scribe

hi it's me Aldrin.

scribe for last Friday's class (05/08/09)

At the start of the class, Mr. K promised us that he was going to blow our minds,(whoah!!), but before that, we had a short quiz.

I'll go though some of the questions on our quiz.

At the first part, we have to simplify the following problems. (refer to the slide - page 3)

(k + 3)! / (k + 2)!
(k + 3)! = (k + 3) (k + 2) (k + 1) & (k + 2)! = (k + 2) (k + 1)
dividing the two, will reduced to k + 3
-the answer is k + 3

7!(r + 2)!r / 6!(r + 1)!
simplifying the expression, you'll get 7 (r + 2) r
~always remember to simply your answers to its simplest form~
-the answer is 7r^2 + 14r

3rd part (refer to the slide - page 4)
in how many ways can 7 books be arranged on a
shelf if 3 particular books must be together?

You have 7 books. Put 3 in a bag, then you'll have 5 items.
You can arrange them in 120 different ways, or a 5!.
Open the bag. There are 3 books in it which will make it a 3!.
multiply the two. you'll get the answer (hope it make sense)

5! 3! = 720


after the quiz, he told us to expand and simplify the following binomials:
(a + b)^0
(a + b)^1
(a + b)^2
(a + b)^3
(a + b)^4
(a + b)^5
(a + b)^6
**refer to slide, page 6




after solving the first five, he showed us a triangle of numbers.
**refer to slide, page 7

we were told to find the pattern in order to add more rows on the triangle

the pattern is that you must add the two numbers on the
previews rows in order to get the numbers on the next rows.



at slide, page 8
he showed us another triangle with combination expressions.

use "choose formula" nCr = n! / (r! (n - r)!)
after evaluating all these expressions we found out
that this is the same triangle as the previews one.

now getting back at the previews slide
(page 6)

-looking at the coefficients carefully(the ones in red)
we can see that they are the same as the numbers in the triangle.

we then figure out how to solve binomials using the the the pattern of the triangle we had.
it is much more easier rather than going through all the expanding and simplifying thing.



PASCAL'S TRIANGLE




he also showed us pascal's triangle.
looking at this triangle, you can find lots of patterns

~the triangles on the slide pages 7 & 8 are also pascal's triangle~

Well, that's all i remember. I'm sorry for mistakes on my post.
I promise to improve it more.

also sorry for a late scribe.

next scribe is emmelion

BOB

hi everyone, this is aldrin b.

well, i don't have much to say because
i'm still having trouble regarding this unit so,
i just want to wish you all luck for this exam.

just remember,

~A LOGARITHM IS AN EXPONENT~

MAY 1 – Make the questions

MAY 8 – Complete questions 1 and 2

MAY 15 – Complete questions 3 and 4

MAY 22 – Complete questions 5 and 6

MAY 29 – Finish Final Project and make the presentation

JUNE 7 – Final Due date

bob

hi every one, just doing my bob, --morning right before school..-- awtz

I found this unit interesting. there were some challenging parts, but the rest was pretty easy. I just lack of practice. I agree with them that you really have to practice to be good at something. I'm looking forward for the next unit, time for me to strive harder.

well.. good luck everyone for the test. enjoy!!

time to go to school =D

scribe!!

Hi, its me, Aldrin B. It's my first time to scribe so i hope it'll go smoothly.

Here is today's scribe.

At the start of the class, Mr. Kuropatwa introduced an online social bookmarking website.

delicious.. was it!?
Here's a link if anyone of you guys forgot the url. (or just too lazy to type it)
http://delicious.com

It's a bookmarking service that allows users to tag, save, manage and share web pages from a centralized source. Like Mr. Kuropatwa said, instead of having different bookmarks on every computer, Delicious makes it easy to set bookmarks on every computer,
even if your not on your own.

I 'm not going to discuss it briefly because i know a lot of you know how it works better than i do..

There are just few things he said we must do.

-First, you must register to this site.
(if you're still using Internet Explorer for browsing
well its up to you..XD.)
No, seriously. It has been suggested that
you use Fire fox because they say it's better, plus you need it
and its add-ons for easy tagging.

http://delicious.com/help/quicktour?tour=firefox
(above is a direct link where you can download and install fire fox add-ons)
I had trouble looking for them, so i hope this will help you.

-Then start looking for resources related to our first and second unit the circular functions and transformation.
You have to put three tags (UNIT TITLE, YOUR NAME, and our blog name, pc40sw09)
it is due before the end of this unit.


Now let's go to our class discussion.

At the first, he gave us problems about translation and stretching.(refer to slide #2 - 03/03)

-3f ( 1/2x - 2 ) + 1

---

Given A ( -2 , -3 ) find the coordinates of its image under the transformation given above.

We must first reveal the true form regarding with the x axis( the ones inside the parentheses) to get how many units it really shifted.

-3f ( 1/2x - 2 ) + 1 = -3f ( 1/2 ( x - 4 ) ) + 1

After knowing that, you can now solve for the coordinates of x after transformation.

(-2) times the reciprocal of 1/2 which is 2 plus 4
(-2)(2) + 4 = 0

Focusing now on the y axis, will not be a problem because they are on the outermost of the equation.

Solving for y after transformation:

(-3)(-3) + 1 = 10

We now lead to our answer, ( 0 , 10 )

Just remember: stretching first before translation

---

The image of point B after the transformation shown above is ( 1 , 4 ), find the original coordinates of B.

We need to do an Inverse of the steps made above.
Solving for the x coordinate
( (1) - 4 ) / 2 = -3/2

Solving for the y coordinate
( (4) - 1 ) / -3 = -1

We now lead to our answer, ( -3/2 , -1 )

---

After that, we tackle about odd and even functions
Looking at them you can see that Odd functions if rotated 180 degrees remain the same while even functions is like functions reflected through y axis.

Testing Algebraically whether its odd or even

a function is even IFF f(-x) = f(x)
(refer to slide # 3 - 03/03)

f(x) = x^2
f(-x) = (-x)^2
f(-x) = x^2
since f(-x) = f(x)
f is an even function

a function is odd IFF f(-x) = -f(x)
(refer to slide # 4 - 03/03)

f(x) = x^3 - x
f(-x) = (-x)^3 - (-x)
f(-x) = -x^3 + x

-f(x) = -((x^3) - x)
-f(x) = -x^3 + x
since f(-x) = -f(x)
f is an odd function

I found some site which may help you understand more regarding these.
click here

So that's it for my scribe.. I hope Its not too long or short for a scribe and did not confuse you more..
but I'm really sorry if it did. If there's any correction, feel free to tell me.

by the way.. I almost forgot about our homework...
exercise #9 num's 1 - 10.

see you guys tomorrow. have a good night everyone!!

oh..? for the next scribe.. i picked kalekalekale! ???