:rJle Calculus AB Exam
CALCULUS AB
A CALCULATOR CANNOT BE USED ON PART A OF SECTION I. A GRAPHING CALCULATOR.FROM THE
APPROVED LIST IS REQUIRED FOR PART B OF SECTION I AND FOR PART A OF SECTION II OF THE
EXAMINATION. CALCULATOR MEMORlES NEED NOT BE CLEARED. COMPUTERS, NONGRAPHING
SCIENTIFIC CALCULATORS, CALCULATORS WITH QWERTY KEYBOARDS, AND ELECTRONIC WRITING
PADS ARE NOT ALLOWED. CALCULATORS MAY NOT BE SHARED AND COMMUNICATION BETWEEN
CALCULATORS IS PROHIBITED DURING THE EXAMINATION. ATIEMPTS TO REMOVE TEST MATERIALS
FROM THE ROOM BY ANY METHOD WILL RESULT IN THE INVALIDATION OF TEST SCORES.
SECTION I
Time- 1 hour and 45 minutes
All questions are given equal weight.
Percent of total grade-50
Part A: 55 minutes, 28 multiple-choice questions
A calculator is NOT allowed.
Part B: 50 minutes, 17 multiple-choice questions
A graphing calculator is required.
Parts A and B of Section I are in this examination booklet; Parts A and B of Section II, which consist of longer problems,
are in a separate. sealed package.
General Instructions
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE INSTRUCTED TO DO SO.
--.... INDICATE YOUR ANSWERS TO QUESTIONS IN PART A ON PAGE 2 OF THE SEPARATE ANSWER SHEET. THE
ANSWERS TO QUESTIONS IN PART B SHOULD BE INDICATED ON PAGE 3 OF THE ANSWER SHEET. No credit
will be given for anything written in this examination booklet. but you may use the booklet for notes or scratchwork. After
you have decided which of the suggested answers is best. COMPLETELY fill in the corresponding oval on the answer
sheet. Give only one answer to each question. If you change an answer, be sure that the previous mark is erased completely.
Example:
Sample AnSWer
What is the arithmetic mean of the numbers 1.. 3, and 6 ?
(A)
(B)
3"
(C) 3
0
(D) 13
(E)
Many candidates wonder whether or not to guess the answers to questions about whichtlley are not certain. In this section
of the examination, as a correction for haphazard guessing, one-fourth of the number of questions you answer incorrectly
will be subtracted from the number of questions you answer correctly. It is improbable, therefore, that mere guessing will
improve your score significantly; it may even lower your score, and it does take time: If, however, you are not sure of
the best answer but have some knowledge of the question and are able to eliminate one or more of the answer choices
as wrong, your chance of answering correctly is improved, and it may be to your advantage to answer such a question.
r---. Use your time effectively, working as rapidly as you can without losing accuracy. Do not spend
too much time on questions that are too difficult. Go on to other questions and come back to the
difficult ones later if you have time. It is not expected that everyone will be able to answer aU
the multiple-choice questions.
2003 AP Calculus Released Exam Excerpt
Calculus AB
Part A
CALCULUSAB
SECTION I, Part A
Time-55 minutes
Number of questions-28
A CALCULATOR MAY NOT BE USED ON TIDS PART OF THE EXAMINATION.
Directions: Solve each of the following problems, using the available space for scratchwork. After examining the
form of the choices, decide which is the best of the choices given and fill in the corresponding oval on the answer
sheet. No credit will be given for anything written in the test book. Do not spend too much time on anyone problem.
In this test:
(1)
r---
Unless otherwise specified, the domain of a function
I(x) is a real number.
(2) The inverse of a trigonometric function
l
prefix "arc" (e.g., sin- x
is assumed to be the set of all real numbers x for which
may be indicated using the inverse function notation I-I
Or
with the
= arcsin x).
2003 AP Calculus Released Exam Excerpt
Calculus AB
1. If y
(A)
= (x 3 + 1)2, then : =
(3x 2 )2
(B)
r e- 4x dx = .
