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Sunday, April 30, 2006

counting: a blogging on bloggin tale

successfully another unit is almost completed. i am not sure if we will be having a couple more classes on counting this week. Hopefully, if we do have 1 or two more classes, that we will get more practise to work on some problems. This unit poses some difficulties that lie below the underneathe. For some questions that we worked on the past week, the wording of some questions stumped me. I didn't realize that i read the question wrong until one of my peers in my group notified me or we went over that question as a whole class.
If a question asks for one thing, i tend to solve for that unknown and then usually you actually have to do the opposite to obtain the answer. I think a little more practise on the word problems would help prepare me for the test this week. I will also take some time to review concepts in this unit to better understand what a question wants and the possible options i have to solve that question.



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Saturday, April 29, 2006

Counting - Binomial Theorum

Hey guys, it's me Michael reporting from my computer. Well let's get this thing off by telling some cool jokes. The world todays seem to be mixing. In that, I mean racial. The world might even be coming up with new races, since everyone's blending! With that in mind, what race would you get when a Holland male and Filipina woman mate? ............Halipinos (just like Jalepino). hahahaha. Okay then let's get to the scribe. We had two class periods today and we started the day by Mr.K telling us how to find PHI or also called the GOLDEN RATIO. Here's how it goes:
After showing us this, we wrote in our dictionaries. This is what we wrote:
Still during the first class, we went over more examples just like our example in our dictionary. Here's what we did:
In the afternoon we were given problems on the board. Here are the questions and the soultions underneath.
After doing this we were put into groups and were given an assignment. I don't know where I put mine and therefore cannot show the problems. Basically it was a review of everything that we have learned. It's been a pleasure and thank you all for reading. Michael out!!

O Yeah, i almost forgot I get to choose the next scribe. I'll do something different and do a cheerleader chant to determine the next scribe. Give me a J...J, give me an A....A, give me a N....N, give me an E.....E, give me a T.....t!! What does that spell JANET!!!!!!!!!!! There you go folks, the next scribe is Janet. haha. It's only fair!!!



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Wednesday, April 26, 2006

Scribe ?

Hello. That's enough introduction.
For today's class, Mr.K put three problems on the board that we were to solve.

Expand and Simplify

(a+b)^o= 1

(a+b)^1= a+b

(a+b)^2= a^2+2ab+b^2

(a+b)^3= a^3+3a^2b+3ab^2+b^3



Fill in the next rows
(Look for patterns)

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1



Evaluate each Expression

oC0
1Co 1C1
2Co 2C1 2C2
3Co 3C1 3C2 3C3
4Co 4C1 4C2 4C3 4C4

*There is a pattern. It has a connection with the first two problems.
oCo is the same thing as 1. 1Co and 1C1 is the same thing as 1. 2Co is the same thing as 1. 2C1 is the same thing as 2. 2C2 is the same thing as 1. See the pattern?

In the first problem, (a+b)^0 is the same thing as 1. (a+b)=a+b. Their coefficients are 1.

In the second problem, the first row is 1, the second row has two 1's. The third row has 1,2, and 1, and so on.

Point is from all that rambling, is that there is a pattern.


He also said something about a guy named Pascal and how he used the triangle but there was actually a chinese dude who discovered it first. His name was Chi Che? Later on, another French guy used the triangle and made triangles inside the pascal triangle. And if you shade all the odd numbers in the pascal triangle, you'll see what that french guy was talking about.


Now, Mr. K gave us a hand out about Pascal's Triangle. Sorry guys. I don't got a printer right now so you had to be in class to see this. Anyways, there were many patterns and encodings we found out from this triangle.

One significant one was Fibonacci's numbers. This is when you add the sum of the two previous numbers in a number sequence.

Ex.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55....etc..

Bees populate this way. Female bees have two parents and male bees have one. If you create a family tree, you'll see that it follows fibonacci's numbers. Same with how rabbits populate, the petals on a flower, how trees grow, our body structure, etc.

I think Mr.K said that dividing these numbers get you the golden ratio. 1.6-ish. And he went on about how people like 6 by 4 pictures because of the golden ratio.

And that's about all I remember from today's class. It was fun listening.


Oh yeah. The next scribe will be Michael.



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Tuesday, April 25, 2006

Scribe of the day!

sorry guys about the late post, just got home a little while ago. well lets start! today we followed the morning day with notes in our dictionaries. they were the following.








after these notes, we were placed into groups of three and was handed group work sheets that consisted of many questions that related to "the choose formula"

Following the afternoon, we were brought up with these questions to start off the class.



















after these questions, we followed through with more practice questions. my favourite of all was the deck of cards. for those who dont know much about a deck of cards, theres 52 cards in a deck. 4 suits and 13 different cards in each suit.




















next scribe is the one and only regine



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Monday, April 24, 2006

PERMUTATIONS OF NON-DISTINGUISHABLE OBJECTS

The number of ways to arrange n objects that contain
k, k2, k3, .... sets of non-distinguishable
objects is given by:
n!/k1!k2!k3!

Circular Permutations

The number of ordered arrangements that can be made from
n objects arranged in a circle is given by:
(n-1)!
Ok people that was all for today (notes) but we talked about
this new assignment that we had to do and be done by the end
of may. This assignment can be found at this web site,
www.pc40s.pbwiki.com
The assignment is a math problem that each one of us
had to solve (just one problem per person). This is
race, first person that gets to a problem and solves it
gets the mark for that question. And the second part
is to fix someone's problem if he/she gets it wrong.
Anyways that was all for the day and now its pay back
time, hahahaha anddddd the next scribbbe is calvinw.



