final? :)

Math Magic

Andrea’s Reflection

At first, this calculus project was really difficult.  I now have a new respect for those AP people who write all of our stupid free response questions!  IN the beginning, it was really difficult to think of a topic to write about.  I tried to think of the things that I do every day that involve calculus.  Believe it or not, I found something.  Even though the data is more than likely incorrect, this problem gave me a new understanding of integrals.  I am ashamed to say that until about one week before the AP exam, i didn’t know that calculators could do all of the hard work for me.  What a discovery that was!  It made me excited and bitter, but it worked out to my advantage.  On the second problem that I made, the area of R, I had originally planned to use the volume of semi-circles.  The answer to this didn’t make much sense because the volume of R was smaller than the area of R.  I thought that since other people would be doing my problem, i better make it more believable.  This project taught me a lot because it really stressed to me how hard it really is to make a multi-part calculus problem.  I also learned how to use a blog (which was the downfall of my English class last year)! 

My reflection on this project…

Truthfully, this project was a bit of an eye opener for me. I believe that I am pretty competent at solving most calculus problems, but I really got to learn the mechanics of the problem by “teaching” it. In this project, I felt like I was learning the problem all over again. I just wish I had more time to get into the project.

My five minute…err….compilation of what calculus has yielded for me.

            The first problem I created focused on finding the derivative and rate of change of functions.  I gave little information and forced the person solving to use their own knowledge of volumes and find derivatives with respect to variables not present in the problem.  I chose these problems to show the complexity of calculating derivatives.  The second problem I created focused more on integrals of trigonometric functions.  It shows the complexity of integrals, as well as forcing the person solving to be able to use their calculator to find an integral and derivative.  I chose both these problems to demonstrate the main types of problems in calculus.

Area R

Turn Up The Heat

Carter’s calculus project

Emalee’s Calculus Final

So that’s my slideshow. I really hope it made some sense, I have a hard timeexplaining math in words. I chose integrals and riemann sums because they were the best way to express what I wanted to find, and they’re fairly easy problems to figure out and relate to the real world. They also incorporate derivatives and many other concepts we’ve learned in Calculus. I did learn from this project. I learned that Riemann Sums  don’t have to be divided up into rectangles of equal width, but can be a combination of rectangles of various widths. I also learned a lot about how to create a problem, and that limits and derivatives are really hard to relate to the real world (but then isn’t all math irrelevant at times?). I think it was valuable as an end of the year assignment. Obviously at this point there’s not much else to learn so I can’t say that I learned any new concepts. But I did learn how to relate what I’ve learned to daily life and how to use different blogs and sharing programs.

Oh, and guess what? I just finished my last Calculus assignment EVER!!!!! And I may just possibly have finished my last math class ever too….hopefully I did well on the AP test.

Yay!!!!!!!

Good luck future AP students! It’s hard but don’t quit. Take it from me, you’ll regret it if you do.

<3 Emalee