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__626.gif)
b) ![](images/AP_BC_version1__627.gif)
c) ![](images/AP_BC_version1__628.gif)
d) ![](images/AP_BC_version1__629.gif)
e) ![](images/AP_BC_version1__630.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__631.gif)
b) ![](images/AP_BC_version1__632.gif)
c) ![](images/AP_BC_version1__633.gif)
d) ![](images/AP_BC_version1__634.gif)
e) ![](images/AP_BC_version1__635.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__637.gif)
b) ![](images/AP_BC_version1__638.gif)
c) ![](images/AP_BC_version1__639.gif)
d) ![](images/AP_BC_version1__640.gif)
e) ![](images/AP_BC_version1__641.gif)
4) Determine dy/dt, given that
and![](images/AP_BC_version1__643.gif)
a) ![](images/AP_BC_version1__644.gif)
b) ![](images/AP_BC_version1__645.gif)
c) ![](images/AP_BC_version1__646.gif)
d) ![](images/AP_BC_version1__647.gif)
e) ![](images/AP_BC_version1__648.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__650.gif)
b) ![](images/AP_BC_version1__651.gif)
c) ![](images/AP_BC_version1__652.gif)
d) ![](images/AP_BC_version1__653.gif)
e) ![](images/AP_BC_version1__654.gif)
6) Determine![](images/AP_BC_version1__655.gif)
a) ![](images/AP_BC_version1__656.gif)
b) ![](images/AP_BC_version1__657.gif)
c) ![](images/AP_BC_version1__658.gif)
d) ![](images/AP_BC_version1__659.gif)
e) ![](images/AP_BC_version1__660.gif)
7) Give the polar representation for the circle of radius 3 centered at ( 0 , -3 ).
a) ![](images/AP_BC_version1__661.gif)
b) ![](images/AP_BC_version1__662.gif)
c) ![](images/AP_BC_version1__663.gif)
d) ![](images/AP_BC_version1__664.gif)
e) ![](images/AP_BC_version1__665.gif)
8) Determine![](images/AP_BC_version1__666.gif)
a) ![](images/AP_BC_version1__667.gif)
b) ![](images/AP_BC_version1__668.gif)
c) ![](images/AP_BC_version1__669.gif)
d) ![](images/AP_BC_version1__670.gif)
e) ![](images/AP_BC_version1__671.gif)
9) Determine![](images/AP_BC_version1__672.gif)
a) ![](images/AP_BC_version1__673.gif)
b) ![](images/AP_BC_version1__674.gif)
c) ![](images/AP_BC_version1__675.gif)
d) ![](images/AP_BC_version1__676.gif)
e) ![](images/AP_BC_version1__677.gif)
10) Give the radius of convergence for the series![](images/AP_BC_version1__678.gif)
a) ![](images/AP_BC_version1__679.gif)
b) ![](images/AP_BC_version1__680.gif)
c) ![](images/AP_BC_version1__681.gif)
d) ![](images/AP_BC_version1__682.gif)
e) ![](images/AP_BC_version1__683.gif)
11) Determine![](images/AP_BC_version1__684.gif)
a) ![](images/AP_BC_version1__685.gif)
b) ![](images/AP_BC_version1__686.gif)
c) ![](images/AP_BC_version1__687.gif)
d) ![](images/AP_BC_version1__688.gif)
e) ![](images/AP_BC_version1__689.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__691.gif)
a) ![](images/AP_BC_version1__692.gif)
b) ![](images/AP_BC_version1__693.gif)
c) ![](images/AP_BC_version1__694.gif)
d) ![](images/AP_BC_version1__695.gif)
e) ![](images/AP_BC_version1__696.gif)
14) Determine the y-intercept of the tangent line to the curve
at x = 5.
a) ![](images/AP_BC_version1__698.gif)
b) ![](images/AP_BC_version1__699.gif)
c) ![](images/AP_BC_version1__700.gif)
d) ![](images/AP_BC_version1__701.gif)
e) ![](images/AP_BC_version1__702.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__704.gif)
b) ![](images/AP_BC_version1__705.gif)
c) ![](images/AP_BC_version1__706.gif)
d) ![](images/AP_BC_version1__707.gif)
e) ![](images/AP_BC_version1__708.gif)
16) Give the average value of the function
on the interval [1,6].
