Unlucky Guesses

The most recent exam in the Calculus Circus covered the tail end of derivatives (mostly max-min) and the beginning of integration (very basic anti-derivatives). Instead of overloading them with many word problems that would make the exam too long, I made up a three-part, 10 point question that got to the heart of the matter: do you know when to differentiate and when to integrate. I came up with some scenarios, like "You have the function for cost, and you want the function for marginal cost," or "You have a function that models the rate of change of the population and you want to find the total change in population," and they were asked whether they would solve the problem by integrating or differentiating. No specific function was given, no calculations needed to be done. Just choose whether you should integrate or differentiate.

It was sort of alarming how many of the students got the problem wrong. Especially since all semester I've been emphasizing the key words that tell you which technique to choose. Someone (that would probably be me, huh) needs to teach them that on this type of problem if you don't know, then you should pick one choice and put it down for all the parts of the question.