2015 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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2015 AP Calculus BC Free-Response Questions Free Download

2015 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）The rate at which rainwater flows into a drainpipe is modeled by the function R, where cubic feet per hour, t is measured in hours, and 0≤ t≤8. The pipe is partially blocked, allowing water to drain out the other end of the pipe at a rate modeled by D(t) = -0.04t³ +0.4t² +0.96t  cubic feet per hour, for 0≤ t≤8. There are 30 cubic feet of water in the pipe at time t=0.

1. How many cubic feet of rainwater flow into the pipe during the 8-hour time interval 0≤ t≤8？
2. Is the amount of water in the pipe increasing or decreasing at time t = 3 hours? Give a reason for your answer.
3. At what time t, 0≤ t≤8, is the amount of water in the pipe at a minimum? Justify your answer.
4. The pipe can hold 50 cubic feet of water before overflowing. For t>8, , water continues to flow into and out of the pipe at the given rates until the pipe begins to overflow. Write, but do not solve, an equation involving one or more integrals that gives the time w when the pipe will begin to overflow.

Section II，Part B，不可使用任何计算器： 4） Consider the differential equation

1. On the axes provided, sketch a slope field for the given differential equation at the six points indicated.
2. Find in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
3. Let y =f(x) be the particular solution to the differential equation with the initial condition f(2) =3. Does f have a relative minimum, a relative maximum, or neither at x=2? Justify your answer.
4. Find the values of the constants m and b for which y=mx+b is a solution to the differential equation.