2008 AP Calculus BC微積分真題系列之簡答題免費下載

歷年AP Calculus BC微積分BC系列

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2008 AP Calculus BC Free-Response Questions Free Download

2008 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

完整版下載鏈接見文末

部分真題預覽：

Section II，Part A，請使用Graphing Calculator：

1）Let R?be the region bounded by the graphs of y =sin(πx)and y=x^3?-?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，不可使用任何計算器：

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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