Calc AB: Inquiries.

<p>Analysis of curves, including the notion of monotonicity:
Eh? Read this on the course description, but I've never heard the term before.</p>

<p>Curve sketching:
My teacher stressed this, but is it really so important? Are such questions likely to appear in no-calculator parts?</p>

<p>Slope fields:
To plot the points, solve d.e. for (dy/dx) and then just plug in x- and y-values, solve, and draw in that slope for that point, right?</p>

<p>FR Part A (Calculator allowed):
For area, volume, etc. of regions bounded by curves one need only give integral, limits, and solution, right? It's not necessary to actually show the work of solving the integral, is it? Also, can one find the limits with a calculator instead of showing the work to find them analytically? This seems to be the case, judging from answer guidelines for the 2006 test, but I'd just like to be sure.</p>

<p>Volume:
Should I even worry about the shell method at all? For cross-sections, I'm basically clueless. I'm guessing for a square cross-section it would look something like: V = integral from a to b of f(x) - g(x)?</p>

<p>Integration by parts:
It's not listed on the course outline, but is it possible that it may be necessary? I do have a good understanding of this technique, regardless.</p>

<p>Trapezoidal Riemann sum:
(.5f(x0) + f(xn+1) + ... + f(xn-1) + .5f(xn)) * deltax, where deltax = (b-a)/n Is that right? I can't seem to remember this very well for some reason.</p>

<p>Derivatives/antiderivatives of absolute value functions:
keep finding this on practice problems (Barron's 8th ed.) but couldn't find an adequate explanation.</p>

<p>Derivative of a function that is not a smooth curve:
when given an arbitrary graph of f(x) but no equation and asked f'(a), where a is the abscissa of an intersection of two line segments, how does one fine f'(a)?</p>

<p>Related rates:
Write equations to relate the variables that change with respect to time, differentiate with respect to time, substitute known values, solve for unknown. Seems simple, but I always manage to mess this up somehow; any suggestions?</p>

<p>Position, velocity, acceleration:
finding final velocity of an object, given its total displacement (e.g. v at 5m above ground falling from starting point of 20m). Will I need to know how to solve something like this? I remember seeing a problem like it in the Barron's book, but not exactly what it was.</p>

<p>I have a Ti-83+ - what techniques are useful for calc, in particular? I've found nDeriv( and fnInt( but am unsure how to use them, exactly.</p>

<p>What information, exactly, is provided? Will I need to know how to find volume of sphere, cone, etc. or will such formulas be provided?</p>

<p>Sorry for all the questions; it's been a year since I've actually had this class, and the calc teacher at my school isn't very competent (out of 30 examinees last year, including myself, the highest score was 2). I've been studying off-and-on since then, but there seem to be many fundamental topics that my teacher really didn't cover (judging from my perplexion). I just want to make sure I actually score high this year.</p>

<p>Analysis of curves is useful for a lot of the questions but I don't think they will ask you specific questions on how to analyze a curve..</p>

<p>Slope fields are commonly tested in FR. Know how to sketch one and how to find the general/specific solution (usually separation of variables and integrating)</p>

<p>I think you're meant to use the calculator on the FR for the area/volume ones. A lot of the times you have to find the intersections by calculator and it's very hard to evaluate them at the point. I think as long as you show the integral with the limits and get the right answer, you get full credit. </p>

<p>Integration by parts is useful. I'm not sure if it's directly tested or not. In the PR book, they have a question that you must use integration by parts for; but as for the exam, I don't know. </p>

<p>Derivatives/Integrals of Absolute Value: I have never seen this in my PR or on the collegeboard FR. It was in an older Kaplan book though, so I don't know. </p>

<p>All the related rates one i've seen usually involve a ladder sliding or how fast the radius/volume is changing given the rate of change of the other quantity. They seem pretty simple.</p>

<p>Pos, Vel, Acc: the ones on Collegeboard aren't that complex. The ones in the practice books (Kaplan) that seem more complex I use my physics formulas.</p>

<p>nDeriv and fnInt are only useful for definite integrals/derivatives. If they ask you to evaluate the derivative at a certain point or ask you to evaluate an integral from a to b use the calc-- much less room for error.</p>