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2014 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） Grass clippings are placed in a bin, where they decompose. For 0?≤ t ≤ 30 , the amount of grass clippings remaining in the bin is modeled by A(t)=6.687(0.931)^t, where A(t) is measured in pounds and t is measured in days.

1. Find the average rate of change of A(t) over the interval 0?≤ t ≤ 30. Indicate units of measure.
2. Find the value of A'(15) . Using correct units, interpret the meaning of the value in the context of the problem.
3. Find the time tfor which the amount of grass clippings in the bin is equal to the average amount of grass?clippings in the bin over the interval 0?≤ t ≤ 30.
4. For t > 30,L(t), the linear approximation to A at t = 30?, is a better model for the amount of grass clippings remaining in the bin. Use L(t) to predict the time at which there will be 0.5 pound of grass clippings remaining in the bin. Show the work that leads to your answer

Section II，Part B，不可使用任何計算器：

4）Train A runs back and forth on an east-west section of railroad track. Train A’s velocity, measured in meters per minute, is given by a differentiable function v_A(t) , where time t is measured in minutes. Selected values v_A(t) for are given in the table above.

1. Find the average acceleration of train A over the interval 2 ≤ t ≤ 8
2. Do the data in the table support the conclusion that train A’s velocity is -100 meters per minute at some time t with 5 < t?< 8?? Give a reason for your answer.
3. At time t = 2, train A’s position is 300 meters east of the Origin Station, and the train is moving to the east. Write an expression involving an integral that gives the position of train A, in meters from the Origin Station, at time t = 12. Use a trapezoidal sum with three subintervals indicated by the table to approximate the position of the train at time t =12.
4. A second train, train B, travels north from the Origin Station. At time tthe velocity of train Bis given by v_B(t)= -5t² + 60t +25?, and at time t = 2 the train is 400 meters north of the station. Find the rate, in meters per minute, at which the distance between train A and train B is changing at time t = 2.

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