### Questions and Worked Solutions for AP Calculus AB 2011

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

AP Calculus AB 2011 Free Response Inquiry 1Determining whether rate is boosting. Difference between rate and acceleration.

For 0 ≤ t ≤ 6, a pwrite-up is moving along the x-axis. The particle’s position, x(t), is not clearly offered.The velocity of the pwrite-up is given by v(t) = 2 sin (e1/4) + 1. The acceleration of the pshort article is provided bya(t) = 1/2 e1/4 cos (e1/4) and x(0) = 2.(a) Is the rate of the pshort article increasing or decreasing at time t = 5.5? Give a reason for your answer.(b) Find the average velocity of the particle for the time duration 0 ≤ t ≤ 6. (c) Find the full distance traveled by the pwrite-up from time t = 0 to t = 6.(d) For 0 ≤ t ≤ 6, the pshort article changes direction precisely once. Find the position of the ppost at that time.AP Calculus AB 2011 Free Response Question 2Approximating rate of change and also complete location under a curve. Trapezoidal sums to approximate integrals.2. As a pot of tea cools, the temperature of the tea is modeled by a differentiable feature H for 0 ≤ t ≤ 10, wright here time t is measured in minutes and temperature H(t) is measured in degrees Celsius. Values of H(t) at selected worths of time t are displayed in the table over.(a) Use the information in the table to approximate the price at which the temperature of the tea is changing at time t = 3.5. Sjust how the computations that bring about your answer. (b), (c)(d) At time t = 0, biscuits through temperature 100°C were rerelocated from an oven. The temperature of the biscuits at time t is modeled by a differentiable feature B for which it is known that B"(t) = -13.84e-0.173t. Using the given models, at time t = 10, exactly how much cooler are the biscuits than the tea?

AP Calculus AB 2011 Free Response Question 3Equation of a tangent line and also area between curves. 3. Let R be the region in the first quadrant enclosed by the graphs of f(x) = 8x3 and also g(x) = sin (πx), as displayed in the number above.(a) Write an equation for the line tangent to the graph of f at x = 1/2.(b) Find the location of R.(c) Write, but carry out not evaluate, an integral expression for the volume of the solid generated as soon as R is rotated around the horizontal line y = 1.

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AP Calculus AB 2011 Free Response Inquiry 4Taking derivatives and also integrals of strangely defined attributes. Absolute maximum over an interval. Critical points and differenticapacity.

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Finding the points of inflection for a strangely identified attribute. Mean Value Theorem and also differenticapacity. 4. The continuous attribute f is defined on the interval -4 ≤ x ≤ 3. The graph of f is composed of 2 quarter circles and also one line segment, as presented in the number over. Let g(x) =(a) Find g(-3). Find g"(x) and evaluate g"(-3).(b) Determine the x-coordinate of the suggest at which g has an absolute maximum on the interval -4 ≤ x ≤ 3. Justify your answer.(c) Find all worths 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 price of adjust of f on the interval -4 ≤ x ≤ 3. Tright here is no point c, -4AP Calculus AB 2011 Free Response Question 55. At the beginning of 2010, a landfill included 1400 tons of solid waste. The raising function W models the complete amount of solid waste stored at the landfill. Planners estimate that W will certainly meet the differential equation dW/dt = 1/25(w - 300) for the following two decades. W is measured in lots, and t is measured in years from the begin 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 has 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 identify 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 certain solution W = W(t) to the differential equation dW/dt = 1/25(W - 300) through initial condition W(0) = 1400.

AP Calculus AB 2011 Free Response Question 66. Let f be a function defined by f(x) =.(a) Sjust how that f is continuous at x = 0.(b) For x ≠ 0, express f"(x) as a piecewise-defined feature. Find the value of x for which f"(x) = -3.(c) Find the average worth of f on the interval <-1, 1>.

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