Monday, December 5, 2011

Open Precalculus Textbook

I am almost through my first semester using the following open source Precalculus textbook:

It covered all of the topics that I needed without supplementation and the students liked its readability... and of course the cost. I especially liked the continuing coverage of inequalities and heavy use of sign charts throughout. The pdf is well produced and easy to navigate using the linked TOC. Buying a printed copy was easy and the quality was good -- the Trigonometry portion is printed separately.

I will definitely use it again and I recommend it to anyone teaching this course.


Saturday, December 3, 2011

Sample Algebra Test Questions

Sample exam questions for Elementary Algebra chapters 1 - 7. These are pdf files stored in google docs.

Ch. 1 - Real Numbers and Their Operations
Ch. 2 - Linear Equations and Inequalities
Ch. 3 - Graphing Lines
Ch. 4 - Solving Linear Systems
Ch. 5 - Polynomials and Their Operations
Ch. 6 - Factoring and Solving by Factoring
Ch. 7 - Rational Expressions and Equations

You can use these to study for the final exam.


Friday, December 2, 2011

Solving Rational Equations in Beginning Algebra

A thorough explanation for solving rational equations can be read for free in the Elementary Algebra textbook that is available on the Flat World Knowledge website:

Also, you can click on the following rational equation to watch a video solution.

The basic steps for solving these equations are as follows:

Step 1: Factor all denominators and determine the LCD.
Step 2: Identify the restrictions. 
Step 3: Multiply both sides of the equation by the LCD. Distribute carefully and then simplify.
Step 4: Solve the resulting equation. 
Step 5: Check for extraneous solutions.

The complete solution is presented below:

Basically, we multiply both sides of the equation by the LCD as a means to clear the fractions.  This introduces the possibility for extraneous solutions and so we must check our answers.  Look for more Chapter 7 videos here.

Thursday, December 1, 2011

Elementary Algebra (Ch. 9) Solving Quadratic Equations and Graphing Parabolas

Elementary Algebra is an open textbook that is available to read for free on the flatworld knowledge website. Chapter 9 gives an introduction to solving general quadratic equations and graphing quadratic functions. In addition, complex numbers and complex solutions are covered.

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

You will find a complete review exercise section and a practice test.

9.7 Review Exercises and Sample Exam

Feel free to copy and paste the links found here and post them in your LMS. Links to all of the chapters can be found by clicking the Elementary Algebra course button at the top of this page.