Analytic Geometry Assignment

Here it is!

If you need a little help with this stuff here is another tutorial for you. (Important: Gradient is another word for slope. And the stuff about the area of a polygon is cool, but we don't study that in our course -- go ahead and learn it if you like!) If you think you understand this stuff take this quiz from the end of that tutorial.

Also, check out my previous post if you haven't already.

Cheers!
Mr. K.

What Mathematicians Think...

Earlier this month Jan Nordgreen at Caymath posted about an interview of a couple of professional mathematicians talking about their work. Here's one quote.

Isadore Singer: ... when I try out my ideas, I’m wrong 99% of the time. I learn from that and from studying the ideas, techniques, and procedures of successful methods. My stubbornness wastes lots of time and energy. But on the rare occasion when my internal sense of mathematics is right, I’ve done something different.

Another quote:

Michael Atiyah: My fundamental approach to doing research is always to ask questions. You ask “Why is this true?” when there is something mysterious or if a proof seems very complicated. I used to say — as a kind of joke — that the best ideas come to you during a bad lecture. If somebody gives a terrible lecture — it may be a beautiful result but with terrible proofs — you spend your time trying to find better ones; you do not listen to the lecture. It is all about asking questions — you simply have to have an inquisitive mind! Out of ten questions, nine will lead nowhere, and one leads to something productive. You constantly have to be inquisitive and be prepared to go in any direction. If you go in new directions, then you have to learn new material.

The full interview is right here.

These are two things I find myself constantly belabouring in class when teaching problem solving:

• Take risks! Experiment, play, try something out and see where it takes you. Good math isn't knowing what to do with any problem -- good math is knowing what to do when you don't know what to do. ;-)


• Ask questions! If you don't ask questions then I can't tell whether you understand or not. I'll either go on to something new, leaving you confused in the dust, or go over and over something you already understand trying to help you but really just wasting our time.

Food for thought ...

Hare and Hounds

In this game you have to "run for it!" You can be the Hare or the Hounds. The hare has to escape; the hounds are trying to corner him.

The real question is: Are you an expert Hare or expert Hounds? ;-)

Have Fun!

Gimme Your Coordinates!

Here is a review of what we learned in class today.

Practice your test taking skills here (every time you [Refresh] the page you'll get a new set of 5 questions).

postblog before the test

Mmkay, so heres my post before the test. =P

Wow, this unit went by pretty fast. And we have covered alot. I think I'm okay with finding the sum & product of the roots, the quadratic formula (yes, i sing it alot too =P "pop goes the weasel :D"),how to tell if the equation has one, two or no roots (the discriminant), imaginary numbers? im not sure if that one is on the test. is it?? the one with the "i^2" and "i". well ya.. anyways.. im still having trouble doing some problem solving =P uh-oooh. yeah...i gotta go review that one again. okee im done here.

GOOD LUCK EVERYONE :)

Sunday Funday (Oops, I missed a beat...)

Here are the rules.

Here is the game.

Have fun with it!

Random Post. LOL

So. How's life. Fine. Thank you Very Much. How's math. Cool as always. How's everything else? Um... Great. I think. Hahaha. So the Scribe is Aichelle right? Yes sir. That's cool. How do you know. Secret. I see. Haha. Alright. So what you doing tomorrow? Um... I dunno. School? What about the day after tomorrow? Um. School. How bout. Um.. Nevermind. So when is this conversation gonna end? Now I guess. Hahaha.

IF YOU DIDN'T GET THAT AICHELLE'S THE SCRIBE TOMORROW!!!


Hahaha. That was totally random. Hahahahahaha.

THE SUPER MUDDIEST ALGEBRAIC POINT

Let us take advantage of this situation that we are in... So anyways... Blogging, Homework, Class, 3/6. We learned this material 3 times already. Now we need more. More help, more math, more math, more... oh I said that already. Hahaha. So anyways. You guys get it right. Same rules apply and this post will be the first post you'll see until Saturday night. If you guys remember how to do that. Haha so ya. To quote a famous math teacher.

"You can use your name or leave your comment anonymously, but, whatever you do, share your troubles here. Remember, not only can Mr. Kuropatawa help you but you can help each other too! Leave tips and advice in the comments for your classmates. And don't forget, you can form an online study group and "meet" in the chatbox of our blog! Unlike Sysiphus, you're being set up to succeed! Take advantage of every opportunity you've got! "

So ya. I'm out for the weekend. Later.

BTW... I hope this works and... Thanks Robert fot the idea in class. Hahahahaha

Next Round of Bloggers...