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Sunday, April 23, 2006

The DaVinci Code Quest Sunday



It started last week. Google releases one puzzle each day for 24 days until the movie "The Da Vinci Code" is released in May. So far 7 puzzles have been released. You have to solve the puzzle to reveal a clue. Then you have to answer the clue question(s) to advance to the next puzzle. You can win a prize for solving all 24 puzzles. Now I realize this is all about marketing and they're really just trying to get as many of us as possible to go see the movie but the puzzles are really cool! Google searching often helps to find the answers. One of the puzzle questions can be answered using The Fundamental Principle of Counting and the very first (sudoku-like) puzzle uses a couple of mathematical symbols.

Challenge 1: What is the question that can be solved using The Fundamental Principle of Counting and how do you use the counting principle to find the answer?

Challenge 2: What mathematical symbol is used in the very first puzzle and what number does it represent? (Not the "delta," in a later puzzle it has a different meaning.)

You have to sign up for a Google Homepage in order to play, but that's a free and very useful service. After that you can begin the game. Click on the US button to start 24 days of fun! (Actually, 17 because you could work through the first eight today.) Don't forget to also find the answers to the Challenge Questions above!. ;-)



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Friday, April 21, 2006

Scribe # ???

Hi my name is Charlene, you guys might hardly recognize me because this is my first time being scribe. So sorry if my scribe sucks haha. Anyways to start things off I would like to say that today we had a double period class and during those two periods we both had group assignments. The first period worksheet was not a hand in assignment however the second period worksheet was.

examples from the first worksheet:

1) The last part of your telephone number contains four digits. How many such four-digit numbers are there?
10*10*10*10 = 10,000

2) How many such four-digit numbers are there if the same digit numbers are there if the same digit cannot be used twice?
10*9*8*7 = 5040

3) How many four-digit numbers begin with a 2,4 or 0 if the same digit cannot be used over?
3*9*8*7 = 1512

The second class started off with Mr.K teaching us more about counting and arranging things in a circle.

Heres an example from the board:



In a circle with three beads you can only arrange it in two ways because even though you switch the beads around it will be the same due to rotating it. In a bracelet (3D world) there is only one way you can arrange three beads because you can flip it over and it will still be the same.

Mr K. stated that the the first thing you should do when arranging things in a circle is to put down a reference point(the first thing you put down) and then build around it.

umm I guess this is the end of my scribe, sorry its to hard to remember everything else considering the fact that today was full of a lot of things. Anyways the next scribe is.........Abdi (alphabetical order)




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Thursday, April 20, 2006

Bloggerization

All I can say is, thank the lord for a little extra time to study. I'm studying as we speak/read [whatever], and it's all thanks to postponing the test from Tuesday to today. Yes, it's very easy to catch on with a little time put into it. So, hopefully I will be prepared enough for this test. All I know is that I'm doing more preperation for this test than I have for previous tests. Let's go test day.



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Finally, Marcquin's first Scribe

THE ULTIMATE SCRIBE!

Hello one and all, this is Marcquin and I will be your scribe for April 19, 2006. Get ready folks! You guys will be in for a ride. Now away we GO!

I will first start off my scribe with a joke. I am not sure if it is appropriate, but I am putting it down. Here it goes:

A hippie walks into a bar and goes up to the bartender and says, "I would like to order a steak please. Not well done, not too rare, but in the groove". The bartender replies sorry sir we don't have steaks at this bar. The hippie stares at him blankly. So the bartender goes to the back to where his manager is and tells him some guy just ordered a steak.

The manager was having a bad day, so all he said was, "Just give him what he wants so he can go away". The bartender says ok.

The bartender then again goes up to the hippie. Then the hippie says, "I would like to order a milkshake. Not to watery, not to thick, but in the groove". The bartender replies sorry sir we don't have milkshakes at this bar. The hippie stares at him blankly. So the bartender goes to the back to where his manager is and tells him some dude just ordered a milkshake.

The manager's day was getting so bad but he kept his cool and said, "Just give him what he wants so he can go away!". The bartender says ok.

The bartender then goes up to the hippie and says here is your food. The hippie stares at his steak and says, "I would like to cancel that steak order, and order a burger. Not to big, not to small, but in the groove". The bartender asks are you serious? The hippie stares at him blankly. So the bartender goes to the back to where his manager is and tells him now he ordered a burger.

The manager has had enough! His day is just going so bad he exploded. The manager went storming out from the back office and went up to the hippie and said, "Look here hippie, I want you to kiss my behind. Not on the left cheek, not on the right cheek, but in the groove!".

And that was the joke of the day. Thank you, thank you.

Alright time to get down to business. So, in the morning class we had a pre-test. After the pre-test we got into groups and went over the questions. Sorry guys I didn't have enough time to write the solutions down so I have no graph to go by. Moving on to the afternoon class. In the afternoon class we got a stencil as the assignment. Honestly, I dislike couting right now. I mean I love counting.
And that my friends is what we did today.

The next scribe will be.... chosen in class by a joke telling contest. He/she who tells the funniest joke will be scribe. Forever! Just playing. Im out!



