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 learn a little bit of coding?
Below you will find all my solutions using a programming language called Python. Python is a great first language to learn and use as it is very intuitive and powerful especially when solving math and science problems!
The final YouTube ScreenCast is my Pythonic Calculus Executive Summary! This video summarizes everything we figured out in python related to solving Graphing Calculator Active Free Response Questions by coding instead! If you want a slower introduction to these numerical methods, please view the first 3 ScreenCasts. These ScreenCasts will take you through the solution of each Free Response Question step by step using python.
2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral
2016AB1c/BC1c) Definite Integral
2016BC2a) Definite Integral
2016BC2d) Definite Integral
Pythonic Calculus Executive Summary:
Includes plot() command!
PS, here's a shot from the traffic jam I hit going home after the graduation!