applying the laws of exponents to simplify expressions containing rational exponents (Section 1.6)
   5. Applying the laws of radicals to perform addition, subtraction, and multiplication on expressions involving radicals and rationalizing denominators containing radicals  (Section 5.1)
   6. Simplifying radicals containing negative radicands and performing arithmetic operations on complex numbers  (Section 4.3)
   7. Evaluating functions using function notation  (Section 2.1)
2. Solve equations and inequalities
   1. Solve linear equations in one variable  (Section 1.4, Section 3.1)
   2. Solve linear inequalities in one variable showing solutions both on the real number line, in interval notation, and in set-builder notation  (Section 1.5)
   3. Solve literal equations  (Section 1.4)
   4. Solve systems of equations in two variables  (Section 5.7)
   5. Solve equations by factoring and quadratic formula  (Section 4.4; Section 4.5)
   6. Solve equations containing rational expressions  (Section 5.6)
   7. Solve equations involving radicals  (Section 5.2)
   8. Develop and solve mathematical models such as variation, mixture, motion, work and geometrical applications  (Section 5.8)
3. Produce graphs on a coordinate plane by
   1. Graphing linear equations and inequalities  (Section 3.2)
   2. Graphing functions, including linear and quadratic  (Section 2.4, Section 3.2, Section 4.2)
4. Analyze equations and graphs to
   1. Determine an equation of a line given sufficient information such as point and slope, two points, point and a perpendicular/parallel line (Section 3.2 - Section 3.5)
   2. Calculate the distance between two points (Section 2.2)
   3. Distinguish between functions and relations using the Vertical Line Test  (Section 2.3)
   4. Identify the domain and range of a function  (Section 2.1, Section 2.3)

Errata

This text was released for use in Fall 2022, and is continually undergoing improvements and updates to better serve students and instructors working with intermediate algebra.  There are without doubt errors contained in the text.  To suggest corrections or improvements, please reach out to intermediatealgebra010@gmail.com(opens in new window).

Contributing Authors

Stanislav A. Trunov, Kansas State University

Elizabeth J. Hale, Kansas State University

Acknowledgements

Stanislav and Elizabeth would like to thank Dr. Andrew Bennett, department chair of the Kansas State University Department of Mathematics, for suggesting and supporting this work.

This work was supported by the Open/Alternative Textbook Initiative at Kansas State University.