Pre-Cal 40S (Winter 2009)

So Long ...

noreply@blogger.com (Darren Kuropatwa) — Fri, 26 Jun 2009 08:54:00 -0500

We had our graduation exercises today. A gentle push into the world for all of you. I hope you're leaving with the keys to your future in your hand.

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!

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

324th post; It's the end

noreply@blogger.com (Jennifer) — Tue, 16 Jun 2009 19:22:00 -0500

So I've been meaning to do one final post, forever will I no longer have to blog for school. Exams are over and I'm sure you all did excellent. The school year has ended and it is now time for the exams. Study hard everybody, good luck with the rest of the exams.

I dreaded going to class everyday but I THINK I'm gonna miss it. It's weird that its all finally over. All the memories created through out the semester. As classes went by I think my interest in math sparked.

Thank you Mr.K for educating us so well in math, math wasn't so boring with you teaching us. Those interesting little facts and stories you always feed us. It was awesome how you got each student involved in someway. It is a shame that DMCI will be losing a teacher like you. Congratulations on your new job, take care and good luck in the future.

On the other note were you this type of student? I know I was.
New school semester:

At the first week:

At the second week:

Before the mid-term test:

During the mid-term test:

After the mid-term test:

Before the final exam:

Once know the final exam schedule:

7 days before final exam:

6 days before final exam:

5 days before final exam:

4 days before final exam:

3 days before final exam:

2 days before final exam:

1 day before final exam:

A night before final exam:

1 hour before final exam:

During the final exam:

Once walk out from the exam hall:

After the final exam, during the holiday:

Isn't that cute, I just thought I'd share.

Farewell Pre-cal 40S Winter 2009 Class

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

noreply@blogger.com (jayp) — Thu, 11 Jun 2009 00:17:00 -0500

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

noreply@blogger.com (d~i~o~n) — Wed, 10 Jun 2009 21:53:00 -0500

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

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

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!!

Final BOB: Good Luck To All

noreply@blogger.com (D-S Skyline) — Wed, 10 Jun 2009 07:24:00 -0500

Hey guys this is the last time I will probably get the chance to blog in this site so I'm gonna take my time saying good luck to everyone who is taking the exam.
Since the exam is tomorrow and today is our last day i wanted to make sure i post a day before the exam just like how we would usually blog on test. The only exception is that this is gonna be the biggest test were gonna have.
In the classes I've spent here I've learned quite a lot of things. Besides math of course we were taught some pretty cool stuff too. For all of you guys who are reading i encourage you to take at least 5-10min from your busy schedule to post up our last blog reflecting this semester.

Why?

Why not? For some of us it will be our last time to blog so why not give it a go, for the others well you can probably just say good luck to everyone.

If there is something i do want to reflect on is how inspiring our teacher is. I for one am sure gonna miss him when we depart. We will someday meet again and everything you taught us we will remember in our own ways. The only thing i regret is that our time with you was short, but the memories last for a life time so i guess that compensates it.

Good luck to you our teacher. With patients and skills you taught us what we need to know. Now it is our turn to take the test and try our very best to succeed with the knowledge you provided us.

Once again good luck to everyone who will be taking the exam and don't over strain yourself in studying at the last minute. Take a break, look over the notes, have a little fun, and have plentiful of a good nights rest. When the exams comes your efforts will be tested.

Good luck again to everyone

Hope you do alright

Today's Slides: June 8

noreply@blogger.com (Darren Kuropatwa) — Mon, 8 Jun 2009 14:58:00 -0500

Here they are ...

Pre-Cal 40S June 8, 2009

View more Microsoft Word documents from dkuropatwa.

Scribe...i accidentally put BOB earlier-__-

noreply@blogger.com (Jonno) — Sat, 6 Jun 2009 13:31:00 -0500

*note* Mr. K. made a correction to the formula we learned in previous sessions:
the correct formulas are now and
If you look the june 5 slides, pg 6 and 7 shows how we get to these formulas (sorry, my print srn doesn't really work)

On friday, the main thing we learned was solving infinite geometric series!...here's the deal...basically, any fraction that is below 1 and over 0, to the power of infinity will be equal to zero...of course it's not REALLY zero, but our calculators don't have the potential to hold a number less than google, and there is no exact value for it since infinity is an idea and not a number...since it's really ultimately infinitely close to zero, we make it equal zero, making our lives easier. Look at the June 5th slides, page 13 for an example.

