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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Thursday, September 29, 2005

Blogging On ... Blogging On Blogging!

( ^_^ ) Get it?! haha.

I guess it's about time to put some humor on this since we do have an audience. Hope everyone's enjoying it btw!

Here's my blog so I can put that "yes" on the first question on the page:

Probably everyone in the class knows, that I'm one of the people taking both Calculus and Pre-Cal 40S. I have to admit, that I was very intimidated, at first, as the first few weeks of calculus have started. For one, my summer was so full of memories that my mathematical knowledge somehow slipped away :S (very bad, I know). Second, everything seemed so new to me that my brain was crammed with so much new information each day. It's pretty hard to learn all these new terms such as logarithms when, pretty much, it's review for most of the people in the class. For example, logarithms. Last night, I remember doing my homework and attempted to catch up on some homework since my book went missing. I was doing the section on logarithms. The first couple of questions were pretty easy, but when I came to questions with the words "log" or "ln" everything became much more confusing. I kept telling myself, "A LOGARITHM IS AN EXPONENT!" But afterwards I told myself, "O.k. .... then what?!" (Now I feel like Mr. K, cramming that phrase into your head). I remember reading over the introduction a couple times but, based on my VARK test, I'm not that kind of learner. The next morning, I asked Mr.K for some help during lunch and of course, he agreed. I came right after third period and got ready to learn about logs. By the end of lunch, I finally understood it! *bows down* (Thanks Mr. K!) What helped me with logs are these properties:


1. logb(xy) = logbx + logby
2. logb(x/y) = logbx - logby
3.logbxr = rlogbx

(Note: They're very helpful- trust me)

Maybe some of you didn't know this, but I was this close: → ← (see the space?) to dropping out the course :S. I found it hard and difficult to put all this new information in my head in such a short period of time. I guess I just wanted to give up and my brain was still in "summer mode". I really don't like giving up on anything that I know i could do. It's getting much easier though and a lot more helpful for pre-cal. I learn something new in calculus class and when I go to pre-cal, I'm learning the exact same thing, but more thoroughly! Unfortuanetly, it probably won't be like this the entire year, but I'm ready! So in conclusion, I'm staying in calculus!
I guess that wraps everything up for my blog.
-me :)






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Scribe

Today in class, we discussed about the graphing of trig. functions, more specifically, sine and cosine functions. There were examples on the board that we copied and tried to answer. The basic form for a sin function looks like this:

f(x)= A (sin or cos) B(x-C)+D

A represents the amplitude of the function.
B helps tell you the period of the curve.
C is the phase shift (moves the function left or right).
D is the vertical shift and is the sinusoidal axis.

The one problem with graphing the function is B because you have to solve for the period.

Period = 2π/B

If you know B, and want to know the period just use the formula below.

B = 2π/P

When graphing the sine or cosine function, remember DABC. The order of the letters when graphing are D, A, B, and C, hence DABC. How you label the x-axis is important because you can label it π/2, π, etc. or you can label it 1, 2, 3, etc. No matter what you need at least four increments along the x-axis.

That's about it.
Next scribe is ... Prince.



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1000 Words

I love pictures! This applet will show you pictures of what sine, cosine, tangent, secant, cosecant and cotangent represent on a graph. Very cool! Play with it and we'll talk about it in class tomorrow.

BTW, do you know what they call a man who goes south for the winter?

A trig function! No, they call him a Tan Gent. ;-)

What does that picture have to do with this joke?



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Wednesday, September 28, 2005

Test b-LOG

Symbolically, Graphically, and Numerically. Everything we’ve learned from this point on forward has been showed to us in different perspectives. Before I always relied on my graphing calculator on showing me how the function looks like. Like a block of wood. It has 3 different sides. A function isn’t a function when its only represented in one perspective. To give us a mental picture and a better understanding of the function, we need to look at it symbolically (it’s equation), graphically (drawn in a Cartesian plane), and numerically (table of values).

