This week I spent a decent amount of time contemplating whether or not I should spend $93 to take the AP Calculus exam. I was accepted to the college of Literature, Science and the Arts at UMich a few weeks ago and I am pretty sure that's where I'll be next year. The issue is that they require a 5 on the AP test to be considered for any AP credit at LSA. I know that it is possible to score a 5 on the test but knowing myself and my abilities I do not think it is a good idea for me to take the test because I am not the most proficient when it comes to mathematics. While I could study a lot for the test and potentially get a the score I need to, knowing myself and my current mentality towards school I do not think it is a good idea to take the test. But I did appreciate the lessons I have learned from Calculus over the past year. While the class itself seemed to be easy at times we were still learning. So I may not be taking the test but I can confidently say that I feel that Cresswell's class has given me the tools to do well at the next level. ( Or at least I hope it has XD)
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The shell quiz from last week didn't go as well as I had hoped but I figured out what I was doing wrong. Just simple mistakes like I had done earlier last week with the disks and washers method. Also I just realized that I was misspelling the word "disks" the whole time, it is disks not discs. But now we are finished up learning known cross sections which are fairly straight forward and working on a packet for solids of revolution. And we just took a test and I know I did better than I had on the past two quizzes. Probably did not get an A on the test but I did spend much time outside of class of homework other than looking briefly at my mistakes on the quizzes.
This week we tied up loose ends about discs and washers for finding the area under a curve. I had an alright understanding of what I was doing but for some reason on the quiz this week I made a couple of silly mistakes. It was tough for me to decide which method should be used in some situations because I was having a difficult time picturing what was going on in my head. The revolving around a line that is not an axis proved to be frustrating since (I am pretty sure) the way Gavin and I had used in class was not the way you had initially taught us. But in the end I think I learned what I needed to about discs and washers.
This week was test week. We started off with a couple of review assignments that were not too bad. Except that the bulk of the learning for this test was before break and here I am over a week later without having done any sort of school related work. I am not exactly remembering what all we learned before break but I think that I can remember enough to not fail the test. So I have that going for me. But other than that I feel like optimization is pretty straight forward for the most part. It was confusing at first like the first week we learned it but after the first quiz it seemed to click for the most part. I get a bit more confused with the no calculator portion of the stuff. Not because I am not sure what I am doing but rather I do not really know how to share the information that I think I know. If that makes any sense.
Monday was mostly spent finishing up the Optimization quizzes from Friday. The quiz did not go too poorly but the thing that I had gotten caught up with while taking it was the second question on the first page. When it comes to surface area I always seem to blank. I know what it is usually but the question said to remove top and it raised too many questions for my exahuasted brain to handle early on a Friday. However after thinking about it for the weekend I managed to get a grasp of what it was asking. This week we also got a visit from a Mount Pleasant High School Alumni, Jean Han, and her friend from CMU. They shared with us a lesson about number sets and how they can prove that there are multiple infinities. Then we got to do an activity as a class with this idea in our heads. Where whoever played as Cantor ended up winning the activity because they could always choose something that would not match the other players row. Jokingly I covered up my answers as the not Cantor player and made the game a little more challenging. I ended up beating Corey on a fifty/fifty split on whether he picked x or o. https://en.wikipedia.org/wiki/Set_theory This week felt pretty straight forwards. Having the notes printed out was handy, took away that extra bit of work in the class. The graphing activity went better than expected, our pod was able to get most of it done which was surprising to say the least. I did a lot better on the curve walk than I had expected I would. Both times around the class I did pretty well the first I got 9/10 and the other I got 10/11 so it was not too bad. I think I got the basic concept for that activity. Curve sketching on the whiteboard was pretty fun too. It's always a good time to bust out the old whiteboards and do a bit of writing. Makes the class more engaging.
Not feeling the most confident with the quiz from Thursday this past week. When I am doing problems like the (I think) second to last of the front side with multiple uses of dy/dx I have a tendency to mess up a bunch and after five attempts work myself into a corner. The corner then becomes a trap where I convince myself that half of the steps are correct but do not yield the right results. So it can't actually be right way of doing things so I end up just leaving the space blank and not giving an answer. Which is always fun so I'll probably have to add this quiz to my list of things that I should retake before the end of the six weeks.
U substitution went a little different that I had expected which makes me think that I did it wrong. I just replaced x with U or something like that for what ever the string of numbers following f(x). It could be right but also it could just as easily be wrong. Following up on what seemed to be to easy was the C^3 which was an derivative. I think that I forgot to add +c at some point along the way in it but I can't remember. If it is the same thing I am thinking of right now I will see it when I get the quiz back and than promptly have to retake it sometime later. http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?doc=..&topic=ma&chap_sec=02.5&page=theory Chain rule overall seems pretty straight forward. The only time that I find myself having issues with it is when there are trig functions involved. I have a tendency to forget to use the chain rule and leave an unfinished or incorrect answer. I should probably make a note of that or something on my formula sheet or something. Other than that I feel okay with using the chain rule in the mini quiz. Things are making sense only that one problem on the mini quiz I think gave me any issues. But I guess I'll find out in a little bit.
There was not much to do as far as issues with the homework this week. My biggest issue is usually near the end of the assignment just because I begin to get lazy and it tends to be later at night so I do less of the problems. Other than that the homework felt about as straight forward as the quiz did. So we expanded a lot on derivatives this week. I am pretty confident in them so far, Monday we were introduced to anti-derivatives. These are probably the most straight forward thing that I learned from the past week. The trickiest part is remembering to add +c after you finished the little work that goes along with it.
The product and quotient rule took up most of the week. Neither of them are too bad, however the quotient rule seemed a little backwards at first. For the first half of the assignment every time I used the quotient rule I mixed up U and V and kept getting odd answers. Starting with the denominator just took some getting used to.Then later we moved into incorporating trig functions which were pretty easy. Minus the part that I was using csc as the derivative of sin for like four problems, but asides from that nothing too extreme. Our test this week did not seem awful. I felt like most things went well nothing stood out as impossibly hard but I do have a habit of convincing myself that I am right; especially when I end up being wrong. If I had to guess a score I'd guess better than half, just giving a bit a room for some error. https://www.khanacademy.org/math/calculus-home/integration-calc/antiderivatives-calc/e/antiderivatives I feel like I am understanding pretty much everything that we are doing in class as of right now. However when it comes to test day I keep forgetting simple things that are completely obvious after the fact. An example being the C^3 on the test this past week. It asked something about what function F(x) is or something along those lines. Which looking back at what I know now it is clear to me the f(x) = 8x^3 or something along those lines. BUT during the test it did not click with me so I all I did was look at the part where I was taking the limit as h was approaching zero and said f(x) must be zero because I wasn't thinking clearly I guess. To fix this over thinking in the future I am just going to take a step back and see what the question is actually asking for instead of just writing down an answer.
There were a couple more questions that tripped me up. One was on the front side lower left corner. It asked about finding the equation and it gave f(x) = a and then f'(x) = b. I completely blanked on how to do that problem during the test but after talking about it with some classmates it dawned on me what I supposed to do and yeah... The last question I wanted to talk about was the one on the backside top right that asked why zooming in was just an estimate. I said it was only an estimate because we did not have enough information which is partly true, or at least I think it is. My thought process behind this was that when you are zooming in you are taking a really rough limit as you get closer to a number. So its like trying to find a derivative except you don't have enough information about the slope of the tangent line to actually find it. Since when you zoom in it just creates a line that get more accurate as you zoom in further hence not having enough information. http://webspace.ship.edu/jehamb/s08/211/1-5%20Zooming%20Derivatives.pdf |
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March 2017
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