Week 31

Fourth Quarter is now here. Your grade from the first three quarters cannot be changed--the only thing you can control, as a student, is your grade fourth quarter. Please, scholars, do thy best to finish strong. A great way to keep your basic skills up as we move through fourth quarter and prepare thyself for finals is to login at www.khanacademy.org and keep marching through the exercises.

*For Parents: I added an e-mail subscription to the sidebar so that you can receive an e-mail everytime the blog is updated. Just type your e-mail in and follow the steps that follow. It should take about 20 seconds.

Algebra II begins rational functions, which are graphically somewhat different than previous functions, but they nevertheless require a great deal of the skills we have been building all year. Factoring fun will remain a large part of our life. Here are two graphical examples of rational functions:


To explore the graphs of rational functions try this applet.

Videos:
Rational Expressions and Functions, part I
Rational Expressions and Functions, part II

Rational Functions Blank Note Guide and Graphing Powerpoint:



Reference Sheet:




Homework:


Saturday School:


Precalculus is ending the year with a bang. We are investigating the graphs of the six trigonometric functions and the unique types of behavior they can model. The coming week we will start with graphing sin(x), cos(x), and possibly tan(x). We will be relying on a curriculum that can be found online here. Here is a graph of sin(x):

To explore transformations of sine functions try this applet.

Videos:
Trigonometry Videos

Homework:


Saturday School:

Week 30

The Abel prize was awarded last week to John Milnor for his work in topology. It is an annual prize that recognizes innovative thinkers in mathematics and comes with a $1,000,000 award. The two-dimensional picture of a seven-dimensional sphere below demonstrates some of the work for which Milnor was recognized.

Algebra II's month long journey deep into the heart of polynomials is coming to an end this Thursday. Please find the test review posted below. We will be completing this in class on Tuesday and Wednesday--answers are at the end of this document! The exam will be answering some essential questions about polynomials, which will only be posted here for your perusal--start thinking.

1. How many max's or min's could an even degrees polynomial have? How few can it have?
2. Could a polynomial have two max's, but no local minimums?
3. If a polynomial has two max's and two min's, can it be of odd degree? can it be of even degree?
4. Can a polynomial have local max's or min's without having any real zeros?
5. Why must every polynomial of odd degree have at least one real zero?
6. Can a polynomial have two distinct real zeros and no local max's or min's?
7. Can an x-intercept yield a local max or min? Can it yield an absolute max or min?
8. If the y-intercept yields is the lowest point the polynomial reaches, what can we say about the degree of the polynomial and the sign of the leading coefficient?

Test Review

Homework:

Saturday School 5.2:

Precalculus will finish with solving trigonometric equations and have an exam over basic trig identities, the unit circle, and trigonometric equations! The homework is short this week, but be diligent. Exam Thursday!!

__________________________________________________________
BONUS ASSIGNMENT FOR ALL-
Step 1: Go to www.khanacademy.org
Step 2: Login with a gmail account or a facebook account
Step 3: Once your logged in, at the bottom of the screen is a link to "Add a Coach"--click it!
Step 4. Add me as your coach! My ID is my e-mail address is darren.burris@gmail.com
Start with addition and advance!