Question

How to study for the AP Calc AB test?!?!?! HELP OMG this is so panic-making...

Answer 1

Open book, read.

Answer 2

Open stuff; read stuff.

Answer 3

TT0TT any fast way to review?

Answer 4

I think your notes is the best thing to stick to when reviewing...
touching new resources can make u loose time

however u can practice new problems if you have already finished with your textbook and others....


just my general opinion...

Answer 5

Also, youtube is great :) in 10 minutes sometimes you can learn a whole unit!

Answer 6

That assumes you've already read the assigned sections of the book and need only a review. I sense you need more than that.

All I can suggest at this point is to pick out some practice problems, post them here one at a time, and ask questions to help yourself get started out solving those problems. Can you do that? Please at least try one problem now.

Answer 7

I'm doing a practice AP Calc AB test in class and it's KILLING ME SO UTTERLY...and my teacher says that it's for a grade, and I can't solve any of them all of the way through!!!!!!!!

Answer 8

Lucy, I truly sympathize, but where have you been? The time to start preparing for an exam is well before the test. Have you done problems similar to this practice AP test before? I hope so. If not, why not?

Answer 9

I haven't done problems like these...and it's because I had no idea they would be this hard...! I know the fundamental stuff in general and I have a high B in the class, yet I have no idea what to do~ TT0TT

Answer 10

So you've learned something truly valuable: Start early and judge how much time you're going to need to complete the more challenging questions.

Again, if you want help now, choose and post one question at a time, and do at least something, and share it, before asking for help. Congrats on your high B and your knowing the "fundamental stuff." Let's now put that knowledge to good use.

Answer 11

TToTT

Answer 12

uhm ok so how do you integrate a(t)=[4t-3]/[e^4t-3] ? It's part of a bigger word problem, and I feel that this is the first step but I don't know quite where to start...

Answer 13

hi ganeshie8 <3

Answer 14

I saw you doing hard differential equations and integration problems many weeks ago. Actually you know a lot and very good for AP test... just need more practice i feel...

Answer 15

Aw Ganesh baby <3 someone else doing hearts for you :3

Study, have people test you. Create questions and answer them to train your brain. Good luck.

Answer 16

more practice...ok~ will do! haha first i have to complete this AP test my teacher let us take home... it's due tomorrow and I have 5 question s left...the others I kind of made an educated guess on heetee~

Answer 17

\(\large \int \frac{4t-3}{e^{4t-3}}dt\)

Answer 18

like that ?

Answer 19

yeah!

Answer 20

and I'm having trouble with generally integrating e raised to any function...such as tanx...

Answer 21

okay, looks "integration by parts" is your weakness

Answer 22

Well there is no really fast way, you have to put in the time to prepare to the exam, there are no shortcuts to it unfortunately
It is like this for many high level courses.

Do you have a particular problem on what you're currently struggling with? We can help you with that @lucy4104

Answer 23

If you have a solution book, you can always do review sections of that and if you're not getting it the solution books usually show the steps. Also, sometimes teachers put up practice tests and put "last years test" and put very difficult questions on it at times even though it wasn't the actual test from the year prior, this is to scare students.

And your integral looks like a u sub + by parts.

Answer 24

In this case you'd need u=a substation meant to simplify the appearance of the integral, along with du=the differential of u.

Supposing you wanted to integrate:\[\int\limits_{}^{}e ^{\tan x}dx\] ... as stated, that'd be tough. However, supposing you let u=tan x and also have \[du=\sec ^{2}x dx\]
then the integration would be relatively easy:\[\int\limits_{}^{}e ^{\tan x}\sec ^{2}x*dx\]
This would be simplifiable to \[\int\limits_{}^{}e^u*du=e^u + C.\]

What would the last step be?

Answer 25

Again, Lucy, do as many actual problems from that practice exam as you can. Start with the easier ones so that you can build up confidence in y our ability to solve such problems.

Answer 26

@Miracrown uhm, integrating a(t)=[4t-3]/[e^4t-3], and in general integrating e raised to a function~ as well as this one other problem: A spherical balloon is being blown up. When its volum is 36(pi) cm^3, and increasing at the rate 20(pi) cm^2/sec, how fast is its diamete changing at that moment in cm/sec?

