Calc AB aftermath





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Discus: SAT/ACT Tests and Test Preparation: May 2003 Archive: Calc AB aftermath
By Andy7733 (Andy7733) on Thursday, May 08, 2003 - 03:21 pm: Edit

despite the subject title, I didnt feel the AB test was that bad at all. The multiple choice was very doable, both calc and noncalc part. The free response were harder, and took up much, if not all the time.

subject matter: barely any limits, and no tricky arctrig functions. a good number of graph interpretation problems, though

By Pat57575 (Pat57575) on Thursday, May 08, 2003 - 03:32 pm: Edit

I feel the same way. The multiple choice wasn't much of a problem. The calc free response was harder, but still doable. However, I thought the no calc free response portion was very hard. On the coffee related rate problem I kept getting a negative answer for t when the container would be empty (think I set it up wrong). On the last one, did anyone else get 2/5 and 8/5 for m and k? (don't remember which was which)

By Soozievt (Soozievt) on Thursday, May 08, 2003 - 03:39 pm: Edit

Hi, I am a parent of a junior in HS and I want to thank you for your post as I have copied it for my daughter. I gather you took this exam today? Was today like a national date for Calculus AP? She is in Calculus at our high school but our school's courses are not referred to as AP but simply as Honors though they are like AP. Despite it not being officially an AP course, she will be taking this AP exam. I think she takes it next week and this may be a make up date cause if today was the testing date, she is away at All States for music.

I know last week, for the final exam for the course, the teacher gave them an AP test from a prior year and that was his final exam. She is very happy to have learned yesterday that she got a 5 so that is an A+ for school but she sure would like that for the AP test that counts for AP officially. The teacher gave them unlimited time for the test and she knows that will NOT be the case for the AP test that counts for the AP thing.

I think it is nice of you to share your thoughts of what the test was like. I will show her your feedback, thanks.
Susan

By Andrew123s (Andrew123s) on Thursday, May 08, 2003 - 03:43 pm: Edit

Your daughter will have a different test next week, so there might be different topics covered on the make-up version of the test. The APs have two administrations (same all across the country): one normal, and one make-up.

By Andy7733 (Andy7733) on Thursday, May 08, 2003 - 03:48 pm: Edit

true. however, the difficulty in tests should be comparable. probably the best advice would be to take time on the multiple choice, because they seemed to be easy points, and to work at a faster pace for the free response, which took up almost all of the allotted time.

By Sixerztres (Sixerztres) on Thursday, May 08, 2003 - 03:51 pm: Edit

m and k were 2 and 4

By Andy7733 (Andy7733) on Thursday, May 08, 2003 - 03:54 pm: Edit

i dunno. the last problem of the last free response was tricky, in that u had to take limits and derivatives. by taking derivatives, u got k/(2*(t+1)^(1/2). the derivative of mx+3 was just m. after substitution x=3, u got k/4=m, meaning that k=4m. through taking the limits, and substituting using k=4m, i came up with -1/5 and -4/5, i believe. maybe? hopefully..

By Bdk (Bdk) on Thursday, May 08, 2003 - 04:01 pm: Edit

I got 2/5 and 8/5 for m and k (not sure of order). For the coffee cylinder part B:

dh/sqrt(h) = -1/5 dt

integrate

2 sqrt(h) = -t/5 + c
sqrt(h) = -t/10 + c
h(t) = t^2/100 - c*t/5 + c^2

Solve for c based on initial conditions given (h = 17 at t = 0)

17 = c^2
c=sqrt(17)

h(t) = t^2/100 - sqrt(17)*t/5 + 17

Part c:
I got h to be 0 at t = 10 sqrt(17) using quadratic formula

By Bdk (Bdk) on Thursday, May 08, 2003 - 04:05 pm: Edit

Continuity ( at x = 3)
k * sqrt(x+1) = mx + 2
k * sqrt(4) = 3m + 2
2k = 3m + 2
k = (3m + 2)/2

Differentibility ( at x = 3 )
k/2(x+1)^(-1/2) = m
k/2(4)^(-1/2) = m
k/4 = m
k = 4m

(3m + 2)/2 = 4m
3m + 2 = 8m
5m = 2
m = 2/5

k = 4m
k = 8/5

By Pat57575 (Pat57575) on Thursday, May 08, 2003 - 04:09 pm: Edit

oh, that's relieving bdk. I got the same answers you did for m and k, and the same equation relating h and t on the coffee one. For some reason, on the one where it asked for the time when h=0, I got what you got for t, except negative...? Nonetheless, it's good to see some familiar numbers :)

By Pat57575 (Pat57575) on Thursday, May 08, 2003 - 04:13 pm: Edit

Did anyone find f(3) or f(4) (can't remember what it asked for) on the one where it gave you the graph of f'? I found f(-3) or f(-4) (again, can't remember which it asked for), but only had time to set up the process for the other one.

By J_Jay (J_Jay) on Thursday, May 08, 2003 - 04:36 pm: Edit

for the coffecup one...it was -5dh/radh..so wen u integrate t= -10radH
then u plug in 4 c and all and i believe the final answer was -10radH + 10rad17
so the coffe cup was empty wen H = 0..therefor its 10rad17.

By Quarky (Quarky) on Thursday, May 08, 2003 - 04:50 pm: Edit

I took BC, but many questions were the same. I also got 10sqrt(17).

On the piecewise functions with f(-3) and f(4) or whatever, I got f(-3) = 0.6, but got the other one wrong. I tried integrating some ugly function, but it was not integrable. All you had to do was find the area of the cemicricle and subtract it from the area under the rectangle (an imaginary one). Integral=area, you know. I think the right answer was 2Pi-8, but I was not the one who got it..

By Sixerztres (Sixerztres) on Thursday, May 08, 2003 - 05:36 pm: Edit

f(-3) was 9/2 i think.

