AP Calculus Practice Exam
BC Version - Section I - Part A
Calculators ARE NOT Permitted On This Portion Of The Exam
28 Questions - 55 Minutes
1) Given
Find dy/dx.
a) ![](images/AP_BC_version1__158.gif)
b) ![](images/AP_BC_version1__159.gif)
c) ![](images/AP_BC_version1__160.gif)
d) ![](images/AP_BC_version1__161.gif)
e) ![](images/AP_BC_version1__162.gif)
2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x = 1 and x = e, about the y-axis.
a) ![](images/AP_BC_version1__163.gif)
b) ![](images/AP_BC_version1__164.gif)
c) ![](images/AP_BC_version1__165.gif)
d) ![](images/AP_BC_version1__166.gif)
e) ![](images/AP_BC_version1__167.gif)
3) The graph of the derivative of f is shown below.
Find the area bounded between the graph of f and the x-axis over the interval [-2,1], given that f(0) = 1.
a) ![](images/AP_BC_version1__169.gif)
b) ![](images/AP_BC_version1__170.gif)
c) ![](images/AP_BC_version1__171.gif)
d) ![](images/AP_BC_version1__172.gif)
e) ![](images/AP_BC_version1__173.gif)
4) Determine dy/dt, given that
and![](images/AP_BC_version1__175.gif)
a) ![](images/AP_BC_version1__176.gif)
b) ![](images/AP_BC_version1__177.gif)
c) ![](images/AP_BC_version1__178.gif)
d) ![](images/AP_BC_version1__179.gif)
e) ![](images/AP_BC_version1__180.gif)
5) The function
is invertible. Give the slope of the normal line to the graph of f -1 at x = 2.
a) ![](images/AP_BC_version1__182.gif)
b) ![](images/AP_BC_version1__183.gif)
c) ![](images/AP_BC_version1__184.gif)
d) ![](images/AP_BC_version1__185.gif)
e) ![](images/AP_BC_version1__186.gif)
6) Determine![](images/AP_BC_version1__187.gif)
a) ![](images/AP_BC_version1__188.gif)
b) ![](images/AP_BC_version1__189.gif)
c) ![](images/AP_BC_version1__190.gif)
d) ![](images/AP_BC_version1__191.gif)
e) ![](images/AP_BC_version1__192.gif)
7) Give the polar representation for the circle of radius 4 centered at ( 0 , 4 ).
a) ![](images/AP_BC_version1__193.gif)
b) ![](images/AP_BC_version1__194.gif)
c) ![](images/AP_BC_version1__195.gif)
d) ![](images/AP_BC_version1__196.gif)
e) ![](images/AP_BC_version1__197.gif)
8) Determine![](images/AP_BC_version1__198.gif)
a) ![](images/AP_BC_version1__199.gif)
b) ![](images/AP_BC_version1__200.gif)
c) ![](images/AP_BC_version1__201.gif)
d) ![](images/AP_BC_version1__202.gif)
e) ![](images/AP_BC_version1__203.gif)
9) Determine![](images/AP_BC_version1__204.gif)
a) ![](images/AP_BC_version1__205.gif)
b) ![](images/AP_BC_version1__206.gif)
c) ![](images/AP_BC_version1__207.gif)
d) ![](images/AP_BC_version1__208.gif)
e) ![](images/AP_BC_version1__209.gif)
10) Give the radius of convergence for the series![](images/AP_BC_version1__210.gif)
a) ![](images/AP_BC_version1__211.gif)
b) ![](images/AP_BC_version1__212.gif)
c) ![](images/AP_BC_version1__213.gif)
d) ![](images/AP_BC_version1__214.gif)
e) ![](images/AP_BC_version1__215.gif)
11) Determine![](images/AP_BC_version1__216.gif)
a) ![](images/AP_BC_version1__217.gif)
b) ![](images/AP_BC_version1__218.gif)
c) ![](images/AP_BC_version1__219.gif)
d) ![](images/AP_BC_version1__220.gif)
e) ![](images/AP_BC_version1__221.gif)
12) The position of a particle moving along the x-axis at time t is given by
At which of the following values of t will the particle change direction?I) t = 1/8
II) t = 1/6
III) t = 1
IV) t = 2
a) II, III and IV
b) I and II
c) I, II and III
d) III and IV
e) I, III and IV
13) Determine![](images/AP_BC_version1__223.gif)
a) ![](images/AP_BC_version1__224.gif)
b) ![](images/AP_BC_version1__225.gif)
c) ![](images/AP_BC_version1__226.gif)
d) ![](images/AP_BC_version1__227.gif)
e) ![](images/AP_BC_version1__228.gif)
14) Determine the y-intercept of the tangent line to the curve
at x = 2.
a) ![](images/AP_BC_version1__230.gif)
b) ![](images/AP_BC_version1__231.gif)
c) ![](images/AP_BC_version1__232.gif)
d) ![](images/AP_BC_version1__233.gif)
e) ![](images/AP_BC_version1__234.gif)
15) The function f is graphed below.
Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval [2,5].
a) ![](images/AP_BC_version1__236.gif)
b) ![](images/AP_BC_version1__237.gif)
c) ![](images/AP_BC_version1__238.gif)
d) ![](images/AP_BC_version1__239.gif)
e) ![](images/AP_BC_version1__240.gif)
16) Give the average value of the function
on the interval [1,3].
a) ![](images/AP_BC_version1__242.gif)
b) ![](images/AP_BC_version1__243.gif)
c) ![](images/AP_BC_version1__244.gif)
d) ![](images/AP_BC_version1__245.gif)
e) ![](images/AP_BC_version1__246.gif)
17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 60 square feet. Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of 1/2 ft/sec.
a) ![](images/AP_BC_version1__247.gif)
b) ![](images/AP_BC_version1__248.gif)
c) ![](images/AP_BC_version1__249.gif)
d) ![](images/AP_BC_version1__250.gif)
e) ![](images/AP_BC_version1__251.gif)
18) The graph of the derivative of f is shown below.
Give the number of values of x in the interval [-3,3] where the graph of f has inflection.
a) ![](images/AP_BC_version1__253.gif)
b) ![](images/AP_BC_version1__254.gif)
c) ![](images/AP_BC_version1__255.gif)
d) ![](images/AP_BC_version1__256.gif)
e) ![](images/AP_BC_version1__257.gif)
19) A rectangle has its base on the x-axis and its vertices on the positive portion of the parabola
What is the maximum possible area of this rectangle?
a) ![](images/AP_BC_version1__259.gif)
b) ![](images/AP_BC_version1__260.gif)
c) ![](images/AP_BC_version1__261.gif)
d) ![](images/AP_BC_version1__262.gif)
e) ![](images/AP_BC_version1__263.gif)
20) Compute![](images/AP_BC_version1__264.gif)
a) ![](images/AP_BC_version1__265.gif)
b) ![](images/AP_BC_version1__266.gif)
c) ![](images/AP_BC_version1__267.gif)
d) ![](images/AP_BC_version1__268.gif)
e) ![](images/AP_BC_version1__269.gif)
21) Determine![](images/AP_BC_version1__270.gif)
a) ![](images/AP_BC_version1__271.gif)
b) ![](images/AP_BC_version1__272.gif)
c) ![](images/AP_BC_version1__273.gif)
d) ![](images/AP_BC_version1__274.gif)
e) ![](images/AP_BC_version1__275.gif)
22) Determine![](images/AP_BC_version1__276.gif)
a) ![](images/AP_BC_version1__277.gif)
b) ![](images/AP_BC_version1__278.gif)
c) ![](images/AP_BC_version1__279.gif)
d) ![](images/AP_BC_version1__280.gif)
e) ![](images/AP_BC_version1__281.gif)
23) Give the exact value of![](images/AP_BC_version1__282.gif)
a) ![](images/AP_BC_version1__283.gif)
b) ![](images/AP_BC_version1__284.gif)
c) ![](images/AP_BC_version1__285.gif)
d) ![](images/AP_BC_version1__286.gif)
e) ![](images/AP_BC_version1__287.gif)
24) Determine![](images/AP_BC_version1__288.gif)
a) ![](images/AP_BC_version1__289.gif)
b) ![](images/AP_BC_version1__290.gif)
c) ![](images/AP_BC_version1__291.gif)
d) ![](images/AP_BC_version1__292.gif)
e) ![](images/AP_BC_version1__293.gif)
25) Give the derivative of ![](images/AP_BC_version1__294.gif)
a) ![](images/AP_BC_version1__295.gif)
b) ![](images/AP_BC_version1__296.gif)
c) ![](images/AP_BC_version1__297.gif)
d) ![](images/AP_BC_version1__298.gif)
e) ![](images/AP_BC_version1__299.gif)
26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function![](images/AP_BC_version1__300.gif)
a) ![](images/AP_BC_version1__301.gif)
b) ![](images/AP_BC_version1__302.gif)
c) ![](images/AP_BC_version1__303.gif)
d) ![](images/AP_BC_version1__304.gif)
e) ![](images/AP_BC_version1__305.gif)
27) Determine![](images/AP_BC_version1__306.gif)
a) ![](images/AP_BC_version1__307.gif)
b) ![](images/AP_BC_version1__308.gif)
c) ![](images/AP_BC_version1__309.gif)
d) ![](images/AP_BC_version1__310.gif)
e) ![](images/AP_BC_version1__311.gif)
28) Which of the following series converge(s)?![](images/AP_BC_version1__312.gif)
a) A and B
b) A, B and C
c) B only
d) A and C
e) B and C