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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.

Sunday, October 30, 2005

What Mathematicians Think...

Earlier this month Jan Nordgreen at Caymath posted about an interview of a couple of professional mathematicians talking about their work. Here's one quote.
Isadore Singer: ... when I try out my ideas, I’m wrong 99% of the time. I learn from that and from studying the ideas, techniques, and procedures of successful methods. My stubbornness wastes lots of time and energy. But on the rare occasion when my internal sense of mathematics is right, I’ve done something different.

Another quote:
Michael Atiyah: My fundamental approach to doing research is always to ask questions. You ask “Why is this true?” when there is something mysterious or if a proof seems very complicated. I used to say — as a kind of joke — that the best ideas come to you during a bad lecture. If somebody gives a terrible lecture — it may be a beautiful result but with terrible proofs — you spend your time trying to find better ones; you do not listen to the lecture. It is all about asking questions — you simply have to have an inquisitive mind! Out of ten questions, nine will lead nowhere, and one leads to something productive. You constantly have to be inquisitive and be prepared to go in any direction. If you go in new directions, then you have to learn new material.

The full interview is right here.

These are two things I find myself constantly belabouring in class when teaching problem solving:
  • Take risks! Experiment, play, try something out and see where it takes you. Good math isn't knowing what to do with any problem -- good math is knowing what to do when you don't know what to do. ;-)

  • Ask questions! If you don't ask questions then I can't tell whether you understand or not. I'll either go on to something new, leaving you confused in the dust, or go over and over something you already understand trying to help you but really just wasting our time.

Food for thought ...



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Scribe Post from a very long time ago

My bad. I’m sorry this is late. I don’t even remember what day I’m scribing for. But I do remember what happened. I think this is for Monday. That day we were suppose to write our pre-test, but due to many of us not done our homework, it was post-poned. The whole class was spent on doing the homework. Kind of shameful don’t you think? Instead of having to have learned about Chapter 3 on Wednesday, we learned it on Thursday? Well I guess homework check is a great idea, it keeps us on track. Like Mr. K said, none of you have written an exam like the AP Calculus exam. If you think the Pre-Cal 40S Provincial Exam is hard, then the AP exam for this class doesn’t even come close to the provincial. It’s hard. I’ll admit that. But maybe if we put a lot more effort into getting our homework done, just maybe it wouldn’t be so hard.




“Genius is one percent inspiration and ninety-nine percent perspiration.”

- Thomas Edison


I think that quote fits very well don’t you think? To perspire, we need to work hard. If genius is 99% of it, imagine how much we have to work hard?

Well I’m off to finish typing up my blog for the other blog, it should be up by tonight. Hopefully. Hope you guys had a great weekend.

P.S. Happy Advance Halloween. I kinda have to dress up, so no one better make fun of me tomorrow when I come to class :P



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Scribe

First thing we did in class was we recieved programs from Mr. K, programs like Angle Conversion, Area, Riemann sum which were going to learn on that period, and also the Rsum which also an important thing we learned from class. Mr. K showed us these different programs and showed how it works. We learned that in using the Rsum program it shows us the graph and we punch in some values in order to get the area of different number of rectangles in the graph. Then we found out that when we do an infinite number of rectangles we shaded thewhole region on the graph and it gives us almost the exact value for the area of the function. Then the Riemann sum program is like the Rsum program but it would calculate more faster because the calculator doesn't graph it and it just gives you the values right away.

Also in class, we talked about Riemann, a german mathematician. He has the famous Reimann's hypothesis and its about prime numbers. Also he has something to deal with our lesson for today in calculating the area of the rectangles in a function. Riemann says the key to calculate and estimate accurately the area of the function you need "a lot of rectangles".

We're going to talk more about Riemann sum next class. The next scribe is Steve....



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Hare and Hounds


In this game you have to "run for it!" You can be the Hare or the Hounds. The hare has to escape; the hounds are trying to corner him.

The real question is: Are you an expert Hare or expert Hounds? ;-)

Have Fun!



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Saturday, October 29, 2005

In the Beginning - Chapter 3

Previously, we had an incredible road trip and figured out the rates of velocities we have traveled...
and then...
we went backwards.
Now we needed to solve the distance for a specific velocity.
How did we do it?
Here's how:

If in the previous chapter, we spent hours and hours on calculating velocities, slopes or derivatives, this time the DISTANCE is what we will sweat on. It is like reversing the solutions we have done in Chapter 2.

Basically, to acquire the distance, we use the formula:

DISTANCE = VELOCITY * TIME ELAPSED

Obtaining the precise distance is not as easy as multiplying the velocity by the time elapsed, since in a typical graph, the velocity is changing moment by moment. So to have better measure, a LOWER ESTIMATE and an UPPER ESTIMATE must be considered. These estimates are the slowest and largest estimates of the graph, respectively. But having those won't make it any closer to an accurate distance. SMALLER INTERVALS must be used. At a particular point, its LEFT-HAND SIDE and RIGHT-HAND SIDE are to be added and divided into half.

