[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.

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~

DEV sneak peak

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

BOB!!!! (OBB, BBO, xD)

Wow time just flies doesn't it? We're already almost done another unit! And you know what that means......It's time to let the BOBs FLY!!!! So now I have decided to release my BOB and let it fly freely across the web. Here we go!

OK, so Combinatorics, it was fairly easy. I finally got to use that wonderful "!" key on my calculator and I got to write it down so many times. I thought that the most easy part about this was actually the "Pick" and "Choose" formulas and using the factorials ("!"). Yea, I guess you could call that three things, but they were all still pretty easy. Once I found out how and when to use each formula, I found them pretty easy to use and remember. The factorials were really helpful in keeping my work clean, short and most of all ELEGANT!! (lol.)

The hardest parts came when the "tricky" word problems arose from their long slumber in Mr.K's Smart Board lessons. I just really need to learn to really carefully read the questions and think about the scenarios. I also need to just relax and keep my cool. If I lose it, then I'll over think and miss little important details. To be honest, it was just today that it dawned on me that this unit could actually be very confusing and difficult. Then again, it could just be me. I do feel that after today (after struggling), I think I feel more confident about these kinds of questions.

The test? Yea I think I'll do well. Actually (and I hope I don't jinx anything by saying this), I feel like I'm going to blow this test out of the water and make it beautifully arch before going back into the water. I'll let you interpret what I just said. Haha, let your imaginations go wild!

Well now's about the time that I give the advice right? Let's start!

1. Permutations are when the order matters (medal standings, picking president/vice president/secretary of a committee, PERMUTATION (not combination) locks). If it's a permutation, then use the "pick" formula: nPr=(n!)/(n-r)!
   n=number of things to pick from
   r=number of "spots" to fill
   
2. Combinations are when the order doesn't matter (picking members w/o ranks, giving away identical ribbons/medals (like for participation), picking lottery numbers). If it's a combination, then you can use the "choose" formula: nCr=(n!)/[(n-r)!r!]
   n=number of things to choose from
   r=number of "spots" to fill
   
3. How can you remember what formula to use with what? Permutations get the Pick formula (PP) and Combinations get the "Choose" formula (CC).
4. A number followed by "!" doesn't mean you yell the number out loud. It means (n)(n-1)(n-2)............1.
5. 0! is equal to 1.
6. If there are N ways of doing something and M ways of doing another thing, there are NM ways of doing both.
7. To do non-distinguishable objects, use the formula (n!)/(k1!)(k2!)(k3!)..........
   n=number of objects to choose from
   k1, k2, k3.....=number of each non-distinguishable objects
   ex) In "access" there are 2 C's and 2 S's and 6 letters in total so it's (6!)/[(2!)(2!)]
8. Circles! Basically it's (n-1)! because one person is used as a reference point and the others are arranged according to the first "thing" placed. (I think.)
9. Bracelets and Necklaces are a special circle case because you can flip them over so instead of (n-1)! it's (n-1)!/2.
10. Label your work!
11. Remember the patterns for binomial expansions and possibly how to construct Pascal's Triangle and the patterns it contains.
12. PRACTICE, PRACTICE, PRACTICE!

Well I guess that's all I can say for now? Don't forget to do your delicious links, the poker homework and to CORRECTLY LABEL YOUR POSTS IF YOU SCRIBED!!! Good luck on the test everyone! I hope we all do well.

jayp, signing off!

~jayp~

An Exponentially Exhausted BOB!

LOL. Yes this BOB maker is exponentially exhausted. The number of activities I had exponentially grew and my energy exponentially decayed. xD Anywho, here's my BOB post.

This unit, Exponents and Logarithms, started off very easy for me. But of course, back then, we were just starting off reviewing some of the basics such as the "anatomy of a power" and rewriting numbers as powers and vice versa. We were also doing some simple equation solving with them which also came quite easy to me.

