<p>I was just self-studying for the Calc AB exam, and was wondering if these topics are included on the AP exam:</p>
<ul>
<li>Inverse Trignometric Functions (Integration)</li>
<li>Hyperbolic Functions (Integration)</li>
<li>Simpsons and Trapezoid Rule (Integration - Numerical Integration)</li>
</ul>
<p>I think only the Trapezoid Rule will be on the AP exam. Simpsons is not on the AB exam, right?</p>
<p>I know for sure that the others are in the BC exam.</p>
<p>Simpson's Rule is not on the AB Exam.</p>
<p>Since integrating inverse trig functions usually requires integration by parts (or memorization), it is not on the AB Exam.</p>
<p>Hyperbolic functions also are not on the AB exam.</p>
<p>Also im guessing inverse trigs in general (not intergation functions) will be coming on the test right?</p>
<p>You will need to know how to differentiate them.</p>
<p>Although in the worst case scenario, if you forget how to take the derivative of one of them, you can rederive them:</p>
<p>Example
Suppose you forget the antiderivative of y = tan^(-1) x.</p>
<p>Then x = tan y, and take the derivative implicitly to get 1 = sec^2 y * y'. So y' = 1 / (sec^2 y) = cos^2 y.</p>
<p>Then use right triangle trig to write that in terms of x.</p>
<p>y represents an angle whose tangent is x (or in our helpful case, x/1). So the OPPOSITE side is x, the ADJACENT side is 1, and using the Pythagorrean Theorem, the HYPOTENUSE is the sqrt(x^2 + 1).</p>
<p>The cos of this angle y = 1/sqrt(x^2+1), and therefore, the cos^2 = 1/(x^2 + 1), and you're back to your formula.</p>
<p>It's not particularly quick, but if you end up in the situation where you have the time to go look at a question, but just forgot the knowledge, you have a fighting chance.</p>
<p>Heh. That's actually our primary method of tackling inverse trig differentiation problems. -_-;</p>
<p>It'll certainly work.</p>
<p>But it's a lot faster to memorize three formulas* , and then apply them when faced with questions like: d/dx[tan-inverse (2x)] = (2x)/(1 + 4x^2).</p>
<p>*You only need the derivative of three functions, because the derivatives of the inverses of each of the cofunctions are opposites of the derivatives of the inverses of the regular functions:</p>
<p>d/dx[sin-inverse x] = 1/sqrt(1-x^2)
d/dx[cos-inverse x] = -1/sqrt(1-x^2)</p>
<p>d/dx[tan-inverse x] = 1/(1 + x^2)
d/dx[cot-inverse x] = -1/(1 + x^2)</p>
<p>d/dx[sec-inverse x] = 1/(|x|sqrt(x^2-1))
d/dx[csc-inverse x] = -1/(|x|sqrt(x^2-1))</p>
<p>Hey guys thanks for all the help, really useful. </p>
<p>I have some more questions:
- Will work, centers of mass/centroids/moments, and fluid pressure/force be on the AB test.
- Will L'Hopital's Rule be on the AB test?
- Are differential equations very common on the test? Are they very common or are there just a couple of questions on the test? What i'm trying to say is should I study differential equations in depth. </p>
<p>Also in my textbook differential equations are:
-Slope Fields and Eulers Method
-Growth and Decay
-Seperation of Variables
-Logistic Equations
-First-Order Linear Differential Equations
-Predator-Prey Differential Equations</p>
<p>Which ones are most important and which ones (if any) can I skim/skip through?</p>
<p>Here's the Official Course Description with exactly what's on the AB and BC tests: (pages 11-14)</p>
<p>Thanks for the website rb9109, but i've already checked it out.
L'Hopital's Rule I guess isn't on it, but that list isn't very specific, and I was hoping you guys would know.</p>
<p>However, you can use some techniques learned in BC to make some AB problems easier. For example, you can use L'Hopital's Rule if you feel more comfortable doing that. You can use the concept of cylindrical shells when finding the volume of a graph rotating horizontally, if you're not comfortable doing that with washers. But do refer to what's on College Board, so you don't learn stuff you won't need to know.</p>
<p>work, centers of mass/centroids/moments, and fluid pressure/force: no</p>
<p>L'Hopital's Rule: no, but there are times where if you know it, it might save you a little bit of work and energy</p>
<p>Are differential equations very common on the test? Are they very common or are there just a couple of questions on the test? What i'm trying to say is should I study differential equations in depth. They're pretty common on the FRQ's, and when it's on there it's worth 5-6 of the 9 points on the question it's on. It's not as common on the multiple choice.</p>
<p>Also in my textbook differential equations are:
-Slope Fields and Eulers Method
-Growth and Decay
-Seperation of Variables
-Logistic Equations
-First-Order Linear Differential Equations
-Predator-Prey Differential Equations</p>
<p>You should know Slope Fields. Euler's Method isn't quite as important.
You should know the basics of growth and decay to be able to set up some equations.
All the differential equations that you have to solve for y are separable differential equations, so I would only focus on those of the remaining items.</p>
<p>Thanks again MathProf.</p>
<p>I was reviewing the PR book, and am wondering if we have to know how to solve a problem through the defination of a derivate:
[f(x+h)-f(x)]/h
Can we just derive them (x^2 = 2x) instead of using the defination of a derivate to derive it. </p>
<p>Also do problems requiring the defination of a derivate ever show up on the FRQ?</p>
<p>Thanks</p>
<p>Not "explicitly", but on the multiple choice they might have something like </p>
<p>which tests your knowledge of the form of the definition of the derivative.</p>
<p>o ok thanks for posting the link. </p>
<p>Btw what was the answer lol? (B i think?)</p>
<p>I finally ventured into the disk, washer, and shell method today.
I get the disk and washer method, just the shell method seems confusing to me.
From what I see most shell method problems can be done through the disk method.
Will there be any problems on the AB test that specifically require the shell method?</p>
<p>Definition of the derivative usually doesn't show up on the test in the sense that you'll actually have to calculate a derivative using it.</p>
<p>The way it usually shows up is in recognizing a limit as providing the definition of the derivative, and these are usually on the multiple choice.</p>
<p>For instance,</p>
<p>lim h->0 [tan (x + h) - tan x]/h is another way of asking you to find the derivative of tan x, and your answer should be sec^2 x.</p>
<p>You only need disk and washer methods for the AP Exam, but the shell method is usually usable if you know it.</p>
<p>The difference between the two methods is that in the disk method, the cross-sections lie perpendicular to the axis of revolution, while in the shell method, the cross-sections lie parallel to the axis of revolution.</p>
<p>The only time that you're really forced into using one method over the other is in the case where you have a function that really can't be written in terms of the other variable (or at least not easily). For instance, if you're working with the function y = x^2 + x + 6, technically, you could solve this for x, but why would you want to? This means, that if you're revolving about the x-axis (or any other horizontal axis), you'll almost certainly want the disk method, but if you're revolving about the y-axis (or any other vertical axis), you'll almost certainly want the shell method.</p>
