I learned what slippery slope meant 2 years ago in debate. Basically, it means you're starting down a path that slippery, and once you start slipping you can't save yourself, and then you just slide on down the hill until you crash into the bottom.
I got my 18.02 test grade back today and, sure enough, failed it. No surprise there, but I wanted to see what went wrong, so I looked back at the test and what I found made me sick.
You can't take the integral of without using a trig identity, mainly . So, in the very first part of a three part problem, I was asked to take the derivative of (while also doing other complicated things, which I'll leave out of this entry). Instead of just using the chain rule and realizing that , I used the identity that I normally would have used for an integral, forgetting that I didn't have to use it for a derivative. This, in turn, was supposed to be set equal to something else. For those of you mathy types, setting trig functions that are in terms of equal to trig functions in terms of just and expecting things to cancel is a mess. The result was me spending about 10 minutes on the first part of the problem alone, and not even ending up with an answer that was close to looking correct. That, in turn, hosed up part b of the problem, and subsequently part c. All in all, that one problem on the test took me 15 to 20 minutes, eating up a HUGE chunk of time. Huge enough, in fact, to eliminate any time I had to finish the last question on the test. Add that to a few minor mistakes in other problems due to rushing (trig identity's fault) and you end up with a 54/100.
But remember, I understand this material, and I'm not lying when I say that. When I got back to the dorm from dinner tonight I sat down, extremely frustrated, and took the test again (he posted it online, along with the answers). I did each problem, including the last one (the one I hadn't looked at while taking the test), just to prove to myself that I know what I'm doing. What happened? I finished the entire test in 27 minutes with a 100%. I promise I can do math, but I also promise that one simple little trig identity can be disastrous enough to destroy an entire test. Thank you little trig identity, I hate you. Now I have to take the make-up test on Tuesday, which I'll probably get a 98% on, just like the last one. FRUSTRATING!