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__170.gif)
a) ![](images/AP_AB_version1__171.gif)
b) ![](images/AP_AB_version1__172.gif)
c) ![](images/AP_AB_version1__173.gif)
d) ![](images/AP_AB_version1__174.gif)
e) ![](images/AP_AB_version1__175.gif)
2) Find the slope of the tangent line to the graph of f at x = 4, given that![](images/AP_AB_version1__176.gif)
a) ![](images/AP_AB_version1__177.gif)
b) ![](images/AP_AB_version1__178.gif)
c) ![](images/AP_AB_version1__179.gif)
d) ![](images/AP_AB_version1__180.gif)
e) ![](images/AP_AB_version1__181.gif)
3) Determine![](images/AP_AB_version1__182.gif)
a) ![](images/AP_AB_version1__183.gif)
b) ![](images/AP_AB_version1__184.gif)
c) ![](images/AP_AB_version1__185.gif)
d) ![](images/AP_AB_version1__186.gif)
e) ![](images/AP_AB_version1__187.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__189.gif)
b) ![](images/AP_AB_version1__190.gif)
c) ![](images/AP_AB_version1__191.gif)
d) ![](images/AP_AB_version1__192.gif)
e) ![](images/AP_AB_version1__193.gif)
5) Given that
Determine the change in y with respect to x.
a) ![](images/AP_AB_version1__195.gif)
b) ![](images/AP_AB_version1__196.gif)
c) ![](images/AP_AB_version1__197.gif)
d) ![](images/AP_AB_version1__198.gif)
e) ![](images/AP_AB_version1__199.gif)
6) Compute the derivative of ![](images/AP_AB_version1__200.gif)
a) ![](images/AP_AB_version1__201.gif)
b) ![](images/AP_AB_version1__202.gif)
c) ![](images/AP_AB_version1__203.gif)
d) ![](images/AP_AB_version1__204.gif)
e) ![](images/AP_AB_version1__205.gif)
7) Compute![](images/AP_AB_version1__206.gif)
a) ![](images/AP_AB_version1__207.gif)
b) ![](images/AP_AB_version1__208.gif)
c) ![](images/AP_AB_version1__209.gif)
d) ![](images/AP_AB_version1__210.gif)
e) ![](images/AP_AB_version1__211.gif)
8) Determine![](images/AP_AB_version1__212.gif)
a) ![](images/AP_AB_version1__213.gif)
b) ![](images/AP_AB_version1__214.gif)
c) ![](images/AP_AB_version1__215.gif)
d) ![](images/AP_AB_version1__216.gif)
e) ![](images/AP_AB_version1__217.gif)
9) Give the equation of the normal line to the graph of
at the point ( 0 , 4 ).
a) ![](images/AP_AB_version1__219.gif)
b) ![](images/AP_AB_version1__220.gif)
c) ![](images/AP_AB_version1__221.gif)
d) ![](images/AP_AB_version1__222.gif)
e) ![](images/AP_AB_version1__223.gif)
10) Determine the concavity of the graph of
at x =
.
a) ![](images/AP_AB_version1__225.gif)
b) ![](images/AP_AB_version1__226.gif)
c) ![](images/AP_AB_version1__227.gif)
d) ![](images/AP_AB_version1__228.gif)
e) ![](images/AP_AB_version1__229.gif)
11) Compute![](images/AP_AB_version1__230.gif)
a) ![](images/AP_AB_version1__231.gif)
b) ![](images/AP_AB_version1__232.gif)
c) ![](images/AP_AB_version1__233.gif)
d) ![](images/AP_AB_version1__234.gif)
e) ![](images/AP_AB_version1__235.gif)
12) Give the value of x where the function
has a local minimum.
a) ![](images/AP_AB_version1__237.gif)
b) ![](images/AP_AB_version1__238.gif)
c) ![](images/AP_AB_version1__239.gif)
d) ![](images/AP_AB_version1__240.gif)
e) ![](images/AP_AB_version1__241.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__243.gif)
b) ![](images/AP_AB_version1__244.gif)
c) ![](images/AP_AB_version1__245.gif)
d) ![](images/AP_AB_version1__246.gif)
e) ![](images/AP_AB_version1__247.gif)
14) Compute![](images/AP_AB_version1__248.gif)
a) ![](images/AP_AB_version1__249.gif)
b) ![](images/AP_AB_version1__250.gif)
c) ![](images/AP_AB_version1__251.gif)
d) ![](images/AP_AB_version1__252.gif)
e) ![](images/AP_AB_version1__253.gif)
15) What is the average value of the function
on the interval from x = -4 to x = -1?
