Hey bloggers! Its me, Shelly, here to blog again for this cycle, including my little ROFL corner. To start things off we have received handouts of the equation that we were working on Friday and had finished yesterday, but there was a problem, some people were a bit confused due to the long 4 day intermission we had and us continuing off were we had left off in the middle of the equation we were working on. So to clear things up we were given hand out that shows us how to solve the equation.

Hand out
page 1
page 2
page 3
page 4

As we head into something new, this handout of Algebraic Limit Rules is handy (which was given to us on Friday)

Limits and Functions
Suppose that limits



exist and let "c" be a constant

CMR (Constant multiple rule)
The limit of a constant times a function is the constant times the limit of the function

lim c f(x) = c lim f(x)

SR (Sum of Function Rule)
The limit of a sum is the sum of the limit

lim (f(x)+g(x)) = lim f(x) + lim g(x)

DR (Difference of Function Rule)
The limit of a difference is the difference of the limits

lim (f(x) - g(x)) - lim f(x) - lim g(x)

PR & QR (Product of Function and Quotient of Functions Rule)

PR: lim (f(x)g(x)) = (lim f(x))(lim g(x)) QR: lim (f(x)/g(x)) = lim f(x)/lim g(x)

Example 1:












Example 2:




















Example 3:















Note:

The limits are the same but the function itself is different, for
f(x) = (x²/x-1 - 1/x-1) there is a discontinuity at x = 1

For more examples similar to these one look at example 2 and 4 in the Algebraic Limit Rules booklet.
Example 2
Example 4

Homework: Exercise 2.7
1-9 (odd)
14-27 (odd)
and 24

And now it is time for the ROFL corner!
Since the last riddle was a tad difficult, I'll give you guys an easier one, which means that you won't need a hint for this one. ;D

How many times can you take 5 out of 25?

And if that one is too easy try this one! (Sorry!! I don't have a hint for this one!)

What belongs to you, but is mostly used by others?

Have fun!

Finally the next scribe will be...... Hi I'm Justice!

our test day... the mood was not exactly pleasantville :S

Hola... mi llamo Jamie. haha no. English. Today, was.. well a very rough day indeed. Our very first test day. I'm just going to speak for myself and say that I probably succeeded at failing epically. But that's just being pessimistic. You never know. But I think we handled it pretty well; and I'm assuming after the review unit of Functions and Graphs, that we are going to start a new chapter and do some real CALC!!!

While we're on the topic of books and chapters, I just really have to exploit this overrated phenomenon. I cannot resist. I have OCD [not obsessive compulsive, well maybe... but Obsessive Cullen Disorder.] It's and inside out joke for all us vampire conjuring souls out there. I myself have recently jumped on the bandwagon, and read through the series, at least once and now going for a second round before the movie comes out!!! Yeeeee! It's most likely going to ruin readers visions of everything, but it's going to be a distraction for the delay of the Harry Potter movie...... go ahead, call me a conformist and a copycat, but to be honest, these are some of the most recent books I have read like a normal person, and not through audiobook. [I have a bit of dyslexia in me, no joke.] I highly recommend the first one easily as the best, but for continuity's sake, finish the series... please. I'm ready for November. I'm ready for some TWILIGHT!!!

I just noticed that the date on this poster is wrong. In the meantime.. Halloween is coming.....When there's halloween...there's SAW.

I've just exploited so many things. I'm such a subliminal message. I'm ashamed. I pass the scribing stick to...Shelly! :D forgive me for the ads. just close the window just like any other pop up if it's bothering you. :D

Functions and Graphs Pre-Test

We used the same pre-test as last year's. Here's the link to the answers (and explanations).
http://apcalc07.blogspot.com/2007/09/scribe-oo-pre-test.html

Tim-Math-Y says: For Question 3b, we find that the domain is [o,6]. Sadly however, I cannot remember how.

zeph says: We can't have a domain that's less than 0 because it isn't possible for the flag to have a negative area. The largest possible value for the independent variable (the x-value) is 6 because the flag has a width of 6, that is, we can't have a width that's bigger than the flag.

Chapter 1: Functions and Graphs Test is tomorrow.

Next scribe is .:. J + ME .:..

Slides September 19

Here they are ...

AP Calculus Slides September 19

View SlideShare presentation or Upload your own. (tags: apcalc2008 functions and graphs)

Exponentially Exponentializing Exponential Functions Exponentially

Hey the Benchmeister here and this will be my first AP Calc post this year. Today we began on exponential functions if you haven't found that out from my title :P. Okay we were given a worksheet to work on during class. The worksheet can be found on today's slides (Just click on the slide to enlarge).

For exponential functions the y-intercept is represented by a in the form a * b^x. This is because the x-coordinate of any function is 0 (zer0). So by substituting 0 for x, b will be 1 because any base to the exponent of 0 will be 1. Thus leaving us with a. In the worksheet a term called the growth factor is used. The growth factor is the common ratio between the outputs. For example what common factor do you have to multiply the previous output to get the next output. The growth factor is represented by b in the form above.

