BOB

Last unit of the course, probably the fastest too. This basically means the course is over and all that's left is......DUN DUN DAA THE FINAL EXAM!! But you guys don't have to worry, you're all so very bright and smart. I predict that you all will do well on the exam. As for this unit, fairly easy and simple to comprehend. Main idea is to remember the formulas, terms and concepts. If you got all that, the rest is common sense and knowing how to interpret the problems. However do not under estimate the fact that nothing comes easy, so don't expect an easy test to end off what has been an awesome class to be apart of. Good luck to everyone.

BOB

Another unit done and I'm starting to see a trend. As we start the unit, the concepts and questions seem to be quite easy to grasp for everyone, especially with this Probability unit. However, once the pre-test approaches most of us (from the classes reaction, correct me if I'm wrong) seem to be surprised at the complexity of some of the questions. Whatever it may be, the only way we can possibly improve upon that is study, study and study. Exams are coming very soon and we only have one unit left. Let's finish this year off strong. Good luck on the test tomorrow everyone.

BOB

Well this unit went by pretty fast huh? So fast that I almost forgot to do this....again =S It was a pretty simple and quick unit. Mainly involved with graphing and equations I found every concept pretty easy to grasp. On the quiz and pre-test I did fairly well. I think the test won't be too complicated but I could be wrong, so I'm going to look over a bit more of the unit until the test comes later in the day. Good luck to everyone on their test!

Conics Scribe Post

MORNING CLASS:

We did two questions on ellipses to start things off for the class, here they are:
Now the question didn't ask for a sketch but Mr.K told us to make one anyways. However without making the sketch this question would be real tough to answer anyways so the sketch helps =D. You'll find in a lot of these questions you'll need to make a sketch even though the question itself doesn't state that.

For this question the sketch allows us to find the values necessary to make an equation of the ellipse. Knowing the sum of the focal radii is 6 units we can find the value of a (semi-major axis) because a is half the value of the sum we get that a is 3 units. Now that we've found the value of a we now have to find the value of b (semi-minor axis) because that's apart of the equation of an ellipse. We first must find the value of c in order to apply the Pythagorean Property c² = a² - b² which will allow us to find the value of b. To find c we just turn to the foci provided by the question. The distance between them is 4 units, the value of c is half that which gives us 2 units. Now we apply the Property, 2² = 3² - b², and get b² = 5 so b = √5. Having those values we get the equation written on the slide.

I won't explain the solution to this question, it seems pretty straight forward already from the slide. However there were a few important things that sprung from this question that I will talk about. It was very interesting how we just dove into finding the radius and centre of this circle. But how do we know it's a circle? Why not an ellipse? So here's some important things to remember when doing questions that don't state what kind of Conic it is:

- equations of circles always have the same coefficient value on the terms x² and y²
- equations of ellipses have different coefficient values on the terms x² and y²
- equations of horizontal parabolas have a y² term and a x term
- equations of vertical parabolas have a x² term and a y term

(VERY IMPORTANT REMEMBER!!!)
For the next part of class Mr. K just went over in detail the Focal Radii Property and Pythagorean Property of the ellipse (check slides 3 and 4 for what is potentially going to be dictionary notes!)

Then we picked up our sheets with the big circle on it (got from the beginning of class) and drew a point just outside of the circumference preferable 2 cm. Then drew 25-30 points on the circumference having making the points closest to the outer point jumbled up together. Then just like the other day when we folded the paper to make an ellipse we did the same kind of folding method to make......A HYPERBOLA! =D Then DING DING! Class ends.

