AP Calculus BC 2010 Questions And Answers

AP Calculus BC is a challenging, college-level course in calculus that builds upon the concepts learned in AP Calculus AB. It covers topics typically found in the first two semesters of college calculus, providing a more comprehensive understanding of calculus.

Questions And Worked Solutions For AP Calculus BC 2010

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

AP Calculus BC 2010 Free Response Questions - Scoring Guide (pdf)

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1. 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^costcubic 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
2. 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.

3. A particle is moving along a curve so that its position at time t is (x(t),y(t)), where x(t) = t² -4t + 8 and y(t) is not explicitly given.
4. 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.
5. Consider the differential equation dy/dx = 1. Let y = f(x) be the particular solution to this differential equation with the initial condition f(1) = 0. For this particular solution, f(x) < 1 for all values of x
6. The function f, defined above, has derivatives of all orders. Let g be the function defined by

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