What are the best type of answer choices for multiple choice questions? Numerical only like the probability and financial math actuarial exams?
I have an opportunity to utilize a multiple choice computerized system to let students practice and prepare for exams for a first calculus course at a university in the USA. This opportunity would be an optional self-learning/self-assessment supplement; not a requirement.
Course grades are based on three in-person, hand-written, free-response exams and on weekly quizzes. Students are not allowed calculators or notes for them. They are to use analytic-type reasoning and are awarded partial credit. HW is never collected.
Since the only option is multiple choice I need to decide if the answer choices should be all only numerical or not. My concern is that revealing non-numerical answer choices gives away too much. But then numerical only options limits what types of questions I can ask I think.
I mean suppose I want to ask about the MVT. Numerically, I could ask to find a value in the interval guaranteed by the theorem. But I also think it's important for them to verify that the theorem even applies which seems to me to be non-numerical.
Example of a numerical question that does not reveal too much in my opinion:
Q. Suppose there exists whole numbers $c$, $d$, and $e$ in the interval $[1,9]$ such that $f(x) = c\sin(x)$ and $f^{\prime}(\frac{d}{e}\pi) = 4$. Then $c + d$ equals
A. 5 .... B. 6 .... C. 7 .... D. 8 .... E. 9