We then moved onto the next unit: Inverse Functions. The following link will show Mr. K's way of explaining Inverse Functions:
[CLICK HERE]
Well an inverse function is a function that undid what the original function did. If the original function was y = x - 1. Then the inverse would be found by switching the x and y around getting x = y - 1. Then just solve for y and you get the inverse. Also for an inverse all the ordered pairs of a function are switched. In a graphical view, the inverse of a function is the original function reflected over the line y=x.

Well that's all. Homework is Chapter 1.6, odd questions between 1-9 (including 9). But by the looks of it all of them are doable. :D

The next scribe will be le joséph.

This is your local cuddle monster logging off.

And if you haven't tried solving my math fun CLICK HERE

Limits / Compound Interest

Sooo todays class started off with Dr. Eviator introducing us to her physicist/teacher friend who'll be filling in for her on days when she'll be absent later on.

The main things we did today were mostly some review on compound interest, logarithms, and limits. To explain limits, Dr. Eviator used compound interest as an example. The formula for compound interest is A(t)=P(1+r/n)^nt. To make things simpler the variables r, t, and p = 1, the formula will now look like A(t)= (1+1/n)ⁿ. We found out that the more times the money is compounded the higher the interest will be. However there is a limit. After compounding more than 20,000 times, interest will not get bigger but instead decrease.

The rest of the class time was used to solve questions from the exercise books. Ha and Dr. Eviator was disappointed in the book because of how they solved a question with too much calculator graphing work :( and that's all i remember. NEXT SCRIBE IS BENCHMEN.

September 15, 2008

Hello everyone, its Kristina with today's scribe post. Today we found out at the beginning of the class that we were behind in our studies since we were supposed to be halfway through chapter 1 but were not! After finding this out and a little bit of chit chat, Ms. E (I don't know how to spell her name, sorry =( ) told us to work on Exercise 1.4 in the book which was on Exponential Functions. Yes, more review stuff that we should already know.

To help jog your memory about Exponential Functions, here's a link from our blog last year that leads to the page with all the posts tagged with "Exponential Functions".
http://pc40sw08.blogspot.com/search/label/Exponential%20Functions

Also, while I'm at it, here's another link leading towards the page with all posts tagged with "Exponents and Logarithms" since some of the stuff in Exercise 1.4 deals with some of the things in that area.
http://pc40sw08.blogspot.com/search/label/Exponents%20and%20Logarithms

Well then, that is all for today. Next scribe is Joyce. No hard feelings since I put your name in red okay? There's no deep meaning to it =).

September 12, 2008

During Friday's class we reviewed some more on functions and graphs. The teacher helped us by going over some questions in Exercise 1.3. We also read some of the text in Chapter 1 - Functions and Graphs 1.3. Other than that, it was just review.

The next scribe is Kristina....

Trig Review Video

I know you folks won't really be reviewing trigonometry until late this week or sometime next week but I thought I'd share this with you now anyway.

The video is about 15 minutes long, the speaker isn't the most compelling speaker around but he does a real good job of touching on much of the trig you'll need in this course. What you might find most valuable about this video is the archive of videos by the authour: midnighttutor, he regularly publishes calculus problems with detailed solutions on YouTube.



Cheers!
Mr. K.

September 11, 2008

Today in class we received some notification as to what will be happening for the rest of the year. Apparently Mrs. Ingram will no longer be teaching us, which is very sad, but on the other hand Mr. Kuropatwa is going to be returning in approximately 10 weeks time and he will be once again be teaching our class. For the mean while, we will be learning from a substitute teacher, Dr. Eviatar.

Moving on, basically we once again had a work period. We are now on exercise 1.3, which is just another review of the past concepts we have already learned. If you have forgotten any of this there is a section prior to the exercise that you can read, explaining everything that you would need to know.

Oh & the next scribe is Haiyan.

Functions and Graphs Review

So, basically today was another review day. So as usual with our five minutes of chaos in class, Mrs. Ingram had us working in our text books right away, on exercise 1.2... and that's what we did for the rest of the day.


So that leaves me with the job of naming the next scribe and it shall be...

Kimberley.

No hard feelings or anything, you were just in the way >=D. (Outside joke)


-Rence

Hey guys, I'm Not Paul, formerly known as Paul, and I'm scribing today's class of September 8th 2008.

So today something amazingly confusing happened that I'll never forget.


I entered the room and was greeted by Not Kuropatwa, formerly known as Mrs. Ingram. Apparently something had come up with Mr. K and Mrs. Ingram had to take over!!11 ZOMG, AMIRITE!?

I know.

Anyway, Mrs. Ingram will be teaching the class instead, and Mr. K will return in November to teach Mrs. Ingram's classes.

