Calculus AB: reflections

<p>Considering everyone was so worked up about the test, I was wondering how you all feel about your performance on may 9th, and your score. For my part, I thought the MC was pretty easy (I'm thinking I got around 43/45 correct). I thought the first two free response questions were easy, I thought about 2/3 of question three was alright, I had part B of 4 right, and I initially had part A correct too, but I changed it (wording tripped me up). I got all of 5 except for one thing involving Riemann sums. I think I may have missed a point or two on 6. Overall, there was a chance, going by the standard raw score cut-offs, that I could pull of a "regular" 5 (one unaided by a generous curve) with high MC scores and decent (but not great) FR scores. So, what do you all think? Generous curve or no? I got a 5 btw.</p>

<p>I was thinking that I got a 4 due to about 66-70% being a 5 historically. I thought I was just a bit under that but I got a 5. I think the curve was more generous than in the past, but not overly generous.</p>

<p>I think it was a slightly more generous curve than in previous years. I think I did well on the MC, and I did worse on the FR than I usually do, but I still was confident I got a decent amount of points. Based on previous years curves, I probably would have gotten a middle 4, but I think since this year was much harder, they lowered the cutoffs so I probably just made the 5.</p>

<p>I thought it was more difficult than in previous years in that you had to know what you were doing, but if you knew your calculus well it should have been fairly straightforward. I got a 5 without answering all of the FR and forgetting my dx's, so the curve is probably slightly more generous.</p>

<p>Does anyone know when we acutally find out scoring standards??</p>

<p>I think the curve was extremely generous because I got a 5, and I missed like one</p>

<p>I've been at a workshop discussing AP Calculus AB with one of the scorers of the exam. He confirmed the numbers that I've seen posted here as far as the question averages. The total of those means is within one point of the total of the means for the 2003 exam (which is the last exam with released cut scores, and 66 points were needed for a 5), and so I'm guessing that a 5 ended up being in the neighborhood of 65-66 points.</p>

<p>If you scored at the national average of just over 17 points on the FR, that would project to needing 41 questions correct (and 4 skipped) in order to earn a 5. But realistically, most of the students looking to get a 5 almost certainly capitalized in a few places, including picking up almost 5 points on the national average on the areas/volumes question (#1) and picking up some other extra points on other questions (none of whose average was above 4/9), probably reducing the multiple choice burden for a 5 down into the low-to-mid 30's, depending on the number of points picked up.</p>

<p>One other point: the AP Exam does not deduct points for omitting the dx's at the conclusion of integrals, referring to it as a spelling error. It's a practice that I'd personally like to see them change, but I think part of the motivation for it is that they don't want to penalize kids 4-5 times for omitting it on the Free Response, since separate graders grade each numeric question.</p>

<p>Some of the scoring standards are usually released to us at the workshop that I'm attending, but I'm guessing officially that they won't be released to the general public until later.</p>

<p>i have no doubt that the curve must have been ENORMOUS. I literally left 1/2 the free responses blank and still managed to get a 5. Unbelievable!</p>

<p>Wow. Thanks, MathProf, that was extremely helpful.</p>

<p>Felt it might be useful to repost this.
*
*
*
*
*</p>

<p>The last released cut scores were in 2003, so I'm not sure how exactly your teacher would know what the cut scores were two years ago.</p>

<p>Reposting from an earlier thread on this topic:
"Here are the cut scores for the six most recent full exams for which the data has been released. Keep in mind that a philosophical change from computational calculus to conceptual calculus occurred for the 1998 exam.</p>

<p>1985 AP AB exam
84 to 108 = 5
68 to 83 = 4
49 to 67 = 3
34 to 48 = 2
0 to 33 = 1</p>

<p>1988 AP AB exam
83 to 108 = 5
68 to 82 = 4
48 to 67 = 3
32 to 47 = 2
0 to 31 = 1</p>

<p>1993 AP AB exam
67 to 108 = 5
53 to 66 = 4
36 to 52 = 3
24 to 35 = 2
0 to 23 = 1</p>

<p>1997 AP AB exam
72 to 108 = 5
56 to 71 = 4
39 to 55 = 3
25 to 38 = 2
0 to 24 = 1</p>

<p>1998 AP AB exam
74 to 108 = 5
57 to 73 = 4
39 to 56 = 3
24 to 38 = 2
0 to 23 = 1</p>

<p>2003 AP AB exam
66 to 108 = 5
47 to 65 = 4
29 to 46 = 3
16 to 28 = 2
0 to 15 = 1</p>

<p>It's been generally agreed upon that the 2003 cut-scores were considered "low", meaning that most people think the marks for a 5 were too easy, despite the fact that less than 20% of the nation earned them at the time."</p>

<p>I wouldn't doubt a score of 65 has a decent chance of ending up at a 5, but I would be tremendously shocked to hear that it dropped lower than 60.</p>

<p>*
*
*
2006 AP AB Exam Distribution</p>

<p>Score Percent
5 22.3%
4 20.5%
3 18.6%
2 15.5%
1 23.2%</p>

<p>I also got a 5, even though I came out of the test going with that free response, I got a 3. But thinking back on it, the free response really wasn't SO terrible. The MC was really easy so I think we all got over confident and expected it to be a breeze. Plus, my class had just done the 2006 free response and that was extremely easy so we were thrown by the fact that we needed more than 10 minutes to think about the questions. However, there is no doubt in my mind that there was a very generous curve.</p>

<p>So let's see i thought i got a 5 while doing the multiple choice</p>

<p>then i got hit with the F.R> which felt like a bomb.</p>

<p>everyone in my class just started laughing</p>

<p>I attempted to do like 1/2 of the problems... the other 1/2 i left blank because i had no time..</p>

