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.

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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!!

DEV sneak peak

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

Is it a parabola? is it an ellipse? no its.. BOB

Well this unit was pretty short and sweet and fairly simple. I'm going to get right into a review because I've got to work on DEV.

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A parabola is a locus of points a fixed distance from a fixed point (focus) and a line (directrix).

Vertical Parabola: (x-h)^2=4p(y-k)

Horizontal Parabola: (y-h)^2=4p(x-k)

The coordinates (h,k) are the vertex of the parabola. "p" is the distance from the vertex to the focus or the vertex to the directrix.  These distances are both equal. When 4p is greater than one, the parabola is wider and when it is less than one, the parabola is narrower.

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A circle is the locus of points equidistant from a fixed point, the center and the distance to any one point is called the radius.

Circle: (x-h)^2 + (y-k)^2= r^2

The coordinates (h,k) are the vertex of the circle. "r" is the radius of the circle.

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An ellipse is the locus of points which the sum of the distances to the foci is known.

Horizontal Ellipse: [(x-h)^2/a^2] + [(y-k)^2/b^2] = 1

Vertical Ellipse: [(y-h)^2/a^2] + [(x-k)^2/b^2] = 1

In an ellipse addition is used because the locus of points is the sum of the distances. The center of the ellipse is the coordinates (h,k) and is halfway between the two foci. The semi major axis is equal to "a" and the whole major axis is equal to "2a". The semi minor axis is equal to "b" and the whole minor axis is equal to "2b". The distance of either foci to the center is distance "c" and can be determined by c^2=a^2-b^2.

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A hyperbola is the locus of points which the difference of the distances to the foci is known

Horizontal Hyperbola: [(x-h)^2/a^2] - [(y-k)^2/b^2] = 1

Vertical Hyperbola: [(y-h)^2/a^2] - [(x-k)^2/b^2] = 1

The transverse axis is the distance between the vertices of the hyperbola. This is distance "2a". The distance from either vertex to the center is "a" and is the semi transverse axis. The conjugate axis is perpendicular to the transverse axis and it's distance is "2b". Half the distance, "b", is called the semi conjugate axis. The distance of the foci can be calculated c^2= a^2+b^2.

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Well that is all so I'm to work on DEV! I hope everyone did well on the test!

 

What are the chances this is a scribe post?

Hey everyone!! I'm back for round 3 of this exciting scribe postage!!!

We started off class today with Mr. K. teaching us how to do his snappy thing he always does. It starts with a snap, then another on your other hand and finally a clap/pop.

Here's how....

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Anyways, on to our actual math class!

Our first slide of the day depicts a scene of 3 coins being flipped. We need to determine the sample space which is not the amount of outcomes we can have but a list of those outcomes. The number of possibilities is the SIZE of the sample space. 

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We learned about the words "and" and "or". If, for example, you say you want this to happen AND this to happen AND this to happen, you multiply the probabilities of each of the events. If, for example, you say you want this or this or this to happen, then you add together the possibilities of those events.

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We then learned how to plug our outcomes into a chart. We drew a chart for the outcomes of 2 dice ( or die?) being rolled. There were 2 ways to show this on the chart. We either wrote the numerical values of both dice (die?)...

or we put the added value of the dice (die?)...

It just depends what we are looking for and what would be easier. For example, if we were trying to find the ways that we rolled doubles we would perhaps use the first chart but if we were looking for how many ways could you roll 10 then you would use the second chart. 

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The bus and train question on the next slide, can be a bit confusing at first but once you read it it becomes quite easy to understand. In a nutshell, you have all the times the bus can arrive at the station and you have all the times the train arrives at. A wise math teach once said, something along the lines of, math is not the crunching of numbers but the study of patterns, when you find a pattern in one question, you can apply to a ton of others. This is but one of those many times where we can find a pattern. We make a chart, quite similar to that of the two dice being rolled (OMG is that the pattern??) where along one side we have the times the bus arrives at and the top we have the times the train arrives. From here we can clearly see all of the ordered pairs of times that the two vehicles arrive allowing to solve the following questions very easily. I will not show the answers on my scribe post here tonight but just remember, think patterns!

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We then went over independent and dependent events. Independent events are those that have no effect on each other like flipping two coins, or after drawing a card from a deck, replacing that card before you draw the next card. Dependent events are those which do have an effect on following events such as not replacing a card into a deck after drawing it because in this situation the probability for the second event has changed due to a different amount of cards in the deck.

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That's about all, I just have a few small comments before I finish up:

·Good luck on the test tomorrow!! Study hard, do your BOB's and get that link!

·PATTERNS!!!!!!!!!!!!

·Mr. K, there will be several, I believe 5 or 6 of us, not here tomorrow for the test just as a reminder!

