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AP Calculus AB 2009 Free Response Questions - Complete Paper (pdf)

- Caren rides her bicycle along a straight road from home to school, starting at home at time t = 0 minutes and
arriving at school at time t = 12 minutes. During the time interval 0 ≤ t ≤ 12 minutes, her velocity v(t), in
miles per minute, is modeled by the piecewise-linear function whose graph is shown above.

(a) Find the acceleration of Caren’s bicycle at time t = 7.5 minutes. Indicate units of measure - The rate at which people enter an auditorium for a rock concert is modeled by the function R given by
R(t) = 1380t
^{2}hours; R(t) is measured in people per hour. No one is in the auditorium at time t = 0, when the doors open. The doors close and the concert begins at time t = 2.

(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

- Mighty Cable Company manufactures cable that sells 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 6√x dollars per meter.

(Note: Profit is defined to be the difference between the amount of money received by the company for selling the cable and the company’s cost of producing the cable.)

(a) Find Mighty’s profit on the sale of a 25-meter cable. - Let R be the region in the first quadrant enclosed by the graphs of y = 2x and
y = x
^{2}, as shown in the figure above.

(a) Find the area of R. - Let f be a function that is twice differentiable for all real numbers. The table above gives values of f for selected points in the closed interval 2 ≤ x ≤ 13.
- The derivative of a function f is defined by

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