BOB on Conics

Heeey everybody, sorry to say that this will be short and sweet because I've got loads to do tonight unfortunately :<

On with my BOB!
Honestly, this unit sounded intimidating, but in the end, it really wasn't at all! After I got past getting the hang of the geometry, I actually started to enjoy it... (Except for sketching graphs, I always did despise doing that.) :]
So now that I pretty much get the jist of all the geometry involving parabolas, ellipses and hyperbolas, I think I'll do well in that aspect.
However...
Applying them to "realistic" situations won't be my cup of coffee (gonna have to load up on this tmrw huhu). I'm sure with a little more practice I'll have a full understanding of taking pieces of information and constructing the proper equation for it, but waugh! In due time...

What I found interesting was that when you take a line and "spin" it, you end up with two cones, and from there you can derive the parabola, ellipse, and hyperbola! I'd describe/post images of this, but Jessi's scribe post on Conics had very good ones already :].

Now, onto the guidelines which I shamefully hardly ever follow...

• Get at least some sleep! Actually, sleep immediately after you study, you'll remember your stuff better!
• Eat breakfast, brain food = awesome because you don't want to hear your stomach during the test and neither do we lol.
• Take your time, don't rush!
• Keep in mind the equations for vertical/horizontal parabolas, ellipses, and hyperbolas!
• Look at these equations and see the geometry! Remember, "codes!"
• a^2 + b^2 = c^2!
• Be able to take very little given information and build upon them to end up with an equation that will help you out big time!

Anywhoots, I think that's enough brain juice spillage for me. Onto studying!
To everyone who's going on that Kenora trip tmrw... Bye. >_> Just kidding, have fun!
To everyone else, good luck on the test tmrw! :D

BOB on Permutations and Combinations

Sup y'all~ Here I am BOB-ing the night before our scheduled unit test, however I'm not quite sure if I am writing the test tomorrow, so I shall BOB anyway!

What can I say about this unit?
Well, it's certain that I found it a lot easier than Logarithms! I actually got the hang of it at first, I even predicted (n-1)! However, things got trickier and trickier~

The concepts I had a hard time grasping were the table problems and the poker hands (mainly because I'm terrible at card games and am extremely unfamiliar with these "hands!")! So I definitely need to practice those...

What I learned from this unit is to create and utilize even more clever ideas! Without them, this unit would be a big toughie! So remember, read the question carefully, know what it's asking for, and think of a clever way to find a solution!

Also, those necklaces and bracelets! Keep in mind that those things can be turned over and result in a permutation that you've already come up with before. So, you must divide your answer by two! OH! This does not apply to tables lol. Because you can't turn a table over when there are people sitting there, that's just rude.

Hmm.. what else?
Well, with permutations, order matters...
However, with combinations, order does not matter!

Don't forget about the "Pick" (nPr) and "Choose" (nCr) formulas and when they are appropriate to use!

Well, isn't this BOB post all over the place :/
Oh well!

Oooh, don't forget about using them bags, they're quite helpful, but also - don't forget that the objects within each bag still have a number of ways to be rearranged!

Speaking of objects, don't forget about distinguishible and non-distingquishable objects!
That is... (n!)/(k1!)(k2!)(k3!)
Where n = number of objects and k1, k2, k3 are the numbers of each non-distinguishable object!

Aw man, I'm BOB'd out. Sorry if I missed anything, every else had already made such awesome posts anyway!

Good luck everyone! Do your best!

Problem Solving - Combinations

Hey guys Ingrid here today to scribe for y'all!

Anyway, today we tried to finish off the unit so that we could write the pre-test tomorrow and then the unit test on Friday, however, we were not able to do so. Mr. K considered moving the test to Tuesday... BUT, the last couple of slides pertaining to the game of poker is for homework. So yes, you guys are still writing the pre-test tomorrow, and the unit test on Friday :).

BOB AWAY YA'LL.
(Oh yeah, get those deliciosos links in as well ;D)

***

Wow, everyone's pretty much bumped my scribe post down with their BOB posts, but hey that's a good thing - you guys are listening! Haha.
For those of you who need help for today's homework from the slides... Aldrin included them on his most recent post! Thanks bro!

Okay, now to get to scribing~ Please forgive my lack of explanation skills!