·Congratulations to Ann and Rebecca for finishing their DEV already!

·And lastly the next scribe will be......... John!

It's time once more!

Looks like it's time to BOB once more! This unit has been all about the very interesting topic of combinatorics! I found this unit to be very interesting and quite a lot easier than past units. I found the entire part about combinations and permutations quite simple and straight forward. Those 2 days we spent on Pascals Triangle (or as Zhu Shijie called it, the precious mirror of the four elements) totally blew my ind just as Mr. K had promised! XD This last new part about the expansion of binomials is a little tricky still but I'm pretty sure i know what I'm doing!! So time for a review because a refresher will do me good!

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When the order of a grouping of object matters with no repetition, it is called a permutation. When the order does not matter then it is called a combination.

The Fundamental Principle of Counting says that when you have N ways to do one thing and M ways to do another you have MxN ways to do both. I remember Mr. K said that this was a good way if you need a lot of suit combinations because if you have only 2 pairs of dress pants and 4 dress shirts you have 8 different suits!

We learned about factorials. A number, lets say n, factorial, symbolized by !, is written n!. This does not mean that that you shout out the letter n, it means (n)(n-1)(n-2)(n-3)......(3)(2)(1). Just incase you forgot 0!=1, that is important!!

We got a nifty little formula known as the pick formula. However Mr.k always reminds us never to rely on formulas because mathematics is the study of patterns and not crunching numbers. The pick formula if you must know is n!/(n-r)! where n is your total number of objects and r is how many ways they are to be arranged.

When dealing with non-distinguishable objects you need to divide n! by the factorial of the number of non-distinguishable objects. An example, if you did not understand that would be if you are trying to arrange the letters in book to form all possible 4 letter words. There are 4! ways to do it but because you cannot tell the 2 letter o's apart so you divide 4! by 2!.

When placing objects around a table or in a circle, the first object placed is the reference point and would not be taken into account. so for around the circular object your formula would be (n-1)!. If you have a bracelet however you need to divide your answer by 2 because you can turn your bracelet over and cut the number of possibilities in half. It is a special case. 

We also got another formula called the choose formula. It goes a little something like this. n!/(n-r)!r!. You use this when you arrange objects and order does not matter. You use this formula when the order does not matter with the objects you are arranging.

Well I believe thats all so pretest tomorrow? Or is it that we're doing another workshop to finish off the poker hands we started? Who knows!, and no, that isn't know factorial. I still may update my BOB post more so who knows. Final word of advice is that a logarithm is an exponent!! Good luck everyone!!

BOBlog

Good Morning bloggers! I could not sleep so what better time to do my blogging on blog post! :)

This unit was exponents and logarithms. It started of as a scary subject but as it went on I did not find it terribly difficult and understood things quite well and quickly.  Time for a review!

Alright, first thing to say is that a logarithm is an exponent!!!! I have not forgotten that yet and I don't plan on it!!!

The basic form an exponential equation is A^B=C where A is the base, B is the exponent and C is the power. Ex. 95^2=9025....... (It's over 9000!!!!! XD sorry for that)

The basic form for a logarithmic equation is logAC=B where A is the base, C is the power and B is the exponent. 

A logarithm is the inverse of the exponential function. For the exponential function you "feed it" exponents and it gives you powers where as a logarithmic function you "feed it" power and it gives you exponents. (I'm really tempted to make more over 9000 references XD)

Now there are several laws when working with logarithms you should know. There is the Product law, Quotient law, Power law, and Change of Base law.

Product law: loga(MN)=logaM+logaN 

Quotient law:loga(M/N)=logaM-logaN

Power law:loga(M^N)=NlogaM

COB law:logN(M)=loga(M)/loga(N)

There is also the mystic and all powerful number e!! Check out the history of it here!! Anywho... Using the number we we can make The exponential function and The logarithmic function, being f(x)=e^x and f(x)=ln(x) respectively. (ln is the same as loge)

Woah! Almost forgot but there is some things on exponential growth and decay as well! Now if I remember correctly we can use the Pert formula of A=Pe^rt where A is equal to the final amount, P is what you start with, e is e, r is the rate and t is time in years. With this little bad boy of an equation we can solve INTERESTing problems.....XD.... as well as we can calculate half lives with it. If all else fails you can whip out A=P(1+r/n)^tn where n is the number of times we compound the principle value per year. As a side note, if you take 1 dollar and compound interest on it at 100% for a year and you did it enough times, like more than once per second it would eventually plateau out at number e!

One more thing, I remember Mr K. going over those modeling questions there are 2 formulas for that!! A=AO(model)^t where A is the final amount of what ever at the end of the time, AO is the beginning amount of what ever at the start of the time, the model is how much it has either grown or decayed and t is the time that has passed. This is used when you have minimal information.

