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!

Week 27

Algebra II will continue with our examination of polynomial functions, and start to integrate the algebraic, tabular/numeric, and graphical dimensions more directly. Please find a two summary documents on polynomials below that will help us structure the conversation in a concise user-friendly way.

Factoring a Polynomial Using its Graph


Finding Zeros of Polynomials


Polynomial Guided Notes:


Completed Polynomial Notes in the previous week:








Completed Polynomial Notes for this week:
Polynomial Note Guide, part 9

Polynomial Note Guide, part 10

Polynomial Note Guide, part 11


Homework with odd answers:


Saturday School work:


Links to videos on Polynomials
Polynomials, Part I
Polynomials, Part II
_________________________________________________________________

Precalculus will start to build the unit circle and develop their concept of trigonometric ratios beyond that of 180 degrees. This will serve as the building block for our transition to trigonometric functions.



Radians, arc length, and the area of a sector:


Central angles, arcs, and angular velocity


Unit Circle Notes:


Precalculus HW:


Precalculus Saturday School:


Precalculus videos on TRIGONOMETRY