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Wednesday, April 19, 2006

blogging on blogging

this unit is pretty easy for me. The only thing that i am having problems with problem solving and figuring out the equation of a conic when given a point. We did a problem like this on our pretest and it gave me difficulties. Overall though, just sketching them and using the equation of a conic is easy.



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Tuesday, April 18, 2006

Sribe #?

Hello fellow classmates. Long time no type. It's been awhile since I've been in class... well back to business. Today for class we had only one period of class which was a good thing for me. We did some notes on Counting .



If there are M ways to do a first thing and N ways to do a second thing then there are ways to do both things.





We also learned what the formula is to solve something like this but I won't put that in.
Well it's been fun doing this scribe. I hope get many more like this.

Don't forget guys to do your homework
P. 336 # 1-14

Oh and before I forget the next scribe shall be....... dun dun dun......SENAIT.
GOOD LUCK WITH THE SCRIBE!



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Monday, April 17, 2006

scribe post

hi i'm aldridge and i'm the scribe for today. our morning period class started by grouping the class into five groups and we are expected to work on a problem exercise. i forgot that i was the scribe for today that time so i wasn't able to copy the problem but i'll try to recreate the problem.

1. there is a tunnel, it was created as a railway. the shape of this tunnel is half an ellipse. graphing the tunnel, it would look like this:



1. what is the equation of the whole ellipse following this form:
Ax2Bxy+Cy2Dx+Ey+F=0
answer: what we did in our group is we determine first some valuable information from the graph
centre @ (0,0) c or semi major axis=4 b or semi minor axis=3




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Blog

conics...where should i start? well first of all i would of have say that the most difficult area of this unit are the word problems. i have trouble finding the lengths of a and b, its hard to figure it out when you don't have any visuals. Another problem i have is figuring out what type of conic an equation is especially when its in general form. its hard for me to remember all the rules about it. when it comes to everything else, i guess im getting it. good luck to everyone.



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Bloggin on Bloggin

Wow this unit had a ton of notes. But yeah we learned how to look at the 4 conic equations in a more build it from stratch perspective. Overall I really get most of this stuff. But word problems give me a little problem just because you have to think outside the box. And making sure it makes sense in the situation. I really got to work on analyzing the geometry of the question.



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Sunday, April 16, 2006

bloggin for the test!

I guess the most confusing thing in this unit is how the signs change for the equation of the hyperbola. Sometimes I get confused whether if it is a parabola or a hyperbola. I just got use to the parabola, then the signs now have to change. Sometimes I also get confused on how to apply the word problems into actually drawing a picture to solve it. It's just hard trying the get the picture in mind. Well either then those things, I actually like this unit, with all the drawing, and figuring how to do it, it wasn't as hard as I thought it would be. Okay well goodluck everyone on the test!



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blogg on bloggingg

hmm parabolas...where do I start? It's very straight forward but I still get messed up on when the equations are equal to -1, which isn't all that difficult because you just switch the signs but I always mess up. I also have a problem with knowing which equations are circles, which are parabolas and which ones are hyperbolas. This unit wasn't that bad thanks to charlene =) for explaining things. Good thing I remembered last minute about this blog or else that 1 mark on the test would be wasted. Anyway I'll go study now.



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Thursday, April 13, 2006

BoB

Parabola = easy
Elipse = take time and it's easy
Hyperbola = Just need to tell the difference of which value is transverse axis and conjigate axis.

That's all. Van's BoB! (blogging on blogging)



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Wednesday, April 12, 2006

blog ? WHY? haha

wow i keep forgetting to do this and when i do it's when i'm already sleeping haha just excited. anyway conics has been and unusal road for me. the same thing happend to me when we were doing the trig word problems. I understood in class then at home it's like holy what's with the math language ? haha it's been like that for the past week so i tried getting it all straight. then today just today when we went over hyperbola's and we did that pre test it was like someone went into my head and was like 'look dude why were you ignoring me, i've been giving you answers for ages.' haha interesting huh i have voices in my head. don't worry i'm not crazy... *runs to corner rocks back and forth and whispers to self. lol just joking, sorry if i affended anyone it was supposed to be used as a pun. anyways the only thing confusing me right now is the elllipse. i don't know it's just something about that egg shaped thingy thats annoying me. i don't know what it is, or why it's doing it to me. i guess i'm just not clicking on all cylinders just yet. vroom vroom....



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blogging on blog

Hi it is me zaenab, i like the ellips and the hyporbolas assignment and i now how to find the box and some other things like the foci and the vertices. I have problems with the home work assignments from the text book. And the word problems they are my weeknas.



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Hyperbola




hi this is raymond
this is my 1st time 2 scribe so this it.

Definition : the Locus of a point that moves in such a way so that the
Difference of the distance ( Focal Radii ) from Two Fixed Point
( The Foci )
is constant.



[ PF1 - PF2 ]


The Anatomy of Hyperbola




  • a hyperbola has two Branches
  • A1A2 is called the transverse axis ; its lenghtr is 2a
  • the point of A1 and A2 are called verticies
  • B1B2 is called conjugate axis ; its lenght is 2b
  • 0 is the centre of the hyperbola
  • the foci are at F1 and F2 . they are located c units long
    the transverse axis from the centre 0.
  • the line y=b/a x and y= -b/a x are the equation of the
    asymptotes of the hyperbola .
    [NOTES: this example has centre (0,0)]
  • the transverse axis and conjugate axis are lines of symmetry for the hyperbola.

ok i'm done now the scribe sorry for the late scribe ,I don't know wat its 1st to do. I'm confused!!! so the next scribe is aldridge




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Tuesday, April 11, 2006

That's it

We didn't really do much in class except we did get home work containing questions on hyperbolas which was kind of weird since the questions said precal and the answer sheet said consumer...I want to leave it at that but then there's so much space I just don't know what to do with it. Well I guess I could leave you with a brain teaser...You have four nines(9,9,9,9,). Using only these four nines, arrange them to total 100. you can use any mathematical function you want, but each nine can only be used once. You probably remember this from before but then still maybe some of you don't know this one...for the next scribe I will put the names of the ones who haven't been scribe, write them down on paper and put them into my pocket and I will get some one to put their hands in my pocket and pull out a random name...



