AP Calculus BC Multiple Choice Practice

Calculus BC Multiple Choice Practice

A calculator may not be used for questions 1-7

Question 1:

Question 2: If f is a continuous function for all real x, then

is equal to:

Question 3: A curve is described by the parametric equations x = t3 + 2t and y = t2 + t + 1. An equation of the line tangent to the curve at the point determined by t=-1 is:

Question 4: Write an equation in terms of x and y of the line tangent to the graph of the polar curve r = 1 - 2sin(θ) at the point where θ=0.

Question 5: What are the values of x for which the series is divergent?

Question 6: Consider the closed curve in the x-y plane given by 2x2 + 5x + y2 + y = 8. Which of the following is correct:

Question 7: The function given by:

is differentiable at x = 1. What is the value of f(b-a)?

Question 8: If the average of the function on the [-1,1] interval is 5/8, what are the values of a?

A calculator is required for questions 8-14

Question 9: Determine the area of the inner loop of the polar curve r = 1 - 2sin(θ).

Question 10: The base of a solid is the region in the first quadrant bounded by the graph of y = -x2 + 5x - 4 and the x-axis. If cross-sections of the solid perpendicular to the x-axis are equilateral triangles, what is the volume of the solid?

Question 11: The graphs of the polar curves r = 1 and r = 1 + cos(θ) are shown in the figure below. If R is the region that is inside the graph of r = 1 and outside of the graph of r = 1 + cos(θ), the area of R is:

Question 12: What is the average value of the function f(x) = sin2(3x) + x on the interval [0, π]?

Question 13: At what value of x are the tangent lines to the graphs of f(x) = ln(x) and g(x) = 6x parallel?

Question 14: A trapezoid is inscribed in a semicircle as shown in the figure below. The AB base has the same length with the diameter of the semicircle and is equal to 6cm. What is the maximum area of the trapezoid in cm2?

Question 15: The graphs of the functions f(x)=cos2(x) - 1/4 and g(x)=cos(2x) are shown in the figure below. If A is the region bounded by the graphs of f(x) and g(x) as shown below, the area of A is:

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