Here's the weeding out question from my intro physics final. We had been studying pendulums (pendula?), levers and rotation. Then on the final:
Consider a hockey stick laying on the ice. (To simplify, one-dimensional rod on a frictionless surface.) It is struck by a hockey puck, traveling perpendicular to the stick, transferring 100% of its energy. In terms of length of the stick l, distance from the end of the stick of the impact d, mass of the stick m, mass of the puck m', and velocity of the puck v, describe the resulting motion of the stick as it travels and/or spins on the ice.
Sure, I'd like to have spent some time working with the formulas for two- and three-dimensional problems like that. But this was asking us to derive those formulas on-the-fly during a timed exam.