In solving, it is better to first look at how the graph behaves. It is easier to get the distance of a point in a graph that looks like a line - a linear function. This graph is called MONOTONIC since it can only be STRICTLY INCREASING or STRICTLY DECREASING. But sometimes, NON-MONOTONIC graphs can be turned into MONOTONIC.

In an INCREASING GRAPH, the LEFT-HAND side is the LOWER ESTIMATE and the RIGHT-HAND side is the UPPER ESTIMATE. In a DECREASING GRAPH, the LEFT-HAND side is the UPPER ESTIMATE and the RIGHT-HAND side is the LOWER ESTIMATE.

... There you go. My own summary of what I learned in the first discussion of CALCULATING THE DISTANCE TRAVELED.

and... as planned, Prince is the next scribe. (^_^)



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Tuesday, October 25, 2005

What impression do you want to make?

Berrien County Intermediate School District (BCISD) is a school division in Michigan. They have an online workshop on educational blogging and other web 2.0 tools. Look at the impression you made (under the heading "Teacher Blogs").

Dean Shareski is an Educational Technologist in Saskatchewan. He made a list called The Best of the Blogosphere for New Bloggers. You're on it. More than that, he suggests that you guys are THE example of how math students can also be bloggers.

A new teacher blogger writes about you and mentions Sarah's blog in particular to demonstrate to her students how they can benefit from blogging.

On October 17, 2005, an online news article entitled Blogging 101--Web logs go to school mentions you on the second page as the only example of how blogs are being used in mathematics.

You are the number 2 hit when someone uses Google's Blogsearch to look up calculus.

You've already made an impression.

Now what are you going to do, not just to maintain it, but move it up to the next level?



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Monday, October 24, 2005

Graphs Graphs Graphs

Try this little exercise/game. It deals with the definition of the derivative and matching up the related graphs of f, f' and f''.

Have fun with it!



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Blogging on Blogging on the Derivative Function

When you talk graphs, the derivative function and its parent function can confuse you till your blue in the face. I myself have had the that happen to me before. You could be looking at the graph of the derivative function, looking for where the parent function is positive and accidentally take the slope from the graph of the derivative function, instead of looking for where on the graph it is above the x axis. An example of this is:

f (x) = x^2
f ' (x) = 2x
For this example the derivative function f ' (x) = 2x is a line. When you use it for applications on the parent function, remembering that this represents the slope of the parent function and that the y values are the slope not the slope of the derivative function. This is something that I remind myself when I attempt a problem involving the derivative function. I find that it helps to check your work after attempting the question because you never know if you made an "oops" or not.
this is my blog for the Derivative Unit



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Sunday Funday (Oops, I missed a beat...)

Here are the rules.

Here is the game.

Have fun with it!



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Saturday, October 22, 2005

Be an Optimist

"The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty."

Again, my first sentence have nothing to do with my scribe but I just don't know how to start.

First off, we reviewed continuity. You can say informally that functions are not continuous if you have to lift you pencil to draw them. The formal definition is:

    • f(c) exist
    • lim f(x) exists
    • x-> c
    • f(c) = lim f(x)
      • x->c

After the short review, we did the test on limits. The class decided that we do this test like a pre test where we do it ourselves in 20 min. or so and then talk to our classmates about it. Personally I find it hard at first but I get it somehow after we talked.

Well like I said there is hope if we don't understand things. Look for opportunities and use them wisely.


The next scribe is.....
Sarah



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Wednesday, October 19, 2005

Continuity

In today's class we learned if a function is continous or discontinous. According to Sarah's blog a continous function is predictable. In order for a function to be continous it should have no breaks, no holes, and no jumps. A function is continous it must have a limits at every x value, meaning it should have no breaks in its graph. Also it should have no holes, meaning f(x) cannot have an undefined point or any kind of vertical asymptotes. Then an important key to continuity is that if f(x) is continous, then for every x=a in the function, lim x->c f(x)=f(c). In other words, the function should exist at the height indicated by the function. Then Mr. Clark pointed to us that we should know about the Intermediate Value Theorem. It just states that if a function f is continous in a given interval [a,b], and k is a number between f(a) and f(b), then there exists at least one number c in (a,b) for which f(c) =k.

Basically that's all we learned in class today and we mostly spend our time doing our exercises. Btw some of the information I put in this summary are from Sarah's blog. Thanks Sarah! I guess that's all for now, because I still have to catch up on a lot of things. That's all folks!!!


Jayson your next....



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Tuesday, October 18, 2005

LIMITS! LIMITS! LIMITS!

OK guys.. I've been sitting here infront of my computer, and I asked myself.. What is a limit? Today in class we were told that the definition of a limit were as follows:

lim f(x) = L
x -> a
- which means the function has a limit, L, as x approaches a.
We also looked at graphs and how you have to look at the left and right side of the function to see if the function exists.

