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Early Solutions to the 2024 AP Calculus Free Response

We're excited to once again share with you our early solutions to this year's AP Calc Free Response Questions. This post will cover both the AB and BC solutions. Note that questions 1, 3, and 4 were identical on both exams. We've listed all 6 AB questions first, and then the three BC only questions.


Some of our exam predictions turned out to be spot on (graph of f with an accumulation function, and an area/volume FRQ 6), but we were wrong (again) about a rate-in/rate-out problem. Notably this year we did NOT see L'hospital's rule or as much of the chain rule as we had predicted.


You can see this year’s AB questions here and BC questions here. Although the official scoring guidelines don’t release until the summer, here’s a first attempt at solutions. (Please be gentle if we have any errors!).


AB/BC Question 1

AB Question 2

AB/BC Question 3

AB/BC Question 4

AB Question 5

AB Question 6


BC Question 2

BC Question 5

BC Question 6


Reflections:

We thought the questions this year were fair, and actually quite similar to last year's. Some skills seemed to be repeated in AB1 and AB2, while much less emphasis was placed on the chain rule and product rule. No questions were related to the IVT, MVT, or L'hospital's rule. Most notably, there was not a single question about an absolute extrema requiring the Candidate's Test! This is usually a big hit on the exam!


The contextual differential equation (AB/BC 3) is becoming quite of a trend, especially with sketching a solution curve in part a and solving the differential equation in the final part.


We think our BC students may struggle with FRQ 6 as there was a lot going on, but they should feel fairly comfortable on BC 2 and BC 5. Nothing too surprising there!


Note that for the sake of these solutions we have simplified our answers a bit more than we might recommend to students. Remember that all equivalent answers are accepted!


What did you think about this year's questions? How might they inform our teaching practice moving forward?


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Alex Rowland
Alex Rowland
2 days ago

I am not sure about 1(d). I think you must consider both the sign of C' and the sign of C''. Since the signs are opposite, the temperature is changing at a decreasing rate. Also consider the situation intuitively: hot coffee cools rapidly at first then asymptotically approaches the ambient temp; it cools at a decreasing rate. Perhaps I am missing something in the wording of the question.

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Serena Gay
Serena Gay
3 days ago

Thanks for posting your solutions - mine were very much the same (except, while I know FTC backwards and forwards, apparently I can't multiply! For #4, I said that 1/2*4*2 is 8 - ugh! lol)

There is only one thing I'm curious about where my result was different and that was on #1 part d. I interpreted their question as a speeding up/slowing down-type thing and used the fact that 2nd derivative is positive and first derivative is negative, to say that the temperature was changing at a decreasing rate (i.e. slowing down). But I went back and forth on that - the wording tripped me up a bit. I see what everyone's talking about, though...but I got everything else…

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Tim Fish
Tim Fish
3 days ago

Besides Limit Comparison on 6a, what other correct methods do you think readers will see students use? Are there other correct methods they could use besides those two?

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Koa Okano
Koa Okano
3 days ago
Contestando a

I took the test and used the integral test.

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Mike Yee
3 days ago

My students who had these questions felt pretty good, but there were two versions administered to my students, and those with the other version were NOT pleased with how they felt afterward. They said the questions were all similar to what we'd prepared for, but then there was always some kind of twist that made it feel significantly different. This is the third time in recent years where my students had more than one version administered where one version made the students feel significantly worse about their performance.

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Scott Kennedy
3 days ago

I agree with the solution to #5 part d. But why wouldn't dx/dt = (dx/dy)*(dy/dt) = 11/4 also work? I can't seem to find my error.

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Scott Kennedy
3 days ago
Contestando a

Right! I didn’t even notice that. As I always say when I make a mistake, “There goes my 5!”.

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