AFTERNOON CLASS:

Having done the folding in the morning class, we sketched out the hyperbola we just created by making the folds. Then we drew in the foci points and discovered a few things....- line PF1-line PF2 = line QF1-line QF2 = line RF1-line RF2, therefore, any point drawn on the hyperbola when connected to the two foci produces two lines with a constant distance between them
- labeled A1 and A2 on the slide are the vertices, the distance between the two, line A1A2 is known as the Transverse Axis
- folding the paper so that the foci are on top of each other we see that when we open it up we get a line that's directly perpendicular to the transverse axis, the end points for this line are labeled B1 and B2, this line is called the Conjugate Axis
- half the transverse axis is the semi-transverse axis and that's labeled a
- half the conjugate axis is the semi-conjugate axis and that's labeled b
- drawing a line from the centre of the hyperbola to F1 we find that the value of this line is the same as the value of a line connecting B1 to A1, therefore a² + b² = c²
- drawing dotted lines parallel to the conjugate axis going across A1 and A2, then drawing dotted lines parallel to the transverse axis going across B1 and B2 we see a dotted box
- using the dotted box we draw a dotted diagonal line from the top left corner to the bottom right corner anda dotted diagonal line from the top right corner to the bottom left corner
- these diagonal dotted lines represent the asymtotes of the hyperbola
- slides 5 and 6 show the equations of horizontal and vertical hyperbolas

This was the last thing we did in class, a question on hyperbolas. We never actually got to finish the question, Mr. K finished it off for us. It's pretty much self-explanitory. What's important however is, posibility of a PRE-TEST on FRIDAY and TEST on MONDAY!

oh and next scribe will be........VINCENT!

Questions, Questions, and More Questions!

FIRST CLASS:

We did a quiz and a couple of questions here's the answers in a more detailed explanation:

For this question, you can think of log 2000 as log (2 x 1000). Then knowing that logs are exponents, we know that when exponents are being multiplied they're really being added together, therefore we get log 2 + log 1000. The value of log 2 is already given as 0.301 and the value of log 1000 is 3 because 10^3 is 1000. Add the two numbers together and you get 3.301, the closest answer to this value would be B).

In log 8 we can change the 8 to 2^3 because that's equivalent to 8. Then since 3 is an exponent we can take it out and put it in front of log so it looks like 3log 2. We know the value of log 2 which is 0.301. Multiply it by 3 and you get 0.903. Closest answer to that is C).

There's actually two ways you can come about to answer this question. First way, you know that log 2 = 0.301. With that you can take the reciprocal and punch it into your calculator to give you an answer around 3. Then there's the much easier way of just finding values for x in 2^x that would give you an answer closest to log2 (1o), which would be 3, that answer is C).

The first one basically explains itself so I'll move onto the next one. This is basically just like the first one however there's an extra step to finding the answers. You must first factor the 4 as an exponent which gives you 2². since the exponent 2 and the log are both exponents you can place the 2 as an exponent of 3. This allows the two bases of 2 cancel out along with the log which leaves you with 3² which gives you 9 as an answer.

To find the answer to this question you change both logarithms into exponents which gives you 3^k = 10 and 9^x = 10. Then in order to solve for x you must make the bases of each exponent the same, we do this by changing 9 to 3² which is the exponential equivalent to 9. Now since we have the same bases all we need to do is solve for the exponential part of the power which gives us x = k/2. That would be answer C).

SECOND CLASS:

We had a Pre-test on Logs & Exponents, here's the answers in more detailed explanations:

.........ok nevermind, the blog is refusing to let me upload my pictures onto this post therefore I can't provide you with questions and detailed explanations, this will have to wait even longer now, I'm sorry but this WOULD'VE been done tonight if it weren't for this DAMN glitch, my apologies again.

SCRIBE FOR TOMORROW IS JENG!

BOB

This semester has surprisingly gone extremely fast and here we are done another unit. This one by far is one of the most annoying units I've ever had to learn haha. It started off fairly easy for me and as the unit progressed things became more complicated. Like Sandy I missed a day of work but it didn't seem like much and thankfully there's the blog to keep me up to date! I hope everyone studies hard and good luck on the test! REMEMBER LOGARITHMS ARE EXPONENTS!!!