When logarithms were introduced, I'll have to admit, I was pretty worried because it seemed very confusing but it was actually straight forward. Although I almost never forgot, it took me a few days to grasp the concept that "A Logarithm is an Exponent!" [and you're gonna forget that! (the wise, wise words of Mr.K) :D]. Once I did get that concept, I felt a little bit more relieved about the logarithm part of the unit. The equation solving also came relatively easy to me.

I would have to say the hardest part of the unit was when the compound interest stuff showed up. I guess it was because at first, I had a bit of a hard time understanding it, but it's sort of clear now. However, when it got combined with the concept of "e" that's where I got lost. Me missing a week of school didn't help that too much but luckily us university goers worked together to try to piece together information from the scribe posts and from the slide shows (BTW thanks for the scribe posts guys! It really helped.). However there were some things that still needed to be cleared up(such as the word problem stuff that was covered while we were away) and that was cleared up through our visit to Mr.K on Friday (Thanks Mr.K!).

Well now that I've covered what I thought of the unit, what was hard and what was easy, I guess it's advice time! Well there's really no sense in giving advice now when the majority of the class has already written the test but I'll mention the important parts anyways in hopes that this will miraculously stick to my brain.

1. A LOGARITHM is an EXPONENT.
2. a^b=c can be rewritten as loga(c)=b to find the exponent
3. Product law (log MN= log M + log N)
   Quotient Law (log M/N= log M-logN)
   Power law (log M^N=Nlog (M))
   and the Change of Base law (log a(b)= logc (b)/logc (a) )
4. Remember the exponential modelling equations (like A=Pe^(rt))
5. "ln" is the same as log e

What else can I say? Eat, sleep, study, yenno the normal test routine.

Hmm.....I know I'm missing something.......ahhh, yes.

I think that I will do well on the test. I'm not too confident however because of the week of class that I missed. Do I regret doing that? Well, yes because I feel like I've missed a lot in my classes (especially math at the moment) but at the same time no because then I would've missed out on such an amazing experience with some amazing people! Hopefully I do well on the test and I don't forget anything (please let there be a formula sheet -_-", if there isn't that's fine too).

Good luck to my fellow classmates who are going to take the test and to those who have, it'll be nice to be back in class again.

~jayp~

P.S. A LOGARITHM IS AN EXPONENT!!!! lol.

D.E.V. Timeline for...well.........us!

Heeeey there all you matheees! Here's is our ever so short and ever so vague (well not really) TIMELINE for our D.E.V. (which stands for DEVELOPING EXPERT VOICES!). Haaah as you can see I am veeery excited to do this project and so are my two amigos, Dion and Mary! (Okay well one amigo and one amiga.) So anyways, I'll stop myself before I ramble on.

This timeline is brought to you by me (jayp) on behalf of my group members (Dion and Mary). It's also brought to you by the letters D, E and V and the number 6! Here it is!

Apr.24-30: Figure out/Finalize our EPIC storyline.

Apr.30-May 13: Figure out/Answer/Finalize all 6 questions and add them into the storyline.**

May 14-16: Make a video filming plan so we aren't filming around aimlessly.

May 17-June 2: Film and edit video so that it looks beee-yoou-tee-full!

June 3-4: Make sure everything is "movie" perfect and upload.

June 5: ABSOLUTE DAY OF DOOM!

**We basically gave ourselves 2 days/question (2 days*6 questions=12 days) plus one day just in case. We didn't give ourselves days for each question because we know that each question may take a little more time than others so we just thought we'd give ourselves around two days for each question. If we have extra time, then we'll use that for the tougher question(s).

So there it is! In black, Arial font, size "normal" open for all of you guys to see! Good luck with all of your project guys! And also good luck on our next test!

BOB!!!!! Who Are You?

Okay so another unit done, another test to take. As I slowly wait for my videos to upload so that I can finally cross my name off the scribe list, I figured that I might as well do this now.

