AP CALCULUS AB 2014 FREE RESPONSE

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AP Calculus AB 2014 Free Response Questions - Complete Paper (pdf)

AP Calculus AB 2014 Free Response Question 1 A graphing calculator is required for these difficulties.
1. Grass clippings are placed in a bin, wbelow they dewrite. For 0 ≤ t ≤ 30, the amount of glass clippings remaining in the bin is modeled by A(t) = 6.687(0.931)t, wbelow A(t) is measured on pounds and also t is measured in days. (a) Find the average rate of change A(t) over the interval 0 ≤ t ≤ 30. Indicate systems of measure. (b) Find the value of A"(15). Using correct units, analyze the definition of the worth in the conmessage of the difficulty. (c) Find the moment t for which the amount of grass clipping in the bin is equal to the average amount of grass clipping in the bin over the interval 0 ≤ t ≤ 30. (d) For t > 30, L(t), the direct approximation to A at t = 30, is a much better model for the amount of grass clippings continuing to be in the bin. Use L(t) to predict the time at which tright here will certainly be 0.5 pound of grass clippings continuing to be in the bin. Sjust how the work that leads to your answer. AP Calculus AB 2014 Free Response Concern 2

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2. Let R be the region enclosed by the graph of f(x) = x4 - 2.3x3 + 4 and also the horizontal line y = 4, as presented inthe number above.(a) Find the volume of the solid generated when R is rotated about the horizontal line y = -2.(b) Region R is the base of a solid. For this solid, each cross area perpendicular to the x-axis is an isoscelesright triangle through a leg in R. Find the volume of the solid.(c) The vertical line x = k divides R right into 2 areas with equal areas. Write, but perform not solve, an equationentailing integral expressions whose solution provides the worth k.

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AP Calculus AB 2014 Free Response Inquiry 3

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AP Calculus AB 2014 Free Response Question 4

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4. Train A runs back and forth on an east-west section of railroad track. Train A’s velocity, measured in metersper minute, is offered by a differentiable feature VA(t), where time t is measured in minutes. Selected worths forVA(t) are given in the table over.(a) Find the average acceleration of train A over the interval 2 ≤ t ≤ 8.(b) Do the data in the table assistance the conclusion that train A’s velocity is -100 meters per minute at sometime t through 5 (c) At time t = 2, train A’s position is 300 meters east of the Origin Station, and the train is moving to the east.Write an expression involving an integral that gives the position of train A, in meters from the OriginStation, at time t = 12. Use a trapezoidal amount via 3 subintervals indicated by the table to approximatethe place of the train at time t = 12.(d) A second train, train B, travels north from the Origin Station. At time t the velocity of train B is offered byVB(t) = -5t2 + 60t + 25 and also at time t = 2 the train is 400 meters north of the station. Find the rate, inmeters per minute, at which the distance between train A and also train B is altering at time t = 2 AP Calculus AB 2014 Free Response Concern 5

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AP Calculus AB 2014 Free Response Concern 6

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