Revisiting the AP Calc BC FRQ that I took back in high school
Revisiting the AP calculus BC FRQ I took back in high school. Today we will retake the free-response questions in AP Calculus BC I took back in 2004. Hope this video can be helpful for your calculus class and the AP calc test! Good luck with your AP calc exams!
Check out 2023 AP calculus AB FRQ: • Solutions to the 2023 ...
Try the problems first: secure-media.c...
0:00 2004 AP Calculus BC FRQ (the one I took when I was a student)
Q1 (both calc AB and calc BC)
0:42 Q1a The change of a function
1:46 Q1b Determine if a function is increasing or decreasing
3:24 Q1c The average value of a function
4:48 Q1d The average rate of change of a function
Q2 (both calc AB and calc BC)
6:07 Q2a Area between the curves
6:54 Q2b Volume of a solid of revolution
11:27 Q2c Volume of a solid with square cross-sections
Q3 (calc BC only)
16:05 Q3a parametric equation and change of x-coordinate
17:49 Q3b equation of a tangent line
19:43 Q3c speed of a moving particle with parametric equation
21:05 Q3d acceleration vector of a moving particle
Q4 (both calc AB and calc BC)
24:47 Q4a implicit differentiation
27:30 Q4b horizontal tangent line
30:31 Q4c second derivative & local extremas
Q5 (calc BC only)
34:34 Q5a carrying capacity of a logistic differential equation
36:11 Q5b half of the carrying capacity
36:54 Q5c separable differential equation
40:31 Q5d find the limit
Q6 (calc BC only) the series problem
41:15 Q6a 3rd deg Taylor polynomial
44:56 Q6b find the coefficient of x^22 in the Taylor Series
47:22 Q6c Lagrange error bound
52:30 Q6d LAST QUESTION!
55:00 end
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Пікірлер: 168
Me in high school 0:33
@fuji_films
3 жыл бұрын
😄
@ojaskumar521
3 жыл бұрын
Imagine bprp sir when young Lol you looked really good!
@JashXD
3 жыл бұрын
:D
@Jatin-gm5zx
3 жыл бұрын
Hey can u give me the answer of Laplace of x^-3/2
@user-xo8dn9jc8w
3 жыл бұрын
ممكن ترجمه بالعربي للفيديو Can I translate it in Arabic for the video please
I used to teach AP Calculus AB and that was one of the most fun experiences that I had. One of my favorites is related rates and the other one is optimization problems! It's amazing how a teacher can make such a huge difference in your life. My 8th grade math teacher was one of the best teachers that I have ever seen in my life and he is the one who inspired me to pursue math. Btw, great video! 🤩
@blackpenredpen
3 жыл бұрын
Thanks for sharing! : )
@SyberMath
3 жыл бұрын
@@blackpenredpen Absolutely! Thank you!
Good luck to everyone testing on Tuesday the 4th! May the fourth integrate well with you.
good luck to all you brethren taking the calc bc exam this year :)
@braedenrubin4234
3 жыл бұрын
Thxx
@keltondsouza5409
3 жыл бұрын
I failed
@prakashshekhar8346
3 жыл бұрын
@@keltondsouza5409 the Top question :(
Interesting that the first two ‘calculator’ problems would not have been too bad and certainly possible for a first year student without a calculator. Recent exam questions pretty much always give crazy equations on the calculator section (more like your #3) to hopefully make it obvious that they want you to go immediately to go to the calculator after setting up the integral or derivative.
47:31 is the funniest thing I have seen in a while
@blackpenredpen
3 жыл бұрын
Lol thanks
@respectpartii6302
3 жыл бұрын
Because it's accurate lol
Ayy I’ve got my BC test this Tuesday so this is great practice 😁
@imbatmanlol
3 жыл бұрын
How was it
@raysmith6731
3 жыл бұрын
Got a 5 😄
I love how the non-college board released videos are more helpful than the actual AP review videos
This makes the AP calc test feel so much easier, hopefully the test on Tuesday is as easy as this.
