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__272.gif)
b) ![](images/AP_AB2_version1__273.gif)
c) ![](images/AP_AB2_version1__274.gif)
d) ![](images/AP_AB2_version1__275.gif)
e) ![](images/AP_AB2_version1__276.gif)
2) The function
is invertible. Give the derivative of f -1 at x = 3.
a) ![](images/AP_AB2_version1__278.gif)
b) ![](images/AP_AB2_version1__279.gif)
c) ![](images/AP_AB2_version1__280.gif)
d) ![](images/AP_AB2_version1__281.gif)
e) ![](images/AP_AB2_version1__282.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__284.gif)
b) ![](images/AP_AB2_version1__285.gif)
c) ![](images/AP_AB2_version1__286.gif)
d) ![](images/AP_AB2_version1__287.gif)
e) ![](images/AP_AB2_version1__288.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) 1 and 3
b) 2 and 4
c) 2 only
d) 1 and 4
e) 3 only
5) Given
Determine![](images/AP_AB2_version1__291.gif)
a) ![](images/AP_AB2_version1__292.gif)
b) ![](images/AP_AB2_version1__293.gif)
c) ![](images/AP_AB2_version1__294.gif)
d) ![](images/AP_AB2_version1__295.gif)
e) ![](images/AP_AB2_version1__296.gif)
6) Give the approximate location of a local maximum for the function ![](images/AP_AB2_version1__297.gif)
a) ![](images/AP_AB2_version1__298.gif)
b) ![](images/AP_AB2_version1__299.gif)
c) ![](images/AP_AB2_version1__300.gif)
d) ![](images/AP_AB2_version1__301.gif)
e) ![](images/AP_AB2_version1__302.gif)
7) Give the approximate average value of the function
over the interval [1,4].
a) ![](images/AP_AB2_version1__304.gif)
b) ![](images/AP_AB2_version1__305.gif)
c) ![](images/AP_AB2_version1__306.gif)
d) ![](images/AP_AB2_version1__307.gif)
e) ![](images/AP_AB2_version1__308.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__310.gif)
b) ![](images/AP_AB2_version1__311.gif)
c) ![](images/AP_AB2_version1__312.gif)
d) ![](images/AP_AB2_version1__313.gif)
e) ![](images/AP_AB2_version1__314.gif)
9) What is the approximate instantaneous rate of change of the function
at t =
/3?
a) ![](images/AP_AB2_version1__316.gif)
b) ![](images/AP_AB2_version1__317.gif)
c) ![](images/AP_AB2_version1__318.gif)
d) ![](images/AP_AB2_version1__319.gif)
e) ![](images/AP_AB2_version1__320.gif)
10) What is the error when the integral
is approximated by the Trapezoidal rule with n = 3?
a) ![](images/AP_AB2_version1__322.gif)
b) ![](images/AP_AB2_version1__323.gif)
c) ![](images/AP_AB2_version1__324.gif)
d) ![](images/AP_AB2_version1__325.gif)
e) ![](images/AP_AB2_version1__326.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) $4,500
b) $21,250
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__329.gif)
b) ![](images/AP_AB2_version1__330.gif)
c) ![](images/AP_AB2_version1__331.gif)
d) ![](images/AP_AB2_version1__332.gif)
e) ![](images/AP_AB2_version1__333.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 4 square meters and the radius is increasing at the rate of 1/6 meters per minute?
a) ![](images/AP_AB2_version1__334.gif)
b) ![](images/AP_AB2_version1__335.gif)
c) ![](images/AP_AB2_version1__336.gif)
d) ![](images/AP_AB2_version1__337.gif)
e) ![](images/AP_AB2_version1__338.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__340.gif)
b) ![](images/AP_AB2_version1__341.gif)
c) ![](images/AP_AB2_version1__342.gif)
d) ![](images/AP_AB2_version1__343.gif)
e) ![](images/AP_AB2_version1__344.gif)
15) A rough approximation for ln(5) is 1.609. Use this approximation and differentials to approximate ln(519/100).
a) ![](images/AP_AB2_version1__345.gif)
b) ![](images/AP_AB2_version1__346.gif)
c) ![](images/AP_AB2_version1__347.gif)
d) ![](images/AP_AB2_version1__348.gif)
e) ![](images/AP_AB2_version1__349.gif)
16) The function
is differentiable everywhere. What is n?
a) ![](images/AP_AB2_version1__351.gif)
b) ![](images/AP_AB2_version1__352.gif)
c) ![](images/AP_AB2_version1__353.gif)
d) ![](images/AP_AB2_version1__354.gif)
e) ![](images/AP_AB2_version1__355.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__356.gif)
b) ![](images/AP_AB2_version1__357.gif)
c) ![](images/AP_AB2_version1__358.gif)
d) ![](images/AP_AB2_version1__359.gif)
e) ![](images/AP_AB2_version1__360.gif)