2024 AP Calculus AB & BC FRQ #3

Free Response Question 3 from the 2024 AP Calculus AB & AP Calculus BC exams.

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)

[drybowser]

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

[MovieWatcher-sxib]

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)

[machodynamix]

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?

[nak_attak]

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 😂

[anikethvivek]

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

[falldownstairs]

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?

[jellybeans]

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?

[tektonik-eezh]

thank you! your explanations are quite helpful!

[itsdavid]

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?

[yna]

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

[edvantagetv]

your amazing! Please consider making tutorials and lectures

[ashvinjaishankar]

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?

[andewws]

th;ank yuou my name is erick and I find these very helpful, im from prhs

[Roddd]

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

[RaahiIbdp]

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)

[OverlordJojoo]

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

[drumzstringz]

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

[itsdavid]

u are awesome bro, just wanted to remind you

[乃randon]

wow the only part i got right was part A 😭