AP Calculus BC Review Thread

Test Preparation AP Test Preparation
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<p>
[quote]
yski: PatrickK: I know about fnInt and nDeriv, but could you tell me about what Solver is and how helpful it is? Thanks.

[/quote]

Solve helps you solve equations. For example, say you want to find where e^x and ln(x) intersect. Just set them equal to 0, so e^x - ln(x)=0. Then graph that, and make take a rough guess as to where you think they intersect. Then (I use a TI-84 Plus) go to Math, put the up button to go to the last option, section Solver. Then enter in the equation, push enter, take a guess (has to be relatively close), then push alpha+enter (which is the solve button). It will give you the exact value. These tests are more and more becoming calculator tests, and you will need to know how to use your calculator on these tests. I use solver probably more than anything, so make sure you can use it or something similar to it. Hope that helps.</p>

<p>
[quote]
wow patrick. 65% for the BC? THat means that it is very hard to get points...

[/quote]

Yeah, I was amazed too. I took a 2003 practice AB test the other day, and to get a 3 all you needed was 29 points, yes, 29 points.</p>

<p>
[quote]
What is fnInt?

[/quote]

Under Math menu for TI-84's. It solves definite integrals. So select that option, enter in the equation, then with respect to what, then the bounds. For example, the integral of e^x - ln(x) from 1 to 2 with respect to x would be this:
fnInt(e^x-ln(x),x,1,2)</p>

<p>sl8r000: Can you post the program you have? I'd be interested in seeing it just for the heck of it.</p>

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<p>Oh. I don't have a TI-84. That's probably why I don't know what fnInt is.</p>

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<p>Can you use TI-89's on the BC?</p>

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<p>Sure (sorry about my horrible program organization). I use the 3D functions on the 89, though, so you might have to find a different way to do it.</p>

<p>1.Ok, first enter the differential equation in z1(x,y) [//because I have no clue how to get information from the program into that space - anyone have any ideas?]
2. Set up four prompts for the initial x value (a), the initial y value (b), the final x value (c), and the change in x (d). I did this with a Disp "whatever" followed by a Input "whatever," but you could use prompts if you remember which variables mean what.
3. set a work variable (e) equal to the initial x value
4. set a work variable (f) equal to the initial y value
5. Then:
While e<=c
f+d*z1(e,f)->f
e+d->e
EndWhile
Disp f
EndPrgrm</p>

<p>So, I put y into z1(x,y), say that y(0) = 1, set the change in x to .01, and try to find y(1) [//e], getting 2.73186. Does anyone have any idea as to speeding this up? The above takes about 5 seconds, so using .001 would require 50 seconds... I think.</p>

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<p>sl8: Too bad I have a TI-84. Do you think the TI-89 will help you a lot as opposed to a TI-84. As far as the speed, it is a pretty small program. You could always add more RAM to your calculator if you want to speed it up.</p>

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<p>Anyone here want to chat on MSN or AIM about Calc. BC stuff? I could use some help on a few things. My info is:
AIM : dragonofwars
MSN: pjksportscards [at] hotmail</p>

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<p>I don't know - at this point, it's just the calculator that I'm more used to. I use the solve function fairly frequently, so that's a plus. Other than that, I mainly use it to evaluate integrals and take derivatives. I don't think that there's a huge difference in the difficulty of taking the exam with a 89 vs an 84, but I don't really know much about using either, so there might be.</p>

<p>True. Someday I'll break down and learn assembly.</p>

<p>You might try ticalc.org for 84 programs. The 84s are fairly popular, so I wouldn't be surprised if you found a lot of useful programs there.</p>

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<p><a href="http://math.arizona.edu/%7Ekrawczyk/calcul.html%5B/url%5D"&gt;http://math.arizona.edu/~krawczyk/calcul.html&lt;/a&gt;&lt;/p>

<p>END OF CONVERSATION. :)</p>

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<p>W00T! All hail fhqwgads2005! Long live!</p>

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<p>The site seems to be great but here's my warning and advice: you're only couple days from exam; don't spend trying to add new stuffs to calculator but learn/review any concept that you're weak at.</p>

<p>For me, that's Lagrange Remainder and Volumes of Known Cross Section.</p>

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<p>Lagrange remainder questions are usually in the no calculator section.</p>

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<p>Could someone explain how to solve this: </p>

<p>If F' is a continuous function for all real x, then lim as h approaches 0 of (1/h)integral of F'(x) from a to (a+h) is...</p>

<p>Answer: F'(a)</p>

<p>The answer doesn't make sense.</p>

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<p>Why are the bounds of integration of the answer for question 1. c) from S-2 to T-2? I can get numerical values for those bounds, but where do those -2 come from? The question is here: <a href="http://apcentral.collegeboard.com/apc/members/repository/ap06_calcBC_samples_q1.pdf%5B/url%5D"&gt;http://apcentral.collegeboard.com/apc/members/repository/ap06_calcBC_samples_q1.pdf&lt;/a&gt;&lt;/p>

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<p>
[quote]
Could someone explain how to solve this: </p>

<p>If F' is a continuous function for all real x, then lim as h approaches 0 of (1/h)integral of F'(x) from a to (a+h) is...</p>

<p>Answer: F'(a)</p>

<p>The answer doesn't make sense.

[/quote]
</p>

<p>The derivative of an integral is the function by the fundamental therom of calculus. You are taking the definition of a derivative for an integral SF'(x)dx</p>

<p>d/dx SF'(x) dx = F'(x)</p>

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<p>How important is the trig substitution?
Ones where you have: if the sec is even, you leave one as sec x tan x and change the other one to tan x using the trig identities.</p>

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<p>So our calculators will not get cleared before the exam, right?</p>

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<p>Yeah, about the trig substitution, i have no clue. I learned it over the year, but I have not seen it anywhere when I have been reviewing. </p>

<p>Calcs are not cleared, but programs won't help much.</p>

<p>ysk1, remember, the derivative of the integral of f(x) from c to x (where c is a constant) is just f(x). </p>

<p>But, if it is the derivative of the integral of f(x) from c to 3x^2, you have to use the chain rule, so it would be 6x*f(x)</p>

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<p>lim(x → ∞) 4x*sin(1/x) = . . .</p>

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<p>lim(x-> inf) sin(1/x)/ 1/4x -> (cos(1/x) * -1/x^2 )/ -1/4x^2 = 4cos(1/x) = 4</p>

<p>lim (x->inf) 4(cos(1/x)) = 4(cos0) = 4</p>

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<p>With limits, just remember. "When in doubt, go to the Hospital" That is, use L'Hopital's rule. Make sure it is 0/0 or inf/inf form though. or one of those others.</p>