In a traditional exam, there is a strong focus on facts and techniques. For instance, in a course on linear algebra, students are asked to diagonalize matrices and they have to check whether a given set forms a vector space, etc. Sometimes I think that a well-trained monkey should also do this well.

Recently I read a report on a different kind of task in an exam which had the following style: 

*Assume $f$ and $g$ to be real-valued functions satisfying $f(1)=2$, $f(2)=3,$ $f(3)=6$ and $g(2)=5$, $g(5)=3$, $g(6)=3$. Is this information sufficient to calculate $f\circ g$ of the value $5$? If the answer is "yes", then calculate the value, if not then argue why.* 

I found this task very interesting since it seems very easy for students who are familiar with the composition of functions and it seems nearly impossible for students who are not. 

**Question: Where can I find more non-standard tasks for (written) exams that try to focus on deeper understanding?**

I would like to concentrate on undergraduate level.