In pre-cal 40, I always had problem with logarithms. The simple statement “A log is an exponent”, was never really planted into my head. I hated logs. I always thought it was something more complicated. All along, one of the units that always took me a long time to work on, is nothing but JUST an EXPONENT. A big shocker. The natural log function, or the ln function, I was never really taught how to use it in pre-cal 40. How we could just plug it in and apply basic rules of logarithm in the equation. It made things more clear to me and a lot easier. How it could be applied on solving unknown exponents.
i.e. Solve for x.


So for those who has problems with logarithms. Some teachers don’t stress this enough, and I shall do it in my test blog…


“A LOGARITHM IS AN EXPONENT.”

Always remember that. If you ever get stuck on a log problem, its probably because you’re forgetting what a log is. “IT IS AN EXPONENT.” Never forget it.

Hope this gets me my one mark. =D




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SCRIBE



In today's class, we had a review class about inverse function, how to find composition functions from f(x) and g(x) . And we talked about the unit circle and the function f(x)=AsinB(X-C)+D

How to find a composition function,
Example: f(x)=x^2-1, g(x)=sinx, find h(x)=((fog)(x) o (gof)(x))
(fog)(x)=(sinx)^2 -1
or =(sinx+1)(sinx-1)

(gof)(x)=sin(x^2-1)
=sinx^2-sinx

h(x)=((sin(sinx^2-sinx))^2-1

we talked about the Unit Circle, how to find x-corrdinate and y-corrdinate in four quadrants for those special radius, like pai/6, pai/4, pai/3, and their relative radius in quadrand 2, 3, or 4. see the diagram above,( Sorry, it's too dark; ).

And last we talked about the function F(x)= AsinB(X-C)+D
D means shift graph up or down D units ;
A changes the maximun or minimum points of the graph; sign of A means flip the graph of
x-axis or not;
B is effect the input of the graph, it can change the line section chief which arrives the apex.
C mean shift graph left or right C units.
And that'a all for today!




And next scribe is Steve!;)



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Tuesday, September 27, 2005

sKribe

Greetings of Peace!!! Our class started with a review of even and odd functions. Firstly, the name odd and even was associated with the exponent's value. A function is said to be odd because odd function includes only odd powers and said to be even because even function includes only even powers. The formal definition of an even function was f(-x)=f(x) and the odd function was f(-x)=-f(x). You substitute -x whether the function is odd, even or neither. What this means is that if you substitute a -x to a function, if you get the same function that you started with then it is even and if you get its' inverse then it is an odd and if you get completely different then it is neither. Graphically, it is said that an even function symmetrical with respect to the y-axis(meaning its' graph does not change after reflecting in the y axis.) and an odd function is symmetrical with respect to the origin(meaning its' graph is unchanged after 180 degree rotation about the origin).

Next is we talk about how to get inverses of function.We learned about a new concept of how to get the inverse of a function. Composing a function to its' inverse will give you x. It is the same thing with reversing the x and the y in the algebraic method. It's just different on how you look at it. Instead of using y we just used the inverse of f(x) and solve for it. Well that is it for now. Until next time.

The next scribe is...
Xun:D




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Monday, September 26, 2005

Glenney's Scribe-aler


^(Get it? Scribe-aler... scribbler?... not very funny I guess? hey, at least I tried :P)

This morning was better than it usually is. With more enthusiasm and energy, this year's going to be pretty good. I guess everyone's getting a lot more used to each other and it's not so quiet whenever Mr. K asks us if we get what he's saying. The morning started off with our usual challenging problems that sometimes makes us think until our head hurts :S. As soon as we all talk about the problems the first thing Mr. K always says:

"A LOGARITHM IS AN EXPONENT!"
Remember that :)
Mr. K's trying to plant that in our heads for the rest of lives! It'll be worth it though in the future. In university, the prof's going to ask what is a logarithm and you'll stand up, and say.. "A logarithm is an exponent!"
After a very interesting list of mascots, we finally made our decision with "The Prince of Calculand" featuring our very own Prince. I guess I'll be one of the first to say congrats! haha. It was pretty much a unanimous decision and I think our story plot's going to be very interesting.
Back on track with the problems, we learned that sometimes an extraneous root may appear. With this showing up, we had to remember to always check if our answer can fit the equation properly. In this case, -10 or any other negative number cannot be true because any number to any exponent cannot equal a negative number. The number must be positive and cannot equal 0 or be a negative number.
Near the end of class, we learned about the graph: f(x)=1/x and how it never touches the x or y axis'. No matter what number you substitute for x, whether it be a fraction or a large number, it'll never touch.
I guess this wraps up my daily blog, see you all tomorrow :)
Up next... Jay :D



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Spikes and Spears

To refresh or enhance your understanding of rational functions I'd like you to work through the activities in this lab called "Spikes and Spears". Spikes are the vertical asymptotes and spears are the horizontal (or slant) asymptotes of rational functions.