Firstly, for this specific post, let's keep the choose formula in mind. That is;


We immediately started off with some exercises...
Alright, here we were asked to find the 4th term in the given expansion. In order to do so;

• We let a =
• and b = or
• We then use the choose formula and the binomial theorem.
• Remember that n is the number of terms in the expansion
• and that r is the term we are looking for... BUT it is always one less than what we are looking for, keep in mind the first term is to the power of 0 and the second term is to the power of 1, etc etc... Does that make sense? >_<
• Oh, the exponents on the variables always equal to the degree on the expansion.
• So since r is the exponent on the variable b, it is then easy to see that the exponent on the variable a is 4.
• 3 + 4 = 7!
• Mmk from there we just substitute everything in...
• and solve!

NEXT!This one was an interesting problem. All we really need to know is that

• There is no middle term when the expansion has an even number of terms!
• This is because there is no zeroth term, even in University!
• However, we did talk about the zeroth row.
• BUT, we don't deal with that in HS either.
  

NEXT!

• For this question, there were three different solutions, however only one was correct!
• Thanks Alex, PJ, and Jessica for your clever ideas!
• It turns out, that Alex's (the first slide) was the correct method.
• This is because his method took into account all three possibilities without making it into a permutation.
• The other two methods on the other hand, were permutations, not combinations.

• Firstly, Alex took into account that only one boy is in the committee, and the other two spots are girls. So that makes 12 choices for the boy, and 10 girls for the last two spots.
• Here, he used the choose formula then multiplied that answer by the number of choices for boys (12)!
• Then he did a similar thing for the next set, which is two boys and one girl..
• For the last set, he took into account that all three spots are taken by boys.
• For the final result, he added all three sets!

• NEXT!

• Here we have another interesting problem...
• There are nine chairs in a row but four of these nine students must sit in a consecutive order!
• First, we figure out that there are 6 possible ways to seat a group of four people with nine chairs.
• So we placed those four people in a bag, but now we let them out!
• 4! is the number of ways we can rearrange the four people consecutively within the four seats.
• Therefore, 6 x 4! = 144 ways!

NEXT!

• For this particular question, we had a really interesting debate.
• Some said that the direction each group took was relevant but in reality, it is not!
• Realize that we are working with combinations (where order does not matter), not a permutation (where order does matter).
• So in the solution on the slide, we have 7 choose 4 because there are 7 people and 4 of them have two choices to take but can only take one...
• However, we also have 3 choose 3 because the three people left only have one direction to choose from! (3 choose 3 = 1)
  
• So we multiply those two together and end up with 35 ways!
• Keep in mind that 7 choose 3 x 4 choose 4 is the same thing!

***

Alright, so for the poker questions, not only does Aldrin have hints for them, but John beat me to actually solving them! Here is his BOB post on Combinatorics which includes the solutions to the last few slides from today! Thanks bro!

***

Mmk, that's all about that comes to mind from today... Sorry if I forgot anything! Good luck on your pre-tests everyone, study hard, do homework, and don't forget to BOB!

The next scribe is... Jessi!

BOB on Exponents and Logarithms

Hey guys, please excuse this extremely out of place BOB-post! As some of you may know, I missed last week's test on Exponents and Logarithms and so my test is scheduled for tomorrow :].
I will try to make this BOB post substantial enough, but I don't know exactly how much I'm going to say so here I go!

Honestly, I think I'm going to find certain aspects of this unit test difficult! I've got the hang of everything we learned from the beginning of the unit up until the part when I left for the week. That means natural logarithms and the accounting portion will probably throw me off big time :/ Oh! And graphing logarithms... Ugh D: Nonetheless I will study hard!

Firstly, I must remember that a logarithm is an exponent! Don't forget!
This, as we all must know, is the basic form of an exponential equation:
On the other hand, the basic form of a logarithmic equation is:

In both cases;
a is the base
b is the exponent
c is the power

Now, there are several laws pertaining to logarithms. They are the Power, Product, Quotient, and Change of Base laws.
Power Law:Product Law:Quotient Law:Change of Base Law:
Ah, I almost forgot to mention that a logarithm is the inverse of an exponent! This comes in handy when dealing with graphing! We know that the exponential function results with the power when given an exponent. Therefore, a logarithmic function results in the exponent when given the base and power.

Alright, I can't quite say much about e other than I have noo idea what it is other than a "natural number" (?). I'm looking up websites and working on exercises as we speak! I will get the hang of thiiiis.

Also, we were given formulas pertaining to exponential/logarithmic growth and decay! Here they are, sadly though - they remind me a whole lot of Business class lol. Maybe that's a good, helpful thing?

