2B + O --> BOB

Well this last unit was a good one to leave off on. I actually had and am still having a little bit of trouble with the homework because I keep mixing up which formula's are used for what and what goes where within them. But with the blog open in front of me it's not that bad. I'll have it pegged by tomorrow. But just to clarify...

To find a term in an arithmetic sequence:
tn = t1 + (n -1) * common difference
(I used t1 because that "a" confused me for a good long while, had no meaning for me)

To find a term in a geometric sequence:
tn = t1(common ratio)^(n-1)

To find the sum of the terms in an arithmetic series:
Sn = (n/2)(2t1+(n -1) * common difference)
or
Sn= n(t1 + tn)/2

To find the sum of the terms in a geometric series:
Sn = (t1(1-r^n))/(1-r)

To find the sum of the terms in an infinite geometric series:
Si = t1/(1-r)

So I'm going to finish up my homework now.
byebye

proBOBly should have done this sooner....

Haha morning of the the test! Not the best time to bob... Well this unit I'm feeling fairly confident in considering the amount of effort I have put into the homework in the exercises and on the blog. A couple of the questions are still worded trickely so I'm fairly certain that a 100% won't happen as I seem to go too fast and miss simple things in the questions on tests. So my goal for this test would be to take it slow and meticulously..... and still finish on time.

TranSCRIBIN'

Well today we had some different classes....

We started off with a Gizmo call to the Blogical Minds class in the US. Unfortunately I had completely forgot that this was going to happen in the hectic last couple of weeks so I did not have any questions prepared for them. But they had plenty for us :-). I must say that trying to answer something on the spot is brutally hard (These weren't easy questions either) so people, including me, were a little hesitant at times to respond. So that was a fun deviation from our usual routine.

But to the mathematics....

Easy mathematics :-)....

Well we all seemed to grok this probability thing. Today we learned to distinguish between dependent and independent events and how to calculate dependent event probabilities.

A dependent event is an event that the first event effects and and independent event is an event that does not depend on what happens in the first event. So we did a few questions to demonstrate this concept...


The only one event that effects the other event is the removal of the card without replacement because that changes the sample space.

Changes in sample is not the only way to cause dependency. If something within the sample space is changed it changes the odds of the events as shown in the next question.



When a marble is drawn it is replaced with a marble of the other color changing the odds and making this another dependent situation. We got the odds at the end of the probability tree by multiplying along the branches. Then to get a combined probability figure you add all the favorable outcomes.

As we saw with other questions this process generally works for calculating the odds of a singular/series of event(s) . We also found another way this relates to combinatorics in this class because Mr.K showed us that the questions can seem different but they will actually be the same like the flipping of the coin and the children. So this concept seems to be fairly simple but Mr. K will find a way to make this hard on the test. Which I hope will be soon so we can get a few days of review at the end of the year.


Auf Wiedersehen (See if answer tips can get that)

BoBiNg

Guten Tag,

Awesome test wooo! I am über-prepared for this puppy! Just going to do some of mista siwwy's links to make sure. Don't know why but I just completely grokked in fullness this unit. Though kinda disappointed that we lost our last review class for the exam. But that's why the blog exists and I'm sure that Mr.K will have all sorts of mathematical goodies posted for preparation for the exam. Well I wish everyone luck!

(P.S. Miles! Remember the VB.NET book!)

Conan O'Scribin

Hello everyone! Today Mr.K became one with the sword, he became samurai... Then with a dazzling display of speed, his beautifully forged, ancient.... meter stick, cut through the cone that was placed in front of Richard. With each slice glorious knowledge poured out! The horizontal slice yielded a circle. The slice on a slight angle gave us an ellipse. The slice with the more intense angle gave us a parabola. Then the vertical slice gave us a hyperbola.





Then we move onto this mess....



This all started with a piece of ordinary white paper...
The we drew a dot in the middle (horizontally) and a wee bit up from the bottom of the page...
We then proceeded to draw roughly 9 more dots on the bottom of the page spaced evenly, or about evenly...
They we folded the paper each time overlapping a different dot over our center dot...
Then we darkened the innermost line in respect to the middle dot that we created and guess what! It was a parabola....
We knew that doing a little bit of origami and coloring wasn't the point of this...
So we proceeded to name all the points...
We then plotted two more points, P and Q, and proceeded to draw a line perpendicular to the bottom edge of the paper going to each of the points....
Then we drew a line from the points to point F...
Measured and....
They were the same!....
We then drew a line straight down from F....
The two sections of that were also the same....
Starting to see a pattern?....
So we then learned a special name for these points on the parabola....
Locus points, "A set of points that follow a certain rule."....
These locus points follow the line of the parabola and this gives us the pattern that any point on the parabola can have two segments drawn from it, to the directrix and the focus (explained a lil' bit later) and those two segments will have the same length....
Here they are....
We found out that F stands for Focus, kinda related to the focal point in physics I'd assume...
Then we found out that the line the D's were on had a special name, the directrix....
So now that all those patterns had been pointed out we decided that we needed to find relationships between the coordinates of the points...
We found a bunch....
Vertex (h,k).....
P (x,y)....
D1 (x, k-p) because it has the same x-co as p and a y-co of the vertex's minus P...
Focus (h, k + p) because it has the same x-co as V and is located p units above V...
So now that we had all this information we embarked on setting a couple of lengths that had the same lengths equal to each other, I can't remember what the initial reasoning for doing that was but we ended up with the standard form for the equation of a parabola....
Then using the distance formula and simplifying we got our standard form, as shown below...





Well that's my scribe for the night....
Now to go study a bit for chem....
Then try to bring closer to completion Miles' and my comp. sci. project deep into the morning....
*sigh*....