Have fun with it!



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Sunday, September 25, 2005

Blogging Logs and Exponents

One of the hardest things that I have found in this unit is logs, more specifically when you have a log in the exponent.

x^(ln x) = e^100

When you solve a power where there is a log in the exponent, if the base of the log in the exponent is the same as the base of the power itself, then the solution is easy. But when you don't know the base, then it's not as easy.

x^ln x = e^100
ln (x^ln x) = ln(e^100)
(ln x)^2 = 100
(ln x)^2 -100 = 0
(ln x -10)(ln x +10) = 0
ln x = +/-10
x = e^-10 x = e^10

This is an example of one of the problems we in class but it helped me learn how to deal with solving equations with logs and exponents better. I found this to be tough at first, but once we started working on it in class, it got easier and now I finally understand it. My moment of clarity came when Mr. K showed us a less complex example using base 2, seeing something you're so used to just got me over the hump, it feels good to get over the hump. An exponent is a log!

(this is my blog for the unit)



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Our Readership

I thought you might be interested to know about our readership. Our blog is being read by people all over the world. The graphic below shows where the last 88 visitors to our site have come from. Of course, this is constantly changing as more and more different people pop in to see what we're doing. While some of them visit only once a number of them do keep coming back. (The "unlisted" reader is from Belgium.) People are interested in what you have to say and what you are learning.

Ladies and gentlemen, you have an audience. It's worth your while to make a good impression by making sure your spelling and grammar are correct when you post. ;-)




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Friday, September 23, 2005

Scriber Blogs

Another day in Calculus, where we sat and did problems from up the board. No that’s not all or what we did today. There was actually only one problem up on the board today =D. And today I believe was actually quite fun. Everyone threw out their ideas when we were brainstorming for our year story. I liked every idea that was up on that board. I could already tell that this year’s story will be great and something that would make us laugh looking back on it. Like what last year’s story does to me. So the ideas we all came up with were: The Knights of the 360 degrees table, 9 Something, Star Wars Calculus, Pirates and the 9 C’s, Superman (Superheroes), The CalcuFamily (CalcuMan, CalcuLady, CalcuBaby), Dr. Seuss, Snow White and 9 Dwarves and Handsome Princess, and Prince of CalcuLand. (I’m in favour for the latter idea ;) and of course everything else thrown into the story.) Place your votes on MONDAY :D

“You learn something new everyday.” I think I did anyways. Or was my memory just being refreshed? When you start of with two original functions, you can add, subtract, multiply, or divide them. With adding and multiplying, order of which function goes first doesn’t matter, it’s called the cumulative law. It’s like adding: 5 + 10 + 4 = 19, you can add it 10 + 4 + 5 and it’ll still equal 19. Same goes for multiplication: 2 x 5 x 3 = 30, you can also multiply it this way: 3 x 2 x 5 and it’ll still equal 30. But not the same law applies to subtraction or division. 5 - 3 is not the same as 3 - 5 and 8 / 3 is not the same as 3 / 8. Another thing we talked about is domains of the functions. You may have started off with two functions whose domains were the element of Real. The new function you get by applying an order of operation may not always give you a domain of Real. So the two steps you carefully have to follow in finding the domain is 1) Find the domain of your original functions and 2) Find the domain of your new function by watching your restrictions. Another thing we went over today was composite functions. Where a function is inside the other function. Kind of trippy. So in this kind of function with its domain, when there’s a restriction on one of the functions, there will be a restriction on new function. So my words of advice would be, “You could or may have been looking, but you weren’t really seeing.” In other words, don’t just look but actually see it ALL.

