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?
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!
2017AB2b) Numerical Derivative
2017AB2d) Definite Integral
2017AB1c/BC1c) Definite Integral
2017BC2a) Definite Integral
2017BC2c) Definite Integral
PS, here's a shot from the traffic jam I hit going home after the graduation!