a) ![](images/AP_BC_version1__710.gif)
b) ![](images/AP_BC_version1__711.gif)
c) ![](images/AP_BC_version1__712.gif)
d) ![](images/AP_BC_version1__713.gif)
e) ![](images/AP_BC_version1__714.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 30 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__715.gif)
b) ![](images/AP_BC_version1__716.gif)
c) ![](images/AP_BC_version1__717.gif)
d) ![](images/AP_BC_version1__718.gif)
e) ![](images/AP_BC_version1__719.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__721.gif)
b) ![](images/AP_BC_version1__722.gif)
c) ![](images/AP_BC_version1__723.gif)
d) ![](images/AP_BC_version1__724.gif)
e) ![](images/AP_BC_version1__725.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__727.gif)
b) ![](images/AP_BC_version1__728.gif)
c) ![](images/AP_BC_version1__729.gif)
d) ![](images/AP_BC_version1__730.gif)
e) ![](images/AP_BC_version1__731.gif)
20) Compute![](images/AP_BC_version1__732.gif)
a) ![](images/AP_BC_version1__733.gif)
b) ![](images/AP_BC_version1__734.gif)
c) ![](images/AP_BC_version1__735.gif)
d) ![](images/AP_BC_version1__736.gif)
e) ![](images/AP_BC_version1__737.gif)
21) Determine![](images/AP_BC_version1__738.gif)
a) ![](images/AP_BC_version1__739.gif)
b) ![](images/AP_BC_version1__740.gif)
c) ![](images/AP_BC_version1__741.gif)
d) ![](images/AP_BC_version1__742.gif)
e) ![](images/AP_BC_version1__743.gif)
22) Determine![](images/AP_BC_version1__744.gif)
a) ![](images/AP_BC_version1__745.gif)
b) ![](images/AP_BC_version1__746.gif)
c) ![](images/AP_BC_version1__747.gif)
d) ![](images/AP_BC_version1__748.gif)
e) ![](images/AP_BC_version1__749.gif)
23) Give the exact value of![](images/AP_BC_version1__750.gif)
a) ![](images/AP_BC_version1__751.gif)
b) ![](images/AP_BC_version1__752.gif)
c) ![](images/AP_BC_version1__753.gif)
d) ![](images/AP_BC_version1__754.gif)
e) ![](images/AP_BC_version1__755.gif)
24) Determine![](images/AP_BC_version1__756.gif)
a) ![](images/AP_BC_version1__757.gif)
b) ![](images/AP_BC_version1__758.gif)
c) ![](images/AP_BC_version1__759.gif)
d) ![](images/AP_BC_version1__760.gif)
e) ![](images/AP_BC_version1__761.gif)
25) Give the derivative of ![](images/AP_BC_version1__762.gif)
a) ![](images/AP_BC_version1__763.gif)
b) ![](images/AP_BC_version1__764.gif)
c) ![](images/AP_BC_version1__765.gif)
d) ![](images/AP_BC_version1__766.gif)
e) ![](images/AP_BC_version1__767.gif)
26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function![](images/AP_BC_version1__768.gif)
a) ![](images/AP_BC_version1__769.gif)
b) ![](images/AP_BC_version1__770.gif)
c) ![](images/AP_BC_version1__771.gif)
d) ![](images/AP_BC_version1__772.gif)
e) ![](images/AP_BC_version1__773.gif)
27) Determine![](images/AP_BC_version1__774.gif)
a) ![](images/AP_BC_version1__775.gif)
b) ![](images/AP_BC_version1__776.gif)
c) ![](images/AP_BC_version1__777.gif)
d) ![](images/AP_BC_version1__778.gif)
e) ![](images/AP_BC_version1__779.gif)
28) Which of the following series converge(s)?![](images/AP_BC_version1__780.gif)
a) B only
b) A, B and C
c) B and C
d) A and B
e) A and C