AP Calculus BC 2009 Questions And Answers

Questions And Worked Solutions For AP Calculus BC 2009

AP Calculus BC 2009 Free Response Questions - Complete Paper (pdf)

AP Calculus BC 2009 Free Response Questions - Scoring Guide (pdf)

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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.
   (a) Find the acceleration of Caren’s bicycle at time t = 7.5 minutes. Indicate units of measure
2. The rate at which people enter an auditorium for a rock concert is modeled by the function R given by R(t) = 1380t² hours; R(t) is measured in people per hour. No one is in the auditorium at time t = 0, when the doors open. The doors close and the concert begins at time t = 2.
   (a) How many people are in the auditorium when the concert begins?
   (b) Find the time when the rate at which people enter the auditorium is a maximum. Justify your answer

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
4. Consider the differential equation dy/dx = 6x² - x²y Let y = f(x) be a particular solution to this differential equation with the initial condition f(-1) = 2.
5. Let f be a function that is twice differentiable for all real numbers. The table above gives values of f for selected points in the closed interval 2 ≤ x ≤ 13.
6. The Maclaurin series for

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