When I teach calculus 1, I usually put a "high discrimination" question at the beginning of every exam. Student performance on that question is usually very well correlated with the exam grade. It helps me quickly assess class performance right at the start of the grading process.
Examples of such questions:
Draw the graph of a function f, continuous on the reals, such that: f(x) > 0 always, f'(x) < 0 always, and f''(x) always has the same sign as x.
The line y=3x-2 is tangent to the graph of y=f(x) at x=4. What is f'(4)?
Examples of such questions:
Draw the graph of a function f, continuous on the reals, such that: f(x) > 0 always, f'(x) < 0 always, and f''(x) always has the same sign as x.
The line y=3x-2 is tangent to the graph of y=f(x) at x=4. What is f'(4)?