AP Calculus AB 2005 Questions And Answers

Questions And Worked Solutions For AP Calculus AB 2005

Click on the following image to get the complete paper of AP Calculus AB 2005 Free Response Questions. Scroll down the page for step-by-step solutions.

 
AP Calculus AB 2005 Free Response Questions - Complete Paper (pdf)

1. Let f and g be the functions given by f(x) = 1/4 + sin(πx) amd g(x) = 4^-x. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let S be the shaded region in the first quadrant enclosed by the graphs of f and g, as shown in the figure above.
   (a) Find the area of R.
   (b) Find the area of S.
   (c) Find the volume of the solid generated when S is revolved about the horizontal line y = -1.
2. The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by
3. A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of the temperature T(x), in degrees Celsius (°C), of the wire x cm from the heated end. The function T is decreasing and twice differentiable.
4. Let f be a function that is continuous on the interval [0, 4). The function f is twice differentiable except at x = 2. The function f and its derivatives have the properties indicated in the table above, where DNE indicates that the derivatives of f do not exist at 2.
5. A car is traveling on a straight road. For 0 24 £ £t seconds, the car’s velocity v t( ), in meters per second, is modeled by the piecewise-linear function defined by the graph above.
6. Consider the differential equation

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