[8]Now that we've come, to the end of the road...[8]

Awwwuh. How sad, it's the last day of math and the semester is almost over. It feels like time has just passed us by so quickly, not even taking a short moment to stop and glance back. And thus, the last few posts for this class blog start to appear.

I will truly miss this class. A whole whack of memories have been created in such a short amount of time that we will all surely remember throughout the course of our lives. In all honesty, I thought this class would be boring at first, but man was I wrong. Each day presented a new challenge Even if some of it was review, things were somehow twisted to create a brand new challenge. I swear, after this class, I will never look at life the same way again. As I go home, or even when I'm out running, I always find myself looking at the math around us all of a sudden. It's as if a whole new light has suddenly been shone on the Earth. One time me and Dion even stopped to count the branches on a tree to see if the way they grew followed the Fibonacci Sequence (and to our surprise, they did). A lot has been taught in this class, not only about math, but about life and other subjects as well.

About my progress throughout the class, all I can say is that I did the best that I could and that's all that I wanted to do. The mark had some importance to me as it made me want to work harder to raise it up but overall, I'd say it was the experience that suddenly became important to me.

Now that I've done a few older exams for practice, I think I have found my strengths and weaknesses in this course. I would have to say my biggest strength is Identities. I think it was because it came really easy to me when we learned it and when I saw how it could take such complicated looking things and turn them into 1 term answers, I was amazed. It made me even more interested in the subject. The hardest thing would've had to have been Combinatorics. Who knew counting could be so difficult?! For me, the most difficult part is probably the Binomial Theorem. It was a hard concept for me to grasp right away, but I think I get it now. Hopefully I will have known it enough for the exam.

Am I worried about the exam? Not too much. I've graded myself on the previous exams I've done and I've gotten pretty consistent marks that I'm proud of. Hopefully I do really well on the exam. I will try to aim for that 100%.

I guess I should end this by saying a few things.

Thank you so much to the rest of the pc40sw09 class. You have all helped to make this semester a lot less stressful. Math was kept fun because we weren't afraid to speak up. The heat of "competition" was kept burning by a small handful (you know who you are) and it made things a whole lot more interesting. We shared each other's struggles and celebrated each other's triumphs. We were always there to help each other out where it was needed. We were like one big happy math family. I'll always cherish the memories from this class.

Thank you to Mr. K. Math would be so boring if it weren't for people like you. So passionate and so energetic. It makes us kind of want to go to math class. I guess the coffee would explain all the energy, but passion, that comes from straight the heart. So many great memories were made in this class and a lot of them involve you like

• the sine dance
• Pi Day
• your block of wood
• that "ninja" who came to visit
• your cool tricks on the smart board
• the snapping thing you taught us
• that quadratic equation song
• and a whole lot more!

Your cool little sayings made the day a little more interesting as well. Like that whole "rabbit's foot" thing you say before we take a test or a quiz and that thing you say when you ask if anyone has a question then you ask if anyone has a good joke (even though none of us ever did). Even on a really gloomy and bad morning you never fail to show up with a big smile and a surplus of energy. It amazing, really.

It's such a shame that we must already say our goodbyes after such a short amount of time, right when I was looking forward to AP Calculus, but it's destiny. Even when you leave, remember that you have left your mark at DMCI and you've made a great impact on the lives of many of the people whom you've taught. For that, we all salute you. Congratulations on your new job and good luck.

And lastly, to my D.E.V. partners Mary and Dion. I know this has been said before, but you two really made this semester a lot less stressful, especially when it came down to making our D.E.V. A potentially (non-intentional) stressful project was made really fun because I had the great honor of working with you two. If it had been anyone else, our project wouldn't be the same. Thank you so much for making this experience everything that it was.

It was a great honor and a pleasure to be in a class filled with such brilliant minds. I wish you all the best in your future studies and that you continue to shine. Remember that we'll always have this blog to keep us connected. Good luck to everyone on our exam tomorrow. Everything we have done in this unit has been leading up to this point. Let's knock this one out of the park!

For one last time, peace out!
~jayp~

There are never any final goodbyes and ends, there are only "see you later"s and new beginnings.

