AP Calculus AB

Test Preparation AP Test Preparation
341

<p>OM*G,</p>

<p>I actually got the right answer for 4 a...wow..Well, it seemed like the right answer for sometime..I got pi/4 but apparently it is 5pi/4..whatever..I'm still happy to have worked that beast out and gotten something sensible.</p>

<p>Part b of that question..I realized what I did...I went A(2x)+x = 0</p>

<p>So a is obviously 2...stupid mistake there</p>

<p>I think I got 1 right...discounting a couple marks for stupid errors..
2 a and b were right. I got 5.07 for part c but that was when I went brain dead..everything after that is Fun (NOT)
I think I got 3
4 was half right for both</p>

<p>5, I think I got part b wrong.
6 a, I got no change in sign at the critical point...
6 b, I didn't fully solve the equation.</p>

<p>Not looking bright so far.</p>

<p>P.S. How do you get a min for the critical value on question 6? Me and a lot of my friends didn't.</p>

342

<p>Working from f '(x) = k/(2sqrt(x)) - 1/x:</p>

<p>At x = 1, f '(x) = k/2 - 1</p>

<p>Since x = 1 is a critical value, f '(x) = 0, and k = 2.</p>

<p>So at k = 2, f '(x) = 2/(2sqrt(x)) - 1/x = 1/sqrt(x) - 1/x = (sqrt(x) - 1)/x</p>

<p>Now evaluate sign changes on both sides:</p>

<p>At x = 1/4, (sqrt (1/4) - 1)/(1/4) = (1/2 - 1)/(1/4) = (-1/2)/(1/4) < 0</p>

<p>At x = 4, (sqrt (4) - 1)/4 = (2 - 1)/4 = 1/4 > 0.</p>

<p>Therefore, f(x) has a minimum at x = 1 when k = 2, since the sign of f ' changes from negative to positive at that point.</p>

343

<p>Thanks Mathprof, </p>

<p>I had the same equation but it seems I may have used something like -1 for my x value and somehow taken the sq root of a neg number.</p>

<p>Or made some other addition errors now that I think of it. </p>

<p>Thank you for explaining it.</p>

344

<p>No worries. My sign chart originally had x = 0 on it as just a reflex value when x = 1. :)</p>

345

<p>wait, mathprof, question... I did it differently. I used the 2nd derivative test for that question, would I still be awarded credit?</p>

346

<p>I would think so.</p>

<p>I know they're being picky on the justification points lately, but I'm pretty sure so long as you said something like "f has a minimum at x = 1, because f ' = 0 and f " > 0 at that point" and demonstrated that f " > 0, you should be fine.</p>

347

<p>Ok so here are my ideas for distrubtion of points. This is just my guess though. So don't expect it to be 100% right..</p>

<p>question 1.
a. 1 point for the actual integral. 1 point for your limits. 1 point for your answer.
b. 1 point for integral. one point for limit. 1 for answer.
c. 1 point for the integral. Two for the answers..
question 2
a. 1 point for integral. 2 points for answer.
b. 1 point for correct intervals. 1 point for explanation
c. 1 point for correct time. 1 point for the actual amount at the time. 2 points for justifying your answer.
3. a. 2 points for explanation
b. 2 points for explanation
c. 1 point for explanation. 1 for answer.
d. 3 for answer.
4. a. 1 point for derivative. 1 point for critical points. 1 point on farthest left point. one point on justifying.
b. two points on correct derivatives of both x`(t) and x(t). 1 point for answer of A.

5a. 1 point for correct line. 1 point for lesser or greater. 1 point for reason. b. 2 points for correct answer and units c. 1 point for answer. 1 point for explanation d. 1 point for lesser or greater. 1 point for reason

6a. 2 points for f(x) and f(x)
b. one point for identifying first derivative. one point for plugging in 1 and solving for k. one point for k. one point for justifying.
c. 1 point for f`(x). two points for x.</p>

<p>What do you guys think. I am not saying any of these with 100% confidence. I just want to see what you guys think.</p>

348

<p>Form B this year seems easier? </p>

<p>How does CB determine the curve for these frqs? Do the two different versions of the test have the same curve or are they calculated differently?</p>

349

<p>
[quote]
question 1.
a. 1 point for the actual integral. 1 point for your limits. 1 point for your answer.
b. 1 point for integral. one point for limit. 1 for answer.
c. 1 point for the integral. Two for the answers..

[/quote]
</p>

<p>I'm guessing:
1 point for the correct limits in (a), (b), or (c)
1 for the integrand in (a)
1 for the solution in (a)
2 for the integrand in (b)
1 for the solution in (b)
2 for the integrand in (c)
1 for the solution in (c)</p>

<p>
[quote]
question 2
a. 1 point for integral. 2 points for answer.
b. 1 point for correct intervals. 1 point for explanation
c. 1 point for correct time. 1 point for the actual amount at the time. 2 points for justifying your answer.

[/quote]
</p>

<p>There are almost never 2 points for the answer itself if it's numerical.</p>

<p>My guess:
1 for the integral in (a)
1 for the solution for (a)
1 for g(t) > f(t) or g(t) - f(t) > 0 in (b)
1 for <a href="open%20interval%20OK">0, 1.617</a> in (b)
1 for <a href="open%20interval%20OK">3, 5.076</a> in (b)
1 for identifying critical values (including t = 3) in (c)
1 for identifying endpoints as candidates and evaluating at endpoints and C.V.'s in (c)
1 for correct time in (c)
1 for correct gallons in (c)</p>

<p>
[quote]
3. a. 2 points for explanation
b. 2 points for explanation
c. 1 point for explanation. 1 for answer.
d. 3 for answer.

