Post...

Okay so it's Sunday night...I'm slightly bored/aggravated, and I have no idea what to blog about... I guess I will take a look at the previous tests we took and see what you guys often missed and see if I can explain it a little better.

Okay, one question that surprised me that people still didn't know was a question about "change in y with respect to x". Basically all this means is take the implicit derivative. If you have forgotten, all you do for implicit derivatives is take the derivative like normal except whenever you take the derivative of y, write dy/dx. After you have taken the derivative, move all like terms to one side (i.e. move the dy/dx's on one side, and the terms without dy/dx's on the other side). Factor out dy/dx and then divide by what's left on that side. You should now have dy/dx = something/something. That is your answer.

Something that some of you are still not doing is a little trick for determining local minimums... Say for instance you have a function. You take the derivative of that function, and set equal to 0 and solve. This will give you the possible points of inflection. The easiest way to determine if it is a minimum (on multiple choice) is to take the second derivative and plug in. If it comes out negative (concave up), it was a minimum. If it comes out negative (concave down), it was a maximum. Using shortcuts like this is really really useful when you need to save time on the AP multiple choice (or at least I imagine it would be).

I can not stress the following enough: simplify an integral before you do it. It's almost always easier...especially on those ones where it looks really difficult to integrate, like it was something you've never done before...Well most of the time it's just written in an odd way...for instance, the integral of 4e^(2lnx)...that's a bit annoying to integrate...you can change it to 4e^(lnx^2) which makes it a lot easier because now the e and the ln cancel, leaving you with 4x^2, which is a very simple integral. So please, just remember to simplify before you integrate.

Anyway, going to go find something to do.

9th Week

Calculus - Week 9

So this week in Calculus was a very stressful one for most...but I got through it rather easily. On Sunday I went to Kaitlyn's house to study with Chelsea, Mamie, and Mabile and we finished our short answer packets. Monday and Tuesday we got the answers for those and revised any questions we had etc. We were having some issues with limiting on optimization problems but it turned out okay. Wednesday was the first part of the exam which was Multiple Choice. The multiple choice wasn't that bad. We were allowed to miss 5 so what I did was go through and do all of those that I knew how to do correctly instead of worrying about one particular problem. Then I went back and focused on those I was unsure of and made educated guesses. It turned out okay because I missed 4 or 5 but that was allowed so I made a 60/60. Next day we got to take the free response part. I think it was very very easy. I felt comfortable with everything about it. I knew how to do the problems and justify myself well.

All in all, all of the preparation for the exam was much needed and helped out a lot. If people didn't make as good of grades this time, maybe next time a little more preparation will help.

As far as what else we did this week, we did implicit derivatives. The reason implicit derivatives (I think anyway) are useful are for those problems that it's hard to solve for y only in terms of x. I think this will come in handy for those.

Basically implicit derivatives are nothing new at all... the steps are pretty much just this:

1. Take the derivative of both sides (implicit derivatives usually have an equals sign)

2. When you take a derivative of a y term, state that. Do so by putting y prime or dy/dx. Like ( taking the derivative of y^2 would be 2y(dy/dx) )

3. Move all of the terms that don't have a dy/dx in them to one side. Factor out a dy/dx out of all the terms that do have it, then divide to finish solving for dy/dx.

That's basically all it is. Just make sure when you are doing these is like...say you are doing product rule with like sin's and cos's...make sure you put cos(x) where its supposed to and cos(y) where its supposed to. It would really mess up problems (like the one we were working in class) if you mix this up. So take these longer derivatives slow and just avoid making silly mistakes.

Anyway, I'm going eat Taco Bell. :-)
-John