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blogging for this unit

wow, time is really passing very fast. we got less than 3 months before the graduation. i recieve my report card and my mark is ... so low! i should study hard now cause i dont want to recieve a 2nd line of 6 final mark! well for this unit, learning parabola is easy to understand but when it comes to hyperbola, its so confusing! i have a bit problem about remembering the transverse axis and conjugate axis. i first taught while working in the problem exercises given to us in class this afternoon that in hyperbola, transverse axis is always bigger than conjugate axis. analysing my notes from yesterday, i saw that that is wrong. also about our class today, i found something that can really help me a lot in this pre-cal class. while looking at jackie, emile and zaenab working together in the problem exercises, i remember my friends back in my home country. i think that having a study partner rather than working problems alone will really help to me gain interest and develop my skills in working out math problems. sometimes laziness strikes me doing every assignment but if there is somebody out there that will remind me even not during class time to do my homework and also that increases my willingness to study better cause i will not let my study partner to feel that im only the one benefiting from him while he's gaining nothing from me. well this is my blog for this unit and i hope to recieve a better mark on our upcoming test.



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blog on blogging blog blog

man. Conics are hard. especially the hyperbola and finding making the box and creating the asymptotes. i think that's where i'm struggling the most. Also finding the foci. Is that just finding the value of c? In other words, it's the graphing that's killing me. haha. Hope you go over this Mr.K. My pride is depleting for this exposure of weakness....so please go over it....



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Sisyphus' Bloggon the Blog 4

So, today's class was with a substitute teacher because Mr.K wasn't here! I wonder why... Anyway, he was pretty good at explaining things for me on the topic of Hyperbolas in our Conics sections. I have clearly understand how to find just about anything about the hyberbola because of this class and the worksheet given. Drawing these graphs are pretty fun. Although I do not understand how to interpret some, well most, word problems what-so-ever about the hyberbola, like when it asks to write the standard equation when all you're given is, the center, a verticie, and a point that it runs through. It's not like the circle that's for sure, or the parabolas, but similar in ways to the ellipse. I've sisyphus through it for over an hour trying to figure it out, well more like stare mindlessly at it, but you get the point.

To wrap things up, the Conic section, or Analytic Geometry, as some might call it, for me it's not too bad. Circles, Ellipses and Parabolas, like most people in the class, find it not too difficult. It's just some parts for the Hyperbola. It could be due to the fact that we really only spent roughly a class on it. I need notes ;D! Well, I know I can look foward to that in tomorrow's class, right Mr.K.



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Blogging on Blogging

This unit is half-half.Half easy and half average. The part that bothered me is the problem when you have given the focus and directrix then you have to find the equation of the parabola, but the rest is good except the hyperbolas maybe because Mr. K didn't explain that much with example but it's alright. Adios....



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conics blogging on blogging

The Conics unit wasn't as bad as I thought it would be. I didn't really have any problems understanding things. There was only one thing I had a problem with and that was with the hyperbola. The circles, porabolas and ellipses were all very clear to me but I'm still having difficulty with graphing the hyperbolas. It's hard for me to compare the hyperbola to the ellipse. I know they're similar but it's still unclear to me how. I understand what the transverse and conjugate axis are and how to get them however I don't know how to get the asymptote and how to draw the "box" between the two vertices of the hyperbola. Maybe I need to see the anatomy of the hyperbola written down in my dictionary so I can look at it more clearly.

Just yesterdays class we learned everything there is to know about the hyperbola in a short period of time. What really helped me learn the four different types of conic sections were the paper folding. I really liked it cause it helped me see the difference and similarities with the four different conic sections and I also thought I was good at it.



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Monday, April 10, 2006

BLAHGING ON BLAWGING!

Well the test is coming up soon, so its time to do blogging on blogging. The conics section of this course is going pretty well for me actually, I get all the things like circles parabolic(EASY!),ellipses(EASY!), and hyperbolic(not so easy..). We just got introduced to hyperbolic and I found it a little on the bumpy side of the road. I understand how things go. Such as the transversal axis is the distance between the vertices and the conjugate axis is the distance between the length(horizontal hyperbola)/ width(vertical hyperbola).I also get how to find the slope of the asymptote but I'm not to clear on how to graph the asymptote. And where the box in between the vertices came from. I hope we do more practice questions on hyperbolic and another explanation on where that box came from.



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Monday's Scribe

Alright, so Zaenab picked me to be the scribe for today's class. So, it was two periods today and we started the class with a problem on the board. Given x² + 121y² - 726y + 968 = 0, we were suppose to find:

-the centre and focii
-the lengths of the major & minor axes and;
-sketch the graph.

