Other Topics (Type 7)

Any topic in the Course and Exam Description may be the subject of a free-response question. The two topics listed here have been the subject of full free-response questions or major parts of them. Implicitly defined relations and implicit differentiation These questions may ask students to find the first or second derivative of an implicitly…

Good Question 9

This is a good question that leads to other good questions, both mathematical and philosophical. A few days ago this question was posted on a private Facebook page for AP Calculus Readers. The problem and illustration were photographed from an un-cited textbook. Player 1 runs to first base [from home plate] at a speed of…

Painting a Point

Accumulation 7: An application (of paint) Suppose you started with a point, the origin to be specific, and painted it. You put on layers and layers of paint until your point grows to a sphere with radius r. Let’s stop and admire your work part way through the job; at this point the radius is…

Related Rate Problems II

If you look in most textbooks for related rate questions you will find pretty much the same related rate problems: ladders sliding down walls, people walking away from lamppost, water running into or out of cone shaped tanks, etc. Here are two somewhat different related problems you may like. A girl starts riding down an…

Related Rate Problems I

Related rate problems provide an early opportunity for students to use calculus in a, more or less, real context and practice implicit differentiation. One of the problems students have with these problems is that almost all of them involve writing the model or starting equation based on some geometric situation. Students have to switch from…