Most Difficult AP Calculus FRQ Parts (Everyone in AB & BC Should Know)
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- Опубликовано: 16 июл 2024
- In this video we go over the specific parts of FRQs from the AP Calculus AB exam since 2007 that my students (and youtube commenters) have found the most challenging and the hardest. I will be writing out the solution, but you’ll have to pause the video if you want to read most of them. I’m just pointing out the challenging parts so you can review them quickly (if 35 minutes is quick) as you wrap up your studying for the AP exam. This video only covers things that have been on the Calc AB exam, but many of the questions appeared on both the AB and BC exam--and any of them can appear on the BC exam in any year since all AB material is also in BC.
Timestamps:
00:00 Intro and list of all the problems/parts we’re going to cover
00:54 2008 1d Unique area of a cross section problem
02:22 2016 5b The funnel problems! Volume of revolution everyone hated
03:47 2021 3c The spinning toy problem! People freaked out for no reason over this
05:12 2007B 5d Finding m and b so a line is a solution to a diff eq
07:49 2015 4d Basically the exact same problem...which is why we study!
08:23 2009B 3a One-sided limits; limit definition of the derivative
10:04 2011 6a Definition of continuity
11:38 2019 6d The Squeeze Theorem (first time appearing on a Calc AB exam?)
14:45 2007B 3c Related Rates (or chain rule)
17:09 2008B 2b Related Rates (or chain rule) again!
19:22 2009 2c & d How question parts can be linked together
21:24 2009 3a Why do we need an integral here?
23:37 2010 1c Don’t over or under-think the problems!
26:00 2010 5c Adding a line to a given graph can help a lot
27:46 2011B 1d Using IVT to show functions are equal (a great technique!)
29:24 2017 2d Paying attention to the given information!
30:20 2017 6 Just pointing out all the different representations!
31:01 2018 3d Definition of a POI; be confident!
32:07 2019 1c Knowing the best strategy for absolute maximum
33:56 2021 2b Considering position before deciding; don’t be afraid!
#apcalculus #apcalc #apfrq #APexam
time to start studying at 8 pm the night before :)
Right on . . .
taking the test tomorrow, you have been incredibly helpful!
me too lol, wanna check back in like august and see what we got
thanks! good luck to anyone else taking the exam tomorrow!!
yes sir
30 minutes left 😬
Much appreciated! I always tend to score badly on frqs. This will very much help me on my ap exam on monday
I have my exam on Monday D: How did you do on yours?
@@advancedstudy0 how did u think u did
Just in time😭 thank you 🙏
good luck on the exam!
WOW, i have watched most if not all your FRQ and MCQ vids and cannot expres how much I appreciate this. Thank you for all your work, and explanations!!!!
Thanks so much for the comment! Please share with anyone else you think they will help! Good luck on the exam!!! You've got this!
@@turksvids THANK YOU!!!!! I will for sure!
Thank you so much for posting this video!! This is exactly what I needed.
Hey! Just wanted to say a really big thank you. Your videos were definitely the little extra push that I needed to ace the exam the way I did today. I’m confident I got 9/9 on multiple frqs and no lower than half points on any so that’s good news. Thanks a bunch seriously😁
Glad to help. Hope to hear how you did when scores come out. I know you worked hard and should be proud of yourself!
thank you for doing so much videos for us.also you were talking my students and showing 2000s frqs however you sound like same as me
yeah, neither my voice nor my vocabulary has really aged all that much despite the years going by!
Coming in clutch like always ⚡️
Good luck on the exam!
Just wanted to say your videos helped especially for the FRQ but the ones today were rough idk if one of the writers were made lol. Can’t wait for your explanation once the questions release
Glad they helped! I'll get working as soon as they release the questions! I'm looking forward to seeing them!
Thank you so much for this video! I found it really helpful, and it was a great review of some topics that I forgot about.
awesome. love to hear it!
You are amazing, tysm!!!
THIS IS PERFECT
Test on monday, I can't wait!!!
thank you so much ❤️‼️
thanks sm for this!!
np! Good luck on the exam!
super helpful!!!
glad to hear it! good luck!
The test is in 30 minutes, thank u sm for this
thanks man
Good luck on the exam! Please consider sharing my channel with the rest of your classmates!
i think im even more cooked 😭😭
hi! did you take down the multiple choice practice tests you had? I can’t find the second one and was really hoping i could use it for extra practice before the exam
hi. unfortunately i got a copyright strike from those videos. so even though i wrote all the problems and made the videos i had to pull them down...not worth risking the whole channel over! sorry! (like really sorry for myself...it was a ton of work...but also sorry you don't get to use them!)
hi, Im trying to understand the first problem, but I am confused because i cant figure how the length of the pond at that specific point is f(x)-g(x), it just doesn't make sense in my brain, thank you for any clarification!
imma clutch up last second frfr
hi! What happened to your practice multiple choice exams? Part 1 and 2?
^^??
I got a CB copyright strike from them so I pulled them down. They weren't official CB tests but I'm not sure how to fight it so those are gone...it was a lot of work to write them and make the videos, so it's kind of sad.
