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AP Calculus BC MCQ Question with Answer

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

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Question No : 29
Separation of variables is a technique commonly used to solve which type of differential equation?

Linear differential equations
Exact differential equations
First-order ordinary differential equations
Second-order ordinary differential equations
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Question No : 30
What is the magnitude of the vector <3, 4, 5>?

v6
7
v50
25
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Question No : 31
If a function f(x) has a local minimum at x = a, what can be said about f'(a) and f''(a)?

f'(a) = 0 and f''(a) < 0
f'(a) < 0 and f''(a) = 0
f'(a) = 0 and f''(a) = 0
f'(a) > 0 and f''(a) > 0
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Question No : 32
What is the derivative of ln(x) with respect to x?

1/x
x
e^x
0
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Question No : 33
If F(x) is an antiderivative of f(x), what is the relationship between F(b) and F(a) in the context of the Fundamental Theorem of Calculus?

F(b) = F(a)
F(b) - F(a) = f(b) - f(a)
F(b) - F(a) = ?(a to b) f(x) dx
F(b) - F(a) = 0
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Question No : 34
In polar coordinates, what is the equation of a circle with radius r and center at the origin?

r = 1
r = vx^2 + y^2
r = 2?
r = 2
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Question No : 35
The Mean Value Theorem for Integrals states that for a continuous function f(x) on the interval [a, b], there exists a c in (a, b) such that:

f(c) = 0
f'(c) = 0
f(c) = (b - a) * f'(c)
f'(c) = 1/(b - a)
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