By Bdk (Bdk) on Thursday, May 08, 2003 - 05:39 pm: Edit

For the semicircle/triangles derivative graph, I got f(-3) = 4.5 and f(4) -5 + pi

By Andy7733 (Andy7733) on Thursday, May 08, 2003 - 05:46 pm: Edit

agreed with both sixerztres and bdk

By Quarky (Quarky) on Thursday, May 08, 2003 - 05:54 pm: Edit

damn. I got 10.5 for f(-3), I think.

For the straight line, the slope was -1, so the equation was:

y = -2 - x (there was a point 0,-2 on the graph)

integrate to get f:

f = -2x - 1/2x^2 + C
and they gave us point (0,3)

so 3 = C

f = -2x - 1/2x^2 + 3

f(-3) = 6 - 4.5 + 3

WTF???????????????? I HATE MYSELF! What a huge piece of poop!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I remember that on my paper, I had 12 - 4.5 + 3... damn, such a silly mistake and cost me the point!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

By Heatwave345 (Heatwave345) on Thursday, May 08, 2003 - 05:58 pm: Edit

WAIT A MINUTE

did you have to do tangents for that question???

i just found the area under the graph, are we talking about something different?

By Quarky (Quarky) on Thursday, May 08, 2003 - 06:00 pm: Edit

no. all you do is find the equation of the straight-line derivative, integrate the equation to get the function, and find the value of the function. I AM SO PISSED OFF RIGHT NOW. I AM LOSING POINTS FOR NON-CALCULUS MISTAKES LIKE -3*-2 = 12!!!!!!!!!!!!!!!!!!!! WHAT THE HELL?

By Gammon (Gammon) on Thursday, May 08, 2003 - 06:30 pm: Edit

Ok, on the Calc AB free response:

For the question about the airplane fuel where it asked for a left Rieman sum, did you guys get 3700?

Also for one of the questions, the one with a piecewise function, where it asked for the average value over the range from 0 to 5, did you get 4/3?

And on the coffee problem, if I derived the wrong equation for h, will I still get at least one point for using it to get the numerical value?

By Aqt3144ever (Aqt3144ever) on Thursday, May 08, 2003 - 06:37 pm: Edit

yup...i got 3700 for that airplane fuel question =)

By Callmecollege (Callmecollege) on Thursday, May 08, 2003 - 07:46 pm: Edit

ab free-response

-was the particle in question 2's speed increasing or not? i put not b/c v(t) and a(t) had different signs
-was the function in number 6 (i think) continuous? I put yes
-what was the inflection pt in one of the middle questions?
-how did u do the integral for the 1st question, part c, the rectangle thing? i did pie, integral(5(top function-bottom function)^2
-what was the farthest distance away from the origin for part 2, i got 2 something I think...
-can somebody explain the differential eq in 5b?

By Callmecollege (Callmecollege) on Thursday, May 08, 2003 - 07:48 pm: Edit

oh yeah for the descriptions of the integrals in the airplane fuel question (part c i think--it was last part all i know) was the first integral just the amount of gasoline used at any time and the second one the average amount of gasoline used at any time? anyone?

By Noclass (Noclass) on Thursday, May 08, 2003 - 07:50 pm: Edit

The speed is increasing because acceleration is greater than 0. This means that the velocity increases and thus speed increases

By Useatoothbrush (Useatoothbrush) on Thursday, May 08, 2003 - 07:59 pm: Edit

No, you are incorrect. The velocity was increasing, but the asolutel value of the velocity--the speed--itselft was decreasing.

By Noclass (Noclass) on Thursday, May 08, 2003 - 07:59 pm: Edit

Does anyone remember the rectangle at 1c...
For that one question when it asked you like the greatest distance from the origin, did anyone get 2.something.

For one of the multiple choice questions, when it said to find a diff. equation when the volume is increasing proportional to the square root of the volume of the cylinder was that DV/DT=ksq.rootV

By Noclass (Noclass) on Thursday, May 08, 2003 - 08:01 pm: Edit

Does anyone want to discuss multiple choice questions.

By Jason817 (Jason817) on Thursday, May 08, 2003 - 08:08 pm: Edit

I found the test to be VERY HARD. The multiple choice was pretty easy, there were 4 or 5 I couldnt do. The free response was INSANE. I took the practice exams from 1999-2002 and this year, it was SO MUCH HARDER. I could hardly do any of them, if any.

By Noclass (Noclass) on Thursday, May 08, 2003 - 08:08 pm: Edit

bump,

By Noclass (Noclass) on Thursday, May 08, 2003 - 08:11 pm: Edit

lets discuss multiple choice!!!

By Callmecollege (Callmecollege) on Thursday, May 08, 2003 - 08:39 pm: Edit

was the derivative of the inverse function one towards the end of part b on the multiple choice 1/13? or what?

By Sixerztres (Sixerztres) on Thursday, May 08, 2003 - 08:41 pm: Edit

v(t) and a(t) were both positive and therefore the particle was speeding up since the velocity and acceleration vectors were in the same direction.

By Gammon (Gammon) on Thursday, May 08, 2003 - 08:54 pm: Edit

The answer to the multiple choice question about the inverse function was 1/4

The original function was y=x^3 + x

The inverse was x = y^3 + y

Solving for y isn't necessary. By implicit differentiation we get dy/dx = 1/(3y^2 + 1).
Since g(x) represents the inverse function, y corresponds with g(x) in the derivative function. Since g(2)=1 g'(2)=1/(3(1)^2 + 1) = 1/4

By Flippanda328 (Flippanda328) on Thursday, May 08, 2003 - 09:05 pm: Edit

Does anyone know approximately how many scaled points you need for a 5?

I aced the multiple choice, but I had horrible time allocation for free response section 2. I left the very last subpoint blank and didn't have time to finish subpoints b and c of the coffee problem.