Answer 27

@mathmale wait hold on, Are you saying that I can put in another variable??????

Answer 28

That's a "related rates" problem. Share what you've done towards solving this problem. Someone will then give you feedback.

Answer 29

well, it's still x, but still...!

Answer 30

one problem at a time, finish with tanx first..

Answer 31

Yes, but you're introducing time by finding the derivative of x with respect to time. Thanks, @ganeshie8: sound advice.

Answer 32

ok e^tanx, then the 4t-3 thing, then the related rates

Answer 33

you cant integrate e^tanx using elementary methods

Answer 34

These will help:
https://apstudent.collegeboard.org/apcourse/ap-calculus-ab/exam-practice

http://www.elainetron.com/apcalc/apcalc.pdf

Answer 35

what mathmale cooked up is an easy problem :

\(\large \int e^{\tan x} \sec^2x dx\)

Answer 36

go thru it again quick

Answer 37

hmmm I know that e^x*dx rule but I'm still not quite sure what it's telling me to do...

Answer 38

would that come out as just e^tanx / [secx]?

Answer 39

Referring to your problem, is that e to the power of 4t, or to the power of 4t - 3?
@lucy4104

Answer 40

in your power, I'm asking you to what power is the e taken to
What is it's exponent?
Is it just 4t, or 4t - 3?
I can't tell through here is that -3 is part of the exponent, or just subtracting to the side?

Answer 41

\(\large a(t) = \frac{4t-3}{e^{4t-3}}\)

Answer 42

^^ @Miracrown

Answer 43

yesh, that thing ^^

Answer 44

we need to use "integration by parts"

Answer 45

Okay, so it is an exponent. Alright, so any ideas how we might approach this problem?

Answer 46

ue^tanx or the 4t-3 one?

Answer 47

srry diregrd that u in da front

Answer 48

So, we are going to have to use an integration technique here, do you remember what the two main techniques are?

Answer 49

Just the general integration techniques, there are two special ones...

Answer 50

One starts with a u

Answer 51

uhm...one is most likeyly going to be the (int sign) e^u du= e^u, and then the other is maybe...natural log?

Answer 52

Well that just shows what the integration of e^u is, what I was asking as in regards to integration techniques, not just specific to e.
The two I am referring to are u substitution, and integration by parts.
Do those sound familiar?

Answer 53

u substitution sounds familiar...integration by parts, not so much -_-""

Answer 54

Alright, well for this we will be using u substitution
Do you remember how it starts?

Answer 55

would u substute 4t-3 for u?

Answer 56

Very good, yes!

Answer 57

What would we do next?

Answer 58

Need help?

Answer 59

maybe...hehe...yeah

Answer 60

so integrating u/e^u

Answer 61

Ok, Well remember this is a u substitution
So we have to find du
How can we find du?

Answer 62

du is 4~

Answer 63

good

Answer 64

Well not just that We do replace the 4t - 3 with u
But notice that du = 4*dt
What does dt equal?

Answer 65

du/4

Answer 66

Right, so we replace dt with du/4 - And the 1/4 can be moved outside

Answer 67

so...put a 1/4 inside, and a 4 on the outside?

Answer 68

No just the 1/4 outside, we moved the 1/4 from the du, to the outside
Since we have (1/4)*du

Answer 69

oh, it just tags along?oh okay~ so the 1/4 in and 4 out is only if ur working with the raw problem, not using u?

Answer 70

The 1/4 is from replacing dt with du/4
The 1/4 is from replacing dt with du/4 outside

Answer 71

yeah, so it tags along with the du and then since its a constant, you can move that out...so the 1/4 in and 4 out is only if ur working with the raw problem, not using u...right...? idkidk

Answer 72

I'm not sure where you are getting there is a 4 from
There is just a 1/4, no 4

Answer 73

^^

Answer 74

Yes, you can move a constant out, which is what was done, we moved the 1/4 from du/4 outside

Answer 75

ok so now we have [1/4](int sign) u/e^u du...what next....?

Answer 76

What might we be able to do next to integrate this?

Answer 77

Take a guess, Is there a way we can move the e^u to the top?

Answer 78

yes, e^-u

Answer 79

There you go :) So we have this!