The Calculus AB Exam
CAICULUS AB
{ CALCULATOR CANNOT BE USED ON PART A OF SECTION I. A GRMHING CALCIILATOR FROM THE
.{PPROVED LIST IS REQUIRED FOR PART B OF SECTION I AND FOR PART A OF SECTION II OF THE
EXAMINATION. CALCULATOR MEMORIES NEED NOT BE CLEARED. COMPUTERS, NONGRAPHING
SCIENTIFIC CALCI.JLATORS, CALCTJLATORS WITH QWERTY KEYBOARDS, AND ET,ECTRONIC WRITING
PADS ARE NOT ALLOWED. CALCULATORS MAY NOT BE SHARTD AND COMMUNICATION BETWEEN
CALCULATORS IS PROHIBITED DI.]RING THE EXnMINATION. ATTEMPTS TO REMOVE TEST MATERIALS
FROM TIM ROOM BY AI{Y METHOD WILL RESULT IN THE INVALIDATION Otj'TEST SCORES.
SECTION I
Time- I bour and 45 minutes
All questionsare given equal weight.
Percentof total grade-50
Part A: 55 minutes,28 multiple-choicequestions
A calculatoris NOT allowed.
Part B: 50 minutes,17 multiple-choicequestions
A graphingcalculatoris required.
PartsA and B of SectionI are in this examinationbooklet;PartsA and B of SectionII, which consistof longerproblems,
are in a separate,sealedpackage.
GeneralInstructions
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 SFMET. TTM
ANSWERS TO QUESTIONS IN PART B SHOULD BE INDICATED ON PAGE 3 OF Tfm ANSWER SffiET. No credit
will be given for anything written in this examinationbooklet, but you may use the booklet for notesor scratchwork.After
you have decidedwhich of the suggestedanswersis best,COMPLETELY fill in the correspondingoval on the answer
sheet.Give only one answerto eachquestion.If you changean answer,be surethat the previousmark is erasedcompletely.
Examole:
What is the arithmeticmean of the numbersl, 3, and 6 ?
(A)
SampleAnswer
@@@(D@
I
'7
(B) *
J
(c) 3
(o)+
(E)I
wonderwhetheror not to guessthe answersto questionsabout which they arenot certain.In this section
Many candidates
of the examination,as a correctionfor haphazardguessing,one-fourthof the numberof questionsyou answerincorrectly
will be subtractedfrom the numberof questionsyou answercorrectly.It is improbable,therefore,that mereguessingwill
improve your scoresignificantly;it may even lower your score,and it does take time. If, however,you are not sure of
the best answerbut have some knowledgeof the questionand are able to eliminateone or more of the answerchoices
as wrong, your chanceof answeringcorrectlyis improved,and it may be to your advantageto answersuch a question.
Use your time effectively,working as rapidly as you can without losing accuracy.Do not spend
too much time on questionsthat are too difficult. Go on to other questionsand come back to the
difficult ones later if you have time. It is not expectedthat everyonewill be able to answerall
the multiple-choicequestions.
Galculus
CALCULUS AB
SECTIONI, Part A
Time-55 minutes
Numberof questions-28
A CALCULATORMAY NOT BE USEDON THISPARTOFTIIE EXAMINATION.
Directions: Solveeachof the following problems,using the availablespacefor scratchwork.After examiningthe
form of the choices,decidewhich is the bestof the choicesgiven and fill in the correspondingoval on the answer
sheet.No credit will be given for anythingwritten in the testbook. Do not spendtoo much time on any one problem.
In this test:
18
(1)
Unlessotherwisespecified,the domainof a function/ is assumedto be the setof all real numbersx for which
/("r) is a real number.
(2)
The inverseof a trigonometricfunction f may be indicatedusing the inversefunction notation -' ot with the
f
prefix "arc" (e.g.,sin-l-r = arcsin-r).
Unauthorizedcopying or reuse ot
any part ot this page ls itlegal.
GO ON TO THE NEXTPAGE.