So, we had to get it into the proper form and rearrange it.

x² + 121y² - 726y + 968 = 0
x² + 121y² - 726y = - 968
x² + 121 (y² - 6y) = - 968
x² + 121 (y² - 6y + 9) = - 968 + 1089
x²/121 + 121 (y - 3)²/121 = 121/121

x²/121 + (y - 3)² = 1

a² = 121 a = 11
b² = 1 b = 1

c² = a² - b²
c² = 121 - 1
c² = 120
c = root 120 [which can be reduced to root 4 root 30, which is just 2 root 30]

centre: (0,3)
major axis: 22
minor axis: 2
focii: (±2 root 30, 3)

This is what it would look like:





A fairly understandable question, am I right? Well, we shouldn't really be having much difficulty with this, because if we are, then we're going to need some extra study time before the test. Oh yes, and because of spirit week, our test is delayed until next week. Monday, right you guys? After that question, Mr. K gave us three points for a circle:

J (-3,2)
K (4,1)
L (6,5)


With these points, we were suppose to find the centre of this circle. Discussed with the whole class, we figured out that by bisecting the line segments we could find the center. We can use systems of linear equations and use the process of elimination OR we can find the slopes and midpoints of each line segment. Yeah, I know this isn't very clear, but that's basically what I caught. We ended the period with more paper folding, horray!

Second period, we finished up the paper folding and found that we formed a hyperbola, by making a point outside of the circle but close to the edge, and with 30 individual points on the circle. We marked points P, Q, and R, as well as the focii and verticies. We learned that hyperbolas have a transverse axis and a conjugate axis.

[I couldn't upload my image]

So, the equation for a hyperbola is (x-h)² / a² - (y-k)² / b² = 1.

It is similar to the equation of an ellipse, where an ellipse is the sum of the terms, and the hyperbola is the difference. The hyperbolas open horizontally when x is positive. When y is positive, the hyperbolas open on the y-axis.

Then, Mr K. had to leave class early because he had to pick up his son. Hope he feels better Mr. K. We had about 10-20 minutes of a teacherless class, but were assigned homework. Our homework starts on page 159, questions #3 - 48, every third question.

....Lerwyne! You're the next contestant on the Price is Right! Oh, whoops, didn't mean to get your hopes up, I mean you're the next scribe. =)




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blog on the blog

well, i really liked this unit. It seemed that it would be a little difficult, becuase of the title. This unit also had interactions and seeing how parabolas, hyperbolas and ellipses. ellipses and parabolas were easy to understand, so are hyperolas. The only thing with hyperbolas, their the odd functions and so steps to finding coordinates are slightly opposite, but other wise mostly the same. The one question that struck me today was about an equation. I was working on the problem today and i had a fraction, something like this (but not exactly, just made up): (5(x-6)2)/(26) . Since the denominator can't be cancelled out by 5 (5 does not evely divide into 26, do i find the square root of 26 or "5/26".Since im finding the square root i am trying to find the length of a or b. I think this might not be a little clear. Well that's all i wanted to say. =)



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Sunday, April 09, 2006

blogging on blogging.

hi several of millions of people, my name is calvin and here is my post for you to read . well i must say, with out easy topics, i wouldnt be doing so well and feeling so confident about this right now =D well lets begin. each time as we did the paper folding, i think it was the easiset way to show how the ellipse, parabola, and how the hyperbola works. it helped my mind go *click when it came time to describe the formllas and everything just dissolved into my brain and it stays in a place which i can access. knowing that its safely in my brain, i think this unit, i got it pretty packed down, good luck with the test guys =D



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Four Colour Sunday!


You may have heard that any map can be coloured with four colours in such a way that neighbouring countries receive different colours. That it can be always done is one thing. How to do it is another. Are you ready to start colouring?

(Thanks again to Think Again!)



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Friday, April 07, 2006

introducing Focal Radi, pythagoren and standerd form for the equatoin of an ellips.

Today was a one period class and i thank abr13l for choosing me:D because last time i did a two period scribe and i did not like it :D

Today's class was skatching graphs, finding the vertex, finding the foci and writting some notes.

We started class by two questions on the board.
Write the equation in standard form and.....
a) sketch the graph
b)Find the vertex
c)Find the foci

I) X2-4y2-8=0

solution:

x2/8 -4y2 =8/8
x2/8-y2/2=1
c2=a2-b2
c2=8-2
c=sqroot 6
a=2sq2 b=sq2 c=sq6
the vertex= (0,0)
the foci=sq6


II)9x2+4y2-54x+36=0

solution:
9x2-54x 4y2+36=-36
9(x2-6x+9) +4(y2+9y+81/4)=-36+81+81
9(x-3)2 +4(y+9/2)2=126
(1/9)/(1/9) 9(x-3)2/126+(1/4)/(1/4) 4(y=9/2)/126=1
(x-3)2/126/9+(y+9/2)/126/9=1
(x-3)2/14+(y+9/2)2/63/2

the vertex =(3,4 1/2)
the foci=(3,10)
(Sorry i couldn't post the graph)

Then it was time for note taking. Today we had a fair amount of notes to take.

(I couldn't post the ellips to show you where these letters and notes had came from)
O IS THE CENTRE WITH THE COORDINATES (h,k)
A1 A2 is the majour axis its length is 2a
B1B2 is the minor axis ; its length is 2a
OA1 is the semi- majour axis; its length is a
OB1 is the semi-minor axis;its length is b
F1 and F2 are the foci of the ellips, each one is c units from the centre.
PF1 & PF2 are the focal radii
A1&A2 are called the verticies of the ellips they are the end point of the majour axis.