...to be honest i don't really know what else to add...i'm a little preoccupied thinking finishing up my final project and worrying/studying for the exam...if anyone needs more clarification, just leave a comment within the next week and i'll fix this up some more...

-Jonno out

Today's Slides: June 5

noreply@blogger.com (Darren Kuropatwa) — Fri, 5 Jun 2009 15:30:00 -0500

Here they are ...

Pre-Cal 40S June 5, 2009

View more Microsoft Word documents from dkuropatwa.

june/4/09

noreply@blogger.com (Anonymous) — Thu, 4 Jun 2009 17:47:00 -0500

Arithmetic and Geometric series.

We started the class with a quick probability question, one that was brought up by a student.

When solving questions like these, always try to go back to the basics. Probability is the number of favorable outcomes over the possible outcomes. From that, we have something to work with.
Finding the possible outcomes, or Sample Space.

The question states that "4 men and 4 women" would be chosen. This means that out of the 7 men, 4 will be chosen (7C4), and out of 10 women, 4 will be choose (10C4).

Finding the favorable outcomes.

Since the question said that, "Allen and Bridget will be among these 8 chosen people", we already know that they are part of the possible outcomes. They are represented by the green and blue "1"'s.
Out of the 7 men, only one has been chosen, (Allen). This leaves us with 6 more men, and 3 more spots for men, 6C3.
Out of the 10 women, only Bridget has been chosen. This leaves us with 9 more women, and 3 more spots for women, 9C3.

As a result, you would get what is shown on the image above. (:

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

Today's class was focused on:

Arithmetic and geometric sequences
Series
Arithmetic and geometric series.
Sigma Notation

Arithmetic sequences
An arithmetic sequence is a sequence (ordered list of numbers), where a fixed number(common difference) is found between two consecutive terms. (negative numbers are added too! )
This means each term is going up or down by the same number.
When wanting to find the nth term in an arithmetic sequence, refer to the equation below. (use Carl Friedrich Gauss's 7year old story to help you remember the equation.)

Geometric sequences
Geometric sequences are like arithmetic sequence, but instead of adding its multiplying. This means instead of a common difference, there's a common ratio.
When finding the nth term in a geometric sequence, refer to...
Series
Series is defined as, the sum of terms in a sequence. (Sn, where S reads as "sum of" and n would be the rank of the nth term. ex. S4 = sum of the first 4 terms.)

If we were to have a sequence of 1,2,3,4,5,6,7 etc, the series would consist of 1,3,6,10,15. Why? Well the first term is a given, 1. The second term would be 3, because that was the sum of the first and second term from the sequence, (1+2). The third term is the sum of the first, second, and third terms from the sequence. (1+2+3). The orange circled numbers in the above picture are the ranks.

Arithmetic series
Arithmetic series is the sum of numbers in an arithmetic sequence. This would be helpful if you are asked to find the "sum of integers from 1 to 5000" for example. Where n would be 5000, because there are 5000 terms, a would be 1, because that is the value of the first term, and d would be 1, because that's the common difference. (numbers are going up by one)

Or you might be asked "What is the sum of all multiples of 7 between 1 & 5000".
What you know:

From the sequence of multiples of 7 between 1-5000, first term is 1.
Last term is 4998
common difference is 7.

What we need to know:

number of terms within that sequence.

By using the arithmetic equation, tn = a + (n-1)d, plug in known values, do some grunt work, and you'll be able to find n. (or you can just take the last number, 4998, and divide by 7, to see how many times 7 can go into it.4998/7 = 714) Once you've found the number of terms, plug it into the arithmetic series equation. ta-da~
Now don't get too carried away with questions a and b. These kind of questions wont be asked on the exam, but you'll need to know the methods of a&b in order to solve c. (c = a question likely asked on the exam).

Logic:( The sum of all integers 1-5000) - (sum of all multiples of 7) = sum of all integers not multiples of 7. This "build up" to a question, is called scaffolding.

Geometric series.
Sum of numbers in a geometric sequence.

Sigma Notation
Is the shorthand way of writing a series, also known as the weird looking "E". Sigma is really confusing, if you don't know how to read it. The n=1 tells you the value of the first term, which is 1. The 4 on top of the sigma is nth number of term to stop at. The (2n-3) is the "rule" or equation you follow.

bye guys! good luck on the exams and your DEVs!
mary
The next scribe is jonno!

