Questions And Worked Solutions For AP Calculus AB 2008
AP Calculus AB 2008 Free Response Questions - Complete Paper (pdf)
- Let R be the region bounded by the graphs of y x = sin(πx) and y = x3 - 4x, as shown in the figure
(a) Find the area of R.
(b) The horizontal line y = −2 splits the region R into two parts. Write, but do not evaluate, an integral
expression for the area of the part of R that is below this horizontal line.
(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a
square. Find the volume of this solid.
(d) The region R models the surface of a small pond. At all points in R at a distance x from the y-axis,
the depth of the water is given by h(x) = 3 - x . Find the volume of water in the pond.
- Concert tickets went on sale at noon (t = 0) and were sold out within 9 hours. The number of people waiting
in line to purchase tickets at time t is modeled by a twice-differentiable function L for 0 ≤ t ≤ 9.
of L(t) at various times t are shown in the table above.
- Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a
constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder
with both its radius and height changing with time
- A particle moves along the x-axis so that its velocity at time t, for 0 ≤ t ≤ 6 is given by a differentiable
function v whose graph is shown above. The velocity is 0 at t = 0, t = 3, and t = 5, and the graph has
horizontal tangents at t = 1 and t = 4. The areas of the regions bounded by the t-axis and the graph of v on
the intervals [0,3], [3,5] and [5.6] are 8, 3, and 2, respectively. At time t 0, the particle is at x = -2.
- Consider the differential equation
- Let f be the function given by
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.