By Pat57575 (Pat57575) on Thursday, May 08, 2003 - 09:15 pm: Edit

For the area between graphs and volumes problem, is this how you worked them?

a) A= int(f[x]-g[x])dx from the intersection point to 1, where f was the higher one and g was the lower

b) V= pi*int([1-g(x)]^2-[1-f(x)]^2)dx from the intersection point to 1, where f was the higher one and g was the lower

c) V= int(5[f(x)-g(x)]^2)dx from the intersection point to 1, where f was the higher one and g was the lower

By Adamg (Adamg) on Thursday, May 08, 2003 - 09:42 pm: Edit

MC Calculator Question: What did you guys get for that one where the function was like something to the t power and the integral from 0 to 1 was 2 find the intergral from 0 to 2?

By Stanfordhopeful (Stanfordhopeful) on Thursday, May 08, 2003 - 09:43 pm: Edit

Pat57575, thats exactly the way I worked it out.

Did you get 1.55 for part C?

By Pat57575 (Pat57575) on Thursday, May 08, 2003 - 10:03 pm: Edit

stanford, I'm glad to hear that. That number is ringing a bell, though I've forgotten a good portion of the test already :)

By Jason817 (Jason817) on Thursday, May 08, 2003 - 10:07 pm: Edit

what did you get for this question on the non-calculator MC. I couldnt do it:

d/dx [integral [(sin t^3) from 0 to x^2]]

By Andy7733 (Andy7733) on Thursday, May 08, 2003 - 10:18 pm: Edit

2xsinx^6, no? im pretty sure this is it, since it used the second fundamental theorum

By Fender1 (Fender1) on Thursday, May 08, 2003 - 10:29 pm: Edit

Fundamental theroem there.
Answer is 2xSin(x^6)

My take on the whole exam
Sec 1
Part A - Finished in 25 minutes. Breeze!
Part B - Finished in about 30-35 minutes. Little harder, left one blank.
Sec 2
Part A - Ok difficulty, got all of them done in time
Part B - Hardest section, barely got all of them done. Know I missed a few points though

Also, anyone remember this question:
For X > or equal to 0 on f(x), y=2 is a horizontal asymptote. Which of the following is true?
B) X does not = 2 for X> or equal to 0.
E) The limit as x approaches infinity of f(x)is 2.
What's everyone's take on that?

By Lt56boy (Lt56boy) on Thursday, May 08, 2003 - 10:35 pm: Edit

Fender--E is true, if you remember, when a function has a horizontal asymptote, it may cross that asymptote multiple times, but as the function approaches infinity, it will approach the value...B could be true, could be false, but E will always be true

By Reelcool (Reelcool) on Thursday, May 08, 2003 - 11:01 pm: Edit

hey, remember the second to last mult choice question? it was like #91 and the answer choices were like 2.822 and 2.555? it had something to do with ln I think but I dont remember the question at all... what did you get for that one? I got 2.555 but I dont remember how or why.

By Noclass (Noclass) on Thursday, May 08, 2003 - 11:23 pm: Edit

You guys know that there are TWO forms to the exam, right? The people on the west coast and alaska receive a different exam.

Do you remember the second calculator problem where they gave the areas of a,b,c each 2 and then you had to integrate f(x)+1. Was that 4?

Also, in the one where it asked you the temperature of the pie, was that 238?

And, in the free response, for that 3rd problem, how did you do R'(45) and R''(45)?

Also, was the speed increasing at t=2?

By Noclass (Noclass) on Thursday, May 08, 2003 - 11:25 pm: Edit

People! Please do your best to remember some multiple choice questions not mentioned earlier, PLEASE!

By Fender1 (Fender1) on Thursday, May 08, 2003 - 11:29 pm: Edit

Yeah, I eventually put E, but that one stumped me for a long time.

Noclass
1. Yes, I put 4, original area was -2 put 1 times 6 equals 4
2. I got 112 I believe. Integral of whatever the function was from 0 to 5 and take that away from 350.
3. R'(45) - I did R(50)-R(40) over 50-40 for an answer of 3/2.
R'' (45) - They said consumption was increasing the fastest at 45 therefore R'(45) is a max, therefore R'' (45) equals 0
4. No, the acceleration at t=2 was positive, BUT the velocity at 2 was negative therefore speed was decreasing.

By Noclass (Noclass) on Thursday, May 08, 2003 - 11:38 pm: Edit

I disagree on the increase question. As long as your acceleration is positive it means that speed increases!!!!

By Noclass (Noclass) on Thursday, May 08, 2003 - 11:44 pm: Edit

bump, answer the question please.

By Fender1 (Fender1) on Thursday, May 08, 2003 - 11:45 pm: Edit

Sorry to be blunt, but WRONG! "Speed" is a scalar quantity. Velocity and accelertion are vectors. With the negative velocity, you are moving "left" of the origin. A positive acceleration reflects that there is a force pushing the object to the "right", therefore, the velocity will INCREASE from negative to positive, but, assuming acceleration stays constant, the absolute value of the velocity, i.e. the speed, will DECREASE!
(beat that! seven commas in one sentence)

By Reelcool (Reelcool) on Friday, May 09, 2003 - 12:02 am: Edit

HEY! maybe I was too quiet before... WHAT DID YOU GUYS GET FOR #91 on MULT CHOICE!!!?!?! it contained the equation ln(1+2^t) I think...any help is appriciated. This one was the only one I wasnt sure on for mult choice...(thats not to say I didnt make stupid mistakes :) hehehe)

-reelcool

By Reelcool (Reelcool) on Friday, May 09, 2003 - 12:04 am: Edit

oh yea, and did anyone else get 4 a's in a row? I thought that was weird...

By Gammon (Gammon) on Friday, May 09, 2003 - 12:05 am: Edit

I didn't put E for the horizontal asymptote question because it specified only that y=2 was a horizontal asymptote for x > or = 0, but the limit was taken as x approaches infinity, but not specifically positive infinty. We don't know what the function was doing as x approached negative infinity.

