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__2.gif)
b) ![](images/AP_AB2_version1__3.gif)
c) ![](images/AP_AB2_version1__4.gif)
d) ![](images/AP_AB2_version1__5.gif)
e) ![](images/AP_AB2_version1__6.gif)
2) The function
is invertible. Give the derivative of f -1 at x = 2.
a) ![](images/AP_AB2_version1__8.gif)
b) ![](images/AP_AB2_version1__9.gif)
c) ![](images/AP_AB2_version1__10.gif)
d) ![](images/AP_AB2_version1__11.gif)
e) ![](images/AP_AB2_version1__12.gif)
3) The derivative of f is graphed below.
Give a value of x where f has a local maximum.
a) ![](images/AP_AB2_version1__14.gif)
b) ![](images/AP_AB2_version1__15.gif)
c) ![](images/AP_AB2_version1__16.gif)
d) ![](images/AP_AB2_version1__17.gif)
e) ![](images/AP_AB2_version1__18.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 and 4
b) 3 only
c) 2 only
d) 1 and 3
e) 1 and 4
5) Given
Determine![](images/AP_AB2_version1__21.gif)
a) ![](images/AP_AB2_version1__22.gif)
b) ![](images/AP_AB2_version1__23.gif)
c) ![](images/AP_AB2_version1__24.gif)
d) ![](images/AP_AB2_version1__25.gif)
e) ![](images/AP_AB2_version1__26.gif)
6) Give the approximate location of a local maximum for the function ![](images/AP_AB2_version1__27.gif)
a) ![](images/AP_AB2_version1__28.gif)
b) ![](images/AP_AB2_version1__29.gif)
c) ![](images/AP_AB2_version1__30.gif)
d) ![](images/AP_AB2_version1__31.gif)
e) ![](images/AP_AB2_version1__32.gif)
7) Give the approximate average value of the function
over the interval [1,4].
a) ![](images/AP_AB2_version1__34.gif)
b) ![](images/AP_AB2_version1__35.gif)
c) ![](images/AP_AB2_version1__36.gif)
d) ![](images/AP_AB2_version1__37.gif)
e) ![](images/AP_AB2_version1__38.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__40.gif)
b) ![](images/AP_AB2_version1__41.gif)
c) ![](images/AP_AB2_version1__42.gif)
d) ![](images/AP_AB2_version1__43.gif)
e) ![](images/AP_AB2_version1__44.gif)
9) What is the approximate instantaneous rate of change of the function
at t =
/7?
a) ![](images/AP_AB2_version1__46.gif)
b) ![](images/AP_AB2_version1__47.gif)
c) ![](images/AP_AB2_version1__48.gif)
d) ![](images/AP_AB2_version1__49.gif)
e) ![](images/AP_AB2_version1__50.gif)
10) What is the error when the integral
is approximated by the Trapezoidal rule with n = 3?
a) ![](images/AP_AB2_version1__52.gif)
b) ![](images/AP_AB2_version1__53.gif)
c) ![](images/AP_AB2_version1__54.gif)
d) ![](images/AP_AB2_version1__55.gif)
e) ![](images/AP_AB2_version1__56.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) $18,350
b) $4,500
c) $21,250
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__59.gif)
b) ![](images/AP_AB2_version1__60.gif)
c) ![](images/AP_AB2_version1__61.gif)
d) ![](images/AP_AB2_version1__62.gif)
e) ![](images/AP_AB2_version1__63.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 5 square meters and the radius is increasing at the rate of 1/3 meters per minute?
a) ![](images/AP_AB2_version1__64.gif)
b) ![](images/AP_AB2_version1__65.gif)
c) ![](images/AP_AB2_version1__66.gif)
d) ![](images/AP_AB2_version1__67.gif)
e) ![](images/AP_AB2_version1__68.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__70.gif)
b) ![](images/AP_AB2_version1__71.gif)
c) ![](images/AP_AB2_version1__72.gif)
d) ![](images/AP_AB2_version1__73.gif)
e) ![](images/AP_AB2_version1__74.gif)
15) A rough approximation for ln(5) is 1.609. Use this approximation and differentials to approximate ln(128/25).
a) ![](images/AP_AB2_version1__75.gif)
b) ![](images/AP_AB2_version1__76.gif)
c) ![](images/AP_AB2_version1__77.gif)
d) ![](images/AP_AB2_version1__78.gif)
e) ![](images/AP_AB2_version1__79.gif)
16) The function
is differentiable everywhere. What is n?
a) ![](images/AP_AB2_version1__81.gif)
b) ![](images/AP_AB2_version1__82.gif)
c) ![](images/AP_AB2_version1__83.gif)
d) ![](images/AP_AB2_version1__84.gif)
e) ![](images/AP_AB2_version1__85.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__86.gif)
b) ![](images/AP_AB2_version1__87.gif)
c) ![](images/AP_AB2_version1__88.gif)
d) ![](images/AP_AB2_version1__89.gif)
e) ![](images/AP_AB2_version1__90.gif)