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Tuesday, September 30, 2008

Working with Derivatives

Hello again everyone, tis I, Kristina, back for another scribe post! Today we had the wonderful Mrs. Karras as our sub for today, along for the next 3 days.

Anywho, we mostly worked with the formula of a derivative (slope of a tangent line). If you've forgotten what that formula was, here it is again:

While Mrs. Karras finished writing that up on the smartboard, someone asked to re-explore what a limit was. She reviewed it to us briefly, explaining that a limit basically means that something is approaching another without touching it. An example she gave us was that she could get as close to Paul and invade his personal space as much as she wanted but she couldn't technically sit right on top of him since there was basically no room to do so and such, also, he may have exploded =(

She also bestowed us the gift of notes as to what the derivative of a function is in more detail. Due to her not being able to post the slides with these notes on it till Thursday, I shall kindly post them here for anyone that missed it or was not quick enough to take them down.

"The derivative of a fcn (a gift she bestowed upon us, it is short for function) at a chosen input value describes the best linear approximation of the fcn near the x-value under consideration."

With the help of this graph (I forgot the arrows at the ends of the parabola xD), we can see that in this case "a" is the inputted value mentioned in the above note and the line is the linear approximation of the fcn near that inputted value, "a".

"For a fcn with a single real variable, the derivative at that point equals the slope of the tangent line of the graph."

Meaning that we can input that value into the derivative formula since the definition of a derivative is that it is the slope of a tangent line.

Wahoo, now for some examples she gave us!

In the first example, she gave us the function f(x) = 2x2 - 5x + 6. We were told to find f'(4). Solving this is as easy as bringing paper plates and cups for Pi Day (Yes, I'm thinking about it already). Back on track, all you have to do is input the value 4 into the derivative formula shown at the top of this post. If you're still lost, here is what it should look like as you work through the problem:

Tada! The derivative is 11 since as "h" approaches 0, it is shown that the value is close to 11 thus the answer. Simple algebra, right?! And since some people may make mistakes in their algebra during a question like this, here's a song to help you (I was bored so I decided to search "math" on imeem TEEHEE)

Kay, so it doesn't exactly help with the algebra...sorta, but I thought it was kinda neat so HA!

Back on track! The second example we got asked us to find the derivative of f(x) = x2 - 3x for a number "a". How we solve this is the exact same as the last example, except we are working with a variable, "a". Once solved, we should find out that the answer is:

Now, if we were given a question where it asks us to find the derivative f'(1) for the same function given in the last example, you can do it the long and tedious way (but not hard!) by using the same procedure as example 1, but you don't have to! This is because we've already found the derivative for f(x) = x2 - 3x earlier, which is 2a - 3. We can simply think of that as a function and then input 1 into that and voila! Simple and easy, also elegant.

For our last example, we were given the function f(x) = x2 and were asked to estimate the derivative at the points {-2, -1, 0, 1, 2}. First we must graph this. After you have graphed it, draw the tangent line to those points and then just take an estimate at what the slope of that tangent line is. To check your answer, just input the points into the derivative equation and that's that!

Now that that's out of the way, the next scribe is.. Not Paul.
Thanks for the confusing name, Paul :(. Oh and starting from page 100 up to 105 is review on some of the stuff I've talked about. Also, homework is on page 105. There are 8 questions but just do enough of them till you understand it. Anyways, I'm done for tonight. Have a nice day :)

Monday, September 29, 2008

Scribe List

Cycle 2

.:. J + ME .:.

Not Paul
Hi I'm Justus


Sadly, we've lost a few. :'(

Quote of the Cycle ;

"There is no such thing as good or evil...

...But thinking it makes it so."


Rence ~ Out

Deriving Derivatives Using a Derived Derivative

Today, a monday, a tiring monday, a monday that wasn't the same as last monday. Sorry this has nothing to do with Calculus. Okay back to class...

Remember when we were working with derivatives last week? We found the derivative of f(x) = x2 at the point where x=1. that could be found using the derivative definition found on previous slides. There are many ways to use this definition, some are more tedious than others but they should all arrive at the same answer. It is like Mr. K's analogy for using more force than necessary.

When you are going to hang up a painting. You need a nail in the wall, should you use the little hammer or should you use the sledge hammer. Common sense would tell us to use the little hammer, because the sledge hammer would blast a hole through the wall. So use the way that would save you time and effort for more tougher questions.

The easier way to find this is to plug the function and x = 1 into the definition and you get:

Picture courtesy of Sitmo

Now all you have to do is to simply the function. What you have to do is to get rid of the h in the denominator or else when you apply the limit, the equation will explode or be undefined. The answer will be 2 + h. so when you apply the limit, h will be so small towards zero that it will be seen as negligible and so the derivative will be 2.

