Thursday, July 27, 2017

How To Part IIA 2017: What About Desmos?

How To Part IIA 2017:
What About Desmos?
We just had our Graduation Day at the High School. I suppose that's my unofficial start to Summer. I will miss my Seniors, we had a great year together. The whole week before graduation I was finishing up a series of YouTube ScreenCasts about solving this year's AP Calculus Exam Part IIA. This playlist serves as a summary of this year's Final Project! 

Part IIA is the first Free Response section of the AP Calculus Exam. This section consists of 2 AB or 2 BC questions requiring the use of a Graphing Calculator. AB1 and BC1 are the same question. AB2 and BC2 are different. Below you will find the solutions to these Free Response Questions in the following order: AB2, AB1/BC1, BC2. In this fashion, we covered AB only questions first, then AB/BC questions and finally BC only questions, ie in order of increasing difficulty.

For over 2 decades, I have been teaching my students to complete this section using a TI89. Most schools still use a TI83 or TI84. These past few years, my students have been using a class set of TI nSpire CX CAS graphing calculators that were donated to my classroom via DonorsChoose. Thanx to all my donors, my students are indeed very fortunate!

There are 4 functions a Graphing Calculator needs to perform to be allowed on the AP Exam: 

1) Graphing in an arbitrary window, 
2) Solving for the roots of an equation, 
3) Finding Numerical Derivatives and 
4) Finding Definite Integrals. 

All of these capabilities are demonstrated in the ScreenCasts listed below.

However, in this blog post I wish to demonstrate that the use of a Graphing Calculator is, in fact, not necessary. Why don't try an online Graphing Calculator like Desmos

I'm waiting for Doc Brown from Back To The Future fame to come by and say, "Calculators? Where we're going, we don't need calculators!"

Below you will find all my solutions using Desmos. Desmos is a great alternative to a handheld Graphing Calculator such as the TI 84C or TI nSpire CX CAS. I was going to try Geogebra too as it has some CAS capabilities, but Desmos was much more user friendly and powerful. Geogebra is great as a Geometer SketchPad, but Desmos is where it's at if you want CAS!

2017AB2a) Definite Integral
2017AB2b) Numerical Derivative
2017AB2d) Definite Integral

2017AB1c/BC1c) Definite Integral

2017BC2a) Definite Integral
2017BC2c) Definite Integral
2017BC2d) Numerical Root
2017BC2d) Numerical Derivative

PS, here's a shot from the traffic jam I hit going home after the graduation!
Have A Great Summer 2017!!!

Teaching With Technology,

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