Am I worried about this test? Not really, but there is that little doubt. This is just based upon how I'm doing in class. I tend to miss a couple "clever ideas" but that might just be because I'm over thinking the question. Who knows? The only thing I can do now is just keep practicing!

The easiest part of this unit would have to be converting everything in terms of sine and cosine (it's the stuff we were doing at the beginning of the unit; I wasn't sure how else to describe it). This was mainly because we only had a couple "clever ideas" to recognize and deal with. As we learned more "clever ideas" the unit started to get harder and harder because I started to over think things. This caused me to miss some certain "clever ideas" because I was thinking of other "clever ideas", but I guess that's something I just have to continue to work on.

The hardest part of this unit? It would definitely have to be all of the different identities. There are just so many different possibilities for which identity to use, it's just a matter of figuring out what the right one to use is. Like I said, I do over-think things so on the test I feel that this may be my weak point during the test. However, I promise I will try my best!

I honestly think that after seeing my mark today in class I can still step things up and work even harder to get the mark I want in this class (yeah, so I'm a perfectionist, sue me...). Hopefully this test will give me the chance to raise my mark.

Anyways, here is where I would usually add some helpful stuff to help you all prepare for the test. Most of the stuff is the same, and right now I don't feel like repeating myself so I'll put everything in a shorter form.

GET LOTS OF SLEEP!
EAT RIGHT!
STUDY STUDY STUDY!
ASK QUESTIONS!
TAKE YOUR TIME!

And of course, especially for this unit, use the following guidelines (which have already been outlined by Ms. Annabanana (mMmmmMMmmMmMm bananas xD):

1. Work with the more complicated side first.
2. Rewrite both sides in terms of sine and cosine.
3. Use Pythagorean Identities to make appropriate substitutions.
4. Simplify complex fractions and rewrite fractions so that they have a common denominator.
5. Use factoring (difference of squares!!)

Remember that these are only guidelines. You don't have to use them all but they will be helpful.

Good luck on the test guys! I will be rooting for us! Happy Mathing!

~jayp~

P.S. Here's a link to my youtube account. I have semi-dedicated it to our class blog so there will be videos about math that may help us (both made by me and made by others). If you have a video you think I should "favorite" on my channel, feel free to leave me a comment/video response/msg on MSN/wall post on FB/any other means you can think of.

Double Post?!?!

Hey folks! Ok so this will be the last unit-type post before the test on Wednesday (I think?) and it will be a DOUBLE POST!!!! I'll at least post the important non-math lesson related things here right now as I slowly work on the actual material stuff.

First off, we are now on CYCLE 2 of the scribe list. All the names have been "uncrossed" off the list.

Second, here is the schedule for when we get back to school.

MONDAY, APRIL 6 - WORKSHOP DAY (TO REVIEW AND SUCH)
TUESDAY, APRIL 7 - PRE-TEST FOR IDENTITIES
WEDNESDAY, APRIL 8 - ACTUAL TEST FOR IDENTITIES (Don't forget to do your BOB's and look for "delicious links"!)

LOL! I'm pretty sure that's the schedule but I'm not too sure.

The scribe post is currently done:

-a review of the last two days before Spring Break (done. Day 1:scroll down Day 2: click here!)
-links that can help you study/review for this unit (done)
-extra reminders and such (done)
-a whole mess of videos, most likely (done:4/4)

Lastly, if there's anyone out there that wants to help me with this monstrous task, please comment. Don't worry, if you help, this will count towards your scribe posts and you will be crossed off the scribe list for Cycle 2. Thanks to Dion!

Hopefully this will be the last double scribe post. I hope that we can keep this blog up to date and that we continue to make this blog a rich textbook for people visiting our blog!

~jayp~


P.S. The next scribe is the ~Pokemon Champion~! LOL it's only because I was playing Pokemon earlier. xD Have Fun!
**************************************************************************************

Okay so here is the actual post.

Hello guys!