Man... Man... Man... This is great... Test is now on Tuesday... Man... Ok it feels like I'm ranting... But I shouldn't be. Hahaha.

So anyways. This unit is really, really, really, umm.. How would I put this. Intermediate/HARD. Hahahahaha. That was strange... Haha.

Well anyways. I understand the basic concepts. Check.
I know how to apply them. Check?
I can do problem solving questions. D.N.E. Hahaha
Anything else... I am so screwed... Man...

Anyways. To my point of this whole, short & sweet blog post... I'm a bringing back "The MUDDIEST POINT" for this unit and calling it.

"THE SUPER MUDDIEST ALGEBRAIC POINT" Dum dum dum. And I'm going to set the date on the blog post so it's going to be the first blog post you see until Saturday night.

That should work. Hah. So if we have problems on this unit. Cause I know we do. And I know the class as well as I do. And If we do this Mr. K will give us help online. So it's a plus, plus, plus. HAHAHAHAHA

That was queer...

Well anyways. I'm a out. and I'm a back in. BTW I allways put this... If you need help blogging... Go to. BLOGGERS 'R 'US. Later///

Rational Equations

Review solving rational equations and look at these solved examples.

Try this quiz on solving rational equations. Here is another one.

Radical and Absolute Value Equations

Review solving radical equations by looking at these solved examples. You can find more examples here.

Try this quiz on solving simple radical equations. Make sure you can do ones with two radicals in the equation as well -- like this one.

Here is where you can review how to solve absolute value equations. You can see some solved examples and you can take a quiz over there.

Sunday Fun! (or Sunday Madness!)

I got this from a blog called Think Again! A great little math blog full of interesting puzzles. Lucky me, it took a while but I found my way out of the room ... can you?

---

You are trapped in a room. To get out requires some thinking. Good luck!

Over two million people have tried to leave the room already. No one knows how many are still stuck.

Nature of Roots

THE SUM AND PRODUCT OF ROOTS.

Mr. Clark taught us how the sum and product of roots are related to the quadratic equation.

But before talking about that... how can we get the roots? Well, we can get the roots of a quadratic by:

1.) factoring

2.) using the quadratic formula

3.) or completing the square.

For most of us factoring is the easiest way to get the root.

(factoring review? *click here)

(the quadratic formula?*click here)

(forgot how to complete the square?*click here)

When a (leading coefficient) is 1:

the sum of the roots is the negative or the opposite of b (coefficient of x)

the product of the roots is the c (constant term)

Example #1)

If the roots are 4 and 8,then the quadratic is

.

The b (coefficient of x) is −(12), which is the negative of the sum of the roots. The c (constant term) is 32, which is their product.

Example #2)

a = 1; b = -2; c = -15

Sum of the roots is -b/a = -(-2)/1 = 2
Product of the roots is c/a = -15/1 = -15

That`s all for now. CIAO! :)

oh yah... ANNNNND tomorrow's scribe is Jamilyn G. ^_^

Scriber’s Revenge

Man...… You had to pick me...…
Man...…
... ... ...…
Man...…Sigh///
Ok. Fine...…

Ok now that thats over with.…Today in class I get randomly chosen as scribe by Rannell. Thanks...… So anyways. First we had to do three questions like what we usually do.

USE THE QUADRATIC FORMULA TO FIND THE ROOTS

If any of you forgot what the Quadratic Formula was...… Sing the Song. lol

a) f (x) = 2x² - 3x - 4
b) f (x) = - 2x² + 3x + 1
c) f (x) = x²- 6x + 10

Answer to A)

Answer to B)

Then Mr. K. Told us why it's negative over positve.

Answer to C)

Then we went back to factor trees. lol.

Fundamental Therom of Arithmetic. Only 12 can have the number 2,2,3.
We learned about a German Mathematician named GODEL.
He proved that certain things we know can be true but we dont actually know it's true.

For Example.
This Sentence is False.

He invented the GODEL number.
5 = 2⁰*3⁰*5¹

Fundamental Therom of Algebra

Any polynomial, whatever it is, it has to have the roots equal to the degree of the polynomial.

For example
f (x) = (x - 3)²
= (x - 3)(x - 3)

Then we learned that Some Roots can be imaginary. I'm like what...
Then we learned about a Swiss Mathematician called EULER and that he's responsible for PIE and E which is actually 2.17817... etc.
I wonder if Mr. K has a piece of E???
Hm...…Anyways then we get this whole explanation on how there are imaginary numbers outside the real numbers and stuff.

AKA It leads to this...

And This...

Some examples...

