AP Calculus Practice Exam
AB Version - Section I - Part A
Calculators ARE NOT Permitted On This Portion Of The Exam
28 Questions - 55 Minutes
1) Give f(g(-2)), given that![](images/AP_AB_version1__339.gif)
a) ![](images/AP_AB_version1__340.gif)
b) ![](images/AP_AB_version1__341.gif)
c) ![](images/AP_AB_version1__342.gif)
d) ![](images/AP_AB_version1__343.gif)
e) ![](images/AP_AB_version1__344.gif)
2) Find the slope of the tangent line to the graph of f at x = 4, given that![](images/AP_AB_version1__345.gif)
a) ![](images/AP_AB_version1__346.gif)
b) ![](images/AP_AB_version1__347.gif)
c) ![](images/AP_AB_version1__348.gif)
d) ![](images/AP_AB_version1__349.gif)
e) ![](images/AP_AB_version1__350.gif)
3) Determine![](images/AP_AB_version1__351.gif)
a) ![](images/AP_AB_version1__352.gif)
b) ![](images/AP_AB_version1__353.gif)
c) ![](images/AP_AB_version1__354.gif)
d) ![](images/AP_AB_version1__355.gif)
e) ![](images/AP_AB_version1__356.gif)
4) Let
A region is bounded between the graphs of y = -1 and y = f(x) for x between -1 and 0, and between the graphs of y = 1 and y = f(x) for x between 0 and 1. Give an integral that corresponds to the area of this region.
a) ![](images/AP_AB_version1__358.gif)
b) ![](images/AP_AB_version1__359.gif)
c) ![](images/AP_AB_version1__360.gif)
d) ![](images/AP_AB_version1__361.gif)
e) ![](images/AP_AB_version1__362.gif)
5) Given that
Determine the change in y with respect to x.
a) ![](images/AP_AB_version1__364.gif)
b) ![](images/AP_AB_version1__365.gif)
c) ![](images/AP_AB_version1__366.gif)
d) ![](images/AP_AB_version1__367.gif)
e) ![](images/AP_AB_version1__368.gif)
6) Compute the derivative of ![](images/AP_AB_version1__369.gif)
a) ![](images/AP_AB_version1__370.gif)
b) ![](images/AP_AB_version1__371.gif)
c) ![](images/AP_AB_version1__372.gif)
d) ![](images/AP_AB_version1__373.gif)
e) ![](images/AP_AB_version1__374.gif)
7) Compute![](images/AP_AB_version1__375.gif)
a) ![](images/AP_AB_version1__376.gif)
b) ![](images/AP_AB_version1__377.gif)
c) ![](images/AP_AB_version1__378.gif)
d) ![](images/AP_AB_version1__379.gif)
e) ![](images/AP_AB_version1__380.gif)
8) Determine![](images/AP_AB_version1__381.gif)
a) ![](images/AP_AB_version1__382.gif)
b) ![](images/AP_AB_version1__383.gif)
c) ![](images/AP_AB_version1__384.gif)
d) ![](images/AP_AB_version1__385.gif)
e) ![](images/AP_AB_version1__386.gif)
9) Give the equation of the normal line to the graph of
at the point ( 0 , 3 ).
a) ![](images/AP_AB_version1__388.gif)
b) ![](images/AP_AB_version1__389.gif)
c) ![](images/AP_AB_version1__390.gif)
d) ![](images/AP_AB_version1__391.gif)
e) ![](images/AP_AB_version1__392.gif)
10) Determine the concavity of the graph of
at x =
.
a) ![](images/AP_AB_version1__394.gif)
b) ![](images/AP_AB_version1__395.gif)
c) ![](images/AP_AB_version1__396.gif)
d) ![](images/AP_AB_version1__397.gif)
e) ![](images/AP_AB_version1__398.gif)
11) Compute![](images/AP_AB_version1__399.gif)
a) ![](images/AP_AB_version1__400.gif)
b) ![](images/AP_AB_version1__401.gif)
c) ![](images/AP_AB_version1__402.gif)
d) ![](images/AP_AB_version1__403.gif)
e) ![](images/AP_AB_version1__404.gif)
12) Give the value of x where the function
has a local minimum.
a) ![](images/AP_AB_version1__406.gif)
b) ![](images/AP_AB_version1__407.gif)
c) ![](images/AP_AB_version1__408.gif)
d) ![](images/AP_AB_version1__409.gif)
e) ![](images/AP_AB_version1__410.gif)
13) The slope of the tangent line to the graph of
at x = 0 is 4. Give the value of c.
a) ![](images/AP_AB_version1__412.gif)
b) ![](images/AP_AB_version1__413.gif)
c) ![](images/AP_AB_version1__414.gif)
d) ![](images/AP_AB_version1__415.gif)
e) ![](images/AP_AB_version1__416.gif)
14) Compute![](images/AP_AB_version1__417.gif)
a) ![](images/AP_AB_version1__418.gif)
b) ![](images/AP_AB_version1__419.gif)
c) ![](images/AP_AB_version1__420.gif)
d) ![](images/AP_AB_version1__421.gif)
e) ![](images/AP_AB_version1__422.gif)
15) What is the average value of the function
on the interval from x = -3 to x = -1?
