Another year is almost over and of all the memorable events 2 problems (which aren't particularly difficult) caused tremendous difficulties for far too many students. It's especially surprising because I have a class of (mostly) good students: some are highly gifted and others compete for (and win) various math contests.

Problem 1: Solve for $latex x$: $latex \pi^{1-x}=e^x$

Problem 2: Find the domain of $latex f(x)=\sqrt{4x-x^2}$

Problem 1 is from a Thai entrance exam; the Thai version of an SAT test. I put it on a regular test expecting to challenge the bottom 25% of the class. Instead, it took down the "bottom" 75-80% of the class and some good students blanked on it. If you work it out, you'll see there are multiple ways to do it and none of them are particularly difficult. The exponent $latex 1-x$ (as opposed to, say, $latex x-1$) combined with $latex x$ on both side poses problems, even for "good" students. The second problem was actually part of a problem on finding the minima and maxima of the function. It was causing difficulties during the problem session in class so I tried to break the problem into pieces and have them get the domain. You could count the students who could get the correct answer on a mutilated right hand. And I even told them that inside the square root was a parabola....

As a result, I've added these two problems to the Problems page. Try them on your students!