What to memorize for BC Calc?

Test Preparation AP Test Preparation
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<p>What are formulas, series, etc. to memorize for BC calc? A consolidated list would be nice.</p>

<p>Here are some examples of what I am looking for - and these are things that you basically just need to know off the top of your head that you really need memorized - either you know it or you don’t or you’d have to know some long derivation:</p>

<p>Arc Length - S = Integral of square root of 1 + derivative squared</p>

<p>Some Important Taylor Series: e to the x, sinx, cosx (forgot them off the top of my head and need to look them up, though e to the x is easy)</p>

<p>Special Polar Functions like a rose which has 2theta in it</p>

<p>Reimann Sum Formulas (left, right, midpt, trapezoid - these can probably be derived though, but just in case)</p>

<p>Disk, Shell, Washer Methods of Volume of Revolution - Cross Sectional Volume</p>

<p>Partial Integration: Integral of udv = uv - integral of vdu</p>

<p>Parametric Stuff/Euler’s Method</p>

<p>Carrying Capacity Equation as differential formula (can anyone explain it?)</p>

<p>What else is there???</p>

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<p>you dont need to know shell</p>

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<p>derivative/integral formulas (arcsinx, arctanx, b^u, etc.) and error formulas (a_n+1 and lagrange)?</p>

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<p>^^sorry but whats a “rose with 2 theta in it”. Is it some sort of mathematical romanticism or is it something we really need to know?</p>

5

<p>I believe what he means is:</p>

<p>For the rose curves f(ϑ) = sin(nϑ) and f(ϑ) = cos(nϑ), there are n “petals” when n is an odd number and 2n petals when n is an even number.</p>

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<p>^is it bad that i have no idea what you’re talking about?</p>

7

<p>Will we need to know what polar equations look like (without a calculator, I mean)?</p>

8

<p>Well, they’re polar equations, which I’d assume is a somewhat large part of the test [because they are often taught after parametric equations]. I’ve seen a few problems on the PR practice tests asking you to find the area of a polar function in a certain interval. The rose curves are one of the most basic polar equations. I think. :D</p>

<h1>7 - If the polar equations could be easily converted into a rectangular form, then yes. That is my assumption, anyway.</h1>

<p>Maybe we should organize this by topic? Here’s my contribution:</p>

<p>Series
[ul]
[<em>] The nth term test for divergence
[</em>] The integral test
[<em>] The direct comparison test
[</em>] The limit comparison test
[<em>] The alternating series test
[</em>] Absolute and conditional convergence test
[<em>] The ratio test
[li] The nth root test[/li][</em>] Taylor Series
[<em>] Maclaurin Series
[</em>] Finding the radius of convergence
[<em>] Finding the interval of convergence
[</em>] Power series
[<em>] Integrating and differentiating power series
[</em>] Integrating functions using power series
[/ul]</p>

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<p><a href=“http://covenantchristian.org/bird/Smart/Calc1/StuffYouMustKnowColdUpdated.pdf[/url]”>http://covenantchristian.org/bird/Smart/Calc1/StuffYouMustKnowColdUpdated.pdf&lt;/a&gt;&lt;/p&gt;

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<p>Sweet. Thanks. :D</p>

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<p>Although I think that covers pretty much everything on APBC, it also covers stuff you don’t need to memorize (why bother learning the Lagrange error formula when the AP only tests it on MC questions and then also only requires you to say it is less than the next term of the sequence?) Maybe put in calc. A lot of this stuff is extremely easy to derive (integral of ln x by parts, parts formula by integrating product rule, curve sketching section might help some people but I just draw it in my head by visualizing it). Also, they got rid of shell but it makes some problems (where AOR is parallel to the small area being integrated across) so much easier it is worth knowing. Special angles for 37 and 53 would never be tested (radians ONLY). Also, although it gives area in a leaf, the sheet forgets that AP often tests area between 2 polars, meaning that you have to careful with limits of integration. I also feel derivates of cofunctions are not worth memorizing as they can be obtained by replacing all trig functions in the derivate of the original function by their cofunctions and adding a negative sign. For invcofunctions, memorizing that the derivate is simply negative of the derivate of the normal function is easier, and helps you not get confused about which to use when integrating. I don’t know if the error bound for an alt series is necessary to memorize either, I haven’t seen it on a single practice test. Also, it would help to memorize the formula for the sum of a geometric series as well.</p>

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<p>ummm…vectors</p>

<p>like velocity of vector, unit vectors, speed, etc…</p>

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<p>How much of the BC Calculus is limits? How many problems, would you say? Of what difficult are they?</p>

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<p><a href=“why%20bother%20learning%20the%20Lagrange%20error%20formula%20when%20the%20AP%20only%20tests%20it%20on%20MC%20questions%20and%20then%20also%20only%20requires%20you%20to%20say%20it%20is%20less%20than%20the%20next%20term%20of%20the%20sequence?”>quote</a>

[/quote]

Uh…
The error is only less than the next term if it’s alternating.
If it’s a nonnegative series, then you have to use the Lagrange error bound.
I also saw a Lagrange error bound question on one of the FRQs I did the other day.</p>

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<p>lagrange is the one thing that i have no idea to do on series - can someone please explain it (there have been questions asking for that method on released tests)</p>

<p>and yeah about limits, what are a few methods to simplify them, since sometimes i mess up and get stuck since it was the 1st thing we did. i know some ways are lhopital and rationalizing the numerator, but what else?</p>

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<p>I’d say polar isn’t That big a portion, chaos. Parametric is kinda a big part though, but VERY easy and intuitive (except 2nd derivatives, which are still easy nonetheless).</p>

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<p><a href=“except%202nd%20derivatives,%20which%20are%20still%20easy%20nonetheless”>quote</a>

[/quote]
</p>

<p>Second derivative? What. (?) </p>

<p>Uh oh.</p>

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<p>I also don’t remember having to do anything about second derivatives in the parametric section.</p>

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<p>What is Newton’s Law of Cooling?</p>

<p>I saw that on a practice BC MC.</p>

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<p>okay then, never mind, but we learned it. just for the record, you just differentiate the first derivative, and divide it by the dx/dt.</p>