May 26th

Hello,

Today Mr Max started off the class my explaining that there is no accelerated math deadline for this weeks Friday. There will be a deadline for all accelerated math to be done though so keep working hard on it..

After hearing that good news, Mr Max continued into a new unit of Geometric Sequences. First of all he described to us what a geometric sequence was. He did this by explaining what they were recursively and explicitly.. see the below slide for more info

If this doesn't make sense to you.. it is just that a geometric sequence is a line of numbers that are generated by multiplying the previous number by a common ratio. For example, take a gander at the slide below and it should help you out.

By this time in my post I am starting to become extremely irritable because stupid blogger doesn't put my pictures where I want them.. or in the right order.

Anyways, the next three slides are perfect examples of what the formulas are, what each variable means, how formulas are used to find each term in a geometric sequence, or how to find the rate at which you are multiplying them.

Below are three more slides of how to use the formulas that are given, in the proper way. Mr Max showed us how to take the question given and use all parts of it to set up ratios that helped solve the problem. As you can see.. you may need a calculator to do some of the arithmetic so beware.

So.. the assignment today is Exercise 45 #1-7.

Remember there is a homework check in the near future so be sure to have all of the cumulative exercises done!

Keep working hard on accelerated math.

Thanks,

(signature here)

Cramer

May 9th

Hello Pre Calc class,

Once again I am sorry for not getting up this post sooner. No excuses.. I forgot. On Friday we learned about hyperbola's. Mr. Max was teaching us the standard equations for hyperbolas and what exactly they look like.

Above we examined how to simplify the equations in order to find the values of A and B. Also known as the major axis and the minor axis. Once given the values of A and B you can also input the Domain and Range.
As Mr. Max said... some people may be able to just "eyeball" the graph of this hyperbola and be able to figure out what the equation for the asymptotes are. If you are having trouble doing this just remember RISE/RUN, and don't forget to give the equation the sign of "+" or "-" .
Above is how to find the equation of the asymptote mathematically. Also given below are the Standard Forms of the equations of hyperbolas. These will help you to know when the hyperbola opens up or down.

Remember that 49 mental math objectives are due this Friday.

April 24th

Howdy,

Sorry classmates... I had no idea that I was supposed to scribe on thursday but it won't happen again!

Thursday was a test day, due to postponement. Hope everyone did well on the test and got the bonus question right.

Reminder!! Accelerated Math Objectives up to 39 are due on MAY 2ND

April 9th

Fellow Classmates,

Well as I am sure you all have noticed, Mr Max is not present again today. I saw him briefly before class and he said the test is STILL ON for tomorrow.

Key points to remember while studying for the test...
5log(x^4) - 6log(x) - MAKE SURE YOU DIVIDE WHEN SUBTRACTION IS USED!
answer: 30 log ((x^4)/x)

5log(x^4) + 6log(x) - REMEMBER TO MULTIPLY WHEN ADDITION IS BEING USED!
answer: 30 log (x^4)(x)

Good luck on the test tomorrow..
Accelerated Math deadline next Friday - 30 objectives!

Thanks,
Cramer

P.S. Keep your elbows off the table

Graphmatica

best. program. ever.

Double Angle Identities

Hello class,

Sorry this post is a little late.. I never had time yesterday and today it took me awhile to upload images due to the sweet sun computers.

Anywho, today Mr. Maksymchuk continued on his journey to explain identities. Today we did some more work with double angle identities. As shown below, Mr. Max took all the equations given to us in our exam formula sheet and showed how they derived the formula. I found this part very helpful and makes learning identities easier to understand!

Another things that I found useful in today's lesson is to always keep in mind the key triangles that we learned at the start of the year. Also take not of a 30, 60, 90 triangle with lengths of 3, 4, and a hypotenuse of 5. Knowing these triangles will come in very handy.
In this picture below, they wanted to know the value of 2(theta). So Max simply input the values for theta into another formula from our exam formula sheet, and solved for cosine and sine. Always note the signs you apply to the final answer so you make sure you have it in the right quadrant.
Below is just another example of solving double angles using exact values. Remember to FACTOR out like terms!!!


Well this is the end of my post. Any questions or comments on how I can improve PLEASE let me know. Thank you for your time.

Remember!!! Always keep the stick on the ice.

Love Cramer

Idenities Example

I have decided to use an example of one Double Angle Identity, and on example of a Sum and Difference Identity..

1) Find the exact value of the following:
a. sin (π/12) =sin (π/3-π/4) = sin(π/3) cos(π/4) - cos(π/3) sin(π/4)
= (√3/2)(√2/2) - (1/2)(√2/2)
= (√6/4) - (√2/4)
final answer = (√6 - √4)/4

2) Solve for "x" where 0° ≤ x ≤ 360°

a. sin2(x) = sin(x)

2sin(x) cos(x) = sin(x)
2sin(x) cos(x) - sin(x) = 0
sin(x) (2cos(x) - 1) = 0

sin(x) = 0, therefore x = 0, 180, 360

2cos(x) - 1 = 0

cos (x) = 1/2, therefore x = 60, 300

February 29, 2008

Hello peers,



Today we were blessed to have Ms. Norman step in to keep us all in line, as Mr. Maksymchuk was away today. Ms. Norman informed us that today was to be a work period, simply for us to catch up on any assignment, work on accelerated math, and study for the upcoming test.



After learning how to use graphmatica this semester I have found it very helpful in learning more about graphing and visualizing the "a,b,c,d" values of a function. As helpful as this is I encourage all of you to try drawing the graphs on graph paper also as it will help you tremendously come exam time!



I have also been visiting the Ron Blond site and http://www.math40s.com/ to help me understand concepts and for help in the exercises.



Reminder!!! Accelerated Math is due March 12th so get on your horse and get those objectives done! As well as a TEST Wednesday March 5th!

Image idea courtesy of Lucas...

Remember your times tables, and keep your stick on the ice,

Cramer

Febuary 13th

Today in class Mr. Maksymchuk explained some more about the Unit Circle. He got us thinking in terms of sinΘ - referring to Y, cosΘ - referring to X, and tanΘ - X/Y. The class was also introduced to more radian measure and learning to think about what quadrants they apply to. While we were reviewing the unit circle we found it handy to think in proportional triangles to find the values for sin, cos, tan etc... We also talked about calculating cosecant, secant, and cotangent.

CscΘ=1/sinΘ, SecΘ=1/cosΘ, and CotΘ=Y/X.

This picture is continued from the picture above. Here we were just applying signs to values in terms of quadrants and the location of the coordinates.

This is a similar question to the one above where we discovered that Theta was in quadrant II because Sin > 0. Therefore sin is "+" and because tangent is a negative value, it cannot be quadrant one because X and Y are both positive.

Remember, here is todays assignment and there is tutoring after school until ten to five with Mr. Maksymchuk.

Thanks,

Cramer

Goal Setting

Hello fellow class mates....



During the course of this semester in Pre-Calc Math I hope to achieve a goal of 80% or higher. I also am trying to pay more attention and be a more productive student than last semester.


This picture cracks me up everytime I see it. Make sure you don't do this on a test!


Finally, a link that I used briefly last semester and I think will be beneficial for everybody in the class room is as follows:
http://www.math40s.com/
If you ever need help with theory or practice assignment, quizzes, exams etc.. you can go to this website.

Thanks,
Cramer