BIP: bob in peace...

My last bob.... Some what happy but sad too, ill have nothing to complain about anymore. This last unit on sequences was pretty fast. I'm not sure this was the easiest one, it was just interesting. Not much i can really say about it. it's just about figuring out the formula and substituting everything in the right place, BUT I'M NOT SAYING IT'S EASY! Anyhow, i feel i got the main concept of this unit. Hopefully i can make this my best test so far but, good luck to everyone on this last test AND ON THE EXAM IN 7 DAYS hope everyone passes the course.

BBOOOOO for BOB

So apparently we have a test on Monday ... wasn't in class on Friday unfortunately for the quiz. This unit that people call "probability".. is the story of school life. This is the unit i dread every year. This unit Probability was so difficult, hands down this has to be the hardest unit . I honestly wish we had like an extra week so i can actually take the time to understand this unit a bit more, i know for sure this is going to be my worse unit yet.
But, for everyone else Good Luck because i know you'll all need it just as much as i will.

BOBing (Can't think of anymore names right now i'm so tired)

This unit was super fast (which could end up to be a good thing or a bad thing...i would say bad) it felt like we spent maybe 4 classes max.
Otherwise this unit was pretty good understood most stuff because it was somewhat similar to what we did in Grade 11. Love the fact that there's actually formulas to follow and memorize, not like counting. The only thing that I'm not liking about this unit it is the last part where Mr.K started applying it to real life things in those problem solving format, i found those pretty difficult, i either was over thinking it or not thinking at all.
I'm actually almost very tempted to say this unit was relatively ....easy! Almost seems to good to be true(it's a trick), but i know Mr.K is gonna shove those words down my throat eat them and choke on them when we get the test.

Bob The Snob

Hello everyone and good morning just getting back from work...This unit...was wow one of the hardest for me because you actually have to think and theres not really any formula to do the questions, (almost like probability) FYI: i HATE probability. But yeah, this unit somewhat frustrates me because there's very easy questions and there very hard questions and because everything in math is usually a trick =( its very easy to over think the question because you think ts too easy to be true. and Mr. K kept stressing to do all our homework and the unit would be easy ...well i did all mine except for 2 exercises that I'm doing now... and some of the stuff is still very hard especially the binomial theorem. I think that's enough complaining for on unit.

Good Luck everyone because I'm sure we are all going to need it!!!!!

Scribe

So... I guess tomorrows scribe will be Samantha because i don't know who else...UNLESS SOMEONE ELSE WANTS TO VOLUNTEER TOMORROW...if not...Have a good night (for the second time) and good morning if you read this tomorrow.

The Day our Minds were Blown...(swish)

Hello everyone, my name is Kadeem and i was chosen to be the scribe for today by Patrick ( =0... that's my shocked and angry face). And I'm going to work tonight so i don't have very much time so i will start this, go to work, come back and finish.

First, Mr. K promised and reassured us that he was going to blow our minds and show us one way the universe was built, but before that he explained the meaning of "Tedious" to Jojo and whoever else that didn't know the meaning.
Tedious: Tiresome by reason of length, slowness, or dullness; boring.


Binomial Theorem

Mr. K told us to expand and simplify the following:
(a+b)⁰
(a+b)¹
(a+b)²
(a+b)³
(a+b)⁴
(a+b)⁵
(a+b)⁶


After solving the first 5 questions simply using the FOIL method or the short way, he then showed us the PASCAL's Triangle...













The pattern is shown in the red arrows/lines, you must find the sum of the two numbers in the previous row to get the numbers in the next row.

Okay, not watch this carefully...

In this slide you can see the the Pascal's triangle in just basic binomials being raised to an exponent. That is only one of the many patterns in these binomials that make it a lot easier to solve Rather than going through the whole FOIL thing.

Patterns in...
The Coefficient: Adding the two coefficients from the row above.(seen in the Pascal's Triangle)
A: Decreasing by (a ^{n - 1} ), (a ^{n - 2} ), (a ^{n - 3} )...
B: Increasing by (b ^{n + 1} ), (b ^{n + 2} ), (b ^{n + 3} )...

