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AP Calculus BC - Free Response Questions Examples

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AP Calculus BC - Free Response Questions Examples
1. The velocity vector of a particle moving in the (x,y) plane has components given by:
a) For 0 < t < 2, find all values of t at which the line tangent to the path of the particle is horizontal.
b) Write an equation for the line tangent to the path of the particle at t = 1, if the position of the
particle at t = 0 is (1,0).
c) Find the speed of the particle at t = 1.
d) For 0 < t < 1, find all values of t for which the speed of the particle is equal to 0.
2. The graphs of the polar curves r
1
= 2 + 2sinθ and r
2
= 1 for 0 ≤ θ ≤ 2π are shown below:
a) Write an integral expression for the area inside r
2
and outside r
1
.
b) Write expressions for dx/dθ and dy/dθ in terms of θ for the r
1
curve.
c) Write an equation in terms of x and y for the line tangent to the graph of the polar curve r
1
at the
point where θ = 0.

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3. Let f be a function derivabile on the (0, 0.6) interval and f '(x) = 3 + ln(x + 1).
a) If f(.1) = 2, what is f(.6)?
b) Let R be the region in the first quadrant bounded by the y axis and the graphs of f'(x) and g(x) =
2
3x
. 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.
c) Find the area of R.

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 AP Calculus BC - Free Response Questions Examples 1. The velocity vector of a particle moving in the (x,y) plane has components given by: a) For 0 < t < 2, find all values of t at which the line tangent to the path of the particle is horizontal. b) Write an equation for the line tangent to the path of the particle at t = 1, if the position of the particle at t = 0 is (1,0). c) Find the speed of the particle at t = 1. d) For 0 < t < 1, find all values of t for which the speed of the particle is equal to 0. 2. The graphs of the polar curves r1 = 2 + 2sinθ and r2 = 1 for 0 ≤ θ ≤ 2π are shown below: a) Write an integral expression for the area inside r2 and outside r1. b) Write expressions for dx/dθ and dy/dθ in terms of θ for the r1 curve. c) Write an equation in terms of x and y for the line tangent to the graph of the polar curve r1 at the point where θ = 0. 3. Let f be a function derivabile on the (0, 0.6) interval and f '(x) = 3 + ln(x + 1). a) If f(.1) = 2, what is f(.6)? b) Let R be the region in the first quadrant bounded by the y axis and the graphs of f'(x) and g(x) = 23x. 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. c) Find the area of R. Calculus BC Multiple Choice Practice A calculator may not be used for questions 1-7 Top of Form Question 1: -1 0 1 2.72 -∞ Question 2: If f is a continuous function for all real x ...
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