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Integration Techniques
Today, we reviewed integration techniques and formulas. A key is that I memorize the arc-function integrals before the test. Integration by parts and the Mean Value Theorem for Integrals will also come in handy. I need to remember to try the easiest method first. Some difficult-looking integrals can be simplified through u-substitution. -
Differential Equation Review
This topic is pretty far back in my memory because we covered it before winter break.It was a pleasure to hear that first order differential equations and Bernoulli equations will not be on the AP test. They key topics in this unit are Euler's method, exponential growth, and logistic growth. KEY POINT: Remember to separate variables before integration. -
Sequences and Series
I remember this topic pretty well. We had practiced convergence tests pretty thoroughly in the midst of this unit. A key point is that sequences converge when they approach a finite number while series converge when a(n) approaches 0. Just because a(n) of a series approaches 0 does not mean it converges. The nth term test is only a test for divergence. I feel alright with all of the test for convergence. The ratio test is especially useful, but the integral test is one i dread to use. -
Taylor Polynomials and Power Series
Taylor Polynomials and Power Sereies are pretty simple for me. I like the power series because I just use the techniques from the series unit to find the IOC, etc.The most difficult thing from this unit is the LaGrange Error Bound. It's easier when I think of z as any convenient maximum value, but I still have trouble remembering the formula. Jon Peake made a comment that makes this a little easier though. The remainder is just the (n+1) term of the taylor polynomial. -
Free Response Practice Test (Calculator)
I thought this section went pretty smoothly. I worked on the Reimann Sums question individually while Adam worked on the volme of a container problem. We then worked on the 2nd question together. The last part of question 1 confused me as you had to find the total cost of water. -
Ap Free Response Practice Test (No calculator)
This section had a mediocre difficulty level. I did the third problem on my own to start. It had to do with taylor polynomials. I realize that I made a mistake on one section of this problem. I was supposed to substract the taylor polynomial of cos(x) by 1. I mistakenly subtracted each term of the taylor polynomial by 1. Otherwise, this section went ok. -
Practice AP Exam - Multiple Choice 1
This was the non-calculator portion of the practice AP. Adam and I split these problems up between odds and evens. I understood almost everything of what was on this section. -
AP Practice Exam - M.C.
This was the calculator portion of the AP practice exam. Adam and I split this section up between odds and evens, just like the last part.There were only a few that we had trouble with. For Euler's Method, I need to keep in mind one thing. When given an expression for f'(x) that includes f(x), f(x)=y. -
Review of Practice AP
On this day, we reviewed all of the parts of the practice AP exam. Overall, Adam and I did pretty well. We only made a few mistakes. On the multiple choice, one of the mistakes was caused by circling the bubble, which we did not intend to. We also received our take home test today. -
Advanced Integration Techniques
Today we reviewed the advanced integration techniques needed for the AP exam. Luckily, trigonometric substituion is not on the test. Parts , L'hospital's Rule, and integration bounded by infinity or asymptotes are basic to me, so I shouldn't need to study them too much. I do need to remember that when using tabular method, the sign begins as positive before alternating. I also should review the integrals that produce arcfunctions. -
The Uses of Integration
Ingtegration is primarily used to find the area of bounded functions. It can also be used to find the voulme of functions rotated around a line. The disk method uses pi, R^2, and r^2 and revolves a function whose rectangles are perpendicular to the axis. The shell method uses 2pi, and xor y times the function. The shell method rotates a function whose rectangles are parallel to the axis of rotation.When rotating around a line that is not an axis, just subtract from function or vice versa. -
Absent
AP Chem Test -
Absent and Pre-AP Studying
AP Spanish was the test this day. For the night before the Calc BC AP test, I reviewed certain topics that I had had the most trouble with. This included volume formulas (especially revolved around something other than the x or y axis), integrals that form arcfunctions, and logistic growth. I dot a great night sleep too! -
AP Calc BC Test
I thought I was extremely well prepared for this test. I finished with 5-10 minutes to spare for the multiple choice and free response. For the free response, the questions were pretty simple. One was tricky in that it appeared to be logistic problem but really wasn't. Overall, I feel that I did very well.