Jo
-4
(A)~
4
2(x3 + 1)
~\llEl.
CI-\AIN
2.
Part A
(C) 2(3x2
+ 1)
(D)
3x 2 (x 3 + 1)
(E) 6x 2 (x 3
+ 1)
{c\envQ1lve of -the outslde,- let\ve ihE: \nslde a\ane .
1hen (,(\\J\t,pl~ bi the ~eflvQilVe (\1 in~ \l\slde .)
(B) -4e- 4
2003 AP Calculus Released Exam Excerpt
-4
(E) 4 - 4e- 4
-\-\){
--4
(D) --~
(C) e- 4 -1
- -e
-y
-=
"mu'I'" .
Calculus AB
.' Part A
3. For x ;::: 0, the horizontal line y
statements must be true?
Fal&e
(B) I(x):f. 2 foraH x;::: 0
(c)f(2)isundefined. iUl&e.
CD) lim I(x) =
x--?2
(E) lim f(x)
x-+oo
00
n-\r"
.,)..IG.
r u
J{O)
becauSQ.
FQlse
(A) 1(0)=2
= 2 is an asymptote for the graph of the function f
\H\OQf1ned
X~ 0 qlso
KnOW a functlGh.
be(Qu~
aont
f (~) :: 2
We
hfOl.
l(-'
IS
Which of the following
= 2 De-fm \t Ion of 11m 11s
-----~~l
4. If y
2x + 3
dy
= 3x + 2 ' then dx =
(A) 12x + 13
(3x + 2)2
(B) 12x -13
(3x + 2)2
(C) (3x + 2)2
R~ LE I.
u=- nu meraior
. G\lOTIENT
vu' -Uv
U:
2x t 3
V-:.3"Xtl
(E)~
(3Xt z)1
Vz
V~denomH\alOr
-5
(0) (3x + 2)2
(2x-t:1)3
(3x.r 2 )2
u'=l
v';3
-::: bX t4
~q),=
5 1
(3x t1 )
2003 AP Calculus Released Exam Excerpt
""B';,I'
i Part A
Calculus AB
rr
J:
5.
sin x dx =
(A) _ J2
-II
-II
(B)
(C) -2-1
_. COSX na" i
.::
-(~
-1 +
(D)
(E)
-II
-1
-~
{2
tCOS;O
~5
(rQtlana I,!e
deMMlnQior
:: -fi. tl
2
,:
x 3 2x2 + 3x - 4
lim '3
2
X~OO 4x - 3x + 2x - 1
6.
(A) 4
(C)
(B) 1
(E) -1
(D) 0
~ degree of nlJmerotc)r < desree of d~romH\Qior~ ~I~~= 0
II
II
\I
>
"
I,'
"'t
'" '
I'
II
2003 AP Calculus Released Exam Excerpt
1\
,I
i
,
\1
=; , \''''
,,~OO
Dl'\E
trWi''''''
j. PartA .
Calculus AB
--~--~~--~~---+-----+~x
-2
-1
Graph off'
7. The graph of /" the derivative of the function J, is shown above. Which of the following statements is true
about J ?
(A)Jisdecreasingfor-1 ~ x ~ 1.
False. (0 ~~~2) betow
(B) f is increasing for -2 :5 x :5 O. TfU e. Above X- a >\is
(C)
f is increasing for 1 ~ x ~
(D)J has a local minimum at x
2.
Fa Is e.
aOJ ve
= O. Folse .
(E)Jisnotdifferentiableatx=-landx=1.
x - axIs
x-Qxi s;.
from below to above .
folse lhi~ t~ veloc't~ 9ro ph . Noi postioo .
mH)lmum~
2003 AP Calculus Released Exam Excerpt
.fMu,t,., .
Calculus AB
PartA
f x cos(x
2
8.
dx
NO PRODU q R\.\ LE "
U U- SUBSI\1U1\ON
(A) - jSin(x ) + C
(B)
%sin(x
U= x~
du~ 3)(1
+C
2
M
x
dx .