Then we went over the sheet that was given to us the day before. Hmm I shouldn’t really be getting into detail about it since we all have it in sheet for reference. We learned how to factor a polynomial where its degree is higher than two. We were taught to use synthetic division or super speed synthetic division =D. When plugging in possible rational roots into the equation, we may not always get a root (no remainder) and end up with a remainder. But there is always a positive side to everything. You may not have found a root but you have found a point on the graph, which will give you more better sketch of what the graph would look like once you have found the roots.

So in the end we were given two worksheets for homework instead of the usual chapter exercise in the textbook. And as usual the time in the room is wrong, and the bell goes. How time fly in class. Well till Monday. The voting starts then.

I’m done for now. “I think therefore I am.” - Renee de Carte
I think that’s how it goes. Can’t wait to hear the story Mr. K. Don’t think I remember how it goes.

- SarahS.


Oh yeah next scribe will be…dun dun dun… Glenney =D



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Thursday, September 22, 2005

Scribe

Today in class, we learned a new way to represent an exponent. Normally when we look at a power it looks something like this, 32 = 9. Instead of the exponent being 2 it becomes log3 9. So when you look at the power, it looks like this, 3log39 = 9. But Mr. K gave us a power that we could not ascertain the value of the exponent.

10^log (5 + X2) = 5 + X2

From this question, we learned that an exponent is a log.

We also learned how to solve inequality questions. First you solve for x by letting the inequality sign (<, >) just seem like an equals sign. We had a problem that represents that type of question.

Log2 (3X-1) < 4

To solve this problem we let the < sign be an =.

Log2 (3X-1) = 4
24 = 3X-1
16= 3x-1
17=3X
X=17/3 or 5.67

Once you find when x equals 4 you bring the inequality sign back into the equation.

Log2 (3X-1) < 4

Since the log is less than 4, your answer becomes X < 4. But because we are using a log, the value of x cannot make the power equal to or less than 0. So now you have to solve (3X-1) for zero.

3X-1 = 0
3X = 1
X= 1/3

Now that you have the minimum and maximum values for the domain of x you right the final solution:

17/3 >x> 1/3

There was also another problem in class that was scary to look at and it involved the natural log, ln x:

5 + ln x = 14/ln x

To solve this you first have to multiply both sides by ln x

ln x(5 + ln x) = (14/ln x)ln x
5 ln x + (ln x)2 = 14

When you multiply ln x by ln x it becomes (ln x)2 not 2 ln x.

5 ln x + (ln x)2 = 14
(ln x)2 + 5 ln x – 14 = 0
let ln x = a
a2 + 5a – 14 = 0
(a+7)(a-2) = 0
a= -7, 2
ln x =-7, 2

Sorry about the subscripts and exponents not being the proper size.
Now tomorrow's scribe is ... Sarah =)



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Wednesday, September 21, 2005

MORE logs

HALFLIFE, AMOUNT OF SUBSTANCES and POPULATION -> these are the things we discussed today that greatly involved logarhythms. In solving 'the halflife of a certain substance', 'its amount that will remain in a particular time', and 'the exponential growth of the population of a specific country' we used these formula:

A = A0 Mt/p




used in a problem with lots of information


where A is the final amount, A subscript 0 is the original amount, M is the multiplication factor, t equals time and p is the period


A = A0 (MODEL)t





used in a problem with little information
where (MODEL) is the model for the growth of a certain substance

Now that we already have the formula, we can now build an equation using the given figures of the problem. But then again, life can be so tough as not knowing what to do when you have to solve an equation that looks like this:


0.1 = 153 (1/2)t/112500






Then here comes Mr. K to the rescue as he gives us the basic rules in solving logarhythms:

For MULTIPLYING logarhythms with the same base we use:
(simply adding the result of M and N)

Log b MN = log b M + log b N





For DIVIDING logarhythms with the same base we use:
(just as if subtracting the result of N from M)

Log b M/N = log b M - log b N





For logarhythms raised with EXPONENTS we use:
(multiplying the exponent to the result of M)

Log b MC = C log b M





and the CHANGE OF BASE rule:(this im having a hard time to explain (^.^) )

Log b M = log a M

log a B






so... ok , that's it. I think that's about it. Those were all the stuff i learned today in Calculus. LOGARHYTHM RULES.

and now it's time to pass the torch to.... STEVEEEEEEEE. =)



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More About Wooden Beats - Logarithms ;-)

Here is a good interactive review of logrithms and their properties. When you finish you can try the online exercise set.



