<p>Anyone wanna guess what 1-6 will be? There's a very good chance of a series question and a volumes of revolution question. The other 4, however, are up for grabs. Any educated guesses?</p>
<p>There will definitely be a Taylor/MacLaurin series question. There will be one area between curves/volume of revolution/area with cross sections extending out from the base question. (either cartesian or polar). There will be one problem where a rate is given and you have to determine the total amount of whatever that rate is representing over a given time interval. There will be a differential equation where we’ll need to draw a slope field and use Euler’s method. There will be a particle moving along a curve represented by parametrized functions. And finally there will be a random one that they like to toss in every year that may/may not be a combination of some of the previous topics.</p>
<p>I feel like calculus FR is pretty predictable. But then again my teacher is pretty kickas* so…</p>
<p>definitely area/volume/cross sections. possibly in/out rate problems. possibly position/velocity/acceleration problems. Some questions might involve IVT/MVT/Rolle’s. Slope field pops up a lot. basically what IndestructibleSD above said!</p>
<p>I’ve noticed that the Calc FRQ follow a pretty standard format. It should go something like:</p>
<p>Area/Volume of a solid of revolution (first asks area of region R, then volume if R is revolved around a given line, and then the volume if perpendicular cross-sectional squares/triangles/etc. are placed on top).</p>
<p>The graph of a function’s derivative is given and various things about the original function and the derivative itself are asked to be inferred.</p>
<p>Rectilinear/Particle motion. y(t) and x(t) are given, find dy/dx, etc. or the graph of a velocity/acceleration/position function is given, find other things.</p>
<p>Taylor/Maclaurin series question. Could ask for student to use Lagrange error bound.</p>
<p>Euler’s method.</p>
<p>Possible slope field analysis, possible polar graphing question.</p>
<p>I seriously hope there’s no polar FRQ on the test. I will die if there is T_T</p>
<p>Actually my calc teacher said something that made a lot of sense. You know how they took away one of our calculator active parts? Well he suspects they might bring back a section of the test that they haven’t had in over 12 years: a graphing problem. Apparently back before graphing calculators were available to everyone the ap test had a problem where they gave an equation and you had to graph it using f(x) f’(x) and f"(x). He thinks that since they’re doing 4 no-calculator parts that they may decide to bring it back.</p>
<p>^ That would be very sad and time consuming.</p>
<p>^^ That would make sense. Ugh.</p>
<p>Well, if they ask me to graph something, I’ll skip it and just do the other FRQs. The scale is extremely generous. Although that’s more due to the vicious nature of some of the MCQs.</p>
<p>IndestructibleSD: you said its possible that there will be a polar volumes of revolution question??? *** does that look like?</p>
<p>Sorry, I didn’t mean for my sentence to be interpreted that way. The volumes of revolution would only apply to questions in the Cartesian coordinate system. I was trying to consolidate too much information into one post. I apologize once again.</p>
<p>haha no worries dude, don’t stress about it. I was just terrified that it was an actual topic because I’ve never heard of it before!</p>
<p>I think there will be a polar equations one because I noticed that there was one in 2007 and in 2003, both of which are 4 years apart. This year will be 2011 and 4 years from 2007, which would make polar seem more likely, since it hasn’t been tested in a while.</p>
<p>what do you mean by a polar question? give me an example</p>
<p>Area between two polar curves, for example. You would use the formula .5integral((r^2),dtheta,a,b)…limits of integration are the most difficult to determine.</p>
<p>Do you have any tips for determining the limits of integration for finding the areas between polar curves? My prep book doesn’t really explain it…at all. Thanks in advance.</p>
<p>Can anyone explain to me 3a?
<a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;
<p>how do u determine those? don’t you have a calculator?</p>
<p>You have to find where the two polars intersect by setting them equal to one another and solving for the angle theta. In some cases, it’s entirely possible without a calculator.</p>
<p>serenen-</p>
<p>Polar Area = (1/2) * int (f(θ)^2)
The problem gives you the bounds of integration (2pi/3 and 4pi/3).</p>
<p>So, the area of the limacon sector is (1/2) * int ((3+2cos(θ))^2) from 2pi/3 to 4pi/3. Just plug it in to the formula.</p>
<p>The area of the circle sector is a little more tricky. Basically, you want the area of the circle that is NOT between 2pi/3 and 4pi/3. This would be 2/3 of the circle because 4pi/3-2pi/3=2pi/3 (2pi/3 is 1/3 of 2pi, so the unwanted area is 1/3 of the circle and the wanted area is 2/3). Just use the area formula of the circle to get (2/3)pi(2)^2.</p>
<p>Add both together using a calculator. You’re all set!</p>