If you have a lot of info then you may use A=AO(m)^t/p where A is the final amount of what ever at the end of the time, AO is the beginning amount of what ever at the start of the time, m is the growth rate, p is the time required to multiply by m once and t is equal to time.

Well i think that about raps it up. I am off to sleep because I am exhausted.

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!

ByOB (Bring your own Bob)

Hey bloggers, it's the night before the test and I believe it's time to BOB!

Well this unit has actually been pretty fun overall. I was doing alright but a few nights ago I had an epiphany and like the little light bulb in my head turned on!

I have a lot of homework still to do tonight so I'm going to make this short and sweet.

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Always remember you Pythagorean identities and where you can substitute them! 

Start with the more complexer... (is that even a word?)... side so you have more things to work with.

Never cross the great wall of China!

Watch out for those double angled identities!!

Don't freak out on a question!! If you can't do it move on!!

Remember try try try!!! If something is not working try a different approach!!! There's more than one way to skin a cat, just don't actually skin a cat!

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Good luck everyone on the test!!! May you all be smarter than average bears tomorrow!!! God luck and sleep well!!!!

Better Late Than Never!

Hello bloggers!!!! It is my duty and privilege to help Mr. PJ with his post. Now I know that my post will be no where near as awesome as his but it'll be great! Now from his confusing instructions I believe that I am scribing for Friday, March 27 class. Now if only i could remember what we did.....

Tangent! It had something to do with tangent.... O right! There were several purple slides back to back and we taught ourselves all about double angel identities.

We first proved a double angle tangent identity. 

Now don't fear if you look at this and fear for your life, it's really not that difficult! We start off with this:

To get to the next line as we all know tangent is equal to sine over cosine so we simply replace tangent and using our knowledge of sin and cosine double angels we expand it all out to:

Now we're trying to get it in forms of tangents. So you look and see that you have some sines and think tangent is sine over cosine so maybe if i divide EVERYTHING by cosine something wonderful may happen. So your multiplying (because we don't divide) by 1 over cosine or secant!! This will result in:

So you all see how you get that?? You divide each of those by cosine alpha cosine beta. In the first one, both cosine betas reduce to one leaving you with tangent alpha. The second, the cosine alphas reduce to one leaving you with tangent beta. On the bottom, the cosine alpha cosine betas reduce to one. Leaving only the sines to be divided by cosine alpha cosine beta leaving you with tangent alpha tangent beta and zip bing bang.... QED!!!!

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To prove tangent alpha MINUS beta we use the clever idea of instead adding the number we subtract a negative number. This is in fact the same thing!!!!! So where ever there was tangent beta in this proof we simply switch it for a negative beta resulting in:

Then finally ending up with:

WARNING!! We can only do this because we have first proved the identity  of tangent alpha plus beta!!!!!

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The last thing we taught ourselves was the double angel identities of sin(2 theta) and cos(2 theta). Now the clever idea here is to see that 2 theta is the same as theta plus theta. We then use our previous knowledge of the double angle identities for sine and cosine to do the following:

Sine is straight forward and you get only one different identity. For cosine on the other hand there are 3 different ways to manipulate it. Once you get it into the form cosine squared minus sine squared, you can use a Pythagorean identity and substitute in either 1 minus sine squared or one minus cosine squared for cosine or sine respectively. If your unsure of which you need to use have no fear because no one knows which you will need! The only way you will know is by looking at the context of your question!

Well that was the class and I'm signing off i think we already know that P.C. (pokemon champion) is the scribe for todays class. so have fun everyone, happy blogging and don;t forget pre test tomorrow and test Thursday! Study up, do your BOB and find your delicious websites!!! May the force be with you all!

BOB time again

Well, this is an almost late BOB but had to do it and it's done! I've been studying all night and after reviewing everything I really don't see this unit being all that difficult.

Several points that stuck out in my mind are....

1) When graphing those reciprocal functions find the asymptotes (or where y = 0), then find the points at y= 1, -1 because those points are invariant and will be the same on the reciprocal graph, and then finally go to town with Dr. Suess and make your reciprocal graph smallering towards an asymptote if the normal graph is biggering to infinity and visa versa if the normal graph is smallering!

2) STRETCH BEFORE TRANSLATE!!!!!!!!!!!!!!!!!!

3) Watch out for those word problems!! They are not to difficult to understand, just read the problems carefully be smart about labeling your x and y axis because t may help you in your calculations later on.

4) As parameters go, A and D are simple enough A stretches the graph vertically by so many units and D moves the graph vertically.  B and C however are a bit trickier. BE CAREFUL!!! However B tells you to stretch always do 1/B because it lies to you!!!! C also lies to you!! Do not be fooled by its sign, make sure you shift the graph horizontally the right way!!