We must remember that in order for a limit to exist we must look at both sides. If they equal, the limit exists.

I dont want to babble on because I for one am not that comfortable with teaching this stuff to you guys and discussing it because I am not sure about certain things. AND! I dont want to confuse you!

READ SARAHS BLOG! ITS AWESOME =) (high five to sarah!)
I think you'll learn more there...

tomorrow will be......
.

.

.

.

PRINCE



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Limits

Watch this to review the "intuitive definition of a limit." There is a lot of text but stick with it and pay really close attention when the ideas are illustrated on a graph.

Limit Theorems
Check out this page and review the first seven (7) limit theorems. Click on the examples next to each one to see how it gets applied.

Try the examples on this page to see how the theorems are combined to solve limit problems.

Then try your hand at this quiz on evaluating limits using graphs. You will be writing one just like it in class on Thursday so get ready for it. Each time you click that link you'll get a different quiz with similar questions. Have fun with it!

Update
Check out Sarah's blog! It's awesome. ;-)



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Monday, October 17, 2005

Derivative: a CoNtrovErsY ... bRACKET or pARENTHESIS?

Second Derivative - the derivative of the derivative of a function.

>> sounds confusing right?

Well me too, I'm confused. But to fully understand what a second derivative is and how to make it, I'm gonna help you guys, and myself too by recalling the things we've learned in today's discussion.

First up, we started the day with the usual practice activity on derivatives. Mr. K. asked us to

  • write equations for the line tangent to a function at a given point

- to do this, use any formula for getting an equation that is applicable to the given problem. In our case this morning, since the points and the tangent (which is also the slope) are provided, we used the POINT - SLOPE FORMULA.

  • name the interval where f' is positive, f'' (or second derivative) is positive and determine the critical numbers of f, given the graph of f (...too much f's :))

- this is the part where the controversy began. it is pretty much easy to find the interval where f' is positive because you only have to know where the graph of f is increasing, but to write it down, there we've got a problem. Some of us may probably use "[ ]" than "( )" in giving intervals or points because we consider those "points" part of the increasing graph. But according to Mr.K, it is more preferable to use "( )" for the fact that at those "points", the graph is stationary, that is neither increasing nor decreasing.

- to get the points where f'' is positive, we first have to know the graph of f'. then, looking at f', try to plot its derivative and that becomes f''. So to get its positive points, take a look at the point where the graph of f' is increasing and wWALAHH! there you have the points where f'' is positive.

- lastly for this portion, critical numbers are the points where the tangent or slope is equal to zero

*** the second derivative is just like considering the first derivative your mother or parent function and plotting a derivative on it.

In addition to this, here are some important notes that we took up today:

  • the vertical position of a point has nothing to do with the derivative
  • where the graph of the parent function is concave down, the graph of the second derivative is below x-axis, and vice versa
  • the parent function's increase/decrease tells you about the first derivative, while its concavity tells you about the second derivative
  • to get the maximum and the minimum points, you don't only have to look for the point where f' equals zero, but also where f' is undefined or does not exist

There you go. that's all i can remember from this morning's class.

There'll be more on derivatives tomorrow, as MaryAnn update you guys.

cYa! :)




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Sunday, October 16, 2005

Sunday Fun! (or Sunday Madness!)

I got this from a blog called Think Again! A great little math blog full of interesting puzzles. Lucky me, it took a while but I found my way out of the room ... can you?






You are trapped in a room. To get out requires some thinking. Good luck!

Over two million people have tried to leave the room already. No one knows how many are still stuck.



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Friday, October 14, 2005

Graphs And Derivative

^-------^*
In today's class, we had two questions on the board. the first question is about f' ( derivative function) and f ( original function). We had the graph of f', and we need to know where is f increasing, ( for looking for where f increasing or decreasing, we need to know the slope. Since a derivative is the slope of the tangent line at any point on the graph we choose (provided the derivative exists there, of course), positive slopes correspond to f ' > 0 , negative slopes correspond to f '< 0 and zero slops correspond to f'= 0

Where f have a horizontal tangent line means where are the zeros on f’, because when f have a horizontal tangent, the slop is 0, and zero slops corresponding to f’=0. Does f have any maxima or minima numbers? When we looking for if f have any maxima or minima number, first of all we looking for a function has to be a derivative function, and we look for the left or right side where x=0.because we know when x=0, that point is either max point or min point on the graph of f. The curve is increasing at the beginning and then reaches the zero and then decreasing, so we know, this point is a maximum point. The curve is decreasing and then reach the zero and then curve increasing again, and we can know this is the minimum point of f. If f(1)=0 is f(0) positive or negative? Since we know the graph of f, is increasing, reach the maximum point, and then decreasing , reach the minimum point and then increasing again. We know f’(1) is the maximum point of the graph f, if f(1)=0, and f(0) is the previous point of f(1), so, f(0) is a positive number

