2011 AP Calculus BC微积分真题系列之简答题免费下载

历年AP Calculus BC微积分BC系列

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2011 AP Calculus BC Free-Response Questions Free Download

2011 AP 微积分 BC 简答题部分免费下载

此套Section II试卷共分两个部分组成

Part A计时30分钟，共2题

Part B计时1小时，共4题

每道大题含有不同数量的小题

Part A可使用绘图计算器

Part B不可使用任何计算器

完整版下载链接见文末

部分真题预览：

Section II，Part A，请使用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，不可使用任何计算器：

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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