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__508.gif)
a) ![](images/AP_AB_version1__509.gif)
b) ![](images/AP_AB_version1__510.gif)
c) ![](images/AP_AB_version1__511.gif)
d) ![](images/AP_AB_version1__512.gif)
e) ![](images/AP_AB_version1__513.gif)
2) Find the slope of the tangent line to the graph of f at x = 4, given that![](images/AP_AB_version1__514.gif)
a) ![](images/AP_AB_version1__515.gif)
b) ![](images/AP_AB_version1__516.gif)
c) ![](images/AP_AB_version1__517.gif)
d) ![](images/AP_AB_version1__518.gif)
e) ![](images/AP_AB_version1__519.gif)
3) Determine![](images/AP_AB_version1__520.gif)
a) ![](images/AP_AB_version1__521.gif)
b) ![](images/AP_AB_version1__522.gif)
c) ![](images/AP_AB_version1__523.gif)
d) ![](images/AP_AB_version1__524.gif)
e) ![](images/AP_AB_version1__525.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__527.gif)
b) ![](images/AP_AB_version1__528.gif)
c) ![](images/AP_AB_version1__529.gif)
d) ![](images/AP_AB_version1__530.gif)
e) ![](images/AP_AB_version1__531.gif)
5) Given that
Determine the change in y with respect to x.
a) ![](images/AP_AB_version1__533.gif)
b) ![](images/AP_AB_version1__534.gif)
c) ![](images/AP_AB_version1__535.gif)
d) ![](images/AP_AB_version1__536.gif)
e) ![](images/AP_AB_version1__537.gif)
6) Compute the derivative of ![](images/AP_AB_version1__538.gif)
a) ![](images/AP_AB_version1__539.gif)
b) ![](images/AP_AB_version1__540.gif)
c) ![](images/AP_AB_version1__541.gif)
d) ![](images/AP_AB_version1__542.gif)
e) ![](images/AP_AB_version1__543.gif)
7) Compute![](images/AP_AB_version1__544.gif)
a) ![](images/AP_AB_version1__545.gif)
b) ![](images/AP_AB_version1__546.gif)
c) ![](images/AP_AB_version1__547.gif)
d) ![](images/AP_AB_version1__548.gif)
e) ![](images/AP_AB_version1__549.gif)
8) Determine![](images/AP_AB_version1__550.gif)
a) ![](images/AP_AB_version1__551.gif)
b) ![](images/AP_AB_version1__552.gif)
c) ![](images/AP_AB_version1__553.gif)
d) ![](images/AP_AB_version1__554.gif)
e) ![](images/AP_AB_version1__555.gif)
9) Give the equation of the normal line to the graph of
at the point ( 0 , -2 ).
a) ![](images/AP_AB_version1__557.gif)
b) ![](images/AP_AB_version1__558.gif)
c) ![](images/AP_AB_version1__559.gif)
d) ![](images/AP_AB_version1__560.gif)
e) ![](images/AP_AB_version1__561.gif)
10) Determine the concavity of the graph of
at x =
.
a) ![](images/AP_AB_version1__563.gif)
b) ![](images/AP_AB_version1__564.gif)
c) ![](images/AP_AB_version1__565.gif)
d) ![](images/AP_AB_version1__566.gif)
e) ![](images/AP_AB_version1__567.gif)
11) Compute![](images/AP_AB_version1__568.gif)
a) ![](images/AP_AB_version1__569.gif)
b) ![](images/AP_AB_version1__570.gif)
c) ![](images/AP_AB_version1__571.gif)
d) ![](images/AP_AB_version1__572.gif)
e) ![](images/AP_AB_version1__573.gif)
12) Give the value of x where the function
has a local minimum.
a) ![](images/AP_AB_version1__575.gif)
b) ![](images/AP_AB_version1__576.gif)
c) ![](images/AP_AB_version1__577.gif)
d) ![](images/AP_AB_version1__578.gif)
e) ![](images/AP_AB_version1__579.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__581.gif)
b) ![](images/AP_AB_version1__582.gif)
c) ![](images/AP_AB_version1__583.gif)
d) ![](images/AP_AB_version1__584.gif)
e) ![](images/AP_AB_version1__585.gif)
14) Compute![](images/AP_AB_version1__586.gif)
a) ![](images/AP_AB_version1__587.gif)
b) ![](images/AP_AB_version1__588.gif)
c) ![](images/AP_AB_version1__589.gif)
d) ![](images/AP_AB_version1__590.gif)
e) ![](images/AP_AB_version1__591.gif)
15) What is the average value of the function
on the interval from x = -4 to x = -1?