The second question we had today is draw a graph showing "mathmatical knowledge gained over the semester." Well, it can't be a straight line. And everyone knows that the line should be going up. Before we started our semester, we had some knowledge, so, when the line started, it's not zero or neither a negative number, and then the curve is going up, at the middle of the course we kind of stuck, some kind of suff we couldn't get it right way,because the course is going harder and harder. And before the test, the line is going slow or stop for a while. And then after, it's going up again, stuck, we need more time to study, or we have test again. .. and then it's over and over again till this semester is finish. So, basically, the curve is look like, start a postive number, concave up, concave down a little bit, and then stay a horizontal line. and then go over again because we started a new unit... ( I talked too much, bad explaination)Sorry!

P.S a critical pointis a point on the domain of a function where the derivative is infinite, underfined, or equal to zero. :P

And that's all for thday!

Next Scribe is Ara! :)






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Thursday, October 13, 2005

More on the derivative, and some blocked sites

In today's class, we went into the Mac lab to do an online assignment that Mr. K wanted us to do while he was away today. It was more of a look at the derivative and derivative functions. The problem was that the school's server blocked access to the first page and almost all of the images, thus greatly reducing the material for us to look over. I would go into a long explanation on what happened and the material, but other than what I've already said, I believe thats all.(Next time its my turn, I'm sure that I'll have more material to write on)

Tommorows scribe is.... I'll roll dice on it..... and the dice say Xun.



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Online Class #1: Critical Numbers

Tomorrow's class will be done entirely online in the iMac Lab, Room 58. Here we go ....

We will be learning how to use derivatives to find local minima (the plural form of minimum) and maxima (the plural form of maximum) for a given function. We'll be looking at lots of graphs to see if we can identify the relationship between:

i)  The roots of a derivative function, and
ii) where (the x-coordinate) its parent function has a maximum or minimum.

  1. Watch this tutorial where we look at a cubic function.


  2. Read through this tutorial. All the graphs are interactive. See what happens when you move the mouse over the graphs or pictures. Don't calculate any derivatives algebraically; use your calculators to create the graphs of derivative functions using the nDeriv command ([Math]:[8]). We'll learn the algebra next week. ;-) Pay attention to how the derivative changes where the parent function has a local max or min.


  3. Look up the definition of a Critical Number (follow the link to the definition of a stationary point as well). Write it down, in your own words in your notebook.


  4. Your assignment is in your textbook. You can review the introduction to this topic on pages 114 and 115. Then do all the ODD numbered exercises beginning on page 116. Also do questions #10, 16 and 22.


If you have the time, comment on this post and let me know what you thought of this lesson. Did you enjoy having the entire lesson online? What were the advantages and disadvantages of learning this way? Should we do this again? Why or why not?

Have a great day and do someone a good turn for no good reason. ;-)

Cheers,
Mr. K.



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Wednesday, October 12, 2005

Smarter Than The Average Bear

My title doesn't have anything to do with my scribe but I just had to say it. I felt that we say this often that it stucked in my mind now. I don't know if that's good but hey, it wouldn't hurt me.

To start of today we as usual had to do questions on the board related to what we've talked about yesterday. The first question was about calculating the average rate of change(slope) between two points values of the function. Then we had to approximate the intanteneous rate of change of the values. The second question is again finding the rate of change but by using the derivative of a function f at x=a denoted by f'(a), is

f'(a) = lim [ f(a+h) - f(a)] / h
h-> 0

For question one and two nobody had any problem with because its just a review from yesterday's class. For number three, i didn't quite understand it. It is very new to me and I had no idea answering the problem. Mr. K then explained what it is about. The question was;

A function f has a derivative f ' (x) = X^3 - 3x + 1 use your calculator to graph f'
  • Where on the graph of f will the tangent lines be horizontal
  • Suppose f(-1) = 5 write the equation of the tangent line to f when x= -1
To answer this question we have to understand that the given function is the function of the derivative not the actual function and the values of f(x) is the slope. For a line to be horizontal the slope must be zero so you just find the value where X^3 - 3x + 1 = 0
To get the next question we have to remember that to get the equation we need the slope and a point in the line and use the point-slope formula which is y - y1 = m( x - x1 )
for this question the answer is y - 5 = 3(x + 1) . Mr. K said we can leave it like this because we might make little mistakes and get the answer incorrect.

The next question we looked at is about absolute functions. We learned today that you can't find the derivative of a corner or a cusps because it doesn't respect the definition that if we get the slope of the secant line on either side of a point it should be coming to a same number. In corners, the left side and right side of the point are different.

We also learned the nderiv and dy/dx function of our calculator. both calculates the slope but just in a different way. dy/dx must have a given graph to be used. you select a point in the graph then "calc dy/dx" then there you are with the slope. The nderiv one is a bit complicated. you put nderiv then type the equation comma the variable which is x then you put the point where you want to calculate the derivative and then there it is.

