2018 AP Calculus BC微積分真題系列之簡答題免費下載

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2018 AP Calculus BC Free-Response Questions Free Download

2018 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

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部分真題預覽：

Section II，Part A，請使用Graphing Calculator： 1）People enter a line for an escalator at a rate modeled by the function r given by where r(t) is measured in people per second and t is measured in seconds. As people get on the escalator, they exit the line at a constant rate of 0.7 person per second. There are 20 people in line at time t=0 .

1. How many people enter the line for the escalator during the time interval 0≤t ≤300 ?
2. During the time interval 0≤t ≤300 , there are always people in line for the escalator. How many people are in line at time t=300???
3. For t >300, what is the first time t that there are no people in line for the escalator?
4. For 0≤t ≤300 , at what time t is the number of people in line a minimum? To the nearest whole?number, find the number of people in line at this time. Justify your answer.

Section II，Part B，不可使用任何計算器： 4） The height of a tree at time t is given by a twice-differentiable function H, where H(t) is measured in meters and t is measured in years. Selected values of H(t) are given in the table above.

1. Use the data in the table to estimate H' (6 ). Using correct units, interpret the meaning of H ' (6 )?in the context of the problem.
2. Explain why there must be at least one time t, for 2 < t <10?, such that H ' (t)=2.
3. Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate the average height of the tree over the time interval 2 ≤t≤10?.
4. The height of the tree, in meters, can also be modeled by the function G, given by , where x is the diameter of the base of the tree, in meters. When the tree is 50?meters tall, the diameter of the base of the tree is increasing at a rate of 0.03 meter per year. According to this model, what is the rate of change of the height of the tree with respect to time, in meters per year, at the time when the tree is 50 meters tall?

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