This is it I guess

Well, this semester of math is coming to a close and I must say that I have greatly enjoyed this class! It's been difficult at many times but for each hard time there has been a greater number of laughs and even more learning. I feel confident going into the exam but that is not what this post is about. It's more about looking back at the year and especially at our great teacher Mr. K.

-------------------------------------------------------------------------

It's going to be so different with out you Mr. K.

Here are a few memories gathered from your class Mr. K. that we're not going to forget(mostly XD).

These last 2 mornings without you in the room, it's been oddly quiet so we've turned on your music ourselves!!

It's just not going to be the same, "Any questions, complaints, concerns, uncertainties, anxieties.... etc..".

We're going to miss your one lie per class!

The story you told where when you were a little kid, you always wondered how so many people fit "in" the radio.. and they came to YOUR radio, and not someone else's radio!!!!

The time, not long ago, when learning about conics, you took the role of a samurai and amazed us with your skillz and vocabulary! (and calling it a shu-hords)

The time when you wanted to make sure we never forgot this thing... which i forgot... and you went NO NO NO NO NO NO NO NO NO NO NO NO NO all over the smart board!

Someone has just told me that you always wear crocs! Not sure if it's true, is it?!?! If it is why??

Were going to miss your little block of wood with the 3 different views.

Were going to miss your amazing snapping technique!!!!!

Pi day was amazing as was going around sharing the love that was pie to the school.

Your cup of coffee every morning!

The story you told of how pythagorus thought beans had souls!!!

Your mathematical hero is Euler.

A LOGARITHM IS AN EXPONENT (almost forgot).

Putting blogging into a whole new light for us.

Although I was not there, people are telling me of how you thought

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Well, this is it. Have a great summer everyone! Come back and visit Mr. K.!! If anyone has any other stories or memories let me know and I'll update my post!!

Last Minute BOB... probably won't count...

Haha so until today I had completely forgot about the math test I missed on Friday and realized when i arrived at school today that I would be doing this test today. SO i decided I should write my BOB now... it may not count cuz oif the super lateness of it, but I'm gonna do it just in case.

All right, so Conics is one crazy unit. Started out learning about the ancient Japanese art from Samurai Kuro Pat Wa and all the different shapes you can form from cutting a cone. A cone is basically if you took a line and just spun it around. From here you can cut out 4 shapes. You can cut out a circle, an ellipse, a parabola, and a hyperbola. Each one is different.

Some commonalities include:

• Vertices
• Foci
• Focal Radii
• Locuses (Loci?) of points

Equations to remember~

Parabola:

• (x-h)^2=4p(y-k) (vertical parabola)
• (y-k)^2=4p(x-h) (horizontal parabola)
• (h,k)=Vertex
• p=distance from vertex to directrix or a focal point

Circle:

• (x-h)^2+(y-k)^2=r^2
• r=radius
• (h,k)=center

Ellipse:

• ((x-h)^2/a^2)+ ((y-k)^2/b^2)=1 *horizontal*
• ((y-k)^2/a^2]+[(x-h)^2/b^2)=1 *vertical*
• a=semimajor axis
• b=semiminor axis
• c= distance from center to foci
• (h,k)=center

Hyperbola:

• ((x-h)^2/a^2)-((y-k)^2/b^2)=1 *horizontal*
• ((y-k)^2/a^2)-((x-h)^2/b^2)=1 *vertical*
• a= transverse axis
• b= conjugate axis
• c= distance to foci
• (h,k)=center

My struggles:

• Have had some trouble in identifying vertical/horizontal in some instances.
• Sometimes get confused between the ellipse and hyperbolic equations.
• Issues with completing the square.

But I have done some looking over things this weekend and, all in all, this un it is not extremely difficult and so hopefully I will do quite well on it. Next period here I come!

~ Pokemon Champion

BOOOOOBBBB!!!!!!

lol Hey Everyone
Well this unit has practically zoomed by and, for me, has been the easiest unit of them all. It was made especially easy by the fact that there were only a very small number of formulas to memorize and a lot of graphs and patterns. The only thing I really need to remember for these is how to find the focuses on ellipses and how to graph a hyperbola.

Ellipses
take the square root of the difference between the semi-major axis squared and the semi-minor axis squared. this is how far, along the major axis, the foci's are from the center.