3
3 )
x
(C) - Tsin(x
+ C
(D)
x; sin(x
(E) x33 sin
==
(x4)
4 +c
~ J(ps\Jdu
-: . ~ r Sin u .. C J
j cos u-d~
<
~ ~ lSlt'I (y.~ )
9. If/(x) = In(x + 4 + e-3~), then 1'(0) is
2
5
(A) - .
1
(B) 5.
1
4
(C) -
CHAIN RULE.
.JL (e\I) =e dv
dx
(E) nonexistent
(D) }
U.. X i 1 t
~ (In\J)~ ~ dll
dx
dx
2003 AP CalCulus Released Exam Excerpt
d\l:
d~
dA -
e -31\
I -3e -3x
I
Xi'4
Te-3 '(
(,
-3e -3~)
c]
Calculus AB
10. The function f has the property that f(x), j'(x), and f"(x) are negative for all real values x. Which of the
following could be the graph of f ?
e~ {\ t I lie 't.... CO () CO ve dow 1\
t (\
(A)
y
oM
--------~o+----------.x
(C)
--------~r_----~~.x
(E)
--------~+_---------.x
(D)
--------~+_---------.x
----------r---------~x
2003 AP Cakulus Released Exam Excerpt
Calculus AB
. 11. Using the substitution u
1
(A) -2
11/2 JU du
-1/2
(2
(B)
2" Jo JU du
= 2x + 1, Jo
1
r;:--~
.J2x + Idx is equivalent to
r2
* cha n3 e 11m Its of
u~2x
-tl
= dx
= k.JV
dV
(C)
dt = k.Jt
(D)
dt = .JV
dV
(E) dV
dt
= kG
(D)
J: JU
o~ U -;.
X= 2~
II
\A
=-
j -ru -k du
5
=
du
Inte3ra tlon
f{(l d~
r.
kx
dV
.,,-. (B) Vet)
2"1 1,51 JU du
x :-
aU = ldx
d\l
. (C)
dt
-IV
dV
dt
2003 AP Calculus Released E:x:am Excerpt
-=
~fv'
Calculus AB
Part A
Graph off
13. The graph of a function
(A) a
f is shown above. At which value of x is f continuous, but not differentiable?
. (B) b
(C) c
(D) d
(E) e
~
- femOVQ bl~
nord \\ f1
\lp
~nc\ \
- corner
- cu~p
"vertlCQ I
-jUmp
14. If y
= x 2 sin 2x, then
2=
(A) 2x cos 2x
(B) 4x cos 2x
rR~D\l CT
dIsmnim\.llt~
fangevli
R~LE
\A~ XZ
\J I : lx
V-=
V~
I
slnlx
1cos? X
cha In ru \e)
(C) 2x(sin 2x + cos 2x)
(D) 2x(sin 2x - x cos 2x)
(E) 2x(sin 2x + x cos 2x)
Uv + vu
= x1(lCOSlx)t
sln2x (2X)
~ 1~1.
cos 2x + lX Sln Zx
~ 1X ( Xcos 1X 1 SIr\ LX)
2003 AP Calculus Released Exam Excerpt
fm".;;;.
CalculusAB
r PartA
15. Let f be the function with derivative given by f'(x)
decreasln5
isfdecreasing?
(A) (-00, -1] only
(B) (-00,0)
(C) [-1, 0) only
. (D)
(0, V2]
(E)
[;v2, 00)
= x2 -
: . On
which of the following intervals .
v.lM-D
f()() <a
.,. cr I h en I pi s :
) X~ - -2 ~ 0
f ()( ) . ~ 0 - - - - - ?
or
J'()()'" ONE
to \n d&n om .)