But now that I think about it, E is probably the best answer given the other choices. I don't know.

By Ford (Ford) on Friday, May 09, 2003 - 12:07 am: Edit

I took the AP Calc and the AP Stat test together this yeah and i am about dead, i was worried about the stats test so much and it ended up being easier than the cal test. I Did soooo many frickin free response from previous years and NONE of them were as hard as the part B of today, i left the whole coffeepot problem blank (#5) did anybody else have a problem with this or was it just me?@!#@ thanks alot FORD P.S. breifly descibe #91 reel and ill help ya

By Gammon (Gammon) on Friday, May 09, 2003 - 12:10 am: Edit

Reelcool, I got 4 As in a row.

By Aqt3144ever (Aqt3144ever) on Friday, May 09, 2003 - 12:10 am: Edit

usually when they say infinity...it's positive...i think unless they say negative, they mean positive infinity...that's just my guess

By Fender1 (Fender1) on Friday, May 09, 2003 - 12:12 am: Edit

I remember starting off part b with 3 Cs and a few questions later, 4 As

By Reelcool (Reelcool) on Friday, May 09, 2003 - 01:59 am: Edit

yea, I got the same thing fender!! cool...
ok Ill try my best at rememebering 91.
I think it said that something intigral ln(1+2^t) at x=1 equals 2 then what is the value at x=2...I really dont remember the rules involved but I asked a friend and he said he used a tangent line aprox...I personally didnt do it that way and we ended up getting different answers ( I got 2.555 and he got 3.something). were just trying to settle a little dispute ;) hehe

By Reelcool (Reelcool) on Friday, May 09, 2003 - 02:01 am: Edit

oh yea, I didnt get any e's on part b of mult choice either...weird.

By Noclass (Noclass) on Friday, May 09, 2003 - 11:56 am: Edit

You guys remember that one multiple choice question where it gave you a value for f of -2 and f of 3 and asked you which one could be false about the value of c, I put that it may be false that f of c=0

Anyone else?

By Noclass (Noclass) on Friday, May 09, 2003 - 11:59 am: Edit

What were the questions that involved the 4 A s?

By Noclass (Noclass) on Friday, May 09, 2003 - 02:17 pm: Edit

bump guys c'mon.

By Pat57575 (Pat57575) on Friday, May 09, 2003 - 02:56 pm: Edit

noclass, the false one on that was that there had to be a point x at which f'(x) was 0. The equation was continuous so it had to cross the x-axis somewhere inbetween the points it gave.

By Noclass (Noclass) on Friday, May 09, 2003 - 02:58 pm: Edit

Anyone remember the last non-calc. multiple choice question number 28?

Was it 24, because the derivative between the three points would have to be consistent?

If you remember, let me know immediately!!

By Noclass (Noclass) on Friday, May 09, 2003 - 02:59 pm: Edit

Pat57575, that was choice B right?

By Noclass (Noclass) on Friday, May 09, 2003 - 03:18 pm: Edit

bump, someone answer my darn question. I am stressing out

By Brd (Brd) on Friday, May 09, 2003 - 03:28 pm: Edit

"bump, someone answer my darn question. I am stressing out"

Why? The test is over. You can't go back and change anything. Fretting and worrying right now will have no effect (save make you miserable). So calm down, relax, take a deep breath. Don't stress over what you can't change, it's just a waste.

By Noclass (Noclass) on Friday, May 09, 2003 - 03:31 pm: Edit

someone answer the question regarding question 28! Brd, instead of criticing my worrying, why don't you go to another website!

By Noclass (Noclass) on Friday, May 09, 2003 - 03:40 pm: Edit

bump

By Boo (Boo) on Friday, May 09, 2003 - 03:53 pm: Edit

No, I believe the answer was 27 because they were looking for where the second derivative was positive, and the first derivative must increase...I may have forgotten the question.

By Brd (Brd) on Friday, May 09, 2003 - 04:12 pm: Edit

Noclass: I wasn't criticizing; I was trying to give you some valuable life advice. Spending your time worrying about things you have no control over will not make you happy, though some day it might give you an ulcer or hypertension, if that's what you want.

By Noclass (Noclass) on Friday, May 09, 2003 - 05:09 pm: Edit

Enough said Brd!
Can somebody PLEASE tell me the answer to number 28? Was it 24?

By Noclass (Noclass) on Friday, May 09, 2003 - 05:53 pm: Edit

bump

By Boo (Boo) on Friday, May 09, 2003 - 05:57 pm: Edit

I did, see above

By Thehof (Thehof) on Friday, May 09, 2003 - 06:14 pm: Edit

How many points do u need to get a 5?

By Noclass (Noclass) on Friday, May 09, 2003 - 07:01 pm: Edit

Answer is 24. Derivative must remain consistent from one point to the next. Anyone else got 24 for the last non-calc. mc question number 28?

By Pat57575 (Pat57575) on Friday, May 09, 2003 - 07:39 pm: Edit

The one with the charts was E (27)... I'm positive. f, f', and f" all had to be positive. For f" to be always positive, the average slope between the points must continue to increase. I solved the equation and ended up getting y > 24. 27 is the only answer the would work.

Brd meant no wrong noclass; his information is valuable. Nonetheless, it's quite understandable to feel anxious and tense after a big test.

By Adamg (Adamg) on Friday, May 09, 2003 - 07:45 pm: Edit

According to the Cliffs AP prep book you need 65. I think it is more like 70-75. But 65 could be correct.

How you get your score
(MC Correct - 0.25*MC Incorrect)*1.2 + FR Points

By Fender1 (Fender1) on Friday, May 09, 2003 - 07:50 pm: Edit

what was the question for 28?

