Unit 4 review

Here are some hints for the Unit 4 Practice Test (which you should get in support, and it counts as a quiz grade), and some recent class notes from my 4A and 4B:

Unit 3 test review - hints and help.

As you know, the test is Thursday/Friday.

If you are in my 4A or 4B, I will accept your station papers on Friday, or when you finish your test. If you want to use the papers I already collected, just ask.

In support, you were given a review packet, as a quiz grade. I'm posting it here, with hints. This is not an answer key - I've just put enough to get you started on each question. If you're stuck or not quite getting something, this is for you.

Please ask questions on the GroupMe or in class (and support).

Note: I know some of you have made other arrangements for the quiz grade. I would still advise you to look through this, as I BASED IT ON THE TEST! Just sayin'.

Here's the first 8 pages, which has questions that might show up on your test, no matter whether you are in my class or in Ms. Meade / Ms. Talley's class.

Remember, you can download these images and zoom in on them - I am attaching them at full resolution.

And here is the 2nd section. Only the students in Ms. Meade / Ms.Talley's class have to do this, because they will need to know these skills, without using a calculator, for the test.

Students in my 4A and 4B will be allowed to use a graphing calculator. However, you are also perfectly welcome to  look through this and ask me questions - it will help you understand the math in a different way.

Unit 3

There are really only 2 main ideas in Unit 3:
(1) Finding ALL roots (solutions) of any polynomial, no matter how many. We've started this (see below).
(2) Graphing polynomial functions, and describing the graphs in certain mathematical ways. We'll get to this.

For finding the roots, you must be able to:

[1] Use the Rational Root Theorem to list all the POSSIBLE roots that are either whole numbers or simple fractions (so, without square roots or i's).

[2] Use the graphing calculator ([y=], [graph], and [2nd][graph] for the table) to figure out which of the POSSIBLE whole number roots actually ARE roots.

[3] Use Synthetic Division (from Unit 2) to divide the original long polynomial by the roots you know, to reduce it down to a quadratic.

[4] Solve the quadratic that's left, using factoring or the Quadratic Formula (we learned how to do this in Unit 1).

[*] Putting all those steps together, we can take a polynomial with 3, 4, or even more roots, and get ALL of the roots.

[*] Here are some additional examples of synthetic division, that we did in support Monday/Tuesday.

This might help for the Unit 2 test ...

Reference Flow Chart for Polynomial Identities:

Answer Key for the Review Pages (PURPLE - my 4A and 4B test will look similar to this) :
PART 1

PART 2

PART 3

PART 4

Answer Key for the Review Pages (YELLOW -Ms. Meade/Ms. Talley's test will look similar to this):
PART 1

 PART 2

 PART 3

 PART 4

Composition and Inverses - last new stuff for the test.

Notes from Thursday and Friday (10/8 and 10/9):

Review examples for test

The test is coming up next week (Thursday or Friday).

Here are some example problems:

 

 

 

Polynomial DIVISION

We have two methods for dividing polynomials:

(1) Long division. Long (like the name), takes time, and is kind of hard. But it's the ONLY method that works if you are dividing by ax+b, where a is ANYTHING besides =1.

Long division is shown on the left examples in the picture here.

(2) Synthetic division. Shorter, most people seem to find it easier. But it ONLY works if a=1 (dividing by x+b or x-b).

Synthetic division is shown on the right examples in the picture here. (click to enlarge)

Long Division Steps: 

1. Does                           Divide
2. McDonalds                 Multiply
3. Sell                             Subtract
4. Cheese                       Compare/check
5. Burgers?                     Bring down      then  Go back to step 1.

Synthetic Division Steps:  Bring Down 1st number.  Multiply, Add.  Multiply,Add; until done.

Review Polynomials for Quiz!

Y'all have a 4 day weekend. But as a reminder, there will be a review and then quiz on Monday or Tuesday after you get back. Here is what you need to know:

Classifying

Adding and Subtracting:

Multiplying:

 All 4 Identities!

Using Pascal's Triangle to expand polynomials (this is new):