Hyperbola
first you need to draw the box created by the conjugate and semi transverse axises. from there you can draw the diagonal lines that make up the asymptotes of the hyperbola. Each one intersects the two opposite points on this box that has been created. Now take the lengths of the conjugate axis and the semi-transverse axis. Now square both of them and add them together. Then take the square root of that to find the distance between the centre and one of the foci's.

Well that is practically everything that I can think of at the moment so Wish Me Luck!!
See you guys in class.

Jessi

Long Distance BOB....Will You Accept The Conic Charges?

LOL well ok, it's not really long distance. But I just came back from Kenora so I thought that would be appropriate. It's great to be back home (although I do miss the bus and the hotel a bit).

Man this unit just zoomed by! It's making me realize that in a couple weeks, I, along with the rest of us grade 12 math takers, will be taking the provincial exam for math. (I'm kinda nervous but I think I'll pull it off. :D)

I'll have to admit that at first, Conics sounded really intimidating. For me, it was because we had to deal with graphing parabolas/circles/hyperbolas/ellipses and see the patterns that accompany them and I really dislike parabolas and graphing them. I'm more of a problem solver and equation person. I guess as the unit went on, a lot of the stuff came pretty easy to me and the unit became easier. I learned to recognize the patterns easily and pull off a "Matrix"-esque move in math. We all learned how to do that didn't we? I think that's pretty awesome.

The easiest part of this unit was learning the different patterns and remembering what stood for what in each equation. I may not remember a lot of things, but for some reason, I do remember things relating to math fairly well. I also felt that how and why the equations worked was pretty interesting. 8)

The hardest part of this unit was the word problems. It's only because I end up thinking about the wrong things, but then again that might just be a coincidence. Hopefully, with the practice I took today with those types of problems, I'll be able to conquer them with ease. Graphing wasn't as hard as I thought it would be, but it was a pain (but that's just me being lazy xD).

I feel that there's only a couple things I need to remember for this test. One of these things being the pictures relating to the parabola/circle/ellipse/hyperbola showing how each parameter relates to the other. The second of these things being the equations for each of the conic chapes.

Parabola:
(x-h)²=4p(y-k) [vertical]
(y-k)²=4p(x-h) [horizontal]
(h,k)=Vertex
p=distance from vertex to directrix or vertex to focus point

Circle:
(x-h)²+(y-k)²=r²
r=radius
(h,k)=center

Ellipse:
[(x-h)²/a²]+[(y-k)²/b²]=1 {horizontal}
[(y-k)²/a²]+[(x-h)²/b²]=1 {vertical}
a=semimajor axis
b=semiminor axis
(h,k)=center

Hyperbola:
[(x-h)²/a²]-[(y-k)²/b²]=1 {horizontal}
[(y-k)²/a²]-[(x-h)²/b²]=1 {vertical}
a= transverse axis
b= conjugate axis
(h,k)=center

If I remember all this stuff, I think I'll do fine. I really am not too worried about this test.
Well, I guess that's all? I will see you all tomorrow! If you ahven't seen the intro to our (Dion, Mary, me) DEV yet, you can view it by clicking the link in the previous post (which should be very short :D). Hopefully, our DEV will be able to fulfill your expectations after watching the intro.

pc

~jayp~

BOB on Conics

Heeey everybody, sorry to say that this will be short and sweet because I've got loads to do tonight unfortunately :<

On with my BOB!
Honestly, this unit sounded intimidating, but in the end, it really wasn't at all! After I got past getting the hang of the geometry, I actually started to enjoy it... (Except for sketching graphs, I always did despise doing that.) :]
So now that I pretty much get the jist of all the geometry involving parabolas, ellipses and hyperbolas, I think I'll do well in that aspect.
However...
Applying them to "realistic" situations won't be my cup of coffee (gonna have to load up on this tmrw huhu). I'm sure with a little more practice I'll have a full understanding of taking pieces of information and constructing the proper equation for it, but waugh! In due time...

What I found interesting was that when you take a line and "spin" it, you end up with two cones, and from there you can derive the parabola, ellipse, and hyperbola! I'd describe/post images of this, but Jessi's scribe post on Conics had very good ones already :].

