It’s time for that midterm exam!  And usually students look forward to my “Bonus Question” section.  I’ll put bonus question harder and more challenging than the usual Calculus question.  And they are worth much less than a typical question. This is to discourage weak students to write pages and pages of junk to try their luck.  A typical question like

Find the volume of a solid of revolution if a region bounded by $y=x$ and $y=x^3$ is revolved about the x-axis (for solution see PatrickJMT‘s video).

That could be 30 points and a typical bonus question will be

Find the volume of a solid whose base is a unit circle on the xy-plane and every cross-sectional slice (perpendicular to the x-axis) is a rhombus of interior angles 60 degree and 120 degree.

and that if answered correctly will be only worth 10 or 15 points with no partial credit for partially correct answers.  Every semester, students who are very strong in Mathematics still got drawn towards these questions and spend a lot of time answering it to my satisfaction.  Sometimes, it’s not all that difficult, it’s just the vocabulary that they had seen before but seldom used and forgot like “rhombi” (instead of rhombuses), “quadrilateral”, “isosceles”, “orthogonal”, “heptagon”, “octagon” and “frustum”.  I usually get lots of surprises and funny answers.  Many think octagon has 10 sides because of October!

Why vocab?  Because I have kids in my class who thought “washer” in the Washer Method in Calculus 2 is referring to a Washing Machine!

But sometimes, when I feel like doing something funky, I’ll ask them

What’s the name of that capital city in Asia that has exactly three words? (I got a lot of studetns putting Ho Chi Minh City as answer to this one.)

Or like today, where tomorrow is Groundhog Day,

Spell the name of the city in our state that’s famous for Groundhog Day.  What is the name of that groundhog?

Other ones I’ve tried in class are:

• When was Issac Newton born?
• Which famous scientist died in the year Newton was born?
• Which is bigger 2^2^2^2 or 3^3^3?  Explain.
• Which mathematician won the Nobel Prize?

The first ones is a little tricky because Newton was born in both Xmas 1642 and Jan 1643, because England was torn between using the Julian calendar and Gregorian calendar.  The last one has multiple answers too, because Dirac (who won the Nobel Prize in Physics in 1933) could be considered a mathematician, like many other Physicists.  And Nash won the Nobel Prize in Economics but many Econ Nobel Laureates after him could be argued as mathematicians, considering the kind of Math they used in Economics now.  Today, many Econ graduate students take classes in Topology in their first year.