<p>the 1/2 that i did attempt to do, i was not confident about, i just tried getting as many technical points as possible. so i maybe got 1/4th of possible F.R. questions right..</p>

<p>leaving the test, i almost cried (not) and thought i def. got either a 1 or a 2 in AP CALC..</p>

<p>there was no way i did better than a 1... ti was so hard.. but secretly i was optimistically hoping the curve was extremely generous and myabe i would do well...</p>

<p>i come home to facebook and was invited to like 3 THE AP CALC AB FREE RESPONSE WAS THE HARDEST THING OF MY LIFE/IT WAS A JOKE..</p>

<p>that being said</p>

<p>i got a 4.</p>

<p>I came out thinking what the hell was that I skipped only 1 MC. I did all of the FR except 1, but I wasn't very sure about a lot of it. I came out thinking, aw crap I got a 3 then I heard people saying they skipped half. So then I figure I got a 4. Bam I get a 5.</p>

<p>One piece of info that I have is the scoring from question #4. My predictions in May from <a href="http://talk.collegeconfidential.com/showthread.php?p=4131452#post4131452%5B/url%5D"&gt;http://talk.collegeconfidential.com/showthread.php?p=4131452#post4131452&lt;/a&gt;.&lt;/p>

<p>
[quote]
Not convinced I've found nine good points on this one, but my guess:</p>

<p>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)</p>

<p>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]
</p>

<p>And what they actually did:</p>

<p>
[quote]

2 - finds x'(t) in either part (a) or (b) [if answers are in both and disagree, the answer in part (a) takes precedence]
1 - sets x'(t) = 0 in (a) [could literally write x'(t) = 0 here]
1 - finds the correct minimum in (a) [there was a really interesting situation on one of these, and I'm still not sure I agree with how they graded it]
1 - justification [requires checking of endpoints and critical values of t = pi/4 and t = 5pi/4] for part (a)
2 - finds x"(t) in (b)
1 - substitutes x", x', and x into specified equation in (b)
1 - finds the value of A in (b)

[/quote]
</p>

<p>Looks like I misallocated one of the points, but wasn't too far off. I actually think this scoring standard is nicer than the one I was guessing (for instance, you get 3 points on part (a) even if you never get to t = pi/4 and/or t = 5pi/4).</p>

<p>We're supposed to be going over a few more questions. Given what I've heard so far, I think it's likely that the May guess on points for question #3 is correct, although I should get confirmation later this week (probably tomorrow).</p>

<p>As far as the others, I'm really not sure. I have a feeling that giving two points for the two intervals in question #2 didn't happen, although I'm not sure where the allocation of the 9th point goes if it doesn't go there. The others look like they might hold up.</p>

<p>Math Prof, do you happen to know when the scoring guidelines for calculus (and other AP exams) will be put online on AP Central? THanks.</p>

<p>I am amazed I got a 4. If it were a practice test based on past curves in my class, I definitely would not have scored that high. But almost everybody seemed to have some problems with it, so I guess I didn't do too terribly.</p>

<p>rb9109, I don't know when the scoring guidelines will be posted officially on the AP website. What I've heard nebulously was "sometime this summer", and that was as it committal as it got.</p>

<p>I do, however, have the rest of the AP Calculus AB scoring rubrics for the main form.</p>

<p>Quotes represent my May prediction. Bold represents additions or clarifications, while pieces that are incorrect are marked in italics.</p>

<p>AB-1

[quote]
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)

[/quote]
</p>

<p>(I'm a genius!)</p>

<p>AB-2

[quote]
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)

[/quote]
</p>

<p>The above is the only part I got right. The rest of the scoring:
1 for both intervals in (b) [I predicted 2 points, one for each]
1 for identifying t = 3 as a candidate
1 for identifying the "integrand" of f(t) - g(t) [I lumped this in with other points]
1 for amount of water at t = 3
1 for amount of water at t = 7 [I lumped the previous 2 points together]
1 for the number of gallons AND the time [I predicted 2 points]</p>

<p>AB-3</p>

<p>See my earlier post in this thread. (It's not that far back.)</p>

<p>AB-4

[quote]
1 for identifying h(1) and h(3) properly in (a)
1 for invoking Intermediate Value Theorem in (a) Mentioning that h(x) is continuous was required to earn this point
1 for confirming the average rate of change = -5 in (b)
1 for the Mean Value Theorem in (b) Mentioning that h(x) is differentiable was required to earn this point
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)

[/quote]
</p>

<p>I predicted the points pretty well here, but was surprised that they were as picky as they were on the IVT and MVT points.</p>

<p>AB-5

[quote]
1 - tangent line equation in (a)
1 - tangent line equation used to find r(5.4) in (a)

1 - estimate of r(5.4) from tangent line
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)
2 - 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]
</p>

<p>I've heard a rumbling but haven't yet confirmed, that to earn the point in (d), you must also have stated that r'(t) is decreasing because r is concave down, and that determining this from the table was insufficient. I haven't yet confirmed this.</p>

<p>AB-6

[quote]
1 - f '(x) in (a)
1 - f "(x) in (a)
1 - f '(x) = 0 => k = 2 in (b)
1 - f '(1) = 0 or f '(x) = 0
1 - k = 2

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 - Determines either f(x) = 0 or f "(x) = 0
1 - Writes an equation in terms of one variable (either x or k)

1 - k = 4/e^2 (keep in mind this question asks you to solve for k) in (c)

[/quote]
</p>

<p>Some of the additional pickiness that I didn't expect here probably served to lower scores more than usual, probably contributing to a nicer curve.</p>