AP Calculus BC 2008 Questions And Answers

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)

• Show Solutions for Q1

• Show Solutions for Q2

• Show Solutions for Q3

• Show Solutions for Q4

• Show Solutions for Q5

• Show Solutions for Q6

1. Let R be the region bounded by the graphs of y x = sin(πx) and y = x³ - 4x, as shown in the figure above.
   (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.
2. 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.
   Values of L(t) at various times t are shown in the table above.

3. 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.
4. 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.
5. The derivative of a function f is given by
6. Consider the logistic differential equation

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.