By Gammon (Gammon) on Friday, May 09, 2003 - 09:33 pm: Edit

The question was something like, for a function f, f, f', and f'' are positive, if f(4) = 12 and f(5) = 18, what is a possible value of f(6)?

A. 12 B. 18 C. 21 D. 24 E. 27

The numbers may be off a bit, but I'm sure that 27 is correct. Since f' is positive, f must be increasing so A and B are out. Since f'' is positive f' must be increasing. By the mean value theorem, there must be a value c on [4,5] such that f'(c) = (f(5)-f(4))/(5-4) = 6. Using this for the rest of the answers, we can see that c only guarantees a slope of 3, D only guarantees a slope of 6. E is the only one for which f' and f'' are positive.

By Noclass (Noclass) on Friday, May 09, 2003 - 10:29 pm: Edit

What did you guys get for that one question in the Part A mc that said to give a differential equation that the volume of the cylinder is proportional to the square root of the cylinder was that dv/dt=ksq.V ?

By Noclass (Noclass) on Friday, May 09, 2003 - 10:33 pm: Edit

bump

By Noclass (Noclass) on Friday, May 09, 2003 - 10:48 pm: Edit

bump, was it what I stated above?

By Fender1 (Fender1) on Friday, May 09, 2003 - 11:01 pm: Edit

Thanks gammon, now i remember that one. Yeah, definetely 27.

BTW, Noclass, there is no need to bump the thread four minutes after the last post. That just creates unnecessary posts. Have some patience, it will do you good later in life.

By Noclass (Noclass) on Friday, May 09, 2003 - 11:09 pm: Edit

Hey, fender.

Was that one mc question proportional to the cylinder differential equation dv/dt=krad.V

By Noclass (Noclass) on Friday, May 09, 2003 - 11:24 pm: Edit

bump, someone answer.

By Noclass (Noclass) on Friday, May 09, 2003 - 11:29 pm: Edit

Someone please try to remember mc and free response questions. Lets discuss the answers so we can help ease the tension!

By Noclass (Noclass) on Friday, May 09, 2003 - 11:36 pm: Edit

I have to bump because the damn history kids are posting too many damn messages.

C'mon let's talk calculus.

By Noclass (Noclass) on Friday, May 09, 2003 - 11:59 pm: Edit

bump

By Stanfordhopeful (Stanfordhopeful) on Saturday, May 10, 2003 - 12:07 am: Edit

Noclass, that was the correct answer.

By Brd (Brd) on Saturday, May 10, 2003 - 12:34 am: Edit

If you really want to ease the tension, you should go running in the park. Or go watch a movie. Or read book. Listen to or play some music. Paint. Cook. All of the above. I'm not joking.

By Noclass (Noclass) on Saturday, May 10, 2003 - 12:36 am: Edit

Thanks Stanford.. hey, do you remember in the airplane question when it asked to evaluate the meaning of the integral, I just said that it expressed the total amount of jet fuel and that the average value expressed the mean amount.

Can you remember the coffee pot question, I got
y= ((-1/5x+17)/2)^2

For part c I got 10rad17 Familiar?

By Noclass (Noclass) on Saturday, May 10, 2003 - 12:39 am: Edit

Remember the MC question that gave you two points and asked which of the following could be false, was that f(c)=0?

By Noclass (Noclass) on Saturday, May 10, 2003 - 12:52 am: Edit

bump, stanford or fender help out.

By Stanfordhopeful (Stanfordhopeful) on Saturday, May 10, 2003 - 01:03 am: Edit

I took the BC test, so I didn't get the airplane question. And the answer to part C of the coffeepot is indeed 10sqroot17.

I don't remember the other MC question...

By Noclass (Noclass) on Saturday, May 10, 2003 - 01:08 am: Edit

But you do remember the one mc that asked you for a diff. equation relating the proportional change of the square root of the volume of a cylinder?

By Noclass (Noclass) on Saturday, May 10, 2003 - 01:13 am: Edit

bump

By Reelcool (Reelcool) on Saturday, May 10, 2003 - 02:14 am: Edit

was the test for the west coast different than the one for the east coast? or the same? someone said different but you guys all sound like your talking about the same thing

By Leia (Leia) on Saturday, May 10, 2003 - 02:30 am: Edit

The last or second to last multiple choice(calculator part)..the one where you had to take the integral of a natural log...how were you supposed to do that?


You say yes, I say no...

By Noclass (Noclass) on Saturday, May 10, 2003 - 03:01 am: Edit

Can someone please comment on the cylinder problem I asked about?

By Noclass (Noclass) on Saturday, May 10, 2003 - 03:06 am: Edit

bump, plz help

By Jason817 (Jason817) on Saturday, May 10, 2003 - 03:08 am: Edit

Noclass: no idea on the cylinder problem.

Leia: Do you mean the integral of ln(1+2^x)?? My ti-89 couldn't do that so I had to use Integration By Parts.

By Leia (Leia) on Saturday, May 10, 2003 - 04:18 am: Edit

Yes, Jason, how did you do that? My Calculus teacher claimed that they didn't test on the integrals of natural logs anymore, and therefore didn't teach us how to do it. *sigh*

By Fender1 (Fender1) on Saturday, May 10, 2003 - 02:36 pm: Edit

wow, your calc teacher is sadly misinformed

By Noclass (Noclass) on Saturday, May 10, 2003 - 03:21 pm: Edit

Fender, was that proportional cylinder problem
dv/dt=k sqrt.V ?

By Noclass (Noclass) on Saturday, May 10, 2003 - 03:23 pm: Edit

bump

By Noclass (Noclass) on Saturday, May 10, 2003 - 03:29 pm: Edit

bump it up.

