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__2.gif)
b) ![](images/AP_BC_version1__3.gif)
c) ![](images/AP_BC_version1__4.gif)
d) ![](images/AP_BC_version1__5.gif)
e) ![](images/AP_BC_version1__6.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__7.gif)
b) ![](images/AP_BC_version1__8.gif)
c) ![](images/AP_BC_version1__9.gif)
d) ![](images/AP_BC_version1__10.gif)
e) ![](images/AP_BC_version1__11.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__13.gif)
b) ![](images/AP_BC_version1__14.gif)
c) ![](images/AP_BC_version1__15.gif)
d) ![](images/AP_BC_version1__16.gif)
e) ![](images/AP_BC_version1__17.gif)
4) Determine dy/dt, given that
and![](images/AP_BC_version1__19.gif)
a) ![](images/AP_BC_version1__20.gif)
b) ![](images/AP_BC_version1__21.gif)
c) ![](images/AP_BC_version1__22.gif)
d) ![](images/AP_BC_version1__23.gif)
e) ![](images/AP_BC_version1__24.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__26.gif)
b) ![](images/AP_BC_version1__27.gif)
c) ![](images/AP_BC_version1__28.gif)
d) ![](images/AP_BC_version1__29.gif)
e) ![](images/AP_BC_version1__30.gif)
6) Determine![](images/AP_BC_version1__31.gif)
a) ![](images/AP_BC_version1__32.gif)
b) ![](images/AP_BC_version1__33.gif)
c) ![](images/AP_BC_version1__34.gif)
d) ![](images/AP_BC_version1__35.gif)
e) ![](images/AP_BC_version1__36.gif)
7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ).
a) ![](images/AP_BC_version1__37.gif)
b) ![](images/AP_BC_version1__38.gif)
c) ![](images/AP_BC_version1__39.gif)
d) ![](images/AP_BC_version1__40.gif)
e) ![](images/AP_BC_version1__41.gif)
8) Determine![](images/AP_BC_version1__42.gif)
a) ![](images/AP_BC_version1__43.gif)
b) ![](images/AP_BC_version1__44.gif)
c) ![](images/AP_BC_version1__45.gif)
d) ![](images/AP_BC_version1__46.gif)
e) ![](images/AP_BC_version1__47.gif)
9) Determine![](images/AP_BC_version1__48.gif)
a) ![](images/AP_BC_version1__49.gif)
b) ![](images/AP_BC_version1__50.gif)
c) ![](images/AP_BC_version1__51.gif)
d) ![](images/AP_BC_version1__52.gif)
e) ![](images/AP_BC_version1__53.gif)
10) Give the radius of convergence for the series![](images/AP_BC_version1__54.gif)
a) ![](images/AP_BC_version1__55.gif)
b) ![](images/AP_BC_version1__56.gif)
c) ![](images/AP_BC_version1__57.gif)
d) ![](images/AP_BC_version1__58.gif)
e) ![](images/AP_BC_version1__59.gif)
11) Determine![](images/AP_BC_version1__60.gif)
a) ![](images/AP_BC_version1__61.gif)
b) ![](images/AP_BC_version1__62.gif)
c) ![](images/AP_BC_version1__63.gif)
d) ![](images/AP_BC_version1__64.gif)
e) ![](images/AP_BC_version1__65.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, II and III
b) I and II
c) I, III and IV
d) II, III and IV
e) III and IV
13) Determine![](images/AP_BC_version1__67.gif)
a) ![](images/AP_BC_version1__68.gif)
b) ![](images/AP_BC_version1__69.gif)
c) ![](images/AP_BC_version1__70.gif)
d) ![](images/AP_BC_version1__71.gif)
e) ![](images/AP_BC_version1__72.gif)
14) Determine the y-intercept of the tangent line to the curve
at x = 4.
a) ![](images/AP_BC_version1__74.gif)
b) ![](images/AP_BC_version1__75.gif)
c) ![](images/AP_BC_version1__76.gif)
d) ![](images/AP_BC_version1__77.gif)
e) ![](images/AP_BC_version1__78.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__80.gif)
b) ![](images/AP_BC_version1__81.gif)
c) ![](images/AP_BC_version1__82.gif)
d) ![](images/AP_BC_version1__83.gif)
e) ![](images/AP_BC_version1__84.gif)
16) Give the average value of the function
on the interval [1,3].
