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2015年AP微积分BC简答题真题+答案+PDF下载

来源:原创作品 | 2019-11-2618

2015年AP微积分BC简答题真题+答案+PDF下载SectionII,PartA1)TherateatwhichrainwaterflowsintoadrainpipeismodeledbythefunctionR,wherecubicfeetperhour,tismeasuredinhours,and0≤t≤8.Thep...

2015年AP微积分BC简答题真题+答案+PDF下载

Section II,Part A

1)The rate at which rainwater flows into a drainpipe is modeled by the function R, where2015国际课程AP calculus bc真题与答案下载 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.

How many cubic feet of rainwater flow into the pipe during the 8-hour time interval 0≤ t≤8

Is the amount of water in the pipe increasing or decreasing at time t = 3 hours? Give a reason for your answer.

At what time t, 0≤ t≤8, is the amount of water in the pipe at a minimum? Justify your answer.

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.

2) At time t≥0,a particle moving along a curve in the xy-plane has position(x(t),y(t))with velocity vector At t=1,the particle is at the point(3,5).


(a) Find the x-coordinate of the position of the particle at time t=2.

(b) For 0<t<1, there is a point on the curve at which the line tangent to the curve has a slope of 2.At what time is the object at that point?

(c) Find the time at which the speed of the particle is 3.

(d) Find the total distance traveled by the particle from time t=0 to time t=1.


SECTION II, Part B部分

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天道智思提供AP微积分BC课程培训,具体内容如下

科目 智思5分率 师资 课程目标 课程大纲 教材
AP微积分BC
Calculus BC
91.1% 许和鑫,
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完成AP微积分BC阶段的知识点的学习。通过系统地梳理,充分的练习熟悉考试的题型和难点重点,冲5分。 课次1-2 Derivatives I &Application of Derivatives I Barron 和 Princeton版教材
课次3-4 Application of Derivatives II&
The Definite Integral
课次5-6 Differential Equation &
Application of Definite Integrals
课次7-8 L' Hôpital's Rule, Improper Integrals&
Parametric vector, Polar functions
课次9-10 Infinite series I&
Infinite series II
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