After that little review we learned about locally linear points. Points can be called locally linear when you zoom into a point on your calculator and eventually it appears as a straight line. Take the graph of f(x)=|x2+1| for example:

Picture courtesy of

If you zoom into the point (2, 3) you will eventually find a straight line meaning that the point is locally linear. But if you zoom into any point where this function has a zero you will never find a line. You will only see a corner or a spiky spot. It will never be a line so it is not locally linear.

So that is what we did today in class. Homework is exercise 2.2 question numbers: 1, 2, 3, 5, 10a, 11, 12, 14, 15, 17. But remember if you do not feel comfortable with the subject just practice more. Everybody is more than welcome to do the entire exercise.

So the next scibe will be Kristina.
Good night...

Slides September 29th

Here they are ....

Sunday, September 28, 2008

September 26th

Hi! I'm Yi Nan. ^_^

On Friday, we continued on the unit of derivative function.(2.2)
First, we start with reviewing tangent lines.

Then we did the questions on page 84
instantaneous velocity (at t+a) :

\begin{figure} \begin{center} \<span class=

average velocity= distance traveled over time elapsed:

I didn't really get it so I don't really know how to explain it. Sorry!!!*_*

I think that's all we have done! So the next scribe will be Hai Yan!!!
Have a nice day!!

Friday, September 26, 2008

Slides September 26th

Here they are. Sorry about the long slide - I couldn't really see a good way to split it up. I'm open to suggestions ;-).

Thursday, September 25, 2008

September 25th

Today, we went over Chapter 1 Test: Functions and Graphs to correct together in class. And teacher said that the highest mark is 26, not sure....but nobody got zero!! Actually, no one got under 8, I luck for next time...

The next scribe is Yinan ...


Slides Test Answers September 25th

Here they are. Don't feel bad. This test was a brute.

Wednesday, September 24, 2008


Hey, this is Shelly here. At the start of class today Dr. Eviatar informed the class that we`ll be receiving our test on Functions and Graphs tomorrow, because she had to discuss a few thing with Mr. Kuropatwa and hopefully none of us will fail epically... Aside from that the class moot (my word of the day) about what is speed and how it is represented.

- A distance covered per unit time
- Change in postion depending on time

- Graph on a input-output (xy) grid
- Table of values (where theres a graph theres a T-table)
- Equation
- Symbolically

Input-output graph

Assuming that nothing is happening between the 2 labeled points calculate the speed using this equation:

Note: It can't be a ridiculously big gap. If it was, you will have a speed of 0 or a negative number.

To those who have forgotten
*The light red and blue are on the increasing side of the concave, making it positive, while the dark blue and maroonish red are on the decreasing side, making it negative*

When concave reaches its peak, in that duration nothing happens so velocity is equal to zero. (example: When Coyote chases Road Runner and runs off the edge of a cliff

Secant line: Average velocity over any interval is the slope of the lines joining the end points of the interval.

The secant line is use to calculate the average velocity for small amounts of time, which you also use to calculate the approximate instantaneous velocity.

Chapter 2: Exercise 2.1
Questions: 3, 5, 6, 9, 11, & 12

And for something not related to Calculus, here is a brain teaser!!

Random Oblivious Fun Logic (ROFL)
What is the pattern?
A _ _ _ E F _ H I _ K L M N _ _ _ _ _ T _ V W X Y Z
Note: The answer is not "the alphabet" and all letters has to be capital.

Here is a small hint to those who want it (It may not help though unless you think outside of the box)
If you have an answer post it in this post's comments!!

Finally the next scribe is..... YICONG!

Slides September 24th

Here they are ....

Tuesday, September 23, 2008

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

Monday, September 22, 2008

On changing bases and other things

Hi guys,

This guy is lip-synching to a great mathematician and musician known as Tom Lehrer. It is a funny video, but it is also quite helpful if you are having trouble visualising changing bases.

Functions and Graphs Pre-Test

We used the same pre-test as last year's. Here's the link to the answers (and explanations).

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 .:..

Sunday, September 21, 2008

Scribe List

Cycle 1

.:. J + ME .:.
le joséph

Not Paul
Hi I'm Justus


So, I thought I'd just post this, since we had a bit of confusion last time. :D

Quote of the Cycle ;

"In the beginning there was discovery. A confusion of elements. The first snowfall of impossible change. Old lives undone, left behind. Strange faces, made familiar. New nightmares, to challenge sleep. New friends, to feel safe with. Only then comes control. The need to impose order unto chaos, through determination, through study, through struggle. All in defiance of a thundering truth. They're here, and the earth shudders underfoot."