After that whole big thing (announcement), we searched for some sort of lesson for the class. Everyone was handed textbooks and we started working on the exercises in the book (Exercise 1 - Odd numbered questions + #4) until the end of class.

And that's what happened today.

And the next scribe is....

Francis

September 5 2008

Today's class went by pretty smoothly. most of us use this math class to catch up on school some of us used it to catch of with their friends and some of us played chess it was a fun class today but to bad it had to end so soon

Rguy out

PS the next scribe will be not Paul(Paul)

Today's Slides:September 4

Here they are ...

AP Calculus September 4, 2008

View SlideShare presentation or Upload your own. (tags: apcalc2008 calculus)

Ahhh So Here We Go Again D:

Alrighty, another year, another grade level and thus another set of scribe posts. For some reason (In retrospect I cant really think of what it is) I decided to VOLUNTEER (yes you read that correctly) to be the first scribe poster. So far it isn't working out so bad for me, but we'll see if I still feel the same way in 20 minutes ;]

Anyways off we go!

SCRIBE POST NUMBER 1
UNIT: FUNCTIONS AND GRAPHS (again?)

After our initial half hour time wasting but still enriching talk, we got into the math portion of the period, which happened to begin with a task,(a task I remember from last year, when I was in calculus a whole 40s precal credit too early, thanks to the magic of computer generated schedules. Thats another story however.)

This task went exactly along the lines of, "Talk to your classmates. Make a list of everything you know about a function; from the definition to specific features or characteristics they may have." Now if you dont believe me that thats what our task was, you can check the slides for yourself, the info would be on the one with the graphical heart.

Now, my original plan was to type out everything Mr.K was saying after we had gone up and written our ideas, but he was talking to fast and I couldn't copy it down. So instead, I'll copy what I have, and I'll pull up a couple definitions for everyone mmkay? K sounds good :]

So, away we go with functions and everything relating!

• Quadratic functions
• Functions pass the vertical line test. This is because functions may be, "Many to 1" or, "1 to 1", but not "1 to many" or "many to many"
• Functions may be expressed as a table of values (I believe Mr.K said this was the numerical representation
• A vertical parabola is an example of a function
• Functions have a domain and a range where, the domain is, "All permissible independent values (inputs) of the function" and the range is, "All permissible dependent values (outputs) of the function."
• Sine, Cosine, and Tangent are examples of functions
• Functions may be expressed as an equation (I believe this was symbolically according to Mr.K)
• The Roots of a function are where the function meets the x-axis
• There are odd and even functions
• A parabola may be represented as, y-k = 4p(x-h)² if it is vertical and as x-h = 4p(y-k)² if it is horizontal
• Functions may have Horizontal and/or vertical asymptotes
• Only 1 to 1 functions are invertible
• Logarithmic functions are another kind of...function.
• f(x) = AsinB(x-C)+D where A is the amplitude, B/2P is the period, C is the phase shift, and D is vertical shift.

As promised, heres a couple links for your functiony goodness and viewing pleasure, assuming you would like some more definitions or memory jogging.

http://en.wikipedia.org/wiki/Function_(mathematics)

All posts from our old blog with the keyword "functions"

What was written by other people (some of which is here as I copied them into my own notes while we went along.) may be found on slides 2,3 and 4. I will post the slides directly into this scribe post later, as I'm typing it on a macbook, and its being a bit wonky and giving me issues with right click and things. I'll fix it up once my mom gets here with the pc -_-; Anyways moving onward. *Edit* Okay! Pictures! Heres the slides I was talking about in the earlier paragraph :]







After the collaboration of minds to create our almost exhaustive lists of things characteristic (or not) of a function, we began to get into a review of describing functions.

As seen on the slides (again I will post this image shortly, I apologize for any inconvenience this may cause you ._.;)

This review started with the table of values seen on the slide (Number 6 that is), and the questions beside it. It was at this point that Mr.K revealed one of his goals here, to get us using our calculators so well we cold , "make them sing."

In the interest of making your calculator sing, he told us how to graph that table of values shown on the slide.

The first step to doing this is to hit the, "stat" button on your calculator, followed immediately by hitting enter. This should bring you to a screen which allows you to input values into a table.



Column "L1" is for your independent variables, while "L2" is for your dependent variables. After you've input the values, hit 2nd y=, and then enter again, and then zoom stat (or the number 9 followed by enter to select). If you've done all this correctly you should have a graph, based on the values you've input! Whewhew!



So lets re-cap, the steps are,

Stat-> Enter -> Then, input all the values from the table.
part 2
2nd y= -> Enter -> Zoom Stat (9).

Voila! You now have graph!

Okay, I think thats everything that happened this morning in class, so I'm going to go ahead and dub scribe status on Mr. Richard, since he said it was all good. Again I'm sorry about the images being late, but they should be up shortly :)

Alrighty, Justus out! :]