Pre-Cal 30S

The Adventure Continues ...

2006-01-30T15:49:00.000-06:00

Our adventures in blogging continue....

Watch for 3 new blogs going live February 3, 2006 ...

Applied Math 40S (Grade 12)

Pre-Cal 40S (Winter '06) (Grade 12)

Calculus 45S (Grade 12)

So Long ...

2006-01-29T15:49:00.000-06:00

I'm so glad we've had this time together,

Just to have a laugh or learn some math,

Seems we've just got started and before you know it,

Comes the time we have to say, "So Long!"

So long everybody! Watch this space in February for pointers to new blogs for each of my classes.

Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)

LAST SCRIBE POST!!!

2006-01-28T23:51:00.000-06:00

Oh my sorry I totally forgot I was chosen to be scribe, well what can I say this last class was amazing we decided to do the podcast even if it was only Craig, Richard, Kasia and I…but it was great we still manage to do it haha well let’s see, the first part of the class was spent on doing the podcast and for the remaining of the class we did a pre exam test or w/e you call it and it really was helpful in many ways especially with reviewing some of the things that I’d had a hard time doing before, but man was it hard to do some questions without having a calculator but hey I managed…after that we were put into groups and were able to discuss the type of answers we got…and that’s where we ended our last class =( …I am so upset that math class is over because this year has been such a great experience I’ve met a lot of wonderful people that I’ve talked to in and out of class, and we all had our share or laughs either laughing with or at Mr. K and his jokes haha and or pointing and always choosing Richard for everything, etc overall I’d like to say that you guys are awesome and never change nor forget about the great times we had in pre cal class…and my last words would have to be exams start this Monday so good luck to everyone and I hope to see you all there! BYE…

Message in a Podcast

2006-01-28T02:13:00.000-06:00

We had our last class on Thursday and made a podcast to celebrate! We left ourselves a "pod capsule" in instead of a "time capsule."

Here is our Message in a Podcast (4 minutes, 26 seconds). Please leave any questions, concerns, complaints, compliments, confusions, uncertainties, anxieties or other inquiries in the comments to this post.

This isn't our last post yet -- I've got at least two more I want to get out before the end. ;-)

Blog before the EXAM...

2006-01-27T16:13:00.000-06:00

Hahaha...... Wow... To think I'd post here before an exam. Pretty Ironic eh? Oh shoot... Didn't finish my scribe post. lol. Yeah I did. But anyways... Before the Pod get's Cast's out of the school. I'd like to say... Bye to everyone again. Espically to the Study Crew. Haha. The Blogging Crew. And the MATH Crew. Hahaha. Which is all of you guys. Math won't be the same ever again. And if we don't blog... I start a blog. Hahaha. But... Also A BIG THANK YOU TO Mr. Kuropatawa. The best Math Teacher ever. I can't live with out his jokes. lol.

So I probably won't see you guys for about....... A year or so but... I'll be arround on the blog(s). The Sargent Park Grade 8 blogging run... Some other random blogs and I'll sneek into the PC40 Winter 06 blog to leave a ton of comments. Hahaha. Hey I'll even show up to PC40s on the first day back in Semester 2. Hahaha. Also ahhh... Nevermind. lol.

Well anyways.. I'd just like to say. Good-bye and... GOOD LUCK ON YOUR EXAM!!!!

Peace. Richard C.

My last scribe post...

2006-01-25T23:11:00.000-06:00

Hey guys sorry this is late...

Well today in class we started off with a super secret survey! Whhooppeee! Well not really secret but close to. The survey was all about what we thought about the math class and teacher that happened to teach us. It was a simple circle the answer that best suits your thoughts on this topic type of thing until the end where you could right personal comments if you so wished. This was of course anomynous.

Next we were given a pre exam type pre test thing on what the class voted had been the hardest concept to understand...triginometry! This pre test was an awesome way in my opinion at least to help refresh our memories, because of this I feel that if you missed class today and the test I'm sure Mr. K would be happy to hand you a copy of it to do. I found that learning from the mistakes you made was way easier then watching Mr. K do the work on the board. I will post all the questions and answers tomorrow so that everyone else still doesn't miss out on the correct way of doing things.
Of course following the pre test we were split into groups and within them tried to figure out the best way to solve the problems. (Show you later on as I said)
Mr. K continued by showing us the answers on the board and going over only the first problem solving question (boy was that a doozy). The bell then promptly rang and class ended like any other day. :)

PreScribe

2006-01-23T23:26:00.000-06:00

So you’re probably wondering... Why I asked Liz to pick me as scribe? Why am I scribing even before class started? and... Who am I in general? Well I asked Liz to pick me as scribe because I wanted to scribe one last time before Math ends. Hahaha. I’m going to miss math… *cries. Well anyways. To answer the second question. I have to make up for taking Liz’s math Dictionary right now. Hahaha… yes I’m sorry. Don’t blame Liz… Blame me. Haha… And also… The scribe for tuesday would be up at like… 12:00 Midnight because I get home at like 11:30 lol… (Unless I do it at lunch… Which is highly unlikely…) And My name is Richard. Well anyways… Tonight I scribe about Yesterday.

Well we had allot of notes… And allot of notes… And… A few jokes. (Anyone get the punch line) [Probably Not] {Dang I suck} We also had a story and a “pod casting news event” lol

We took allot of stuff in our dictionary… And because I forgot my glasses I took Liz’s dictionary instead… lol. Haha.

[Insert Example 1 - 4]

After that we took a visit to consumer math. One lesson we dare not learn… And put it in our Math Dictionary.

[Insert Consumer Math Diagram & Notes]

Well that’s it for tonight... Hehehe… Scribe tomorrow… Hehe…

Homework was the last exercise to whenever and Mr. K keeps on forgetting his pennies

Today.... We finished our Math Dictionary. AND..

END OF COURSE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

So... We had a good time the whole class. (AKA PARTY!!!)

Tomarrow's scribe is.... Kasia. Hahaha

SCRIBE ?

2006-01-23T21:38:00.000-06:00

ahh i wasn't aware that i was the scribe because i was the first one to be on the new cycle =\ . UNFORTUNATELY i can't make much of a scribe post because richard borrowed my dictionary . SORRY GUYS . BUT YEAH Today we wrote in our Math Dictionary's. Graeme's going to put that up. And Mr. K told us another story about a professor or somthing. After that the class was over. The next scribe is..... RICHARD because he wants to be again ? hah ..

Sunday Punting Practice

2006-01-22T09:04:00.000-06:00

Like sokoban the target is to push objects (in this case punt-discs or 'pucks') around a maze to cover various targets. In a punt maze however the pusher slides forward tilt-style until it hits an obstacle, and a puck that gets struck will be punted forward a matching distance.'

'Aim: Use the black cross as a pusher to 'punt' the yellow pucks onto the blue targets.
Movement: Use the arrow buttons provided to move the pusher (black cross). The pusher will run in a straight line until it hits a wall or a yellow puck. If it hits a puck the puck will be punted forward a matching distance.'

Are you ready to play?

(Thanks again to Think Again!)

Scribe's scribe

2006-01-20T15:56:00.000-06:00

Today in class, we started off with problems on the board:

That pretty much covered the whole class. And by the way! Go for Gold is due on Tuesday, not Monday. So you have have a one day extention guys!

The next scribe is... elizabethh. (: Have fuuuun (;

scribe

2006-01-19T20:06:00.000-06:00

So today we started off by talking about the coin hunt and how fun it was last year. Then he ask "who wanted to be part of the committee?"and how surprised he was when no one i mean no one raised there hand. Anyways we took out our handy- handy dictionary and discussed rational functions.

Graphing Rational Function
Rational Functions are written as the Quotient of two polynomial.
F(x) = a(x) ; b(x) 0
. b(x)
appearance; f(x) = 1 f(x) 1
. n x^n
the graph will be posted shortly........
where n is odd

where n is even

Sketching:
step1: Factor everything if possible
step 2: find the y- intercept (let x= 0)
step3: find the roots of the function by finding the roots of the numerator [ a(x)]
step4: find the vertical asmptote( s) by finding the roota of the denominator [b(x)]
step 5: find the horizontal asymptote.

case1: degree of a(x)<>
horizontal asymptote @ y= 0
case 2 : degree of a(x) = degree of b(x)
Horizontal asymptote found by: leading coefficient of a(x)
. leading coefficient of b(x)

case 3: degree of a(x) > degree of b(x)
no horizontal asymptote there may be a "slant asymptote" or a hole in the graph.

Step 6: Do a sign analysis of the function over the intervals defined by the roots and vertical asymptotes.
step 7: Sketch the graph
and the 4 examples we're doing tomorrow. and was it for our dictionary.

as the fraction gets smaller the product increases.
the denominator is getting closer to 0.
the answer is getting closer to infinity.
example:
1/1/10 = 10
when you divide by 0 you get infinity. You are not allowed to divide by zero because you can't get infinity as an answer. infinity is not number.

Then next thing we knew the bell rang......
oh yeah the scribe for tomorrow is ..........................
rannell d. hope you have fun!

My LAST Scribe before EXAMS =/

2006-01-18T11:58:00.000-06:00

Well I know that it Aichelle's scribe stated that Larisa's today's scribe, but apparently she has already been scribe so Aichelle chose me to be today's scribe =/.

Anyway today's class started off regulary with Mr. K puting questions on the board for us to do for a little review from yesturday's class, but today's class was kind of weird for the start. We only had ONE question to work with. Kind of odd don't you think ? Usually it would be the whole white board with 4 questions or sometimes just 2, but today we had only 1 ? I think Mr. K believes we're getting the hang of things here. Question: Do you Mr. K ? Anyway we should be starting to get used to them anyway from the homework and reviewing our notes. HINT HINT exam less than 2 weeks, time to test our long term memory guys.

4x³-7x+3 <--- that was the question from today. I will put up the process later today just because I feel like annoying you guys and making you work at it and not just copying it down =D.

EDIT: Solution
y-intercept @ y=3
possible numberators: ±1, ±3
possible denominators: 1, 2 ,4
possible roots: 1/1, -1/1, 3/1, -3/1, 1/2, -1/2, 3/2, -3/2, 1/4, -1/4, 3/4, -3/4

f_(x) = (x-1)(4x2+4x-3)
f_(x) = (x-1)(2x-1)(2x+3)
roots @ x = 1, 1/2, -3/2

Then you graph it, lol it's not because i'm lazy to put in the graph myself but I think we all should be able to create the graph using our calculators. IE. extra practicing using our calculators =D
Edit done

Afterwards Mr. K gave us the schedule for the rest of the week:
Today: Polynomial Function graphing notes and start on ~~Radical~~ Rational Functions
Tomorrow: Continue ~~Radical~~ Rational Functions, graphing and notes
Friday: Finishing off the rest of our notes and finishing off the cirriculum.

Today we had A LOT of notes written down in our dictionaries, mine came to about 2 and a half maybe 3 pages ? lol, but they were in-depth so they should help us when we study for our exam.

~~Radical~~ Rational functions we started with Mr. K explaining to us why we can not divide by the number 0. It is because if we divide by 0, 0 can be any number.
ie.
2 *2 = 4
4/2 = 2
2*0 = 0
0/0 = 2 <--- CAN'T HAPPEN
Afterwards we then began to look at the graph of this function, f_(x) = 1/x, and saw that it never touches 0. It gets close and close and closer to 0 but never touches it. This lead to Mr. K's lesson of "The History of Google," which is acually a number that looks like this 1x10¹⁰⁰. Lol I know I cheated but I'm not going to sit and count 100 zero's lol it's lunch time I still have to eat ;). And that is how class ended today with Mr. K yelling (exageration) out our homework while we piled out of the classroom. (Homework Ex. 56)

BTW tomorrow's scribe is...... Robinna =P

and a little reminder
ODD POWERS CUT THROUGH THE X-INTERCEPT, AND EVEN POWERS BOUNCE OFF THE X-INTERCEPT.
something I thought might help =D

ESS-CRIBE

2006-01-17T18:55:00.000-06:00

Today’s class started off with Mr. K. handing back our project evaluations. He also talked about acrostics for this unit. Yesterday we learned how to graph a polynomial function without a calculator or started to learn how and today we did some more of that.

Important stuff to know:
-The maximum number of roots a polynomial function can have is the number of the highest degree in the polynomial [ex. x²+6x+9~the maximum number of roots this equation can have is 2]
-the end behavior determines which way the arms of the function go [like in a parabola if the end behavior is positive then the arms go up but if it is negative the arms go down]
-polynomial functions are smooth and continuous-they have no jagged points
-the Fundamental Theorem of Algebra says that the number of roots a function has to have is the highest degree in the function [like x³~this has to have 3 roots]
—but not all polynomial functions have roots, they have complex/imaginary roots.

This then brought Mr. K. to talk about how we should stay in math when we go to university/college and he also talked about jobs—for more info go read his blog post:http://pc30s.blogspot.com/2006/01/why-should-i-learn-math_17.html

After that we finished drawing the polynomial function without using a calculator that was on the board yesterday by doing this in these steps: [pictures may be blurry just click them]

We then got this sketch by plotting the roots and the y-intercept onto the grid and drawing the function’s basic shape:

After that Mr. K. put a question on the board that we had to do by ourselves which was draw f(x) = x³ + 3x² -13x – 15 without using a calculator. To figure this out you need to follow the same steps as in the question above ^. If you did then you got something like this:

The last function we had to graph without our calculator was f(x) = 2x^4 + x³ - 17x² - 16x + 12. We only got so far as to find the y-intercept [@ 12] the possible numerators [±1, ±2, ±3, ±4, ±6, ±12], the possible denominators [1, 2], the possible roots [±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2], and we also did some synthetic division but we didn’t get to finish the whole thing because we ran short of time due to the bell, so Mr. K. said we will go over the question tomorrow.