Then we finish question C. In the "Complex number system"

Then we learned about The Discriminant
b² - 4ac <' 0

No Real Roots

(2 Complex or Imaginary Roots)

b² - 4ac = 0

One Real Root
b² - 4ac > 0

2 Real Roots

Then we get some notes in our Dictionary... I'll get Graeme to fill you in next time he has some notes. lol.

Mr. K. Then went over some question's on Exercise 14 & 15. Provided by Robert.
Homework if you didn't do it is Exercise 16 but leave out Questions 10, 11, 12, 13
Tomarrow we have a sub. Mr. Clark.

AND THE SCRIBE FOR TOMARROW IS... KAT L.

Pop Goes The Weasel!

Today we derived (watch this!) the Quadratic Formula in all its glory!

Here it is explained.

You can practice using it over there!

Now sing it with me folks!



x equals negative b
plus or minus the square root
of b squared minus 4ac
all over 2a

Factoring Review

Today I emphasized how to solve equations and trig equations by "recognizing the quadratic pattern". You can find a review of factoring here and practice your skills there and try harder questions here, here, here and there.

That review also explains why we call them quadratics -- "Doesn't quad mean four?" ;-)

Blogging MARK?!?!

If you guys were wondering about your one point blogging mark. Don't worry about it. It's covered. If your wondering why? Check the chat box. or just read this.

Originally Posted by Mr. Kuropatwa October 4th 9:42 pm On the Chat Box

Whoever reads this please tell the rest of the class tomorrow. I forgot to put "Did you blog?" as the 1st question on the test but your blog post STILL counts for 1 mark on the test -- I'll adjust it accordingly when I'm back at school. BTW, I posted a few practice quizzes online to help you study over here --> [link]

So ya. Blogging is Covered.

- Malcolm X
Hahaha... New Nickname... Hahaha

another blog before the test...

we had a pre-test today and it was okay =) i actually get it now... yay! I think i like this unit better than the last. haha i think i like trigonometry now.. ahaha the only thing that im having trouble with is uhmm... the word problem and just drawing the diagram. but everything else is okay ^_^ anyways... the test is tomorrow! oh yah... before i end this post..when writing the test DO NOT FORGET: -to put the degree sign when righting an angle. -when graphing something, label your graph. (x&y axis, the points...etc.)

thats all for now... GOODLUCK GUYS!

bloggin' before the tesssssssst

hey everybody,

well today we had the pre-test and it went pretty good. well the the whole there was two cases to answer the last question was just weeirrdd haha... i never even saw that we can do that. well i hope the test is clear if there's a question like that hmmm.. what else to say. well if you think the pre-test was pretty good then you're probably ready but you might as wekk study riiighhht!?! you'll be twice as ready and there's no harm at that. well i hope you guys did the muddiest point comment i think it would help mr. k know where we are all at =)...

i don't know about you guys but....

I LOVE TRIGONOMETRY

well you guys i dont have anything else to day but....

STUDY ( awww.. look at him)

DONT WORRY... IF YOU PAID ATTENTION IN CLASS... DID YOUR HOMEWORK.... AND STUDIED... YOU'LL DO FINE =)

(DOESN'T HE LOOK LIKE A GHOST... HAH)

BONNE CHANCE!

Short & Sweet

So... How's Math... LOL. Anyways. I'm just here to help and stuff. You know. Do math. Pass Math. Hahaha. So. Personally I think Trig is easy. Cause I understand allot of it. (It's like the only thing that I really Understand in math...) But of course not all of it.

So anyways...
What was I going to say...
Oh Ya...
Here's a REMINDER!!!


BLOG BEFORE THE TEST!!!

It's an easy mark.
Remember That.
Just thinking of you guys... ;)

Btw...
If you can't think of anything...
Go back to BLOGGERS' R' US
or...
Go back to Blogging on Blogging

scribblin' scribe....

Today we worked on some problems on the board. Here they are:

1. Graph y = -2cos(x+45)+3

A = 2
B = 1 <<>
C = 45
D = 3

Y = A sin B (X-C) + D
Y = 2 sin (X-45) + 3

2. Write two equations ( Sine, Cosine) for this graph.

Y = A sin B (X-C) + D

A = 3
B = 1
C = -135 / 45
D = -1

Y = 3 sin (x+135) - 1

Y = -3 sin (x-45) - 1

Y = A cos B (X-C) + D

A = 3 Y = 3 cos (X+45) - 1

B = 1 Y = -3 cos (X-135) - 1

C = -45 / 135

D = -1

3. A car is driving due east along a road. The driver sees a radio tower in the direction N56'E and 5280m away. The radio tower had a range of 3500m.

a) How much farther must she drive to get "in range" of the radio.

b) For what length of the road (distance) will she be able to listen to this radio station.