a) ![](images/AP_AB_version1__255.gif)
b) ![](images/AP_AB_version1__256.gif)
c) ![](images/AP_AB_version1__257.gif)
d) ![](images/AP_AB_version1__258.gif)
e) ![](images/AP_AB_version1__259.gif)
16) Compute![](images/AP_AB_version1__260.gif)
a) ![](images/AP_AB_version1__261.gif)
b) ![](images/AP_AB_version1__262.gif)
c) ![](images/AP_AB_version1__263.gif)
d) ![](images/AP_AB_version1__264.gif)
e) ![](images/AP_AB_version1__265.gif)
17) Find the instantaneous rate of change of
at t = 0.
a) ![](images/AP_AB_version1__267.gif)
b) ![](images/AP_AB_version1__268.gif)
c) ![](images/AP_AB_version1__269.gif)
d) ![](images/AP_AB_version1__270.gif)
e) ![](images/AP_AB_version1__271.gif)
18) Compute![](images/AP_AB_version1__272.gif)
a) ![](images/AP_AB_version1__273.gif)
b) ![](images/AP_AB_version1__274.gif)
c) ![](images/AP_AB_version1__275.gif)
d) ![](images/AP_AB_version1__276.gif)
e) ![](images/AP_AB_version1__277.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__279.gif)
b) ![](images/AP_AB_version1__280.gif)
c) ![](images/AP_AB_version1__281.gif)
d) ![](images/AP_AB_version1__282.gif)
e) ![](images/AP_AB_version1__283.gif)
20) Compute![](images/AP_AB_version1__284.gif)
a) ![](images/AP_AB_version1__285.gif)
b) ![](images/AP_AB_version1__286.gif)
c) ![](images/AP_AB_version1__287.gif)
d) ![](images/AP_AB_version1__288.gif)
e) ![](images/AP_AB_version1__289.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__292.gif)
b) ![](images/AP_AB_version1__293.gif)
c) ![](images/AP_AB_version1__294.gif)
d) ![](images/AP_AB_version1__295.gif)
e) ![](images/AP_AB_version1__296.gif)
22) Determine![](images/AP_AB_version1__297.gif)
a) ![](images/AP_AB_version1__298.gif)
b) ![](images/AP_AB_version1__299.gif)
c) ![](images/AP_AB_version1__300.gif)
d) ![](images/AP_AB_version1__301.gif)
e) ![](images/AP_AB_version1__302.gif)
23) Determine![](images/AP_AB_version1__303.gif)
a) ![](images/AP_AB_version1__304.gif)
b) ![](images/AP_AB_version1__305.gif)
c) ![](images/AP_AB_version1__306.gif)
d) ![](images/AP_AB_version1__307.gif)
e) ![](images/AP_AB_version1__308.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__310.gif)
b) ![](images/AP_AB_version1__311.gif)
c) ![](images/AP_AB_version1__312.gif)
d) ![](images/AP_AB_version1__313.gif)
e) ![](images/AP_AB_version1__314.gif)
25) Determine![](images/AP_AB_version1__315.gif)
a) ![](images/AP_AB_version1__316.gif)
b) ![](images/AP_AB_version1__317.gif)
c) ![](images/AP_AB_version1__318.gif)
d) ![](images/AP_AB_version1__319.gif)
e) ![](images/AP_AB_version1__320.gif)
26) Determine the derivative of
at x =
/2.
a) ![](images/AP_AB_version1__322.gif)
b) ![](images/AP_AB_version1__323.gif)
c) ![](images/AP_AB_version1__324.gif)
d) ![](images/AP_AB_version1__325.gif)
e) ![](images/AP_AB_version1__326.gif)
27) Compute the derivative of![](images/AP_AB_version1__327.gif)
a) ![](images/AP_AB_version1__328.gif)
b) ![](images/AP_AB_version1__329.gif)
c) ![](images/AP_AB_version1__330.gif)
d) ![](images/AP_AB_version1__331.gif)
e) ![](images/AP_AB_version1__332.gif)
28) Determine![](images/AP_AB_version1__333.gif)
a) ![](images/AP_AB_version1__334.gif)
b) ![](images/AP_AB_version1__335.gif)
c) ![](images/AP_AB_version1__336.gif)
d) ![](images/AP_AB_version1__337.gif)
e) ![](images/AP_AB_version1__338.gif)