BOB

Wow I totally forgot about this =S I hope Mr. K still accepts this as a BOB even though I'm doing it the morning of the test =S Well anyways here we go. This last unit wasn't too tough, more or less it was exactly quite easy. The only problem basically was doing the proofs for the identities. Without practice those things can take quite a long time to figure out. They're not necessarily challenging, more like a longer processes to figure out then most other problems and really the only way to get better at them is to practice, so I hope you guys pracstices! Other then that, I don't really see anything else in the unit that was too complicated. However we must remember to "algebraically massage" the problems. Another problem was, it seemed that people forgot about factoring, and that is a possibility when doing this problems so remember that too guys! Most of you won't even see this post so I apologize. Once again I hope Mr.K forgives me for this one time I forgot and considers this as my BOB

Scribe Post: Insanely Crazy Long Question And Insanely Crazy Pre-Test

Hi! This is Danny, and I'm your scribe for today. First of all I'd like to apologize in advance for having this up so late, I had vocal jazz and work after school and only had the time to start my post now (which is 11:00 pm but will be some other time when I'm done). I'd like to make a twist to this scribe post. Instead of just writing normally what we did during our classes today, I'd like to make it into a story. So with no further ado here I present my story.....

Captain K and his crew of math genius' continued their travel through The Land Of Pre-Calculus in search of the Legendary Holy Golden Credit!! When they came across an obstacle in their way of eternal bliss.....A SEA PORT! This sea port was the only way they were able to cross the sea without being swept away by its' tides of sinusoidal functions.

"What do we do now Captain K?" said Craigmyer.
"Look there's a sign near by, let's see what it says" said Melk
"Trying to get across the sea port? It's not going to be as easy as walking across, first you must solve these problems. Then you shall see what happens next..." read the crew.

At this sea port, the depth of the water, h meter, at time, t hours, during a certain day is given by this formula:

h(t) = 1.8sin[2Π (t-4.00)/12.4] + 3.1

a) State the: (i) period (ii) amplitude (iii) phase shift
b) What is the maximum depth of the water? When does it occur?
c) Determine the depth of the water at 5:00 am and at 12:00 noon.
d) Determine one time when the water is 2.25 meters deep.

"WHAT ARE WE SUPPOSE TO DO!?!?!" yells Danny Boy frantically
"No need to worry Bertman is here! We just have to sketch a graph of this sea and we'll get our answers from there!" says Bertman speaking in a voice strangely close to that of Batman's.
"Easier said then done, but I'll give it a try" says Mr. Siwwy.


"What a minute, we don't even need the graph for the first part of the question!" states Kasiaw Cole (get it, Keyshia Cole, the singer?). She continues, "to find the period don't you have to go 2Π/B? But that fraction, that makes it so much harder then usual."
"I got it!" says Vinsanity "you just got to multiple it all out first, then this will give you the answer for the period"

Vinsanity shows his work to the rest of the crew:

2Π X (t-4)/12.4
= 2Π/1 X (t-4)/12.4
= 2Π (t-4)/12.4
= 2Π/12.4 X (t-4)

B = 2Π/period
B = 2Π/12.4
PERIOD = 12.4

"Nice! I got the amplitude and phase shift!" says Dr. Grey-M "By looking at the formula we get the amplitude to be 1.8 and the phase shift to be 4.00."
"Awesome, on to the next questions!" says Danny Boy

NOTE: This is where my story kind of just stops for a bit and I just post the answers to the remaining questions b), c), d). This is taking way longer then I expected and it's already cutting into my sleep time, forget about my studying time =S. Continuing......

b) The maximum depth of the water is 4.9 meters. You get this by taking your sinusoidal axis and adding the amplitude to it:

3.1 + 1.8 = 4.9 meters

To find when it occurs you plug in 4.9 into the formula:

4.9 = 1.8sin[2Π (t-4.00)/12.4] + 3.1
1.8 = 1.8sin[2Π (t-4.00)/12.4]
1 = sin[2Π (t-4.00)/12.4]
Π/2 = [2Π (t-4.00)/12.4]
(12.4)(Π/2) = 2Π (t-4.00)
(12.4)(Π/2) / (2Π) = t-4.00
3.1 + 4.00 = t
7.1 = t
7:06 am = t

c) For each time, you just plug them into the formula to find your depth at that time:

h(5 am) = 1.8sin[2Π (5-4)/12.4] + 3.1
h(5 am) = 3.9735 m

h(12 noon) = 1.8sin[2Π (12-4)/12.4] + 3.1
h(12 noon) = 1.6766 m

NOTE: If you were given a time value of 5:00 pm this would be equal to 17 hours, and that would be the value you plug into the formula.

