Posted by: Alexandre Borovik | December 15, 2010

## Multiple choice questions, in a sensible way

It is universally accepted that multiple choice questions are evil. Unfortunately, sometimes they are unavoidable evil. Do my readers know any work on systematic generation and use of semi-encrypted “direct procedure + reverse procedure” questions like these:

1. One of roots of the polynomial x2-5x+6 is also a root of (A) x2-4x+3; (B) x2-7x+12;  (C) x2-x-6.  [Put cubic polynomials instead of quadratic, and you will have a problem which will challenge our best students].
2. Which of the following matrices has multiple eigenvalues? (and a list of matrices is given). [In questions like this one, it is useful to have “none of the above” among answer options].
3. Which of the following polynomials has a largest root?
4. Find solutions of the following initial value problems for first order differential equations (list is given). Mark the one which satisfies the condition y(1)=1.
5. Mark two matrices which have a common eigenvector.
6. Etc.

Together with use of scaling which penalises random answers, this type of questions appear to avoid the more odious side effects of multiple choice.  Any references, any links? Many thanks!