Now, onto the guidelines which I shamefully hardly ever follow...

• Get at least some sleep! Actually, sleep immediately after you study, you'll remember your stuff better!
• Eat breakfast, brain food = awesome because you don't want to hear your stomach during the test and neither do we lol.
• Take your time, don't rush!
• Keep in mind the equations for vertical/horizontal parabolas, ellipses, and hyperbolas!
• Look at these equations and see the geometry! Remember, "codes!"
• a^2 + b^2 = c^2!
• Be able to take very little given information and build upon them to end up with an equation that will help you out big time!

Anywhoots, I think that's enough brain juice spillage for me. Onto studying!
To everyone who's going on that Kenora trip tmrw... Bye. >_> Just kidding, have fun!
To everyone else, good luck on the test tmrw! :D

BOB for Conics

This unit was extremely short but I learned alot about it. this unit involved graphs like the parabola, ellipse, circle and hyperbola. In order to get these different types of graphs we can cut a double-sided cone( looks like an hour-glass) from different angles. If we cut the top it will create a circle. If we cut at an angle we can create an ellipse. If we cut the bottom it will create a parabola. and also if we cut it at a 90 degree angle down it will create a hyperbola.

The most interesting thing I learned and most useful was the anatomy of the Hyperbola.
This mini box allows us to find the hyperbola with ease and with less information required. Like if you have the conjugate axis and transverse you can find everything else like the asymptotes, vertex and center. Or if you have the slope of the asymptote and know the coordinates of an axis then you can find all the rest of the information also. Hyperbolas involve the difference of distances will always be constant.

((x-h)^2)/(a^2) - ((y-k)^2)/(b^2)

+ or - determines whether its vertical or horizontal. Positive x = horizontal, negative x = vertical.

The ellipse was quite interesting. I was quite amazed that it does not have a radius but instead foci that help determine the value of c. Also within it are the major axis and minor axis. Which help determine the value of a and b in the standard form equation:

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)

the a and b's are switched in a vertical ellipse.

All in all it was short, but very straight forward. Mr.K said we should see the geometry when we see the equations like in the matrix where it shows code but they see people. I can safely say I'm ready and hope they're no big surprises.

Bobing for conics

ha ha made a mistake there =P
k for this up coming test i made sure to keep an eye out on the hyperbola because i thought that it might be the hardest in the conics unit.
-hyperbola is identified by having both x^2 and y^2 and is the difference between the two
-opens vertically if y is positive and horizontally if x is positive
-finding the foci is found by add the square of the minor transverse axis and minor conjugate axis. Like a^2 + b^2 = c^2
The rest of the conics; circle, ellipse, and parabola I'm gonna go over some more.
Best of luck guys for tomorrow!
Oh one last thing i just remembered about conics, remember the pattern i think or the geometry of the object in order to give yourself a picture.
I believe that's what I'm trying to say...
ha ha well good luck again!

BOB

This was really a quick unit! I understood that it's just really comprehending what the equation is telling you. The equations have been posted a lot of times here so i won't list them here on my BOB. Anyway, here are some random things that are to be noted:

1. The general equation of a conic is .

2. Completing the square is done to convert an equation's general form to standard form.

3. An ellipse has two axes of symmetry: the major axis and the minor axis.

4. If a hyperbola is parallel to the x axis, then x^2 is positive. If it is parallel to the y axis, then y^2 is positive.

5. (h,k) is the center of the conic.

6.a is the transverse axis in a hyperbola, while b is the conjugate axis. they indicate whether the hyperbola will be opening up and down, or left and right.

7. A parabola has only one variable squared, unlike the other ones.

Okay, good luck to everyone on the test! I know we'll all do well on it. :)
Night!

BOB not just sweet words

Reflection time again!!! I think that I'm current a very messed up canvas. It's not that I don't understand, I do but its just when it come test time that I feel that I don't. Everyone already posted most of the stuff you need to know and it will just be redundant if i say the again.

Success for the test(?):
- remember the formulas/equations!
- when we see the equations were suppose to see the graph!
- completing the square
- practice makes close to perfect
- eat, sleep and study
- confidence!

Good luck on the test tomorrow, study, study study.

