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__470.gif)
b) ![](images/AP_BC_version1__471.gif)
c) ![](images/AP_BC_version1__472.gif)
d) ![](images/AP_BC_version1__473.gif)
e) ![](images/AP_BC_version1__474.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__475.gif)
b) ![](images/AP_BC_version1__476.gif)
c) ![](images/AP_BC_version1__477.gif)
d) ![](images/AP_BC_version1__478.gif)
e) ![](images/AP_BC_version1__479.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__481.gif)
b) ![](images/AP_BC_version1__482.gif)
c) ![](images/AP_BC_version1__483.gif)
d) ![](images/AP_BC_version1__484.gif)
e) ![](images/AP_BC_version1__485.gif)
4) Determine dy/dt, given that
and![](images/AP_BC_version1__487.gif)
a) ![](images/AP_BC_version1__488.gif)
b) ![](images/AP_BC_version1__489.gif)
c) ![](images/AP_BC_version1__490.gif)
d) ![](images/AP_BC_version1__491.gif)
e) ![](images/AP_BC_version1__492.gif)
5) The function
is invertible. Give the slope of the normal line to the graph of f -1 at x = 4.
a) ![](images/AP_BC_version1__494.gif)
b) ![](images/AP_BC_version1__495.gif)
c) ![](images/AP_BC_version1__496.gif)
d) ![](images/AP_BC_version1__497.gif)
e) ![](images/AP_BC_version1__498.gif)
6) Determine![](images/AP_BC_version1__499.gif)
a) ![](images/AP_BC_version1__500.gif)
b) ![](images/AP_BC_version1__501.gif)
c) ![](images/AP_BC_version1__502.gif)
d) ![](images/AP_BC_version1__503.gif)
e) ![](images/AP_BC_version1__504.gif)
7) Give the polar representation for the circle of radius 2 centered at ( 0 , -2 ).
a) ![](images/AP_BC_version1__505.gif)
b) ![](images/AP_BC_version1__506.gif)
c) ![](images/AP_BC_version1__507.gif)
d) ![](images/AP_BC_version1__508.gif)
e) ![](images/AP_BC_version1__509.gif)
8) Determine![](images/AP_BC_version1__510.gif)
a) ![](images/AP_BC_version1__511.gif)
b) ![](images/AP_BC_version1__512.gif)
c) ![](images/AP_BC_version1__513.gif)
d) ![](images/AP_BC_version1__514.gif)
e) ![](images/AP_BC_version1__515.gif)
9) Determine![](images/AP_BC_version1__516.gif)
a) ![](images/AP_BC_version1__517.gif)
b) ![](images/AP_BC_version1__518.gif)
c) ![](images/AP_BC_version1__519.gif)
d) ![](images/AP_BC_version1__520.gif)
e) ![](images/AP_BC_version1__521.gif)
10) Give the radius of convergence for the series![](images/AP_BC_version1__522.gif)
a) ![](images/AP_BC_version1__523.gif)
b) ![](images/AP_BC_version1__524.gif)
c) ![](images/AP_BC_version1__525.gif)
d) ![](images/AP_BC_version1__526.gif)
e) ![](images/AP_BC_version1__527.gif)
11) Determine![](images/AP_BC_version1__528.gif)
a) ![](images/AP_BC_version1__529.gif)
b) ![](images/AP_BC_version1__530.gif)
c) ![](images/AP_BC_version1__531.gif)
d) ![](images/AP_BC_version1__532.gif)
e) ![](images/AP_BC_version1__533.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__535.gif)
a) ![](images/AP_BC_version1__536.gif)
b) ![](images/AP_BC_version1__537.gif)
c) ![](images/AP_BC_version1__538.gif)
d) ![](images/AP_BC_version1__539.gif)
e) ![](images/AP_BC_version1__540.gif)
14) Determine the y-intercept of the tangent line to the curve
at x = 6.
a) ![](images/AP_BC_version1__542.gif)
b) ![](images/AP_BC_version1__543.gif)
c) ![](images/AP_BC_version1__544.gif)
d) ![](images/AP_BC_version1__545.gif)
e) ![](images/AP_BC_version1__546.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__548.gif)
b) ![](images/AP_BC_version1__549.gif)
c) ![](images/AP_BC_version1__550.gif)
d) ![](images/AP_BC_version1__551.gif)
e) ![](images/AP_BC_version1__552.gif)
16) Give the average value of the function
on the interval [1,7].