I hope you guys enjoyed this "wonderful" Spring Break! xD

The first thing that happened on this Thursday class was a quiz on what we had previously learned on Trigonometric Identities. In case you missed it, or you want to refresh your memory, here is the quiz!


Youtube Version


And here are the answers:


Youtube Version

Haah ok. Now the hard part. For the rest of the class, we discussed where the sum and difference identities came from.

If you can recall, the identities are:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
sin(a -b) = sin(a)cos(b) - cos(a)sin(b)
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

First, we'll start off by proving cos(a-b)=cos(a)cos(b)+sin(a)sin(b).

Recall from the previous class when we figured out that:

*In my written explanations, I will be using "a" to represent "alpha" and "b" to represent "beta".

Just to refresh your memories, when we were finding the coordinates of P and Q, we remembered that the "x" value is the same as the cosine value and the "y" value is the same as the sine value.
Therefore:
P (cos b, sin b)
Q (cos a, sin a)

When we were finding the coordinates of R, we remembered that when you rotate a point (x,y) 90^o counterclockwise, the new coordinates are (-y,x).

Therefore, if point R is point P rotated 90^o counterclockwise, that means that point R must be (-sin b, cos b).

After we "rigidly rotated" (rotate, but didn't change the actual shape) angle ROP so that P lies on the x-axis, we found out the coordinates of R¹, P¹ and Q¹.

Since P¹ lies on the x-axis, this means that the coordinates of P¹ are (1,0).

Since R¹ lies on the y-axis, this means that the coordinates of R¹ are (0,1).

Doing what we did earlier to find the coordinates of P and Q, the coordinates of Q¹ are (cos(a-b), sin(a-b)).

Now, since we rigidly rotated angle ROP, this means that the distance between P and Q and the distance between P¹ and Q¹ are equal. Because, the distances are equal, we can plug the "x" values and the "y" values into the distance formula and say that:
distance PQ=distance P¹Q¹

Here is a video to show the "grunt work".


Youtube Version

Now let's prove sin(a-b)=sin(a)cos(b) - cos(a)sin(b).

To do this, we use the same method that we used for cos(a-b), but instead of using the points P, Q, P¹ and Q¹, we will use the points R, Q, R¹ and Q¹.

Here is the "grunt work" for proving the sine difference identity.


Youtube Version

Now, to prove the sum identities. Both sum identities can be proven using the same clever idea. This clever idea is simply seeing that a+b=a-(-b). It also involves using what we know about even and odd functions.

For the sine sum identity, if we replace sin(a+b) with sin(a-(-b)), this means that whenever we see a "b" in the difference equation, we replace it with a "-b". This would change the equation into:
sin(a-(-b))=sin(a)cos(-b) - cos(a)sin(-b)

Now if you recall that sine and tangent are odd functions and that cosine is an even function, you will also recall that:
sin(-x)=-sin(x)
tan(-x)=-tan(x)
cos(x)=cos(-x)

Using that knowledge, we can even further rewrite this equation as:
sin(a+b)=sin(a)cos(b) - cos(a)(-sin(b))

which simplifies to:
sin(a+b)=sin(a)cos(b) + cos(a)sin(b)
* notice the sign change

For the cosine sum identity, we do the exact same thing.
cos(a-b)=cos(a)cos(b) + sin(a)sin(b)

becomes

cos(a-(-b))=cos(a)cos(-b) + sin(a)sin(-b)

Then by using our knowledge of even and odd functions, that equation turns into:
cos(a+b)=cos(a)cos(b) + sin(a)(-sin(b))

which will simplify to:
cos(a+b)=cos(a)cos(b) - sin(a)sin(b)

Tada! We have just proven the four sum and difference identities!
This is basically what we did this whole class. Knowing some of this may be handy in the future and it's always important for us to understand where the formulas we use in math originate from. I think that this was the whole point of this exercise. Remember, if you ever forget these sum/difference identites.................DO THE SINE DANCE!!!!!!!! LOL. It's the dance craze that's sweeping the......classroom? Haah.