a) ![](images/AP_BC_version1__86.gif)
b) ![](images/AP_BC_version1__87.gif)
c) ![](images/AP_BC_version1__88.gif)
d) ![](images/AP_BC_version1__89.gif)
e) ![](images/AP_BC_version1__90.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 20 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__91.gif)
b) ![](images/AP_BC_version1__92.gif)
c) ![](images/AP_BC_version1__93.gif)
d) ![](images/AP_BC_version1__94.gif)
e) ![](images/AP_BC_version1__95.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__97.gif)
b) ![](images/AP_BC_version1__98.gif)
c) ![](images/AP_BC_version1__99.gif)
d) ![](images/AP_BC_version1__100.gif)
e) ![](images/AP_BC_version1__101.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__103.gif)
b) ![](images/AP_BC_version1__104.gif)
c) ![](images/AP_BC_version1__105.gif)
d) ![](images/AP_BC_version1__106.gif)
e) ![](images/AP_BC_version1__107.gif)
20) Compute![](images/AP_BC_version1__108.gif)
a) ![](images/AP_BC_version1__109.gif)
b) ![](images/AP_BC_version1__110.gif)
c) ![](images/AP_BC_version1__111.gif)
d) ![](images/AP_BC_version1__112.gif)
e) ![](images/AP_BC_version1__113.gif)
21) Determine![](images/AP_BC_version1__114.gif)
a) ![](images/AP_BC_version1__115.gif)
b) ![](images/AP_BC_version1__116.gif)
c) ![](images/AP_BC_version1__117.gif)
d) ![](images/AP_BC_version1__118.gif)
e) ![](images/AP_BC_version1__119.gif)
22) Determine![](images/AP_BC_version1__120.gif)
a) ![](images/AP_BC_version1__121.gif)
b) ![](images/AP_BC_version1__122.gif)
c) ![](images/AP_BC_version1__123.gif)
d) ![](images/AP_BC_version1__124.gif)
e) ![](images/AP_BC_version1__125.gif)
23) Give the exact value of![](images/AP_BC_version1__126.gif)
a) ![](images/AP_BC_version1__127.gif)
b) ![](images/AP_BC_version1__128.gif)
c) ![](images/AP_BC_version1__129.gif)
d) ![](images/AP_BC_version1__130.gif)
e) ![](images/AP_BC_version1__131.gif)
24) Determine![](images/AP_BC_version1__132.gif)
a) ![](images/AP_BC_version1__133.gif)
b) ![](images/AP_BC_version1__134.gif)
c) ![](images/AP_BC_version1__135.gif)
d) ![](images/AP_BC_version1__136.gif)
e) ![](images/AP_BC_version1__137.gif)
25) Give the derivative of ![](images/AP_BC_version1__138.gif)
a) ![](images/AP_BC_version1__139.gif)
b) ![](images/AP_BC_version1__140.gif)
c) ![](images/AP_BC_version1__141.gif)
d) ![](images/AP_BC_version1__142.gif)
e) ![](images/AP_BC_version1__143.gif)
26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function![](images/AP_BC_version1__144.gif)
a) ![](images/AP_BC_version1__145.gif)
b) ![](images/AP_BC_version1__146.gif)
c) ![](images/AP_BC_version1__147.gif)
d) ![](images/AP_BC_version1__148.gif)
e) ![](images/AP_BC_version1__149.gif)
27) Determine![](images/AP_BC_version1__150.gif)
a) ![](images/AP_BC_version1__151.gif)
b) ![](images/AP_BC_version1__152.gif)
c) ![](images/AP_BC_version1__153.gif)
d) ![](images/AP_BC_version1__154.gif)
e) ![](images/AP_BC_version1__155.gif)
28) Which of the following series converge(s)?![](images/AP_BC_version1__156.gif)
a) B only
b) A, B and C
c) B and C
d) A and B
e) A and C