Homework is Ex. 54 [1, 2, 3] & Ex. 55. [and if I made any errors or mistakes just let me know, thanks] ohhh and the scribe is:

Why Should I Learn Math?

2006-01-17T14:38:00.001-06:00

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.

Scribe: Very Sorry Guys!

2006-01-16T22:28:00.000-06:00

Okay, I know it's late, but I just got home for the first time since 8:30 this morning so please bare with me. Also to add to my frustrations Firefox is lost on my harddrive and I dont have enough time to dig it out or re-download it so I'm going to have to do this without pictures or diagrams.

So, it all started off with Mr. K. going around and handing out the "Go For Gold" assignment. Just as a reminder:
-Must get 100%; anything else is unacceptable.
-You can recieve help from anyone at any time on this assignment
-Copying other people's work is completely unacceptable

-Due Monday, January 23, 2006

Then, we had to take some notes into our dictionaries. They were:
-Remainder Theorem
-Factor Theorem
-Synthetic Division

(I will not write the notes in this post, because that's Graeme's job and I don't want to steal his chocolates!)

Following this we continued with today's concept:

GRAPHING FUNCTIONS W/O A CALCULATOR!!!
~We first learned a couple properties of the graphs of functions:
- All even exponents for the equation ( y=x^n ) look like parabolas ( U-Shaped)
- All even exponents for the equation ( y=x^n ) have 3 points in common: (-1,1); (0,0); and (1,1)
- All even exponents for the equation ( y=x^n ) have a minimum of 0 roots.
- All odd exponents for the equation ( y=x^n ) look like cubics (attétude position)
- All odd exponents for the equation ( y=x^n ) have 3 points in common: (-1,-1); (0,0); and (1,1)
- All odd exponents for the equation ( y=x^n ) have a minimum of 1 root.

*Note* The maximum number of roots that a function can have is equal to "n" in the equation ( y=x^n ).*

Finally, we briefly learned about the "Descartes Rational Root Theorem". However, I did not quite understand this so I will only provide the example we were taught and hopefully tomorrow Mr. K. will teach us some more about it.

EXAMPLE: ƒ(x) = 3x^3 - 4x^2 - 5x + 2

Possible Numerators( taken from the the positive and negative factors of the last term): ±1, ±2
Possible Denominators ( taken from the positive factors of the coefficiant of the first term): 1, 3
Possible Roots:(Hope This Works!)

1 ,-1, 1 ,-1, 2 ,-2, 2 ,-2
___ __ ___ __ ___ __ ___ __
1 , 1 , 3 , 3 , 1 , 1 , 3 , 3

Then you check by a new form of Synthetic Division:

* | 3 -4 -5 2
_____________
1 |3 -1 -6 -4 x
-1| 3 -7 2 0 √

.: 3x^3 - 4x^2 - 5x + 2 = (x+1) (3x^2 - 7x +2)

Well that about wraps it up, I'm very sorry, but I was very busy tonight and it didn't help that I've lost Firefox, so thank you for baring with me and I'll try to fix the problems right away.

Oh yeah! By the way there's a couple things (reminders) for Mr. K.
1. Tests back
2. Assignments back ( Mathland)
3. New Acrostic Words

Thank You

and the next scribe is...

Aichelle

Friday's Scribe Post

2006-01-15T20:09:00.000-06:00

Well here I go again doing my scribe post. Sorry that it's so late!! Well todays class started off with two questions. Question 1. (a) on the Factor and Remainder Theorems sheet and a question on the board. We then did the questions together as a class and went through the answers. After that we went into our dictionaries and wrote some notes. (Those notes will we posted or added to Graeme's massive notes post. Don't forget to thank him once again and give him his chocolates.) As class went on we continued writing our notes. Mr. K gave us our homework and then class was over.And the next scribe is CRAIG!!

Friday's Scribe Post

2006-01-15T19:53:00.000-06:00

Sunday Slither!

2006-01-15T12:42:00.000-06:00

Thanks go out to Mrs. Armstrong for pointing to today's game from Think Again!.

The game, from Japan, is called Slither Link.

Rules of Slither Link

    1. Connect adjacent dots with vertical or horizontal lines.

    2. A single loop is formed with no crossing or branches.

    3. Each number indicates how many lines surround it, while empty cells may be surrounded by any number of lines.

Play here.

HAPPY BIRTHDAY REESHARD!

2006-01-15T01:22:00.000-06:00

hahahaha HAPPY BIRTHDAY TO RICHARD a.k.a. ORCHARD a.k.a. REESHARD a.k.a. RICO SWAVI a.k.a. RICKY a.k.a. MALCOLM X a.k.a. ROY!!

Scribe's Sililoquy

2006-01-12T17:49:00.000-06:00

So today in class Mr. K layed out exactly what he wanted to get done. It seemed that division was the "theme" of the day. So first there was the review of last class and grade 5 and 10 division which would be the topic for the class. He gave us the following problems:

Then after we had finished those he asked us if we could see a pattern in relation to the P(-2) for a), P(1) for c) and a P(3) for c) of the numerator of each of those functions that he gave to us and the remainder. Then Craig (of course) had found it and told us, it seems that the answer that was in the numerator after the evaluation had been complete was the remainder! Now we needed a bit more information on how this happens and Mr. K obliged us. It seemed that after a bundle of explaining if you take the root of the denominator and put it in the numerator of the division question and solve you will get your remainder. I don't know if I explained it well but it will have to suffice as my explanation. That would be the Remainder Theorem.

Well I was thinking... "And the use of this is...?" He then went onto explaining his point with the grade 5 problem. The answer to the problem is 718. It takes 3 of those to give you 2154. Well those two numbers they are factors of 2154. Well that also works with polynomials. If it divides evenly then you have factors of that polynomial (no remainder). Which can be useful I guess. That would be the Factor Theorem.

Well we never did get to the Grade 11 way of doing the division but that will be done tomorrow and the scribe for that will be

.... *Drumroll*.........

SCRIBE POST

2006-01-11T13:18:00.000-06:00

Today in class we continued off the notes that we did not finish off yesterday and this was what we wrote.

Many-to-one function

more than one member of the domain
is mapped to a single member of the range. (I could not upload the image because there was an error and I don't know what it is)

One-to-one function

Function where each (one) member of the domain is mapped to a unique (one) member of the range.
(same thing happened I could not do it)

Horizontal line test

Used only on the graphs of functions. (i.e the vertical line test has already been satisfied).
sweep a horizontal line across the graph of any function if the line crosses the graph more than once the function is many-to-one if the line crosses the graph everywhere exactly once then the function is one-to-one.

Relations

Functions

Many-to-one---------One-to-one

A FUNCTION CAN BE LOOKED UP AS A GRAPH, EQUATION, AND TABLE OF VALUES.

One-to-one functions are "special" because they are always "invertible".

Inverse: - the inverse of any operation returns a value from its result to its original value.
- the inverse of a function "undoes" what the original function did.
Example 1:
clean room----------------------messy room }domain
BABY PLAY----------------------PARENT CLEAN-UP
messy room----------------------clean room }range

BABY PLAY and PARENT CLEAN-UP are inverses of each other. Each "undoes" what the other one "does".

NOTATION: given any function f(x) its inverse is written as f-1(x) (-1 is a power more like a square but different)
IMPORTANT: f-1(x) can not equal 1/f(x)
REMEMBER: given any function f(x) and its inverse f-1(x), the domain of f is the range of f-1 and the range of f is the domain of f-1 (see example 1)

Inverses Defined Numerically

Given any ordered pair (x,y) its inverse is (y,x). Given any function defined in a table of values, the inverse function is found by exchanging the domain and range.

Example 2:

f
x----y
(-2)--(-1)
(-1)--(1)
(0)--(3)
(1)--(5)
(2)--(7)

f-1
x----y
(-1)--(-2)
(1)--(-1)
(3)--(0)
(5)--(1)
(7)--(2)

Inverses Defined Symbolically (as equation)

1- Algebraically: to find the inverse of any function exchange the variables x and y and solve for y.

Example 3: Find the Inverse of y=2x2-3

finding the inverse
x=2y2-3
x-3=2y2
x-3/2=y2
square root of x-3/2=y

so that was it for today but the notes are unfinished and we will finish tomorrow in class.
OH YAH DON'T FORGET GraemeW CHOCOLATE BARS TOMORROW
Since GraemeW is getting chocolate bars tomorrow u can be the SCRIBE FOR TOMORROW.
HAVE FUN

Super... (secret) SCRIBE!!!

2006-01-10T16:40:00.000-06:00

Well today... Like OVER HALF THE CLASS WAS GONE!!! (doing an English exam) So... We fooled around and partied the hole class!!!! Hahahaha. Just kidding. Well we partied until I mentioned the scribe post... Then they elected me as scribe... Thanks guys... Robert... Hahaha Well anyways.. Today in Class.. We. Talked like forever... On math... and it was fun... Hehehe...

Anyways... We did questions... Hahaha... Questions on functions that we did yesterday.

Question #1

Question #2

Question #3

Well figure them out... Hahahahaha. Answers will be posted at 10:00 ;) Hahaha.

After that we put some Function notes in or Handy Dandy Dictionary. Hahaha... (couldn't resist)

Functions

Function: A function is a rule that changes one number or expression (The Input) into another number or expression (The Output)

The set of all possible inputs is called the domain.
The set of all possible outputs is called the range.

Functions (as opposed to relations)
Are rules that nave a special constraint:
Each member of the domain (the inputs) is mapped to (can be changed into) only one number of the range (only one output).

Notation: f(x) means "the rule f is appilied to a number or expression x."

Many-to-one Functions

Functions where more than one (many) members of the domain are mapped to a single (one) member of the range.

So then... The bell rang... and he never finished... Hahaha. Then... Yeah... My new name is... Richard, Roy, Malcolm, Orchard, Rico Swavi, Von-E-Rechard, Rechard, Kraimer, Ricky etc... etc... etc..

Hahaha.. Math was fun today... lol.

Well I'm out. NO HOMEWORK!!! Unless you want to figure out those questions. Hahaha. Remember Answers at 10. Hahaha. Later.

Oh yeah... Tomarrow's scribe is... YESTERDAY'S SCRIBE!!!!!

And that is... ABDI

Oh I almost forgot... SUPRISE QUIZ TOMARROW!!!

HAHAHAHAHA... Just Kidding :P

10:00... ANSWER KEY

Functions!

2006-01-09T18:26:00.000-06:00

Well we started off the new year with a new unit. FUNCTIONS!
A function is a rule that puts in an input and give only 1 output. You can determine its a function by doing a verticle test line, and if it touches the graph just once, then it is a function.

All functions are relations, but not all relations are functions.

An example of a relation, that is a function is:

An example of a relation, that is not a function is:

When Adding or Multipyling functions, order in which you put them in doesn't matter, this is called the Commutative Law.

When Subtracting or Dividing, order in which you put them in does matter because it can result in different answers.

With that said if you are given 2 elemenatary functions:

Adding them:

Subtracting them:

Mulitplying them:

Dividing them:

Well this is all I got for now, if there is anything missing or something is wrong, please feel free to correct me. It's the beginning of coming back from 2 weeks off, so there's probably more things missing then usual. (hehe..)

The next scribe is Abdi

Just For Fun (or Getting Ready to Think Again!)

2006-01-07T13:48:00.000-06:00

I found this "test" over at Teaching and Developing Online. Try it out .... just for fun. ;-)

Below are four (4) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately.

OK?

Let's find out just how clever you really are. No looking at the answers in advance.

Ready? GO!!! (scroll down)

First Question:

You are participating in a race. You overtake the second person.

What position are you in?

Answer:If you answered that you are first, then you are absolutely wrong!

If you overtake the second person and you take his place, you are second!

Try not to mess up in the next question.

To answer the second question, don't take as much time as you took for the first question.

Second Question:

If you overtake the last person, then you are...?

Answer:If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST Person?

You're not very good at this! Are you?

Third Question:

Very tricky math! Note: This must be done in your head only.

Do NOT use paper and pencil or a calculator. Try it.

Take 1000 and add 40 to it. Now add another 1000. Now add 30.
Add another 1000. Now add 20. Now add another 1000 Now add 10.

What is the total?

Scroll down for answer.

Did you get 5000?

The correct answer is actually 4100.

Don't believe it? Check with your calculator!

Today is definitely not your day.

Maybe you will get the last question right?

Fourth Question:

Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono.
What is the name of the fifth daughter?

Answer:Nunu?

NO! Of course not.

Her name is Mary!

Read the question again.

Okay, now the bonus round:

There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one's teeth he successfully expresses himself to the shopkeeper and the purchase is done.

Now if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?

He just has to open his mouth and ask, so simple.

