2024 AP Calculus AB & BC FRQ #3

Рет қаралды 7,107

2 ай бұрын

Free Response Question 3 from the 2024 AP Calculus AB & AP Calculus BC exams.
All 2024 FRQs: • 2024 AP Calculus FRQs
All past FRQs: • AP Calculus Free Respo...
Calc AB Review Videos: • AP Calculus Review Vid...
Calc BC Review Videos: • AP Calculus Review Vid...
Differential equation problem. Non-calculator.
sketching solution curve on slope field; critical point from differential equation; determining maximum, minimum, or neither; first derivative test; second derivative test; separation of variables (separate and integrate)

Пікірлер: 39

@drybowser1519 2 ай бұрын

I like watching these videos, hoping I said the same thing on the AB exam.

@nak_attak 2 ай бұрын

For B I went through and made a number line and plugged in horrible values to the trig functions and relied on my unit circle very heavily 😂

@turksvids 2 ай бұрын

nice work. i think a number line can justify it.

@MovieWatcher1-sx5ib 2 ай бұрын

For part C, would I lose points for not simplifying? I believe I had C = ln3 and then I left the ln3 in the exponent instead of bringing it down as a coefficient, so I had H = 1 + e^(sin(t/2) + ln3)

@eninjeth4615 2 ай бұрын

ur good crodie

@lyonkang7402 2 ай бұрын

They can’t dock you for a mathematically equivalent answer. Idk the grader could be lazy tho lol

@machodynamix5567 2 ай бұрын

For part b, i just used the slope field as my justification as you can see the slopes are positive before pi and negative after pi. Would i still get the justification point?

@turksvids 2 ай бұрын

I think you will have to make specific reference to the sign of some derivative (first or second) to get justification points. so you could maybe look at the slope field to determine that dH/dt >0 and then dH/dt < 0, but definitely saying "looking at the slope field" will not be enough. still lots of points to be earned otherwise, though!

@tektonik-ee6zh 2 ай бұрын

thank you! your explanations are quite helpful!

@turksvids 2 ай бұрын

no problem!

@yna418 2 ай бұрын

does it still count if i left 3 in the exponenent of with the sin t/2

@falldownstairs7712 2 ай бұрын

hi turksvids, thank you for making these videos, they really helped me study prior to the exam 2 days ago. for part b, do you think i would get full marks if i justified the critical point being a local maximum if I used a number line for the derivative of the function?

@turksvids 2 ай бұрын

i think you can do that if you also mention that H>1 so H-1>0 and doesn't impact the sign. there was another question like this a year or two ago where that would have worked and i missed the opportunity there as well. (I think I just like finding the second derivative more than the average person.)

@jellybeans2991 2 ай бұрын

For part c, I had everything you had but I was being stupid and thought sin(0) = 1. So I put 3/e as c and 3/e in the final equation. Do I still get any points for part c?

@explaindofficial 2 ай бұрын

your amazing! Please consider making tutorials and lectures

@turksvids 2 ай бұрын

Um…have you checked out my channel?

@anikethvivek4228 2 ай бұрын

For the justification on part b, could you just sign test the first derivative to prove H(t) has a max?

@turksvids 2 ай бұрын

now that you mention it, I think you can because we know H(t)>1 we can do a sign test. that's a good move!

@user-pv3zu1sy4m 2 ай бұрын

in part c if i remove the 1/2 from the right side of the equation and bring it outside does it still work ? 1/2 integral cos t/2 = 1/2 (sin t/2 + c)

@turksvids 2 ай бұрын

are you asking if 1/2 sin(t/2) + C is the same as 1/2 (sin(t/2) +C)? if so, then yes, those are equivalent.

@accxlxrxtxr9107 2 ай бұрын

Let’s go I got all correct

@itsdavid5601 2 ай бұрын

quick question, if i drew the horizontal asymptote on the slope field but also the line through the point, will i get points taken off or no?

@turksvids 2 ай бұрын

if it's a dotted/dashed line i would think you'll be fine.

@itsdavid5601 2 ай бұрын

@@turksvids great!

@ashvinjaishankar3813 2 ай бұрын

For part b, would the 1st Derivative Test be faster because (H-1) > 0 and cos(t/2) changes from positive to negative at pi, so dH/dt changes from positive to negative, meaning there’s a relative maximum?

@turksvids 2 ай бұрын

yes, definitely. i regret not doing that. there was another question a year or two back like that where I also did not note that fact and dove in with second derivative test. (It was 2021 5d. (I'm still not convinced you can use first derivative test confidently on that one, though, it turns out now that I'm rereading the problem.)

@ashvinjaishankar3813 2 ай бұрын

I remember that question in 2021 and I don’t think you can use the 1st derivative test because dy/dx was in terms of both x and y, but all you were told was that y > 0 and x was an angle in the 1st or 2nd quadrant. The numerator I don’t think is an issue but I think the denominator might have been ambiguous.

@itsdavid5601 2 ай бұрын

u are awesome bro, just wanted to remind you

@turksvids 2 ай бұрын

thanks so much!

@OverlordJojoo 2 ай бұрын

Im doing the ap calculus ab retake , how different is the retake from the actual exam ???

@turksvids 2 ай бұрын

It's pretty much as different from this year's exam as this year's exam was different from any other exam in the last 5-10 years. They just roll out a different set of questions. Still these are great new practice problems for you!

@OverlordJojoo 2 ай бұрын

@@turksvids Oh ok thanks

@drumzstringz 2 ай бұрын

for a dont you have to draw the line y=1? Is that an asymptote?

@turksvids 2 ай бұрын

i don't personally think so. if the x-axis was expanded far enough, i would think so. or you would at the very least need to approach the asymptote. but in this case the curve we draw cuts off way before the asymptote is relevant. we'll see for sure when the scoring guidelines come out! (I did think it was suspiciously easy!)

@bruhmomenthdr7575 2 ай бұрын

Its (H-1) not (t-1) 🤦‍♂️

@Roddd2333 2 ай бұрын

Hi bro, just wanna ask why aint we get the same paper here in singapore?

@turksvids 2 ай бұрын

For as long as long as they've only released one set of FRQs the one they've released has been the form taken on the East Coast of the US--maybe it covers most of the US, I just know my students have always taken it so far. I don't exactly know why (maybe it's the most common version?), but it seems to be what they do. It's a shame they don't release more (though it saves me hours of my life...)