AP Calculus AB MCQ Question with Answer

AP Calculus AB MCQ with detailed explanation for interview, entrance and competitive exams. Explanation are given for understanding.

Question No : 8
What is the derivative of the vector-valued function r(t) = <2t, t^2, 3t + 1> with respect to t?

<2, 2t, 3>

<2, 2t, 3t + 1>

<2t, 2t^2, 3>

<0, 0, 0>

Question No : 9
What is the integral of 3x^2 with respect to x?

x^3 + C

x^2 + C

x^3/3 + C

3x + C

Question No : 10
What is the area of the region enclosed by the polar curve r = 2sin(?)?

p square units

4 square units

2 square units

0 square units

Question No : 11
What are the parametric equations for a circle of radius r centered at the origin in polar coordinates?

x = rcos(?), y = rsin(?)

x = rcos(t), y = rsin(t)

x = r?, y = r?

x = cos(?), y = sin(?)

Question No : 12
In three-dimensional space, what are the coordinates of the origin?

(0, 0, 0)

(1, 1, 1)

(0, 0)

(1, 1)

Question No : 13
If a point has polar coordinates (r, ?), what are its Cartesian coordinates?

x = rcos(?), y = rsin(?)

x = r?, y = r?

x = cos(?), y = sin(?)

x = rsin(?), y = rcos(?)

Question No : 14
Which trigonometric substitution is commonly used to integrate rational functions involving v(a^2 - x^2)?

u = sin(x)

u = cos(x)

u = sec(x)

u = tan(x)