2011 AP Calculus BC微積分真題系列之簡答題免費下載

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2011 AP Calculus BC Free-Response Questions Free Download

2011 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） At time t, a particle moving in the xy-plane is at position (x(t) , y(t)), where x(t)and y(t)?are not explicitly given. For t ≥0,? dx/dt=4t +1 and dy/dt=sin(t²)?. At time t =0, x(0)=0 and y(?0) =-4.

1. Find the speed of the particle at time t =3,? and find the acceleration vector of the particle at time t =3.
2. Find the slope of the line tangent to the path of the particle at time t =3.
3. ?Find the position of the particle at time t =3.
4. Find the total distance traveled by the particle over the time interval 0 ≤t?≤3.

Section II，Part B，不可使用任何計算器：

3） Let f(x)=e^2x. Let R be the region in the first quadrant bounded by the graph of f, the coordinate axes, and the vertical line x =k, where k >0. The region R is shown in the figure above.

1. Write, but do not evaluate, an expression involving an integral that gives the perimeter of R in terms of k.
2. The region R is rotated about the x-axis to form a solid. Find the volume, V, of the solid in terms of k.?
3. The volume V, found in part (b), changes as k changes. If dx/dt= 1/3, determine dV/dt when k =1/2.

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