Last Bob of the School Year!!!

Hmmm... what does Craig have to say about the past unit??? Let's see, well it has been quite an easy one, which has helped out a lot, considering I have had so much else on the go! I'm not sure what else there is to say... I would post each of the formulas, but Graeme has already covered that, and we get a formula sheet anyway. Just as a reminder, watch the wording of the questions! Especially when they deal with the bouncing of golf balls and such (i.e. the final question on the pretest). Otherwise, this course has been a great one and I believe the unit was a good one to finish it off. Good luck to all on the test and the upcoming exam!!!

For the final time =D

LONG Weekend = LONG Scribe

This class was the second one of the unit of PROBABILITY. That is, as Grey-M stated in the last scribe post, the easy unit of PROBABILITY, but anyway...

...The class started with the student elections. 3 of the 4 candidates for the executive council were in our class so it was a fairly bid deal. (To see the results, check the post prior to this one by Sandy.)

After that, we reflected upon the extraordinary video display by Richard in the previous day's candidates' speeches. We liked it so much in fact, that we searched YouTube for it. We didn't find it, so instead we watched a video that was completely irrelevant to math, or anyone in our class for that matter =D.

Then, we got down to some "ACTUAL MATH!"

The first slide shown was a little too easy I believe, but Mr. K. didn't find it as such (haha!)
Then, Mr. K presented us with on that was a little higher on the difficulty scale. We were to "TEST THE QUESTION FOR INDEPENDENCE".
We'll take a quick trip back and review exactly what an independent variable is:

Thank You Grey-M! =)

Now, to test a question such as:

30% of seniors get the flu every year. 50% of seniors get a flu shot each year. 10% of seniors get the flu even though they've had a flu shot. Are getting the flu and getting a flu shot independent events?

•The first step is to look at the set. (In this case it is the SENIORS)
•Next, identify the categories. (Whether they GOT THE FLU SHOT or NOT)
•Now, we identify what event can occur to each category. (they can GET THE FLU or NOT)
• The fourth step in the solving in this problem is to draw a tree diagram:
•Now we can write in the probabilities of each event.
•Then, find the favourbale outcome, or the outcome which we want.
•Now just calculate the probability of the favourable outcome and compare it to the given percentage:
Here we see that the probability of catching the flu and getting a shot is not 10%, it is 15%. This means that they are not independent events.


Next, we moved on to questions that dealt with events that were "MUTUALLY EXCLUSIVE". This means that it is a situation in which one(or more) of the outcomes of the event becomes impossible if the other(s) is(are) chosen.
EXAMPLE:
If Mr. K. were to pick from the class one boy, he will not be a girl. If he picks a girl, she cannot be a boy.
An event can be determined to be mutually exclusive (or "disjoint") if the probability of getting both outcomes is zero(Ø), also known as an empty step.

**both events would be written as "A", "(upside-down U)", "B".**

After that we did problems that asked for the probabilities of "AUB" (A or B). If it is mutually exclusive, then simply add the probability of "A" and the probability of "B".
However, if it is not Mutually Exclusive, we must also subtract the probability of "A and B", because it is not A OR B if both are chosen:

We continued the class by doing more questions dealing with "AND" and "OR" and finished off with a couple situations for which we had to decide whether it was either:
INDEPENDENT or DEPENDENT and MUTUALLY EXCLUSIVE or NOT MUTALLY EXCLUSIVE.
This can be found in the slides (2 posts previous to this one).

To finish off:
•CONGRATS RICHARD AND VINCENT!
•Hope everyone's Long Weekends were better than mine.
•TUESDAY'S SCRIBE IS MR. SIWWY!!!
•Enjoy your day off =D

BOBbing On BOBbing

Another unit come and gone. The pre-test and test loom over the class, as nervous students prepare for "the day of two tests". Myself, I'm continuing with my busy life and finally sitting down at my computer at 11:00 pm to write a quick BOB. This unit has been fairly tricky considering the introduction to quite a few new topics, while embellishing on older ones.
The hardest part for me so far is simply remembering which formula goes with which shape, and what the difference between the horizontal and vertical versions of each. However, it is a very correctable problem with lots of practice. I'm sure most of the class is comfortable with the material, or at least that's what I thought based on Friday's class. So , without further ado, "Good Luck!" I think I will eat a bowl of Lucky Charms for breakfast tomorrow, "They're Magically Delicious!" Although, I don't think I'll need it, and I hope no one else does.
Do I even have to say it???

BOBinatorics

Well, well, well, once again I find myself sitting in front of my computer and thinking about the previous unit. I have enjoyed this unit actually (yes, I enjoyed MATH!) I cleary understood most of the most topics and was able to apply them accurately to the questions (with a little help from Chris, Vincent, Aichelle, and of course Mr. K.). I think this may be because it sort of deals with logic, in the sense that you have to think about the question and then design a model to use for it. Anyway, with the test a little more than 12 hours away, I have one thing to say: Good luck to all, but I hope that not many of us need it because we have all been studying hard and are now confident with the material in the unit. Also, I hope that there is a lot of poker questions on the test (I love those!) and very few that deal with the binomial theorem, Pascal's Triangle, etc.
KEEP PUSHING!!! (do I even have to say it any more?)

