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__314.gif)
b) ![](images/AP_BC_version1__315.gif)
c) ![](images/AP_BC_version1__316.gif)
d) ![](images/AP_BC_version1__317.gif)
e) ![](images/AP_BC_version1__318.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__319.gif)
b) ![](images/AP_BC_version1__320.gif)
c) ![](images/AP_BC_version1__321.gif)
d) ![](images/AP_BC_version1__322.gif)
e) ![](images/AP_BC_version1__323.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__325.gif)
b) ![](images/AP_BC_version1__326.gif)
c) ![](images/AP_BC_version1__327.gif)
d) ![](images/AP_BC_version1__328.gif)
e) ![](images/AP_BC_version1__329.gif)
4) Determine dy/dt, given that
and![](images/AP_BC_version1__331.gif)
a) ![](images/AP_BC_version1__332.gif)
b) ![](images/AP_BC_version1__333.gif)
c) ![](images/AP_BC_version1__334.gif)
d) ![](images/AP_BC_version1__335.gif)
e) ![](images/AP_BC_version1__336.gif)
5) The function
is invertible. Give the slope of the normal line to the graph of f -1 at x = 3.
a) ![](images/AP_BC_version1__338.gif)
b) ![](images/AP_BC_version1__339.gif)
c) ![](images/AP_BC_version1__340.gif)
d) ![](images/AP_BC_version1__341.gif)
e) ![](images/AP_BC_version1__342.gif)
6) Determine![](images/AP_BC_version1__343.gif)
a) ![](images/AP_BC_version1__344.gif)
b) ![](images/AP_BC_version1__345.gif)
c) ![](images/AP_BC_version1__346.gif)
d) ![](images/AP_BC_version1__347.gif)
e) ![](images/AP_BC_version1__348.gif)
7) Give the polar representation for the circle of radius 3 centered at ( 0 , 3 ).
a) ![](images/AP_BC_version1__349.gif)
b) ![](images/AP_BC_version1__350.gif)
c) ![](images/AP_BC_version1__351.gif)
d) ![](images/AP_BC_version1__352.gif)
e) ![](images/AP_BC_version1__353.gif)
8) Determine![](images/AP_BC_version1__354.gif)
a) ![](images/AP_BC_version1__355.gif)
b) ![](images/AP_BC_version1__356.gif)
c) ![](images/AP_BC_version1__357.gif)
d) ![](images/AP_BC_version1__358.gif)
e) ![](images/AP_BC_version1__359.gif)
9) Determine![](images/AP_BC_version1__360.gif)
a) ![](images/AP_BC_version1__361.gif)
b) ![](images/AP_BC_version1__362.gif)
c) ![](images/AP_BC_version1__363.gif)
d) ![](images/AP_BC_version1__364.gif)
e) ![](images/AP_BC_version1__365.gif)
10) Give the radius of convergence for the series![](images/AP_BC_version1__366.gif)
a) ![](images/AP_BC_version1__367.gif)
b) ![](images/AP_BC_version1__368.gif)
c) ![](images/AP_BC_version1__369.gif)
d) ![](images/AP_BC_version1__370.gif)
e) ![](images/AP_BC_version1__371.gif)
11) Determine![](images/AP_BC_version1__372.gif)
a) ![](images/AP_BC_version1__373.gif)
b) ![](images/AP_BC_version1__374.gif)
c) ![](images/AP_BC_version1__375.gif)
d) ![](images/AP_BC_version1__376.gif)
e) ![](images/AP_BC_version1__377.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) I and II
b) I, III and IV
c) I, II and III
d) II, III and IV
e) III and IV
13) Determine![](images/AP_BC_version1__379.gif)
a) ![](images/AP_BC_version1__380.gif)
b) ![](images/AP_BC_version1__381.gif)
c) ![](images/AP_BC_version1__382.gif)
d) ![](images/AP_BC_version1__383.gif)
e) ![](images/AP_BC_version1__384.gif)
14) Determine the y-intercept of the tangent line to the curve
at x = 3.