Also, here are some links to help you refresh your memory about this unit or to help you study for the test:
* You need a .pdf reader to view these links.
Identities 1:Product/Quotient
Identities 2: Sum/Difference
Identities Practice Test (a few questions do not deal with Identities)
Identities Practice Test Answers

Well anyways, I'd just like to say a few words before I sign off. I'm terribly sorry for this really late post. I know I had a full week to work on this but I guess my other Spring Break plans just got in the way. Also, I had to do a lot of planning for an English project that is worth 35% of our course mark (without the exam). Please forgive me, I will do my best to have the two videos I'm missing in this post up and running tomorrow.

Peace out, see you guys tomorrow and always do your best!
~jayp~

Trigonometric Identities......BEGIN!!!

Hey guys! It's me, jayp (AKA PJ)! Today we started what seems to be a very exciting unit in our Pre-Cal Class and we also got a little side lesson on the Greek Alphabet!

So starting with the main part of this scribe post, the NEW UNIT! It gives me great honor to be able to introduce to you all, TRIGONOMETRIC IDENTITIES!!!!!
Okay so just in case you didn't get the picture today in class, or you don't get it right now, this picture explains what Trigonometric Identities is all about! So the girl in the picture has many different hairstyles on so she has many different looks or identities, but they are all the same person!


What was shortly explained above is pretty much what this unit is all about! In this unit, we look at the different identities or "looks" trigonometric functions have. This means we aren't exactly solving equations. We are manipulating expressions. As Mr.K put it, we are "algebraically massaging" expressions.


Have I lost you? No worries. Here's what I mean.


In class, we looked at the number 3. How many ways can you write the number three?

Well there's 3.0, ,, and so on. These all look different, but they all mean the same thing. They all mean "3".


Now, because the unit is called "Trigonometric Identities", we will be dealing mainly with the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent). Rather than just plain old numbers, like "3" (Sorry "3").


In class we first talked about how all of the trigonometric functions are made up of two main functions: sine and cosine.

This means,









Now that we had that in mind, we went on to answer some questions from the Smart Board. All of the questions asked us to take an expression which contained multiple trigonometric functions and rewrite them using only the sine and cosine functions and the number "1".
Before you start asking questions about this, yes I made these videos and yes that's me writing things down.



Here is a YouTube version if you find this too small!

After these questions, we looked at the Pythagorean Identities! Now this is a little complicated for me to explain here in words (mostly because my head is POUNDING at the moment) so I decided to make a little video!


YouTube Version

For some reason the end got cut off. It supposed to say "It can be further reduced to 1."

Now if you didn't get that, feel free to leave me a comment and I, or one of my fellow classmates will be more than happy to answer your question!


Earlier, I talked about how the Trigonometric Identities unit is all about manipulation. It is also about proving things. I'm in a video-making mood so I made a video for this too!


YouTube Version

Gotta remember that "Great Wall"!
NOTE: Because you can't put equal signs on the "Great Wall" you cannot solve this as if it were an equation. You must manipulate one side using what you know about identities in order to solve it. (Thanks Anthony for catching that!)
BTW, Q.E.D. stands for Quod Erat Demonstratum which means "which was to be demonstrated".Read more here.


We're almost at the end of today! Next we talked about how we could get other identities from what we have just learned! Cue the VIDEO!!!!


YouTube Version
LOL! The music ends early. Darn Movie Maker and laggy computers!!! xD

Tada! This is basically everything we have learned today about Trigonometric Identities! Oh right, about that little mini lesson on the Greek Alphabet. During this unit, many Greek letters will show up. Don't be alarmed with how they look, treat them just like "x" or "theta".

Any who, I was going to make a video about Greek Letters as well but it's getting really late. If you are really interested, wikipedia it or look on the sidebar in the "Equation Maker" thing. The Greek Letters are found under "Characters" and if you hover over them, it tells you their names!