Lastly, then again we found out that our calculator is a liar and stupid because when we use the dy/dx capability of our calculator it still calculated the a derivative in corners. It is like this because mainly it calculates the symmetrical difference quotient of the point but doesnt know the restriction that there is no tangent at that point. Well we just have to remember always that we are smarter than the average bear.



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Tuesday, October 11, 2005

All About the Derivative Function

Today in class we learned how to calculate the derivative of a function several different ways. One way to find the derivative, is by using the symmetric difference quotient. All you need is a table of values and then you simply calculate the forward secant line and the backward secant line, then take the average of the two and that is usually a fairly accurate way to determine the derivative. An example we used in class was:

f(x)= x^2 -6x +10

x y
0 10
1 5
2 2

Delta y/ Delta x
(2-5)/(2-1) = -3
(5-10)/(1-0) = -5


((-3)+(-5))/2 = -4

Another way of finding the derivative is by using the definition of the derivative with algebra to solve for d.
First off, evaluate using the function f(x) = x^2 -6x +10 for f(1) and for f(1+h).

f(1) = (1)^2 -6(1) +10
f(1) = 5


f(1+h) = (1+h)^2 -6(1+h) +10
f(1+h) = 1+ 2h +h^2 -6 -6h +10
f(1+h) = h^2 -4h +5


lim (f(1+h)- f(1))/h
h->0


lim ((h^2 -4h +5) -(5))/h
h->0


lim (h^2 -4h)/h
h->0


lim (h(h-4))/h
h->0


lim h-4
h->0

Assume h = 0, therefore d = -4
.

You can determine a function that will give you every derivative value for the function you are using. You use the formal definition of a derivative to solve for f^1 (x).

f(x) = x^2 -6x +10
f(x+h) = (x+h)^2 -6(x+h)+10
f(x+h) = x^2 +2xh +h^2 -6x -6h +10

lim ((x^2 -6x +10 +h^2 + 2xh -6h)-(x^2 -6x +10))/h
h->0

lim (h(h +2x -6))/h
h->0


lim h +2x -6
h->0


f^1(x) = 2x -6

You can also draw a tangent line if you are given a graph that is draw to scale. Your ruler can be important if you have a graph.
Your calculator has a SLOPE program and you can use this program to calculate the derivative but it is still only an estimate. You can also use your calculator to draw a tangent line on the graph of the function.
In case you forget what the formal definition of a derivative is:

(f(x+h)-f(x))/h

The next scribe is ... Jayson.



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Secant Lines and Tangents

We talked some more today about how to find derivatives and exactly what the definition of a derivative is.

Play with this applet. You can use the given function or type in another one of your own choosing. You also get to pick the "step size" of h and see what happens to the slope of the secant line as it approaches the tangent line. Try changing the "step size" of h and see how this affects the estimate of the slope of the tangent line by clicking on the [+] or [-] buttons. At some point you will see that the secant slope is undefined. Can you explain why this happens?



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Monday, October 10, 2005

Intro to Derivatives

I think I made an improvement this week of not going on the computer at all. But for some reason that improvement caused me not to see what’s been posted up on the class blog. I didn’t know I was scribe for Friday. I’m sorry this scribe is late guys. I only saw that Mary Ann chose me as scribe just last night, during midnight. I made some images but I was to sleepy to type up a scribe. Other than that, I don’t exactly remember what we did Friday. But I’ll try my best to recall some things that were bought up on Friday.

Finally Calculus was introduced to us on Thursday with a fieldtrip. The idea of looking at smaller intervals within the function was taught to us. The smaller the interval was, the more accurate our result was. That is only because we are looking at the instantaneous rate of change. The rate of change at that instant.

On Friday we learned or we were taught in greater depth on certain “new” vocabularies.

What is a tangent line?
A line that results from several secant lines as the change in its x value gets smaller and smaller, closer to zero. In other words, a line that touches the curve at one point, as a result of many secant lines.







What is a derivative?
A derivative is a rate of change. Or to be exact it is the total change in a function within that interval.

There are many ways to find a derivative at a point. We were taught three ways on Friday. (I think it was three. :S)

1) Difference Quotient. Which can be showed in different ways, but mean the same thing.



2) Zooming in at the point till what appears on the screen is a straight line.

3) Table of Values.
We didn’t exactly look at it in a table of values. We actually just calculated it in our calculators. This was when the change in x got smaller and smaller. (1/1000, 1/10000, 1/1000000, 1/1000000000) Our resulting values got closer and closer to a more accurate value.