\B
Calculus AB
=
1.If y = (r3+ t)',tn"nfr
(A) (3.12)2
2.
tn) z(;3 + r)
G) 2(3x2+r)
(D) 3x2(x3+ 1)
(E) 6x2(x3+ t)
=
Jt"-+"dr,
@+
(B)-4e-a
Unauthorlzodcopying or r€u3€ ot
env D.rt ot thls Daaab llloqal,
-r
(c) e-4
(D)-l-+
(E)4*4e-a
GOONTOTHENEXTPAGE.
19
Calculus AB
3. For .r 2 0, the horizontalline y = 2 is an asymptotefor the graphof the functionf Which of the following
statementsmust be true?
(A) /(0) = 2
(B) ,f (r) * 2 for all -r > 0
(C) f (2) is undefined.
(D) lim f (x) = q
x-+2
-
(E) lim /(r)
= I
4.rfy =#+, nenfl=
,O,
'
20
12r + l1
(3x + 2)'
lZx - 13
(B) -----------
rlzcd copylng or rrurc
ot thl. D.oc h 11L0.l,
(3x + 2)'
Q) al.'"
-\
(D)' _:___
(3x + 2)'
@)tr
GO ON TO THE NEXTPAGE.
tffi
lrny Frt ol
AB
Calculus AB
5.
J T s i nx d x =
G )- +
O.
p 1- $ + r
o t$ - r
,3-zr2 +3x-4
lllll --;JS+r3 -3x\2x-I(A) 4
GE.
-$-t
rc>
@+)
(B) l
Un.uthorlzcd copylng or Eu.. ot
eny part ol thl. p.gt l. llLg.l,
(c)
*
(D) 0
(E) -1
GOONTO THENEXTPAGE.
21,
Calculus AB
Graphof /'
7. The graphof f
about / ?
', thederivativeof the function is shownabove.Which of the following statementsis true
/
(A) / is decreasing
for -1 < x < l.
(B) / is increasingfor -2 < x < 0.
(C) / is increasingfor I S x < 2.
(D) / hasa local minimum at x = 0.
(E) / is not differentiableat -r = -l and x = l.
22
Unauthorlzedcopylng or reuse of
any part ot this pags b illsgal.
GO ON TO THE NEXTPAGE.
Calculus AB
J '2.o'(")a, =
8.
(A) (B)
lsin(,3)+ c
{sin('3)
+c
(c) - { , i n ( " 3 ) +
(D)
(E)
c
c
{,in("')*
.'
+.-(+J
9. If/(x) = tn(r + 4 + e-3").then/'(0) is
(A)-3
tn)+
Unauthorizedcopying or reuse ol
.ny part of this page is illegal.
(q+
o r )?
(E) nonexistent
GO ON TO THE NEXTPAGE.
_._^.qq!E
Calculus
10. The function / hasthe prop€rtythat /(x), /'(x), and f "(x) arenegativefor all real valuesx. Which of the
'l
following could be the graphof f
(A)
ZA
Uneuthorired copylng or reure
any prrt ot thl. Drgc b lllcgrl.
(B)
GOON TO THENEXTPAGE.
lalculus AB
- l. Using the substitution a
I cU2
(A);1,,",!udu
2x + t,
t
O;ndx
is equivalent
to
G ) + E a * e )+J:
Jo *
ro)f Jiau
re)l: Ji au
12'Therateof changeof thevolume,V,of waterin a tankwith respect
to time, t, is directlyproportional
to the
squarerootof thevolume'Whichof thefollowingis a differentialequationthatdescribes
thisrelationship?
(A) Y(t) = kJ7
(B) Y(t) = kJV
, ^ . d v= . klt
dt
\v)
D ' t dt
{-=L
JV
@)#=kfi
Unauthorlz€dcopying or reuse
airy p.rt ot thl. pago ls ill€ga|.
GO ONTO THENEXTPAGE.