Later on, Mr. K gave us the same triangle and told us to find patterns in the triangle , and we found a number of different ones:
Regular counting numbers
The Sum of Counting numbers a.k.a. "triangular numbers"
Sum of Triangular numbers
powers of 11

Fibonacci Sequence

Leonardo Fibonacci was an French/Italian mathematician...More Info.

the sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... (you get the next number by finding the sum of the two previous numbers). As you can see this sequence appears in Pascal's Triangle and in a lot of the natural living things on earth such as plants, bee's, flowers, even in a Leonardo Da Vinci painting. He was also explaining how "Phi" was in the sequence and how it's in everything from 4x6 pictures and our body's to what we consider beautiful, and then the bell rang...

The next scribe will be....

i haven't decided yet i will get back to you... Good Nite!

BOB Marley

This is our third unit Exponents and Logs, yeah, not very easy. Well it started off easy when we were doing all the simple stuff, and it feels like we just ran right though all the complicated things. So it's like i get it, but i dont really understand it. Just wish i had more time or help to understand it fully, but no time for that TEST IS TOMORROW.

G00d LucK Every0n3!

BOBby Brown

So we are wrapping up our second unit on TRANSFORMATIONS. Overall it was bad because it was all pretty much graphing, and as some of yous might know i despise anything thats has to do with graphing. Doing alot of this graphing though is helping furthure my understanding of the whole concept.

The first half of the unit was pretty straight forward learning such things as ƒ(x) = aƒ(bx) controls the vertical stretch and compressions of a function. Also learning how to graph reflections and inverse functions: (x,y) (y,x). And even and odd functions. The only thing i had a alittle trouble with was the whole STRETCHES BEFORE TRANSLATIONS &or MULTIPLYING BEFORE ADDING/SUBTRACTING, but i think i got it now :).

Now the reciprocal functions was a tab bit more difficult, and learning some new things like invariant points and absolute value functions.
And everything was fine and fanastic, until....we got to Trigonometric Modeling which is pretty much putting everything we learned all together into to one big, long question that takes like 30 minutes to complete, having some trouble but i will eventually get the hang of it. Could really use another extra day, but overall this unit had its ups and downs.

!!!Good Luck Everyone!!!

The Time Has Come...

Yes everyone, the time has come. im finally blogging ( for the first time in my entire life). Since grade 10 i've always been able to just avoid doing this blogging thing, but, not this semester. So please be nice if it's awful. Oh yeah the scribe for tomorrow will be...


...anounced after my scribe


Morning Class:
Our class started off without me there unfortunately, but none the less it went on anyway :'(. Mr. K and the rest of the class was praising Chris' amazing scribe, ( thanks for setting the bar really high for the people who have never done a scribe before). Also Danny had been choosen to be scribe for the day, and i heard he was crying. luckily KADEEM SAVES THE DAY! and arrives late, after Sandy and Albert, but prior to Miles.

Back to business. Mr. K started us off with 10 questions, with the first 5 we were given a function y=f(x) and a point on the graph (-2.-3) and told to find the coordinates of it's image on the graph.So basically what your doing is finding the X or Y coordinates using f(x).

Here's a few examples:
y=f(x) + 2 --> shows this function being translated up 2 units, so the original point (-2,-3) is moved up 2 units, giving us a new point at (-2,-1)

y= f(x+3) --> shows the function being shifted to 3 units to the left (8)"to the left, to the left"(8). Ha ha. so you use the point (-2,-3) // (x,y) and put it int he function giving us the point (-5,-3)

If your not understanding that lets just put it this way:

***REMEMBER STRETCHES BEFORE TRANSLATIONS***

OK let's say the original value was (-2, -3) for example. Ha ha ha. First you add the X value to the coordinate than you do the same to the Y value and you get your answer. Remember ADBC. (Stretch, translation, stretch, translation). First you check if f(x) has any stretches and multiply accordingly, then you add/subtract to figure out the location of the x/y coordinate.



The next set of questions Mr. K assigned we were given the final point of the functions prior and told to find the original function.