a) ![](images/AP_AB_version1__593.gif)
b) ![](images/AP_AB_version1__594.gif)
c) ![](images/AP_AB_version1__595.gif)
d) ![](images/AP_AB_version1__596.gif)
e) ![](images/AP_AB_version1__597.gif)
16) Compute![](images/AP_AB_version1__598.gif)
a) ![](images/AP_AB_version1__599.gif)
b) ![](images/AP_AB_version1__600.gif)
c) ![](images/AP_AB_version1__601.gif)
d) ![](images/AP_AB_version1__602.gif)
e) ![](images/AP_AB_version1__603.gif)
17) Find the instantaneous rate of change of
at t = 0.
a) ![](images/AP_AB_version1__605.gif)
b) ![](images/AP_AB_version1__606.gif)
c) ![](images/AP_AB_version1__607.gif)
d) ![](images/AP_AB_version1__608.gif)
e) ![](images/AP_AB_version1__609.gif)
18) Compute![](images/AP_AB_version1__610.gif)
a) ![](images/AP_AB_version1__611.gif)
b) ![](images/AP_AB_version1__612.gif)
c) ![](images/AP_AB_version1__613.gif)
d) ![](images/AP_AB_version1__614.gif)
e) ![](images/AP_AB_version1__615.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__617.gif)
b) ![](images/AP_AB_version1__618.gif)
c) ![](images/AP_AB_version1__619.gif)
d) ![](images/AP_AB_version1__620.gif)
e) ![](images/AP_AB_version1__621.gif)
20) Compute![](images/AP_AB_version1__622.gif)
a) ![](images/AP_AB_version1__623.gif)
b) ![](images/AP_AB_version1__624.gif)
c) ![](images/AP_AB_version1__625.gif)
d) ![](images/AP_AB_version1__626.gif)
e) ![](images/AP_AB_version1__627.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__630.gif)
b) ![](images/AP_AB_version1__631.gif)
c) ![](images/AP_AB_version1__632.gif)
d) ![](images/AP_AB_version1__633.gif)
e) ![](images/AP_AB_version1__634.gif)
22) Determine![](images/AP_AB_version1__635.gif)
a) ![](images/AP_AB_version1__636.gif)
b) ![](images/AP_AB_version1__637.gif)
c) ![](images/AP_AB_version1__638.gif)
d) ![](images/AP_AB_version1__639.gif)
e) ![](images/AP_AB_version1__640.gif)
23) Determine![](images/AP_AB_version1__641.gif)
a) ![](images/AP_AB_version1__642.gif)
b) ![](images/AP_AB_version1__643.gif)
c) ![](images/AP_AB_version1__644.gif)
d) ![](images/AP_AB_version1__645.gif)
e) ![](images/AP_AB_version1__646.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__648.gif)
b) ![](images/AP_AB_version1__649.gif)
c) ![](images/AP_AB_version1__650.gif)
d) ![](images/AP_AB_version1__651.gif)
e) ![](images/AP_AB_version1__652.gif)
25) Determine![](images/AP_AB_version1__653.gif)
a) ![](images/AP_AB_version1__654.gif)
b) ![](images/AP_AB_version1__655.gif)
c) ![](images/AP_AB_version1__656.gif)
d) ![](images/AP_AB_version1__657.gif)
e) ![](images/AP_AB_version1__658.gif)
26) Determine the derivative of
at x =
/3.
a) ![](images/AP_AB_version1__660.gif)
b) ![](images/AP_AB_version1__661.gif)
c) ![](images/AP_AB_version1__662.gif)
d) ![](images/AP_AB_version1__663.gif)
e) ![](images/AP_AB_version1__664.gif)
27) Compute the derivative of![](images/AP_AB_version1__665.gif)
a) ![](images/AP_AB_version1__666.gif)
b) ![](images/AP_AB_version1__667.gif)
c) ![](images/AP_AB_version1__668.gif)
d) ![](images/AP_AB_version1__669.gif)
e) ![](images/AP_AB_version1__670.gif)
28) Determine![](images/AP_AB_version1__671.gif)
a) ![](images/AP_AB_version1__672.gif)
b) ![](images/AP_AB_version1__673.gif)
c) ![](images/AP_AB_version1__674.gif)
d) ![](images/AP_AB_version1__675.gif)
e) ![](images/AP_AB_version1__676.gif)