Intermediate Algebra Course Outline

Below you will find the topics for Intermediate Algebra as published by College of the Sequoias in their course outline:

Intermediate Algebra (Algebra II)

COURSE TOPICS:
Absolute Value Equations and Inequalities

• Solve absolute value equations and inequalities

Radical Expressions and Equations

• Properties of radicals
• Rational exponents
• Simplify radical expressions
• Operations with radicals
• Solve radical equations
• Solve radical equations which come from real-world applications
• Operations with complex numbers

Quadratic Equations

• Solve quadratic equations using factoring, extracting roots, completing the square, and quadratic formula
• Solve applications (for example: max/min problems)
• Graph quadratic equations
• Solve quadratic and rational inequalities
• Solve equations that are quadratic in form

Functions

• Understand and apply the definition of a function
• Function notation
• Apply the vertical and horizontal line tests
• Graph and determine the domain and range of the core functions
• Evaluate and apply the algebra of functions including addition, subtraction, multiplication, division, and composition
• Find the inverse of core functions

Logarithmic and Exponential Functions

• Graph logarithmic and exponential functions
• Apply the properties of logarithmic functions
• Solve logarithmic and exponential equations
• Solve applications of logarithmic and exponential functions including exponential growth and decay, pH, compound and continuous interest, carbon dating, half-life, and earthquake magnitudes

Conic Sections

• Apply the midpoint and distance formulas
• Convert the following conic sections into standard form by completing the square: parabolas, circles, ellipses, and hyperbolas
• Identify and graph the following conic sections: parabolas, circles, ellipses, and hyperbolas

Optional Topics

• Solve 3X3 systems of linear equations
• Solve nonlinear systems of equations

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Elementary Algebra Course Outline

Below you will find the topics for Elementary Algebra as published by College of the Sequoias in their course outline:

Elementary Algebra (Algebra 1)

COURSE TOPICS:

Numbers and Sets

• Set or interval notation
• The number line
• Arithmetic and algebraic operations of basic math symbols
• Order of operations
• Simplifying algebraic expressions

Solving Linear Equations and Inequalities

• Solving linear equations
• Evaluating and solving formulas
• Solving single variable word problems
• Solving linear inequalities

Graphing Linear Equations

• Graphing linear equations
• Slope and intercepts
• Find equations of lines
• Parallel and perpendicular lines
• Graphing linear inequalities in two variables

Systems of Linear Equations & Problem Solving

• Solving by graphing, substitution, and addition methods
• Solving applications
• Graphing systems of linear inequalities

Exponents and Polynomials

• Rules of exponents
• Negative exponents
• Scientific notation
• Addition, subtraction, multiplication, and division of polynomials

Factoring

• Greatest common factor
• Trinomials
• Difference of squares
• Difference and sum of cubes
• Factoring by grouping
• Solving polynomial equations by factoring including applications

Operations and Rational Expressions

• Simplification of rational expressions
• Addition, subtraction, multiplication, and division of rational expressions
• Complex rational expressions
• Solving rational equations with applications
• Solving rational literal equations for a given variable

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My Three Favorite Things...

Check out my guest blog on the Flat World Knowledge website:

[  Teaching Algebra? An Instructor’s 3 Favorite Tips ]

Sample Algebra Tests

Sample chapter tests to accompany the online Elementary Algebra textbook published by Flat World Knowledge.

Sample Chapter Tests 

[ Sample Test Questions Chapter 1 ]

[ Sample Test Questions Chapter 2 ]

[ Sample Test Questions Chapter 3 ]

[ Sample Test Questions Chapter 4 ]

[ Sample Test Questions Chapter 5 ]

[ Sample Test Questions Chapter 6 ]

[ Sample Test Questions Chapter 7 ]

[ Sample Test Questions Chapter 8 ]

[ Sample Test Questions Chapter 9 ]

[ Sample Final Exam Ch. 1 - 7 ]

More worksheets can be found at the bottom of this page.

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Solving Linear Systems - Sample Intermediate Algebra Test Questions

Sample test questions for Intermediate Algebra - Chapter 3 - Solving Linear Systems have been posted.

[ Sample Test Questions Chapter 3 ]

Please feel free to use this worksheet or cut-and-paste anything you find here into your course. Below you will find the associated videos for this section. Click on a problem and watch it worked out on YouTube.

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Adopt One Open Textbook and Make a Difference

The passage of the Open Textbook bills in California is a significant development in the open educational resources (OER) space. We have been working on getting the word out as to the benefits of Open Textbooks for some time now. However, when the largest higher education system in the US takes action like this – folks will take notice. In fact, I think this news could be the “tipping point” for an Open Textbook revolution.

Consider the $172 cost of the new edition of one of the top selling algebra books for one of our highest enrolled mathematics courses - Algebra. Now consider that I have over 40 students in each of my 3 sections - that is over 120 students:

$172 x 120 students = $20,640

This is a lot of money for one instructor's one semester of Algebra - now scale this up to the over 340,000 Algebra students in California and you start to see the significant amounts of money involved here!  Here is an info-graphic made by the 20 Million Minds Foundation and an open textbook savings calculator. I like to say that adopting an open textbook is like your very own local stimulus plan!

http://www.20mm.org/infographic-open-source-impact.html 

Now some might argue that the top selling textbook is better for any number of reasons... and yes it might be.  But we have to start considering student cost in our decisions to adopt.  

Is it $172 better?

Is it $100 better?

Is it $50 better?

Is it $25 better?

Can I supplement any shortcomings?

Do I have the time to make change?

I happen to think the 21st century college instructor will use a LMS to aggregate OER as a means to present a course that leverages his/her expertise. High quality modular Open Textbooks and resources are the key. Modifying open textbooks, collecting good content and building courses is time consuming. However, the benefits in course relevance and cost far outweigh any upfront effort. New editions are totally up to you and not a product of the bottom line!