a) ![](images/AP_BC_version1__554.gif)
b) ![](images/AP_BC_version1__555.gif)
c) ![](images/AP_BC_version1__556.gif)
d) ![](images/AP_BC_version1__557.gif)
e) ![](images/AP_BC_version1__558.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 40 square feet. Give the rate of change of the width (in ft/sec) when the height is 11 feet, if the height is decreasing at that moment at the rate of 11/10 ft/sec.
a) ![](images/AP_BC_version1__559.gif)
b) ![](images/AP_BC_version1__560.gif)
c) ![](images/AP_BC_version1__561.gif)
d) ![](images/AP_BC_version1__562.gif)
e) ![](images/AP_BC_version1__563.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__565.gif)
b) ![](images/AP_BC_version1__566.gif)
c) ![](images/AP_BC_version1__567.gif)
d) ![](images/AP_BC_version1__568.gif)
e) ![](images/AP_BC_version1__569.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__571.gif)
b) ![](images/AP_BC_version1__572.gif)
c) ![](images/AP_BC_version1__573.gif)
d) ![](images/AP_BC_version1__574.gif)
e) ![](images/AP_BC_version1__575.gif)
20) Compute![](images/AP_BC_version1__576.gif)
a) ![](images/AP_BC_version1__577.gif)
b) ![](images/AP_BC_version1__578.gif)
c) ![](images/AP_BC_version1__579.gif)
d) ![](images/AP_BC_version1__580.gif)
e) ![](images/AP_BC_version1__581.gif)
21) Determine![](images/AP_BC_version1__582.gif)
a) ![](images/AP_BC_version1__583.gif)
b) ![](images/AP_BC_version1__584.gif)
c) ![](images/AP_BC_version1__585.gif)
d) ![](images/AP_BC_version1__586.gif)
e) ![](images/AP_BC_version1__587.gif)
22) Determine![](images/AP_BC_version1__588.gif)
a) ![](images/AP_BC_version1__589.gif)
b) ![](images/AP_BC_version1__590.gif)
c) ![](images/AP_BC_version1__591.gif)
d) ![](images/AP_BC_version1__592.gif)
e) ![](images/AP_BC_version1__593.gif)
23) Give the exact value of![](images/AP_BC_version1__594.gif)
a) ![](images/AP_BC_version1__595.gif)
b) ![](images/AP_BC_version1__596.gif)
c) ![](images/AP_BC_version1__597.gif)
d) ![](images/AP_BC_version1__598.gif)
e) ![](images/AP_BC_version1__599.gif)
24) Determine![](images/AP_BC_version1__600.gif)
a) ![](images/AP_BC_version1__601.gif)
b) ![](images/AP_BC_version1__602.gif)
c) ![](images/AP_BC_version1__603.gif)
d) ![](images/AP_BC_version1__604.gif)
e) ![](images/AP_BC_version1__605.gif)
25) Give the derivative of ![](images/AP_BC_version1__606.gif)
a) ![](images/AP_BC_version1__607.gif)
b) ![](images/AP_BC_version1__608.gif)
c) ![](images/AP_BC_version1__609.gif)
d) ![](images/AP_BC_version1__610.gif)
e) ![](images/AP_BC_version1__611.gif)
26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function![](images/AP_BC_version1__612.gif)
a) ![](images/AP_BC_version1__613.gif)
b) ![](images/AP_BC_version1__614.gif)
c) ![](images/AP_BC_version1__615.gif)
d) ![](images/AP_BC_version1__616.gif)
e) ![](images/AP_BC_version1__617.gif)
27) Determine![](images/AP_BC_version1__618.gif)
a) ![](images/AP_BC_version1__619.gif)
b) ![](images/AP_BC_version1__620.gif)
c) ![](images/AP_BC_version1__621.gif)
d) ![](images/AP_BC_version1__622.gif)
e) ![](images/AP_BC_version1__623.gif)
28) Which of the following series converge(s)?![](images/AP_BC_version1__624.gif)
a) A and B
b) A, B and C
c) B only
d) A and C
e) B and C