LOL! So I hope you enjoyed my little scribe post with all of the videos. Leave me a comment if they don't work and I promise I will fix them right away!
And now I have the honor of announcing the next scribe! The next scribe is Jessi? Yay Jessi!

P.S. Thanks to jamendo.com for the music! All the music there has a creative commons license so you can use it for free! And the music there is actually pretty good.

Reflection? Or BOB? For Transformations!

Wow! It's already time for our second test! Time is just flying by so quickly. I figured I should do this now before I forget or get bombarded with work tomorrow. Before I continue on with my reflection I would just like to give a few reminders to my fellow classmates.

Because Pi Day will be on a Saturday this year, don't forget that we are celebrating Pi Approximation Day on Friday. Bring your pies as well as your appetites!

Please also don't forget that when you scribe, you have to tag your work and tag it correctly! I know it seems like a little thing, but by putting in the correct tags we are making it easier for our fellow classmates, as well as the many math adventurers around the rest of the world that visit our blog (Hi, People of the World! :D), to find the things that they want to find, study or even learn. When you make a tag on Blogger, separate the tags using a comma (,) instead of a space ( ) like you do on delicious.com. If you use a space instead of a comma, you will end up with one long tag and it will be counted as incorrect.

Okay, back to the main point of this post. The Translations unit is quickly coming to an end and we have learned so much in the past few days. The easiest thing in this unit for me was graphing absolute value equations. I'm sure it was pretty easy for many of you too. I felt that it was a great way to end a kind of difficult and confusing unit. Another thing that I found easy was doing the stretches and shifts of the various functions and graphing them or finding the equation. This was mostly because we had just finished quite a bit of it during the last part of the Circular Functions unit and it was still fresh in my mind (like all of the parameter stuff).

One thing that I found a little bit difficult was everything about reciprocal functions.Graphing them, at first, seemed very confusing. I was trying to understand it the first time Mr.K said it but as soon as words like "Invariant Points" and "Asymptotes" entered through my ears my mind just went "Huh?" And then when was drawing the graphs I got even more lost because I had forgotten everything he had said prior to that. However, after doing a couple more questions like that and looking through the slides Mr.K posted on the blog, I find them a lot easier to deal with.

Another thing I found hard was the word problem we did in class today. I was trying to think of Mr.K's way of solving the problem and what I would've done to solve the problem at the same time. My way had some errors in it but I corrected them as we went along. I think I just got really mixed up with what he was saying and what I was thinking and that caused me to not pay enough attention what was being done on the Smart Board. I'll work my way through it and I'll figure it out so I think I'll be OK.

As for the actual test? I'm pretty confident in myself. I think that I'll do really well on this test. The only thing that might mess me up on the test is the drawing part. I think I'll make little mistakes here and there (like extending the graphs too much or forgetting to put arrows) but that just means that I have to be extra careful with my answers.

So yea, I guess I'll just say a few things before I go.

• Read the questions and answer them to the best of your abilities!
• Remember how each parameter affects the functions by stretching/reflecting/shifting it.
• Remember to graph the original function first (if you have to) when doing reciprocal graphs and find the invariant points (where y= 1 and -1).
• Draw in asymptotes using a dotted line, not a solid line. You can also put in, somewhere around your graph, y≠(insert numbers here) for horizontal asymptotes and x≠(insert numbers here) for vertical asymptotes.
• An inverse function (f^-1(x)) is NOT EQUAL to 1/f(x).
• Remember how to determine and graph even and odd functions.
  
• Get lots of sleep and be prepared!

I'll stop here.

So yes, good luck fellow classmates on the test! We can do this! We are smarter than the average bear! Good night everyone! See you in math class!

-jayp



P.S. Join the Yearbook Fundraising event! This time around it is a Treasure Hunt! For full details, ask me (PJ), Ingrid or Mary in class or, if you have a Facebook account, click here!

Time to Reflect on the Past........

