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CALCULUS
AB
SECTION I, Part A
Time-SO
minutes
Number of questions -
J
=
2. If I(x)
x--J2x - 3, then 1'(x)
25
=
(A) 3x - 3
..J2x - 3
(B)
~x_
--J2x - 3
(C) _1_
..J2x - 3
(D) -x + 3
--J2x - 3
5x - 6
(E)
2--J2x - 3
/
=
4. If f(x)
-x'
I
+ x + -,
x
.../ 5. The graph of y == 3x4
(C) x < -2 or x
(E)
2
3'
<
2
3"
or x > 2
< x < 2
-
2
> --3
~
\0) x
then 1'(-1) ==
16x3
+ 24~2 + 48 is concave down for
./
7.
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A bug begins to crawl up a vertical wire at time t = O. The velocity
t $ 8, is given by the function whose graph is shown above.
o~
j
,/
8. At what value of
..
does the bug change direction?
.
'
..
9. What is the total distance the bug traveled from t
=0
to t = 8 ?
v of the bug at time t,
CalculusAB ~partA
n
j
10. An equation of the line tangent to the graph of .v = cos(2x)
(A) .v -
I =
(B) y -
I
=
at x =
4"
IS
-(x - ~)
-2(X - ~)
(C) y
= 2(X - ~)
(0) y
=
-(x - ~)
(E) y
=
-2(X - ~)
j
II. The graph of the derivative of
graph of I?
f is shown in the figure above. Which of the following could be the
I
Calculus AS ~part
12. At what point on the graph of y
,/
(B)
13. Let
1be
=
~x~ is the tangent line parallel to the line 2x - 4y
=
A
3 ')
G, i)
a function defined for all real numbers
x. If 1'(x)
=
14x -_ xli2
' then
1is decreasing
on the
j 14. Let 1 be a differentiable function such that 1(3) = 2 and 1'(3) = 5. If the tangent line to the graph
of 1 at x = 3 is used to find an approximation to a zero .of 1, that approximation is
I
A
Calculus AS ~part
I
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j
J
5. The graph of the function
is true?
(A) lim I(x)
is shown in the figure above. Which of the following statements about
f
= lim I(x)
x-w
(B) Jim
f
x-;b
f(x)
=
2
x-;{/
(0 Iim f(x)
= 2
x-;b
(D) Jim f(x)
x-;b
= I
(E) lim f(x)
does not exist.
x-;{/
J
J
7. If x2 + y2
=
d2v
25, what is the value of d;2 at the point (4, 3) ?
7
(C) 27
(D) ~
4
(E) 25
27
GO ON TO THE NEXT PAGE
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CALCULUS
AB
SECTION I, Part B
Time -
40 minutes
15
Number of questions -
A GRAPHING
CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON
THIS PART OF THE EXAMINATION.
/
/
!
77. The graph of the function
y
=
x3 + 6x2 + 7x - 2 cos x changes concavity at x
Calculus AB ~part
I
7"
=
lIb
~et
e a f'unctIon suc h t h at I'1m 1(2 + h)h - 1(2) --. 5
h---,>o
WhoICh
0f
th e
10II'oWing
j:
B
---
must b e true. ?
I. 1 is continuous at x = 2.
II. 1 is differentiable at x = 2.
III. The derivative of 1 is continuous at x = 2.
(A)
(B)
(C)
(D)
(E)
I only
II only
I and -II only
I and III only
II and III only
/
81. A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the
crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per
second is the train moving away from the observer 4 seconds after it passes through the intersection?
I
j
86. Let f(x)
(A)
1.
4
= ...&.
If the rate of change of
f
at x
=c
is twice its rate of change at x
=
I, then c
(D) _1
-Ii
=
(E) 2~
Calculus AB ~part
87. At time t ~ 0, the acceleration of a particle moving on the x -axis is a (t) = t + sin t. At t = 0, the
.~ velocity of the particle is -2. For what value of t will the velocity of the particle be zero?
B
I
I
x
=
88. Let f(x)
.
f·
h (t) dt, where
h has the graph shown above. Which of the following could be the
Q
graph of f?
y
(C)
y
(D)
")
Q
0
x
X
a
C
GO ON-_.~---TO THE NEXT PAGE
-
36
I"
Answers to the 1997 AP Calculus AB and
Calculus Be Examinations
Section 1: Multiple Choice
• Blank Answer Sheet
Listed below are the correer answers to the multipleSection II: Free Response
choice questions and the percentage of AP candidates
• Student Preparation
who answered each question correctly. A copy of the
for the Exams
• Free-Response Questions, Scoring Guidelines,
and Sample Student Responses with Commentary
blank answer sheet appears on the following pages
for reference.
• Section II, Calculus AB
• Section II. Calculus BC
Section I Ansvver Key and Percent Ansvvering Correctly