This week in AP Calculus we started chapter 7 (our last chapter!) this is exciting because it is my last high school chapter of math I will ever begin. We began learning how to find the net sum of an area under a curve that is restricted by another function. We learned that the absolute value allows you to find the real area while antiderving the function without the absolute value would only give you the positive area. We also went back to velocity problems which are actually quite confusing to me because I am never quite sure how to set up the problem.
This week in AP Calc we worked on preparing for the chapter 6 test. We mostly reviewed since we only had 3 days of school this week. On Wednesday we did a review assignment that we went around to different tables to work on and it was fun although some of the questions were tough. I think my biggest challenge is with u subsition because I have troubles finding the u value to take out. This is especially troublesome for me when using sin or cos. This week in AP Calc we learned about slope fields. Slope fields are cool because they allow you to find a graph when both y and x values are used without having to solve for y. I am not confident in drawing the curves in after creating the slope fields though because in the examples I did them wrong. In addition we brought back u-substitution, but this time we are using it with integrals. This proves to be a challenging task for me because I am never quite sure what to use for my U and once I use my U and I antiderive it, I can't really figure out how to fit it back into the equation. I feel like I am really struggling with u-substitution even though Lauren and Savannah have tried explaining it to me.
This week was primarily planning for the chapter 5 test. I am a bit nervous for this test because I am not confident in using the integral rules and finding the area under a curve without using my calculator will be challenging. I feel pretty confident in using the reaman sums to find the areas but other then that I am a bit confused.
In addition, I think I am still in need of a trig refresher because I am not fully confident in my abilities with trig. Hopefully with the notes that I take I will be able to answer the problems on the test. In AP Calc this week we learned about using reaman sum to find the area under a curve. This was a interesting lesson because there happens to be three different ways you can find the sum while practicing reaman. You can use Lram, Rram, or Mram! I like the fact that you can use different methods to find the area because this allows you to get a more accurate answer when the shape of the curve varies. Throughout the week we got to practice using this method but then on Thursday things got even better when we found out that there's a fourth method that you can use that may be even more accurate! This method uses trapezoids to find the area. The only tricky part about this for me is remembering the formula for finding the area of a trapezoid!
Week 6 of this marking period consisted of looking back to the old and diving into the new. We started off with a project in geometry by finding the areas of shapes. This proved to be a fun activity that lead perfectly into chapter 5 where we learned how to find the area underneath a curve because it allowed us to see that there are different ways to find the area of a shape (see pictures above for examples . Using LRam MRam and RRam were quite easy to me because all I had to do was find the area in each rectangle under the curve and then add them up. When then learned how to use Sigma notation to find the area and after this I began to get confused because I do not understand Sigma notation very well. Hopefully after doing the homework for this section I will begin to catch on and then know how to do it for the quiz.
This week in AP Calc we learned liniarization. This subject seemed pretty easy to me and I think I understood it well. I think it will be something that I can use to help me on the non-calculator portion of the exam to help me find my answers because it allows you to find a close estimate of a number that can not easily be square-rooted. Week 11 was mostly about reviewing what we have learned from the trimester and preparing ourselves for the exam. I found the exam review to be quite easy other then the very last page when we had to sketch a graph by using the first and second derivatives but without a calculator. When Mr. Cresswell explains this in class it really makes since to me but as soon as I try to do it myself I do not know what to do. I struggle to find the critical points and I never know when I do find the critical points if I have enough points. In the examples we used in class, we used equations that were in fractions which made it easier for me to find the critical points, but in the equation on the exam it was not in a fraction. As soon as I had to start finding the domain and the critical points I felt lost and confused. This showed with my grade as I got an unacceptable D+. I wish we could do a mastery form on the exam! Lol As for the calcutor portion I felt very confident in my answers but I only got a C+ on this portion which greatly confuses me. I hope we are able to get our exams back for review so I can understand what went wrong because I thought I was going to do quite well. I believe that if there was one area that I struggled in the most it would probably be limits because I studied them the least. I suppose I will find out if/when we get our exams back! This week in AP Calc we started chapter 4. So far it has not been terribly difficult because we are taking what we learned about derivatives in the last chapter and then adding on to it. For example, when before we would find the anti-derivative and then add a +C at the end to represent the possible constant, now we are given a point on the derivative so we can find what C actually represents.
We also are using the derivatives to find equations for position and velocity. The process for finding these equations confused me because I wasn't quite sure if we were suppose to use the chain rule in the example we were given. Lauren promised she would help me with it on Monday though! Next week we are going to spend several days on section 4.3 so I am assuming that there are more difficult concepts for us to learn in this section. We have finally come to the end of chapter 3 which makes me very very happy becuase this was a rough chapter for me and I can't wait to move on to the next chapter (even though it's all story problems). I was SOO happy when Mr. Cresswell told us we could push our test back to Monday becuase now I have all weekend to study and I will deffinitly take advantage of that! For the extra credit assignment I was able to better understand the chain rule. When before I would get very confused when you had to use the chain rule and the product rule together, I now have the process figured out and it is quite easy! |
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March 2014
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