25
Calculus
13. The graphof a function/ is shownabove.At which valueof .r is / continuous,but not differentiable?
(E\ e
(D) d
(c) c
(B) b
(A) a
, d y
1 4 . l f y = x 2 s i n 2 x , men
E-
=
(A) 2xcosZx
(B) 4x cos2x
(C) 2x(sin2x + cos2x)
(D) 2x(sin2x - x cos2x)
(E) 2x(sin2x * x cos2x)
26
Unauthorizedc
.nv Dart of thia
or reuse of
GO ONTO THENEXTPAGE.
lalrulus AB
^ " ,
Let f be the function with derivativegiven by f '(x) = x" - a. On which of the followine intervals
x
"
is / decreasing?
(A) (--,-llonly
(B) (-"",0)
(C) [-1,0) only
(D) (0,1,U]
fBl [V7,-)
16.Ifthe line tangentto the graphofthe functionf atthepoint (1,7) passesthroughthe point (-2,-Z),
then/'(l) is
(A) -5
r@ part
i any
(B) 1
of this pags is lllegal.
I
(C) 3
(D) 7
(E) undefined
GO ON TO THE NEXTPAGE.
27
Calculus AB
t7 . Let / be the functiongiven by /(x)
(A)-r<-2
(B)x>-2
x
2xe' . The graphof / is concavedown when
(C)x<-l
*4
s'G) 2
-3
J
.|
0
(D)x>-l
(E)x<0
-l
0
I
2
3
4
-3
a
-l
0
J
2
18. The derivativeg' of a function g is continuous and has exactly two zeros. Selectedvalues 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 1 x < 2 only
( B ) - l < r < 1 only
(C) x >- -2
(D)x)2only
(E) x< -2orx
28
> 2
Unauthorized copying or reuse of
ot this page ls illegal.
GO ON TO THE NEXTPAGE.
Calculus AB
- l. A curvehasslope2x + 3 at eachpoint (x, y) on the curve.Which of the following is an equationfor this curve
if it passesthroughthepoint (I,2) ?
(A)Y = 5x-3
(B) y = x2+l
(C) y = xz +3x
(D)y = xz+3x-2
( E )y = 2 x 2 + 3 x - 3
='
f ( x )= {l 4' .x*-'7- T
'
ifx>3
:0. L€t / be the function given above.Which of the following statementsare true about / ?
I. lim f(x) exists.
x-5
II. / is continuousat x = 3.
IIL / is differentiableat x = 3.
(A) None
(B) I only
(C) II only
(D) I and II only
(E) I, II' and III
Unauthorizedcopylng or reuse of
any part ot this pag6 ls ill€gal.
G O O N T O T H EN E X T P A G E .
29
Calculus AB
y =f"(x)
2 I . T h e s e c o n d d e r i v a t i v e o ft h e f u n c t i o n / i s g i v e n b y - f " ( x ) = x ( x - a ) ( x - b ) ' . T h e g r a p h o f
above. For what values of -r does the graph of / have a point of inflection?
(A)0andaonly
30
(B)0andmonly
Unauthorizedcopying or r€use of
any part of thl! pagp is illegal.
(C)bandionly
(D)0,a,andb
J f" i s s h o w n
(E)b,j,andk
GO ON TO THE NEXTPAGE.
3alculus AB
rr-/
='f('r)
22.Thegraphoff ',thederivativeofJ isthelineshowninthefigureabove.If
/(0) = 5, thenf (l) =
(A) 0
(B) 3
(C) 6
(D) 8
(E) ll
23
*U:,i"(r3)ar)=
(A) - co'(r6)
@) sin(.r3)
(c) sin(.r6)
(D) 2xsin(x3)
(E) 2xsin(x6)
-
Unauihorlzedcopytns - rrt;A
. any plrt ot thl. p{96 l! ttt!g.t_
|
GO ON TO THE NEXTPAGE.
Calculus
24. Let/ be the functiondefinedby .f (x) = 4x3 - 5x + 3. Which of the following is an equationof the line tangent
to the graphof / at the point wherex = -l ?