-jennifer

bob

still reviewing for tomorrow.
I was on this net to review
http://webct.merlin.mb.ca/webct/urw/lc4130001.tp0/cobaltMainFrame.dowebct
i didn't find the foci, and how you solve that part.
I still didn't get the foci, and i think I'm good with other stuff.
good luck guys!!!!!

BOB

Hi. Here's my reflection on this unit:

I actually found this one interesting, since it felt cool when I successfully completed a question that asked me to graph something. Makes me feel like some kind of pro artist. :P Anyways, I struggled a little in the beginning. -Not- because it was hard, but because of some other issues that were affecting my work ethic.

I'm fairly confident about this test. I'm hoping to to get atleast 50% on it (just the passing. :P) but if I do better, then boo yeah. And yeah, I know I should "aim higher", but I'm just being realistic.

I won't bother going over anything, since everyone else probably will be doing it. (And better, I might add.)

Good luck on the test tomorrow.

-ConstantEcho

BOB on Conics

This is Jonno doing my BOB on our Conics unit before the test.

So, this unit was mainly about circles, parabolas, ellipses and hyperbolas...
For each of the stated above, we learned that each of them comes from a line that is spinned in a circle, basically, forming two cones. Depending on how you slice it, you can get one of the shapes/graphs/etc, stated above. We also learned the equations for each of the stated above. After Mr. K's talk about the matrix and such, he said we should also be able to identify what it is and what it looks like just by looking at the "code" or equation. I tagged a delicious link that can help you with this a bit, so if you're interested here it is!

Basically:
Parabolas - only have one squared term (ex. x^2 + y = 1)
Circles - have 2 squared terms that have equal coefficients (ex. x^2 +y^2 = 1)
Ellipses - hav 2 squared terms whose coefficients are not equal (ex. 2x^2 +y^2 = 1)
Hyperbolas - (I'm not 100 percent sure because i wasn't here for class that day, but from what I've seen...) have two squared terms, one being positive and one being negative? (ex. x^2 - y^2 = 0).

Another thing we learned was to change equations to general form from standard form and vice-versa.

I'm pretty sure i covered most of what we learned. I know there's more stuff, like the pythagorean theorum and such being used in the ellipse and hyperbola graphs, but I don't think I currently have enough skills to explain it.

What i found hard (until today) was finding the asymptote lines of the hyperbolas, but Mr. K. cleared that up for me.

Well, that's all I'm going to put up for my BOB.
Good Luck on the test everyone!

Jonno- Out

BOB

Hey there. This recent unit we did was conics. It was all about cones and stuff. I found this to be pretty simple, just like the stuff we did in grade 11 pre cal with parabolas.
there is a little diagram of how the shapes were formed.


Circle formula:
Elipse formula:
Parabola formula: or horizontal parabola:
Hyperbola formula:

I hope everyone gets an A+! don't forget about DEV projects

Conics BOB~

The conics section is one of my favorites. There weren't any big surprises and it seemed "short and sweet".

What we learned:

Parabolas

• vertex (h,k), a directrix (straight line, fixed distance from vertex), and focus(fixed distance from vertex)
  
• Standard form VERTICAL:

• Standard form HORIZONTAL:

• When 4p, also known as a, is greater than 1 the parabola is wide.
• When 4p is less than 1 the parabola is skinny.

Circles

• focus= center (h,k)
• Standard form:
• remember, the r is squared.

Ellipses

• center (h,k), Vertices's (endpoints on Major axis), major axis (length of 2a), semi-major axis (length of a, center to one of the vertices's), Minor axis (legnth of 2b), Semi-minor (length b),Foci (c units from center), Focal radi (distance b/w Foci and point on ellipses.
  
• The midpoint of two foci would center of ellipses.
• Standard form HORIZONTAL:
• Standard form VERTICAL:
• a^2 is the bigger number.
  
• c^2 = a^2 - b^2

Hyperbola

• center (h,k), Transverse axis (the distance b/w the vertices's, which are also the vertex. Is the difference of foci to pt, foci2 to pt. length of 2a), semi-transverse axis ( a),conjugate axis (length of 2b), Sem-iconjigate (b), Foci (c units from center), asymptotes.
  