That’s only a couple of ways to find a derivative. There are more ways to find it. We’ll learn several of it in this chapter. ;-)


Looking at the rate of change also showed us what the “particle” was doing at a certain point. Take for example, the door opening and closing. We saw that if the rate of change or the slope at a point was above 0, the door was opening. If it was below 0, the door was closing. If it was 0, it had stopped. So overall, the rate of change, or the “derivative” shows us what the particle was doing at that point.


I’m not sure if I’m missing anything, and if what I just typed makes sense. Hope you guys can understand it. Well next Tuesday’s scribe will be Steve. Oh yeah, comments are welcome.



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Friday, October 07, 2005

The Difference Quotient

Watch this to see a little review of some the things we talked about in class today. Here is a movie illustrating the same thing.
This will illustrate how we can do the same thing numerically, using a table of values.

And here is an animation of what we were doing with our graphing calculators. Play with this applet too.



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Thursday, October 06, 2005

DRIVE SAFELY!

Today in class we went on a road trip ;) Boy! Did we learn a lot today.. We looked at a graph displaying the journey to our destination.. It looked like we took a VERY long time.. We calculated the average speed or velocity using the formula, change of distance over the change of time. With our results being 45km/hr for the whole tirp, we thought that JAYSON drove pretty darn slow. But you see there was a constant line, which meant we stopped.. Also, we thought that he was driving slow, but in fact, the more we looked into the velocity in x amount of time.. we realized that, he was driving pretty fast! Then we tried XUN! We thought she would be better! She was worse ;) We could have gotten hit into a building like Chris mentioned because on the graph we didnt have a complete stop; the car was still moving! We discussed about secants and tangents, but that will go into more detail in another class.. But anyhow, the whole point of this 'trip' of ours, in my view was to realize that depending on where you look at the graph, you can come up with one answer, and then look at the whole graph and see such a big difference. You see, calculating the average speed was determined by looking at the whole graph. By looking at only on piece of the graph, you determined the instantaneous velocity. Which is.. dun! dun! dun! The topic for tonights homework!

The next scribe will be the one and only SARAH!



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Wednesday, October 05, 2005

The Muddiest Point (Glenney's version)

Well, well, well. It seems that my title is very self-explanatory when it came to the first test of the year. I bet that everyone was a bit nervous as soon as they entered the classroom- I know I was. To be honest, I was expecting a lot of logarithms and ready to tell myself: "A logarithm is an exponent!" But I was disappointed to see that there wasn't really any?! Or am I wrong? (Short memory span. That's why I try to write almost everything Mr. K says in detail.) I, personally, found that test to be really tough and after class I started having my doubts again. But then I read Mr. K's comment to Emjay. He basically says that it's only one test and we will have many more opportunities to possibly raise our mark from more tests in the future. So I guess I'm not going to let this bring me down so hard. So since we didn't really learn anything new, I'll keep this short.

Mr. K- Come back soon.. we need more laughs... even though we don't laugh when you tell us a joke that we don't get right away :) haha jk!
Mr.Tram- If you're reading this... you really do know your calculus. haha like me and Prince say while you describe something: "You're smart!"

Since Emjay was supposed to be the scribe today... she'll be the next one for tomorrow =)



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Tuesday, October 04, 2005

Test Blog (........I like math........)

Well, balancing Pre-Cal with calculus at the same time seems to be turning out easier than I though, but then I think, "wait the semester is just getting started". I haven't taken Pre-Cal 40 before now because of my own personal fault which will remain unmentioned. So naturally this review unit has contained a little bit of info that I haven't seen before(logs for example) but when you look at anything from the right perspective, it can be as easy to understand as even the simplest math. I'm still kinda itching to learn the sine dance though, I don't believe that I lean toward kinesthetic(that VARK test should have had more questions to accomodate the "statistical anomolies"), but it will still be useful, and worth a laugh to do during the AP exam like Mr. K mentioned. :P I wish all of you, my peers the best of luck on the test.

Don't forget to teach us that dance Mr. K



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"B" - "LOG"

"B" is not the period, "LOG" logarithm is an exponent. Here are the things that I should remember in tomorrow's test. B is not the period it helps us determine the period. Also, we should remember that a logarithm is an exponent. If ever we got stuck answering a logarithmic function maybe we juss forgot that it is an exponent.
When I was in Pre-cal 40s I dont really get logarithms. If I see a logarithmic function I freak out and tended not to answer it first, because I juss dont get it. But now its pretty clear, and logarithm is really an exponent. Also, when I was pre-cal 40s, I always taught that B is the period. Well now I know that B only helps us determined the period of a trigonometric function.
Well the title blog really fits into me because it helps me remember two things for tomorrow's test. Well I'm tired from work and I guess that's all for now, Cheers :) Btw: Mr. Tram your smart (I wish I'm as smart as you so that I can pass my test tomorrow j/k) and a good substitute teacher, thank you for helping us answer our work today.



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A little something to read..

