2008 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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2008 AP Calculus BC Free-Response Questions Free Download

2008 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）Let R be the region bounded by the graphs of y =sin(πx)and y=x³ - 4x, as shown in the figure above.

1. Find the area of R.
2. The horizontal line y=-2  splits the region R into two parts. Write, but do not evaluate, an integral expression for the area of the part of R that is below this horizontal line.
3. The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of this solid.
4. The region R models the surface of a small pond. At all points in R at a distance x from the y-axis, the depth of the water is given by h(x)= 3-x.  Find the volume of water in the pond.

Section II，Part B，不可使用任何计算器：

3） Let h be a function having derivatives of all orders for x > 0. Selected values of hand its first four derivatives are indicated in the table above. The function h and these four derivatives are increasing on the interval 1 ≤x≤3.

1. Write the first-degree Taylor polynomial for h about x = 2  and use it to approximate h(1.9) . Is this approximation greater than or less than h(1.9) ?  Explain your reasoning.
2. Write the third-degree Taylor polynomial for h about x = 2  and use it to approximate h(1.9) .
3. Use the Lagrange error bound to show that the third-degree Taylor polynomial for h about x=2 approximates h(1.9) with error less than 3 x 10^-4

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