2021 AP Calculus AB & BC Exam FRQ #3
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- Опубликовано: 21 авг 2024
- 2021 AP Calculus AB and AP Calculus BC Exam Free Response #3
The Spinning Toy problem!
Full playlist: • 2021 AP Calculus FRQs
area/volume problem; finding area using FTC by hand; u-substitution; understanding rotating a curve; finding maximum of a function; finding an arbitrary constant; volume of revolution; solving for constant; ugly values!
This. This was the question I confidently got 1 point on.
I hope my AP reader likes the smiley face I drew for them.
@@williamarchacki571 funny seeing you here will
I did it right except I missed a negative when integrating on part a. Couldn't progress after that😐
They couldn’t just give us a normal cross section question🤦🏻♂️
i b tryna say 😭
I think part b was so confusing for so many students (and me) because kids intially wanted to set up pi times the integral of the radius squared. I don't think the actual math is that hard. I think that college board just made the question/scenario sound a little too complicated especially compared to the past exams that I took for practice.
Yeah, it wasn't the easiest to figure out what was going on there. One thing I considered when thinking about it was that part c definitely wanted me to calculate a volume so it seemed unlikely they'd want me to do that in consecutive parts of the same problem.
Idk I think making that connection is what that question was about. I don’t think it was too difficult either because I have a friend who got like a 6/54 on the practice free response and he was able to figure out c = 0.6 and everyone else seemed to get it as well
i actually did that for part one, but yea the way the question background was worded made me think that it was asking about volume lol
what in gods name is this question
I love how he talks about the problems as if we can go back and change our answers
Next year’s group will be studying from them.
@@turksvids ye I'm studying these right now
@@turksvids yup, exam is tomorrow
@@davidp2537 lol
I was doing this in class today for practice, I can see why people were pained over this.
Feel so stupid for forgetting that you can just square each term in the integrand individually in part c and spent so long just messing around trying to make it work. Feels good though because everyone else said they couldn’t get it either
why didnt he take the square of 2 as well
I did this for practice for the upcoming 24th test and I don't know why people were so confused about this one. I haven't gone over 4,5,6 but the last 1-2 look like the ones that would cause me the most problems.
Was probably on the spot stress. Encountered something different and panicked.
Ahhh don't even wanna look
PASSED WITH A 5 BABY
@@Gubuyguy happy ending
@@Gubuyguy taking mine tomorrow, let's hope i have the same justice as you haha
i was only able to do part a of this question
On # 1) So apparently in my calculus class, the teacher said that if you use substitution rule you can keep the u and change the bounds to match it, you end out with something like 2(4)^3/2. Could it just be a different way they solved it, are both answers accepted?
As long as you correctly change the bounds and correctly finish the problem you'll end up in the same place! Both methods are fine.
@@turksvids ok, thanks 😊
I absolutely loved this problem, wish I had it for my test. Got a different version though
Do you recall what type of questions came back for yours?
spinning top, my beloved
Why can you square each term in the integrand individually in part c?
its just one product
Should the answer in part a have in^2 with it as units since the question states x and y are measured in inches?
The units would definitely be square inches. I forgot to write them (if the problem doesn't specifically mention including units, you typically do not lose points for not including them).
This damn question…this freaked me out so much on the test, I still got it but wowwww
I have a question please in part b why we didn't consider x=2 a critical point too since it's undefined there ?
i didn't consider x = 2 because there's only one critical point on the domain of 0 to 2. So mainly because it was the endpoint of the domain.
Great video!
goat
thanks! good luck studying!
wait b is so easy
For the first one, why don't you have to change the bounds of the integral when you U sub?
I didn’t do u-sub, I just found the antiderivative (every part of my work is in terms of x). If you rewrite in terms of u, you need to change the bounds as well. Hope this helps!
@@turksvids interesting, I Usubbed and didn’t change bounds but ended up getting to the same exact answer as you.
did you leave it in terms of u at the end or did you back sub to return to x? if you returned to x, then you found an antiderivative using u-sub but evaluated the original; that'll always work. if you didn't go back to x as your variable but used x-values for your bounds, then you got it right by coincidence, but would lose a point for using the wrong bounds for the integral in terms of u.
@@turksvids I returned it to x. Does this mean I only have to change the bounds according to u when I don’t return the equation back to x at the end? I’m a bit confused on when to / when not to change the bounds when using u sub.
if you're going to turn everything back into x at the end, then don't change the bounds. if you're going to leave it as u at the end, change the bounds. the bounds need to represent the same variable you're using. integral(x+1) from x = 1 to x = 2 gives the same value as integral(u) from u = 2 to u = 3. personally i almost never change the bounds and instead just find an antiderivative (however i can do it) and then use the original given bounds.
Was this a no-calculator question?
This was non-calculator. Starting in 2015 and going forward the first two FRQs are calculator and the next four are non-calculator. That's how it will be this year as well. Hope this helps!
this is light af 😹😹
How did I get this wrong 😔
Why was the 2021 FRQ so hard?
I kind of think 2007 form b and 2019 are the hardest exams I’ve seen.
@@turksvids huh, thanks for the information, and do you any like specific way to encounter frqs, is there any sort of method or thinking process you need to go to or am I just overthinking things? Keep up the great content btw!