Sixthsense

wow for number two part b i assumed the intervals were all of one, so i did the b-a/2n instead of doing it the way u did MathProf. Do you think I will still receive any credit?

Sixthsense

btw what did u guys get for number 4?

TheMathProf

My guess is that if you did the average value, you'd probably get one, maybe two points. I suspect that there are three points on this question: one for doing the trapezoidal rule, one for the average value, and one for the solution. Assuming that point distribution, it's the first point that I'm not sure about whether you can earn it or not without the different subinterval widths (I would be inclined to say yes.)

An0maly

Pretty sure you would not get the points if you did the b-a/n method.

seanbow

For 2(d), was the answer really as simple as http://img509.imageshack.us/img509/8297/apcalc2ddg6.jpg, or 973 tickets? That seemed way too easy for a part d question but I couldn't think of any more complicated way to do it.

Also, I wish we could embed images.

WantIvy

4a. t=3, position = -10
4b. 3 times
4c. Speed is decreasing. V<0, but increasing. speed = |V|, so speed decreases.
4d. acceleration is negative when velocity is decreasing, so 0<x<1 or 1.5, idr, and 4<x<6

Sixthsense

ya thats all i wrote for 2d as well. i was surprised as well when i was doing it during the actual test.

TheMathProf

seanbow, it seems that way to me.

Sixthsense, I have this for #4:

(a)
x(0) = -2
x(3) = -2 + integral (0,3) v(t) dt = -10
x(5) = -10 + integral (3,5) v(t) dt = -7
x(6) = -7 + integral (5,6) v(t) dt = -9
The particle is furthest left at time 3. Its position is x = -10.

(b) 3 times, by the Intermediate Value Theorem.

(c) v is negative and increasing. Since v is increasing, the acceleration is positive. Since v<0 and a>0, the speed is decreasing.

(d) Acceleration is negative when v is decreasing, which occurs on [0,1] and [4,6].

An0maly

^ Yep my answers as well.

AKittka

what was the integral for the question with the oil thing.. i think i put - 2000 instead of + 2000.. will i get any credit?

Sixthsense

TheMathProf, based on the free response questions and what you have heard regarding the multiple choice what do you think will be the approximate scale/curve(neccesary raw score) for a 5?

TheMathProf

For 3c, I had V = 60000 + integral(0,25) (2000 - R(t)) dt.

I've been having trouble with the points allocation for this question, but I'm guessing that there are three points: one for the limits, one for the integrand, and one for the rest of the equation. I have no idea if that's accurate at all, because the limits point seems to double reward you for finding 25 from part (b), but I'm not sure where else to put the 9th point. Maybe it's 2 points for dV/dt in part (a); I only have it as one currently.

seanbow

My answers:

1(a) -> 4

(b) -> integral from .53918 to 1.6751 of (-2 - (x^3 - 4x))

(c) -> integral from 0 to 2 of [(sin(pi x) - (x^3-4x))^2] = 9.978

(d) -> integral from 0 to 2 of [(3-x)(sin(pi x) - (x^3 - 4x))] = 8.370



2(a) -> 8

(b) -> 155.25

(c) -> 3

(d) -> 973



3(a) -> .038

(b) -> t=25

(c) -> integral from 0 to 25 of (2000-400sqrt(t)) + 60000



4(a) -> (3,-10)

(b) -> 3

(c) -> decreasing

(d) -> [0,1] and [4,6]



5:

(a) -> slope field!

(b) -> -e^((x-2)/2x) (I forgot the +1. Bleh.)

(c) -> -e^(1/2) (Again forgot the +1...)



6:

(a) -> 3 e^(-2) - x e^(-4)

(b) -> x = e

(c) -> x = e^(3/2)

(d) -> negative infinity

TheMathProf

I don't have a good guess with regards to cut scores. I gave a tongue-in-cheek 70+ as an answer on another thread, and it seems as good a guess as any, but I don't really have any special info there.

An0maly

The free response were not difficult; they were simply "different" from what has been standard on the past, although very slightly. In my opinion, to get a 5 it will remain at like 70-72, because I'm pretty sure the nation didn't do THAT bad that they would drop it to like 66 again.