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## AP Calculus AB Test 2

Question 1: The base of a solid is the region in the first and second quadrants bounded by the graph of y = 1 - x2 and the x-axis. If cross-sections of the solid perpendicular to the x-axis are squares, what is the volume of the solid?

Question 2:

 t(hours) 0 0.5 1 1.5 2 2.5 3 v(miles/hour) 32 30 16 22 20 24 26

A speedboat travels on a river. Its speed v, in miles per hour, at certain times is given in the table above. Using a left Riemann sum, what is the approximation of the total distance traveled by the speedboat from t = .5 to t = 3?

Question 3: At what value of x are the the tangent lines to the graphs of f(x) = ln(x) and g(x) = 6x parallel?

Question 4: What is the average value of the function f(x) = sin2(3x) + x on the interval [0, ¶]?

Question 5: The base of a solid is the region in the first quadrant bounded by the graph of y = -x2 + 5x - 4 and the x-axis. If cross-sections of the solid perpendicular to the x-axis are equilateral triangles, what is the volume of the solid?

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