So simple it is ... ;-)

Morning before the test

2005-12-22T07:08:00.000-06:00

Well isn't this strange that I nearly forgot to blog. Hahaha. Why does this keep on happening to me. Well I like to say that this unit was fun in the way that it was. Hahaha. Craig. Hahaha. What a guy. Finishes the logic puzzle and then the second logic puzzle next peroid. Hahaha. Wow. You have to do this to us you know. Hahahaha. Well anyways.... Um.. Back to studying I guess. Hahaha... and Good Luck you guys.

blogging before the test

2005-12-21T23:21:00.000-06:00

wow this unit went by fast! it was pretty much all common sense after everything else fall into place. So basically this unit was pretty easy except for the Venn Diagram because I always get confuse on where to shade the parts that your suppose to do. The logic unit was pretty fun. It made us all think until our brains hurted lots! Unlike Craig who can figure it out in less then twenty minutes!! so yeah if i don't see you guys i just want to say:

merry christmas and a happy new year=)

and good luck

last blog before the break =)

2005-12-21T23:13:00.000-06:00

WOW almost forgot to post a blog up...but good thing Craig reminded me haha well he didn't really but you know what i mean haha....all i have to say is that this unit went by so quick, and to me i found this unit to be really easy i understood practically everything that was goin on from the venn diagrams to those logic problems, and i really did enjoy this unit it was nice and simple haha...but yeah just want to wish everyone a good luck and to craig i will TRY to succeed in beating you tomorrow haha even if you are fast and real crazy at doing those logic problems haha

blog before the test

2005-12-21T22:38:00.000-06:00

I think this unit is the shortest unit and the one that i enjoyed the most. I think its fun solving the Logic Problems. But unlike Crazy Craig,who can finish it in less than 25 mins., it takes me awhile to figure them out. The one that i liked the most is the one with the forensic experts. The uh, Kansas one. ^_^ pretty cool. I like this Unit because its the easiest unit so far. haha. At first, i didnt really understand the converse, inverse and contrapositive because i was away when they talked about it in class but Mr. K's post helped me alot. ahah. Doing the Venn Diagrams are fun too. The thing that im having a little difficulty with is the indirect reasoning but i still think that this unit is fun.

GOODLUCK ON THE TEST YOU GUYS. ^_^

blog post

2005-12-21T22:24:00.000-06:00

so tomorrow will be our last test for this year in pre-cal. we had tackle up a lot of unit before this test. doing logic problems needs a lot of patience specially if only few clues are given. the part that i'm still having a problem with is the NOTATION part. i got screwed up when i see "union", "intersection", "compliment" or "exclusion" being used together in one problem. i still need to study up that part. i hope i'm doing good in consumer math part cause i did it last year.

Advance Merry Christmas to all and Happy New Year too...

blogging

2005-12-21T21:09:00.000-06:00

wow this unit just flew by. wasn't as packed with so much info as i thought it would be when Mr. K talked about what we were going to do this week. From starting to relearn about venndiagrams!? Wow take me back to grade 6 and 7. From comparing characters from books. haha. I had the most trouble with the venn diagrams though because having to shade in which particular region got me very confused but after doing numerous question it seemed a bit easier. Also the logic stories and questions weren't as hard but your mind just has to be in that habit of getting the hang of thinking that way. Then the matrix questions didn't seem that hard to do because it's just the matter of reading clues and sticking the information you find from those clues to figure out what you're looking for. Well that's about it, good luck to everyone on the test tomorrow.

Blogging at its Best!

2005-12-21T20:21:00.000-06:00

Hey, well its that time again. Man has this past month been psycho or what! Crazy. Anywho, the concept of logic is actually in my opinion a pretty simple concept. (That's going to come back to haunt me). But the thing is it is simple in a complicated way. At first glance my mind was careening in all directions! "What! No formula's! No rules! AARRGG!" but once you understand what your looking for and how to find it, things just fall into place. Not only that but this concept has sort of opened my eyes to the "fun" part of math. Or at least ways of making it fun and challanging. Well that is all for me tonight so good lucj everyone on the test tomorrow and Merry Christmas if I don't get the chance to mention it. :)

My Logic Acrostic

2005-12-21T19:46:00.000-06:00

L ogic is a matter of controversy amongst philosophers.
O ther definition of logic is the study of the origin and natural sequence of fundamental ideas.
G uides reasoning within a given situation.
I s most often said to be the study of arguments.
C omplete, sound, and consistent, but not decidable.

Last Scribe Post before the Holidays !

2005-12-21T19:44:00.000-06:00

WHY THANKS ALOT LIZ FOR MAKING ME SCRIBE .

Anyways today in class We first went over the "A Usual Day at Unusual School". Mr.Kuropatwa went over each person in the class and we figured out who was which.

Here are the answers :
Mrs. Smart - bright
Mr. Bumbleton - brave
Ms. Boss - brave
Jan - bright
Mike - bright
Pat - brave
Denise - bright
John - bright
Emily - brave
Billy - bright
Susan - brave
Sandra - bright
Pete - brave
Dan - bright
Alice bright
Tom - brave
Connie - bright
Mark, Pam , Tony and Becky are - unknown

To figure out this problem [or any other problems like this] you should assume one is either a bright or brave then if there is a contradiction for what you had assumed then the opposite must be true.

After that we went over Number 3 on the Matrix Logic Problems Sheet.
If you had trouble making the matrix remember the *staircase and the number of different categories that go across the top and vertically is one less than the number of categories. If you're stuck while trying to fill in the matrix look at the boxes that are completely filled for other clues to fill in the other boxes. AND once you've decided you can't find out any more boxes from the clues try and switch pen colors to help you determine who did what.

Next Mr. K explained some of the things we need to know for the test:
BE SURE KNOW YOUR DEFINITIONS [IN YOUR DICTIONARY]
KNOW HOW TO WORK WITH SETS [WE LEARNED FOUR OPERATIONS]
HOW TO SOLVE PROBLEMS WITH VENN DIAGRAMS [GOOD QUESTIONS IN "GETTING READY FOR THE TEST POST"]
BE ABLE TO KNOW HOW TO FIND COUNTEREXAMPLES
KNOW HOW TO SOLVE LOGIC TYPE QUESTIONS!

*** PRETTY MUCH JUST STUDY EVERYTHING WE'VE LEARNED, DO THE REVIEW =) and You'll DO GRRRREAT ! ***

OH, AND CONGRATULATIONS TO CRAIG FOR SOLVING MULLINER'S MIRACLE CURES LOGIC CHALLENGE IN LESS THAN 25 MINUTES!!! YOU ARE TRULY AMAZING hahah .

and the first scribe for 2006 is .. JACKY S.

HAPPY HOLIDAYS
MERRY CHRISTMAS TO ALL & A HAPPY NEW YEAR.

blogg'n for the test

2005-12-21T19:30:00.000-06:00

Doing this early, before I once again lose an easy mark for the test. Well I thought this unit was easier than the last unit. It was also alot shorter. But I guess the thing I had trouble on in this unit was the matrix problems, so confusing! and the fact that everything in this unit doesnt have to deal with just one thing but a whole other stuff at one time. I think the most fun for me in Logics were the venn diagrams, only because their the ones I actually still remember doing from last year. Well I guess this is it for now, Good luck on the test everybody!!

blogging before the logic test

2005-12-21T18:55:00.000-06:00

Well, this unit went by really fast. To me, this unit was a bit confusing. I thought the Venn Diagram problems were pretty easy. The thing I had trouble with was indirect and direct reasoning. It was pretty confusing at first but I think I got the hang of it now. I thought the matrix problems were fun. Even though some of them were difficult, it was fun to do. Well that wraps it up for today. Remember, the assignments for booklet 2 are due tomorrow. Study for the test and good luck!

Blogging Before The Test

2005-12-21T17:43:00.000-06:00

Wow this unit went by QUICK . I don't think I can really sum this unit up in this post because it's logical, it's basically using some common sense and thinking out of thee box from time to time . Well just a few reminders .. remember to always put a Universe for your Venn Diagrams . Also an argument is ONLY valid if thee result is a direct consequence of it's premise. And a sound argument is when it's both valid and true . Also the difference between inductive and deductive . Well there's are just a few definitions from YOUR dictionary .. make sure you read over them . Good luck to everyone and I hope you all have a happy holiday =)

reflection

2005-12-21T17:28:00.000-06:00

Logic...eh? haha..When we first started with the Venn Diagrams it reminded me of elementary...oh what memories...just kidding. I thought it was pretty straight forward and I understood it. The operations sort of get confusing when they are operations within operations but it's easy once you work it out. Conditional statements...those are funny haha "It will rain today if and only if I wear a hat" I still have to remember the notation for each of the types of statements because I don't know some of them, I'll just reread them until I'm comfortable---actually everyone should do that. Indirect reasoning...that can get quite confusing, it's also sort of funny. Matrix logic problems...those are quite fun because it's like a mystery that you need to solve..fun, fun, fun...except the super hard ones...or more challenging ones are...harder to solve..unless you are hardcore like Craig...he's a smart cookie..

I hope you all do well on the test tomorrow and don't forget to do a reflection..it's an easy mark, as well as your acrostic if you want to do one
study your defintions
do the review
and do the online quizzes that were provided for us..Good Luck!

A-Log-tic

2005-12-20T22:35:00.000-06:00

•Venn stole Eüler's Circles and named them after himself.
•Each Venn Diagram has a UNIVERSE which includes all the numbers inside and outside of the circles.
•Null sets are a subset of every set.
•Not all objects in a universe are inside the circles

•Definition of a SET is a collection of objects
•In English, COMPLIMENT ( ' ) means "NOT"
•A complimented set excluding a regular set is equal to the compliment of the two regular sets unioned together. e.g. [ A'\B = (AUB)' ]
•Give all of your Venn Diagrams a universe around it and labels for each set when drawing them
•Reading "AUB" in English would be said "Set A UNION(or) Set B"
•A set must have at least two subsets: itself, and a null set
•Meaning of INTERSECTION (Ω) in English is "AND"

A-Log-tic

2005-12-20T22:13:00.000-06:00

Scribe or what ?

2005-12-20T18:15:00.000-06:00

Well we started off today with some questions on the board :
1) One of the Isle of view (say it aloud =P) knights always tell the truth and knaves always lie. You just arrived and met two people, Mr. A and Mr. B. Mr. A says, "At least one of us is a knave" . What are A and B ?

First make the assumption that the speaker (Mr. A) is one or the other. We'll pretend that Mr. A is a knave, meaning he only lies. If he was a knave and he said that he'd be speaking the truth and he can't do that. They both can't be knaves because then the statement would be a true statement. If we had one knave and one knight, the statement would be true, therefore Mr. A can't be a knave and he has to be a knight.

Mr. A = knight
Mr. B = knave

* Proof by contradiction
- assume the opposite
- if there is a contradiction, then the opposite must be true

2) A little later you meet Ms. C and Ms. D. Ms. C says "I'm a knave but D isn't." What are C and D?

C can't be a knight because she can't say she's a knave because that would be a lie. Therefore she has to be a knave. (indirect)
Assume : Ms. C is a knave (liar)
In logical a conjuction both ideas have to be true for the statement to be true. However, if one idea or part of the conjuction is false then the whole thing is false.

Ms C is knave meaning that she can't say that she's a knave .. BUT when she used a conjuction and put together a true AND a false statement .. meaning that she lied .

Ms. C is knave meaning that Ms. D must also be a knave because the second part of her conjuction has to be false "but D isn't" meaning the opposite.

Next we got a hand out called "Matrix Logic Problems". We did that first one in class.

1) Three of our Olympic swimmers took 1st, 2nd, and 3rd in their race at the Olympic games. When they went to the victory stand each wore a different colored swimsuit. From the clues below tell the name, place, and swimsuit color of each swimmer.

a) The first place swimmer wore a red swimsuit.
b) Tract took 3rd place.
c) Nancy wore blue.
d) Mary and the girl in the white swimsuit were roommates.

Using the clues above and using a matrix, we get this :
Now using some thinking ..We get that Mary must be red because she can't be white or blue, and she has to be 1st because 1st place wears red. Nancy wears blue (given), which means that the only color that Tracy can wear is white. Also Tracy is 3rd (given) meaning that 3rd place winners wear white. Then the only place left is 2nd, and Nancy is the only one left and she wears blue.

Meaning:
Mary - 1st - Red
Nancy - 2nd - Blue
Tracy - 3rd - White

Also we got a story called "A usual day at Unusual School" BUT .. I won't give you my answers because it's due tomorrow and it's more fun figuring things out on your own =)

Getting Ready For The Test

2005-12-19T22:22:00.000-06:00

A few links you may find useful in preparing for your test on Thursday:

Venn Diagrams

Conditionals (If ... then ...)

Biconditionals (... if and only if ...)

Related Conditionals (the other ones)

And here are a few quizzes (refresh the page for more) ...

Inductive Reasoning and Conjecture (5 questions)

Conditional Statements (5 questions)

Venn Diagrams Self Test (13 questions)

And finally, here are some logic puzzles to practice with ...

Dude Ranch Blues

Afterschool Activities

Monkey Business

Farmyard Pandemonium

What did you order?

Study hard and do your best work; work you're proud of!

The Massive Notes Post

2005-12-19T21:57:00.000-06:00

Allright folks, here are the up-to-date set of notes with the other notes in it just for the sake of easy access, I still need to put the Venn Diagram Notes and the Chart but I'm lazy. I'll do them during the holidays. Use them well.