@@turksvids woww :( that really sucks, they were super helpful sorry to hear this
I LOVE TURKS VIDS
For the wind chill one I don't understand why it's dw/dt * dv/dt. Could you explain please?
I think you mean dw/dt = dw/dv*dv/dt. (I hope that's what I wrote!) So it's given that w, windchill, is a function of v, velocity, so w(v). That means that dw/dv is the most natural thing to find directly from w(v). The question asks for rate of change of windchill, w, with respect to time, t, so "what's dw/dt?" Any time you run into this scenario (derivative of a function with respect to a variable that is NOT its independent variable) you'll need the chain rule (or to use related rates, depending on how you like to think about it). So in this case we know that we can find dw/dv and we need dw/dt, so we'll need dv/dt for the chain rule to work out. Velocity is a function of time, so dv/dt is a thing that makes sense to talk about (and is given in the problem when you're told velocity increases at a rate of 5 mph per hour). So finally we have dw/dt should be dw/dv*dv/dt. I hope this helps!
May I ask how you got root2 as your critical point for 2010 5c? I understand exactly what you did in your work and why x=3 could not be a maximum/minimum, but I am not entirely sure how to then solve for the critical point to be root2
The curve is the top half of a circle with radius 2, so the equation of the circle is x^2 + y^2 = 4, if y = x, this becomes x^2 + x^2 = 4 or x^2 = 2, so x = +sqrt(2) or -sqrt(2), but we definitely know it's +sqrt(2). (I actually did it in the video in my head by thinking of y = x as a pi/4 angle, knowing that hits the unit circle at (sqrt(2)/2, sqrt(2)/2), so thinking it will hit a circle of radius 2 at (sqrt(2), sqrt(2)).) Hope this helps! Good luck on the test!
Is integration by long division included on ap calc ab exam? Thanks
Yeah, long division before integrating and completing the square before integrating are the two Calc AB algebraic things you could need for sure. If you're in BC you also need to know partial fraction decomposition.
Around 3:38 , shouldnt it be pi/3 times the integral? Cause were integrating very small cones to get volume of funnel?
volumes of revolution uses cylinders, pi*r^2*h, not cones. that's why we use pi, not pi/3. hope this helps!
@@turksvids thanks! This does help!
Could someone please explain the "chain rule" with the dg/dx and dx/dt like at 18:56? How to understand these are given from the context of the problem? Our teacher never covered this method.
You're probably used to thinking of the chain rule as d/dx(f(g(x))) = f'(g(x))*g'(x) or d/dx(f(u)) = f'(u)*du/dx.
Take d/dx(f(g(x))) and instead of g(x) let's say that function is really v = g(x), so d/dx(f(g(x))) will become d/dx(f(v)). So what's weird about that is that we're finding the derivative with respect to x but the independent variable of f is seemingly v. Since we're finding the derivative with respect to x, it must be the case that v is actually a function of x. So if d/dx(f(v)) = f'(v) * dv/dx. But we can rewrite f'(v) as df/dv, so d/dx(f(v)) = df/dv * dv/dx. Now remember we're really just finding the derivative of f with respect to x, which we can write as df/dx. So overall we get df/dx = df/dv * dv/dx.
Consider this: y = 3v+4 and v = 5t+2.
Using the chain rule we can find: dy/dt = dy/dv*dv/dt = 3 * 5 = 15.
We can also just sub in to get y = 3(5t+2) = 15t + 6 and then dy/dt = 15, which is the same.
I hope this helps! It does take some thought and maybe someone else will jump in and explain it more clearly.
@@turksvids This does help. Thanks for all of your time and effort for your videos.
Good luck on the exam! Don't forget these are literally the hardest parts of the FRQs, there's tons of other parts that aren't nearly as challenging. You've got this!
BABE WAKE UP TURKSVIDS JUST DROPPED
Literally 8 hours until my test 😎
is there any reason as to why we don't have to simplify? i get nervous and I simplify anyway even if my teachers tell me and I can't break that habit 😅
it's just philosophical. on a timed test to figure out if you know calculus they don't want you wasting time simplifying arithmetic stuff. (I also struggle with not simplifying!)
AP 2024 THREAD
selam bebem 🥵
we're so cooked bro😭😭
@@mertkangtrhayirdir
@@hakokremsa
@@Pal-605 I'm gonna get a 1 fr
the FRQ's this year were pretty moderate on the BC Exam but that MCQ section was written by satan imo
Yes! Non calc was hell imo. But Calc section mcq was easy.
Wait I'm confused that u say we have to solve it by hand...
Aren't we allowed to use the calculator for the whole test(in 2022)? If not, which sections are we not allowed to use it?
Multiple choice:
30 non-calculator, 60 minutes
15 calculator, 45 minutes
FRQ:
2 calculator, 30 minutes
4 non-calculator, 60 minutes
I think im gonna fail this test :(
Still plenty of time to study! If this video is scaring you, remember: these are only problems that my students/youtube comments have found challenging over the years! I'm intentionally skipping anything "normal" or straightforward. There's plenty of straightforward stuff every year! Here's my AB topic review video playlist: ruclips.net/video/pLCyPMbf6iI/видео.html
thanks daddy
who's here for 2024 AB???