"End of the Year Final Exam" Blog Post

Dear Student,

If you're reading this letter, I bet you've heard all about the flipped classroom. But whether or not these stories or rumors bring about positivity or negativity all depends on you. The flipped classroom is very different from a traditional classroom setting because it involves more independence and drive (as in get ready to manage your own work schedule). What you can expect to see is a lot more computer use in your life--not that you don't already do enough of that *cough* facebook/tumblr/twitter/instagram/flickr/youtube *cough*--through various websites that will be used throughout the school year. In the beginning you might feel very stressed especially once Mrs. Kirch asks for you to create your own blog or mentormob, but don't fret, in time you will get...it.
The first few weeks of the school year will be all about your rate of adjustment. Because the flipped classroom requires you to do nearly all of the learning at home, "homework" (which for your benefit to know is ACTUALLY, PQs, PTs, Quizzes, WPPs, Student Videos, and Student Problems) must be done in class. Go ahead, open your eyes a little wider, I know your freakin' out a bit because ALL of this is different from your previous math class. However, I assure you it is manageable as long as you stay motivated to do work day-in and day-out.

The best way to adjust to the flipped classroom is to master the inevitable struggle that all of us juniors/seniors face, time management. But of course! how could I forget, you're growing older, more independent, your parents finally let you have a boyfriend (girlfriend?)! and on top of that you've got all of your extracurricular activities and AP classes, well get ready to pile on the Math Analysis flipped classroom because this class is just as important--if not more useful--than going out to the movies on Friday. I remember at the beginning of my junior year when I struggled with this exact situation. If the task of creating a math blog and WPPs/Videos was not difficult enough, I had to stack that frustrating job on top of my AP classes, Red Cross Club, and Band activities. And well, knowing me, I am definitely technologically challenged. The first WPP I ever made took me all day (like hours on end) because I just couldn't figure out how to use the technology on my computer and phone!

But don't let my little mishap startle you, everything is rough at the start. With a little enthusiasm, a dash of dedication, and a load of hard work, you'll make it through this year before you know it! Just make sure to keep up with all of the videos and WSQs every night and ask plenty of questions! The work load that Mrs. Kirch gives may seem tedious and overwhelming but you certainly will learn A LOT :)


Sincerely,

               Tiffany Tran

Unit V Big Question

Explain in detail where the formula for the difference quotient comes from.

The picture above is just to refresh your memory on how to evaluate the difference quotient. (and for me to reference to the formula to instead of typing it out)

What is the difference quotient? The difference quotient is just a fancy way of writing out the slope of an equation. And in calculus it is used when introducing a concept called the derivative.

Because the difference quotient is just another way of saying slope, we know that this formula must relate to the slope formula:

Moreover, we know that the slope formula needs two coordinate points on the graph, this is much like a secant line. A secant line looks like this: (in red)

Using this information, lets figure out how the difference quotient formula came to be!
Watch this video up to minute 6:15 to see how the slope formula turns into the difference quotient formula.

As you can see, the difference quotient comes from using two points to find slope, and these two points on the graph form to make a secant line. But what about tangent lines? Well, we know that tangent lines only touch the graph once, so how to we find the equation of the tangent line of a graph?
First off, the slopes of tangent lines are referred to as derivatives.
To find the derivative, do the difference quotient formula normally, but take one more step, find the limit as "h" approaches 0
Here's an example: (watch starting at 2:30 to the end of the video)

Sources: First picture-http://www.coastal.edu/mathcenter/HelpPages/Difference%20Quotient/sld002.htm
Second Picture-http://math.about.com/od/allaboutslope/ss/Find-Slope-With-Formula-JW.htm
Third Picture-http://clas.sa.ucsb.edu/staff/lee/secant,%20tangent,%20and%20derivatives.htm
Difference Quotient Video- http://youtu.be/1mlkc3Pfxu4
Derivative video- http://youtu.be/vzDYOHETFlo