a) ![](images/AP_BC_version1__386.gif)
b) ![](images/AP_BC_version1__387.gif)
c) ![](images/AP_BC_version1__388.gif)
d) ![](images/AP_BC_version1__389.gif)
e) ![](images/AP_BC_version1__390.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__392.gif)
b) ![](images/AP_BC_version1__393.gif)
c) ![](images/AP_BC_version1__394.gif)
d) ![](images/AP_BC_version1__395.gif)
e) ![](images/AP_BC_version1__396.gif)
16) Give the average value of the function
on the interval [1,5].
a) ![](images/AP_BC_version1__398.gif)
b) ![](images/AP_BC_version1__399.gif)
c) ![](images/AP_BC_version1__400.gif)
d) ![](images/AP_BC_version1__401.gif)
e) ![](images/AP_BC_version1__402.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 10 feet, if the height is decreasing at that moment at the rate of 1 ft/sec.
a) ![](images/AP_BC_version1__403.gif)
b) ![](images/AP_BC_version1__404.gif)
c) ![](images/AP_BC_version1__405.gif)
d) ![](images/AP_BC_version1__406.gif)
e) ![](images/AP_BC_version1__407.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__409.gif)
b) ![](images/AP_BC_version1__410.gif)
c) ![](images/AP_BC_version1__411.gif)
d) ![](images/AP_BC_version1__412.gif)
e) ![](images/AP_BC_version1__413.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__415.gif)
b) ![](images/AP_BC_version1__416.gif)
c) ![](images/AP_BC_version1__417.gif)
d) ![](images/AP_BC_version1__418.gif)
e) ![](images/AP_BC_version1__419.gif)
20) Compute![](images/AP_BC_version1__420.gif)
a) ![](images/AP_BC_version1__421.gif)
b) ![](images/AP_BC_version1__422.gif)
c) ![](images/AP_BC_version1__423.gif)
d) ![](images/AP_BC_version1__424.gif)
e) ![](images/AP_BC_version1__425.gif)
21) Determine![](images/AP_BC_version1__426.gif)
a) ![](images/AP_BC_version1__427.gif)
b) ![](images/AP_BC_version1__428.gif)
c) ![](images/AP_BC_version1__429.gif)
d) ![](images/AP_BC_version1__430.gif)
e) ![](images/AP_BC_version1__431.gif)
22) Determine![](images/AP_BC_version1__432.gif)
a) ![](images/AP_BC_version1__433.gif)
b) ![](images/AP_BC_version1__434.gif)
c) ![](images/AP_BC_version1__435.gif)
d) ![](images/AP_BC_version1__436.gif)
e) ![](images/AP_BC_version1__437.gif)
23) Give the exact value of![](images/AP_BC_version1__438.gif)
a) ![](images/AP_BC_version1__439.gif)
b) ![](images/AP_BC_version1__440.gif)
c) ![](images/AP_BC_version1__441.gif)
d) ![](images/AP_BC_version1__442.gif)
e) ![](images/AP_BC_version1__443.gif)
24) Determine![](images/AP_BC_version1__444.gif)
a) ![](images/AP_BC_version1__445.gif)
b) ![](images/AP_BC_version1__446.gif)
c) ![](images/AP_BC_version1__447.gif)
d) ![](images/AP_BC_version1__448.gif)
e) ![](images/AP_BC_version1__449.gif)
25) Give the derivative of ![](images/AP_BC_version1__450.gif)
a) ![](images/AP_BC_version1__451.gif)
b) ![](images/AP_BC_version1__452.gif)
c) ![](images/AP_BC_version1__453.gif)
d) ![](images/AP_BC_version1__454.gif)
e) ![](images/AP_BC_version1__455.gif)
26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function![](images/AP_BC_version1__456.gif)
a) ![](images/AP_BC_version1__457.gif)
b) ![](images/AP_BC_version1__458.gif)
c) ![](images/AP_BC_version1__459.gif)
d) ![](images/AP_BC_version1__460.gif)
e) ![](images/AP_BC_version1__461.gif)
27) Determine![](images/AP_BC_version1__462.gif)
a) ![](images/AP_BC_version1__463.gif)
b) ![](images/AP_BC_version1__464.gif)
c) ![](images/AP_BC_version1__465.gif)
d) ![](images/AP_BC_version1__466.gif)
e) ![](images/AP_BC_version1__467.gif)
28) Which of the following series converge(s)?![](images/AP_BC_version1__468.gif)
a) B and C
b) A, B and C
c) B only
d) A and B
e) A and C