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Tuesday, September 20, 2005

Scribe

In today's class, Mr. K put us in a group again to do the Inverse Functions Lab. We use parametric mode to graph inverse of the function. Letting X1=T and Y1=f(T). And the inverse of this function can be graphed by letting X2=f(T), and Y2=T. And Finally, control the accuracy of our graph, and values found by tracing along the curve, by changing the size of the step found in the WINDOW menu. a small step will increase the accuracy and the time nessary to draw the graph.

Also we looked over the logarithm function. We know the inverse of the exponential function y=b^x is the logarithm function to the base b. To do the inverse of the function is, we change the input "exponent" to output "exponent" of f(-1)x. and change the output "power" to the input "power" of f(-1)x. We interchange the input (domain) and range of f^-1(x). We didn't finished it today about logarithm function, and I think Mr.K will continues tomorrow and I guess that's all for today's scribe.

Sorry, I am not a good scribe. ;^^*
And Nest Scribe is Ara ;))



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Wood with a Beat - Logarithms!

Ouch, sorry about that title. ;-)

Several links to review logs:

    What on Earth is a Logarithm?

    Definition, Graphs and the Natural Logarithm

    Change of Base and other Logarithm Properties

We'll be talking more about logarithms tomorrow.



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Monday, September 19, 2005

Scribe

In todays class, Mr. K gave us our first quiz of the year. The quiz was on functions, functions which he actually just pulled right out of our previous classes, a good way of seeing if we are paying attention I might add. We exchanged papers and corrected them, he says that its to get a feel of how we are being evaluated. We then took a look at some things about inverse functions. We re-looked at the different kinds of relations, by those I mean relations (like circles), many-to-one functions (like parabolas), and one-to-one functions (like lines, inverse functions, and some cubics).

Mr. K went into quite some detail after that explaining inverse functions, and gave the example of the functions Baby Play and Parent Clean-Up. Baby play is a function that takes a clean room and transforms it into a messy room. Parent clean up takes a messy room and turns it into a clean room. For baby play, the domain(input) is clean room, and the range(output) is messy room. For parent clean up, the domain is messy room and the range is clean room. Because the domain of one is the range of the other, and the range of one is the domain of the other, the two are inverse funtions. Functions that are the inverses of each other undo what the other does.

With inverses, the restrictions of one function apply to its inverse function.
Ex. the ristriction on the square root function with which it can not have negative numbers in its domain, same would be true for its inverse, so the inverse would be f(x)=x² but only the positive part of the graph.

Now as for tommorow's scribe, were down to two, tommorows scribe is Xun@



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It's Invertable!

Today we talked about inverse functions. We've got lots of resources here if you need any help or extra practice:

To learn more (or review) about inverses follow the three links below. In each case you will need to have two windows open. In one, you'll be playing with an interactive graph -- it opens up when you click the button marked [click here to start] -- in the other are the directions to follow to learn the material. Have fun with it!


You can practise applying your skill in these online quizzes:


After you click on the [submit quiz] button DO NOT click on the [email to instructor] button -- it won't get to me. ;-)

Remember also to have thought about:

(1) When is a good to to "meet" in the chatbox.
(2) We need a "character" for our year long project.
(3) Are you interested in creating an instructional video instead of the story project?

Cheers,
Mr. K.



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Saturday, September 17, 2005

Scribe

In yesterday's class Mr. K put us into groups and we compare linear functions and exponential functions. As a group we found out that this two functions has a lot of common, one of it is that when you substitute 0 to both of its equation you would get its y-intercept. Like in a linear function , if you put 0 on x, y=ax+b you would get b which is the y-intercept. Also, in an exponential function when you put 0 in its x you would also get the y-intercept of the function, y=a.b^x. Also, we talked about its differences and one of them is that a linear function has a constant slope while an exponential function has a common ratio. Then we talked about exponential decay, which we found out that if the multiplication factor is 0 < b < 1 its an exponential decay because the number is decreasing very fast at that number but it won't get into 0 eventually.

