2010 AP Calculus BC微積分真題系列之簡答題免費下載

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2010 AP Calculus BC Free-Response Questions Free Download

2010 AP 微積分 BC 簡答題部分免費下載

此套Section II試卷共分兩個部分組成

Part A計時30分鐘，共2題

Part B計時1小時，共4題

每道大題含有不同數量的小題

Part A可使用繪圖計算器

Part B不可使用任何計算器

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部分真題預覽：

Section II，Part A，請使用Graphing Calculator：

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^{cos t}?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

1. How many cubic feet of snow have accumulated on the driveway by 6 A.M.?
2. Find the rate of change of the volume of snow on the driveway at 8 A.M.
3. Let h(t) represent the total amount of snow, in cubic feet, that Janet has removed from the driveway? at time t?hours after midnight. Express h?as a piecewise-defined function with domain 0 ≤t?≤9.
4. ?How many cubic feet of snow are on the driveway at 9 A.M.?

Section II，Part B，不可使用任何計算器：

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. Both x and y are measured in meters, and t is measured in seconds. It is known that dy/dt=te^t-3 - 1

1. Find the speed of the particle at time t =3 seconds.
2. Find the total distance traveled by the particle for 0 ≤t?≤ 4?seconds.
3. Find the time t, 0 ≤t≤4,?when the line tangent to the path of the particle is horizontal. Is the direction of motion of the particle toward the left or toward the right at that time? Give a reason for your answer.
4. There is a point with x-coordinate 5 through which the particle passes twice. Find each of the following.
   1. The two values of t when that occurs
   2. The slopes of the lines tangent to the particle’s path at that point
   3. The y-coordinate of that point, given y 2 =3+1/e

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