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Integration Review
Today we did a review on calc AB stuff, including the concepts related to antidifferentiation. An integral is the area under the curve on [a,b] and area below the axis is negative whereas area above it is positive. Also, the idea of integration can be fused with other concepts such as area, volume, and statistics. Mean value theorem is one such infused concept because it is used to find the average value of an integral on a certain interval. I thought this was easy. -
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AP Calculus BC Review
Review for the AP test -
Differential Equations and Slope Fields
We will not have to know the Bernoulli method of solving differential equations, basically meaning that only separable diff eq's will be tested. If we treat y' as separate delta-y and delta-x, we can integrate each rate of change in order to get a relationship between y and x. We also reviewed logistical growth and decay equations (y=Ce^-kt), but I thought these were all fairly simple. Slope fields corresponds to small tangent lines on the curve of the original equation, f(x). -
Sequences and Series
We went over the different types of series and we review the tests that can be used to determine convergence. I feel like I know the series formulas pretty well, and as long as one understands the rates of increase, then determining convervgence is a piece of cake. i.e. x^x > x! > x^n > x > C -
Taylor Polynomials and Power Series
Using the generic formula a power series for any function can be found. There is also a certain interval of convergence associated with the power series, because it is only an approximation to the true curve, and lies exactly on the curve for only a certain interval of x. The error amount can be found using the LeGrange error bound, which I still don't really understand. A power series is the collection of taylor polynomial terms from n=0 to infinity. -
Free Response w/ Calculator
Today we did three practice AP problems with calculator, and my partner for this assignment was Justin. He wrote the first problem and I wrote the last two problems, and I felt that all three problems were easy. I think I could've done really well alone, but with his help we sorted out a few contradictions and doubts in our answers. -
Multiple Choice w/o Calculator
Today Justin and I did a 27-question multiple choice section without a calculator, and we finished right on time. When we had 10 minutes left, we thought we would finish early but the last few questions stumped us and we ended up guessing on one of the questions. Some questions were very straightforward and easy, whereas others seemingly gave not enough information, such as the question about rate of chage of circumference in relation to change in area, but it gave limited information. -
Free Response w/o Calculator
Today Justin and I did three problems without a calculator, and I feel like we didn't do as well as we did on the three problems with calculator. A few of the concepts on the first problem (#4) confused us and I doubted myself as to whether collegeboard was trying to be tricky or my thinking was flawed. -
Multiple Choice w/ Calculator
Today we did 17 MC questions with a calculator. A lot of them could have been done without a calculator, and they were generally pretty easy. There were maybe 2 or 3 that I was confused on. There was also one question about the Lagrange error bound, but we managed to determine an answer to a reasonable degree of certainty. -
L'Hopital's Rule and IBP
Today we reviewed integration by parts and l'hopital's rule. L'hopital's rule can be used only with a function in fractional form, so sometimes a function not in fraction form can be manipulated, such as by diving numerator and denominator, or multiplying by its conjugate to get a denominator. IBP is pretty simple with tabular method. -
Volumes of Revolution
We can use shell method, disk/washer method to calculate such areas revolved about an axis. the dy or dx of the integral has to match up with the respective axis of revolution. Also, a volume has three dimensions; this can be obtained by integrating a function that already has two dimensions. Integration adds the "height" dimension via dx or dy. -
Review of Tests
Today we got back both the partner test and take home test, and although I didn't go to school today, I'm confident that I got 5's on both of them. So... I think I'll be fine on the AP. -
Review Stuff
As review, we went around the class to see who knew the answers to various topics that we covered throughout the year, I felt very confident afterwards. -
Study Day!
I stayed at home and studied for the BC test using my review book. -
AP Calculus BC Test
Finally the day of the AP! Easy 5 test :)