The Focal Radi property ( I couldn't post the ellips)
By defination PF1+PF2 is constant assum that P is at A1
therefore PF1+PF2=A1F1+A2F2
By summary A1F1=A2F2
=A2F1+A1F2
=2a
The phthagoren property: (I couldn't post the ellips)
By defination PF1 +PF2 is constant and we know that PF1+pF2= 2a
Assum P is at B1 By summary PF1=PF2

PF1=PF2=2a
2PF1=2a

PF1=a
therefore c2+b2=a2
or c2-a2=b2



The standard form for the equation of an ellips
Horizontal Vertival orientation
(x-h)2/a+(y-k)2/b2=1 (x-h)2/b2+(y-k)2/a2=1

(I couldn't post the ellips.)

We have an assignment parabolas,circles,and ellipses. This assignment shows every thing we did in conics so far.

And the next scribe is Jessica (good luck on a two period scribe)



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Thursday, April 06, 2006

Scribe Number Ellipse

Today we had the joy of having a double class today. A lot of lectures and writing and diagrams. That was all we had done today the people in our class could give you what we did =P.

Just joking, the first class started good with two questions on the parabola's; basically a review from yesturday.

For each parabola we were supposed to find
a) sketch the graph
b) vertex
c) focus
d) Equation of directrix
e) Axis of Symmetry

1) y2 - 20x + 2y + 1 = 0
First thing's first, we figure out which way it opens, and seeing as y is being squared we notice that it opens either right or left. Therefore we isolate all the 'y' onto one side and everything else on the other.

y2 + 2y = 20x - 1

Secondly we have to complete the square for the 'y' in order for us to get that nice ( y - k )2 = 4p(x-k).

y2 + 2y + 1 = 20x -1 + 1

Then we just simply simply and factor out.

( y + 1 )2 = 20 x

With that figured out, we now had to find 'p'. To find p we simply set 4p = 20 because nomrally where 20 would be 4p would be, and we get :

4p = 20x
p = 5

Simply just divide both sides by four in order to isolate 'p.'

With all the information we figured out we could basically figure out the questions that were asked.

b) Vertex (0, -1)
c) Focus ( 5, -1)
d) Directrix: x = -5
e) Axis of Symmetry: y = 2

The sketch should be easily figured out now with the answers. I will provide a sketch for you guys if you would like a reference, or if you're having trouble sketching it. Try it first, because me telling you and showing won't get you anywhere.

2) x2 - 4x + 8y + 4 = 0

This question was done exactly the same was as the first question. The only difference here is now notice that the parabola opens up or down therefor we isolate the x's on one side and the other's on the other. I'm pretty sure you wouldn't like me to show you again how this is all done but unless you want me too i'll go back and edit =P

Still in the first period...
Remember that paper we manipulated, abused and everything else you could do with a peice of paper ? Well today we put it into good use. We created an ellipse with the folds that we had made, similiar to the parabola that we manipulated with the other peice of paper. With the Ellipse we made 3 different points on the ellipse and constructed lines to connect them to the two dots we had made, which we found out was called 2 focus' or foci? (spelling ?). From this construction we found a pattern to show that any line from a point on the perimeter of an ellipse to the focii had all the same sums. The lines we constructed were also called 2 focal radii. We then constructed the major axis, which is the longest line in the ellipse that crosses the center and found that it was also the same length of two focal radii. Afterwards we then created the minor axis, which is the shortest line from one point on the ellipse to another point on the ellipse passing the center. Using these two axis' we constructed a right angle triange by connecting on of the points of the minor axis to one of the points. Btw we also found out that a semi minor or major axis is half of the major or minor axis. We then used the pythagorean thearom to figure out the hypotenous of the triange.

NOTE : THIS IS NOT LIKE THE THE ONE WE LEARNED IN JUNIOR HIGH IT IS NOT A2 + B2 = C2

The one we had learned is a2 = b2 + c2. This is because since the that created the hypotenous is equal to the semi major axis we defined that as a and major axis A. The semi minor axis labeled b and the minor axis labelled B. C was the distance from the centre of the ellipse to one focus.

With that we had learned everything we needed to know about ellipses, and went straight into our dictionaries.

DICTIONARY:
The Elllipse
Definition : the locus of a point that moves in such a way so that the sum of it's distances (focal radii) from two fixed points (the foci) is constant

The Anatomy of an Ellipse

A more simplified diagram of our folding method but less confusing and more neat.


Second Period

We learned about the standard fomula of an ellips

Horizontally :
( x - h )2 / a2 + ( y - k )2 / b2

Vertically
( x - h )2 / b2 + ( y - k )2 / a2

The joy of copy and paste =D, haha anyway we learned that the difference of the two equations was in fact a and b. This was because since a is the bigger line which ever it is the denominator for (either x or y) depends where it will stretch either up and down or left and right. Also since b is the smaller side, similiarily like a, which ever it is the denominator for (either x or y) depends whether the ellipse will either become compressed either up and down or left or right.

We also found out where c was. from the formula a2 = b2 + c2 we notice that the denominators are in fact a and b in the formula. There fore in order to find c. We place in the values of a and b and solve for c. I'm pretty sure a and be will already be given in their squared form so you do not have to worry about squaring them. I am not 100% sure about this but Mr. K did not say and no one asked and I just questioned it now. SO MR. K IF YOU ARE READING THIS (which i know you are) I WOULD LIKE TO KNOW IF IT IS ALWAYS SQUARED ?