[/quote]
</p>

<p>Pretty much agreed here, though I have it broken down further:</p>

<p>1 for identifying h(1) and h(3) properly in (a)
1 for invoking Intermediate Value Theorem in (a)
1 for confirming the average rate of change = -5 in (b)
1 for the Mean Value Theorem in (b)
1 for correct dw/dx in (c)
1 for dw/dx | x = 3 in (c)
1 for g-inverse(2) = 1 in (d)
1 for derivative of g-inverse | (x = 2) = 5 in (d)
1 for tangent line equation in (d)</p>

<p>
[quote]
4. a. 1 point for derivative. 1 point for critical points. 1 point on farthest left point. one point on justifying.
b. two points on correct derivatives of both x`(t) and x(t). 1 point for answer of A.

[/quote]

Not convinced I've found nine good points on this one, but my guess:

1 - finds x'(t) in (a) 1 - finds t = pi/4 in (a) 1 - finds t = 5pi/4 in (a) 1 - considers endpoints and evaluates in (a) 1 - correct minimum from their derivative (0/1 if x' trivialized) in (a) 2 - finds x"(t) in (b) 1 - substitutes x", x' (from a), and x into specified equation in (b) 1 - finds A in (b)

I'm pretty sure they won't give 1 point for x' in (a) and then 2 points again for it in (b) when you don't need to recalculate it.

[quote] 5a. 1 point for correct line. 1 point for lesser or greater. 1 point for reason. b. 2 points for correct answer and units c. 1 point for answer. 1 point for explanation d. 1 point for lesser or greater. 1 point for reason [/quote]

My points:

1 - tangent line equation in (a) 1 - tangent line equation used to find r(5.4) in (a) 1 - explanation based on r' decreasing/r concave down [0/1 for calculating r(5.4) by hand] in (a) 1 - dV/dt in (b) 1 - solution [ignore units] in (b) 1 - correct Riemann sum in (c) 1 - correct interpretation of integral in (c) 1 - less, based on r'(t) decreasing in (d) 1 - UNITS of cubic ft/minute in (b) and feet in (c)


[quote]
6a. 2 points for f(x) and f(x)
b. one point for identifying first derivative. one point for plugging in 1 and solving for k. one point for k. one point for justifying.
c. 1 point for f`(x). two points for x.

[/quote]
</p>

<p>My points:</p>

<p>1 - f '(x) in (a)
1 - f "(x) in (a)
1 - f '(x) = 0 => k = 2 in (b)
1 - min at x = 1 in (b)
1 - justification in (b)
1 - uses y = 0 to determine that ln x = k*sqrt(x) in (c)
1 - f "(x) = 0 in (c)
1 - x = e^4 in (c)
1 - k = 4/e^2 (keep in mind this question asks you to solve for k) in (c)</p>

<p>
[quote]
Form B this year seems easier? </p>

<p>How does CB determine the curve for these frqs? Do the two different versions of the test have the same curve or are they calculated differently?

[/quote]
</p>

<p>Not sure if the two versions of the test have the same curve or not. My guess would be that they can't. However, on the most recent released exam (2003), the cut scores are only released for the exam as a whole, and not disaggregated into the two different versions.</p>

350

<p>The reason I added with units is that the problem said add correct units.</p>

351

<p>
[quote]
The reason I added with units is that the problem said add correct units.

[/quote]
</p>

<p>Agreed, but (c) also refers to the proper units, and usually when the units are requested on two different parts, they don't provide each with its own units point, and usually lump one giant unit points at the end.</p>

<p>I suppose it's possible that the answer for (b) would require units, and the units for (c) would get its own separate point, though.</p>

352

<p>wait, question did I get 2c right? I said that at t= 3 it was the greatest and got a value of 5127 gallons, is that correct?</p>

353

<p>I found the Form B Free Response Questions:
<a href="http://apcentral.collegeboard.com/apc/public/repository/ap07_calculus_ab_form_b_frq.pdf%5B/url%5D"&gt;http://apcentral.collegeboard.com/apc/public/repository/ap07_calculus_ab_form_b_frq.pdf&lt;/a&gt;&lt;/p>

<p>and yeah, i do totally agree they're easier than what we had.</p>

354

<p>looking at the possible score breakdowns for FRQ is really depressing :(
do u thinik they give partial partial credit, like 1/2 pt on something</p>

355

<p>
[quote]
looking at the possible score breakdowns for FRQ is really depressing
do u thinik they give partial partial credit, like 1/2 pt on something

[/quote]

they don't</p>

<p>you either get the point or you don't get the point.</p>

356

<p>To maelstrom99: That's what I have.</p>

<p>To chickenboi8008: What wxmann says is correct. No 1/2 points.</p>

357

<p>This sitting definitely seemed tougher than the practice tests, on the practice I would generally get ~ 40 out of 54 on the FRQ, but I felt like I completely bombed this one, although the MC seemed slightly easier</p>

<p>At least I'm not the only one</p>

358

<p>Thank god everyone thinks free-response was hard... After MC I thought I was doing great, and this was a definite five, then the FR just shattered my hopes.</p>

359

<p>has anyone answered the question of whether the form b FR affects the curve for those of us who had the super-difficult regular FR questions?</p>

360

<p>I was researching into that question with a couple of folks who would actually know the answer to this question, and the most committal answer I could hear is that they can have different curves, but they're not required to. I also couldn't find out whether they ever have, which I think is a critical answer to determining whether it could happen this year.</p>