(i) X=:O
~ ~ ~~ - \
f (,o
5 (x 1:0 X3
-t
_ L~
.
lX)
- I
~x
coni be
\lesat\ve
16. If the line tangent to the graph of the function f at the point (1, 7) passes through the point (-2, -2),
then f' (1) is
,
(A) -5
(B) 1 . .
ihe
(D) 7
(C) 3
(E) undefined
w X:= I
slope
1- (-z) ~
\ - (-l)
2003 AP Calculus Released Exam Excerpt
9 =3
5i4;B';'"
i PartA
Calculus AB
17. Letf be the function given by f(x)
< -2
(A ) x
(B) x > -2
~\lLE
\A = Z
PRODU cT
u":. Zx
"t
><.
VIJ I
'2 Ae T
5' (x) ~ 2x eX
The graph of f is concave down when
L~
2e X
Xtl
leX.
Lx re" i 7e'A
l-
2>
(D) x > -1
(C) x < -1
~ l"l)<,.}.::
y =- eX
\J v'
= 2xe.t.
2e x
r' lx) < 0
2 eX (
.,
i-
+
i
(E) x < 0
(!)
CD
-!
I
Q
-4
-3
-2
-1
g'(x)
-3
-2
-1
I)
-=.
2e x (>(t2)
2e'< -:. 0
<l.
X tit
CD
X~l '" O
~ ~-1
18. The derivative 8' of a function 8 is continuous and has exactly two zeros. Selected values of g' are given in
the table above. If the domain of g is the set of all real numbers, then g is decreasing on which of the following
intervals?
(A) -2 ~ x
(B) -1
2 only
1 only
(C) x
-2
(D) x
2 only
(E) x
-2 or x
4\, \ -n
h
w , I Vb
IS
-the d.0nVQj,ve
less tho h O.
2003 AP Calculus Released Exam Excerpt
,.mu.t11
Calculus AB
It--
O\,q
has~x
Part A
..Iflnvatlve
~ UJU
19. A curve
+ 3 at each point (x, y) on the curve. Which of the following is an equation for this curve
if it passes through the point (1, 2) ?
~\
(A) y
= 5x -
(B) y
= x2 + 1 ~ \ -::
(C) y=x +3x
CD) y
(E) y
::0
5 ~ 2)1. t 3
1)(
1 Xt 3
~. \ = 1)( t3
= x 2 + 3x - 2 ~ I
= 2x2 + 3x - 3 'j I
:0
-::
2x
4- X
1
3 f
(\.2)
'2
x+2
= {.
4x - 7
x~3
II.
III.
f is continuous at x = 3. Tr~
f
is differentiable at x
= 3. raise (corner)
(A) None
(B) I only
(C) II only
CD) I and IT only
(E) I, II, and III
2003 AP Calculus Released Exam Exrerpt
ifx:S;3
.
If x > 3
be the function given above. Which of the following statements are true about
~r'Ic-,. lun -5
lilT' -5
I. lim f(x) exists. I v~ l(~3- )(~3'
(3)(1) ~ 2 ~ Y
j2 t
3 ~ 2X t 3
f(x)
20. Let
NoW p\\l9 III
2;
12
t-
3(1)-2 ~' 2=2
Calculus AB
21. The second derivative of the function f is given by f"(X) = x(x - a)(x - b)2 . The graph of f" is shown
above. For what values of x does the graph of f have a point of inflection?
(A) 0 and a only
(B) 0 and m only
S"(x)"O
thas ta go
(C) b andj only
from
(D) 0, a, and b
to -
(E) b, j, and k
or
~ touct\Qs X -a~1 S
roX--o,o
2003 AP Calculus Released EXaIil Excerpt
ftflU,.t.il
Calculus AB .
PartA
~+----lIr---_X
22. The graph of f'. the derivative of f, is the line shown in the figure above, If f(O)
(A) 0
(B) 3
(C) 6
area
rasltlon ~
(D) 8
~nclfrr
'------v----~
'3
POSltIOY)
J (0 J ~ 5
f(l) ==
(E) 11
curv~t milial
~(,)(6)
= 5. then
8
23.
