So, this year we spent a whole day on these types of questions. However, instead of just throwing several past AP questions at my kids, I gave them ten different questions they may be asked to answer for these free responses. Of course, the College Board can ask whatever they want, but these are questions that seem to arise frequently.
We answered these ten questions for two arbitrary functions, I(t) (the rate IN) and O(t), the rate OUT. This seemed to really help my students. I'm relieved that I finally found a way to make these questions easier to digest because these really can be fabulous questions that model real-world situations beautifully.
Below are the ten questions with answers:
And here is the student handout (the ten questions, two past AP FRQs, and two FRQs I wrote).
A great follow-up to this is to have kids create their own Rate In/Rate Out problems. Unfortunately, I don't have time for this project until after the AP Exam, but it's still one of my favorites.