<p>2 WEEKS TIL AP TESTING <<< I AM SWEATING SO MUCH!!! AAAAHHHHH!!!</p>
<p>I am going to do the Sparknotes Calc bc test.</p>
<p>^I thought you did College Calc in the community college. So, why worry?</p>
<p>The community college i went to did not allow calculators in math courses. So I had to learn how to do finite integrals, etc on my own . . . no problem.
We didn’t cover logistic differential equations either and I’m having a hard time with that. </p>
<p>BUT after taking the Sparknotes . . . that is so HARD!! I cant believe i got a 3 on that thing. “14 answered out of 35. You got 13 right and 22 wrong. You left 21 blank.” Some questions are so unexpected and harder than the real deal imho.
Have you guys tried it?</p>
<p>^Oh, no calculators. (wow, nice calc class). Since you have taken a college calc course, don’t you have your calc textbook with you? if you do, doesn’t your calc textbook has a section of logistic differential equations for you to learn?</p>
<p>nope 
The book (I still have it) is from 1991, calculators were not as popular as they are now. There is no logistic section anywhere.</p>
<p>Oh…logistic differential equations. My teacher showed us how to do those today. What they ask for most of the time is the limit as time goes to infinity (according to my teacher), which is pretty simple if you know how. </p>
<p>Out of curiosity, have any of you seen any logistic differential questions that ask for something other than the limit as time –> infinity?</p>
<p>EDIT: How to find the limit as t–>infinity, for those who want to know:</p>
<p>Assume we have a differential equation (dP/dt). Set that equal to 0. and solve for P. One answer (the smaller one) is the limit as time goes to negative infinity and the larger number is the limit as time goes to infinity.</p>
<p>This is because of the shape of the logistic. There is a horizontal asymptote as time goes to both negative and positive infinity (i.e. derivative equals 0 at t=positive and negative infinity). So, setting dP/dt (derivative) equal to 0 gives you the value of the horizontal asymptote as t goes to negative/positive infinity. </p>
<p>If you don’t get this, find a picture of a logistic graph (probably Google it or something). It should make sense.</p>
<p>check the 2006 (form b) FRQ from college board, yes they ask more than just the limit to infinity, which i can’t even do. Thanks 314159265 (wow thats hard lol), I get what the function looks like, but the other parts on the FRQ really sting me.
<a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;
<p>how long did it take you guys to learn the Taylor series and everything associated with it? What about parametric equations?</p>
<p>Can you tell me somewhere I can upload a photo or something? I can work out #5 (I’m assuming that’s the one you want) and post it if I know how to do that.</p>
<p>@xrCalico23 - for me, 2 days for Taylor series, including the power series. They can be so tedious to work out the problems. Parametric, including polar, - 1 day. I had a lot of time during the weekend.</p>
<p>^fabulous :)! (I’ll be super happy if I can manage to get the basics down in three weeks.)</p>
<p>The 2006 Form B #5 - yea, I can’t do and I can’t believe I skip that topic when I was learning from and reviewing the textbook. Look like I’m going to learn something new today.</p>
<p>I’ll explain how to do #5. Be sure to have this image open, as I will refer to it often: <a href=“http://www.squarecirclez.com/blog/wp-content/uploads/2009/10/logistic-equation.gif[/url]”>http://www.squarecirclez.com/blog/wp-content/uploads/2009/10/logistic-equation.gif</a></p>
![http://www.squarecirclez.com/blog/wp-content/uploads/2009/10/logistic-equation.gif[/url]](http://www.squarecirclez.com/blog/wp-content/uploads/2009/10/logistic-equation.gif%5B/url%5D){kind=link}
<p>a) I don’t think I need to explain this part. Just separate variables and integrate</p>
<p>b) This is where it gets a little tricky. You need to know the shape of a logistic
differential equation. The dy/dx of g is given. Knowing the shape of the graph, you should be able to tell that the limit of g’ as x->infinity is 0, since there’s a horizontal asymptote. To find the value of the asymptote, set the dy/dx equal to 0. You should get y=0 and y=3. Using common sense, y=0 is the limit as x->negative infinity and y=3 is the limit as x->positive infinity.</p>
<p>c) Knowing the shape of the graph, you can tell that the graph changes concavity about halfway between the asymptotes. In fact, it changes concavity exactly halfway between the asymptotes. So, having found the asymptotes to be 0 and 3, the POI is at x=3/2. But, it asks for the slope at the point. Plug 3/2 into dy/dx and solve. You should get 9/2.</p>
<p>I just want to get a 4. Which topics are the most popular ones on the test? Integrals? Because the test is coming is two weeks and I still don’t know most of the stuff =.=</p>
<p>On the FRQ, expect a Taylor polynomial problem.</p>
<p>Derivatives & Integrals on non-calculator MC (i.e. mechanical work)
More conceptual stuff on calculator MC (since definite integrals would be kinda silly for CB to put on a calculator section)</p>
<p>FR: Area/Volume of rotation, Taylor, Parametric/Polar, Riemann Sums with a table of values. I think those are the most common ones.</p>
<p>Here is another way to think about the logistic differential equation:</p>
<p>Try to always make it into the form</p>
<p>dP/dt = kP(1 - P/L)</p>
<p>Note the one inside the parenthesis. That’s very important. k just represents any constant. The L value here is the limit as t goes to infinity. So, for example, in 2006 #5, we can change g(x) from</p>
<p>dy/dx = 2y(3-y)</p>
<p>to</p>
<p>dy/dx = 6y(1 - y/3)</p>
<p>by pulling out a 3. Now it matches the form I posted above, and you can clearly see that L=3 without having to do any real math. Hope it helps!</p>
<p>Also, another question that I’ve seen asked is when is the population increasing the fastest? That is when P = L/2, or, in this case, when P = 3/2.</p>
<p>is it just me or is the time constraint on the BC exam slightly tight?</p>
<p>Thanks 314159265 and ChemE14, this really helps! </p>
<p>@Anshu93: yes, basically, if i pace myself, i get get 2 and half of the problems done all right. If work faster i can get through it all, but i might get 2-3 parts wrong in total. You gotta work in a timely manner in order to touch each problem and get them right.</p>
<p>How difficult are the calculations done without a calculator? As in, is it easy to make a mistake/are there many steps?</p>
<p>Also, what calculations are suggested to be done with a calculator? As far as I know that would be Euler’s Method and some integrals. Any more to add on the list?</p>
<p>Specifically, are polar equations on the calculator or non-calculator section?</p>
<p>Why I ask this: I usually perform my math correctly except for one minor error that besieges my entire answer! It’s extremely frustrating now for me to even dare evaluating an integral because I overlook a subtraction sign, forget parentheses. Most of the time, it’s because I don’t recognize or see that there’s a trig identity and I cannot further simplify the equation. Hopefully, these sections are calculator-allowed so I can save time? For polar coordinates, answers will be things such as 24pi, but surely evaluating answers is far better than messing up an integral and searching for the error for a long time. </p>
<p>Yes, time constraints <em>are</em> tight! There are the same amount of questions as on the AB test, though harder and more complicated!</p>