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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