! (f:
sin(t
dt) =
of
2003 AP Calculus Released Exam Excerpt
\A 17 p-B r
'
PI \l j
lh
\I
uDO-er)
- (d-tnv- of
rr
!ol,tV-Q( t
p\V3 ln
10 ~r J
trmu.';;'
j PartA
Calculus AB
24. Let f be the function defined by f(x) = 4x 3
to the graph of f at the point where x = -1 ?
(A) y = 7x - 3
(B) y
= 7x + 7
(C) y
= 7x + 11
'1(. _
= -5x -
5x + 3. Which of the following is an equation of the line tangent
~ , 't (- \)
~~
3 -
S ( -I) t 3
~~f'blnt
(0) y :::: -5x-1
(E) y
~ _~ ~ 1 ( )( t I)
~-4=1)( tl
\j=7x til
25. A particle moves along the x-axis so that at time t ~ 0 its position is given by x(t)
At what time t is the particle at rest?
(A) t
= 1 only
= 2t 3
21t2 + 72t - 53.
'~
(B) t :::: 3 only
(C) t
= "27 only
(D) t
= 3 and t = "27
(E) t
= 3 and t = 4
velocity
~O
6t2-~ltilZ=O
b(t Z - 11 -t 12):::0
(t- 4 )(t-3)
2003,AP Calculus Released Exam Excetpt
...foUt.;,"
Calculus AB
U" -LX.
-
(E)l
(A) 0
\1\
:-z
1_
V"" ~
26. What is the slope of the line tangent to the curve 3y2 - 2x2 = 6 -
II
.
Part A
V -
d~
ax
at the point (3, 2) ?
i(YlpilC it .Oi ff .
b~ ~~ - ~ X
~ (b~ i IX)
d~
= -
x'. - 2~
4x - 2~
4x-l~ _ ~(1)-1{l)
:0
~
dx." b~ilx - b{z) t ZP) -I~= if
27. Let f be the function defined by f(x) = x 3 +x. If g(x)
(A)
,---....
l..
13
(B)
'
J-I(XJ~
.!.
4
(C) 7...
(D) 4
x.-=-~3t~
d~
d)(
d\j _ _
ox - 3~ 1. 1 l
. 2003 AP Calculus Released Exam Excerpt
= f- 1 (x)
(E) 13
and g(2) = 1, what is the value of g'(2) ?
( 2 1 I)
"1#""';;'
i
Calculus AB
PartA
Y\)S\1~~pe
C(){\c~~
~~
28. Let g be a twice-differentiable function with g'(x) > 0 and g"(X) > 0 for all real numbers x, such that
g(4) = 12 and g(5) == 18. Of the following, which is a possible.value for g(6)?
(A) 15
(B) 18
(C) 21
CD) 24
(E) 27
Note;
concave ~P,
the fun c1 (0 n cormot
If J(x)
-then
IS
IInear
be
of"
Be co VSQ
9' (x J)O
-l-- f)1:. is-Ii ~fo
5-4
this: ellI'YlInates
~-\17.~(X-4)
~=bx -12
3(~J
==
1~
\J.le ~now -that
\t 'IS can (O.VD
1~'\S e\lm\Y\ate~
3(~)L4
beCU\JSQ,
up.
I
C~
0,
END OF PART A OF SECTION I
2003 AP Calculus Released Exam Excerpt
.wrmi(.J'"
. i P art B
Calculus AB
CALCULUSAB
SECTION I, Part B
Time-50 minutes
Number of questions-17
A GRAPHING CALCULATOR IS REQUIRED FOR SOIvIE QUESTIONS ON
THIS PART OF THE EXAMINATION.
Directions: Solve each of the following problems, using the available space for scratchwork. After examining the
form of the choices, decide which is the best of the choices given and fill in the corresponding oval on the answer
sheet. No credit will be given for anything written in the test book. Do not spend too much time on anyone problem.
BE SURE YOU ARE USING PAGE 3 OF THE ANSWER SHEET TO RECORD YOUR ANSWERS TO
QUESTIONS NUMBERED 76-92.
YOU MAY NOT RETURN TO PAGE 2 OF THE ANSWER SHEET.
