Tuesday, June 28, 2016

How To Part II 2016: SAGE Computer Algebra System!

How To Part II 2016: 
SAGE Computer Algebra System!
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 2 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 we toss out the Graphing Calculators and just a Computer Algebra System like SAGE


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 a Computer Algebra System called SAGE. SAGE is a free online Computer Algebra System hosted on Google Compute Engine that you can use with just about any web-enabled device! The 3 ScreenCasts below will take you through the solution of each Free Response Question step by step using SAGE.

BTW, you do need the Internet to use SAGECELL. In a recent post I talked about using python on stand-alone PC without Internet access for testing conditions. However, I don't think that using SAGECELL would be so bad for use in class even under testing conditions. The teacher/proctor should be able to watch what the students do during the test. 

I have my PC Lab/Classroom set up with all monitors facing the rear of the room. So the teacher/proctor can easily see that all students are on task at all times. 

Further, we administer a math placement exam at the local college. This placement exam is computer adaptive and is administered via the College Board website. We have had no problems using these PCs with Internet Access during testing conditions.


2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral


2016AB1c/BC1c) Definite Integral


2016BC2a) Definite Integral
2016BC2d) Definite Integral

PS, here's a shot from the traffic jam I hit going home after the graduation!


Have A Great Summer 2016!!!


Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee


Teaching with Technology, 
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