As you can probably assume, the picture to the left is an image portraying Sysiphus. He has so much on his shoulders, so much pressure to get that rock going without failing, but he knows he is set up to fail. In calculus we are being set up like Sysiphus, we have a lot on our shoulders, but we are not to fail, but to succeed.. I feel as if I have set myself up to fail.

I am doing this blog for many reasons. One being, I am still at that point where I am contemplating- to stay in or to leave. And by doing this blog, I am hoping it will help me with my decision. But to be honest, I see no progress in myself, you guys or Mr. K did not fail me, I failed you. If you have not noticed, I have not been in class for the last two days. I have already disappointed myself, but also you guys! Being in this class does have its ups and downs. Its so frustrating when its so quiet but then we get this spark of hope that we are going somewhere as a group. I guess another reason why I am doing this blog is because it may be my last. I dont know yet. It may not. You might see me tomorrow morning in class, you may not.. If you see me there, that means I am giving it another try, and if you dont see me there, I give my apologizies to you all, I didnt mean to let anyone down. We are all in that class for a reason.. believe it or not..*whisper* People think that we're that smart and capable of doing this!

I guess this can be either my TESTblog, or a final blog. So one thing that frustrated me so much was logs! I HATE LOGS! Well, when I went to get some help from Mr. K, and was shown the answer and how to do it, i was thinking to my self "THATS IT?!" I think I tend to look at things a little more difficult than it really is. I was so shocked when I found out that that is all you have to do! I FELT SMART ;)

One thing I have come accross in the 'real world' is feeling like Sysiphus. I had a talk with Mr. K, and he says he sees no effort. I see no effort myself.. SOMEONE! kick me in the butt and tell me to put some effort into this. I guess, i feel as if, every time I attempt to do the homework, I am like hey I can do this! But once I stumble accross a question where I dont know what I am doing, i give up! Unlike Sysiphus he has a rock on his shoulders, I have a lot on my shoulders.. but thats not an excuse to quit! I knew from the start that I was taking a heavy load, and I was willing to do that. I know a lot of these things. Maybe I am frustrated with my ankle and just the way this school year has started.. WHATEVER it is! I still shouldnt quit. I AM NOT A QUITTER. I do not like to quit or give up. ( i know this is long, but and im rambling on and on, but i need a place to let this out and maybe i can come to an answer!)

* A note to MR. K- if and only if i decide to go to class, do not be surprised with my mark on the test. but please be glad that i stayed. If i do stay, I will promise to try. If I do not show up, I am sorry.
*A note to you guys- I am also sorry.

Feel free to comment and voice your opinion, because really I do not know what to do! HELP!



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WORK DAY today!

Chapter 1 SUPPLEMENTARY PROBLEMS - that's all we did.

Boring? Not at all.

It was fun and turned out to be very helpful for tomorrow's test. We divided ourselves into groups and answered the problems. Well, not all 31 problems, not even half of the whole thing, but we tried though. As for our group (xun, steve and I), the "trying" thingy only got us to #5. Hey it was hard! especially for me, i made my groupmates slow. hehehe. - my bad. (^.^)

Anyway, I learned new stuff. New ways of how to get the inverse of a function, and how to determine whether it is odd or even. So Mr. K, you don't have to worry about anything coz Mr. Tram was nice and he taught us a lot. Too much that he kind of answered some of the problems. But really, he was nice. He showed us some of his techniques too.

But the thing that i remembered the most from today's activity was when doing an equation, any kind of equation, there is always an LHS and an RHS.

- - - a LEFT HAND SIDE and a RIGHT HAND SIDE - - -

I am never going to forget that esp. the RHS. Thanks to Glenney! =)

Oh, and speaking of Glenney, YOU'Re the next SCRIBE.

So good luck you guys.

I pray to the Almighty.............. may all of us pass that test - with flying colors! ;D

_ciao_



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bloging on blogging


~^-------^.*

Blogging , Blogging....................^^* At the beginning of this semester,the most hardest thing I found in this course is to do my homework. I understand all questions and problems that we have in class, but when I try to do my homework by my own, I found I always stuck in it. At the first unit I didn't really finished all the exercises. Because the knowledge is not consolidated, I think we need more time to spend on exrcises to be comfortable with all the questions that maybe appear on the test, even though it's hard to keeping on doing all the exercises. But I will try.:)



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The Latest Scribe

Sorry I'm so late posting this you guys. I was exhausted yesterday and I fell asleep shortly after I got home. In yesterdays class, Mr. K gave us a pre-test. A few multiple choice and a long answer. I'm sure anyone, even those who weren't there could guess that the test was on functions(what else have we been doing lately?). We were given 20 minutes, and then we were put into groups to discuss our answers and then hand in a group designated paper. We were given a set amount of time, but then Mr. K extended it because he said that there were some really good discussions going on. I believe that could be accounted to two things. One: we are a little more comfortable with our classmates. Two: if we didn't have any discussions we wouldn't hear the end of it from Mr. K(not in a bad way though) :P
That was pretty much all we did yesterday, didn't cover anything new or the like, so... See you next class.



