AP Calculus BC 2011 Questions And Answers

Questions And Worked Solutions For AP Calculus BC 2011

AP Calculus BC 2011 Free Response Questions - Complete Paper (pdf)

AP Calculus BC 2011 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. At time t, a particle moving in the xy-plane is at position (x(t), y(t)) where x(t) and y(t) are not explicitly given.
2. As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for 0 ≤ t ≤ 10, where time t is measured in minutes and temperature H(t) is measured in degrees Celsius. Values of H(t) at selected values of time t are shown in the table above.
   (a) Use the data in the table to approximate the rate at which the temperature of the tea is changing at time t = 3.5. Show the computations that lead to your answer.
   (b), (c)
   (d) At time t = 0, biscuits with temperature 100°C were removed from an oven. The temperature of the biscuits at time t is modeled by a differentiable function B for which it is known that B'(t) = -13.84e^-0.173t. Using the given models, at time t = 10, how much cooler are the biscuits than the tea?

3. Let f(x) = e^2x Let R be the region in the first quadrant bounded by the graph of f, the coordinate axes, and the vertical line x = k , where k > 0. The region R is shown in the figure above.
4. The continuous function f is defined on the interval -4 ≤ x ≤ 3. The graph of f consists of two quarter circles and one line segment, as shown in the figure above. Let g(x) =
   (a) Find g(-3). Find g'(x) and evaluate g'(-3).
   (b) Determine the x-coordinate of the point at which g has an absolute maximum on the interval -4 ≤ x ≤ 3. Justify your answer.
   (c) Find all values of x on the interval -4 ≤ x ≤ 3 for which the graph of g has a point of inflection. Give a reason for your answer.
   (d) Find the average rate of change of f on the interval -4 ≤ x ≤ 3. There is no point c, -4 < c < 3, c for which f'(c) is equal to that average rate of change. Explain why this statement does not contradict the Mean Value Theorem.
5. At the beginning of 2010, a landfill contained 1400 tons of solid waste. The increasing function W models the total amount of solid waste stored at the landfill. Planners estimate that W will satisfy the differential equation dW/dt = 1/25(w - 300) for the next 20 years. W is measured in tons, and t is measured in years from the start of 2010.
   (a) Use the line tangent to the graph of W at t = 0 to approximate the amount of solid waste that the landfill contains at the end of the first 3 months of 2010 (time t = 1/4).
   (b) Find d²W/dt² in terms of W. Use d²W/dt² to determine whether your answer in part (a) is an underestimate or an overestimate of the amount of solid waste that the landfill contains at time t = 1/4.
   (c) Find the particular solution W = W(t) to the differential equation dW/dt = 1/25(W - 300) with initial condition W(0) = 1400.
6. Let f(x) = sin(x²) + cos x.

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.