"...-..,.
In this test!
(1) The exact numerical value of the correct answer does not always appear among the choices given. When this
happens, select from among the choices the nwnber that best approximates the exact numerical value.
(2) Unless otherwise specified, the domain of a function
f(x) is a real number.
(3) The inverse of a trigonometric function
prefix "are" (e.g., sin -1 x = arcsin x).
2003 AP Calculus Released Exam Excerpt
f is assumed to be the set of all real numbers
may be indicated using the inverse function notation
x for which
-1
-or with the
tr#I'.I,I'
Calculus AB
i PartB
76. A particle moves along the x-axis so that at any time t ~ 0, its velocity is given by v(t)
What is the acceleration of the particle at time t = 4 ?
(B) -0.677
(A) -2.016
(C) 1.633
mATH 8
nDerrv (3i4 .1COS
or
G)RAPH ~
2NO
lO .<ll.)
X.4 ) : :
(D) 1.814
= 3 + 4.1 cos(0.9t).
(E) 2.978
\ . b:3~
~lRAcE? ~', ~ )(::.,
--r-+---~-----r-X
-3
77. The regions A. B, and C in the figure above are bounded by the graph of the function land the x-axis. If the
area ofeach region is 2, what is the value of
(A) -2
(B) -1
JS(1<)
(I(x)
(D) 7
+ l)dx ?
(E) 12
,,3
-3
(C) 4
f3
S'
-~
[-2 i 1- ZJ + [X]
..,
:;
'3
3 - (- ~)
- 2t ~ :;
2003 AP Calculus Released Exam Excerpt
fwn-fill
i Part B
Calculus AB
78 . The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the
area of the circle at the instant when the circumference of the circle is 20,. meters?
(A) 0.047r m2 /sec
dr
dt :: O.Z
A= lirl
(C) 47r m /sec
C'" lOir
dA
CD) 207r m 2/sec
)J
(B) 0.4n- m 2 /sec
2
(E) 100,. m 2/sec
C~
dt
1IT r Q!
dt
=-
11l r
20 li'" 111 r
10 : r
M_
?
cit - .
"
.1.
For which of the folloWing does lim j (x) exist?
X-74
1.
II.
ill.
1
--~Or-r-~~4~~--X
--~-r-r-r-+-+---X
Graphofj
(A) I only
(B) II only
(C) III only
CD)' I and II only
(E) I and ill only
_.
.1 : 1111\ ~
X. ~~t
11m
x~~-"
2003 AP Calculus Released Exam Excerpt
3)
4
Graphofj
. ~w\
.[
--~-r-+-+-+-+--~X
3]
4
Graphofj
10m <
~~~t~~~\
11m _"3
l(~1
]I ~ , 11m
. )( ~1-i
II"m
.l(~ .
~
~
I}
3
Innd
DNE
tri#!iU,"i'
. i PartB.
Calculus AB
80. The function f is continuous for -2 :$; x :$; 1 and differentiable for -2 < x < 1. If f(-2)
Q-:. - 2
which of the following statements could be false?
(A) There exists c, where -2 < c < 1, such that f(c)
=:
(B) There exists c, where -2 < c < 1, such that f'(c)
=:;
= -5 and
f(1)
=:
4,
b= I
o.
O.
= 3.
f'(c) = 3.
(C) There exists c, where -2 < c < 1, such that fCc)
(D) There exists c, where -2 < c < 1, such that
(E) There exists c, where -2
:$;
:$;
1, such that fCc)
f(x) for all x on the closed interval-2
:$;
:$;
1.
""eao VQI"e 1hrn.
J'ft) '" fib) -:fen)
b-Q
if Interm~dlote
if
Valve Th \'fI .
a~c <b t~n ' 5'(Q)~ S'(c)~S'(b)
81. Let f be the function with derivative given by
'(x)
= sin (x 2 + 1). How many relative extrema does f
on tbeinterva12 < x < 4?
wee
endpoints
f(z) -=.sln (22"t1)"!-.9 S1
f (4 J ~ Sin (~Z t I) -.~ ~ I
-4'-
(B) Two
os
~hest I
Not IONe~t
.