a) ![](images/AP_AB_version1__424.gif)
b) ![](images/AP_AB_version1__425.gif)
c) ![](images/AP_AB_version1__426.gif)
d) ![](images/AP_AB_version1__427.gif)
e) ![](images/AP_AB_version1__428.gif)
16) Compute![](images/AP_AB_version1__429.gif)
a) ![](images/AP_AB_version1__430.gif)
b) ![](images/AP_AB_version1__431.gif)
c) ![](images/AP_AB_version1__432.gif)
d) ![](images/AP_AB_version1__433.gif)
e) ![](images/AP_AB_version1__434.gif)
17) Find the instantaneous rate of change of
at t = 0.
a) ![](images/AP_AB_version1__436.gif)
b) ![](images/AP_AB_version1__437.gif)
c) ![](images/AP_AB_version1__438.gif)
d) ![](images/AP_AB_version1__439.gif)
e) ![](images/AP_AB_version1__440.gif)
18) Compute![](images/AP_AB_version1__441.gif)
a) ![](images/AP_AB_version1__442.gif)
b) ![](images/AP_AB_version1__443.gif)
c) ![](images/AP_AB_version1__444.gif)
d) ![](images/AP_AB_version1__445.gif)
e) ![](images/AP_AB_version1__446.gif)
19) A solid is generated by rotating the region enclosed by the graph of
the lines x = 1, x = 2, and y = 1, about the x-axis. Which of the following integrals gives the volume of the solid?
a) ![](images/AP_AB_version1__448.gif)
b) ![](images/AP_AB_version1__449.gif)
c) ![](images/AP_AB_version1__450.gif)
d) ![](images/AP_AB_version1__451.gif)
e) ![](images/AP_AB_version1__452.gif)
20) Compute![](images/AP_AB_version1__453.gif)
a) ![](images/AP_AB_version1__454.gif)
b) ![](images/AP_AB_version1__455.gif)
c) ![](images/AP_AB_version1__456.gif)
d) ![](images/AP_AB_version1__457.gif)
e) ![](images/AP_AB_version1__458.gif)
21) Given y > 0 and
If the point
is on the graph relating x and y, then what is y when x = 0?
a) ![](images/AP_AB_version1__461.gif)
b) ![](images/AP_AB_version1__462.gif)
c) ![](images/AP_AB_version1__463.gif)
d) ![](images/AP_AB_version1__464.gif)
e) ![](images/AP_AB_version1__465.gif)
22) Determine![](images/AP_AB_version1__466.gif)
a) ![](images/AP_AB_version1__467.gif)
b) ![](images/AP_AB_version1__468.gif)
c) ![](images/AP_AB_version1__469.gif)
d) ![](images/AP_AB_version1__470.gif)
e) ![](images/AP_AB_version1__471.gif)
23) Determine![](images/AP_AB_version1__472.gif)
a) ![](images/AP_AB_version1__473.gif)
b) ![](images/AP_AB_version1__474.gif)
c) ![](images/AP_AB_version1__475.gif)
d) ![](images/AP_AB_version1__476.gif)
e) ![](images/AP_AB_version1__477.gif)
24) A particle's acceleration for t > 0 is given by
The particle's initial position is 2 and its velocity at t = 1 is 5. What is the position of the particle at t = 2?
a) ![](images/AP_AB_version1__479.gif)
b) ![](images/AP_AB_version1__480.gif)
c) ![](images/AP_AB_version1__481.gif)
d) ![](images/AP_AB_version1__482.gif)
e) ![](images/AP_AB_version1__483.gif)
25) Determine![](images/AP_AB_version1__484.gif)
a) ![](images/AP_AB_version1__485.gif)
b) ![](images/AP_AB_version1__486.gif)
c) ![](images/AP_AB_version1__487.gif)
d) ![](images/AP_AB_version1__488.gif)
e) ![](images/AP_AB_version1__489.gif)
26) Determine the derivative of
at x =
/2.
a) ![](images/AP_AB_version1__491.gif)
b) ![](images/AP_AB_version1__492.gif)
c) ![](images/AP_AB_version1__493.gif)
d) ![](images/AP_AB_version1__494.gif)
e) ![](images/AP_AB_version1__495.gif)
27) Compute the derivative of![](images/AP_AB_version1__496.gif)
a) ![](images/AP_AB_version1__497.gif)
b) ![](images/AP_AB_version1__498.gif)
c) ![](images/AP_AB_version1__499.gif)
d) ![](images/AP_AB_version1__500.gif)
e) ![](images/AP_AB_version1__501.gif)
28) Determine![](images/AP_AB_version1__502.gif)
a) ![](images/AP_AB_version1__503.gif)
b) ![](images/AP_AB_version1__504.gif)
c) ![](images/AP_AB_version1__505.gif)
d) ![](images/AP_AB_version1__506.gif)
e) ![](images/AP_AB_version1__507.gif)