Heroes is on at 8pm on Channel 12! Don't miss it!

Rence ~ Out

Combining Functions

Hiya peoples! Here's my scribe post... at 1:51 AM Sunday morning... because I'm awesome... ANYWAYS... The stuff on my slides kinda shifted... why? I don't know. You tell me. Next scribe is Mr. 'Zeph'

Oh, since you can't click on the links in the slides, here they are:

AP Calculus Scribe 1
View SlideShare presentation or Upload your own.

Friday, September 19, 2008

Slides September 19

Here they are ...

September Eighteen Two Thousand Eight

Woo! No slides for me from today, but it's all great for I remember everything that happened today, woo! Even that weird stench (Did you guys smell that?), woo!

Okay I don't remember EVERYTHING Dr.Eviatar mentioned, (the beautiful assortment of her colorful vocabulary... are just way to colorful for me to comprehend) but I know she talked something about LOGARITHMS, woo!

Here's what I perceived:

Def'n Logarithm : A LOGARITHM IS AN EXPONENT (this was learned in the ultimate pre calculus 40s class which overshadowed all other pre cal 40s classes, you can find the ultimate blog right here:, woo!)


Def'n Logarithm: The inverse of exponentiation


Exponents interact differently with each other in different scenarios:

When exponents are being multiplied with each other, the exponents form a sum.

(b^x)(b^y) = b^(x+y)

Logarithms work the same way because A LOGARITHM IS AN EXPONENT

[log(x)][log(y)] = log(x+y)

When exponents are being divided with each other, the exponents form a difference.

(b^x) / (b^y) = b^(x-y)

Logarithms also work this way because A LOGARITHM IS AN EXPONENT

[log(x)] / [log(y)] = log(x-y)

When exponents are being exponentiated with each other, the exponents form a product.

(b^x)^y = b^(xy)

Of course Logarithms work this way too because... EVERYONE SAY IT WITH ME! Class says, "
A LOgshi...m AN mnj5ENT," exactly! How many times do I have to say it? Woo!

[log(x)]^y = (y)[log(x)]


That's everything I remember Dr.Eviatar reviewed with us, woo!
We were then told to do Exercise 1.7
This concludes my post. Till next time, Au Revoir!

- Le Joseph

(oh and I pick Not Paul! Woo! Come on down!)

Thursday, September 18, 2008

Domain and Range ... and a whole lot more

Thinking about you guys again when I learned this video was recently uploaded to YouTube. All stuff you really need to know:

Also, check out this fella's archive of videos for calculus students. When you get there, check out the first one. Also, if you ever have a really thorny problem he says he'll solve for you and make a video about it. Hmm ... that sounds like a good idea for a student assignment ... aren't you glad I'm on leave? ;-)

Wednesday, September 17, 2008

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:
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

Slides September 17

Here they are ...

Tuesday, September 16, 2008

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.

Monday, September 15, 2008

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".

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.

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....

Sunday, September 14, 2008

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.

Mr. K.

Thursday, September 11, 2008

Bench's Math Fun I Guess

Okay here is a lil math fun =)

Find the next 3 lines:

1 1
2 1
1 2 1 1
1 2 3 1

and so on...

If you know the answer post in the comments
Have fun =)

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.

Wednesday, September 10, 2008

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...


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


Tuesday, September 9, 2008

The 9th of September

Whoa! Well, the reason why I'm doing this post later than usual is because I forgot about it until now. I decided to start this post at 3pm right after my school, but I decided to wait for the slides to get published so I would of had something to work with. Now, seeing as the slides did not get published, I should have originally done the post at 3pm, instead of 11pm. Sorry class, I should not have waited!

Today in class we pretty much just recapped on functions and graphs from our gr. 12 pre-calculus year. We were given a box with a width of 8 - 2x, length of 11 - 2x, and a height of x. We were asked to find the volume of this block. Even though x is not given we can find the volume quite easily because volume is length multiplied by width and multiplied by height. When the values are input to the equation it should look similar to this : V = (x)(8-2x)(11-2x). We were asked to input this into our calculators as a graph and find the zeros. I found that this graph has one zero at a value of 5.5