FLICKR =o

OH! wow, I didn't know we were supposed to post it on the Blog =o

Sorry Mr. K.

Power-Scribe

Well, well, well; look who's the scribe again. At least this time I can actually fulfill my scriberiffic duties. Anyway, this was, as you know, the first day back from Spring Break and I don't know if I'm in "School-gear" yet, so bear with me.

The class began as any class would with Mr. K. putting the finishing touches on the day's lesson, while students assembled to talk about their various "Spring Break adventures". Then Mr. K. started with a very important notice, which I will repeat:
FLICKR ASSIGNMENT IS DUE BY MIDNIGHT TONIGHT!!!
Then, he continued to remind us about the DEVELOPING EXPERT VOICES project. It went as follows:
1. Make sure everyone has their due date set for the publication of the project.
2. E-mail Mr. K. so that he can invite you to the new DEV Blog. This is where your project is to be published, so join that ASAP, especially if you're project is due soon.
3. Finally both tomorrow and Wednesday's class will be work periods for any homework (Exercise 21) as well as the DEV projects.

Finally, we got down to some math, yay :D
We began with some review from before the break. He went over both the multiplication and division of powers. The main thing to remember is that the bases must be the same to be able to simplify the expression. In the case of multiplication, the exponents can be added. For the opposite of multiplication (division), you would do the opposite of addition (subtraction). From these examples, we can conclude:

Next, Mr. K. applied this to logarithms. ( Which, I will remind you, are EXPONENTS!).

This led to two of the LAWS OF LOGARITHMS:

Mr. K. followed this up with the presentation of a couple questions that dealt with the combination of both multiplictaion and division. They can be seen HERE.(Slide 6/8)

THEN, Mr. K. handed back our trigonometric identities test! This was somewhat of a distraction to many people. There were groans from a lot of the class (including myself) as we flipped through the papers to see where we had made the mistakes.

When all the excitement had died down, Mr. K. was showing us the power within a power. In these examples, the base of the power is a power itself. See there--->. When dealing with such problems, the inside exponent(s) is(are) multiplied by the outside exponent.

However, when this is applied to Logarithms it becomes a little more complicated. There is the usual base, but the argument also contains a base as well as an exponent. If the bases are the same, then obviously the logarithm is equal to the the exponent in the argument. But if they are different, there are two ways to solve it. First (<---), create a 'power within a power' situation out of the argument with the same base as that of the logarithm. For example, in the image to the right the base is 2. The base in the argument is 8 so it can be simplified to 2^3. This makes the bases equal. Then just multiply the inside and outside exponents, as explained above, and you get 2^15. Now that the bases are the same, follow the "rule" above (and seen below and to the left) and get 15 as the final answer.

The second way of solving is by rearranging the expression as seen here-->
This can be rearranged because "log base 2 of 8" is raised to the exponent 5. Since logarithms are exponents you can multiply the exponent 5 by the exponent (log base 2 of 8) to get what is seen to the right. Then it can be determined that "log base 2 of 8 is equal to 3. 3 multiplied by 5 is 15 which gives the correct answer.

Mr. K. then finished by generalizing that last bit as a RULE:
and then gave us a couple of examples seen HERE. (Slide 8/8).

Well, that wraps up my scribe post for the night.

REMEMBER: FINISH YOUR FLICKR ASSIGNMENTS BY MIDNIGHT!!!


Oh yeah, and the next Scribe is:

BOB's your uncle...

It's that time again folks, time to sit down at your computer for a couple minutes to reflect on the previous and increase your anxiety for the upcoming test. The Identities unit is probably the toughest one yet, based on the class' struggles with it. I myself have had some problems with the questions involving different thinking (eg. basics learned in grade 9 or 10). The use of the SMARTBoard hs somewhat increased our learning of the concpet because everyone has a chance to solve it, however sometimes the rest of the class needs a little more time to solve it on their own. Otherwise the time spent in class has been great. The competitions add a sense of fun, and excitement, as well as some tension between the usual competitors. As usual, GOOD LUCK to everyone on the IDENTITIES test. PUSH THAT ROCK!!!
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BOB - Transformations

"The time has come," the Walrus said, "to speak of many things..." ...but mainly our most recent unit, TRANSFORMATIONS. It seems like it was only two weeks ago that I was writing the B.O.B. for Circular Functions... ...Oh. Anyway, the unit just seemed to fly by, considering we missed a grand total of 4.5 (four and a half) classes in the short two week span.

I did not find this unit particularly challenging until Friday when Mr. K. introduced PROBLEM SOLVING. This is because the unit was mainly a combination of last year's Functions unit and our previous Circular Functions unit. However, once we reached the problem solving section of the unit I was surprised by how difficult it actually was. It only uses the concepts that we just learned, but it incorporates them in a way where we must logically make a "plan" or order as to how we will solve the problem. I think that is the hardest part, figuring out what concepts to use where and how to fit them into the question. However I think with some help from the review sheet, exercises, pretest, and a little more class time, we all have a chance to do excellent on the upcoming unit test. Good Luck to all, and remember...