Hello to all you Pre-Calculus enthusiasts and to those visiting our blog! Good evening (or morning/afternoon depending on where you are)! I figured that I should probably do my reflection now before I forget about it later so here goes!

I'd like to start off by saying THE SCRIBE LIST IS UP! There are a few things you should know. In order to be officially crossed off the list your post must be fully completed and correctly tagged! This means that your name cannot be crossed if you say that you will when you get home. It has to actually be there and complete. Also make sure that when you tag it you put (THE UNIT TITLE), (YOUR NAME), SCRIBE. That way you get credit for doing your scribe post. (:

As far as circular functions go in our class, I feel that everything was pretty straight forward. I like the way that Mr. K lets us see where all of these numbers and formulas come from like π, sine, cosine, tangent, cotangent, etc. I think it's pretty cool how we get a math lesson as well as a history lesson! I also think Mr. K has a really great point. Instead of memorizing everything (like the sine value of 5π/6), remember the relationships like where they are in the unit circle and the root 1, root 2, root 3 pattern in the numerators in both sine and cosine. I know that's what helped me get through this unit! (:

The hardest thing during this unit was probably the grade 11 review questions. Now I know what you're all thinking. "Really? Are you serious PJ?" Why yes folks, I am dead serious. I think it's just the fact that I haven't done any streneous Pre-Calculus work in a year and that my mind is just slowly bringing everything back from grade 11 as time goes on. Well I know chemistry and physics involved some math but it wasn't like hardcore Pre-Calculus-type math. But don't worry, I'll remember eveything (eventually!) !.

So yes, I guess now is the part I should give you all advice on the test.

Don't forget any of the basic stuff like circumfrence (2πr) and area of a circle (πr^2). Haah I'm sorry if it sounds like I'm contradicting myself with the whole formula stuff and yea but sometimes there are things you should just know.

Keep the image of the unit circle in your head. Remember the relationships of sine, cosine, tangent, secant, cosecant, and cotangent. Remember SOHCAHTOA and CHOSHACAO (LOL Matthew!). That or you can remember the whole C+S pairs, like Cosine and Secant.

If a denominator has 0 it's undefined. If you have to find the square root number there are two answers (just as SheldonCooper said): one negative and one positive. If you have to solve for more than one x value and one is undefined (like sin x= 0.7384 and 2 but sin (x) can't equal 2 because it's maximum is 1), make sure that you explicitly state that.

Remember that when you have to find angles that there is usually more than one answer like for:
sin (x) = 1/2
x = π/6 and 5π/6

Of course you have to keep in mind the intervals. In my above example, my interval was [0, 2π]. If you have to solve for "all real numbers" use 'k' in your answer. For example:
Solve for 'x'. 'x' is an element of the real number set.
tan(x) = 1
x=π/4 + kπ where 'k' is an element of the integer number set

Don't panic! Stay relaxed and don't fret if you can't get the answer right away. Skip it and move on. It'll come to you eventually.

Take your time! Don't rush! Double check your answers and make sure you did everything right. There's no harm in checking your work. In the end it'll probably be beneficial for you!

Well I think this post is getting a little bit too long. I won't actually be in the room doing the test with all of my wonderful classmates as I, along with Dion and Rebecca will be at S.E.T. that entire day. We still wish you all the best of luck on the test! We're with you guys in spirit! xD

The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post can be quickly accessed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

IMPORTANT: Make sure you label all your Scribe Posts properly (Your Name, Unit Title, Scribe) or they will not be counted.

Cycle 3Probably the last cycle!

annabanana jayp Rebecca WonderfullyExcelent yíＮＡЙ renster Jessi ConstantEcho Johnl D-S Skyline

trinhn92 Pacifico ianayana Mary kalekalekale! Jonno AldrinS emmelion Mr Lollipop

Anthony Jennifer d~i~o~n jeck ~Pokemon Champion~ Laikus the Ficus ale miruiz aldrin

3.23