AP Calculus Practice Exam
AB 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) ![](images/AP_AB2_version1__182.gif)
b) ![](images/AP_AB2_version1__183.gif)
c) ![](images/AP_AB2_version1__184.gif)
d) ![](images/AP_AB2_version1__185.gif)
e) ![](images/AP_AB2_version1__186.gif)
2) The function
is invertible. Give the derivative of f -1 at x = 3.
a) ![](images/AP_AB2_version1__188.gif)
b) ![](images/AP_AB2_version1__189.gif)
c) ![](images/AP_AB2_version1__190.gif)
d) ![](images/AP_AB2_version1__191.gif)
e) ![](images/AP_AB2_version1__192.gif)
3) The derivative of f is graphed below.
Give a value of x where f has a local minimum.
a) ![](images/AP_AB2_version1__194.gif)
b) ![](images/AP_AB2_version1__195.gif)
c) ![](images/AP_AB2_version1__196.gif)
d) ![](images/AP_AB2_version1__197.gif)
e) ![](images/AP_AB2_version1__198.gif)
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) 3 only
b) 2 and 4
c) 2 only
d) 1 and 3
e) 1 and 4
5) Given
Determine![](images/AP_AB2_version1__201.gif)
a) ![](images/AP_AB2_version1__202.gif)
b) ![](images/AP_AB2_version1__203.gif)
c) ![](images/AP_AB2_version1__204.gif)
d) ![](images/AP_AB2_version1__205.gif)
e) ![](images/AP_AB2_version1__206.gif)
6) Give the approximate location of a local maximum for the function ![](images/AP_AB2_version1__207.gif)
a) ![](images/AP_AB2_version1__208.gif)
b) ![](images/AP_AB2_version1__209.gif)
c) ![](images/AP_AB2_version1__210.gif)
d) ![](images/AP_AB2_version1__211.gif)
e) ![](images/AP_AB2_version1__212.gif)
7) Give the approximate average value of the function
over the interval [1,4].
a) ![](images/AP_AB2_version1__214.gif)
b) ![](images/AP_AB2_version1__215.gif)
c) ![](images/AP_AB2_version1__216.gif)
d) ![](images/AP_AB2_version1__217.gif)
e) ![](images/AP_AB2_version1__218.gif)
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) ![](images/AP_AB2_version1__220.gif)
b) ![](images/AP_AB2_version1__221.gif)
c) ![](images/AP_AB2_version1__222.gif)
d) ![](images/AP_AB2_version1__223.gif)
e) ![](images/AP_AB2_version1__224.gif)
9) What is the approximate instantaneous rate of change of the function
at t =
/7?
a) ![](images/AP_AB2_version1__226.gif)
b) ![](images/AP_AB2_version1__227.gif)
c) ![](images/AP_AB2_version1__228.gif)
d) ![](images/AP_AB2_version1__229.gif)
e) ![](images/AP_AB2_version1__230.gif)
10) What is the error when the integral
is approximated by the Trapezoidal rule with n = 3?
a) ![](images/AP_AB2_version1__232.gif)
b) ![](images/AP_AB2_version1__233.gif)
c) ![](images/AP_AB2_version1__234.gif)
d) ![](images/AP_AB2_version1__235.gif)
e) ![](images/AP_AB2_version1__236.gif)
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) $21,250
b) $4,500
c) $18,350
d) $32,560
e) $16,250
12) A particle moves with acceleration
and its initial velocity is 0. For how many values of t does the particle change direction?
a) ![](images/AP_AB2_version1__239.gif)
b) ![](images/AP_AB2_version1__240.gif)
c) ![](images/AP_AB2_version1__241.gif)
d) ![](images/AP_AB2_version1__242.gif)
e) ![](images/AP_AB2_version1__243.gif)
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 2 square meters and the radius is increasing at the rate of 1/3 meters per minute?
a) ![](images/AP_AB2_version1__244.gif)
b) ![](images/AP_AB2_version1__245.gif)
c) ![](images/AP_AB2_version1__246.gif)
d) ![](images/AP_AB2_version1__247.gif)
e) ![](images/AP_AB2_version1__248.gif)
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) ![](images/AP_AB2_version1__250.gif)
b) ![](images/AP_AB2_version1__251.gif)
c) ![](images/AP_AB2_version1__252.gif)
d) ![](images/AP_AB2_version1__253.gif)
e) ![](images/AP_AB2_version1__254.gif)
15) A rough approximation for ln(5) is 1.609. Use this approximation and differentials to approximate ln(259/50).
a) ![](images/AP_AB2_version1__255.gif)
b) ![](images/AP_AB2_version1__256.gif)
c) ![](images/AP_AB2_version1__257.gif)
d) ![](images/AP_AB2_version1__258.gif)
e) ![](images/AP_AB2_version1__259.gif)
16) The function
is differentiable everywhere. What is n?
a) ![](images/AP_AB2_version1__261.gif)
b) ![](images/AP_AB2_version1__262.gif)
c) ![](images/AP_AB2_version1__263.gif)
d) ![](images/AP_AB2_version1__264.gif)
e) ![](images/AP_AB2_version1__265.gif)
17) Which of the following functions has a vertical asymptote at x = -1 and a horizontal asymptote at y = 2?
a) ![](images/AP_AB2_version1__266.gif)
b) ![](images/AP_AB2_version1__267.gif)
c) ![](images/AP_AB2_version1__268.gif)
d) ![](images/AP_AB2_version1__269.gif)
e) ![](images/AP_AB2_version1__270.gif)