Also, in yesterday's class we talked about compound interest and Euler's number. Euler's number "e" is like any kind of number like pi its a little bit lower than 3 and its value is 2.718281828459....and its non repeating. To learn a little bit more of Euler's number you could check this site.

Well, that's yesterday's class and we didnt really cover a lot of stuff because there was Bus ridership and that consume our learning time. Well thats all folks!

The next scribe is CJ....



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Chatting and Study Groups

I noticed a lot of chatting going on in another blog so I installed a little chat window, it's called a Shoutbox. Give yourself a screen name and anyone can talk anytime you're here!

You may recall I talked about you all getting together in groups of 3 or 4 to create study groups. Meet once a week, say Wednesday's at lunch in the library or whatever works for you. Well, with the Chatbox you can set a time anytime when you call all meet online, chat and get whatever help you need with your homework in the Chatbox.

I think this will be a powerfull learning opportunity for all of you. It depends entirely on each of you individually. It's up to you whether or not you choose to get involved.

You'll find the AP Calculus Chatbox window down there at the bottom of the right hand sidebar.

Please leave me feedback in the comments to this post. Is this a good idea? Are you getting anything out of it? Should we keep it or delete the Chatbox? Leave your vote here. ;-)

Cheers,
Mr. K.



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Friday, September 16, 2005

Exponents on Video!

Class time seems to just fly by! Sometimes we get hung up on a difficult problem and time seems to  d r a g  and sometimes we cover so much material in such a short time that it just seems to fly by.

I know some of us are still struggling with exponential functions. Well, help is here. I've got some brief video taped lectures you can watch to help you with this material over the weekend if you need it. The movies are of an instructor from the University of Idaho.

In order to watch the video you need to download the free realaudio player from here. (It's a little more than 11 Mb so if you have a slow internet connection this isn't a very good option for you.) After that, just click on the link below for help with the topic of your choice!


Let me know what you thought of the video in the comments to this post. Did it help you learn? Is it clear and easy to follow? Should I post more of these? ;-)

If you still have trouble help each other through the comments to this post.

Have a great weekend!



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Thursday, September 15, 2005

Scribe

We did plenty of things today!:D First, Mr. Kuropatwa gave us the task to find the best model to fit the given data. He gave us the population of Manitoba from 1901 to 1971. At first glance, I thought that this data will turn out to be a line but I was wrong, even Mr. K seemed to have guessed wrong about the graph. He predicted that it will turn out to be exponential but it was actually logarithmic. I was a bit surpised by the result, but eventuallyI understood why is it that way. If the table was a line, it would have had the same slope for each points but it didn't. Many factors affected how the graph looked like. The war, immigration and also the resourses of the province are some of the factors that may have caused an unusual curve.

We also looked at another graph from the book. We found out that this one was an exponential function because the ratio of each Y value was the same throughout. Also we found out that this ratio was actually the base of the exponential function. Also, we reviewed about the characteristic of an exponential function. An exponential function will never touch the x-axis because the negative exponent is a fraction. It will just get smaller but will never reach it. We also talked about the transformation of the exponential function. If you know the basic form of the function, the rules for transformation are the same.

Well that's it for now. Thank you and see you guys tomorrow. Bye!:)

The next scribe is...
Prince ;)



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Shifted Exponentials

We learned about the exponential function today. A quick review is over here and a review of problem solving with exponentials is over there.

A review of all the ways we can use transformations to move the graph around is just a click away ... right here. ;-)



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Wednesday, September 14, 2005

SCRIBE

What did we do today? (*thinks to herself*)

We first started out with three questions up on the board. I noticed that I never really thought of looking far beyond ZoomSTANDARD in my graphing calculator before. I think it was today's class and yesterday's that Mr. K really emphasized to study the graph even more, looking outside the box kind of thing. Like what Janet stated "Everything isn't always what they seem". Our brains were then refreshed about radical functions. Just because there's a zero under a radical, does not mean it excludes the point. So even though the square root of zero is still zero, zero is a number and therefore recieves square brackets =).