Notes Set 1: Quadratic Functions

Notes Set 2:How to Write Interval Notation and Set Builder Notation

Notes Set 3:The Standard Form for the Equation of a Parabola

Notes Set 4: The Factored Form of a Parabola

Notes Set 5: The General Form for the Equation of a Parabola

Notes Set 6: Completing the Square

Notes Set 7: Completing the Square On the General Form

Notes Set 8: Trigonometry

Notes Set 9: Sinusoidal Graphs

Notes Set 10: Deriving the Quadratic Formula

Notes Set 11: Imaginary Numbers and Working with Quadratic Roots

Notes Set 12: Working with Quadratic Roots

Notes Set 13: Analytic Geometry

Notes Set 14: My Analytic Geometry Toolkit

Notes Set 15: Systems of Linear Equations

Notes Set 16: Circle Geometry

Notes Set 17: The Anatomy of a Circle

Notes Set 18: Circle Theorems

Notes Set 19: Logic

Venn Diagrams

2005-12-19T16:57:00.000-06:00

Venn Diagrams consist of a Universe, which is the set of all objects being considered
Empty sets have nothing in it
Null set is another way of saying empty set
Numbers, people and things are examples of sets in a Venn Diagram

Definition for Union is when you gather all the objects in two or more given sets
Intersections are objects that are common to two or more given sets
A smaller collection of objects taken from a given set is called a subset
Gathering every object outside a given set is a compliment of that set
Remember "\" means exclusion, so that means you gather everything in a given set EXCLUDING other objects within another given set
All sets within a Venn Diagram are also their own subsets
Make sure you draw a Universe for all of your Venn Diagrams, it's very important!

Logical Acrostics

2005-12-19T15:27:00.000-06:00

Here's the new set of acrostics for you.

Blogging Prompt
Your task is to create an acrostic "poem" that demonstrates an understanding of logic related to any one of these concepts:

REASONING
CONDITIONAL
COUNTEREXAMPLE
VENN DIAGRAM
DEDUCTION
INDUCTION

As an extra challenge (worth an additional bonus mark) try to make a Double Acrostic, that is, each line should begin and end with a letter of the word you are working with.

Remember, this is a bit of a race. Your answers have to be posted to the blog in the comments to this post. If someone has already used a word or phrase in their acrostic you cannot use the same word or phrase. i.e. It gets harder to do the longer you wait. ;-)

Here is an example of an acrostic that Mrs. Armstrong wrote:

Always in 2 dimensions
Region between the boundaries
Entire surface is calculated
Answer is in units²

Be creative and have fun with this!!

SCRIBE

2005-12-19T13:53:00.000-06:00

I guess we did not do much in class today. Mr. K. Started up by giving us Consumer Mathematics Student Reference Book 2 and 3 other sheets which are Unit Price And Exchange Rate Assignment, Budgeting Assignment, and Budgeting Form. We are suppose to be working on this and hand-in the Assignment on Thursday. Then he asked us if we had question on Friday's assignment but then we were good. So Friday's assignment was suppose to be hand-in today but then he gave us an extra day, so that assignment is due tomorrow which is Tuesday. Yah and then he asked us something about grade 8, if we still remembered anything from grade 8. Mrs. K. Was there and they argued about this and I think Mr. K. Happen to remember most of things he did in grade 8 and I thought that was weird. And he explained the New Assignment which is to be hand-in on Thursday. And he told us a story about the bank which he said that banks round too much and we should REMEMBER THAT FRACTION ARE OUR FRIENDS. He told us that we should look at the numbers first which I did not get it. That was when he was explaining the second assignment. The last thing is that we wrote notes on "Conditional Statements" but the problem is that I don't how post it because of the table, so if you know how holla at me and I will try fixing it.

AND THE NEXT SCRIBE IS elizabethh

Sunday 3x the Funday

2005-12-18T09:25:00.000-06:00

A triple header this weekend.

Mr. Zhong Kui will make you laugh. I think his "problems" are the easiest ones to solve.

Rat is another "escape" puzzle. Every time you do something wrong he squeaks.

No. 5 is a set of three puzzle/adventures to get a little boy out of trouble.

Have Fun!

scribe post

2005-12-16T21:08:00.000-06:00

today in class, we have a substitute teacher cause mr. k have a meeting with other math teachers. we started a new unit, Consumer Math. this unit will end as soon as we finish reading the "consumer mathematics book 1 & 2" and do the assignments about it. there is nothing much to talk about it because the hand-out have everything on it to describe how things work. about the 1st question in income and wages assignment, just remember that it works almost as same as the graduated commission. the only difference is that instead of percentage, rate per unit is given. income wage assignment and property taxes assignment are to be handed in on monday.

the next scribe is... Abdi.

Scribe for Today

2005-12-15T23:22:00.000-06:00

So the scribe today is me! Well today in class, we had a surprise quiz...as usual :)

The first question was:

1) Which of the following examples of reasoning are INDUCTIVE and which are DEDUCTIVE?

Every time we have a club meeting, I have a test in school the next day.
- INDUCTIVE
REVIEW * Inductive is when we observe several particular examples of something and then conjecture that it must always be the case.
Susan’s father brought her early to school each day. She noticed that Ms. Taylor, her math teacher, arrived at 7:30 each day for several weeks. Susan said, “Ms. Taylor always arrives at 7:30.”
- INDUCTIVE
All students in senior high must enroll in physical education. John is a student, so he concludes that he will take physical education.
- DEDUCTIVE
REVIEW * Deductive is when we argue from basic (inarguable) truths (like definitions) to a valid conclusion.
The sun has risen each morning from time immemorial. We can be certain it will rise tomorrow.
- INDUCTIVE
e. Anyone who likes to play football likes to play basketball. Sheeva likes to play football. We conclude that she likes to play basketball.
- DEDUCTIVE
f. Triangle ABC is an equilateral triangle. We can conclude that AB is congruent to AC.
- DEDUCTIVE
g. Joe counted the number of cars of different colors that passed his house in 15 minutes. More than half the cars were white. He decided that white is the most popular colors for cars.
- INDUCTIVE

The second question was:

2) Which of the above conclusions are VALID and which are INVALID?

A. INVALID
REVIEW * Invalid is when its conclusion is NOT a direct consequence of its premises---even if its premises (basic truths) and conclusion (the result of an argument) are true.
B. INVALID
C. VALID
REVIEW * Valid is when its result is a direct consequence of its premises.
D. INVALID
E. VALID
F. VALID
G. INVALID

After the quiz on logic, Mr. K gave us a Venn Diagram Problems sheet to work on the first problem which was called Music Survey and the problem was:

Recently several students at DMCI were questioned about their favorite music groups, with the following results:

- 22 like Hole
- 25 like U2
- 39 like Third Eye Blind
- 9 like U2 and Hole
- 17 like Hole and Third Eye Blind
- 20 like U2 and Third Eye Blind
- 6 like all three
- 4 like none of these performers

(a) How many students were questioned?

Also in class, Mr. K told us to write down the meaning of Counter Example on our dictionary. For those of you who missed the class today, here it is.

COUNTER EXAMPLES: given any logical argument of mathematical theorem, if you can find only one case where it is NOT true, then the entire argument of theorem is false and must be discarded---this is called a counter example.

Mr. K told us in class today about the “Fermat Theorem” which was really interesting and I even looked up on it on the internet to get more information about the Fermat Theorem. Here it is:

Pierre de Fermat died in 1665. Fermat is the most famous number theorist who ever lived. He was in fact a lawyer and an amateur mathematician. The fact that he published only one mathematical paper in his life and that was an anonymous article written as an appendix to a colleague's book. Because Fermat refused to publish his work, his friends feared that it would soon be forgotten unless something was done about it. His son, Samuel undertook the task of collecting Fermat's letters and other mathematical papers, comments written in books, etc. with the object of publishing his father's mathematical ideas. In this way the famous 'Last theorem' came to be published. It was found by Samuel written as a marginal note in his father's copy of Diophantus' s Arithmetica.
Fermat's Last Theorem states that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2.
Format wrote: “I have discovered a truly remarkable proof which this margin is too small to contain.” Fermat realized that his remarkable proof was wrong when he first studied Diophantus' s Arithmetica around 1630, however, since all his other theorems were stated and restated in challenge problems that Fermat sent to other mathematicians. Although the special cases of n = 3 and n = 4 were issued as challenges (and Fermat did know how to prove these) the general theorem was never mentioned again by Fermat.
In fact in all the mathematical work left by Fermat there is only one proof. Fermat proves that the area of a right triangle cannot be a square. Clearly this means that a rational triangle cannot be a rational square. In symbols, there do not exist integers x, y, z withx2 + y2 = z2 such that xy/2 is a square. From this it is easy to deduce the n = 4 case of Fermat's theorem.
It is worth noting that at this stage it remained to prove Fermat's Last Theorem for odd primes n only. For if there were integers x, y, z with xn + yn = zn then if n = pq, (xq)p + (yq)p = (zq)p.
Euler wrote to Goldbach on 4 August 1753 claiming he had a proof of Fermat's Theorem when n = 3. Euler's mistake is an interesting one, one which was to have a bearing on later developments. He needed to find cubes of the form p2 + 3q2 and Euler shows that, for any a, b if we put p = a3 - 9ab2, q = 3(a2b - b3) then p2 + 3q2 = (a2 + 3b2)3. The next major step forward was due to Sophie Germain. A special case says that if n and 2n + 1 are primes then xn + yn = zn implies that one of x, y, z is divisible by n. Hence Fermat's Last Theorem splits into two cases.
Case 1: None of x, y, z is divisible by n.
Case 2: One and only one of x, y, z is divisible by n.
Sophie Germain proved Case 1 of Fermat's Last Theorem for all n less than 100 and Legendre extended her methods to all numbers less than 197. At this stage Case 2 had not been proved for even n = 5 so it became clear that Case 2 was the one on which to concentrate. Now Case 2 for n = 5 itself splits into two. One of x, y, z is even and one is divisible by 5. Case 2(i) is when the number divisible by 5 is even; Case 2(ii) is when the even number and the one divisible by 5 are distinct.
Case 2(i) was proved by Dirichlet and presented to the Paris Académie des Science in July 1825. Legendre was able to prove Case 2(ii) and the complete proof for n = 5 were published in September 1825. In fact Dirichlet was able to complete his own proof of the n = 5 case with an argument for Case 2(ii) which was an extension of his own argument for Case 2(i).
In 1832 Dirichlet published a proof of Fermat's Last Theorem for n = 14. Of course he had been attempting to prove the n = 7 case but had proved a weaker result. The n = 7 case was finally solved by Lamé in 1839.He sketched a proof which involved factorizing xn + yn = zn into linear factors over the complex numbers. Lamé acknowledged that the idea was suggested to him by Liouville. However Liouville addressed the meeting after Lamé and suggested that the problem of this approach was that uniqueness of factorisation into primes was needed for these complex numbers and he doubted if it were true.
Much work was done in the following weeks in attempting to prove the uniqueness of factorization. Wantzel claimed to have proved it on 15 March but his argument He is correct about n = 2 (ordinary integers), n = 3 (the argument Euler got wrong) and n = 4 (which was proved by Gauss).]
Despite large prizes being offered for a solution, Fermat's Last Theorem remained unsolved. It has the dubious distinction of being the theorem with the largest number of published false proofs. For example over 1000 false proofs were published between 1908 and 1912. The only positive progress seemed to be computing results which merely showed that any counter-example would be very large. Using techniques based on Kummer's work, Fermat's Last Theorem was proved true, with the help of computers, for n up to 4,000,000 by 1993.
Further work by other mathematicians showed that a counter-example to Fermat's Last Theorem would provide a counter -example to the Shimura-Taniyama-Weil Conjecture. The proof of Fermat's Last Theorem was completed in 1993 by Andrew Wiles, a British mathematician working at Princeton in the USA.
This, however, is not the end of the story. On 4 December 1993 Andrew Wiles made a statement in view of the speculation. He said that during the reviewing process a number of problems had emerged, most of which had been resolved. However one problem remains and Wiles essentially withdrew his claim to have a proof. He states
The key reduction of (most cases of) the Taniyama-Shimura conjecture to the calculation of the Selmer group is correct. However the final calculation of a precise upper bound for the Selmer group in the semisquare case (of the symmetric square representation associated to a modular form) is not yet complete as it stands. I believe that I will be able to finish this in the near future using the ideas explained in my Cambridge lectures.
In March 1994 Faltings, writing in Scientific American, said
If it were easy, he would have solved it by now. Strictly speaking, it was not a proof when it was announced.
Weil, also in Scientific American, wrote
I believe he has had some good ideas in trying to construct the proof but the proof is not there. To some extent, proving Fermat's Theorem is like climbing Everest. If a man wants to climb Everest and falls short of it by 100 yards, he has not climbed Everest.
In fact, from the beginning of 1994, Wiles began to collaborate with Richard Taylor in an attempt to fill the holes in the proof. However they decided that one of the key steps in the proof, using methods due to Flach, could not be made to work.
Wiles worked on it for about two weeks, and then suddenly inspiration struck.
In a flash I saw that the thing that stopped it [the extension of Flach's method] working was something that would make another method I had tried previously work.
On 6 October Wiles sent the new proof to three colleagues including Faltings. All liked the new proof which was essentially simpler than the earlier one. Faltings sent a simplification of part of the proof. No proof of the complexity of this can easily be guaranteed to be correct, so a very small doubt will remain for some time. However when Taylor lectured at the British Mathematical Colloquium in Edinburgh in April 1995 he gave the impression that no real doubts remained over Fermat's Last Theorem.

Click for the full information on Fermat Theorem

NEXT SCRIBE IS ALDRIDGE :)

SCRIBE.

2005-12-15T16:09:00.000-06:00

late post? yes, i know... IM REALLY SORRY =(

hmm what happened in class yesterday?
okay,when we got to class Mr. K asked us to draw a BIG circle on a piece of paper. Before we started our activity he mentioned that "Math is science of patterns".

Then Mr. K started off by asking us... "If we connect two points (along the circumference of the circle) how many regions will the circle be divided into ?"