d) To determine one time when the depth of the water is 2.25 meters deep, we just plug 2.25 meters into the formula:

2.25 = 1.8sin[2Π (t-4)/12.4] + 3.1
Let Θ = [2Π (t-4)/12.4]
2.25 = 1.8sinΘ + 3.1
-0.85 = 1.8sinΘ
-0.4722 = sinΘ
-0.4918 = Θ
-0.4918 = [2Π (t-4)/12.4]
(12.4)(-0.4918) = 2Π (t-4)
(12.4)(-0.4918) / 2Π = t-4
-0.9706 + 4 = t
3.0294 = t
3:02 am

BACK TO THE STORY:

"Wow, that took a long time but we finally figured it out" says Richard S.
Just then they saw a magical bridge appear out of no where allowing them to cross the sea safely and on towards their next challenge while in search of....the Legendary Holy Golden Credit!!
"Hey how did you get here before we did Samus?" says Dino
"Didn't you guys see that perfectly safe bridge right down over there?" Samus points towards the bridge.
"WHY DIDN'T YOU TELL US!!??!!??" the crew screams at Samus.
"You never asked? DUH!" says Samus

PART TWO OF THE STORY: Transformator And His Evil Pre-Test..... NOTE: I'm going to use past colours again, there's too many people in our class and not enough colours =S

So after getting past the sea port and it's puzzling questions, our adventurers ventured onward along the "yellow brick road" not knowing that they were about to encounter the EVIL TRANSFORMATOR DUN DUN DUN!

"Why are we walking on this yellow road anyways?" says KaDeeM AbDul Ali JaBBar confused.
"Captain K told us to, he said this road would lead us to......the Legendary Holy Golden Credit!!" says Tim_MATH_y
"But if it lead us to....the Legendary Holy Golden Credit!! I really wish that'd stop happening everytime we mention....the Legendar Holy Golden Credit!! Sigh, anyways, if it lead us to that, then wouldn't the road be gold instead of yellow? Guys? Guys?" says KaDeeM AbDul Ali JaBBar
He turns around only to see the whole crew staring at the biggest transformation ever seen on the face of The Land Of Pre-Calculus, TRANSFORMATOR!!!

"MUAHAHAHAHA!!!! I'm Transformator and I'm here to phase and vertically shift your functions to doom! Then when I'm done with that, I'll stretch and squash your amplitude until you scream for your MAMA!! MUAHAHAHA!!!" says the hideous Transformator
"Ewww, this thing is so ugly it makes me sick. What are we going to do? Stupid Transformator we just want to get the Golden Credit. Oh my gosh leave us alone." says Jeng-Lo
"Never! You're trespassing on my territory there's nothing you can do now to escape from my parameters A, B, C, and D!" says Transformator
"Alright then, I purpose a challenge to you Transformator. I bet our whole crew together can solve any transformation problem you throw at us. If we win then you let us go." says Sandy softly but bravely.
"And if you lose?" says Transformator
"Then we have to stay here forever allowing you to do whatever you want to us" says Sandy
"Alright then, you have a deal! Here's a Pre-test chalk full of challenging problems, lets see if you can get out of this one Captain K! MUAHAHAHA!" says Transformator in delight.

