# AP Calculus Practice ExamAB Version - Section I - Part B

Calculators ARE Permitted On This Portion Of The Exam
17 Questions - 50 Minutes

1) Give a value of c that satisfies the conclusion of the Mean Value Theorem for Derivatives for the function
on the interval [1,3].
a)
b)
c)
d)
e)
2) The function
is invertible. Give the derivative of f -1 at x = 2.
a)
b)
c)
d)
e)
3) The derivative of f is graphed below.
Give a value of x where f has a local minimum.
a)
b)
c)
d)
e)
4) Let
Which of the following is (are) true?
1) f is continuous at x = -2.
2) f is differentiable at x = 1.
3) f has a local minimum at x = 0.
4) f has an absolute maximum at x = -2.

a) 2 only
b) 2 and 4
c) 3 only
d) 1 and 3
e) 1 and 4
5) Given
Determine

a)
b)
c)
d)
e)
6) Give the approximate location of a local maximum for the function

a)
b)
c)
d)
e)
7) Give the approximate average value of the function
over the interval [1,4].
a)
b)
c)
d)
e)
8) The region enclosed by the graphs of
is rotated around the y-axis to generate a solid. What is the volume of the solid?
a)
b)
c)
d)
e)
9) What is the approximate instantaneous rate of change of the function
at t = /11?
a)
b)
c)
d)
e)
10) What is the error when the integral
is approximated by the Trapezoidal rule with n = 3?
a)
b)
c)
d)
e)
11) The amount of money in a bank account is increasing at the rate of
dollars per year, where t is measured in years. If t = 0 corresponds to the year 2005, then what is the approximate total amount of increase from 2005 to 2007.
a) \$32,560
b) \$4,500
c) \$18,350
d) \$16,250
e) \$21,250
12) A particle moves with acceleration
and its initial velocity is 0. For how many values of t does the particle change direction?
a)
b)
c)
d)
e)
13) At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 3 square meters and the radius is increasing at the rate of 1/4 meters per minute?
a)
b)
c)
d)
e)
14) A rectangle has one side on the x-axis and the upper two vertices on the graph of
Give a decimal approximation to the maximum possible area for this rectangle.
a)
b)
c)
d)
e)
15) A rough approximation for ln(5) is 1.609. Use this approximation and differentials to approximate ln(521/100).
a)
b)
c)
d)
e)
16) The function
is differentiable everywhere. What is n?
a)
b)
c)
d)
e)
17) Which of the following functions has a vertical asymptote at x = -1 and a horizontal asymptote at y = 2?
a)
b)
c)
d)
e)