Today we wrapped up our review on transformations. Good job guys. With whatever basic or not so basic function that is given to us, we know how to shift it up, down, left, and right. We know how to reflect it on the x-axis and the y-axis. Now onto the next section in our cal textbooks. We somewhat got a basic review on it in class with the last question. Linear funtions. I guess we should be pulling out those old formula sheets, they can come real handy in class =) I always have mine around. As for the other part of the homework , we'll be using our "stupid" calculators. We are given more practice on using our STAT graphs, and how to find the equation of it by using the possible regressions in our calculators. Hope no one struggles much with tonight's homework.

So today, wasn't such a bad class. A little quiet. (Yes, I know even I was quiet.) We are stuck together for the whole year. Both semesters. Imagine the quietness! So maybe we should start interacting more. It's calculus and our homeroom, lets make it fun.

- Sarah

And as for tomorrow's scribe. Since we've had four girl scribes so far. Why don't I choose a guy this time for tomorrow, sounds good? Tomorrow's scribe is....

dun dun dun

Jayson!



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Playing with Regression Lines

In tonight's homework you're working through the mechanics of generating a linear equation for a given set of data (points in the cartesian plane). It's easy to loose sight of what this all means or what it is exactly that we are supposed to be doing.

I'd like you to take a look at this online tool. It may take a moment or two to fully load in your browser. When it does you'll see a blank, white graph on the left and a horizontal line on a grey graph on the right. Clicking on the white graph will put a blue point at that spot. Add as many as you like. You'll also see a red line whose position changes as you add more points. Basically, this applet is drawing the "line of best fit" for the (random?) set of points you specify.

Play with it for a bit try to:
  • get a line that has NONE of the points you create on it

  • get a horizontal line that has none of the points on it

  • get a vertical line using as few or as many points as you like


We'll talk about your results in tomorrow's class. We'll also talk about what we're looking at in the grey graph.

Have Fun!!



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Tuesday, September 13, 2005

The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post is can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

Cycle 11
Prince ** (Don't choose me now, I'm getting better.)
steve
Chris*
ara
xun
SarahS*



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janet's scribe

Calculators are not that smart, sometimes! When graphing a calculator everything isn't always what they seem. That was one of the things I learned last class, I bet you didn't know that either. First exercise we did were the problem solving questions using our calculator, which really helped me refresh my memory. We wrote equations and sketched graphs to help us solve them. Also, we refreshed our memory on f(x) functions by doing reviews. Next we talked about most of the basic functions, Cubic, square root, reciprocal, absolute value, squaring and identity functions. In that lesson I learned to flip graphs over the y-axis instead of sliding them on the x-axis. It's always good learning different ways to solve problems as Mr. K's famous phrase goes, "There is more than one way to skin a cat, but don't really do that because it's cruel!"
So overall it was yet another productive class, for me that is, and I do apologize for not posting this sooner. I did try! I swear ... and I guess everyone knows who the scribe is for today's class, Sarah!! Have fun!



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Monday, September 12, 2005

SCRIBE

Another productive class don't you think? Again, we got into groups and tried to create a graph representing our little story from Andover to Concord. I think that it was a bit too quiet... or maybe I just have bad hearing? During this activity, we all had different ideas on how we created our graphs- which is a good thing seeing how we can all learn from each other's mistakes. After some contemplation and discussion, we were able to understand how the graph was to be displayed. But hey, some of us might be in "summer mode" still and getting adjusting to the homework and the early morning wake ups.

It probably was a big refreshment to some of us on how to create graphs in our calculators- it was for me. We were taught how to determine if a graph was a line by using the calculator to create an equation and using it to draw a line through our points. We also learned about the r² function which determines how accurately it will go through our five points.

So, it's our first day of real calculus homework! And hopefully, no one struggles too much on it. As the next couple days go, we'll all remember work from s3 & s4 pre-cal! Don't let the forgetting curve get you during this course because it's something that would be very helpful in the future. Anyway, let's not have such a quiet class and start interacting! Let's have a fun year everyone :)

-Glenney


Next scribe. . . . Janet :)



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Students Made This!

