Questions And Worked Solutions For AP Calculus BC 2008
AP Calculus BC 2008 Free Response Questions - Complete Paper (pdf)
AP Calculus BC 2008 Free Response Questions - Scoring Guide (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.
- Let h be a function having derivatives of all orders for x > 0. Selected values of h and its first four derivatives
are indicated in the table above. The function h and these four derivatives are increasing on the interval
1 ≤ x ≤ 3.
(a) Write the first-degree Taylor polynomial for h about x = 2 and use it to approximate h(1.9) . Is this
approximation greater than or less than h(1.9) ? Explain your reasoning.
- 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.
- The derivative of a function f is given by
- Consider the logistic differential equation
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