Our next scribe will be.....

TIMMY!

How many ways can BOB be arranged so that....

So yet again a test looms before us.... We have all been armed with the knowledge to slay the mighty Kuropatwian test. We will go forth pencils loaded, lucky rabbit's foot in hand (but not a real rabbits foot, because that's cruel) and hope for the best as that beast of a paper rears it's cover before us. It's menacing gaze striking fear and anxiety into our hearts... then kindly asking us if we bobbed and wishes us luck. HA, luck, it is of no consequence for the questions seem to be anti-calculator and anti-luck. But as I vowed in the beginning I will slay the mighty test and after I will rise above it and triumphantly say.... *YIPPEE!* Then smile and go to comp. sci.

Well maybe not this test. Feel pretty good but there are so many little itty-bitty things that catch me everywhere.

Good luck all!

Grey-M

Grey-M's Flickr

Bobminton

Hello all, this unit has been easy and deadly hard at times. I have found most identities in this unit fairly easy to solve... spare a few. One thing that seems to get me is when the identities are simplified as far as they can and they are still long. Just end up going around in algebraic circles to come to the same conclusion. So I am feelin' fairly confident for the upcoming pretest and test. Though I am not looking forward to the Flickr assignment. Seems brutally hard to find something around us that has so many mathematical concepts pertaining to what we just learned. But hey, we have no say in this rubric so we'll just have to take it as-is.

>Bob<

Well I must say that this unit has been a smashing good time. That smart board is just a riot. Though I must say that with Mr. K's learning curve on that smart accompanied with the interruptions it seemed to me that we did have some wasted classes. But now that the curve has smoothed out a bit our learning is faster than ever as put our answers up, check and correct faster than ever and more visually than ever. So that leads me to my feelings about the unit and I feel pretty secure about it going into the test. One thing that I drilled into my mind after that quiz we had though is STRETCHES BEFORE TRANSLATIONS, STRETCHES BEFORE TRANSLATIONS, STRETCHES BEFORE TRANSLATIONS and if you are trying to find the original graph from some transformed version do it in the reverse order, translations then stretches. Now after doing a couple of the trigonometry problem solving questions I feel fairly confident about those as well. I wish everyone luck on the upcoming test!

BOB

Well I must say that most of the material that we have been covering in class I have been understanding (though the quizzes say otherwise). The proportional thinking has even helped me in other classes, namely g.12 chem. It makes for easier methods when it comes to the molarity problems. So I have already taken away useful information from this course. I am looking forward to the test actually to see if it is possible to overcome the "Curve Balls of Kuropatwa". It is my goal to ace one of those grueling, genius-spawned tests. I have gained much knowledge from the lessons and now that I look back on the earlier exercises I'm finding them a breeze. This is probably due to the group work in class which has been monumentally effective in my mind. All our minds working synergistically to solve problems shines much more effective light on the questions. All-in-all I'm looking forward to the test. I wish everyone luck. G'night.

Death By Triangle...

Well, I thought that since we only had the morning class today that there wouldn't be too much information for me to cover on the scribe post...

I was wrong...

Mr. K started the class with quick chat about net etiquette and not posting your last names or pics of yourself on the internet because "The internets memory is infinite". You may delete it yourself but it's not really gone. He said it had something to do with RSS and gave examples of how long forgotten original webpages of big sites can still be found in the internets infinite weave. Then people had problems with the homework so we went over those.

Question 11

Find the arc length of a bicycle wheel, given a radius of 24 inches and a central angle of 48 degrees.

The problem with this seemed to be how the answer sheet shows how to get the answer. Mr K expained that it uses a formula that we should completely disregard because their is a better method that is more powerful in solving problems, porportionality. He then showed how porpotions were used to derive that formula.

After that question number 10 was next on the list which served as the perfect segway into our lesson for the day.

Question 10

In what quadrant(s) is the point P(theta) if we know that:

a)cos(theta) is negative?

b)sin(theta) <> 0?

Starting that question he described the unit circle, which is a circle with a radius of 1.

P(theta) is where the angle and the circle meet and would be in a certain quadrant.

Remember:

Cast our CAST because proportional thinking is much more powerful.

Sine is a function of y.

Cosine is a function of x.

Tan is Sine/Cosine

Mr. K then challenged us to come up with side lengths from angles in the unit circle faster than him using our calculators. Of course it was fixed and he had knowledge that we did not. So he shared...

All the angles that he had chosen were 30 degrees away from the x-axis, these are called related angles. With these angles in the unit circle the ratio of the opposite arm of the triangle to the hypotnuse was 1:2, and will always be that because dilatation has no effect on that ratio. Through the pythagorean theorem you can then find the other arm to be the square root of 3.

The ratio of opposite arm to hypotnuse to adjacent arm is 1:2:sqr(3) then.

The next triangle we learned about was the one that got a man hurled off a cliff. The right angle isosceles triangle. The pythagoreans beleived intently that everything could be explained in nice neat whole number ratios. Then there was this triangle... Two sides of 1 and a hypotnuse of the square root of two, which is an irrational number, which completely goes against their beliefs. So they kept it a secret. As Mr. K said any good secret gets out and the person who let it out was killed. Then Pythagoras the leader of the religion met an untimely end in Athens when he would not run through a bean field to escape a couple of guards chasing him for escaping. Anyway back to the math of the triangle. We are taught to rationalize the denominator, so we do so when using sine and we end up with arm lengths of sqr(2)/2. While explaining these triangles he made this circle diagram similar to the one below.

The corner points on the unit circle are in gold. These show that the highest and lowest numbers for sine and cosine are 1 and -1.

I think I got most of what was in class today. The next scribe is...