By Boo (Boo) on Saturday, May 10, 2003 - 03:33 pm: Edit

Your TI-89 can do that natural log, but you have to do it using approx mode with bounds...hehe

By Useatoothbrush (Useatoothbrush) on Saturday, May 10, 2003 - 03:46 pm: Edit

To integrate the natual log function you just use numeric integration, you symbolic 89 dependent whores :-P

By Boo (Boo) on Saturday, May 10, 2003 - 04:00 pm: Edit

Why would you do numeric integration?...that would be a pain in the arse to do when you could just plug it...I love my calculator

Even graphing it and taking the integral on the graph screen is more efficient :)

By Brd (Brd) on Saturday, May 10, 2003 - 06:29 pm: Edit

Hrm. The integral of ln(1+2^x) cannot be expressed in terms of elementary functions (FWIW it's antiderivative involves a function called PolyLog which is defined by an infinite series). I assume the question was really about the integral of ln(1+x^2), which can be integrated by parts fairly easily, as Jason mentioned. Just take u=ln(1+x^2) and dv=1 dx, and you will get -2x + 2 ArcTan(x) + x*ln(1 + x^2) (evaulated on the boundary, of course).

By Leia (Leia) on Saturday, May 10, 2003 - 11:30 pm: Edit

Duh! Duh!! *bonks head on keyboard* Brd! Thank you! Argghh. *bonks herself on the head with mouse* Now i'm mad at myself {sg}... (and i don't have an 89...i think to do the problem for me, i would've had to get the area under the curve of a specific interval and add it to the whole interval specified in the problem..but since my brain was completely fried...i just left it blank)..thanks Brd.


I hope i never have to look at another Calculus problem again. Ever. {sg}

By Reelcool (Reelcool) on Saturday, May 10, 2003 - 11:42 pm: Edit

uhh no, the question said 2^x, its in my calc still...and why would they have intigration by parts on the ab test? I thought that was only covered in the calc bc class?

By Noclass (Noclass) on Sunday, May 11, 2003 - 02:44 am: Edit

For the answer to that problem, I got 3.something

Hey, do you remember a question in the mc where it asked you to find which could be false between the two points, was that f(c)=0?

You guys know the answers to the free response are going to be posted on Monday on mr.calculus' website. I forgot the url, so just type in "mr.calculus" in a search engine.

But... before you do that answer my question plz!

By Boo (Boo) on Sunday, May 11, 2003 - 09:36 am: Edit

It was 2^x, and I believe they just wanted you to graph it and take the area under the curve on the graph screen - 83s and 89s can do this. (Some questions are there to check your calc skillzorz - or actually, some just require a calc)

By Boo (Boo) on Sunday, May 11, 2003 - 09:38 am: Edit

no, it was f'(c) = 0

The function had a range between a negative and a positive number, so it would have to cross the x axis and be 0.

By Noclass (Noclass) on Sunday, May 11, 2003 - 01:05 pm: Edit

Was that choice B? Maybe I am just not remembering the question.. But there was only one answer choice that involved a "0" statement so I guess that's the one I picked.

Let me know if it was choice B.
Also, remember if there was a question with three graphs that involved the limits and you had to pick with graphs had equal limits or something.. What did you put?

By Noclass (Noclass) on Sunday, May 11, 2003 - 02:39 pm: Edit

bump

By Callmecollege (Callmecollege) on Sunday, May 11, 2003 - 06:03 pm: Edit

on the free response, that one function was continuous right? also, the one where they asked for the x value of the inflection pts, was there only one value? also, were there any problems when you needed to check the endpts, cause i didnt do that on the free-response? thanx

By Noclass (Noclass) on Sunday, May 11, 2003 - 06:59 pm: Edit

Hi. Yeah you are correct on all those.
Can you answer my question about the two multiple choice questions plz. The one with whether or not f'(c)=0 being choice B AND the one that gave you three graphs on limits and asked which graphs had limits or something....
What were those two?
Let me know as soon as possible!!

By Noclass (Noclass) on Sunday, May 11, 2003 - 07:06 pm: Edit

For the coffee problem btw... the answer to diff. problem was ((-1/5x+2rad17)/2)^2)

On the airplane question, the third one, the left approx. was less than the actual.
What did you guys put down for the two meanings of the integral and the average value?
Do you guys remember step by step what the m and k value one asked for?

By Boo (Boo) on Sunday, May 11, 2003 - 07:25 pm: Edit

The m and k one had a set of two functions, and you had to solve for m and k that would make the function set continuous and differentiable at some point. You would then solve for m or k by setting the derivatives of each equal to each other, or solve for the other variable by setting the functions equal to each other, plug in the point for x, and then do some substitution. The answers were 2/5 and 8/5, I believe.

I don't remember if f'(c) = 0 was choice B, but I know your answer was there, so you could have chosen f(c) = 0.

I don't remember the airplane question...what was that one again?

By Callmecollege (Callmecollege) on Sunday, May 11, 2003 - 07:47 pm: Edit

i put for the airplane ones (not sure if they are right)
1.) amount of gasoline that has been consumed at any time t (gallons)
2.) average value of gasoline that has been consumed at any time t (gallons)

not exactly what i put, but do these look ok?

By Gammon (Gammon) on Sunday, May 11, 2003 - 08:21 pm: Edit

"the one where they asked for the x value of the inflection pts, was there only one value?"

No, there were two inflection points. One at the corner and one at the top of the circle. The corner would have a second dervative undefined and since f'(x) was decreasing before that and increasing after, f(x) changes concavity. f''(x) at the top of the circle is zero with a similar increasing/decreasing change i.e. a change in concavity.

By Callmecollege (Callmecollege) on Tuesday, May 13, 2003 - 12:54 am: Edit

i thought derivatives (in this case 2nd derivatives) don't occur at corners (cusp's), somebody please tell me i'm right

By Quarky (Quarky) on Tuesday, May 13, 2003 - 01:03 am: Edit

They don't occur in such places, that's why they are extreme points, where maxima, minima, or inflection points may be located, depending on the derivative.