Sin34/3500 = Sin*/5280 = .8436 = 57.5' or 122.5'

Since we are smarter then the average bear we know that the obtuse angle

Now we solve with the sine law.

Sin88.5/X=Sin34/3500 = 6256.9m <>

Sin65/x=Sin57.5/3500 = 3761.1m <>

6256.9 - 3761.1 = 2495.8m

a) She needs to travel 2495.8m more to be in range.

b) Once she starts in range she will travel 3761.1m until she will travel out of range.

4. An 11cm long line is drawn at an angle of 44' to a horizontal line AB. A circle with centre C and radius 9cm is drawn cutting the horizontal line at points C&D. Find the length of CD.

Sin44'/9 = Sin*/11 = 0.8490 = 58.1' and 121.9'

We know the obtuse angle is 121.9' and the acute angle is 58.1'.

Sin61.9/x = Sin 58.1'/9

CD = 9sin61.9'/sin58.1 = 9.4cm

5. A golfer takes two putts to get the golf ball into the hole. The first putt rolls the ball 10.2m in the northwest direction, and the second putt sends the ball due north 3.7m into the hole. How far & in what direction should the golfer have aimed in the first putt to get a "hole in one"?

To solve this problem we'll have to do cosine law.

I don't know how to square do this a*2 will mean a-squared =).

a*2 = b*2 + c*2 - 2 b c cosA

a*2 = 3.7*2 + 10.2*2 - 2 (3.7) (10.2) cos135'

a*2 = 171.1 square root it = 13.1m

To find what angle he should've hit it in...

SINE LAW Sin135/13.1=Sin*/3.7m = .1997

11.5' +45' = 56.5' away from the x=axis.

Well you guys might want to check my math becuase I'm not too sure about myself.

REMINDER pre-test tomorrow with subsitute so study study study!!! Sorry it took so long I didn't realize the pictures were so hard to make.

TEST ON WEDNESDAY DO NOT MISS! COME PREPARED!

Welll I guess that's it.... good luck everybody and before I forget next scribe is....... RoselS

The Muddiest Point!

Test day is Wednesday. I'm away for the next two days. Use the comments of this post to share with Mr. Tram, my substitute, your personal "Muddiest Point". You can use your name or leave your comment anonymously, but, whatever you do, share your troubles here. Remember, not only can Mr. Tram help you but you can help each other too! Leave tips and advice in the comments for your classmates. And don't forget, you can form an online study group and "meet" in the chatbox of our blog! Unlike Sysiphus, you're being set up to succeed! Take advantage of every opportunity you've got!

Let's Be Clear - Not Ambiguous!

If you're still struggling with the sine law and which circumstances lead to the ambiguous case you can review the material here. There's a nice little java applet that you'll find if you scroll down the page with step by step instructions to help you understand what's going on.

I found another applet over there that also illustrates how the ambiguous case arises.

Finally, just to round off this helpful little post you can try your hand at these online quizzes to get ready for the test:

• The Sine Law (5 questions)



• The Ambiguous Case (5 questions)



• Related Angles Worksheet (lots of practice!)



• Trig Word Problems Online
  (Look for the [Get a Different Set of Questions] button -- LOTS of practice here!)

Don't forget to study Trig Graphs as well.

Do your BEST on Wednesday!

Don't Read The Textbook .... Write It!

If you write it you probably understand it a whole lot better than if you just read it.

The internet has made all textbooks out of date. By the time a book gets published the world community has learned a whole lot more and shared it on the internet. Here's your chance to do the same. ;-)

First, the modern internet textbook is written in wiki format. A wiki is basically a website that can be created as easily as creating a blog post. Watch this to see what a wiki is and how it works.

After that check this out. It's a collection of text books that have been or are in the process of being written by an international community of ordinary people like you and I. As a matter of fact, YOU can add to any of them. Go ahead and do so if you wish. ;-)

What strikes me most powerfully about this latest development on the internet is the fact that anyone can write a textbook on any subject they wish! One of the textbooks being written is called How to pass a course. One of the things I really liked about this textbook was this:

Forming an understanding of the ideas behind each lecture requires active thinking. Try to think ahead of the professor: "What is he going to say next?". If the professor asks someone else a question, answer it in your head. If you answer wrong, try to think why it was wrong.

We will be using a wiki for our story project. Each participant will post their story problem and link to the solution which will be written on another page.

Do you think we should have our very own wiki in our very own webspace or should we add a textbook to the growing list of WikiBooks? Leave your thoughts in the comments to this post.

Cheers,
Mr. K.