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Monday, October 03, 2005

The Muddiest Point

Test day is Wednesday. I'm away for the next two days. Use the comments of this post to share with Mr. Tram, my substitute, your personal "Muddiest Point". You can use your name or leave your comment anonymously, but, whatever you do, share your troubles here. Remember, not only can Mr. Tram help you but you can help each other too! Leave tips and advice in the comments for your classmates. And don't forget, you can form an online study group and "meet" in the chatbox of our blog! Unlike Sysiphus, you're being set up to succeed! Take advantage of every opportunity you've got!



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Can You Do It? .... YES You Can!

A wealth of links and practice material to help you get ready for Wednesday's test. Pick and choose the ones you most need to review. Of course, even this extensive list doesn't cover everything we've talked about. Work hard in that review class tomorrow and ask LOTS of questions. ;-)



Do your BEST on Wednesday!



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Sunday, October 02, 2005

bloggerAthon

"dugdug.. dugdug.. dugdug (faster and faster)" goes my heart the moment i heard Mr.K mentioned about this blog. And I was like "okay, I'm not going to do that.. ever!" Everyday i check on it and wish "Please don't let me be the next one!", and that even goes with a prayer. :) Well, luckily, i posted almost last on the list. But then again, after doing my first EVER post on a blog, IT WASN'T THAT BAD AFTER ALL. Because i get to read other posts, i also get to be informed about all those stuff that i didn't get in class. and most especially, i realized from scanniNg those posts, MY CLASSMATES ARE GOOD! ---NO KIDDING. That makes me want to do good too. Because as far as I am concerned, I really need to keep up. The way Mr. K teaches is kind of different from my previous calc teacher, well okay i'll be honest, way different actually. But three weeks of everyday discussions? I'm getting used to it now. Plus the class is getting more and more fun each day, so fun that i don't even feel i'm "new" anymore. That's good right? :)

Anyway, the test is coming at hand (not sure if it's tomorrow). I'm getting worried coz the last time we had a quiz, i failed, real bad. So i want to make good this time, and to do that I need to stick in my head these few things that i think are the most important:

  • All about Functions
  • Logarythms are exponents and
  • B (in a trigonometric function) is NOT the period. It is not the period. NOT THE PERIOD

That's all. Good luck you guys, hope we all do good, oh! I mean... BEST.

And by the way, why bloggerAthon? Because after this blog, i have to make another one tomorrow. Thanks to Mr. CalcuPrince. Heeheehee! - kiddin'! ;D




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Don't Read the Textbook .... Write It!

If you write it you probably understand it a whole lot better than if you just read it.

The internet has made all textbooks out of date. By the time a book gets published the world community has learned a whole lot more and shared it on the internet. Here's your chance to do the same. ;-)

First, the modern internet textbook is written in wiki format. A wiki is basically a website that can be created as easily as creating a blog post. Watch this to see what a wiki is and how it works.

After that check this out. It's a collection of text books that have been or are in the process of being written by an international community of ordinary people like you and I. As a matter of fact, YOU can add to any of them. Go ahead and do so if you wish. ;-)

What strikes me most powerfully about this latest development on the internet is the fact that anyone can write a textbook on any subject they wish! One of the textbooks being written is called How to pass a course. One of the things I really liked about this textbook was this:

Forming an understanding of the ideas behind each lecture requires active thinking. Try to think ahead of the professor: "What is he going to say next?". If the professor asks someone else a question, answer it in your head. If you answer wrong, try to think why it was wrong.

We will be using a wiki for our story project. Each participant will post their story problem and link to the solution which will be written on another page.

Do you think we should have our very own wiki in our very own webspace or should we add a textbook to the growing list of WikiBooks? Leave your thoughts in the comments to this post.

Cheers,
Mr. K.



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Saturday, October 01, 2005

The Scribe of Calculand

"Haloo Everyone" We started yesterday's class by finding an equation of a given graph. As we were trying to find its equation some of us got stuck in finding the "B" of the standard equation, y= Asin/cos B(x-C)+D. Well in order to figure out the period of a given we should know how long did it take for a wave to complete's its cycle and most of us got stuck in that part. Then after that we answer another question that deals with this equation y=a sin(bx+c)+d and those letters are greater than zero. Then we've been asked whats its maximum and minimum value. We learned that in order to get its maximum and minimum value we juss add d and a for the maximum, and subtract d from a in order to get the minimum.

Next, is we learned about Pythagorean Identities. In order for us to memorize the Pythagorean Identities we should know this identity sin^20 + cos^2o= 1. Then after that we could move it around algebraically and we could get other identities. Also if we divide that equation with sin^2o we get another different identity, 1+cot^2o=csc^2o. All of those stuff might looks different but actually they're the same thing. I think that's all we learned last friday.

The next scribe is.....Ara



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