PERT Formula:

Pe ^ rt = A

(for some weird reason the image maker won't allow me to have an exponent of rt :<)

P is the principle
e is the natural number
r is the rate
t is the amount of time
A is the total amount

MODEL Formula:

Ao is the original amount
m is the multiplying factor
t is the amount of time in total
p is the period of time it takes
A is the total amount

PERT's BROTHER Formula:

P(1+r/n) ^ tn = A
(again, some deal with the PERT formal, they really are brothers!)

P is the principle
1+r/n is the principle plus the rate over the number of times it is compounded a year (annually, biweekly, etc)
t is the amount of time

Okay! I think that's all about I can say... Of to study some more~
Wish us luck guys ;D!

DEV Project Timeline

DEV Project Timeline

April 24 - Finalize all questions.

April 26 - Develop story concept.
April 28 - Finalize storyline.
April 28 to May 21 - Work on comic.
May 21 - Finalize all panels.
May 21 to May 31 - Tweak, edit.
May 31 - Absolute DEV project deadline.

BOB on Pythagorean Identities

Hello fellow classmates! Here's to the end of another eye-opening unit!
As routine procedure, here's a quick-fast BOB on Pythagorean Identities.
I feel like this will be bland compared to the BOBs already posted but I will contribute anyhow :]

Firstly, despite the test being on Thursday, April 09, 2009 we will not be having a review class tomorrow. That was today's class, which if I may add; was very helpful!
Tomorrow's class will be dedicated to starting a new unit so get ready guys!

Anyway! I'm going off on a tangent so I better get this done quickly...
There really isn't much to say so hmm...

• Well, I have to admit I totally abandoned the unit circle in my brain so I had to refresh my memory. Don't do what I did guys lol. Keep that unit circle in mint condition!
• Remember but do not memorize those corollaries! They will become extremely useful when proving identities.
  
• Keep the sine/cosine dance in mind, you'll never believe how it actually helps you out biiig time!
• As it occurred to me today, you may have to elaborate on both sides of the great wall in order to prove an identity. Astonishing, I know.
• Since we're on the subject, nothing ever crosses the great wall! Not even Q.E.D.
  
• Double identities may seem tricky, but really they're quite simple, just take your time.
  
• As usual, eat, sleep and study well!
  
• Practice, practice, practice! Unless you're confident enough already, that is.

I thought I had more in mind but I guess not. After today's pre-test, I feel like I need to review a bit more. I totally got pwned. However, that may be due to my lack of clever ideas. Oh me, why do I lack such useful mathematical creativity?

Good luck everyone :]

A BOB for a BOB

Hey guys! You all may have thought that I had forgotten about this by now, but nope!
I can now unveil BOB, our BOB mascot! I had originally sketched him out on paper, with more details and epicness, but figured that it was much too big to be uploaded. And so, I spent about an hour during spring break working on this lol. Enjoy!

To anyone who is interested to know:
- I used Open Canvas 1, which is nowhere near comparable to Photoshop, Painter, etc. Let's just say that it's almost if not more primitive than MSPaint lol. So please excuse the horrid simplicity of this piece!
- Major props to Dion for design inputs!
- I wasn't sure about using the Blogger logo, that's not copyright infringement is it? I mean, it's not like we're making money off of BOB right!?
- I have a full-sized, un-watermarked version of this piece. I also have a scan of the original character-sketch. To anyone who's interested in having a copy of either one, email me at miruuiz@gmail.com!

I'll get to a proper BOB post later lol.

BOB on Transformations

Hey guys! Ingrid here, and it's about time I finally write my BOB on our latest unit, Transformations.
I'd like to say that I didn't find this unit too difficult, but then I'd be lying! I found some aspects of it quite simple since it related to what we had already learned in our previous unit, Circular Functions (that is, parameters ABCD and their properties). However, the newer concepts such as the reciprocal function graphs and the (word) problem solving were a little more confusing to me. But after some reviews and reading up on everyone else's tips and advice, I think I've got it figured out... I hope!
I don't really have much else to say that everyone else hadn't yet covered but do remember:
- Study!
- Don't forget to find links relating to our last two units (Circular Functions and Transformations)!
- Keep up to date with your exercises!
- Believe in yourself~! ;D

BOB - Circular Functions

Hey guises, I know this is late, but better late than never right!?
Well, let me start of this BOB thing by stating that thanks to PJ, I now know what "BOB" means...
"Blogging on Blogging!" Haha, I was so enlightened when I learned that :]