By Brd (Brd) on Tuesday, May 13, 2003 - 01:12 am: Edit

Neither of of those cases sounds like an inflection point. As MathWorld notes, a inflection point is a point where the concavity changes sign, but also a point that is neither a local maxima nor local minima.

Note also that concavity and convexity are concepts defined independently of any notion of a derivative. Having second derivatives exist provides a convenient way to determine concavity in an interval, but a function can be concave or convex in an interval even if these derivatives don't exist.

By Reelcool (Reelcool) on Tuesday, May 13, 2003 - 01:50 am: Edit

yea but this is the graph of the derivative...

By Qwerasdf (Qwerasdf) on Tuesday, May 13, 2003 - 02:11 am: Edit

AB < BC

By Quarky (Quarky) on Tuesday, May 13, 2003 - 08:29 am: Edit

Brd

On that problem, they provide you with a graph of f', the derivative. The function is not given. f' is undifferentiable at x=0, where a straight line changes into a semicircle. The only place on the graph of f' where its slope is 0 is at x=2, so f'' at x=2 must be 0, so x=2 and x=0 are extrema. Furthrermore, the slope of f' changes from positive to negative and vice versa before and after each of those points, proving that conacavity of f changes. Thus, both pts are inflection pts.

By Noclass (Noclass) on Wednesday, May 14, 2003 - 03:35 pm: Edit

Does anyone here remember the answer choices to that damn problem that gave you two points and asked which statement could be false. I KNOW the answer was f'(c)=0, but what were the choices?

Someone remember ahhhh!!!!!

By Drew (Drew) on Wednesday, May 14, 2003 - 04:56 pm: Edit

Yes, Noclass, that was choice B. I am sure...

By Noclass (Noclass) on Wednesday, May 14, 2003 - 07:32 pm: Edit

Does anyone here remember the answer choices because I am completely lost.

I remember one was the mean value theorem
One was like the one I stated above
Another was that there had to be a max....

BUT WHAT WERE THE OTHERS??!!!

By Noclass (Noclass) on Wednesday, May 14, 2003 - 07:42 pm: Edit

Okay guys help me out here.

Does anyone here remember there was a question in the first mc that gave you three graphs AND I believe the question asked you like which graph represents continuity?

The graphs were all limit graphs, the first one was a removable discontinuity, the second graph was a jump, and the third was an absolute discontinuity!!!

I put the one with the removable as my answer, is that right??
PLEASE REMEMBER!!!

By Drew (Drew) on Wednesday, May 14, 2003 - 08:27 pm: Edit

There was

a. f(c) = 0 on [-2, 1] (it did because f(-1)=-4 & f(2) = 5)

b. f'(x) = 0 on [-2, 1] (right answer)

c. f'(c) = 3 (it does, MVT)

d. there exists an f(c) such that f(c) = 2 (it does, interval thing again)

e. there exists an f(c) on f such that f(c) > or = f(x)

By Drew (Drew) on Wednesday, May 14, 2003 - 08:29 pm: Edit

Noclass-

I'm pretty sure None was answer choice A. on that problem, wasn't it?

By Noclass (Noclass) on Wednesday, May 14, 2003 - 09:14 pm: Edit

No, there wasn't an answer choice like that!!!
I was looking for none but it wasn't there!!

Maybe I am just misphrasing the question. Do you remember what you put?
I put graph 1 the one with the removable discontinuity.

By Flippanda328 (Flippanda328) on Wednesday, May 14, 2003 - 09:33 pm: Edit

How do you calculate your score, and what is the cutoff for a 5?

By Pat57575 (Pat57575) on Wednesday, May 14, 2003 - 09:53 pm: Edit

If I recall correctly, there were 45 MC questions. If that's the case, then you can find your score like this:

([# correct on MC]-[.25*#incorrect on MC])*(54/45) + number of points from free response

On the free response, each question is worth up to 9 points, and there were 6 questions, so I guess you'll have to estimate those scores.

Though the curve changes frequently, it's safe to assume that the cutoff for a 5 is about a 75/108.

By Noclass (Noclass) on Wednesday, May 14, 2003 - 10:13 pm: Edit

Hey pat or someone else, do you remember that problem in Part A mc that dealt with the three graphs and asked which graph represents continuity?

Was it the one with the removable discontinuity.
I was looking for "none" but it wasn't there!!

By Noclass (Noclass) on Wednesday, May 14, 2003 - 10:58 pm: Edit

bump

By Callmecollege (Callmecollege) on Thursday, May 15, 2003 - 12:47 am: Edit

i vaguely remember a question with graphs asking SOMETHING about continuity, and i think i remember getting the answer quite easily b/c i dont remember struggling with it, but for some reason i dont thing it was a removable discontinuity

By Fender1 (Fender1) on Thursday, May 15, 2003 - 05:17 pm: Edit

wasn't one of the graphs of like absolute value X?
That would be the correct choice because absolute value x is continuous (it is not, however differentiable at a certian point)

By Callmecollege (Callmecollege) on Thursday, May 15, 2003 - 05:48 pm: Edit

oh yea! i remember the answer being something like that!

By Noclass (Noclass) on Thursday, May 15, 2003 - 06:16 pm: Edit

Well, what the hell was the answer?

Was it graph1, the one with the removable discontinuity?

By Pat57575 (Pat57575) on Thursday, May 15, 2003 - 06:22 pm: Edit

yeah, I also have a vague memory of that question (continuity). I think there was one graph with a sharp peak that resembled an absolute value graph, but with no other abberations. I think that's what I chose.

By Noclass (Noclass) on Thursday, May 15, 2003 - 10:45 pm: Edit

HEY!!

Does anyone remember an answer like (0,2cuberoot)
for one of the mc questions in Part A that asked you where the function was increasing?!!!