We need to take the “all of the above” approach to addressing the soaring costs of education. These bills may not solve the cost issue overnight - but they sure bring the $200 textbook problem into laser focus. I truly hope the use of Open Textbooks tips - where more faculty and students become aware of their viability. 

Instructor Challenge: Start by adopting one open textbook for next semester. They are hard to find, modify, and supplement.  Some links are provided below that might help. Join the OER community:

 http://collegeopentextbooks.ning.com/

Students Challenge: Start by searching out open textbooks and send the links to your instructors.  Sign the petition. This will be your legacy to those who come after you.

My Viable Math Textbook Links

College Open Textbooks: http://www.collegeopentextbooks.org/

Merlot OER repository: http://www.merlot.org/merlot/index.htm

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Algebra Video Help

Our collection of Algebra videos to accompany our Elementary and Intermediate Algebra textbooks is complete.  So far we have over 60,000 views with a definite uptrend.  From the many comments, it is clear that the short and to the point approach is much appreciated!

These videos are embedded in the FREE to read online textbooks. In addition, you can choose the appropriate course below and then visually search the problems. Click on a problem that seems similar and you will be redirected to a video solution on YouTube.

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Elementary Algebra -- Visually searchable YouTube playlist. 

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Intermediate Algebra -- Visually searchable YouTube playlist. 

If a video helps you... please comment or push the like button.  If you are an instructor, feel free to copy-and-paste these links into your LMS.

Intermediate Algebra Textbook

Dear Colleagues,

I am excited to announce that Flat World Knowledge (FWK) has just published a new textbook, Intermediate Algebra.

In order to combat soaring textbook prices, I have written this textbook in a modular fashion to maximize its effectiveness as an open educational resource. It is available under a creative commons license, has been thoroughly peer-reviewed, and is customizable using the “Make It Your Own” MIYO system. This textbook is the second part of a two-part course in Algebra. It builds on the skills learned in Elementary Algebra and blends the traditional and graphical approaches to the subject.

• 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

Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems.  In addition, students might appreciate the embedded video examples.

I am happy to be a part of the solution to the current rising costs associated with one of our essential developmental math courses.  Compare this textbook to other open source algebra projects and you will find that FWK did a great job. The free to read online version makes use of MathJax and images to present the material where the Firefox web browser is recommended.  In addition, the e-textbook and printed versions are available for purchase through the Flat World Knowledge website.

Please feel free to distribute this link to your students and colleagues.  I truly believe that it will be a valuable resource.  Also, feel free to email me with any suggestions or ideas.

Thank You,
John Redden, Professor of Mathematics
johnr@cos.edu
jtredden@gmail.com
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Intermediate Algebra Sample Test Questions

I have added two worksheets that are to accompany the free to read online Intermediate Algebra textbook.

[ Algebra Fundamentals - Chapter 1 ]

[ Graphing Functions and Inequalities - Chapter 2 ]

Remember that you can find a complete list of visually searchable videos that accompany these chapters by clicking the link below.

Intermediate Algebra -- Visually searchable YouTube playlist. 

Instructors: You can find more worksheets by clicking the Intermediate Algebra Textbook link on this site. Please feel free to cut-and-paste anything you find here into your course.

#Open Textbook Tweet

A quick read by Sharyn Fizpatrick on the what and why of open textbooks.

[ e-version on WikiEducator ]

Algebra eBook on Google Play

It took a while... but we were able to get our Free Algebra Study Guide onto the Google Play bookstore.  The basic steps were to:

  1. Create the e-book in the .epub format. We used the open WYSIWYG ebook editor Sigil.
  2. Create a Google Books Partnership Account.
  3. Follow the instructions for submission EXACTLY and set your price.

The Google Play e-reader is actually very nice. You can seamlessly read the study guide on many different devices.  The epub format allows for reflowable text.  Please feel free to download the book and study the mark-up in Sigil.

Doing this was a fun exercise and I hope the guide might help some folks.
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Algebra Video Collection

My algebra video collection is almost complete.

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Elementary Algebra -- Visually searchable YouTube playlist. 

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Intermediate Algebra -- Visually searchable YouTube playlist. 

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Please feel free to cut and paste from Blogger directly into Blackboard or any other CMS.

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Free Algebra Study Guide

A free algebra study guide can be found on this website. You will need an ePub reader.

Over 1,100 solved problems and over 300 video examples.  Feel free to share the link!

Algebra Solving Worksheets

Solving is a very important skill to learn in any algebra course. The ability to solve a variety of different types of equations and inequalities takes time and practice to master.  Below are some worksheets that will help master these skills

[ Ch. 2 Solving Linear Equations ]
[ Ch. 2 Solving Linear Inequalities ]
[ Ch. 6 Solve Quadratic Equations by Factoring ]
[ Ch. 7 Solving Rational Equations ]
[ Ch. 8 Solving Radical Equations ]

If you are an instructor, please feel free to use these worksheets in your algebra course. More supplementary material can be found on our Elementary Algebra Textbook page.

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Elementary Algebra has a Google+ Page

Elementary Algebra now has a Google+ page:

While you are there... add the mathematics circle and join the conversation.

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Algebra: Solving Quadratic Equations and Graphing Parabolas (Study Guide)

Chapter 9: Quadratic Equations

Extra video examples to accompany Elementary Algebra - the free to read online open textbook published by Flat World Knowledge.

9.1 Extracting Square Roots

9.2 Completing the Square
 

9.3 Quadratic Formula

9.4 Guidelines for Solving Quadratic Equations and Applications

9.5 Graphing Parabolas

9.6 Introduction to Complex Numbers and Complex Solutions

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