2015 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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2015 AP Calculus BC Free-Response Questions Free Download

2015 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）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，不可使用任何計算器： 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.