<p>Are any of the following topics on the AP calculus AB exam?</p>
<p>Newton's Method
Hyperbolic Functions
Finding anti derivatives of Trigonometric functions (not easy trig integrals but things like INT tan^5(x) sec^4(x) dx and doing trig substitutions)
Area of a surface of revolution (using S = Int from a to b[2 Pi f(x) Sqrt[ 1+ (f'(x))^2] dx])
Logarithmic differentiation
Logistic differential equations</p>
<p>Linearization and Newton's method do come up.
Hyperbolic Functions, pretty sure they don't.
Trigs, yep
They'll ask for volume of solids of revolution
Logarithmic differentiation, yes, but you'll just need to know the derivative of log (x).
Differential equations come as well. </p>
<p>They're all on AB and BC [I think Newton's method is BC only], and the BC test just has harder versions of them.</p>
<p>Going from memory:</p>
<p>Netwon's Method -- no on AB, yes on BC
Hyperbolic Functions -- no on AB, and I think no on BC
Antiderivative of tricky trig functions -- only if they can be done using u-substitution on AB, only if they can be done by u-substitution or using integration by parts on BC (I don't think that trig substitution is on the BC exam, but could be wrong)
Area of a Surface of Revolution -- no on AB, can't remember on BC (leaning yes)
Logarithmic Differentiation -- no on AB, not sure on BC (NOTE: Logarithmic differentiation meaning that you have to take the log of both sides before taking the derivative, not just referring to the derivative of log functions, as An0maly was saying, which is clearly on the exam.)
Logistic Differential equations -- no on AB, yes on BC</p>
<p>There's a Course description on the AP Central website that will describe these things in better detail.</p>
<p>Also, the BC test has equal difficulty to the AB exam when testing on the same topic. The only inherent extra difficulty to the BC exam are the additional topics themselves (which sometimes makes an AB integral question appear to be more complicated because other integration techniques besides u-substitution are available to be considered).</p>
<p>From what I recall (AB, BC)</p>
<p>Newton's Method - no, yes
Hyperbolic Functions - no, no
Finding anti derivatives of [tough] Trigonometric functions - no, no
Area of a surface of revolution - no, no
Logarithmic differentiation - no, no (I'm not sure if it's explicitly tested but it's very useful for some bulky functions)
Logistic differential equations - no, yes</p>
<p>tan^5 sec^4 </p>
<p>tan^5 (1 + tan^2)sec^2 . u = tan du = sec^2</p>
<p>u^5( 1 + u^2) </p>
<p>u^5 + u^7.</p>
<p>Not hard to integrate. :/</p>
<p>True, but I'm pretty certain that nothing on the AP Exam requires the use of the Pythagorean trig identities.</p>
<p>does anyone know where I could find an explication of Logistic differential equations is? The PR book does not cover them and trying to learn math off Wikipedia borders on the impossible.</p>
<p>edit: sorry for the zombie post</p>
<p>Get Peterson’s. I was using PR, and it is really only good for AB. It skips over a ton of BC topics.</p>