(C)
(A) One
(D) Four
(E) Five
J-' (xJ-=O
(U X-:. 2. Zqq
)(. -:. 1.~ 03
x,. 3.40 1
)(.=
have
b ,01a I extremQ
_\
-\
3.S35
A
5\cbol m~'X
9\obo.~
\Q (O\
2003 AP Calculus Released Exam Excerpt
filii""'"i
Calculus AB
PartB
~e\oCll~
.
~
82. The rate of cbange of the altitude of a hot-air balloon is given by ret) = t 3 - 4t 2 + 6 for 0 :s; t :s; 8. Which of
the following expressions gives the change in altitude of the balloon during the time the altitude is decreasing?
3.514
(A) .
1.572
(B)
f:
(C)
Jo .
CD)
I. ~ 12 ~ X~ 3.'j I L\
ret) dt
WY\Qx\
3.514
1.572
1
0
r'(t) dt
r'(t) dt
2003 AP Calculus Released
~\()W
X -o~\S
r2.667 ret) dt
2.667
(E)
r(t) dt
Exam Excerpt
fMho,11
Calculus AB
i PartB
83. The velocity, in fUsee, of a particle moving along the x-axis is given by the function vCt)
average velocity of the particle from time t = 0 to time t = 3 ?
= et
+ te t . What is the
(A) 20.086 ftlsec
aV3(t)~~ J:f(t)di
(B) 26.447 ftJsec
b-Q
(C) 32.809 ftlsec
(D) 40.671 ftlsec
(E) 79.342 ftlsec
re
J
ttet
i[~O. 257J
=
20. a8h
84. A pizza, heated to a temperature of 350 degrees Fahrenheit (OF), is taken out of an oven and placed in a 75F
room at time t = 0 minutes. The temperature of the pizza is changing at a rate of -11 Oe -0.41 degrees Fahrenheit
per minute. To the nearest degree, what is the temperature of the pizza at time t = 5 minutes?
350 -
Sf-IIOe- oAt Icit
o
=-//1 . 211
2003 AP Calculus Released Exam Excerpt
Calculus AB
'rm!(.J'il
[ Part B
. 85. If a trapezoidal sum overapproximates JI f(x) dx, and a right Riemann sum underapproximates
0
which of the following could be the graph of y
(A)
(B)
= fCx) ?
RKf-\M .
Gb-e rV'Q
(C)
draWl nJ .
tn~ 1fupe rOlds
Tr~
i f(x) dx,
Con cllJS \o . ~ .
(D)
(E)
4
.:';'~.
2003 AP Calculus Released Exam Excerpt
Calculus AB
..
Part B
86. The base of a solid is the region in the fIrst quadrant bounded by the y-axis, the graph of y = tan~l x, the
horizontal line y = 3, and the vertical line x :: 1. For this solid, each cross section perpendicular to the x-axis is
a square. What is the volume of the solid?
(A) 2.561
(B) 6.612
(C) 8.046
(E) 20.773
(D) 8.755
~:3
1\ re-a
of
S~\iQre
~tanl~
I
) (3 - ta n
_I
X) 2
d:x -:. b.fa 11 u~
87. The function f bas fIrst derivative given by f'(x)
point of the graph of f ?
(A) 1.008
(B) 0.473
(C) 0
\f\i\eclI0n rL IS ~~here
.JX. 3 What is the
1 + x +x
(D) -0.278
x-coordinate of the inflection
(E) The graph of f has no inflection point.
f' (X J ~ 0
x x)
2003 AP Calculus Released Exam Excerpt
..miN'
jPartB
Calculus AB
88. On the closed interval [2, 4], which of the following could be the grapb of a function
J!(t)dt =1 ?
