Midterm Exam

I took my midterm exam (30% of my grade) this morning at the testing center. I had a good weekend of studying and felt about as solid on this material as I am ever going to be. I was still feeling quite a bit uncertain of the very hardest proof using the precise definition of a limit from my homework set, but I had come up with a kind of sneaky work-around for that type of problem, and generally, I was ready for the test.

However, this did not mean that I was actually prepared for the exam as my instructor designed it. Oops.

The test was an odd combination of the easy (the questions regarding tangent lines, magnification, related rates, etc., were conceptually quite simple but I may have screwed up the calculations), the initially perplexing that resolved itself with thought (e.g. calculating the limits would not have been possible if I had only memorized the rules of thumb in the book since he picked weird little functions that took me a bit to figure out), and the unexpected and confusing. The maximization problem was, I am mostly convinced, a trick question in that it did not have a maximum value. (The homework problems had been a bunch of the "find the package with the greatest volume"/"maximize the profit" normal story problems which yielded an equation to maximize and a constraint, while this one was just a complicated equation that allowed me to demonstrate my (in-?)ability to take derivatives.) The limit proofs were (1) using an expression with a higher power of x, which we did not cover in the homework and (2) proving that a limit of a trig equation did not exist, which we did not cover in the homework; I was not ready for the test questions on limits to be harder than any of the problems in the assignments.

Fortunately I had spent the time on the hardest of the homework problems involving Rolle's Theorem, so I was able to answer the similar question on the test quite thoroughly it seems to me. I was also glad I had (extraneously, in my previous opinion) memorized the equation for motion under constant acceleration because that was what the problem the study guide had described as a "motion problem as in sections [whatever]" turned out to be; I had expected a "find the velocity and/or acceleration using the distance formula" type story problem, and I think many people will be unpleasantly surprised that it was something else. Tam, I was even able to make use of the little representation of the mean value theorem that I used early on to help remember what it was - that it implies that at some point your car must have been traveling at the average speed for your trip - on one problem. (As you may have noticed, my instructor emphasizes the theoretical/proofy aspects of the material.)

The test was not crazy hard, though. There was not, as I had been half-dreading but could not seriously imagine being possible, an equivalent to the infamous "Leibnitz problem" from the homework (i.e. a physics problem Leibnitz solved in a paper published in 1684) or the "pipe carried down a bending corridor" problem that took forever to get anywhere with. But it was a bit harder overall than I had expected, given that there is no way there can be a curve on a test given to a single individual. I should get at least partial credit even on the limit questions, since I did get some of the way there, and he doesn't take off much for dumb math errors like dropping a sign.

But the very worst thing about the test was that it was a full 3 hours with no bathroom break allowed! After an hour and a half, I was ready for a bathroom break. At two hours, I was hurting. By the time I finally gave up about 10 minutes short of the 3 hours, I was dying. I'd say I spent a good 1/3 - 1/2 of the time in the test distracted by (borderline obsessed by) a need to pee. This makes for suboptimal testing conditions. Maybe my voucher for a free Depends undergarment was lost in the mail at the same time as the postcard that told me my test was ready at the testing center.

When I was checking in, a high school girl brought her exam back to the front desk to tell them that it was the wrong version of the test (an "A" instead of a "B" for whatever exam it was); I do not know if they ever found the correct test or if she was just screwed.

At least I have my test behind me, for good or bad, and if the study guide's description of the cumulative final is to be trusted (I know - not quite 100% up til now), I will not need to know how to do proofs using the formal definition of a limit again. Like, for the rest of my life, I hope! Of course, I still have Taylor series to look forward to.