2009 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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2009 AP Calculus BC Free-Response Questions Free Download

2009 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）Caren rides her bicycle along a straight road from home to school, starting at home at time t=0 minutes and arriving at school at time t=12 minutes. During the time interval 0 ≤t ≤12 minutes, her velocity v(t), in miles per minute, is modeled by the piecewise-linear function whose graph is shown above.

1. Find the acceleration of Caren’s bicycle at time t=7.5  minutes. Indicate units of measure.
2. Using correct units, explain the meaning of  in terms of Caren’s trip. Find the value of 
3. Shortly after leaving home, Caren realizes she left her calculus homework at home, and she returns to get it. At what time does she turn around to go back home? Give a reason for your answer.
4. Larry also rides his bicycle along a straight road from home to school in 12 minutes. His velocity is modeled by the function w given by , where w(t) is in miles per minute for 0 ≤t≤12 minutes.Who lives closer to school:  Caren or Larry? Show the work that leads to your answer.

Section II，Part B，不可使用任何计算器：

3）A diver leaps from the edge of a diving platform into a pool below. The figure above shows the initial position of the diver and her position at a later time. At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver’s shoulders is given by x(t), and the vertical distance from the water surface to her shoulders is given by y(t), where x(t) and y(t) are measured in meters. Suppose that the diver’s shoulders are 11.4 meters above the water when she makes her leap and that

 for 0 ≤ t ≤ A, where A is the time that the diver’s shoulders enter the water.

1. Find the maximum vertical distance from the water surface to the diver’s shoulders.
2. Find A, the time that the diver’s shoulders enter the water.
3. Find the total distance traveled by the diver’s shoulders from the time she leaps from the platform until the time her shoulders enter the water.
4. Find the angle θ,0 <θ< π/2,  between the path of the diver and the water at the instant the diver’s shoulders enter the water.

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