When Test Questions are Impossible

I recently had an unusual experience involving academics and wanted to share. There's no moral, comment, or witty observation here, just an at-the-time frustrating story.

I was working on a graded free-response homework assignment for my online Calculus AB class, specifically about integrals concerning inverse trigonometric functions and logarithms. The first three questions were fairly simple, but the final (fourth) one was unlike anything I had seen in the instructional materials.

The problem required me to integrate something that looked somewhat like it would become an inverse tangent. However, the normal tricks of fraction rearranging and substitution were ineffective; the degree of the numerator was just 1 too low. (Another part of the same question required me to take an integral superficially very similar to this, except the techniques they taught me actually worked.)

Though they didn't teach me partial fractions, I knew of the existence of such things and looked up how to perform the decomposition. (Having to learn or re-learn concepts using external sources is par for the course for my use of this online learning platform.) The decomposition didn't work; I had subtly miscopied the denominator and the real denominator could not be factored in a way that could be decomposed. I then learned and tried integration by parts, but it failed for various and sundry reasons.

At this point, I had been working on the problem for half a Sunday and throughout various classes on Monday for a total of several hours. Unable to get anywhere, I went to ask the on-campus calculus teacher. We worked at it for half an hour; he tried things that I hadn't seen before at all. After lots of complicated-looking approaches, we discovered that the problem was more or less impossible.

He suggested that I "reinterpret" the problem and simply change the denominator to something I can deal with. I did so, solved the revised problem, and included some analogy of this account in my submission.

The teacher gave me a perfect score.

Don't Let the College Board Send You Stuff

I took the PSAT a few months ago and was naive enough to fill in the box that allows the College Board to send me "college opportunities" via e-mail and snail mail. This also allows them to share my contact info with colleges who are interested.

It turns out that every college ever (except the ones that I'm actually interested in attending) is "interested", at least interested enough to flood my inbox, both virtual and physical, with the same unpersonalized junk all day every day. Half of these seem to be offers for some sort of guide to finding the right college, many say something like "find your ____ at _____", and still others are "people" wondering whether I got their first e-mail and/or waiting for a response.

I delete them all.

There is absolutely nothing useful about these e-mails. They are literally all the same. When I need to decide what I'm looking for in a college, I can go to my high school's college counselor. At least she actually knows (roughly) what fields I'm interested in. I'm not sure why these colleges market themselves to me as "liberal arts" when I am (and marked on the optional "possible college major" section that I am) a math/CS/physics/science/anything-but-liberal-arts person.

It is interesting that some colleges set up "individual" "web sites" for me: subdomains of their web site, named after me. Unfortunately for them, I understand exactly how this works, and it requires zero nonautomatable work: have a wildcard "*.whatever.tld." DNS entry that goes to your site and use URL rewriting (ISAPI) to mash the requested URL into a page request that results in the auto-generation of a "personal" page.

I've been clicking the tiny, sometimes almost invisible, "Unsubscribe" links for a while now, but the e-mails still keep coming in. Sometimes, the link is broken (404 error) or even nonexistent. I've considered reporting the latter to the FCC, but I don't understand the complaint form.

Anyway, the lesson you can learn here is don't check that box. You'll regret it.

Preparing a House for Refugees

Several members of my school's National Honor Society did some volunteering with World Relief, the organization through which we distributed Christmas gifts to refugee families in the area. This time, our job was to set up a house for a refugee family from Burma (Myanmar) that will be arriving later this week.

I noticed several things upon entering:

• The kitchen tiles are the dirtiest tiles I had ever seen in my life. Additionally, one of them smack dab in the middle of a doorway (that doesn't have a door) threatens to flip over or break in half if you step on it wrong.
• The stairs down to the basement are wooden and wet (which makes me afraid they're just going to break apart one day) and also really steep. The stairs up to the second floor are much more solid but just as steep. (I almost fell down them once.)
• There are scribbles, dents, and places where the painter missed a spot all over the walls and cabinets.
• There are at least three generations of phone line in the basement.
• The water faucet in the bathtub cannot be turned off.

Let me expand on that last part a bit. As far as I can tell, water had been running in the bathtub for days. The faucet can't turn it all the way off, even what should be the "off" position produces a strong flow. When I arrived, the people already there were trying to figure out how to stop it. I located the main water valve and closed it, solving the constant-waste-of-water problem, but making it hard to do dishes.

World Relief sent two of its staff; they were very helpful, bringing supplies and a checklist of what needed to be done. My first task was setting up beds from frames. Since I actually read the instructions, this wasn't too hard - the trickiest part was getting the mattresses up the very steep and very narrow stairway. After a little bit of furniture rearrangement, the room layout seems to make sense.

I then went on to cleaning the kitchen. I used some wet rags to wipe down the inside and outside of cabinets, drawers, and the refrigerator. This actually took quite a while. I had to take a break because I reached a cabinet that was so dirty the rags needed to be cleaned almost constantly, and the water situation was not such that we could do that. (By then, World Relief had called a plumber and he was working on it.)

So, I went over to the living room and moved a bunch of furniture around until I got a layout that seats everybody in the family and that I think makes sense. This involved moving certain gaudy plastic chairs upstairs where they wouldn't destroy the reasonably nice look of the living room.

We all took a short break to let the plumber finish his job. Apparently, the pipes had frozen and one had burst, resulting in the constant gush of water into the bathtub. I then finished scrubbing the kitchen's storage areas and made an effort to remove the crayon and pencil scribblings from the walls.

The final stage was to wash the dishes. Actually, by the time I got there, they had already been washed with soap - we just needed to rinse, dry, and store them. While I worked on drying them, the kitchen floor was mopped, significantly improving its appearance.

The house could still use a good vacuuming, but we didn't have one. It looks better than when we got there, and I think we did a pretty good job.