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__92.gif)
b) ![](images/AP_AB2_version1__93.gif)
c) ![](images/AP_AB2_version1__94.gif)
d) ![](images/AP_AB2_version1__95.gif)
e) ![](images/AP_AB2_version1__96.gif)
2) The function
is invertible. Give the derivative of f -1 at x = 3.
a) ![](images/AP_AB2_version1__98.gif)
b) ![](images/AP_AB2_version1__99.gif)
c) ![](images/AP_AB2_version1__100.gif)
d) ![](images/AP_AB2_version1__101.gif)
e) ![](images/AP_AB2_version1__102.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__104.gif)
b) ![](images/AP_AB2_version1__105.gif)
c) ![](images/AP_AB2_version1__106.gif)
d) ![](images/AP_AB2_version1__107.gif)
e) ![](images/AP_AB2_version1__108.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) 2 only
b) 2 and 4
c) 3 only
d) 1 and 3
e) 1 and 4
5) Given
Determine![](images/AP_AB2_version1__111.gif)
a) ![](images/AP_AB2_version1__112.gif)
b) ![](images/AP_AB2_version1__113.gif)
c) ![](images/AP_AB2_version1__114.gif)
d) ![](images/AP_AB2_version1__115.gif)
e) ![](images/AP_AB2_version1__116.gif)
6) Give the approximate location of a local maximum for the function ![](images/AP_AB2_version1__117.gif)
a) ![](images/AP_AB2_version1__118.gif)
b) ![](images/AP_AB2_version1__119.gif)
c) ![](images/AP_AB2_version1__120.gif)
d) ![](images/AP_AB2_version1__121.gif)
e) ![](images/AP_AB2_version1__122.gif)
7) Give the approximate average value of the function
over the interval [1,4].
a) ![](images/AP_AB2_version1__124.gif)
b) ![](images/AP_AB2_version1__125.gif)
c) ![](images/AP_AB2_version1__126.gif)
d) ![](images/AP_AB2_version1__127.gif)
e) ![](images/AP_AB2_version1__128.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__130.gif)
b) ![](images/AP_AB2_version1__131.gif)
c) ![](images/AP_AB2_version1__132.gif)
d) ![](images/AP_AB2_version1__133.gif)
e) ![](images/AP_AB2_version1__134.gif)
9) What is the approximate instantaneous rate of change of the function
at t =
/3?
a) ![](images/AP_AB2_version1__136.gif)
b) ![](images/AP_AB2_version1__137.gif)
c) ![](images/AP_AB2_version1__138.gif)
d) ![](images/AP_AB2_version1__139.gif)
e) ![](images/AP_AB2_version1__140.gif)
10) What is the error when the integral
is approximated by the Trapezoidal rule with n = 3?
a) ![](images/AP_AB2_version1__142.gif)
b) ![](images/AP_AB2_version1__143.gif)
c) ![](images/AP_AB2_version1__144.gif)
d) ![](images/AP_AB2_version1__145.gif)
e) ![](images/AP_AB2_version1__146.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) $16,250
b) $18,350
c) $32,560
d) $21,250
e) $4,500
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__149.gif)
b) ![](images/AP_AB2_version1__150.gif)
c) ![](images/AP_AB2_version1__151.gif)
d) ![](images/AP_AB2_version1__152.gif)
e) ![](images/AP_AB2_version1__153.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 3 square meters and the radius is increasing at the rate of 1/5 meters per minute?
a) ![](images/AP_AB2_version1__154.gif)
b) ![](images/AP_AB2_version1__155.gif)
c) ![](images/AP_AB2_version1__156.gif)
d) ![](images/AP_AB2_version1__157.gif)
e) ![](images/AP_AB2_version1__158.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__160.gif)
b) ![](images/AP_AB2_version1__161.gif)
c) ![](images/AP_AB2_version1__162.gif)
d) ![](images/AP_AB2_version1__163.gif)
e) ![](images/AP_AB2_version1__164.gif)
15) A rough approximation for ln(5) is 1.609. Use this approximation and differentials to approximate ln(257/50).
a) ![](images/AP_AB2_version1__165.gif)
b) ![](images/AP_AB2_version1__166.gif)
c) ![](images/AP_AB2_version1__167.gif)
d) ![](images/AP_AB2_version1__168.gif)
e) ![](images/AP_AB2_version1__169.gif)
16) The function
is differentiable everywhere. What is n?
a) ![](images/AP_AB2_version1__171.gif)
b) ![](images/AP_AB2_version1__172.gif)
c) ![](images/AP_AB2_version1__173.gif)
d) ![](images/AP_AB2_version1__174.gif)
e) ![](images/AP_AB2_version1__175.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__176.gif)
b) ![](images/AP_AB2_version1__177.gif)
c) ![](images/AP_AB2_version1__178.gif)
d) ![](images/AP_AB2_version1__179.gif)
e) ![](images/AP_AB2_version1__180.gif)