2024 AP Calculus AB/BC FRQ 1 Solution | Calculus 1 Exercises

We solve Free Response Question 1 from the 2024 AP Calc AB/BC exam. This problem concerns the temperatures of coffee in a cup, with info given in a table. We are asked to find Riemann sums, interpret integrals, and more. #apcalculus #calculus
Calculus 1 Course: • Calculus 1
Calculus 1 Exercises playlist: • Calculus 1 Exercises
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0:00 Part A
2:03 Part B
5:06 Part C
7:18 Part D
8:53 Conclusion
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[@WrathofMath]

Should have a complete solutions video done by tomorrow. 10 Hours of AP Calc AB/BC FRQs: kzbin.info/www/bejne/hYjLZ41_qNSjb68 2024 FRQ2: kzbin.info/www/bejne/p2Gcpn2sZdt7etE 2024 FRQ3: kzbin.info/www/bejne/aZCzdatvZrONnas 2024 FRQ4: kzbin.info/www/bejne/lZy0qH6Hba2We6s

[@rospore5586]

I kind of disagree with part d. When I see the words, "The temperature of the coffee is changing", to me that means that either the temperature is increasing OR decreasing, doesn't matter which. So I interpret this as the absolute value of the first derivative, like speed not velocity. Since the second derivative is positive and the first derivative is negative, that means the rate of change of the temperature is approaching 0. Therefore I don't really think it would make sense to say "The temperature of the coffee is changing at an increasing rate", when the rate is literally approaching zero and getting slower and slower. If the temperature really was "changing at an increasing rate", then as time goes on you should expect to see larger changes in the temperature over the same time interval, which isn't happening in this case as instead, those changes in temperature are getting smaller and smaller.

[@elquesohombre9931]

Yeah that was my understanding of the question when I was taking the exam

[@WrathofMath]

I understand why you would think that, but I also think you're adding interpretation that isn't there. The problem asks us to determine the behavior of the rate of change of the temperature. The rate of change of the temperature is indeed increasing. It is going from negative to less negative, and it never mentioned the absolute value of the temperature. I would pick the interpretation that is faithful to precisely what the question says. You can also find early solutions on AP Calc medic. They're not the College Board, so we'll have to wait and see what the official solutions are, but they have a lot of experience with AP College Board questions, test prep, and all that - and their solution agrees with the one I gave here, so I believe that is the intended solution. I agree the wording is vague enough to make you wonder though, I sat for several minutes considering whether or not to solve the problem the way you described and decided it made the most sense to stick to exactly what the question says.

[@Charlie-kw9jk]

If you calculate the respective C' for the intervals 0-3, 3-7 and 7-12 you will see that C'(t), the rate at which the temp is changing, are -5, -4 and -2.8 so these "rates" are definitely increasing. I think you are confusing the idea that when a value goes from -5 to -4, the value is getting larger (even though it is going closer to 0). Another example, velocity can be increasing, yet you are slowing down. How? When you are slowing down in reverse, the vel goes from negative values towards 0.

[@carebear_yo4760]

I agree with you. It seems like we are in the minority though with this thought process. I am surprised though. Seems easy to see the rate of change in absolute value is decreasing.

[@AnthonyYang0211]

@@WrathofMathchange can mean increasing or decreasing. If the first derivative is negative, that means the coffee is cooling down. Now if the second derivative is positive, that means the coffee is cooling down at a slower rate as time passes. Which in my mind means a decrease in change. Just my thoughts.

[@Mandq.]

is that intenrnational form? why its not the same as what i did...

[@WrathofMath]

Not sure, it's from the College Board website: apcentral.collegeboard.org/courses/ap-calculus-ab/exam/past-exam-questions

[@wolfdesroyer8711]

W i gyatt the first one right

[@WrathofMath]

W