Today's Slides: June 4

noreply@blogger.com (Darren Kuropatwa) — Thu, 4 Jun 2009 13:27:00 -0500

Here they are ...

Pre-Cal 40S June 4, 2009

View more Microsoft Word documents from dkuropatwa.

stress impedes learning?!

noreply@blogger.com (Anonymous) — Wed, 3 Jun 2009 22:14:00 -0500

"What’s your sine? It must be pi/2 because you’re the 1"

HAHAH XD
just to lighten up the moods for all those who are studying hardcore. As pacifico said,"stress impedes learning", so cure it with laughter!

source

Today's Slides: June 3

noreply@blogger.com (Darren Kuropatwa) — Wed, 3 Jun 2009 20:20:00 -0500

Here they are ...

Pre-Cal 40S June 3, 2009

View more Microsoft Word documents from dkuropatwa.

June the Third Scribe

noreply@blogger.com (Rebecca) — Wed, 3 Jun 2009 14:05:00 -0500

First of all we split into groups and Mr.K informed us that we were starting our new unit, sequences. We should be done this unit on Friday or Monday. So be prepared to move really fast!

Okay well apparently today was mostly a review from grade 10 (if you can remember that far back.. good job!)
On the first slide there were four sequences...

4, 7, 10, 13, __, __, __
3, 6, 12, 24, __, __, __
32, 16, 8, 4, __, __, __
1, 1, 2, 3, 5, 8, 13, __, __, __,

Mr. K wanted us to fill in the blanks and explain how we found the missing terms...

4, 7, 10, 13, 16, 19, 22 (Add 3 to the first term to find the second term. This is called an arithmetic sequence. )

3, 6, 12, 24, 48, 96, 192 (multiply the first term by 2 to find the second term. This is called a geometric sequence.)

32, 16, 8, 4, 2, 1, 1/2 (multiply by 1/2.)

1, 1, 2, 3, 5, 8, 13, 21, 34, 55 (this is the Fibonacci sequence! Add the first and second term together to find the third term.)

Now let's take a closer look and try to identify some patterns that can be applied to any other sequence we might encounter in the future.
4, 7, 10, 13, 16, 19, 22

Note: If you are asked to find the 37th term and you plan on adding 3's, you must add 36 threes.How do we get 3n + 1 ?
Well since we found the y-intercept we can graph this.

By looking at this graph we can see that the slope is 3. So for future reference remember that our slope is the constant. So let's make an equation for this sequence.
tn= 3n+1
Where 3 is the slope and 1 is the y-intercept.

Everytime we have an arithmetic sequence it will be a linear function.
This is the graph of our sequence. Here is how you would make that on your calculator! Hit stat, edit. Under L1 enter your rank (1-7) under L2 enter your values (4, 7, 10, 13, 16, 19, 22) Now hit 2nd stat plot (top left corner of the calculator). Hit enter and make sure plot 1 is on, under type make sure the dots are selected. Then hit graph.

Next we covered some definitions:
Recursive: Repeats again and again.
Implicit Definition: This is the teenage way of saying hi, it's an implied hello. Only clear to people who know what they're looking for.
The Common Difference (d): The number that is repeatedly added to successive terms in an arithmetic sequence.
Common Ratio: The number that isrepeatedly multiplied to successive terms in a geometric sequence.

How to find the nth term in an arithmetic sequence.

tn= a + (n-1)d
Where tn is the nth term
a is the first term
n is the rank of the nth term in the sequence
d is the common difference

How to find the nth term in an geometric sequence.
tn= ar^(n-1)
Where tn is the nth term
a is the first term
n is the rank of the nth term in the sequence
r is the common ratio

Here is the next sequence we looked at, 11, 5, -1, -7...
We were asked to find the 51 term.
Look at the difference between the terms.
5-11= -6
-1-5= -6
Therefore we know our constant is -6. Remember we're not subtracting 6 from the first term to get the second term, we are adding -6! :D

Okay so how to find the 51 term. First let's make a formula.

tn= a+ (n-1)-d
Where n is the term. a is the first value and d is the difference. So we have..

t51= 11+ (51-1)(-6)
= -289

Next we looked at the sequence 3, 6, 12, 24, 48, 96, 192
Notice the difference is not constant, so this is not an arithmetic sequence.