5) In a sine or cosine function remember B is not the period!!!! The period=2(Pi)/B!!! Also, parameter D becomes the new sinusoidal axis and parameter A is your amplitude.

That is all! Sleep well everyone!! A good night sleep is the quickest path to victory! May the force be with you all!!!

Pi Day Preperations

Hello everyone! Pi day is approaching fast and we need to get ready!! :D I'm going to make a list of everyones names and keep track of what everyone is bringing! Don't forget that Pi day will be on March 13 because actual Pi day is Saturday. Drop me line or talk to me in class or comment to let me know what your bringing!!

anaabanana-                        Pumpkin Pie

jayp-                                      Strawberry Pie

Rebecca-                               Chocolate Pie

WonderfullyExcelent-         Milk

yiN AN

renster-

Jessi-

Stephen D.-

Johnl-

trinhn92-

Pacifico-

ianayana-

yicong-

Mary-

kalekalekale!-                       Juice

Jonno-

SheldonCooper-

shumei-

Anthony-                                Lemon Meringue 

Jennifer-

~d~i~o~n~-                  Apple Pie

jeck-

Pokemon Champion-

Laikus the Ficus-

ale-

miruiz-

Mr. K-

aldrin-

So let me know A.S.A.P.!!!!!!

Test time draws close!

Time to look back on what I've learned this unit! Flash back! Cue little floating thought bubble!

First in this unit we went over the unit circle. I learned about this last year in math and it was a great reminder! I forgot most of it but once we started again  it all came back. Sin of 30, 45, 60 degrees are 1/2, route 2/2 and route 3/2 respectively and opposite is true for Cos. The same holds true all around the unit circle. Sin is the y axis and cos is the measurement of the x axis. Tan is equal to sin/cos and is undefined at 90 and 270 degrees because cos is equal to 0 and you cannot divide by zero (except Chuck Norris).

If i remember correctly, we then learned about radians which was totally new to me. It was very interesting! 2pi is the full circumference of the circle and pi is half the circumference or 180 degrees. And I'm rambling on a lot.. I'll cut it short.

Sinusoidal axis, DABC, movement of graphs, up, down, stretching, amplitude, wavelength and finally period. :D Well I'm tired so I will follow up on one of those rules which someone said earlier get a good night sleep. 

:O *edited out for content* I'm not here tomorrow... umm Mr. K did you get an email from Ms. Troung... and your not here this week so probably not.... so ya...... see you all Monday..... I'll do the test then, alright Mr. K? :)

Pre-Cal Class, February 3rd/09

Good evening fellow bloggers. It's Dion here! In class today we went over several things including proportions and we continued our discussion on why a circle has 360 degrees.

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I'll start with our circle discussion! We did not finish it, however, we left off at the reason no one uses a different way to count the degrees in a circle is because everyone is just so familiar with the way it is now and it is so widely known. Mr. K. tried dividing a circle by our new unit of measurement called "the Dion". Approximately 10 1/2 Dions made up a circle. There is nothing to say we cannot measure circles like this except no one but us knows about this new system. Unless everyone in the world knew there is no point. We also learned that 360 may have been chosen because of its beautiful divisibility. The number 360 is divisible by 24 numbers (including the number 24, coincidence, I think not!). We are going to continue this discussion in tomorrow's class.

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We also discussed proportions and the many ways to manipulate them in class today. For some reason the "math equation maker" is not working for me... lucky I don't need anything to complex. Basically, a proportion is:

"a" and "d" are called the extremes of the proportion while "b" and "c" are the means of the proportion. We can manipulate this in many ways as following:

Invert both sides:

Exchange the extremes:

Exchange the means:

Adding "a" and "c" as well as "b" and "d":

    Which simplifies to:

The products of the extremes s equal to that of the products of 

the means:

 

Which simplifies to:

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Two extra side notes!

1) When solving equations using Pi, due to the fact that Pi is infinite there is no exact value for Pi.  When solving an equation involving Pi to keep the answer exact leave  it in the form with Pi. For example :

3Pi instead of 9.4247856

Decimals are inaccurate and fractions are friends not fiends!!!

2)A complex fraction is  one fraction over another!!! Example being:

1/2 / 3/4

To solve, simply invert the denominator fraction and multiply them together!!!

1/2 * 4/3 = 4/6 = 2/3

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Well that is all for this evening. I'm sorry if my post is not terribly exciting or have any pictures. My next post should hopefully have some!! I'll see everyone in class tomorrow!! Also questions 11-20 are for homework which Mr. K. has already posted!!! One more thing!!! Tomorrows scribe shall be........Anthony!!!!!!!!!!!!!! WOOO!!!!! GO ANTHONY!!!!

"When we get to the end of the Greek alphabet, mathematics will end."