AP Calculus Multiple Choice Practice Test (2020 AP CED Problems)

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In this video we do 22 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document. I've always called it "The Acorn Book" but I don't think it's the official name. Not enough people know about these problems! These are from the 2020 version.
Find the document here:
apcentral.collegeboard.org/co...
I've included complete solutions, discussion, and helpful hints along the way. Using actual CB problems is the best way to practice for the AP Calculus exam's multiple choice section!
Topics: L'Hopital's Rule (L'Hospital's Rule); Differentiability at a point; product rule; implicit differentiation; related rates; limit of Riemann sum; second (2nd) FTC; u-substitution; slope fields; area (with respect to y); one-sided limits; acceleration from velocity; inferences from tables; points of inflection; integrating rate to get total; integration by parts; logistic differential equation; second derivative of parametric equations; conditional convergence; taylor/maclaurin series; polar area; Lagrange Error Bound
#apcalculus #apexams

Опубликовано:

6 апр 2023

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Комментарии : 20

@izzyarmsby Год назад

thank you, this was very helpful!

@wistfulgraph Месяц назад

For #3, they gave values for 2 because they wanted to trick you up. They might think you might use g’(2) in the place for 2g’(x) or might make you scared that you didn’t utilize everything. That’s my guess at leadt

@ashvinjaishankar3813 Год назад

I don’t know how/where you find the time for all these videos, but they’re awesome! Regarding the polar area problem, would it be easier (or slightly less time consuming) to just set the equation equal to 0 and solve for the bounds that way?

@turksvids Год назад

Thanks! I hope tons of people benefit from them. For the polar question, yeah, that's definitely the best approach. I just always try to stress that we can use graphing for anything that causes us trouble when trying to solve (and my students do not love that, so I do it as much as possible!).

@ashvinjaishankar3813 Год назад

@@turksvids that makes sense. I use that approach for problems like the one in this video about counting the points of inflection.

@ashvinjaishankar3813 Год назад

I just noticed another way to do 1: the numerator simplifies to (sin 2x)^2, so the expression is (sin (2x)/2x)^2

@sigh7310 Год назад

Thank you for the video. Very helpful

@turksvids Год назад

Really happy to help! Good luck studying for the exam!

@ashvinjaishankar3813 Год назад

Also I think what happened in 2 is there’s a typo - that should be -1 and 2. I feel they’re trying to fool students to use differentiability implies continuity because the limits of f’ from the left and right of 2 are the same.

@turksvids Год назад

Looking back at it, number 2 is definitely a typo. So weird that it made it into the CED.

@zappist751 Год назад

Hey Turksvids, I really love your videos! I am a little bit confused on number 8, and I'm wondering how come the answer couldn't be B?

@scrunchees8263 Год назад

you can only change from 1/u to ln(u) and not through 1/sqr of u which means you just have to take the integral of 1/sqrt of u the normal way

@zappist751 Год назад

@@scrunchees8263 Thank u legend

@kaycx6189 Год назад

I understand how to get to the answer A for question #8, but why is D not right? Can't you multiply in the x and divide by 3 to get the correct arcsin(3x) derivative? timestamp: 12:57

@turksvids Год назад

You can never multiply in an x, just constants. A quick way to realize that won’t work is to think about integrating just x. We know we get 1/2x^2 * c. We can’t just decide to multiply in x/x because we’d get 1/3x^2 *c, which we know is wrong. The same always applies to variables. We can’t multiply them in.

@yesmaybeno9222 Год назад

How did you add the colon at 20:13?

@turksvids Год назад

On the handheld it’s best to just press ctrl and then the templates button. Hope this helps!

@nobro8577 Год назад

Is this document available for 2021 and 2022 as well?

@turksvids Год назад

They say that it’s available every year but they only update it when they make changes to the curriculum. 2020 was the last revision so it’s the same for 2021 and 2022. There is a different set of problems in the 2016 version (which you can find online if you search for ap calc ced 2016, I think). I do plan to make a video of those as well but I’m a little under the weather just now.

@nobro8577 Год назад

@@turksvids Alright thank you!