Also, the three graphs... none of them were absolute values. They all had discontinuities which is why I was confused. I picked graph 1 because the discontinuity was removable therefore you could make it continuous. The 2nd graph had a jump and the third an essential!!!

Please brainstorm, and try to enlighten me on those two questions!!!!!!

By Noclass (Noclass) on Friday, May 16, 2003 - 02:05 pm: Edit

bump

By Noclass (Noclass) on Friday, May 16, 2003 - 06:49 pm: Edit

guys c'mon, answer my questions!!!!!!

By Noclass (Noclass) on Friday, May 16, 2003 - 07:01 pm: Edit

Guys on that question with the graphs, I need your assistance on helping figuring out what the hell the right answer is!!!
Now, there were three graphs and if had a discontinuity, I am not sure of the exact question wording...but I DO know it concerned limits and/or continuity!!!!

On that question which was a mc diff. equation, was it dv/dt=k sqrt.V ?!!

Also, was that increasing question in the mc,
like y=3x-2/x or something like that...
was that (0, cube root 2)??!!!

By Callmecollege (Callmecollege) on Friday, May 16, 2003 - 10:03 pm: Edit

i dont remember the graph question well but i do remember not encountering something that made me think TOO hard on section a of the mc, i seriously doubt it was a removable discontinuity

By Fender1 (Fender1) on Friday, May 16, 2003 - 10:17 pm: Edit

there had to be more than 3 graphs because you have 5 choices. I'm telling, one was an absolute value (or V-graph) and that was the correct choice.

By Noclass (Noclass) on Friday, May 16, 2003 - 10:25 pm: Edit

Moving on...

Do you remember the differential mc that I asked about?

Also, do you remember if you got (0, 2 cube root) for one of those interval increasing problems??!!

One final question, I believe I got 2.265 for part D of question 2 in the FR.
I don't remember how I did it, could you provide a brief explanation of how you would go about doing it by antidifferentiation??!!

By Noclass (Noclass) on Friday, May 16, 2003 - 11:35 pm: Edit

bump

By Drew (Drew) on Saturday, May 17, 2003 - 05:05 pm: Edit

Noclass-

What you had to do on #2 FR was find when the magnitude of the integral of velocity was the greatest, or f'(fnInt(v(t)) on [0,3]. That means that the critical points would be the same as they were in the previous problem when it asked when the particle changed direction, or CP: 0, 2.306 (rad2pi), 3. You then would evaluate the integral of v(t) with 0 as the lower limit and each critical point as the upper limit, and whichever critical point produces the greatest magnitude integral will give you the particle's farthest displacement from the x-axis.

By Noclass (Noclass) on Saturday, May 17, 2003 - 05:18 pm: Edit

hey drew!!!

do you remember the mc questions I asked about above?

If you do remember, please let me know!!!!!

By Drew (Drew) on Saturday, May 17, 2003 - 06:53 pm: Edit

Give me more info about the differential mc, but yeah, the (0, cube root of 2) answer is correct.

By Noclass (Noclass) on Saturday, May 17, 2003 - 09:51 pm: Edit

okay... in the diff. question, the problem asked to give a diff. equation for when the volume changes proportionally to the square root of the volume of the cylinder!!!

Was it dv/dt=k*sqrt.V

By Noclass (Noclass) on Saturday, May 17, 2003 - 10:33 pm: Edit

bump.

My other question concerns those three graphs in the non calculator mc. Remember those three graphs that dealt something with continuity and/or limits? Was it the first graph with the removable discontinuity only?

Nobody seems to remember this question.
Do you remember Drew?

By Noclass (Noclass) on Sunday, May 18, 2003 - 02:42 am: Edit

for god's sake, someone answer my questions PLEASE!!!!!!

By Drew (Drew) on Sunday, May 18, 2003 - 11:12 am: Edit

Yes, the answer is dv/dt = kradV. It is direct variation, so that means k is multiplied by radV, and not in the denominator as it is in choice E. Since it is rates, it has to be dv/dt, which ruled out choices A. and B. which had V =, and since it states the square root, that ruled out answer choice D, which just stated dv/dt = kV.

Yeah, and I can't help you with the other question, I don't remember it...I could have sworn though that "None" was an answer choice to one of the graph problems.

By Noclass (Noclass) on Sunday, May 18, 2003 - 11:44 am: Edit

Yeah, I know the answer must have been none, but the question had no choice listed as none. So the answer had to be one that wasn't none.

The question may have been in the calc. mc, but I am fairly sure it was in the non-calc. mc..

So I need you to remember that question, I can't quite remember... the question may have dealt with limits..
Try to remember then let me know!!!!!

By Noclass (Noclass) on Sunday, May 18, 2003 - 11:47 am: Edit

Try to remember some questions from the calculator mc!!!

By Noclass (Noclass) on Sunday, May 18, 2003 - 02:53 pm: Edit

bump

By Noclass (Noclass) on Sunday, May 18, 2003 - 09:03 pm: Edit

C'mon now people.

Drew, I hope you can remember that mc question with the limits.... what was it I only or I and II only???!!! thnx.

By Noclass (Noclass) on Monday, May 19, 2003 - 04:38 pm: Edit

bump

By Pat57575 (Pat57575) on Monday, May 19, 2003 - 06:57 pm: Edit

noclass, it's probably about time to move on! What's done is done!

By Noclass (Noclass) on Monday, May 19, 2003 - 08:30 pm: Edit

Just answer the question!!!!!!

Try to remember questions!!!!!

By Quarky (Quarky) on Monday, May 19, 2003 - 09:21 pm: Edit

Noclass, you really need to chill. How can you let a few questions bother you to such an extent? This is just a test nobody will care about in a few years. One-two questions doesn't make a difference anyway, so who cares? Be patient and wait a bit over month to get your scores.

By Noclass (Noclass) on Monday, May 19, 2003 - 10:55 pm: Edit

Guys, does anyone here remember the limit graph?


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