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. I have come across posts from my students on blogs as far away as Sweden! That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Two teachers in the U.S.A. worked with their classes last year to come up with a list of guidelines for student bloggers.

One of them, Bud The Teacher, has these suggestions, among others:

  1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.


  2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.


  3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.


  4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.


Another teacher, Steve, developed a set of guidelines in consultation with his students. You can read them here.

Look over the guidelines and add the ones you like in the comments section below this post; either from one of Steve's students or one of your own. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Cheers,
Mr. K.



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Saturday, September 10, 2005

SCRIBE

(scribe for Friday, September 9'05)

So yesterday was a productive class. We went into groups to discuss all the facts we knew about functions after doing it our selves. THAAAAAAAAT, was a great idea! I think you tend to get more when you have a conversation going on, and hearing things that either refresh your mind, or be like 'OH, i learned something new today =)' I mean, it is great to work independantly, but another way to learn is to have some sort of communication going on..

As Mr. K mentioned, there are three ways to present a function- numerically, symbolically and graphically.. It's kind of cool how one thing can be presented to you in different ways.. Just like how he showed us that block of wood.. Its kind of like for basketball, you can be told a play either, verbally, drawn on paper or see it demonstrated to you.. The same play, just presented in different ways.

We also tried to draw a graph of the lengths of our hair in a year... That was pretty difficult to draw.. But once we discussed how everyone's graph looked, and actually questioned; does this really look like how its supposed to be?, it turns out NO.. After seeing how it should be drawn, i was like OHHHHH! That makes so much sense!

-- Mary Ann

This is all for today folks..
( *glenney your next =D )



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Friday, September 09, 2005

Blogging on Blogging

A good class today folks! You worked together really well in groups and gave good verbal feedback over the course of the lesson. Thank you. There's still a little more room for growth here though. When you find that everyone in your group is stuck and doesn't know how to proceed please let me know immediately. Don't wait until I come around to ask. Time is precious and we don't want to waste any of it.

We were talking about exactly what sort of post you're supposed to make to get that mark on your test. The kind of post I'd like you to make should have one or more of these characteristics:

  • A reflection on a particular class (like the first paragraph above).

  • A reflective comment on your progress in the course.

  • A comment on something that you've learned that you thought was "cool".

  • A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.

  • Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.

  • Respond to a Blogging Prompt I posted. (see below)


Your posts do not have to be long. I'm far more interested in the quality of what you write rather than the quantity.

Blogging Prompt
To help us along our blogging journey I've decided that I will also occasionally post a Blogging Prompt. It will be easy to find because I'll always put it under a heading like the one above this paragraph. Feel free to create your own Blogging Prompt for the rest of us if you like. If it's a really good one (i.e. has rich possibilities for blogging) we'll count it as your post. ;-) Here's my first one:

We've learned about three different ways to represent a function; symbollically, numerically and graphically. Blog a brief paragraph identifying ways in which these three representations are similar. Blog a second paragraph outlining the ways in which they are different.


This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw three large overlapping circles. List the similarities in the appropriate overlapping sections and the differences in the non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram we'll talk about how to post pictures sometime in class. ;-)

Happy Blogging!



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Thursday, September 08, 2005

You're Here! Let's Begin ...

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); 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, or make your own blog and link it to this one, or....the sky's the limit...let your imagination soar and lets get down to some serious blogging!

Here's your first online assignment:

Do you see the Links list in the side bar over there on the right? Follow the Study Skills Resources link. Browse through the sites until you find one that you think has excellent suggestions on how to study math; then, on a piece of loose leaf paper (or this worksheet) to be handed in on Monday:

  • Write the address and name of the site you most liked.

  • Rate the site out of 100; i.e. give it a grade!

  • Write a brief description (no more than 4 or 5 sentences) of the site.

  • Include a comment on what it was about this site that made it stand out for you (no more than 1 or 2 sentences).


Repeat this exercise for the second link that deals with Test Taking, i.e. how to write a test.

If you take this assignment seriously now and invest some real time and energy into it, you'll probably do real well in my class this semester...who knows, it might even help you in your other classes too! ;-)

Have Fun!



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