We all know that if we connect two points then it will be divided into 2 regions.

"how about 3 points connected all together?"
he drew on the board three points along the circumference of a circle then counted the number of regions. 4 regions.

and then he asked us to choose 4 points along the circumference of the circle, connect it and count how many regions the circle was divided into. 8 regions.

then we made a chart that looked like this:

looking at the table/chart, is there a pattern? yes there is..

what is the pattern? the number of regions goes up by multiplying 2 to it.

then Mr. K asked us to guess what the next number would be.

"16" the students answered...

is that correct?

well, we have to check if it is...so we drew 5 points along the circumference of the circle and counted the number of regions.

16! we were right !

Then Mr. K asked if the number of points was "n", can we come up with a formula for it?

one of the students said " if n represents the number of points then the number of regions will be 2^n-1.

why "n-1"?

n-1 because the exponent of the number of regions is always one less than the number of points.

Then Mr. K asked what if we have 6 points connected all together? how many regions will the circle be divided into?

using the formula : 2^6-1 or 2⁵ we got 32.

and just like before we have to check... so we drew a circle with 6 points connected to each other then counted the regions.

31 regions ?! only 31. That means that the formula we came up with is not true and must be discarded.(some may have gotten only 30 regions. why? maybe you just missed counting a little region or you drew your circle too many) notice that there`s a little triangle region in the middle of the above diagram? if you drew your circle big enough then it should show.

Therefore 6 is the counter example for the formula 2^n-1.

coun·ter·ex·am·ple;

-an example that disproves a hypothesis, proposition and/or theorem.

"PRIME PRODUCING" POLYNOMIAL

F(x)=x²+x+41

is this really a prime producing formula? let`s check it out.

F(1) = 43 prime

F(2) = 47 prime

F(3) = 53 prime

F(4) = 61 prime

F(5) = 71 prime

okay, so far all the result are prime numbers but is it right to conclude that f(x) will be prime for ALL intergers?

answer: NO

why?: because if you try to solve it with x = 40

F(4o)=4o²+4o+41

F(40)=40(40+1)+41

F(40)=1681 which is also 41²

MARIN MERSENNE.

(picture taken from:http://shl.stanford.edu/Eyes/kircher/mersenne.html)

Marin Mersenne is a french theologian, natural philosopher, and mathematician who tried to find a formula that would represent all primes but didn't succeed. Although he failed, his work on numbers of the form
2^{p - 1}

p prime

is still of interest in the investigation of large primes.

He's name is best remembered today for Mersenne Prime.

Mersanne Prime: are primes of the form 2^p-1.

For more about Mersanne Primes: *click_here* or here

(it includes a table of known Mersenne Primes, who discovered it and when)

So far they have only found 42? mersenne primes.

Wanna become world famous? or even win some cash? You can participate in what they call GIMPS. Great Internet Mersenne Prime Search. They have already found seven of them on GIMPS.

If you're interested you can CLICK_HERE. It tells you how it works, how long it will take, how much you can win, what you need to have, EVERYTHING you need to know. :)

for more about Marin Mersanne clickhere

VENN DIAGRAMS

Mr. K also posted up some questions on the board.

1.) In a group of students 12 are taking chemistry, 10 are taking physics, 3 are taking both and 5 are taking neither. How many students are in the group?

ANSWER: 24 students are in the group

2.)In a third-rate rock band, 3 people play guitar, 4 sing, 2 do both and 6 have no talent for singing or guitar so they do something else. How many are in the band?

ANSWER:There are 11 people in the band.

3.)There are 64 kids in the "Tiny Little Cherubs"(TLC) Daycare. At lunch 59 ate green beans, 56 cauliflower, 60 ate brocolli, 55 ate green beans and cauliflower, 54 cauliflower and brocolli, 56 green beans and brocolli and 53 ate all. How many ate none?

ANSWER: One kid ate none.

OKAY... maybe i exaggerated when i said it wasnt half way yet -_-". lol. hhm, thats all i could remember...so i guess this is it.

THE EEND :)

sorry again for being late!
*if i missed anything please let me know*

oh and i found a cool site about prime puzzles and problem connected. I don't have a delicious account so i guess ill just link it in here.

primepuzzles

There's a new puzzle every saturday and the solutions will be up one week later.

oh... the scribe today was jamilynG. check out her scribe post for tomorrow's scribe.

Venn diagrams

2005-12-13T16:10:00.000-06:00

Today we discuss about Venn Diagrams and how they were originally called Eulers circles. Then we started talking about how 6 is the first perfect number. Then we talked about how Euler had 11 children. But Sadly only 5 survive because of all the deceases back then. So anyways we started to take notes about sets.

set: a collection of objects may be things, people, numbers, etc....

subset: a "smaller" collection of objects taken from a given set.
universe: the set of all objects being considered.
null set: (A.K.A. the empty set) the empty set (it's got nothing in it) is a subset of every set. It is written as {O}.

operation on sets:
union (U) aUb means gather all the objects in set A with all the objects in set B.
Union(U) means "or".

Compliment: (A') means everything that is outside set A
compliment (A') means "not".

exclusion(/) a/b means everything that is in set A excluding those things that are also in set B
exclusion(/) means excluding.

Intersection A (upside down U) B means gather all the objects that are in both set A and B
intersection A(upside down U) B

After we wrote in our dictionaries we had a worksheet that we worked on. Mr. K. gave us the answers for #1. By the way the answer to the second worksheet for #1 e) is wrong it should be (e,u) not (a).

The next scribe is............................

LATE POST SORRY!

2005-12-13T01:10:00.000-06:00

Alright well i know its like 2 in the morning sorry you guys i had work today till 12 and got home around 12:30 i just want to apologize again but dont worry i'll let you guys know who the scribe is for tomorrow...well technically for today haha!

Well today Mr. K started class off with asking us what we thought average meant and what an average person would be like, and which one of us believed that we were average...and of course nobody raised their arm except for JENNIE haha its okay though because it was funny =) Oh yea another thing mr. k asked us during class was can you picture a triangle with angles but no lines? what a good question dont you think haha, and after that we discussed about inductive and deductive reasoning, and we also talked a bit and wrote in our dictionary, where we wrote and learned some new words...here's what we wrote;

logic: the branch of mathematics (and philosophy) that deals with sond reasoning.

agreement: a logical arguement consists of two (2) parts:

a set of premisis
a conclusion

premise: a basic truth

conclusion: the result of an argument

valid argument: an argument is "valid" when it's result is a direct consequence of it's premisis

example:

all men are mortal (premisis)
mr. k is a man (premesis)
therefore mr. k is mortal (conclusion)

An argument is not valid when it's conclusion is not a diret consequence of it's premisis even if its premisis and conclusion are true.

example:

all men are mortal (premisis)
Mr. k is a man (premisis)
therefore mr. k wears glasses (conclusion)

sound argument: an argument is "sound" if it is both valid and true.

induction: when we observe several particular examples of same things, and then conjecture that the "discovered" pattern must always be true.

example: all our "investigaion" activities in the circle geometry unit

deduction: when we are form a certain inarguble basic truths (like definitions) to a valid conclusion.

example: thales proof that every inscribed angle subtended by a diameter is 90 degrees.

Alright after we finished writing and discussing the different words and reasoning, Mr. k gave us some class time to do exercise 45, and that's how we ended our class i know this post isn't as long and im guessing it's cause we didnt' do as much today in class, but sorry again that this post isnt as great and detailed as my other ones, and sorry im trying my hardest right now im just really tired from work but dont worry i'll fix this up tomorrow night alright.

Till then the scribe for tomorrow is...i'll let you guys know in class haha

blogging before the test

2005-12-11T21:14:00.000-06:00

wow, almost forgot about this. well this unit wasn't as hard as i thought it was and i was pretty shocked on how much better i did on the pop quizzes. Somethings do still confuse me like the statement and reason part. Also knowing which theorem to use and how you have to find one part of an answer to figure out another part. There's so many steps to do and theres a big possibility to make one little mistake. I'm lucky enough to do my test on monday since i was excused on friday. I need to get studying, implant those theorems into my head =)

Sunday Jumping Funday!

2005-12-11T00:00:00.000-06:00

'The goal of the puzzle is to switch the the pegs on the left with the pegs on the right by moving one peg at a time.

Move pegs by clicking and dragging them to open slots. A peg may only be moved to an open slot directly in front of it or by jumping over a peg to an open slot on the other side of it. You may not move backwards. The game ends when you win or get stuck.'

Play the game here. Can you win the 8 peg game? ;-)

(Thanks again to Think Again!)

blogging before the test

2005-12-09T01:13:00.000-06:00

this unit, circle geometry, is interesting to do but i often got a hard time doing the statement and reason part. doing a question is quite complicated because there's a lot of possible different ways to solve a question but there are also lots of theorems to be consider in answering a question. it seems that i'm just the fourth one to post a blog and everyone may be busy doing the assignment.
just don't forget to blog, and goodluck on the test.

blogging before test once again

2005-12-08T23:56:00.000-06:00

well good thing i remembered to blog almost forgot, been too busy lately and yeah sorry i didnt go to class today haha and yea i know im the scribe for monday, but yeah this unit we just finished which was circle geometry i found was kind of confusing. i feel pretty good with a lot of the things in this unit but sometimes i just dont know how to explain myself when it comes to doing the statement and reason, im guessing that i should practice some more and hoping i do good on this test, since i've been doing pretty bad but yeah im trying to study haha anyways good luck to you all tomorrow...

Blog. Test tomarrow... Blog

2005-12-08T22:13:00.000-06:00

Well I guess it's me who nearly forgot to blog. Hahaha. So lazy these days... So anyways. Well Let's see. This unit is... Confusing. Well sorta. I get it and all that but you know it's all good. Yeah. Well I know most of the concepts so I'll be fine. Becides this week has been so crazy. With the math Assigment and all that. Wooo Nearly forgot. Eh Robert. Hahaha. Well I hope that I do good on the test. Good luck to all of you too. Hahahaha. Well I got nothing else to do. Maybe some studying would do me good... Anybody up for an all nighter on the chat box. lol.

Blogging Before The Test

2005-12-08T21:54:00.000-06:00

Hello once again! Wow this unit is a tough one! At first it seemed like Circle Geometry was going to be easy. Now that it’s coming to an end, I have realized that there is so much to it. There are many theorems that you have to remember and also how to use them. It suddenly becomes more difficult with the different problems that are challenging. Good luck to all and don’t forget to do your best.

Congruent

2005-12-08T21:39:00.000-06:00

C hords that are congruent are equidistant from the center of the circle.
O pposite angles are congruent.
N o two tangents drawn from a common point exterior to a circle is different. They are always congruent.
G eometric term for equal.
R egarding the parallel chord theorems, the arcs between parallel chords are congruent.
U nanimous that congruent chords subtend congruent arcs.
E qual in shape or size.
N o two or more inscribed angles subtended by congruent arcs are different. They are always congruent.
T wo or more inscribe angles subtended by the same arc are congruent.

Chapter: Pre-Test, Scribe: Mr. K Late =/

2005-12-08T12:49:00.000-06:00

Class started pretty strange, with no questions on the board. Except today we got to wait about 20 minutes for Mr. K to get into class. Side note: Mr. K, if you expect us to follow your guidelines to pass this class I think we ALL should follow them especially the BEING IN CLASS ON TIME thing ? Lol i'm not ranting on you I just thought it would be fun =D.

Today's class despite the wait, happened with a pre-test, OMG test tomorrow. Yeah that kind of thing lol, and here's the questions from the pre
test.

Question 1: The segment AB is tangent to the circle at point T. Which angle is qual to r ?

Choices: a) a b) b c) c d) d e) none of the these
Answer: a) a
Why you ask ? It's because of the tangent chord therom.

Question 2: Determine the value of x.

Choices: a) 50° b) 80° c) 90° d) 100° 3) none of these
Answer: b) 80°
Why you ask ? It's because of the central inscribed therom.

Question 3: Given the circle with centre O, which of the following best describes the relationship between x and y ?

Choices: a) x = y b) x + y = 180° c) x + y = 360° d) x + 2y = 360° e) none of these
Answer: d) x + 3y = 360°
Why you ask ? It's because of the central inscribed therom.

Question 4: In the diagram below, O is the centre of the circle. Determine the measure of angle x, in degrees.

Choices: a) 30° b) 40° c) 50° d) 60° e) none of these
Answer: c) 50°
Why you ask ? It's because of the central inscribed therom, but not really the therom it's better explained with the SPECIAL CASE OF THALES.

Question 5: In the diagram to the left, R, S, T and U are points on the circle with RS = RU = UT and SI = ST. Find the measure of LUST.

Choices: a) 30° b) 35° c) 36° d) 40° 3) none of these
Answer: c) 36°
Why you ask ? It's because triangle UST and RSU are both isoceles trianges LSUT and LSTU are both congruent and same goes with LRUS and LRSU. Which gives us something like this:

180 - 2b + a = 180
a = 2b

and

a + a + b = 180
2a+b = 180

With these two equations we can use substitution and like magic you get a number from a question that had no number. Ok Ok i'll do it for you guys don't have to get mad.

2 (2b) + b = 180
4b + b = 180
5b = 180
b = 36

And that's how question 5 was accomplishes have fun with it boys and girls NAR HAR HAR!

Question 6: Determine the measure of LECB, LBDC, LBAD and LDBE, where E is the centre of the circle. Justify your answers.

