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AP Calculus AB 2010 Free Response Questions - Complete Paper (pdf)

- There is no snow on Janet’s driveway when snow begins to fall at midnight. From midnight to 9 A.M., snow
accumulates on the driveway at a rate modeled by f(t) = 7te
^{cost}cubic feet per hour, where t is measured in hours since midnight. Janet starts removing snow at 6 A.M. (t = 6). The rate g(t), in cubic feet per hour, at which Janet removes snow from the driveway at time t hours after midnight is modeled by - A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box between noon (t = 0) and 8 P.M. (t = 8). The number of entries in the box t hours after noon is modeled by a differentiable function E for 0 ≤ t ≤ 8. Values of E(t), in hundreds of entries, at various times t are shown in the table above.
- There are 700 people in line for a popular amusement-park ride when the ride begins operation in the morning. Once it begins operation, the ride accepts passengers until the park closes 8 hours later. While there is a line, people move onto the ride at a rate of 800 people per hour. The graph above shows the rate, r(t), at which people arrive at the ride throughout the day. Time t is measured in hours from the time the ride begins operation.
- Let R be the region in the first quadrant bounded by the graph of y = 2√x the horizontal line y = 6, and the y-axis, as shown in the figure above.
- The function g is defined and differentiable on the closed interval [-7, 5] and satisfies g(0) = 5. The graph of y = g'(x), the derivative of g, consists of a semicircle and three line segments, as shown in the figure above.
- Solutions to the differential equation

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