From here we did a couple problems on sketching and everything else like we did in the first period but this time working with the standard formula. It was basically the samething you have the vertex at (h,k). Then solving for c using the 'new' pythagorean thearom. From there you could sketch the graphs and that's all about ellipses.

If a question is given in general form you would do the samething as you would do for a circle. Isolate the y2 and the x2 on to one side and the constant on to the other. Factor out anything that could be factored, complete the square, then to make everything equal to 1, you divide that one side by itself to make it one and everything else so that you do not get a constant with the x's and y's. and that's it the whole bottle of wax.

btw the next scribe is zaenab.

homework PG 150 1 - 27 ODD ALSO 32 - 38



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Wednesday, April 05, 2006

PARABOLA

Hey guys
I have nothing to say so im just going stray 2 explaining what happen 2day. But the thing is we did not do much today, it was just 2 question we had to work it out 2gether and play with this circle Mr. K gave it 2 us. Here are the 2 questions:

1) A parabola has vertex (2,-3).
And contains the point (9,-10).
Find its equation and sketch the graph if it is oriented:

a) Vertically

(x-h)^2=4p(y-k)
(x-2)^2=4p(y+3)
(9-2)^2=4p(-10+3)
(7)^2=4p(-7)
49=-28p
-7/4=p
Therefore the equation is (x-2)^2=-7(y+3)
And the graph looks like this:

The point inside the parabola is the focus point which is (2,-19/4)
The line on top of the parabola is axis of symmetry which is Y=-5/4

b) Horizontally

(y-k)^2=4p(x-h)
(-10+3)^2=4p(9-2)
49=28p
49/28=p
7/4=p
Therefore the equation is (y+3)^2=7(x-2)
And the graph looks like the first graph with the same vertex but the graph opens right, the focus is (15/4,-3), and the axis of symmetry is X=1/4.

Anyways i think this was it for today's class, so the next scribe for tomorrow is a-b33-l



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Tuesday, April 04, 2006

Scribe # (insert actual number here)

Yo. This is Van, doing the scribe, and if I didn't have enough work to do already, Calvin felt like messing me up with the scribe for today (sorry if that's inappropriate, I'll change it later if need be, but if it's funny, then I've succeeded in my goal that tried to be slighty humorous). ANYWAYS, onto the scribe which has, 3 pictures. Teddie's right, pictures are actually fun to make... till Paint gets annoying.

So today, we have a double class, (even more reason for me to spite Calvin) and we learn what the focus and directrix means. Meanwhile, Mr.K goes off topic, and onto the USE of these parabolas. He also spites MTS, because he says "What does the rain have to do with my Cable/internet?". So he draws a picture of how we get the signal onto our tv and watch it!

So, the focus, is recieving concentrated signals from the distributors, and the cable box has to be activated to descramble the signal. "Neat stuff he says". "You should go into computer science.". "Wanna make a LOT of money?, Go into MATH". Then he talks about how Amazon.com is cool and how mathamatizing humanity is in progress. Of course, everyone is dumbfounded. I'm off topic myself, off to the real stuff we're supposed to learn. So after his ranting about the parabola and satelites, we begin to write in our math dictionaries!. (Oh joy)










Parabola - The Locus of points that are equidistant from a Fixed line (directrix) and a Fixed point (focus).

The Anatomy of a Parabola

Equation
(x-h)² = 4p(y- k)

Properties
P>0 opens up
P<0 style="color: rgb(51, 51, 255);">Focus at (h, k+p)
Equation of Directrix y= k - p
Equation of axis of symmetry x=h
If |4p| > 1 arms are "wide"
If |4p| <>








Equation
(y-k)² = 4p(x-h)

Properties
P>0 opens right
P<0 style="color: rgb(0, 0, 0);">Vertex at (h,k)
Focus at (h+p, k)
Equation Of Directrix y= h-p
Equation of axis of symmetry y=k
If |4p| > 1 arms are "wide"
If |4p| <>Deriving the Standard Form for the Equation of a Vertical Parabola



















__ __
PD = PF [By Definition]

(y- x)²+[y-(k-p)]² = (x-h)²+(y-[x+p])² [Distance Formula]
(y- k+p)² = (x-h)² + (y- k- p)² [Square both sides & simplify] *Desregard red line on "2kp"
y² - 2ky + 2py - 2kp + k² + p² = (x-h)² + y² - 2ky+ 2kp + k² + p² [expanding]
2py - 2pk = (x-h)² + 2kp + 2py [Balancing]
4py - 4pk = (x-h)² [Balancing]
4p(y-k) = (x-h)² [Factor out 4p]



Okay I'm done the scribe!, Huzzah!. Woohoo, one hour and a half hours invested and time to work on english. Sorry for the late scribe. The next scribe will be Abdi. Enjoy people.

i'm gonna edit this later, someone tell me how to place a square root over a long line of things, and i'll change it



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Why Should I Learn Math?

This is taken from an article (Math Will Rock Your World) from Business Week. A few snippets:


Y'wanna get a really interesting job working with people on lots of interesting things?



But just look at where the mathematicians are now. They're helping to map out advertising campaigns, they're changing the nature of research in newsrooms and in biology labs, and they're enabling marketers to forge new one-on-one relationships with customers. As this occurs, more of the economy falls into the realm of numbers. Says James R. Schatz, chief of the mathematics research group at the National Security Agency: "There has never been a better time to be a mathematician."


