Week 35

Algebra II will be doing some exploration of rational functions from The College Board. One is intended to review their prior knowledge of rational functions and apply it to solve a problem. The other is a review of polynomials applied to running a business and analyzing profit, revenue, and cost. I hope they enjoy it!! See the graph at right from the Rodale Institute explanation of effective pricing.

As promised, I have included a fourth quarter bonus project that allows interested students to get credit as well as learn some of the basics of computer programming using MIT's Scratch. Here is a on all aspects of the program as well as a wiki hosted by scratch that contains examples for blocks of code. Please find the project outline attached below. If you have any further questions just e-mail me!


Algebra II and Precalculus both have exams on Monday!!! Please take some time this weekend to prepare. Use the information on the blog from previous posts to help guide your studies.

Algebra II review packet:


The homework for this week is solving rational equations, which will help you review all the basic operations involved with rational expressions as well as solve them.


Precalculus is reviewing for finals and getting geared up for a strong finish. The link below are some self-practice tests on the topics we covered this year. There are alse paper and pencil tests that have keys as well if you don't want to stay online to take the web-based exams.

Practice Exams, 1
Practice Exams, 2
Practice Exams, 3

 Here are two previous exams from early in the year to start reviewing!

Week 34

Precalculus will be exploring the law of sines and cosines and working through the ever challenging "ambiguous case" for law of sines. To review trigonometry for the upcoming exam try this online set of tutorials and practice or this set of videos. Let me know if it helps!

Homework with odd answers:*

Bonus:
Khan Academy



Algebra II is moving from operations with rational expressions to solving rational equations. We will again apply all modalities to solve these equations: numeric, graphic, and algebraic. It is important to be able move between these modalities and use each to help you solve the more difficult problems.

Examples for Simplifying Complex Rational Expressions:


Videos of the Week:
Adding and Subtracting Rational Expressions 1
Adding and Subtracting Rational Expressions 2
Adding and Subtracting Rational Expressions 3
Solving Rational Equations 1
Solving Rational Equations 2
Solving Rational Equations 3

Reference Sheets:



Homework* with odd answers:



*Modified from University of Houston

Week 33

First and foremost, have a great Spring Break. I know I will.

Secondly, take this extended time to do some work on Khan Academy. It is an excellent tool for you to practice and prepare for finals. In addition, you can take your math skills to new heights and new topics. Enjoy.

Algebra II is moving into basic operations with rational functions. As always, the basics of multiplication, division, addition, and subtraction of fractions comes back to haunt us all. I think the reference sheet for this one could be of real help to keep you organized, focused, and always pointed in the right direction.






Reference Sheet:


Completed Notes on Adding and Subtracting Rational Expressions:


Operations with Rational Expressions Videos:
Multiplying and Dividing Rational Expressions 1
Multiplying and Dividing Rational Expressions 2
Multiplying and Dividing Rational Expressions 3
Adding and Subtracting Rational Expressions 1
Adding and Subtracting Rational Expressions 2
Adding and Subtracting Rational Expressions 3


Homework (with odd solutions):

Final Review Packets:



Precalculus will graph the other 4 trigonometric functions with all their pecularities and nuances. I highly recommend watching some of the videos I have posted below. Remember to pause and rewatch them to get a true idea of how these functions behave.

Cosecant	Secant	Cotangent

Graphing Trigonometric Functions Videos:
Graphs of Trig Functions
Graphing Trig Functions
More Trig Graphs
Determining an equation of a trig graph

Homework:


Final Review Packets:

Week 32

Algebra 2 finalizes their investigation and construction of the graphs of rational functions. It is absolutely essential to make the connection between the algebraic manipulations and understandings of these functions and their graphs. I will be away from school both Thursday and Friday of next week trying to learn how to better use the SmartBoard (you know I need that). Remember to take advantage of the exercise practice at www.khanacademy.org. Please find a rather complicated rational function below. The steps to graphing it can be found here.

Graphing Rational Functions Powerpoint:


Operations with Rational Expressions Guided Notes:



Reference Sheets:




Rational Function Videos:
Asymptotes of Rational Functions
Rational Function Example
Another Rational Function Example!


Homework with odd solutions:


Final Review Packets:



Precalculus is going to continue with sine and cosine functions in the attempt at mastering all the different transformations that result in changes in amplitude, vertical shift, phase shift and period. The change in one parameter, amplitude, is captured in the image below:

Applet:
Transformations of sine functions



Khan Academy videos:
Graphs of trigonometric functions
More graphs of trig functions!

Precalculus Homework:


Final Review Packets:

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!

Week 29

Algebra II will begin to reverse the flow on polynomials. We have been driving from the algebraic to the graphic, and now we will start with the graphic and drive toward the algebraic. It should be both fascinating and mind-blowing. Here is the summary of the week in two pages!


BTW: Answers for

We will continue to plough through our guided notes. I have placed the notes from the previous weeks below.
Blank Note Guide:

Completed Note Guides:












Polynomial Notes Supplement:
Polynomial Note Guide, part 14 (this week)

Polynomial Note Guide, part 15 (this week)


Homework with odd answers:


__________________________________________________________
Precalculus will do a brief unit on trigonometric identities before heading into trigonometric ratios as functions. Please don't forget the development of the unit circle as we take a slight detour through identities.



Guided Notes:
Trigonometric Identities

Trigonometric Functions

Homework:

__________________________________________________________
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!

Week 28

Algebra II will continue investigating polynomials and fully merge the graphical with the algebraic. It should be exciting. Please remember to bring your graphing calculators to class everyday. We are going to rely on them an increasing amount from her to the end of the unit. This coming Thursday we will have an exam in order to break up this large unit a bit. Reference sheets will be able to be used!

Blank Polynomial Notes:


Completed Polynomial Notes from previous weeks:












Polynomial Notes Supplement


Reference Sheets:




Videos on Polynomials
Polynomials, part I
Polynomials, part II
Imaginary Numbers

Algebra II HW with odd answers

_________________________________________________________________

Precalculus will be continuing their work with the unit circle and increasing their level of comfort with it. By the end of next week we will begin to develop the idea of a trigonometric function through our new unit circle informed eyes. It should be awesome, really!
Reflect on the following widget--it is the whole of trigonometry.





Unit Circle Notes:


Trigonometric Identities Notes:


Homework:


Trigonometry Videos:
Trigonometry

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 screan 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!