Answer:
Statment - Reason
EB = EC - Radius
LECB = 40° - Triangle ECB is isoceles
LBAD = 110° - Supplementary to LEBC
LBDC = 50° - Central inscribed therom
LDBE = 20° - Sum of triangle BCD

That was like whoa haha. Anyway that's what we did today in class hard questions ? Somewhat depending on if you know your theroms. Test tomorrow ? Shouldn't too much trouble why ? because EVERYONE should KNOW their theroms lol.

And guess what monday's scribe is PAMELA, haha see what happens when you miss class =P

My Acrostic (tangent)

2005-12-07T22:10:00.000-06:00

Tangent is a straight line that touches a circle but does not cut it.
Any tangent line to a circle is perpendicular to the radius drawn to the point of tangency.
Not only a line but it is also a trig function.
GA (line) is a tangent. Therefore, the angle between tangent GA and chord BC (angle1) is congruent to the inscribed angle subtended by the opposite side of the chord(angle 2).
EG (line) and GB(line) are congruent because they are drawn from the same point.
Note that in the case of a circle, the tangent line will touch it ONLY at a single point.
Tangent and radius create a 90 degree angle when they intersect.

.

All Together Now!

2005-12-06T23:08:00.000-06:00

OK folks, just like we did in class today. Everybody help each other and and solve this one in the comments to this post -- it's good practice for your test. ;-)

Scribe Scribles

2005-12-06T22:11:00.000-06:00

Today in class, Mr. K. put us into groups to work on some problem solving sheets for circles. Sorry if some of this is wrong, feel free to correct me in the comments. (=

Problem Solving Circle 1:

Given:
- DC and DE are tangents to the circle at points C and E respectively
- F is the centre
- AE is a diameter

Prove: L1 = L2

This picture shows:
- Tangent-radius theorem
- ΔCFE is isosceles
- ΔCDE is isosceles

a + b = 90°
L1 = 2b
2a + L2 = 180°
a = 90° - b

2(90° - b) + L2 = 180°
180° -2b + L2 = 180°
-2b + L2 = 0
L2 = 2b

Problem Solving Circle 2:

Given:
- AE is tangent to the circle at A
- CE is perpendicular to AE
- CD is perpendicular to AB
- AC = BC

Prove:
- CE = CD

This picture shows:
- L2 = L6 tangent-chord theorem
- ΔABC is isosceles, L3 = L6
- ΔADC = ΔAEC by AAS
- DC is congruent to EC
Q.E.D. (added that in just to make Mr. K smile)

Problem Solving Circle 3:

Given:
- AB is a tangent
- BD = CD
- AB = BC

Prove:
- L3 = L6

This picture shows:
- ΔBCD is isosceles
- L4 = L5 + L7
- L2 = L5 + L7, by tangent-chord theorem
- L4 = L2
- ΔABC is isosceles
- L1 + L5
- L3 + L6

*Bell rings, and we're out of time folks!

The next scribe is... abriel_S. (=

scribin' at the last minute...

2005-12-05T23:29:00.000-06:00

* sorry guys i did this at the last possible time i was suppose to work until 10:00pm ended up working until 11:00pm.

- Well, today we did a quiz on our circle geometry. Here are the questions on the quiz so you can try it again or for the first time if you were not there. In the end I'll post up the answers.
.............................................................
Circle Geometry Quiz 2

(1) angle BOC = 115'. Find the measures of arcs AB, BC, CD, and AD. Justify your solution (4 marks)

(2) If the measure of chord AB is 14cm and the measure and the measure of chord DC is 7 cm, how far from the centre of the circle is chord DC? Justify your solution. (4 marks)

(3) How far is a chord of length 8 cm from the centre of a circle with a diameter of 10cm? (2 marks)

(4) What is the diameter of a circle in which a chord 16 cm long is 15 cm from the centre? (3 marks)

..........................................................................................

ANSWERS:* i wish i could've made it into columns

(2) STATEMENT / REASON
AB = 14 cm / GIVEN
DC = 7 cm / GIVEN
OB = 7 cm & AO = 7 cm / RADII, AND AB DIAMETER
DE = 3.5 cm & EC = 3.5 cm / PERPENDICULAR BISECTOR THEOREM
OC = 7 cm / Radius
OE = 6.06 cm / PYTHAGOREAN THEOREM

a^2 + b^2 = c^2
3.5^2 + b^2 = 7^2
12.25 + b^2 = 49
49 - 12.25 = b^2
b^2 = 36.75
b = 6.06

(3) PYTHAGOREAN THEOREM
a^2 + b^2 = c^2
4^2 + b^2 = 5^2
16 + b^2 = 25
25 - 16 = b^2
b^2 = 9
b = 3

The chord is 3 cm away from the centre of the circle.

(4) PYTHAGOREAN THEOREM
a^2 + b^2 = c^2
15^2 + 8^2 = c^2
c^2 = 289
c = 17
diameter = 17 x 2 = 34 cm

The diameter of the circle is 34 cm.

............................................................

* PHEW.... sorry again guys well next scribe will be....

rannell d.

hah =) have fun rannell.

YOUR AGE BY CHOCOLATE MATH

2005-12-04T15:07:00.000-06:00

Hey guys, I thought this was kinda cool so u should try it. all u have to do is follow this steps and u will see what happens (u r going to your age), and u might need a calculator.

1. First of all, pick the number of times a week that you would like to have chocolate (more than once but less than 10)
2. Multiply this number by 2 (just to be bold)
3. Add 5
4. Multiply it by 50
5. If you have already had your birthday this year add 1755, If you haven't, add 1754.
6. Now subtract the 4 digit year that you were born.
_ You should have a three digit number.
_ The first digit of this was your original number (i.e., how many times you want to have chocolate each week).
_ The next two numbers are YOUR AGE! (Oh YES, it is!!!!!)
THIS IS THE ONLY YEAR (2005) IT WILL EVER WORK.

Cubeoban Sunday

2005-12-03T22:42:00.000-06:00

The objective of Cubeoban is to push/pull all the blocks to their corresponding lights. Do this by clicking on the blocks and drag them in the direction you want to push them. Play it here.

Level 1 was so easy that even I could do it. Level 2 (the image), started my thinking.

(Thanks again to Think Again!)

Straight From The Pen of a Scribe....

2005-12-02T16:36:00.000-06:00

Well it's my turn for scribe again. Well I guess I should start with the beginning of class, which was a surprise quiz!!! How exciting! So here is the questions on the quiz and how they are to be figured out correctly, with a few helpful hints.
The first question:

In this question you obviously had to solve for x and y and use statement and reason to explain what you did.

Well first you should have been able to figure out that angle DEF= 70 degrees(red) because it is the exterior angle to triangle ADE (blue).

The two black dots indicate that those two angles are congruent. Creating a total angle that equals 140 degrees (yellow). Using that information you then can find the value of X. X=100 degrees because angle CEF is exterior to triangle ACE.

From this information we can derive that Y= 60 degrees because angle ACE (red) is exterior to triangle ABC (blue).

And that is pretty much question one for you. Question two was were you had to find two congruent triangles and then prove it using statement and reason. For this question, instead of demonstrating the diagram I will show you how to do the proper Statement and Reason set up. For this specific question there were two different ways of accomplishing the correct answer.The first is in blue and the second is in red.

The first way is: Statement Reason
angle AFD is congruent to Opposite angles
angle EFB.
angle FAD si congruent to Given
angle FEB
Line AD is congruent to Given
line EB
Triangle FAD is congruent to
triangleFEB AAS

The second way is this: Any of this look familiar. *Looks at previous post*
Line AC is congruent to
line EC Given
Angle ACB is congruent to
angle ECB Reflexive property
Line CB is congruent to line CD Given
Triangle ABC is congruent to
triangle EDC SAS

The third and last question goes like so:

For this question we were given that the diameter is 20 cm and that the chord AB is 12 cm. We were then asked to figure out the distant between the chord and the centre of the circle. Knowing that the diameter bisects the chord we know that each half of the chord is 6 cm. We also know that the radius is 10 cm. You then construct a radi to one of the chords points creating a right triangle. You are now given two of the sides and use the pythagorean to figure the third side out which comes to 8 cm.
*Don't forget that the hypotenuse is always C. Many people forget that small point and just add the two sides given (don't worry I did it myself today). Also don't forget to include the units.*

Last but not least we put more work into our dictionaries! YAY!!!! *Always read before bed*
Congruent Chord Theorem
Congruent Chords subtend congruent arcs. Congruent chords are equidistant from the centre of a circle.
The Tangent Theorem
Two tangents drawn from a common point, exterior to a circle, are congruent.
Tangent-Radius Theorem
A tangent and radius intersect at a right angle.
Tangent Chord Theorem
The angle between a tangent and a chord is congruent to the inscribed angle subtended by the opposite side of the chord.
Cyclic Quadrilaterals
A cyclic quadrilateral, all of whose verticies lie on the circumference of a circle. Opposite angles in a cyclic quadrilateral are supplementary. a+c=180 b+d=180
Interior Angle Sum of in Any Polygon
The sum of the interior angles in any polygon given by S=180(n-2)
S is the sum of all the interior angles.
n is the number of sides in the polygon.
Example: What is the sum of the interior angles in a 12 sided polygon?
S=180(n-2)
=180(12-2)
=180(10)
=1800
Alright that is really it guys. And the next scribe is......

My Acrostic

2005-12-02T11:30:00.000-06:00

Circumscribed surface or space of plane curve everywhere equidistantfrom a given fixed point is a circle.
If only (part of) a circle is known, then the circle's center can be constructed as follows: take two non-parallel chords, construct perpendicular lines on their midpoints, and find the intersection point of those lines.
Ratio between the length of an arc and the radius defines the angle between the two radii in radians.
Circumference means the length of the circle, and the interior of the circle is called a disk or disc.
Line cutting a circle in two places is called a secant.
Every triangle gives rise to several circles: its circumcircle containing all three vertices, its incircle lying inside the triangle and touching all three sides, the three excircles lying outside the triangle and touching one side and the extensions of the other two, and its nine point circle which contains various important points of the triangle.

Circle Geometry Review

2005-12-01T21:58:00.000-06:00

We're gearing for our test now. Here's a bunch of online quizzes you can use to help get ready. Also, check out the links in our del.icio.us box, there are some really good ones there. ;-)

Proof of Congruence (5 questions - refresh the page for more quizzes)

More Congruence (5 questions - refresh the page for more quizzes)

Circles (5 questions - refresh the page for more quizzes)

Arcs &Angles (5 questions - refresh the page for more quizzes)

Arcs & Chords (5 questions - refresh the page for more quizzes)

Inscribed Angles (5 questions - refresh the page for more quizzes)

Tangents (5 questions - refresh the page for more quizzes)

Polygons (5 questions - refresh the page for more quizzes)

Whew! More quizzes than you can shake a stick at! ;-)

Scribe #48 I think... Nah... Make it 50.

2005-12-01T16:44:00.000-06:00

Well... Long time no Scribe... Hahaha. lol Anyways... Today's Chapter is...

One Regular Day in MATH

Today was a regular day. One day too many. Yet one day too late.

"Hi guys" I said as I walked in the room. I was so happy yet so sad... It's math once again and I feel so bad. It's math. It's math. I am so very pleased. Yet I still rhyme. Get to work... Geez...

Ok. Ok. I looked happily. Three problems on the board. Three problems for we.

(Ok I'll stop I have a Poetry English Assignment... Ok. Hahaha)

1. Find the values of x and y. Justify your answer.
Hint. The checkmarks and the o's are congruent.

So we all do the really long way. Then Mr. K. Tells us to check our dictionary's

ALLWAYS BRING YOU DICTIONARY TO CLASS!!!!

All of your tools are there. lol

So to justify you have to use the Statement/Reason that we learned. He showed us that we could use the Exterior Angle Theorem.

Statement

Angle DEF = 70º

X = 100º

Y = 60º

Reason

Ext. to Triangle ADE

Angle CEF is EXT. to Triangle ACE

Angle ACE is EXT. To Triangle ABC

2. For each pair of triangles write the propeterty which proves the triangles are congruent.

For this one... You had to look in your dictionary for one of four propeteries: SSS, SAS, AAS, or RHL. Which translates to: Side-Side-Side, Side-Angle-Side, Angle-Angle-Side and Right Angle-Hypotonuse-Leg. By the way you are only allowed to use those four propeteries.

Also Mr. K. Taught us the Reflexive Property. Quote "In the reflexive Propetry. You are the same thing as yourself." Basicly If you have a diagram and cut it directly in the middle. One half of the diagram is the same as the other half.

Well in the end you should of got (from left to right, top to bottom) RHL, SSS, NOT CONGRUENT, AAS, SAS, AAS

3. Find two congruent triangles and explain why they are congruent.

This one was a mix of the first question and the second question. So it was really hard. Hahaha...

In the end it ended up like this:

Statement

Line Segment DC is Congruent to Line Segemnt BC

Angle BCD is Congruent to Angle DCB

Line Segment AC is Congruent to Line Segment EC

Triangle ACB is Congruent to Triangle DCB

Reason

Given

Reflexive Propetry

Given

SAS

There was another way... To it to. It involved the top triangles and the congruent angles in the middle

After that he gave us two more questions. What fun. Ha ha ha...

To be honest I really forgot how to do these questions... The bell rang when we were going to review them and I was so lost when I was doing them... Ha Ha Ha?

Anyways... Homework is Excerise 35

AND THE NEXT SCRIBE IS...
It reads Kasia... Hahaha.

By the Way... All Math images are made by EUKLID.
Provided By Graeme. ;)

ALSO... I really think there's a PRE-TEST tomarrow... Look's Up...