Scribe's Scribbles

Sorry guys, its kinda late. Took a while to figure out the graphs.

Finally, I get a chance to scribe. After being a victim of technology for the first couple of weeks and then having to deal with some postponed classes, I can finally write a half-descent scribe.

Well.. where should I begin? I guess the beginning of class would be a reasonable place. I walked into class only to see Mr. K. playing with his new favourite toy, actually I think he was just setting it up for the day's lesson, but we all know he loves to use it. Then, Mr. K. handed out part two of "The Test of Doom" (Chris). This consisted of two measly questions that represented the graphing portion of the unit test. However, once the test started those two questions seemed to get a little less 'measly' and a little more difficult (or at least it seemed that way, most people used the whole 15 minutes and were rushing at the end).

After those few minutes of tension, the room became its friendly self once again as Mr. K. pulled the Blog up on the Smart Board, and starting a discussion about BOBs (Blogging on Blogging; see the pc40sw07 Blog). The talk of BOBs went something like this:

1) BOBs are to be done BEFORE the test (preferably 2 days before)
2) The purpose of the BOB is to help us see how we've improved
and show some of the things we need to improve on.
3) Mr. K. needs us to post BOBs (preferably 2 days before) so that
he can help us in areas we have problems with before the test.
4) Finally, Mr. SiwWy posted a very good BOB because of the way
he reviewed each of the mnemonics we learned in this unit.

Then we were interrupted briefly by Mr. Magnusson (sorry if the spelling is wrong) to see if the Smart Board was working okay and ask if Mr. K. had any problems with it. It basically was a chance for Mr. K. to show off his prize possession once again.


Following that, we entered our new unit, Transformations. Basically it has to do with Functions (not only Trig. Functions) and how they can be transformed. For example, if you are given the functions f(x)=sin(x) and g(x)=sin(x-2):

What is the difference? Well, f(x) is the same as g(x), except that g(x) is shifted 2 units to the right. Therefore g(x)=f(x-2).

This also works for any other function. For example, if you are given the functions f(x)=(x)^2 and g(x)=(x-2)^2:

What is the difference? Well, f(x) is the same as g(x), except that g(x) is shifted two units to the right. Therefore g(x)=f(x-2).

Now, both of these examples used a "phase shift" which adds to the x-coordinates. However, I could have used the sinusoidal axis or "vertical shift" which adds to the y-coordinates. Actually any of the parameters from the formula:

y=AsinB(x-C)+D

could have been used. But since we are not only using Trig. Functions anymore, we can generalize this formula to:

y=f(x-b)+a

The other parameters, A and B will probably be learned tomorrow (Stretches).

Then Mr. K. gave us a couple questions, but they were in the form of a COMPETITION. Once again we had people racing up to the front of the room with arms outstretched and shoulders rubbing together to write on the Smart Board. Both occasions ended up with each of the participants with a marker in their hand, so Mr. K. had to declare the winner almost by photo-finish (JoJo). However, there is no need to post these questions in my Scribe post because Mr. K. has a Smart Board!

CLICK HERE

and that was pretty much the class. Just a reminder, Exercise 7 is homework (for those who haven't finished it already), as well as questions 11-15 on Exercise 8.

"Go out and commit random acts of kindness!" -Mr. K.


Goodnight everyone, I'll see you tomorrow.

Oh, Almost Forgot, THE NEXT SCRIBE IS...

...KADEEM!!!

BOB - Circular Functions

Hmmm... Where to start??? Well I guess I could start by saying that this class has been a blast! I enjoy coming to class each day and interacting with Mr. K. and of course, my fellow classmates. This first unit has been a very interesting one. Like all units, different people have problems with different aspects. I myself did not have trouble with many parts of this unit, but that is probably because it is similar to last year's "functions" unit.
As I said earlier, this class has been such a good experience, but there was one class in particular that stood out as both a fun and learning experience. When we wrote our pre-test for the unit, there seemed to be a sense of tension in the air while we wrote the test. Everyone was silence and the sounds of pencil scratching, calculator punching, and the blowing of eraser shavings off one's desk filled the air. I myself was not expecting such a "tricky" test so I was also thinking and working furiously. After Mr. K. told us to stop writing and split us into groups, the sounds of frantic problem-solving seemed to morph into a more relaxed sharing of ideas. I feel this class was great because different people got a chance to get together and share their ideas and methods, all of which were greatly appreciated. Finally as Mr. K. shared the correct answers with the class there seemed to be a great excitement as if each answer was the winner of and Oscar. Groups exploded with cheers, fist-pumps, and hi-fives to members of their groups whom they weren't friends with before. That is why I believe that this was the best class; it made the students of this class a bit closer and I'm pretty sure that no one here is afraid to share their ideas with someone they feel close to.
Finally, I wish to say a formal GOOD LUCK! to everyone for Wednesday morning's Unit Test. Remember Sisyphus, even if you believe it to be impossible, try your best...

"Keep pushing that rock to the top and maybe, just maybe, it will stay"