Chapter 15 Review

Here is a copy of the Chapter 15 Test review.  All material for the chapter has been covered and nothing further will be added.

Here is the key to the review.  

Remember you can find the vertex by either completing the square or using -b/2a to find the x coordinate.  You find the y coordinate by plugging in the x value to the equation.

For interval of increase and decrease, follow the following.

Quadratic function: f(x) = ax² + bx + c 

First we find x-coordinate for vertex: x = -b/(2a) 

If a < 0, then we have a parabola that opens down 

So  the vertex is a maximum point 

Function increases on interval (-∞, -b/(2a)) 

Function decreases on interval (-b/(2a), ∞) 

If a > 0, then we have a parabola that opens up 

So the vertex is a minimum point 

Function decreases on interval (-∞, -b/(2a)) 

Function increases on interval (-b/(2a), ∞)

Remember you can find the vertex by doing -b/2a to find the x coordiante.  Then 

plug in the x value to find the corresponding y value.  Your axis of symmetery is 

x=-b/2a.  

Today we are working on functions written in both vertex and standard form.  There are a lot of elements to identify so the following worksheet should help you with that.  Quiz over sections 1 and 2 will be on Thursday.

Homework is on page 498 5,7,21,23,25.  Locate the vertex and then apply the value of the coefficient in front of x.  

All about Factoring

Factoring, factoring, factoring....if you do page 488 1-12 all, 14-25 all, and 27-32 all, you should be good to go.  if you want to see if you're ready, then look at page 489 1-8 all.   I'll try to add some links later.

Okay....angles associated with circles.   Remember, vertex inside add and take half, vertex outside subtract and take half, vertex on...just take half.  Here is a website with some example problems.

How about simplifying radicals?  If you need help, go here.  If you go there, make sure and check out the second page by clicking the link to "second level" down at the bottom.

Looking for help on complex numbers?  Go here.

Here is a website that might help you with multiplying and dividing complex numbers.  Don't forget to spend some time with angles and segments related to circles.  Remember, vertex inside...add and take half, vertex outside...subtract and take half, vertex on...just take half.  I'll add more in a bit.  Hope the website helps.  This website will be updated repeatedly over the course of the weekend so make sure and check back.

Reviewing for Unit 13

Test for Unit 13 will be on Monday.  Here is a review to start working on.
Test Review

HW for our first day back after snowzilla!  Quiz tomorrow...should be fun!

Live Eagle Cam for when you finish your homework.

Notes for 13.1
We will be starting an investigation of complex numbers now as we work our way towards solving quadratic equations.  Complex numbers are involved in the development of fractals.  They are also used in navigation.  The test over this unit as well as segments and angles related to circles will be next Friday.

Worksheet over other angles for homework 1/27
Today, we are looking at other angles related to circles.  We will be looking at angles formed by secants, tangents, and chords and examining their relationship with their intercepted arcs.

Work from class today.  Hope this helps prompt you on the concepts for the Unit 11 and 12 Test on Friday.

One thing that's left off of the sheet above is the relationship between opposite angles in an inscribed quadrilateral.  Remember the opposite angles are going to be supplementary aka add up to 180 degrees.  Let me know if you have questions and don't miss the review below in the previous post!

Here is the review for Unit 12 and the test on circles.
Test Review

Make sure you can name all of the elements associated with a circle.
Radius          Secant          Chord
Diameter      Tangent         Inscribed Angle
Central Angle

Know the equations for both area and circumference for a circle
Area=Pi*r^2
Circumferenc=Pi*d

Know the volume equations for shapes with 2 bases
V=Ba*h
For either a cone or a pyramid
V=1/3(Ba*h)

THE TEST WILL BE ON FRIDAY.  TAKE TIME TO LOOK OVER THESE CONCEPTS ALONG WITH THE EXAMPLE PROBLEMS.

The test over Circles will be moved to Wednesday of next week.  Unit 12 Notes can be found here.

If you want to experiment with the online spirograph maker, click here.

Here are the notes from class today.

Here are the answers to the volume worksheet.  For the octagonal prism, you have to make a rt. triangle on the octagon by drawing an apothem.  The angle in the corner is 67.5 and half of the base will be 5.  Once you find the apothem, it's 1/2bh*8 to find the area where b=10 and h is the apothem.  Remember, you have to multiply the area of the octagon by the height to find volume.  Hope this helps!

Remember, to find the area of a regular polygon other than a hexagon, square, or equilateral triangle...find the area of one of the triangles within the shape by finding the base and height.  How do we find the base and height?  You will have to rely on your old friend...the trig ratios.  I'll enclose a link for you to review those if you feel a bit fuzzy about them.  Let me know if you have any questions and we will quiz on Monday over this.

Trig Ratios

If you're dealing with a hexagon, square, or equilateral triangle, you might need to use the properties of the special right triangles.  Here is the relationship again, in case you don't have access to it in your notes.

Special right triangle templates

I have been sharing with you my appreciation for the art form of fractals, a mathematical creation that can be incorporated into graphic design.  If you'd like to explore a site dedicated to artists that use this medium, click the image below.

Think we're so advanced?  Eratosthenes discovered the circumference of the earth using a stick in Ancient Alexandria.

We spent a lot of time talking about the proper tool one would need in order to find the measures needed to find the area of a triangle within a regular polygon.  Remember that SOH-CAH-TOA is a great tool for finding a measure in a right triangle if you have a  side and an angle so regardless which measure they give you, you should be able to set up a trig equation to find a missing measure.  I'm looking forward to sharing information on here with you this semester.  If you get an opportunity, go ahead and start on the worksheets in the packet handed out in class today.  Let's see who read the blog page tomorrow!  We will review the volume equations tomorrow for objects with one or two bases tomorrow.  

We begin 2nd semester by talking about circles.  There is a lot to talk about as there are angles, segments, and areas that we can find the measures for.  I have included a couple of images that I hope will help you get started along with some links. Click on the images to enlarge them. Also, tutoring is available in the mornings on the following schedule for the 1st 6 weeks of the semester.

	Tuesday	Thursday
Morning 6:45-7:10	Mr. Yike 1.606	Coach Brundage 1.633
Afternoon 2:15-2:45	Mrs. Taube 1.595	Mrs. Hunsucker 1.620

Here are a few links that I've found over the years that might be of use to you.

Major vs. Minor arcs

What is an intercepted arc?  Interactive with examples

Concepts related to inscribed angles

Angles formed by secants and tangents and their measures

Theorems about segments formed by intersecting chords

Theorems about segments formed by intersecting secants

History of Pi

We will be testing over this material on Friday, January 17th.