<p>Hi, I'm very bored, so I've decided to encourage some friendly competition in College Confidential and review for the AP Calculus AB exam at the same time! (Sorry, I don't know any BC material :/) Every week I will produce one of these tests, on Monday to be exact, and they must be sent back to me by the end of Thursday (which would be 23:59 EST). Then, by Sunday night at 22:00 EST, I'll have the results and commentary posted. If anyone sees any discrepancies in the scoring or solutions, please notify me ASAP. I will then post a cumulative leaderboard, complete with AP score cutoffs and galore. More on that later.</p>
<p>This is just a practice round so that you understand the geist of the format of my tests. There will be one released every week, and you will have until Thursday to send the responses to me via private message. If you post them directly in this topic, I will disqualify you, or as the AP people put it, cancel your score. Please don't, it defeats the purpose.</p>
<p>Alrighty, so here's how all this will work. I'd recommend that you don't use calculator when taking these practice exams. In fact, I highly discourage calculator use. In fact, none of these require a calculator at all. If you don't use a calculator, you'll be strengthening your algebraic and computational skills. These tests will consist of 10 multiple choice questions and will be scaled as 50% of the practice exam, and will be graded like the AP exam will be. Then, there will be 3 free response questions, which will also be scaled as 50% and graded on the 9 point scale. Calculator use is discouraged on either part. I say if you can get questions right without a calculator, then the calculator active part should be a breeze.</p>
<p>Also, if anyone here can make good calculus questions for these tests, they will be put in consideration as well.</p>
<p>Without furtherado, here is the test for the week of March 26th. I am aware that this test doesn't really match the actual difficulty of the actual exam (for now anyway), but I just wrote these up in about 20 minutes just for the heck of it. A good amount of people are still learning material anyway, so this should serve as a decent review. As soon as I figure out how to integrate symbols into these tests or I find somewhere else to host them so I can, there won't be notations involved. So just hit it.</p>
<p>Section 1: Multiple Choice -Send me only the letter of the correct answer. No work is needed. If you need clarification of a question's syntax, you may ask.</p>
<p>1) What is the limit as x approaches 3 of (x-3)/(x^3 - 6x^2 - x + 30)?
a) -1/10
b) 0
c) 3
d) -1/5
e) DNE</p>
<p>2) Find the derivitive of the following: sin(6-2x)
a) 1-2cos^[size=-2]2<a href="6-2x">/size</a>
b) -2sin(6-2x)
c) cos(6-2x)
d) 2(2sin^[size=-2]2<a href="3-x">/size</a> - 1)
e) None of the above</p>
<p>3) Find the integral of 1/(4x-1).
a) (1/4)ln(absval(x)) + C
b) 4ln(absval(4x-1)) + C
c) (1/4)ln(absval(4x-1)) + C
d) ln(4x-1) + C
e) (1/(4x))ln(absval(4x-1)) + C</p>
<p>4) What are the x-values of the closest points to (0,2) on the graph of y= 4 - x^2?
a) 3/2
b) 0, sqrt(3/2), -sqrt(3/2)
c) 0
d) sqrt(3/2), - sqrt(3/2)
e) 4, 5/2</p>
<p>5) What is the maximum value of the slope of f(x) = x^3 - 3x?
a) -1
b) 0
c) 1
d) 4
e) None of the above</p>
<p>6) An airplane taking off from a runway travels 3600 feet before lifting off. If it starts from rest, moves with constant acceleration, and makes the run in 30 seconds, what is its initial speed?
a) 120 ft/sec
b) 240 ft/sec
c) 300 ft/sec
d) 360 ft/sec
e) 520 ft/sec</p>
<p>7) Which method would be inappropriate for approximating the area of the region bounded by f(x)= x^3 ? 6, x=0, and x=2?
a) Definition of a Limit
b) Newton's Method
c) Riemann Summation
d) Trapezoidal Rule
e) Both a and b</p>
<p>8) What is the integral of 2e^(2x-1)?
a) 2ln(2x-1)
b) (2x-1)e^(2x-1)
c) 2e^(2x-1)
d) 4e^(2x-1)
e) e^(2x-1)</p>
<p>9) What is the approximate area bounded between the graphs of f(x) = sqrt(3x) + 1 and g(x) = x + 1?
a) 1.5 sq units
b) 3 sq units
c) 7.5 sq units
d) 1.1 sq units
e) 5 sq units</p>
<p>10) Find all values of c in the interval (-2,2) such that f'(c)=0, given that f(x) = x^4 - 2x^2.
a) 0
b) -2, 2
c) -1, 1
d) -1, 0, 1
e) No such values exist</p>
<p>Section 2: Free Response- Send me justification of your answers as well.</p>
<p>1) Let g(x) = absval(4x^2-1). (Absolute Value.)
a) Given that g(x) is bounded between x=0 and x=3, determine the area of the bounded region.
b) Find g'(x), if possible. If possible, find g'(x). If not, explain why g(x) isn't differentiable.
c) Let the region bounded by g(x), x=3, and the x-axis revolve about the line y=4. Determine the volume of the revolved solid.</p>
<p>2) Let the slope of y be equal to (-9x)/(16y) at (1,1).
a) What is the equation of y?
b) Describe the appearance of the slope field. Also, determine the slope of y at (8,4) and (-1, -2).</p>
<p>3) An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 150 miles from the point moving due west at 450 miles per hour. The other plane is 200 miles from the point moving due south at 600 miles per hour.
a) At what rate is the distance between the planes decreasing?
b) Which plane would get to the point first? Why? How much time does the air traffic controller have to get one of the planes on a different flight path? </p>
<p>NOTE: Justification can be in the form of a paragraph, a xeroxed copy of mathematical work, a copy of work done using a program, but do not send me bald answers. Assuming your answers are right, you'll still receive minimal credit.</p>
<p>Enjoy!</p>