AP PRECALC FRQ 3 PRACTICE

Added: 2026-05-13

[00:00:00]I'm going to love you.

[00:00:05]>> [music] >> Guys, um welcome out to AP Precalc review. This is we're going to be reviewing uh FRQ number three on the 2025 exam. If you want to follow along with what I'm doing, um go to Google, search up 2025 F F Precalc FRQ number or just search up 2025 Precalc FRQ. And you'll see the released FRQ exams, so you can follow along. And you'll also see a scoring guideline, which you can use to grade yourself and make sure you're doing the right thing.

[00:00:36]And um the reason I'm doing FRQ three is because I think FRQ three is like really fun to do.

[00:00:42]I guess it's not I think I uh well, I guess FRQ four is more fun, but um FRQ three is quicker and I've already like this is my thir- four- 14th time um trying to record this video.

[00:00:59]My camera roll is filled with voice recordings and screen recordings of me doing math and then saying the wrong thing and then having to restart, which is really annoying.

[00:01:13]So, um hopefully I'll finish it quick this time.

[00:01:17]So, for number three three is always going to be about unit three, which is uh trig.

[00:01:27]And it's always going to give you um a real-world example of a sinusoidal function, which means that it's going to be a sine function or a cosine function.

[00:01:37]Only these two, it will never give you a tangent function, okay? Don't worry about tangent functions. Or actually, do worry about them, but not for unit three or not for FRQ three at least, okay?

[00:01:48]Now, I'm going to give you a little bit time or pause the video and read these paragraphs.

[00:01:56]That's a horrible Okay, just read these three paragraphs.

[00:02:00]Okay.

[00:02:02]Um now that you guys have hopefully read those three paragraphs, um let's do number A, right? Number A just wants you to solve or not It doesn't want you to solve anything, but it wants you to uh find these five points and just write them out, right? So, let's just say um F Okay, well, it gives us that at T equals zero, it's at its highest position, which is 2 mm above resting position.

[00:02:33]And it also says later the resting position is just, you know, midpoint or midline is your resting position, which will just obviously be zero, right? So, at T equals zero, it'll be two above. And also gives that um this whole like motion of up, down, up again happens 200 times in 1 second, which means that this whole period will be 1 over 200, right? Because this thing happens 200 times in 1 second, so just times it by 200 you get 1, okay?

[00:03:03]Um so, this will have to be uh 1 over 200 and then uh two.

[00:03:12]>> [snorts] >> And um you're technically supposed to write it out as a function of 1 over 800 cuz these go by 1 over 800 each time, but I'm too lazy to do that.

[00:03:25]So, uh Well, we know it's a sinusoidal function, so we know that the distance from here and here will be equal, right?

[00:03:33]That's pretty intuitive. So, um we'll split the difference here, 1 over 400.

[00:03:39]And we know it's -2 cuz it oscillates the same amount up and down, which is 2 mm.

[00:03:46]Now, we'll know that the G and K are both at the midpoint, they'll have to both be zero, right? And then we can just split the difference again. Zero and 1 over 400, 1 over 800.

[00:03:57]Pretty easy. Uh 1 over 400, 1 over 200, 3 over 800. Easy, right? Pretty simple.

[00:04:05]Just label the things and you're set.

[00:04:08]Pretty easy, right? Okay.

[00:04:10]Function H can be written in H of T equals A sine B times T plus C plus D.

[00:04:17]Find the value of the uh constants A, B, C, and D, right? Okay, well, it gives you the sine graph, which is pretty useful to know. And let's just go over really quickly. Let's just do a quick review. This is your amplitude. The thing that goes in what you multiply your sine by, right? Amplitude means the distance between your absolute value distance between your midpoint or I'm sorry, between your uh midline and your maximum. We know that's a distance of 2 mm. But so we say A equals 2.

[00:04:51]Right?

[00:04:52]>> [snorts] >> And so let's just since it's a sine graph, let's assume we're starting here.

[00:04:57]Okay? So A equals 2 sine and B is your uh That's your That's your horizontal dilation, right? And we know that the base period is 2 pi, right? For sine of X um your period will be 2 pi.

[00:05:18]But our period has now become 1 over 200.

[00:05:23]Right?

[00:05:25]So uh what did we do to 2 pi to get 1 over 200?

[00:05:31]Well, we multiplied it by some unknown value, which is X. So we can just say X Let's solve for X here. What is this unknown value?

[00:05:41]1 over 400 pi.

[00:05:43]Right?

[00:05:44]Well, that's not what B is though, cuz remember uh as Dr. S says, the the horizontal stuff is wrong in the head and does the opposite of what it's supposed to. So, we'll just take the reciprocal of it and do 400 pi over 1 equals B, right? So, we'll just do 400 pi. Pretty simple, right? Then T Well, T's basically your X in this situation. Your uh explanatory variable. So, you don't have to write anything for T. Just leave it as T. Um and then plus C. This is a horizontal translation. Now, if T if uh C was zero, then this zero then uh it would start at zero zero here. But, it doesn't. It starts at um Well, I guess it starts at a -1/800.

[00:06:36]We know that cuz that's the distance between here and here has to be the same difference here and here. So, we'll say that it shifted left 1/800, right? So, 1/800 shifted left. Easy.

[00:06:49]Um [snorts] now, we close this and then plus D. D is your vertical up and down. And D's literally just your midline. And our midline here is zero, so it'll be plus zero, right? So, we'll do A equals to B equals 400 pi, C equals 1/800, and D equals zero. Very very very easy stuff. Okay. Now, on interval uh Well, it tells you G Let's actually erase a lot of this stuff.

[00:07:21]Cuz this is all very much in the way.

[00:07:23]Please tell me you guys wrote that down cuz I'm not writing all that back again.

[00:07:27]Okay. Um so, G T1 T2. So, what, you know, T1 J's T2, right? On this interval, what is happening about H?

[00:07:38]Well, H is uh This is zero and this is -2, by the way.

[00:07:45]Those are the Y values. Well, from here to here, it's Well, it's not positive, so we can mark those two out. It's got to be one of these two, cuz it's negative, right?

[00:07:55]And is H increasing or decreasing? It's obviously decreasing, cuz it's negative, and it's going down. Easy, right?

[00:08:04]Now, we're asked to see I Describe the concavity of H and determine whether rate of change is increasing or decreasing.

[00:08:12]So, we'll say um on the interval T1 T2 H is Well, it's concave up, cuz it'll make that smiley face, right?

[00:08:33]is concave up and the rate of change of H is increasing.

[00:08:55]Very easy. That's all you have to write.

[00:08:56]It's like super, super, super simple stuff.

[00:08:59]So, um I hope you guys understood this, and um I'm going to go play Counter-Strike now. Um good luck on your exam, guys.