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Synthesizer: Test Analysis
University of North Dakota
From over 16 years of teaching experience, he has philosophy that it takes humor, patience and understanding when teaching tough subjects.
If you?re in AP calculus now, now you?re probably one of the Math champions. No, not probably you are one of the champions. So it?s most likely you get really good study skills. But you know, you can always use some extra tricks. Especially, when you?re taking an AP test where there?s really heavy time pressure.
I?m going to explain an activity to you that will help speed up your working on the AP test. Will help organize your thoughts. But first I you need you to go and download three different things. The first thing is a synthesizer that?s called test analysis. You?ll find that in the bonus materials. The next item is a little cheat sheet I put together for you. It?s a list of all the episodes in our course, along with all the sub-topics.
The purpose of this exercise, is to use the worksheet that I developed for you, and identify test problems according to episode and sub-topic. Finally, you need to follow the link to the official College Board website, where you will find the link to the May 2009, official course description for AP calculus.
Now within that one, you?re going to find two different sections you need to download. One of them is the sample free response questions. The other is the sample multiple choice questions. We?re going to look at the sample multiple choice questions first, and I?m going to stop for a minute while you download all that stuff.
Got all that stuff ready? Now again, look at the multiple choice. I?d like you to look at multiple question number one. Have your test analysis worksheet ready. Take a minute to read it. Take your time because right not you?re not on a time pressure.
Take your time, read it and try to think about when we covered it in the course. Look for some key words. This one doesn?t have a lot of writing in it, but it says limit, so limit. Pretty darn good chance that it?s in the episode where we talked about doing limits.
Right now, next thing you know says what?s got Cosines in it? So maybe it?s that special cosine limit that I asked you to memorize. Look through the follow along and see if it?s in there. No it?s not quite that. But wait, look how long that thing is. Remind you of something? Yeah the definition of a derivative that's what it is. It?s one of the problems where you?re being asked to recognize the definition of a derivative. And look at that problem and just decide what derivative it is.
So, let?s write that down. The episode name was manual limits. The sub-topic is recognizing the definition of a derivative. Now over in the notes section, you might want to write down anything that occurs to you, you might actually want to do the problem there. And if you?re not remembering how to do this kind of a problem very well, you?ll probably want to check out the box for review.
You?re probably in the last stages of reviewing for AP test now, and you?re time is limited. So one thing you need you need to keep in mind is that, you might not actually do all of these problems. The goal right now is just to go through quickly and analyze all of the problems. Then go back later and as you have time, then actually try doing the problems. Right now just analyze them.
Your teacher might have told you by now, go back and study for the test. Well I hear this from students all time, ?Oh I can?t study for math test you just know it or you don?t.? Nonsense, but you do need to know how to structure what you?re doing to conserve your time. So if you?re going to go back and study, you probably have a stuck of notes about this big and you can?t possibly read it all. You need to prioritize your time.
The purpose of this synthesizer is to help prioritize your study. The first thing I would like you to do, is download a copy of the synthesizer that is entitled 'review your old test'. Then go ahead and get all your old test. You might want to print a few copies of this synthesizer. When you?re prioritizing, what you need to do is rule out the stuff that you don?t need to spend any study time on. Now this activity again takes you again from our course and has you do a broad review of everything that you did in AP calculus.
The first thing to do is to look for your old test. Now any problem that got right the first time, you might not need to review. Look at them again though quickly because, there might have been that you new a few months ago that you have forgotten. Make that a quick scan. If there is something that you have forgotten, well write it down. Let?s see, I?m looking through one of my old test, and oh no there?s an integral, I completely forgotten this thing. Oh no the problem asked me to do the integral of the secant of u, du, I?ve forgotten that thing done.
So look it up write it down. This is one of the ones that you might need to memorize. They do show up on the AP test from time to time. They?re not supper common but you might see it.
This one is the natural logarithm of the secant of u plus the tangent of u, plus of course your old friend the constant of integration. So I wrote that down because I?m probably going to be needing that one. This one was maybe your chapter 4 and it was problem number 12 on the test. So what you?re writing down is a list of things that you?ll want to review now. And maybe briefly look at again the day before the test.
Next, and very important, is to look at any problem that you got wrong the first time. If you did, you definitely want to circle that one and take a close at it. You might have gotten it down since then, but you want to be sure.
The second page of this synthesizer asks you to research additional AP topics. Now, we?ve done our best to make this course complete as possible. I?ve included practically every kind of odd AP problem that I could think of, that I could find. Still, we couldn?t cover quite everything. We skipped a lot of the basic topics. The point of this course was to speed you up on the on the more complex topics.
And there is one additional complex topic that you?ll see from time to time, exponentials ,that I didn?t really cover very well. When you download this, you?ll see a list of the topics that I?ve identified as ones that we haven?t covered thoroughly.
Here is the one I just mentioned. Compare relative magnitudes of functions such as exponential, polynomial and logarithmic growth and the relative rates of change. So here is a possible example problem that you could do.
Your goal is to look through the list of additional topics that I made for you. Find where it is in your textbook or within your notes that will be great too, and try some examples. You?ve probably covered them in your course, but I?m sure you can use the review.
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