The crew recieves the test and starts to begin solving the questions:

1. f(x) = 2x² - 3, where x is greater than or equal to 0, then a function g that will have domain and range that are both different from those of function f is:
a) g(x) = f(-x)
b) g(x) = -f(x)
c) g(x) = f-¹(x)
d) g(x) = kf(x), k greater than 0

"Oh! The answer is C)!" says Aichelle the Incredible
"The answer wouldn't be A) because f(-x) will only result in a different domain, and it wouldn't be B) because -f(x) only results in a different range. For C), f inverse of (x) means your x coordinates would be your y coordinates, and your y coordinates would be your x coordinates therefore giving you a different domain and range!" continues Aichelle the Incredible
"Argh, that's correct, next question" says Transformator angered

2. The graph of a function f is a parabola opening upward, with its vertex on the x-axis. The graph of a new function g, where g(x) = 2f(x), will have:
a) the same domain and the same range as f
b) the same domain but a different range than f
c) a different domain but the same range as f
d) a different domain and a different range than f

"Jojo Rocks!" yells Jojo
"The answer has to be A)! Since it's a parabola, going 2f(x) wouldnt affect the range because the parabola would be going up both sides to infinity so you could trash B) and D) already. It can't be C) either because the vertex is on the x-axis, therefore the domain will be left unchanged so the answer has to be A)!" continues Jojo
"ARGH! Right again! Next one, you won't get this!" grumbles Transformator

3. Given the graph of f(x) below, sketch 1/f(x) in the space provided:

"This one was easy no challenge to it." says Johnny Johnson
"First things first find your invariant points, on this graph there's two. One at (-1,-1) and the other at (1,1). Then find your asymtotes, it just so happens that the asymtotes are the x and y-axis. After that just remember Dr.Suesus' version of math when drawing the actually reciprocal graph in (smallering and biggering). Also remember to have arrows where neccesary and dots that shows an end on the graph where necessary. In this case the graph ends at (-5,-1) but continues on going in the other direction." states Johnny Johnson in what seems like an eternity to explain.
"NO!! RIGHT AGAIN!! THERE'S NO WAY YOU'LL GET THESE LAST TWO!" screams Transformator

4. Given f(x) = cube√3x² -4, write the equation for its inverse f-¹(x).

"They just keep getting easier and easier! I'll show you the work, no sweat." says Bond, Robert Bond



















"THIS CAN'T BE HAPPENING!! THIS LAST QUESTION IS IMPOSSIBLE, NOT EVEN I WAS ABLE TO SOLVE IT!!!" yells Transformator, now shaking the ground with his mighty power.

And this is where I'm going to stop for tonight. Sorry guys I put out more then I could chew, but this final question will be up by tomorrow! Good luck to all on the test in the AFTERNOON. Scribe as you all know already is Mark. =D

BOB

Yet another unit done which means we just past another obstacle in our pre-calculus adventure in search of the ultimate PRECAL40S credit. This unit wasn't too complicated or too bad at all. Oh wait, there is the matter of the problem solving questions! =S These had to be the most complicated and confusing part of the unit, as signs from all the moaning and groaning from all around the class today. But if we continue forward and study our material things should be just fine ;). So GOOD LUCK to all on the test tomorrow, I must go and do my scribe post =P

BOB

Well our adventure through Pre-Calculus Land has come across a barrier, the BIG WALL OF TRIG TEST! The only way to neutralize this barrier is to review our Math Dictionaries and study all of our notes from this "Saga" in order to conquer this seemingly impossible task ;). Only then will we be able to move on ward and continue our adventure of many wild and crazy mathematically related situations.

Okay, so maybe our class isn't THAT dramatic and exciting but it's still very important to review and study our material. I for one have taken this course before (A WHOLE YEAR AGO! PHEW!) and even though I knew most of the things we were learning in this unit, I was still able to take away some new things I hadn't known before. Math is a science of patterns, and by using patterns I was able to memorize the unit circle and all the exact values associated with the trig functions within it. My past class failed to apply such an extremely effective strategy of learning towards the course.

So with that said, I'd like to wish everyone good luck on the test tomorrow, don't stay up too late studying and get a good breakfast. Trust me I'd much rather be completely focused on the test then worrying about filling your stomach cause it won't stop grumbling =D When it's all said and done, we'll be on this adventure together and with hard work we surely will finish this adventure together.