@stephenbeck7222
3 жыл бұрын
The current test/expectations have gone through 2 major revisions I think, and the one in 2017 expects much more verbal analysis (more words to justify your work), though not much more complex actual calculations. Good luck!
@blackpenredpen
3 жыл бұрын
Best of luck!
@griffisme4833
3 жыл бұрын
It won't be sadly, I wish.
@DrLongWang
3 жыл бұрын
@@blackpenredpen Legally I’m not allowed to say any frq problems on the test were similar to one or more frq questions you covered here. But hypothetically speaking, if one of the frq questions was similar to one you went over, I would have gotten it right because of this video. Hypothetically of course.
This is good practice for my BC exam coming up Ty bprp :)
@blackpenredpen
3 жыл бұрын
Glad to hear that. And thanks for coming Albert!
Came here after taking the AP Calc BC exam. Thank you so much for the help this schoolyear; you're amazing!
I miss doing these problems. I’d rather do these problems than real analysis 😫
First :DDDD congrats on 700k that is epic
I’m only in calc A rn but hopefully this helps me out next year!! Thanks for this wonderful walkthrough!
@blackpenredpen
3 жыл бұрын
Half of these were in AB as well. See description for it. Best wishes for u
@spencersant5281
Жыл бұрын
@@blackpenredpenI ended up getting a 5 on the BC test!
It makes sense that I’m able to do these problems because I’m in bc right now, but it’s weird because this is a bprp video lol
@aashsyed1277
3 жыл бұрын
DAMN I LOVE YOU....
@user-fn4ds7zm1i
3 жыл бұрын
This was me last year. I was shook at the fact that I solved the problems. Surprisingly, I still know my calculus
0:33 The sensei of the sensei?
@blackpenredpen
3 жыл бұрын
Yes.
Good luck to everyone on APs! Y’all gonna kill it just relax!! 👍🏼👍🏼
love you Steve, Ahmed from Egypt😍😍😍
@yassineseghrouchni8175
3 жыл бұрын
That's weird
Can you do an Algebra and Trig walk through from subject begining to end?
@lifefutile7974
3 жыл бұрын
kzread.info/dash/bejne/p22kyaafoLyTqpc.html
that first question was so easy. im hoping for a question like that on the 24th
@spendroid8952
3 жыл бұрын
Well just took the test and lemme say, it was nothing like this lol
This is great! Could you also do something similar for an IB Analysis and Approaches Higher Level paper? Thanks and love your content
33:16 That's easy AF, I can do it in my head, right side of the numerator becomes zero because it's being multiplied by 3×2 -2×3. Then it just becomes -2(something) ÷ (something)^2 = -2/7 Now (something) = 16-9 =7
You have an error at 18:50! The result should be negative, not positive. Great work as always, you've helped me so much for BC Calc this year :)
@terraria2009
3 жыл бұрын
Yeah I saw that too and was like: he's probably going to notice right?
In exercise 3 question b -7/(3+cos(2²))=-2.983 not 2.983
@blackpenredpen
3 жыл бұрын
Yea... I forgot the neg sign
Coming back after acing Ap Calc BC. Really appreciated
1:31 - "for this, we can just use the calculator..." Me, taking the exam in 1989: "What? You have a calculator that just spits out this answer? I have to show my work, but you get to use a calculator?!?"
@anonymous-zt5jq
3 жыл бұрын
we have to show work for certain sections, as this is just a part of the problem, using a calculator would be faster
In my high school , the only thing I do is "BAKCHODI"
Imagine steve with his high school hair and his current beard
For 1b) I would have just argued the argument is 7/2=3.5 which is more than pi but less than 3pi/2. Sine is decreasing on this interval. You gotta save as much time as possible on these exams! :-)
Interesting. These questions are all pretty standard and familiar in the Specialist Maths high school subject in Australia (with the exception of taylor series).