Double Acrostic

2005-11-30T23:05:00.000-06:00

Well guys I tried and I had to get a little creative to complete the "Double Acrostic". So just bear with me.

Circles have many parts of their anatomy like a chord, or an arC
Having a radius perpindicular to a chord bisects the chord (meaning the line segment on each side of the intersection should matcH.)
One of the theorems that we learned in this Circle Unit was the Parallel Chord Theorem: it states that the arcs between parallel chords form a 1:1 ratiO.
Radii and chords should be measured with a ruler where as angles should be measured with a protractoR.
Diameters are chords that pass through the center and is equal to the value of the radius, doubleD.

The Next Scribe... Hahahaha?

2005-11-30T20:47:00.000-06:00

Well Robert told me who the next scribe is lol. Since um... Blogger isn't working for him in some strange coincidence. Don't ask me why... I'm having problems too... lol. Well here's the next scribe... (Robert did make this. He sent me it.)

Yeah it's me. lol. What a strange coincidence... Hahahahahahahahahahahaha

My Scribe

2005-11-30T20:32:00.000-06:00

Hello to everyone!  Today’s class started off with two investigations.  Investigation number nine and investigation number ten, which had to do with circle geometry.

Investigation 9:

A cyclic quadrilateral is a quadrilateral all of whose vertices lie in the circumference of a circle.

First we had to construct a polygon with all four points on the circumference.  After that, for that quadrilateral we measured the sum of the opposite angles and found out that they were equal to 180°.  We then did those same steps two more times to confirm that it wasn’t just for that one type of quadrilateral.  The last step for this investigation was to articulate a general rule.  We found out that “If two angles are opposite each other in a cyclic quadrilateral, then the angles are supplementary.”

Investigation 10:

The diagonals of convex polygons are drawn at a single vertex.  Complete the table of values showing the relation between the number of sides in the polygon and the number of triangles formed.

In conclusion, a convex polygon with n sides can be divided into   n - 2    triangles.

You have learned that the sum of the interior angles of a triangle is 180°.  Complete the following table.

Refer to the preceding table.  Describe in words the relation between the number of sides in a polygon and the sum of its interior angles.

The sum of the interior angles is found by the number of sides (n) subtract two, then
Multiplied by 180°.

Again, referring to the table, write a formula that describes this relation.
The sum of the interior angles of a polygon with n sides = ( n - 2 )( 180° )

After all of that we then went into our dictionaries to take some notes.  Here they are:

Perpendicular Bisector Theorem:

Part I     If a line bisects a chord and passes through the center of a circle then it is      perpendicular to the chord.

Part II     If a line is perpendicular to a chord and passes through the center of a circle then it bisects the chord.

Inscribed-central Angle Theorem:

Part I     If a central angle and an inscribed angle are subtended by the same arc then the central angle is twice the inscribed angle.

Part II     If an inscribed angle and a central angle are subtended by the same arc then the inscribed angle is half the central angle.
A.K.A. “The star trek theorem”

Special Case:
     Inscribed-diameter (Thales) theorem
An inscribed angle subtended by a diameter is always 90°.

Inscribed Angle Theorem:

If two (or more) inscribed angles are subtended by the same arc then they are congruent.

Parallel Chord Theorem:

The arcs between parallel chords are congruent.

Congruent Chords Theorem:

Congruent chords subtend congruent arcs.

The next scribe is: (

My Acrostic

2005-11-29T21:23:00.000-06:00

Hey, I feel sort of stupid for picking the shortest word so I had tried to make a double acrostic...well if you can find a word that ends in h and one that ends in o kootoe's to you :D.

Chords are made up of a straight line that joins two points on the circumference of a circle and creates an arC.
Having a radi bisect a chord creates a perpendicular and a right angle for those who remember their matH.
One other fact is that two congruent chords are equidistant from the centre of a circle, this will also work with more then twO.
Right now we have three chord theorems to study: Perpendicular-Biscetor Theorem, Parallel Chords Theorem, and Congruent Chords Theorem which are all under the chord theorem scection to make it easier to remembeR.
Drawing the centre of the circle can be done by using two chords that are not parallel, a ruler, and a pencil that is sharpeneD.

My Double Acrostic

2005-11-29T19:14:00.000-06:00

Circumference is a part of each and every arc.

Inscribed angles that are subtended by the same arcs have equal angles. Like angles BAI and BCI.

Right angles are made when inscribed angles are subtended by a diameter.

Circles are comprised of a 360 degree arc.

Lens flare is an example of circles that gradually go from large to small.

Every tangent line touches a circle once.

If I you already used the one I used for "I" then I'll change it, but I can't remember what you used this morning Mr. Kuropatwa.

bee-logging pee-rompt

2005-11-29T17:43:00.000-06:00

Hi everyone I thought I'd get started early so no one has thing as me. Anyways, here is my acrostic:

If it's blurry just click the picture. ;)

My Angle on Circles

2005-11-29T16:46:00.000-06:00

Hello everybody! Well today in class we started off with a quick presentation by Mr. Kuropatwa on how to get a del.icio.us account. If you need any more info on that look at Mr. Kuropatwa's previous post on it. We then moved on to our first project of the course. There are options for what you can do but the general project is when you answer a question that he handed out then you solve it, communicate and present your results the best you can. He said that with this project it is easy to get an 88%. This is because all you need to do is do the math correctly then present it and communicate in a little above average manner. But if you want the 90's or the fabled hundred then you got to work. Some people have made a webpage, dioramas, videos and things like that. But if you do make one of those it doesn't garauntee anything. If you make a video and it's not decent you can still fail. If you don't want to do the question you can also talk to Mr. Kuropatwa about making a instructional video or something along those lines (your deadline will also be extended).

After he explained the project we went on to our Circle Theorums. We did two today. The Tangent Radii Theorum and The Tangent Chord Theorem.

The Tangent Radii Theorem

"If two tangents are drawn from a common point, exterior to a circle, then they are equidistant."
"If a radius intersects a tangent line, then where they meet it is a right angle."

This is a diagram of that:
All of the angles where the tangent lines and the radii meet are 90 degree angles.

The Tangent Chord Theorem:
"If an angle is formed between a tangent line and a chord then, then on the opposite side of a chord if an inscribed angle is made then those angles are congruent."

Angle RAB = 148.3 degrees
Angle SAB = 21.7 degrees
Angle ACB = 148.3 degrees
Angle ADB = 21.7 degrees
Angle MNY = 34.7 degrees
Angle XNM = 145.3 degrees
Angle NLM = 145.3 degrees
Angle NWM = 34.7 degrees

That concludes my summary on the class. The next scribe is:

It's Robert!!!!

Circle Acrostics

2005-11-28T22:03:00.000-06:00

Kudos to Mrs. Armstrong for turning me on to the idea of acrostics in math.

Blogging Prompt
Your task is to create an acrostic "poem" that demonstrates an understanding of circle geometry related to any one of these concepts:

CIRCLE
INSCRIBE
ANGLE
CHORD
TANGENT
SUBTEND
CONGRUENT

As an extra challenge (worth an additional bonus mark) try to make a Double Acrostic, that is, each line should begin and end with a letter of the word you are working with.

Remember, this is a bit of a race. Your answers have to be posted to the blog in the comments to this post. If someone has already used a word or phrase in their acrostic you cannot use the same word or phrase. i.e. It gets harder to do the longer you wait. ;-)

Here is an example of an acrostic that Mrs. Armstrong wrote:

Always in 2 dimensions
Region between the boundaries
Entire surface is calculated
Answer is in units²

Be creative and have fun with this!!

Scribe of Thales

2005-11-28T17:11:00.000-06:00

Hey guys, I guess it's my turn to put another chapter into our "textbook" so I decided to begin with Thales of Miletus.Now, by looking at this picture, you can probably tell he was, as Mr. K. would say, "A very miserable human being". Apparently, he tricked his best friend by saying his son was dead just to show him why he wouldn't have a family. As well, he made a farmer put sponges on a donkey's back to make it carry more weight. Actually they are all very smart ways of looking at things and proves an intellegent point, but he has cruel methods. But the 'Father of Mathematics' was a genius and he found out about the first investigation we corrected in class today, The Inscribed Angle/Diameter Theorm. This states that,"If an inscribed angle is subtended by a diameter, then it is a right angle."
How did Thales come up with this? What was his proof? He must be a genius!
Well, here's the proof.

So as you can see it is quite simple, the angle subtented by the diameter creates two isoceles triangles when the radius is connected to the inscribed angle. This is because the radius of a circle is always the same so the three congruent lines are all radiuses or radii? Anyways, then the two base angles are congruent and since the three angles of a triangle add up to 180 degrees, then a plus b equals 90 degrees.

The second investigation we corrected (#4) was to do with Inscribed and Central angles. It is the Inscribed angle/Central angle theorm and it states that,"If an inscribed angle and a central angle are subtended by the same arc, then the inscribed angle is half of the central angle."

The angle AOC is done to show what it means by "subtended by the same arc."
We haven't learned the proof yet and Mr. K. has put it up as a challenge to prove this or any of the other investigations so I won't try to tell you.

Also, Mr. K. should be putting up th acrostic list as an alternative for pre-test posting and also I hope everyone's ready to see their test mark because he said he'd have them done by tomorrow.

One last thing before I go eat, I choose

As the next scribe. See Aichelle, I can do it too.

Bye!

Sunday Connected-Slide Funday!

2005-11-27T13:55:00.000-06:00

ConSlide puzzles are a new type of sliding block puzzles invented by M. Oskar van Deventer... The pieces of a ConSlide puzzle move like regular sliding block puzzles, but some of the pieces have sections connected by bars of various heights. This means pieces can pass over and under one another as long as the bars and posts don't run into one another. The goal of each of these puzzles is to move the red block to the upper left corner. Play it here.

(Once again, thanks to Think Again!)

The Editor's Initiative

2005-11-26T21:00:00.000-06:00

Instead of posting a pre-test reflective comment on your progress in this class you may undertake The Editors' Initiative. Here's how it works:

  Step 1: Scan through the previously posted Scribe Posts on the blog. Find one that has one or more errors.

  Step 2: Discuss the error(s) and what you think the correction(s) should be with me. If I agree with your editorial proposal go to Step 3.

  Step 3: Discuss the editorial change with the author of the post. The author will chose to proceed in one of the following two ways.

3a	3b
The Editor is briefly allowed administrative privileges on the blog. They will edit the post to make any necessary corrections. They then sign the post at the bottom: Edited by: [name] on [date]	The author will edit the post in consultation with the editor who will vet the author's changes until they are correct. The author then signs the post at the bottom: Consulted editor [editor's name] on [date]

Students may chose to make more than one edit. Each additional edit will earn them a bonus mark on the next test. Your mark on the previous test determines the maximum number of edits/bonus marks available to you.

Mark on Last Test / Max Edits Allowed
> 90 / 1

80-89 / 2 (1 bonus mark)

70-79 / 3 (2 bonus marks)

60-69 / 4 (3 bonus marks)

50-59 / 5 (4 bonus marks)

40-49 / 6 (5 bonus marks)

30-39 / 7 (6 bonus marks)

20-29 / 8 (7 bonus marks)

10-19 / 9 (8 bonus marks)

0-9 / 10 (9 bonus marks)

You may also assume the role of Content Consultant to earn marks as outlined above. Here's how it works:

  Step 1: Scan through the previously posted Scribe Posts on the blog. Find one that doesn't provide enough detail or leaves out too much information. Decide what additional content should be added.

  Step 2: Discuss the new content you think should be added with me. If I agree with your editorial proposal go to Step 3.

  Step 3: Discuss the editorial change with the author of the post. Together, you will chose to proceed in one of the following two ways.

3a	3b
The Content Consultant will add a new post to the blog inserted at the appropriate time and date. They then sign the post at the bottom: Additional Content by: [name] on [date]	The author will edit the post to include the additional content provided by the consultant. Additional content will appear under a heading "Additional Content". The author then signs the post at the bottom: Additional Content Provided by [consultant's name] on [date]

Students may chose to make several additional content contributions for bonus marks according to the table above.

After discussing the issue with all my classes I have decided that you cannot edit your own scribe posts. When it's your turn to be scribe try to write a post that is so excellent no will be able to edit it. ;-)

Circles R Us

2005-11-25T18:22:00.000-06:00

Today we started class by Mr. K. putting up questions on the board. This was the first question:

To find line AO we used the Pythagorean Theorem (a² + b² = c²). If you plug in the numbers you get:
5² + 3² = c²
25 + 9 = c²
34 = c²
√34 = c

You know that line AB is 10 because line AC and line CB are congruent; and you know they are congruent because of the perpendicular bisector theorem.

This was the second question:

We know that line OE is a radius and we know that the radius is 23. So we subtract line CE from OE and get 10 (23 – 13 = 10). We know that line OC is perpendicular to line AB because of the perpendicular bisector theorem. In order to get line AB we must use the Pythagorean Theorem to get line CB. Once you know line CB you also know line AC because they are congruent. If you do everything properly you find that line CB is √429 or 20.71 if you round it off. Then you know that line AB is 2√429 or 41.42.

This was the third question:

To find line OC we used the Pythagorean Theorem and we got √203. Since line OC is perpendicular to line AB we know that line AC is congruent to line CB because of the perpendicular bisector theorem. The answer is 22 (11 + 11 = 22).

