# Source of conceptual, multiple choice calculus questions

I'd like to give my Calculus 1 class periodic multiple choice questions that really test conceptual understanding. Ideally, I'd like these questions to require very little computation. I know that a lot of textbooks have true false questions, which I like, but I'm hoping to find a source of questions with more than two possible answers. Something along the following lines:

Suppose that $$f(x)$$ and $$g(x)$$ are such that $$f'(x)>g'(x)$$ for all real $$x$$. Which of the following statements must be true?

1. The graphs of $$f$$ and $$g$$ intersect exactly once.
2. The graphs of $$f$$ and $$g$$ intersect no more than once.
3. The graphs of $$f$$ and $$g$$ do not intersect.
4. The graphs of $$f$$ and $$g$$ may intersect any number of times.

For a student who understands the derivative well, this question could be answered in under one minute with absolutely no computations.

Anyone know of a good source to find a bank of such questions? It would be ideal if the TeX code was available too, or if the problems were already encoded into WeBWorK or some other online homework system.

• @mweiss: For brevity's sake I wasn't completely explicit, but implicit in the statement that $f'(x)>g'(x)$ for all real $x$ is the fact that both $f$ and $g$ are differentiable on the reals, and thus continuous. Feb 28, 2016 at 5:30

Cornell's Good Questions Project has a great question bank for conceptual questions.

• That's terrific... and somewhat addictive. Feb 28, 2016 at 21:08
• I found that this site(GQ project) is not available anymore. Does anyone know what happened to it? Jun 25, 2023 at 1:24
• I recommend that you ask the math department at Cornell. If I have time, I'll try to do that. Jun 25, 2023 at 2:10
• I was too busy in June, but a little googling found it: pi.math.cornell.edu/~GoodQuestions/materials.html#GQ I have fixed the link. Sep 3, 2023 at 15:21

The Calculus textbook of Hughes-Hallett, Gleason and McCallum et. al. includes ConcepTests that are rather good for this purpose. Sorry this is not a free online resource, but I hope it helps.

I tend to download testbanks for Pearson's TestGen application (requires instructor account at Pearson, available for almost any text they produce) and hunt through them for conceptual questions for this purpose. Sometimes it's a bit slim pickings in this regard, but it at least gets me started for a first semester, and then more ideas occur to me as I teach the course, and I personalize the quizzes more over time.

Though not nearly as good as some of the other suggestions here, the practice exams for AP Calculus contain decent problems. The sample multiple choice ones are buried inside the "AP Calculus Course Description" pdf.

If anyone is still interested...

Calculus Video Projects have some resources that contain conceptual problems under their 'Resources' tab. They also have conceptual videos for Calculus 1 topics.

https://calcvids.org/videos/