AP® Calculus AB
2009 Scoring Guidelines
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Question 1
Caren rides her bicycle along a straight road from home to school, starting at home at time 0t = minutes and arriving at school at time 12t = minutes. During the time interval 012t ≤≤ minutes, her velocity (),v t in miles per minute, is modeled by the piecewi-linear function who graph is shown above. (a) Find the acceleration of Caren’s bicycle at time 7.5t = minutes. Indicate units of measure.
(b) Using correct units, explain the meaning of
()12
v t dt ∫ in terms of Caren’s trip. Find the value
of ()120
.v t dt ∫
(c) Shortly after leaving home, Caren realizes she left her calculus homework at home, and she returns to
英译汉拍照翻译get it. At what time does she turn around to go back home? Give a reason for your answer. (d) Larry also rides his bicycle along a straight road from home to school in 12 minutes. His velocity is
modeled by the function w given by ()()
sin
井底之蛙英文版,1512
w t t π
英语六级听力下载π
=
where ()w t is in miles per minute for
012t ≤≤ minutes. Who lives clor to school: Caren or Larry? Show the work that leads to your answer.
on to the next oneQuestion 2
The rate at which people enter an auditorium for a rock concert is modeled by the function R given by
()231380675R t t t =− for 02t ≤≤ hours; ()R t is measured in people per hour. No one is in the auditorium at time 0,t = when the doors open. The doors clo and the concert begins at time 2.t = (a) How many people are in the auditorium when the concert begins?
(b) Find the time when the rate at which people enter the auditorium is a maximum. Justify your answer. (c) The total wait time for all the people in the auditorium is found by adding the time each person waits,
starting at the time the person enters the auditorium and ending when the concert begins. The function w models the total wait time for all the people who enter the auditorium before time t . The derivative of w is given by ()()()2.w t t R t ′=− Find ()()21,w w − the total wait time for tho who enter the auditorium after time 1.t = (d) On average, how long does a person wait in the auditorium for the concert to begin? Consider all people
who enter the auditorium after the doors open, and u the model for total wait time from part (c).
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amendsQuestion 3
Mighty Cable Company manufactures cable that lls for $120 per meter. For a cable of fixed length, the cost of producing a portion of the cable varies with its distance from the beginning of the cable. Mighty reports that the cost to produce a portion of a cable that is x
meters from the beginning of the cable is
received by the company for lling the cable and the company’s cost of producing the cable.)
北大青鸟java培训(a) Find Mighty’s profit on the sale of a 25-meter cable.
(b)
Using correct units, explain the meaning of
30
25
dx
∫ in the context of this problem.
(c) Write an expression, involving an integral, that reprents Mighty’s profit on the sale of a cable that
is k meters long.
(d) Find the maximum profit that Mighty could earn on the sale of one cable. Justify your answer.
Question 4
Let R be the region in the first quadrant enclod by the graphs of 2y x = and
2,y x = as shown in the figure above.
(a) Find the area of R .
贸易有限公司英文(b) The region R is the ba of a solid. For this solid, at each x the cross
ction perpendicular to the x -axis has area ()()sin
.2A x x π= Find thepink是什么意思
volume of the solid.
(c) Another solid has the same ba R . For this solid, the cross ctions
perpendicular to the y -axis are squares. Write, but do not evaluate, an integral expression for the volume of the solid.
