Eg. Given a polynomial with real coeficients, find the complex roots and tell me the sum of their imaginary parts.
I had one physics teacher who taught us this lesson. he designed a test where some of the answer choices would be the same number but with a different number of significant figures (0 pts if you choose the wrong one). in a different section of the exam, he made answers that were deliberately off from the calculator result, and you had to know your sig figs to know if it was correct (none of the above was also a choice).
after that, we were all very happy to show our work on the remaining tests.
Yes! The Seed of Doubt! If I ever have to create a multiple-choice test, this will always be one of the possible answers :-)
Just last month I had an exam where the examiner had already helped me correct a few basic errors by saying stuff like "well no you switched that around", then asked: "So what is the minimum distance here allowed by regulation?" Me: "Uuuuhh wait, it has to beeeee... 30!". Him: "So it's not 50 you sure?" Me: "wellllll Iii... (fuck you) no it's 30." Him: "Alright."
Comes the test and one of the questions required calculating total resistance of a grid of resistors. The way the resistors were arranged made it impossible for the result not to be an integer. Except there was one tiny half-ohm resistor in series. And there was only one answer that was not an integer.
So I wrote two steps: The reasoning that the result can only be an integer plus 0.5. Then the reasoning that only one answer was left. I likely spent more time on that than I would have on the calculation. Still I got full points and an extra smiley so it was worth it.