I would have been so happy to get that first frq on my calc ab exam this year
Nice tribute to Mr. Schneider. 👍🏽
Thank you, my teacher can go on tangents while lecturing so I miss some things. This was really helpful :D
41:20 Q6 can be solve by expanding sin(5x+π/4)= cos(π/4)sin(5x) + sin(π/4)cos(5x) and writing each sin(5x) & cos(5x) as taylor series in (5x)…
A good student always thanks his good teacher
I think there is a mistake on 3b. (-7)/(3+cos(4)) = -1.751
2004 BC?? Man you have a beard, but I didn't expect you to be that old!
When I was a senior in hs I was just taking precalc... I wish I had taken hs more seriously
Wow, I feel old... I took the Calc BC exam in 1989 (11th grade). How is this dude 15 years younger than me?
@jasongilder22
3 жыл бұрын
Damn that’s old
You should try the claculus questions from Indian Statistical Institute (ISI) entrance test. They are very tough.
@Rithsomware
3 жыл бұрын
Agreed
Calculators don’t do calculus they use numbers right?
At 18:48, the answer should have been -2.983
@blackpenredpen
3 жыл бұрын
Yes. I forgot the negative.... like always 😆
Why all these numeric answers rather than precise concise expressions in terms of sin and cos.
Congrats AGAIN 17 yrs
I’m in AB calc and the first 5 questions are all things we learned this year 😂 I’m not so scared for bc rn
Couldn't you just say approx 82 cars per min for (c)? What after all, is 81.899 cars? 81 and an accident?
@blackpenredpen
3 жыл бұрын
I went with the official answer. I think we can have decimal for rates.
@mikeh283
3 жыл бұрын
@@blackpenredpen It would have caused me to waste time lol. Love your channel sir. If you have the inclination, could you do some vector calculus content, line integrals, divergence theorem, etc..?? Thank you for your time regardless
@blackpenredpen
3 жыл бұрын
Maybe in the future. Thanks for the comments.
16:00 what is the k value
Can we expect a course on combinatorics on your channel it will be really helpful!
got a 5 on mine last year🤝 good luck all
This is foreshadowing for next year for me
Thanks and greetings from Bolivia!!
Damn this paper is damn easy .glad you are a good teacher
"I will tell those gods you helped in trusts in the maths!" -- peace on you.
how was integral of cos(t^2) calculated?
Just watching you reminiscence back in the high school days and you realize it was a 17 years ago. I started laughing when you had existential crisis. I bet you were having an inner monologue saying "Has 17 years really passed? I am getting old...."
Gotta love that shinchan on right side ❤️
May the 4th be with you, administration round 1 students! They're doing three rounds for the exam this year FYI. May 4th, May 24th, and an online one in June.
@blackpenredpen
3 жыл бұрын
Yea and do you think that’s a good idea? Are they just going to give 3 different tests?
@jonathanmcgreal234
3 жыл бұрын
@@blackpenredpen Yep, three different tests. The online one will likely look pretty different as well since there are too many online tools that can solve basic integrals and such. I think BC needed this. I follow the AP Calculus teacher community on Facebook pretty closely and it is clear that some classes/schools really need the extra time since every district this year has handled class times and meeting arrangements differently. Personally, I was able to finish the curriculum in time, but about three weeks later than I would have liked, so I gave my students the choice on what date they'd like to take it and it was a pretty 50/50 split between the two in-person dates. I'm calling my May 4thers the scouts for the May 24thers!
@blackpenredpen
3 жыл бұрын
@@jonathanmcgreal234 Ah I see. I wish your students the best of luck! : )
Petition for using the the derivative wrt fish
i will take calculus bc tomorrow wish me luck guys
@blackpenredpen
3 жыл бұрын
Best of luck!!
@ardaanil9398
3 жыл бұрын
@@blackpenredpen omg thank you so much
@ardaanil9398
3 жыл бұрын
FRQ part was really hard but i hope i can get a 5 with multiple :)
Can anyone tell me how to ask a question from him,I mean how to reach to him to ask a question
i like your class . it's very helpful for me .
