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Unformatted text preview: ) dt using a
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trapezoidal sum and the subintervals of [0, 8] indicated by the data in the table. Students were further asked to
interpret this expression in context, with the expectation that they would recognize that it gives the average
number of hundreds of entries in the box during the eighthour period. In part (c) a function P was supplied that
models the rate at which entries from the box were processed, by the hundred, during a fourhour period
( 8 ≤ t ≤ 12 ) that began after all entries had been received. This part asked for the number of entries that remained
to be processed after the four hours. Students needed to recognize that the number of entries processed is given by 12 8 P( t ) dt , so that the number remaining to be processed, in hundreds of entries, is given by the difference between the total number of entries in the box, E ( 8 ) , as given by the table, and the value of this integral. Part (d)
cited the model P( t ) introduced in the previous part and asked for the time at which the entries were being
processed most quickly. Students should have recognized this as asking for the time corresponding to the
maximum value of P( t ) on the interval 8 ≤ t ≤ 12 and applied a standard process for optimization on a closed
interval.
Sample: 2A
Score: 9 The student earned all 9 points.
Sample: 2B
Score: 6 The student earned 6 points: 1 point in part (a), 2 points in part (b), 2 points in part (c), and 1 point in part (d). In
part (a) the student sets up a correct difference quotient based on the values in the table and correctly evaluates for
the numerical answer. In part (b) the student sets up a correct trapezoidal sum and evaluates it based on the data in
the table to obtain a correct approximation. The student did not earn the third point in par...
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This note was uploaded on 08/22/2013 for the course CALCULUS AP taught by Professor Staff during the Fall '11 term at Lakota West High School.
 Fall '11
 staff
 Calculus

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