Our next problem was a word problem: "Find the function for the max profit when selling golf balls prcied at $3 and costing 60 cents. At this price you can sell 1000 golf balls. Decrease price by 10 cents for each decrease you sell 50 more gold balls." The equation should look something like this: profit = (price - cost)(# sold), The value I wrote this in was in cents, so $3 would be 300 cents. the filled in equation should be profit = ((300 - 10x) - 60)(1000 + 50x) where 300 - 10x is the price, 60 is the cost and 1000 + 50x is the #sold. The value of "x" should be the amount of times the price of the gold balls is decreased by 10 cents. After a bit of solving it should for from this: ((300 - 10x) - 60)(1000 + 50x) to this: (240 - 10x)(1000 + 50x). When graphed it should look like an upside down parabola. To find the x- value you need to find the roots but solving for x in each bracket, and finding the average of the two root values, which is the axis of symmetry where x should equal 2. To find the max profit you must find the max point of this upside down parabold, which is the y-value of the vertex. Since x is found you can put that into the equation and solve. (240 - 2(2))(1000 + 50(2)). This should workout to the max profit being 242000 cents if you decrease the cost of the $3 golf balls by 10 cents twice, so 20 cents to be specific giving you $2.80 gold balls.

The last review question is of a box that Mrs. Ingram drew and only one given equation being: 4h + 8L = 6. We were asked to find the surface area of the box, and write it as a function of (L). So on a box there are 4 surfaces that are equal, and another 2 that are equal, for a total of 6 surfaces. The area of a surface would be length multiplied by width for each surface. For the 4 equal sides, it would be 4hL and for the 2 smaller sides it would be 2L^2. The equation should then look like SA(L) = 2(L^2) + 4hL. Well, that "4h" looks familiar. It looks like it cam from an equation which was given already:
4h + 8L = 6. By a bit of massaging you can change that equation into 4h = 6 - 8L and then input 6 - 8L in the surface area equation as 4h. The surface area equation should look like this: SA(L) = 2(L^2) + (6 - 8L)L with a bit of solving you can change it into SA(L) = -6(L^2) + 6L and you're done, because that's as simplified as it's going to get.
Toward the end of class we plotted f(x) graphs, they were pretty simple such as: f(x) = x and f(x) = x^3 and those other simple ones. Then we briefly sketched transformations using a square root function. We didn't get to indepth in the area, but I believe we will continue our review on this for tomarrows class. That was pretty much all we did in class today, so our next scribe will be:

- Rence

So long for now. -Francis

Monday, September 8, 2008

To my students ...


By the time you read this you will already have heard from Mrs. Ingram that I will be away from school for an extended period of time. 10 weeks to be exact. I'll be back on November 17.

On August 18 we had our fourth child, a little girl. Her name is Sadie. My wife and I discussed this a lot. As this is our last child, late last week we decided together that I would take a parental leave of absence.

I must admit I had very mixed feelings about taking the leave of absence. We began learning together and were off to a wonderful start with much hope and promise for the year ahead. That hasn't changed. You are all capable of being the person, learner, mathematician you imagine yourself to be.

I have always believed that anyone can learn math, even the most advanced math, as long as they see themselves as able to be successful. So much of your success, in school and in life, has to do with believing in yourself; having confidence in yourself. See yourself as a success and you will be successful; in this and in all things.

In my absence you will be learning from one of the finest teachers in our school, yet don't underestimate yourselves. You can also be the finest teachers of each other. Just making the effort to take on that role for each other will deepen your learning and make you better students. Many of you have been in my classes in the past. If you stop to think about it you'll realize that I did very little teaching myself. I turned it over to you to teach each other. You are your own best teachers. Continue to work together. Teach and support each other. And watch yourselves grow into the finest mathematicians in the school.

Mrs. Ingram is a wonderful teacher, I've worked with her for years, I know. Trust and lean on her, and each other, and you'll go far together. When I return to school in November I may or may not be teaching your class, but then again, I never did teach you. I just set you up to teach each other. You know how to do that. Now you can do it on your own; and you have one of the finest people I know to help you.

I'm going to spend the next little while just being a dad to my kids. I'm looking forward to seeing you all when I come back to school. You'll be surprised how fast 10 weeks fly by. In the meantime I'll be poking in on the blog to see how you're all doing.

Take care of each other. And learn hard.

Your Teacher,
Mr. K
Here's Round One of the scribe list:

Not Paul
Hi I'm Justus
le joseph
J + ME
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....


Friday, September 5, 2008

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)

Thursday, September 4, 2008

Today's Slides:September 4

Here they are ...

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!


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.

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! :]

Wednesday, September 3, 2008

A New Beginning

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline: Part 1 of 2, Part 2 of 2); for parents to find out "How Was School Today;" to share your knowledge with other students. Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, contribute to the conversation and lets get down to some serious blogging!

Here are the slides from today (your homework is on slide #33):

See you tomorrow.

Mr. K.