• Standard form HORIZONTAL:
• Standard form VERTICAL:
• c^2 = a^2 + b^2
• When given slope of asymptotes, you can figure out the value of b or a. b/a = rise over run.

When changing equation from general to standard, you'd need to complete the square.

study hard guys!

BOB likes to eat icecream [cones]

I feel pretty confident for the test tomorrow, I might not get 100% but I believe I'll do better than what I have been doing so far. I liked this unit because it was pretty straight forward and I had no real trouble understanding any concepts.

I think that for this unit I just need to make sure I know the formulas really REALLY well. Let's review shall we ^__^

A PARABOLA:
The equations:

If the x is squared, the parabola is vertical (either opens up or down) and if the y is squared the parabola opens horizontally (opens left or right). p is the distance from the vertex to the directrix and the focal point. If 4p is a big number, the stretch of the parabola is also big. If the number is smaller than one the parabola will be skinny.

A CIRCLE:
The equation:


r is the radius. In general form, the coefficients of x and y are squared and are the same. That's how you know it's a circle!

AN ELLIPSE:
The equations:

When a (the bigger number) is under x, the ellipse is horizontal. If it's under y then its vertical.
a is the length of the semi major axis. b is the length of the minor axis. Use c^2 = a^2 - b^2 if you have to find the distance between the origin and the focal points. In general form, the coefficients for x and y are different.

A(N) HYPERBOLA:
The equations:


When x is positive the hyperbola is horizontal (opens right and left). When y is positive it is vertical (up and down). a is the length of the semi transverse axis, while b is the length of the semi conjugate axis.

use c^2 = a^2 + b^2 to find c, the distance from the origin to the focal points.

hyperbola graphs have asymptotes! use the slope formula to figure out their equations.

To be alright for the test, all we need to know are the formulas and how to graph them. I'm sure everyone will do fine! ;D

Make sure to eat healthy, drink plenty of water and get some rest so you can be in top shape tomorrow morning!

~Bye bye! :D

BOB for Conics

hi everybody, one more unit is done and i was almost forget about the BOB for this unit. T_T .
Anyhow, i just do this BOB briefly.

I think this unit is not really, you just need to know the formula and understand the graph so you could know which formula is parabola, ellipse, or hyperbola.

About the formula, i think some of us already posted it, so i am not going to repeat it. :D

Anyway, Good luck all guys, test on Friday and don't forget your delicious link [which i also almost forgot :-"] ...

BOB BOB BOB BOB :)

Hey everyone!
This unit went by really fast, and since it's the end of the school year, I'm becoming more lazy, so that means that I really haven't been paying much attention to a lot of things happening in class. So I really need to study a lot and make sure I do well on this test! The only thing I really need to review is the day when we learned about graphing parabolic equations since I wasn't in class for that lesson. I have a feeling it's not a hard thing to pick up, so hopefully I learn everything I need to know before our test, which is on friday. Other than that, I think I'll be okay. I'll just have to read through the slides to refresh my memory, and hope that I do well. I guess that's all, good luck! :)

BOBS on Conics?

Well this unit was relatively easy for me. The only things I think I will have problems with is reading the question properally and putting it in the right way.


So the first thing we learnt about was parabolas. We learnt another formula for a parabola which is :


P is the distance from your foci to your vertex or your distance from your directrix to your vertex.

If you want the horzontal graph, you just switch the (x-h) and (y-k).



The next thing we learned was circles and the formula is the same as the one we learned before so I'm not going to go into detail with that.



Then comes the elipses with the formula:

Where "a" is the length of the semi major axis and "b" is the semi minor axis.

If you want the vertical graph you just exchange the "a" and "b"

Then there's hyperbolas (parabolas on steriods, according to Mr. K)

Where "a" is your semi transverse axis and "b" is your semi congurant axis. If you want your vertical graph you just make "x" negative instead of "y".

So that's basically the simple summary of what we learn, time for my nap. Night.

Reflection on Conics

Well that was a quickfast unit. I found it so much easier than any of the previous units. :) But lately I've been lazy sooo... I need to get back with the program and practice, practice, practice! >_< Oh and I still need to look over the formulas a few times to make sure I don't mix them up. Remember that the transverse axis connects the two vertices of the hyperbola and can be either horizontal or vertical.

Good luck to everyone!