4: 2
~ t area \It\dtr curve
(A)
(B)
-2
(E)
4
3
2
1
I...,--+----+-+---+-_x
f with the property thal
234
2003 AP Calculus Released Exam. Excerpt
=-1
..1#"i.illj PartB
,
Calculus AB
89. Let / be a differentiable function with /(2) = 3 and 1'(2) = -5, and let g be the function defmed by
g(x) = x/ex). Which of the following is an equation of the line tangent to the graph of g at the point where
x = 2?
~-3:: -5 ()(.-z)
(A) y == 3x
'1 - 3 : - '5 X 1 IQ
(B) y - 3 = -5(x - 2)
~=-5x+13
(C) Y - 6 == -5(x - 2)
9(>d ~
= -7(x - 2)
6 = -lO(x - 2)
(D) y - 6
(E) y -
(-5 x i 13)
: -5)(2
i 13x
S(2)-= -5 (2Y tl~(2)
2b
I
(z) ~ - iO (2 ) t ( 3
~
1
\j --~, :. -l (X-2J
90. For all x in the closed interval [2, 5], the function f has a positive first derivative and a negative second
derivative. Which of the following could be a table of values for f?
(A)
x
2
3
4
5
I(x)
7
9
12
16
FOSltlvQ
(B)
x
2
3
4
5
slope
I(x)
7
11
14
16
(C)
f(x)
CD) x I(x)
16
12
9
7
4
5
3
4
5
(E)
16
14
x
2
3
11
I(x)
16
13
10
7
concuv'Q dowh
..
2003 AP Calcwus Released Exam Excerpt
fMit.l'"i PartB
Calculus AB
91. A particle moves along the x-axis so that at any time t > 0, its acceleration is given by a(t)
velocity of the particle is 2 at time t
. (A) 0.462
(B) 1.609
= In(1 + 2 t). If the
= 1, then the velocity of the particle at time t = 2 is .
(C)2.555
(D) 2.886
(E) 3.346
Sih (I t Z-t.) di
1i
1T
\.34.b
3 346
92. Let g be the function given by g(x)
= S: sin(t 2 )dt for -1 ::;; x::;; 3. On which oftbe follewing intervals is g
decreasing?
(A) -1 ::; x::; 0
,-..,. (B) 0 $ x $ 1.772
(C) 1.253 ::;; x ::;; 2.171
(D) 1772 ::;; x ::;; 2.507
(E) 2.802::;; x ::;; 3
END OF SEC1"ION I
AFTER TIME HAS BEEN CALLED, TURN TO THE NEXT PAGE AND
ANSWER QUESTIONS 93-96.
2003 AP Calculus Released Exam Excerpt
Calculus AB
Which graphing calculator did you use during the examination?
6300, Casio 7300, Casio 7400,
7700,
11-80, or
(A)
(B) Casio 9700. Casio 9800 l
9200, Sharp 9300, TI-82, or
(C) Casio 9850. Casio
1.0. Sharp 9600, Sharp 9900, TI-83m-83 Plus, or TI-86
(D) Casio 9970, Casio Algebra
2.0, HP 380, HP 390,
40G,
48 series, HP 49 series. or TI-89
Some other graphing calculator
94. During your Calculus AB course, which of the following best describes your calculator use?
(A) I
my own
calculator.
(B) I used a graphing calculator
by my school, both in class and at home.
by
school only
(C) I used a graphing
I used a
calculator funlished by
school mostly in
occasionally at home.
(E) I did not use a graphing calculator.
95. During
a
Calculus
course, which of
In"'''''\I"' ........"...
approximately how often
calculator was used by you or your teacher classroom
activities?
LU..,...,
(A) Almost every class
(B) About three-quarters
the classes
(C) About one-half of the classes
(D) About one-quarter the ........,,"''''.,
(E) Seldom or never
96. During your Calculus AB course, which the following
were allowed to use a graphing calculator?
(A) AU or almost
I'>"'Mho",,,
the portion
testing time you
of the time
(B) About three-quarters of the time
(C) About one-half of the time
of the time
Seldom or never
(D) About
2003 AP Calculus Released Exam Excerpt