Can you please do 100 double integrals?
THAT'S HIGH SCHOOL MATHS?!?!?! damn
@Skankhunt-mv4vd
3 жыл бұрын
are you trying to say its hard or easy?
Can someone tell me who takes AP Exams and what is it for?
Sir i want to share a question to you how can i
Me, a new calc 1 student after question 1: "Wow that wasn't actually that hard" 😄 Me after skipping to the last question: 💀
18:47 there's no way that could equal a positive number, look again
But AP reuses the test questions, right?
did you get a 5 on the exam tho?
@blackpenredpen
3 жыл бұрын
Yes
@BenDover69831
3 жыл бұрын
@@blackpenredpen nice nice nice nice nice nice nice nice nice nice man, what other AP's did you take?
55:17 that's the moment when you think about your life
Can someone tell me how old are the person that passes this type of exam ? Thank you so much !
@powellmunroholzner2941
3 жыл бұрын
anywhere from 15-18, usually
IS THIS PRE RECORDED?
Why are these questions so complicated? And I ain’t at calculus i’m in 10th grade
@hybmnzz2658
3 жыл бұрын
You answered your own question :)
@ryanjagpal9457
3 жыл бұрын
@@hybmnzz2658 Sorry?
@noahtawil8793
3 жыл бұрын
@@ryanjagpal9457 it won’t seem that complicated once you learn calculus
@ryanjagpal9457
3 жыл бұрын
@@noahtawil8793 It seems difficult to answer questions of it like they change it and then change from tan to like sec^2 and i’m like this is nothing to do with maths this is just puzzles
Calc BC test tomorrow, wish me luck
@elimarburger1659
3 жыл бұрын
The frqs weren't too nice this year
@kraze4kicks822
3 жыл бұрын
@@elimarburger1659 IKR I felt like the multiple choice was very easy, and even the calculator free responses weren’t bad, but the no calc free response was hard
This is awesome
I’m in precal this year and I take BC next year and I’m very scared now lol :/
Love from Bangladesh ❤️
2 days to my first AP
@blackpenredpen
3 жыл бұрын
Best of luck!
@menkiguo7805
3 жыл бұрын
@@blackpenredpen thank you! But I do not have any math APs (if computer science a and statistics do not count as math) though, lol! I am also Chinese btw
Who else noticed the Shinchan on the right?
I get free motivation by the way you speak and do math Blackpenredpen is best!
I hope God bless you
Did u get a 5 sir?
@blackpenredpen
3 жыл бұрын
Yes 😃
LOL you got me at 47:30
Question 3 is wrong. Should be -2.98
Hey bprp i hope you find this comment Can you do a video on the following limit? Lim n-> inf (ln(n!)/n) important to mention** Its a calc 2 question(so without gamma function)and its a proof: proof that this limit= infinity.
Uhh my AB calc exam I took like 3 days ago was much harder than this...and this is BC
@seanshameless0
3 жыл бұрын
Yeah curriculum has changed a lot since ‘04
This may be an odd unrelated question, but are you a Muslim?
I like how most questions are jee main level😀😀
JEE Advance: Am i a joke to you!
second :C
Who knows Ramadan here🙂🙂
Yaha pe mat aao. Live comment pe jao
In India,JEE ADVANCED is harder than these Qs!😂
Thirddd
Well When you realise all questions are damn easy for a JEE aspirant 😂😂😂 In India these questions are given to 11th standard students to solve lol
In India, JEE ADVANCED maths is higher level than these Qs! Hit like if you agree!
@yagnapatel3912
3 жыл бұрын
Isn't that a bad thing though? Easier is good.
@karanjadhav818
3 жыл бұрын
Ig the harder the better...Or else you won't learn anything new
@yagnapatel3912
3 жыл бұрын
@@karanjadhav818 good point
Shave that beard bruh
Who knows Ramadan here🙂🙂