Anyway, I really don't have much to say without being redundant. However I still do have some advice for you!
- First off, remember that cos is relative to the x-axis and that sin is relative to the y-axis.
- Also, never write "sin" or "cos" without theta because well... That's just wrong! :]
- Don't forget that when given a negative value in terms of radians or degrees, it means that the direction is opposite that of the direction we would normally go. (Did that make sense? lol sorry)
- Remember 2kpi where k is an integer!
- Come prepared, with back-up ;D That is, pencils, erasers, lead, (graphing) calculators, rulers?
- Don't panic! Relax and read through the entire test before freaking out over a question that may actually be a breeze once you calm down, it's just a test!
- Oh yeah, don't forget to write one of these BOBs! ;D
- Also, look through the rest of the BOBs for more advice and tips :]

Alright, now a little solemn reflection... Just kidding :]
When we were first introduced to this unit, I was freaking out, lost, confused, and overall frustrated because the concept was so unfamiliar, plus I hadn't done any serious pre-cal math in over a year! The concept of dealing with relationships and proportions rather than formulas irked me a bit because I'll admit, my brain works like a computer sometimes. I dealt much better with plugging in variables into formulas. But, after getting the hang of it, I realized how much easier thinking in "proportions" was, and that it also provides me with better understanding!
At the moment, I can't really tell how I feel about the test tomorrow, I just hope I do well, really. Winging the pre-test and getting them all correct gave me a boost of confidence but I know I still need to review/study! Speaking of which, I should get to that now lol.

Good luck everyone! :D

February 5th: Learning Within Groups

Good evening fellow classmates, Ingrid here to scribe for today's classroom events!

We started off the class by being introduced to a less than common approach to learning when it comes to math; group learning!
We were assigned numbers and assembled into groups according to those numbers. As a group, we situated ourselves in a section of the room in order to work as a team for the remainder of the class.

First off, we worked on a question similar to a previous question we were given where we looked for the degree amount a wheel traveled, only this time, we looked for it in radians.


Alright, keeping in mind the proportion of the sector we are looking for to the proportion of an entire circle, we can see that by using the values given, we can easily solve for the variable; in this case theta (θ), which is in radians.

After solving this problem we then discussed how:

The radian is simply the radius of a circle wrapped around the circumference of the circle.

Therefore;
half a circle is approximately 3 radians (π) and
a full circle is approximately 6 radians (2π).(Please pardon my poor excuse of a diagram lol.)

We then worked on a new problem where we were to find the number of radians between the minute and hour hands of a clock at 4:00. This produced one question courtesy of yours truly, which PJ bravely asked Mr. Kuropatwa, that is: "Which arc to we look for?" In the end, we solved for both :]

Here is the solution I particularly liked for its simplicity (the one on the right hand side of the vertical line), courtesy of Mary... Or was it PJ? XD;

Since we know that 2π = 360° (a full circle), and that there are 12 sectors on a clock, we can divide 2π or 360° by 12 to find the number of radians or the degree amount of each sector.
We then find it to be π/6 (radians) or 30° per sector.
From here we can easily figure out the number of radians or the degree amount between the hour and minute hand (the smaller arc). Since we know there are 4 sectors between them, we can multiply the values we found for one sector by four.
We find them to be 2π/3 or 120°.
To find the number of radians or degree amount between the hour and minute hand with regards to the larger arc, we simply subtract those values from our full circle values. That is:

or

Mind you, this was only one way of solving this problem. Other students offered other methods and they can be easily viewed in the slideshow from today. :]

Afterwards, Mr. K made a reference to the Ancient Sumerians and how they derived 360° from the calendar and used that method to find the degree amount in one sector of a clock. That is, there are 12 months in a year, and 30 days in a month. Similarly, there are 12 hours in a day, and 30 days in a month... Multiply those two numbers together and you have 360! It is then easy to see that there are 30° in one sector of a clock.

PHEW! This is getting lengthy but I swear, I'm almost done!

We elaborated a bit on a new term: coterminal.
First off, we defined an angle to be in standard position when the intial side lies on the positive x-axis.
Therefore, coterminal angles mean two angles that start at standard position, but travel in opposite directions, however, still ending at the same place - together.

Finally, we were given one more question where we were to find the area of a sector of a circle. Again, by using the idea of proportionality, this can be easily solved.

All in all the point of today's class was to realize that there are many many many ways to solve a problem. But we must always keep in mind the relationship between the proportions!

Tonight's homework is the 5 questions you did not choose to answer from last night's assignment (Exercise 2: #11-20).

And in return for whipping a dodgeball at my face; Aldrin will be the next scribe :D!