Learn math!


How'd ya like a six figure salary?



...new math grads land with six-figure salaries and rich stock deals. Tom Leighton, an entrepreneur and applied math professor at Massachusetts Institute of Technology, says: "All of my students have standing offers at Yahoo! (YHOO) and Google (GOOG)."


Learn math.


D'ya wanna to work on the biggest most cutting edge issues of our day?



This mathematical modeling of humanity promises to be one of the great undertakings of the 21st century. It will grow in scope to include much of the physical world as mathematicians get their hands on new flows of data .... "We turn the world of content into math, and we turn you into math," says Howard Kaushansky, CEO of Boulder (Colo.)-based Umbria Inc., a company that uses math to analyze marketing trends online.


Learn math.


Y'wanna make one of the most significant contributions to the betterment of humanity?



"The next Jonas Salk will be a mathematician, not a doctor."


Learn math.


What are the implications for k-12 education?



Outfitting students with the right quantitative skills is a crucial test facing school boards and education ministries worldwide. This is especially true in America. The U.S. has long leaned on foreigners to provide math talent in universities and corporate research labs. Even in the post-September 11 world, where it is harder for foreigners to get student visas, an estimated half of the 20,000 math grad students now in the U.S. are foreign-born. A similar pattern holds for many other math-based professions, from computer science to engineering.


The challenge facing the U.S. now is twofold. On one hand, the country must breed more top-notch mathematicians at home, especially as foreigners find greater opportunities abroad. This will require revamping education, engaging more girls and ethnic minorities in math, and boosting the number of students who make it through calculus, the gateway for math-based disciplines. "It's critical to the future of our technological society," says Michael Sipser, head of the mathematics department at Massachusetts Institute of Technology. At the same time, school districts must cultivate greater math savvy among the broader population to prepare it for a business world in which numbers will pop up continuously. This may well involve extending the math curriculum to include more applied subjects such as statistics.



Learn more math!


"But I don't like math. Besides, I don't need it. I'm going into the humanities or business!"



As mathematicians expand their domain into the humanities, they're working with new data, much of it untested. "It's very possible for people to misplace faith in numbers," says Craig Silverstein, director of technology at Google. The antidote at Google and elsewhere is to put mathematicians on teams with specialists from other disciplines, including the social sciences.


Just as mathematicians need to grapple with human quirks and mysteries, managers and entrepreneurs must bone up on mathematics. Midcareer managers can delegate much of this work to their staffers. But they still must understand enough about math to question the assumptions behind the numbers. "Now it's easier for people to bamboozle someone by having analysis based on lots of data and graphs," says Paul C. Pfleiderer, a finance professor at the Stanford Graduate School of Business. "We have to train people in business to spot a bogus argument."



Ya gotta learn more math!



Yes, it's a magnificent time to know math.


'Nuff said.




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Monday, April 03, 2006

blogg scribe for today

Hi guys! IM back for round 2... If I have to introduce myself again... Well I don't want to. Okay lets start off the first day of school with first handing back our quizzes and tests from the previous units, Circular Functions, Transformations, and Inverses. After the long wait, he handed each of us a piece of scrap paper. The class began to talk amongst eachother thinking if he was going to bomb us with something that would cause our brains to combust and explode. As the uneasy class sat back and waited for the reasoning behind the paper, he began to talk about " del.ico.us it " and how most people failed to complete the assignment. If its handed in before wensday, you can STILL get 90%, not 100% anymore because well... We kind of had spring break to do it. And every second day after that, it'll be a -10% for the max mark that can be achieved. After this conversation there was a controversy about wether or not one link that can link into more that one unit was allowed.. well, after a long chat about that it boiled down to you need 3 different links no matter what. after that we finally got to the paper and he told us it was just a scrap piece of paper. The instructions followed as
make a dot near the bottom of the page, as centre as you can.
draw 8 dots on the bottom of the page, evenally spaced would be nice.
the bottom left dot and fold it over so that the dot corresponds with the centre dot, then use your thumb nail and make it a very noticeable crease.
continue with the other dots until your done all the dots.
what does the shape look like? it should look like a parabola.
1) connect all the centre crease marks together to make a parabola.
2) label the dot that you drew in step one as F
3) draw 3 dots along that parabola, and label them P, Q, R.
4) using a ruler perpendicular to the bottom of the paper edge, draw a line to each of the dots, P, Q and R.
5) now use the ruler to connect each dot P, Q, and R to the dot F
6) meause line PF and then measure the other line that is perpendicular to the line.
7) if you've done it correctly, the lines should be equal in length.
8) repeat with the rest of the dots Q and R.
lookie at this example it should look SIMULAR not exactly its not scaled.
click here for example
the reason the point is labeled F, wasn't because i wanted to, it stands for Focus. As the F was the Focus, the edge of the paper, would be known as the "directrix" in simple words it is known as "fixed line". The parabola's definition is : As long as The distance between Focus and the Directrix to a fixed point are equal. ohh yeas, NO HOMEWORK GUYS relax for one last day =D

anndd the scribe for tommorow iss.... VRRRRRRRRRRRRRRRrmmmmmmmmm VAN



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Sunday, April 02, 2006

Roboclaw Sunday!


Move the robot arm to pick up the ball. Clean, simple design. I got to level 19. I died. It's a doozy!



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