Mr. K. showed us a different way of solving these questions by using a chart with two columns, one that says statement and the other that says reason. This is how it would look like for the first question:

This is how it would look like for the second question:

This is how it would look like for the third question:

The fourth question was:
A chord that is 10 cm long is 12 cm away from the centre of a circle. Find the length of the radius.To solve this question we drew a picture and this is how our picture looked like:

We got that from the information given to us and by using the statement and reason chart.

The last question was:
The diameter of a circle is 20 cm. A chord is 8cm from the centre. How long is the chord?

For this question we also drew a picture, we went fairly quickly with this question so here is the picture:

If you are still confused, maybe this can help you. We drew what was already given to us which were a chord that was 8cm from the centre and a 20cm diameter. Then we drew a radius connecting to point C, which was 10cm. Then we used the Pythagorean Theorem to find line BC and got 6. Once you know that it’s 6, you also know that line AB is , then you add 6 and 6 together and get 12.

After all of that Mr. K. gave us two investigations to do and showed us how to construct perpendicular bisectors. The two investigations are for homework if you didn’t finish them in class and Exercise 31 is also for homework.

*Reminders*
*You only have to use the chart when you are asked to justify your reasoning.
**Be careful about putting exact answers and/or approximations.
***You can use your statement as a reason after you have proved it.
**Use different colours with your circles.
*When drawing a radius imagine an infinite number of radii coming out from the centre and see which one connects with another point.

Lastly, the next scribe is:

Mr. Dixon's on eBay - How Trusted is He?

2005-11-25T16:21:00.000-06:00

Mr. Dixon is in my classroom right now and he has a question he needs your help with.

His trust rating on eBay is 99.2%. Out of 122 transactions he's had, 121 people said he treated them well and he can be trusted.

Mr. Dixon wants to know when will his "trust rating" reach 99.3% and he needs your help.

(1) Can you write an equation he can use to solve this problem?
(2) Can you solve the equation and tell Mr. Dixon how many more favourable exchanges he needs to have to raise his trust rating to 99.3%.

All of my classes are working on this. The first student in each class who solves Mr. Dixon's problem correctly gets a chocolate bar. ;-)

Greatful

2005-11-24T19:12:00.000-06:00

Hey Mr. K.

Thank you very much for your advice. I downloaded Firefox and now I release that yes, it is the best browser. It's helped me a lot, I just put up the diagram in my post.

Oh yeah I meant to ask for our tests because some of the people from class are asking ME if YOU will mark the tests by the end of the week so this is for them and me.

Scribing.

2005-11-23T21:11:00.000-06:00

WELL I'm very sorry about the late post. I didn't time earlier.

First in class we went over the Circle Geometry - Investigation #1. And we learned that the relationship between a chord and the perpendicular is that the perpendicular to the chord that passes through the center, bisects the chord.
As you can see here:

BUT..
Then we realized that when we drew the perpendicular on some of the chords it DID NOT cut the chord in half. We figured out that the circle wasn't a circle because the radius wasn't the same throughout the entire circle! But that was just a mistake the computer did so no biggy.

Then we did Circle Geometry - Assignment #2.
AND AGAIN, the circle wasn't a circle (good job figuring that out kasia!) because the lengths of the diameter weren't the same throughout the circle. So we crumpled up the paper and threw in the recycling box. Mr. K ran out and got us fresh sheets with REAL circles.
This assignment was also similar as Assignment #1 but we learned that all bisectors become the diameter of a circle and we know this by measuring. And we can say that the perpendicular bisector of a chord passes through the center of a circle.
Like this:

Then Mr. K talked to us about 4 ways of getting bonus marks.
If you are getting greater than 90's on your last tests you are only allowed to get 1 bonus mark. Then if you are getting 80-89's you can get 2 bonus marks.
70-79 / 3 bonus marks
60-69 / 4 bonus marks
50-59 / 5 bonus marks
40-49 / 6 bonus marks
30-39 / 7 bonus marks
20-29 / 8 bonus marks
10-19 / 9 bonus marks
0-9 / 10 bonus marks

Here are the ways:
1) making an acrossticks
2) Editing someone else's post
- But you have to go to Mr. K first and tell him which post and what you would like to do with it.
3) Editing your own post
- And again you have to go to Mr. K and tell him what you want to edit on your post.
4) Add most content to old posts
- You must go to Mr. K again to tell him what content you believe you missed out on that you want to add.

And that is all for today folks.

Tomorrows scribe is AICHELLE =) .

Proof, but from a different prospective.

2005-11-22T21:49:00.000-06:00

Basically, use the formula about opposite angles and the method of solving systems (you should all be familiar with it):

d=a+b | L1
c+d=180* | L2
____________________

c+(a+b)=180 | L3: sub L1 into L2
.: a+b+c=180

* angles c and d are supplementary

simple right?

untitled

2005-11-22T17:51:00.000-06:00

haha .. well I'm not gonna try to "prove" the thing about the triangle. But I wanted to say that RICHARD i like yours haha . It's so simple and logical =)

Proof that Proof Exists...?

2005-11-22T16:53:00.000-06:00

I can't prove what's allready been proven yet
there is no proof that we have proven anything.
So I'll prove that I proven everyone wrong with
this really simple thing. HAHAHAHA

Look's strange but it's so true. Make a triangle
and cut off the corners. Then put them together.
You make a line. And a straight line is 180º. Now
that's proof that YOU can do at home. Hahahaha.

Oh yeah. It was taken from this site.

Proof By Disproving all other Angles

2005-11-22T16:27:00.000-06:00

Proof that the total of the degrees cannot exceed 180 or go below 180

Here is a right triangle with the two adjacent sides both being three units long

(A and C). In this triangle C + B + A = 180 degrees. Now if the triangle had 185 degrees…

As you can see the line off the 50 degree angle at c does not meet up with the endpoint of line C (And if you extended line C then the angle at the top would no longer be 45 degrees but 40 degrees. So it would still be a 180 degree figure). This would be true for any angle above 180 degrees. Then when it is below 180 degrees line B cuts through line C instead of meeting it at the endpoint. The angle where that meets it ends up being b – c = a (Assuming that you had b as the largest angle). Then if you input any of those into the formula a + b + c = 180 it works. (b – c) + b + c = 180 then you input the largest angle for b any angle for c that doesn't bring the total to 180 into that formula and you will get 180 unless your angle b is 180 or greater or sixty or less (sixty or less and b is not the greatest angle). Then you get a closed figure with three angles, a triangle. If you put anything greater than 180 for the total you get something like 180 = 181. You put something less than 180 than you get something like 180 = 179 which is completely wrong. So by proving that the angles in a triangle cannot be anything greater than 180 degrees or less than 180 degrees and that 180 degrees works, we can state that all triangles have 180 degrees.

I think that this is somewhat correct. I hope it proves it.

Circle scribe

2005-11-22T15:55:00.000-06:00

Hey again

This is post is for today's class
today we wrote in our math journals most of the class and then we did a circle geomerty that we have to finish tonight for homework. This post was edited Nov 23 at 5:45

Circle Geomerty

fundamentals

1) The sum of all angles in a triangle is 180⁰

2)the angle exterior to a triangle is equal to the sum of
the opposite interior angle

3)Congruent: Means the same shape and size

4)Transversal: A line intersects 2 parallel lines

5)Opposite angles: two angles that are opposite
each at the intersection of to two lines are called opposite angles.
opposite angles are congruent

6)Alternate angles: two angles on alternate sides of a transversal are
called alternate angles. They are congruent

7) Corresponding angles: two angles on corresponding sides of a
transversal are called corresponding angles. They are always congruent.

8) Congruent Triangles: any two triangles can be proven congruent using
one of these four properties .

The Anatomy of a Circle

O - is the centre of the circle

is a chord- A straight line that joins two points on the circumference

is a diameter - chord passing through the center of a circle.

is a sector - a lime segment that contains a chord

is a tangent- a line that intersect, (touches) the circle at one point

radius- a straight line that joins a point on the circumference to the centre

is a minor arc- part of the circumference

is a is a major arc some but bigger

segment AB - part of the area of a circle bonded by a core and a minor arc

Sector FOC - part of the area of a circle bonded by the centre angle and an arc

centre angle: angle whose vertex lies on a circumference of a circle.

Inscibed angle: A angle whose vertex lies on the circumference of a circle

"Arc": the measure of an arc is equal to the measure of the centre angle that subtends that arc

This is all the notes I got I think I Missed a couple on the board sorry. If anyone has the rest please send me a comment and tell me so I can edit the post thanks. Thanks Robert for letting me borrow your notes

Tomorrows scribe will be ....... larisa

does this count as proof?

2005-11-22T15:35:00.000-06:00

I'm pretty sure mine is different from Jennie's, so here it is:

is this proof?

2005-11-22T13:11:00.000-06:00

http://www.apronus.com/geometry/triangle.htm

i found this site, who knows this might be useful to all of us.

Blogging Before The Test

2005-11-20T20:58:00.000-06:00

Hello everyone! This unit has been the hardest unit for me because it has so much to it. By studying a lot, I feel good about the test on Monday and hope everyone does well. Just a little reminder for the test:
independent - intersects at one point
dependent - intersects at all points
inconsistent - does not intersect/parallel
Good luck to everyone once again.

test-age

2005-11-20T20:03:00.000-06:00

Wow, this Analytic Geometry stuff has a lot to it. There's a lot to take in and a lot of practical work that goes with it too. Basically it's like if you don't do your homework in this topic you're grabbing that one way ticket to not understanding what is happening. Well at least that's what it seems like to me, but i'm pretty confident that some people might agree with me. Then again not doing your homework is alreayd a one way ticket to not understanding pre cal at all. Anyway, I think analytic geometry was alright, not finding too many things difficult except for the problem solving stuff, but other than that I think this topic was a good intro to how hard precal acually is. So yeah before I end off my blog, i'd just want to say good luck to everyone tomorrow on the test and don't burn yourselves on doing stupid mistakes that could cost you a pass, ie. labels on the graph. Consider yourselves warned =D

blogging before the test

2005-11-20T19:10:00.000-06:00

This unit was okay for me. I think the systems of equations is pretty easy. I also think that solving inequalities are okay. The thing that I have trouble with is using the information when they give you a word problem to solve. Well I'll keep this short and simple and just do my best tomorrow. Good luck on the test everyone.

bloggin' before the big test...

2005-11-20T18:49:00.000-06:00

this is my blog before the test... i need that one mark hah =)... well im pretty comfortable with solving equations.. whats really bothering me is the one with the equation and the greater or less sign then you need to find a coordinate, that really confuses me. plus the asymptote, its a funny word but really hard for me to comprehend. well this unit is pretty hard and we all have got to work even harder. well good luck everybody! especially me haha =)

Blogging Before Test

2005-11-20T18:41:00.000-06:00

This unit was a lot to take in, and I hope that this will be an okay test. Most of the time when Mr. K makes tests, he asks us about it, and then most people say it was hard. But yeah, just read through your notes guys, do your exercises, and everything, and look over the review. And I'm pretty sure it'll be okay! Hope everyone does good. =) You can't really study for this, you either know it or you don't. SO GUYS... know your stuff! =)

blog post before our test

2005-11-20T17:19:00.000-06:00

so tomorrow we're having our test for the unit about linear inequalities ang solving equations with 2 and three variables. from all the unit we tackle, this seems to be the easiest for me (but not that much). we already tackle this topic from my former school. the good thing of studying this topics again is that i learned far more than what i already know about it. with this, the transition from highschool math to university math would be smooth. my classmate friends from the philippines, who loves the subject math when we are still in highschool (yes, im supposed to be a 2nd year university student in the philippines but because it is just equivalent here to grade 12, i need to be back in highschool), were having a hard time in university specifically engineering courses. i'm also stuggling in math when i came here because the lessons here are explained more deeply than just knowing how to solve a specific equation and that's it, we can get our grade if we pass our tests. i hope learning more topics about math can give me back my interest in math.

so goodluck to everyone for tomorrows test!

Post before the big test.

2005-11-20T16:58:00.000-06:00

This unit is really jampacked with so much information. somethings did get me confused especially with the fractional inequality equations. There were things that I thought were really easy that we learned like solving systems of equations. But I think I will do okay cause everything seemed to sink it well. This is supposed to be one of the hardest tests we will receive and I think it will be because the pre-test was so difficult. Well I should be getting back to studying. Good luck everyone. Study hard!

Fourth Powers

2005-11-20T12:46:00.000-06:00

- I hear you have extraordinary powers!

- Not true! What I said to the press was that I have fourth powers at home.

- What do you mean?

- 1, 16, 81, .... That kind of stuff.

- But these are square numbers!?

- Yes, but they are more than that. They are square numbers squared.

- I see. And you have these at home?

- Some of them. Not all of them.

- And what do you do with them?

- Play with them, of course, what else?

- What kind of games?

- This morning I added them.

- That must have been great fun!

- That's what I said to the press, but they didn't believe me.

- How did the game go?

- Not very well. I tried to pick less than nineteen of them, one several times if
neccessary, to get any number in the universe.

- How did you get 20?

- 20 was easy. 1 + 1 + 1 + 16 = 20. I only had to use five of them.

- Which number gave you problems?

- I found a number less than 500 that required nineteen fourth powers.

- So you lost the game?

- Yes, and I can't even remember which number it was.

Quiz scribe

2005-11-17T20:25:00.000-06:00

Hey everyone

So today in class we did a quiz and the corrected it, and I'm not really sure what I should scribe about today. So I just wanted to make a reminder to everyone that tomorrows a pre-test and Monday will be the test. I don't really think there's not going to be much to scribe about until next Tuesday and I'll be scribe on Tuesday and I'll pick the next scribe then.