To make an equation for this kind of sequence we use the formula, tn= ar^(n-1)
a= the first term r= ratio
The ratio for this sequence is 2 because 6/3=2 and 12/6=2 etc.
So the implicit definition is tn= 3(2)^(n-1)

Next question! 32, 16, 8, 4, 2, 1, 1/2
We multiply by 1/2 to get the next term so 1/2 is our ratio. Now we find the 10 term.
tn= ar^(n-1)
t10= 31(1/2)^10-1)
t10= 1/16

Remember!!
If differences in sequences are different it is NOT arithmetic.
If there are common ratios it is geometric.

And the last slide..

Um next scribe is Mary.

Homework is exercise 44 and 45.

Today's Slides: June 2

noreply@blogger.com (Darren Kuropatwa) — Tue, 2 Jun 2009 16:03:00 -0500

Here they are ...

Pre-Cal 40S June 2, 2009

View more Microsoft Word documents from dkuropatwa.

The Probability of a SCIBE is 100%

noreply@blogger.com (Johnl) — Mon, 1 Jun 2009 17:42:00 -0500

So, it seems that I'm the scribe for today (thanks Dion).

Today we learned about mutually exclusive events and non-mutual exclusive events. A mutual exclusive event is when "A" occurs, it is impossible for "B" to occur. Basically means you get one or the other, never possible to get them together. It's like the question that Mr K put on about Chad: 1/3 chance he's in the lounge or a 2/9 chance he's in the library. Since i don't think there are 2 Chads' and he doesn't have some sort of magical powers, I'm pretty sure he's either in the lounge, in the library or in neither places. So, that's mutually exclusive events. The diagram that would represent it would be:

This expresses the mutual exclusive events because either one occurs in circle "A" or circle "B".

Then we learned about non-mutual exclusive events. That basically means when "A" occurs there's a possibility that "B" will occur, in layman terms, if one thing happens the other thing COULD also happen. An example would be if you have a deck of cards and you want to draw either a diamond or an ace. There's one card that would fall into the non-mutually exclusive category: the ace of diamonds. So that part of it would be non-mutually exclusive.

This picture represents a non-mutual exclusive event because one can occur in "A", also in "B" or it could occur in the intersection "AB".

The formula to calculate the mutual exclusive events and non-mutual exclusive events are the same, which is:
So basally in a mutual exclusive event you would just add the probability of "A" and the probability of "B" and subtract zero because it's impossible for the two things to occur together. While in a non mutual exclusive event, you have to minus the probability of "AB" because you would account an event twice. Kind of confusing right? Here's an example: the card one: whats the probability of getting a ace or diamonds? Well you would have 4/52 because you have 4 aces in a deck and 52 cards in a deck. For diamonds you would have 13/52 because you have 13 diamonds and 52 cards, BUT you have accounts for the ace of diamonds TWICE. Once when you considered it an ace and once when you considered it a diamond, but they're the same card so you can't do that. That's why you subtract the probability of "AB, which would be 1 since you can only have 1 card which is both an ace and a diamond. So you end up with 16/52.

Uhh, well that's basically it and apparently we're wrapping this unit up tomorrow (if I remember correctly). Soo, yeah good luck with life and next scribe is ... lets' go with Pacifico.

Today's Slides: June 1

noreply@blogger.com (Darren Kuropatwa) — Mon, 1 Jun 2009 16:36:00 -0500

Here you go ...

Pre-Cal 40S June 1, 2009

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

noreply@blogger.com (~Pokemon Champion~) — Mon, 1 Jun 2009 11:14:00 -0500

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!!!!!!

noreply@blogger.com (Jessi) — Sun, 31 May 2009 23:56:00 -0500

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?

noreply@blogger.com (jayp) — Sun, 31 May 2009 23:07:00 -0500

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~

DEV sneak peak

noreply@blogger.com (d~i~o~n) — Sun, 31 May 2009 16:28:00 -0500

Hello!!! Here is a sneak peak into our DEV!! Enjoy! CLICK

BOB on Conics

noreply@blogger.com (miruiz) — Thu, 28 May 2009 22:52:00 -0500

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

noreply@blogger.com (Anthony) — Thu, 28 May 2009 22:50:00 -0500

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

noreply@blogger.com (D-S Skyline) — Thu, 28 May 2009 22:36:00 -0500

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

noreply@blogger.com (Anonymous) — Thu, 28 May 2009 21:14:00 -0500

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

noreply@blogger.com (Jennifer) — Thu, 28 May 2009 19:18:00 -0500

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