For example:

Function: y=f(x+3) Final Coordinate: (-3,7) Original Coordinate: (0,7)

When your trying to figure out what the original coordinates were, first of all you have to add/subtract the stretches or else the answer will be wrong, then you multiply/divide to figure out what the original coordinates are. For example if you have the coordinates (3, -2) and are using y= f(2 ( (x+1) + 2 you first have to use translations to find the X and Y values before the stretches, in this example that would be (4, 0) and then you use stretches dividing/multiplying to figure out what the final value is which is (2, 0).

The Next thing we learned was:

Even and Odd Functions

Even Functions

A function is "even" its graph is symmetrical about the origin
or
IFF (If and only if) ( f(-x) = f(x) )

f(x) = x²
f(-x) = (-x)²
f(-x) = x²
Since f(-x) = f(x) the function is even

Odd Functions

A function is odd if you are able to rotate it 180 degrees and it would be the same graph
or
IFF f(-x) = -f(x)

ex.
f(x) = x³ - x
f(-x) = (-x)³ - (-x)
f(x) = -x³ + x
Not an even function

-f(x) = -(-x³ - x)
-f(x) = x³ + x
Since f(-x) = -f(x) the function is ODD!


There is a few more examples of these even and odd examples in Mr. K's slide posted today and in our exercise ( go over them and practice it). So that's was the end of our morning class... all i can remember was my head spinning.


Afternoon Class:
The afternoon class, i knew what was expected of this class already since Mr. K said he would be leaving half way through the class, but not until he taught us this reciprocal thing, and you know what that meant (rush and cram) but fun, and this is what we learned:

We found the reciprocals of the following numbers:

DOCTOR SUESS' PRE CALCULUS CLASS
1 2 4 10 100 1000 1000000 0.5 0.25 0.1 0.01 0.0001 0.0000001
then we found the reciprocals of...
-1 -2 -4 -10 -100 -1000 -1000000 -0.5 -0.25 -0.1 -0.01 -0.0001 -0.0000001

And because Mr. K always reminds us that mathematics is the sign of patterns, we observed the following:

• As the positive numbers got bigger their reciprocals got smaller, and as the numbers got smaller their reciprocals got bigger
  
• As the numbers were "biggering negatively" their reciprocals were "smallering negatively" and as the numbers were "smallering negatively" their reciprocals were "biggering negatively"

The Graph shown above is (x+2) and its reciprocal 1/(x+2)
the purple circles indicate the invariant points. The invariant points are points that don't move on the graph,the points where the function and its reciprocal meet/touch.
As you can see if the function is biggering negatively, the reciprocal is smallering negatively and vice-verse.

And last but not least how to draw the reciprocal when you know the function already, you can see it here.

So all though we've come, to the end of the road, i am so very excited to let go. I'm sorry my scribe went up so late this honestly was the hardest thing I've ever done and it's still pretty bad because i am now half asleep haven't even gotten to study for my AP Chemistry test tomorrow. With that said, tomorrows scribe will be...

Lauressa Lauressa LauressaLauressa Lauressa Lauressa Lauressa Lauressa Lauressa Lauressa Lauressa Lauressa asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL

I know the anticipation is making you anxious!

Hey everyone,

I know is looking forward to my horrible first scribe (not really), BUT your just going to have to wait one more dreadful day for it, ha ha. Okay that's all i wanted to say. Enjoy the rest your Sunday.

BOB

Well, i came into this AP Pre-Cal class expecting the worse from hearing all the comments from past/former students. Unfortunately it's not half as bad as i was being told. Saying that, its only been the first 2 weeks of this course. Our first unit, Circular Functions started off alright, until we were given the angle measures and exact values in a unit circle i told to memorize it, surprisingly i did that and it also happen to be the easiest thing of the whole unit. Most of everything in this unit was review except for converting and obvisouly the radians. The hardest thing for me would of had to been the "GRAPHING", though that's nothing new never really understood it.
as for how well i think I'm going to do on the test, we can just say I'm not very good when it comes to anything that goes by the names of: Test, Exam, or Quiz.
P.S.
Good luck to everyone... (spiritually)