Good Question 6: 2000 AB 4

Another of my favorite questions from past AP exams is from 2000 question AB 4. If memory serves it is the first of what became known as an “In-out” question. An “In-out” question has two rates are working in opposite ways, one filling a tank and the other draining it. In subsequent years we saw a…

Euler’s Method for Making Money

Chip Rollinson is a teacher at Buckingham Browne & Nichols School in Cambridge, Massachusetts. Today’s post is a note he sent to the AP Calculus Community bulletin board that I found interesting. I share it with you with his permission. I have done some minor editing. Chip wrote on February 5, 2015: I had an epiphany today…

A Family of Functions

Good Question 2, continued.  Today we continue looking at Good Question 2 from our last post. The jumping off place was the BC calculus exam question 5 from 2002. We looked at the differential equation  and its slope field and discussed the questions asked on the exam. Then we saw how to actually solve the equation…

Good Question 2: 2002 BC 5

This is the second in my occasional series on good questions, good from the point of view of teaching about the concepts involved. This one is about differential equations and slope fields.The question is from the 2002 BC calculus exam. Question 5. while a BC question, all but part b are suitable for AB classes.…

Euler’s Method

Differential Equations 3 – Euler’s Method Since not all differential equation initial values problems (IVP) can be solved, it is often necessary to approximate the solution. There are several ways of doing this. The one that AP students are required to know is Euler’s Method. The idea behind Euler’s Method is to first write the equation…

Slope Fields

Differential Equation 2 – Slope Fields Of course, we always want to see the graph of an equation we are studying. The graph of a differential equation is a slope field.  A first derivative expressed as a function of x and y gives the slope of the tangent line to the solution curve that goes…