(A)Y = 7x-3
(B) Y = 7x+'l
(C)Y ='7x+ll
(D)Y=-5x-1
(E) Y = -5x-5
x-axissothatattime/> 0 itspositionisgivenby;(r)=2t3 -21t2 +72t -53.
25. Aparticlemovesalongthe
At what time t is the particleat rest?
(A)t=lonly
(B)t=3only
1
(C)l=7only
(D) t = 3 a n d=t l
(E) t = 3 a n d t = 4
32
Unaulhorizedcopying or r€us€ of
any part ot this page is illegal.
GO ON TO THE NEXTPAGE,
}lstrlus
AB
16. What is the slope of the line tangent to the curve 3 y ' - 2 x 2 = 6 - Z x y atthepoint(3,2)?
(A)o (B)f
G)+
ro)f
(")*
27.Let/bethefunctiondefinedby f(x) = 13 + t. If g(-r) = f -r U) md g(2) = l, what is the value of g'(2) ?
(A)+ (B)+ G)I
*nuOorlzld copyfngpr nur
rt p.rl ot lhl. pte l. llLgrl.
ofl
..-|
co)4
(E) 13
GO ONTO THENEXTPAGE.
Calcrrlus
28' Iet g bea twicedifferentiable
functionwith g'(.r) > 0 andg"(x) > 0 for all realnumbers.r, suchthat
=
=
12
and
18.
8@)
of thefonowing,whichis a possibre
c(5)
valuefor 9(6) ?
(A) 15
(B) ls
(c) 2l
(D) 24
(E) Zt
ENDOF PARTA OF SECNONI
34
ot thl.
ot nr||..
Frsulus AB
CALCULUSAB
SECTION I, Part B
Time-50 minutes
Number of questions-l7
A GRAPHING CALCULATOR IS REQURED FOR SOME QUESTIONSON
THIS PART OF TIIE EXAMINATION.
Directions:Solveeachof thefollowingproblems,
usingtheavailablespacefor scratchwork.
After examiningthe
:-'rmof thechoices,
decidewhichis thebestof thechoicesgivenandfill in thecorresponding
ovalon theanswer
ireet.No creditwill begivenfor anythingwrittenin thetestbook.Do not spendtoomuchtimeon anyoneproblem.
BE SUREYOU ARE USINGPAGE3 OF THE ANSWERSIIEET TO RECORDYOTJRANSWERSTO
NUMBERED76-92.
QUESTTONS
YOUMAY NOT RETURNTO PAGE2 OF THE ANSWERSIMET.
In this tcst:
l)
The exactnumericalvalue of the correctanswerdoesnot alwaysappearamongthe choicesgiven. When this
happens,selectfrom amongthe choicesthe numberthat bestapproximatesthe exactnumericalvalue.
t2) Unlessotherwisespecified,the domain of a function / is assumedto be the set of all real numben x for which
/(r) is a real number.
(3) The inverseof a trigonometricfunction -f maybe indicatedusing the inversefunctionnotation -l or with the
f
prefix "arc" (e.g.,sin-lr = arcsin,r).
Unauthorlzed copying or l€us€
ot this pag6 is
G O O N T O T H EN E X T P A G E .
35
Calculus AB
T6.Aparticlemovesalongthex-axissothatatanytimet20,itsvelocityisgivenbyv(r)=3+4'lcos(0'9t)'
-- 4 ?
What is the accelerationof the particleat time t
(A) -2.016
(B) -0.677
(c) r.633
(D) 1.814
(E) 2.978
und the 'r-axis' If the
77. Theregions A, B, and C in the figure above are bounded by the graph of the function "f
areaof eachregion is 2, what is the value
(A) -2
36
p.rt ot thl.
(B) -l
or tluaa
rlllcgal,
(c) 4
tf ttl + l)dx 2
"f J .
(D) 7
(E) 12
GO ON TO THE NEXTPAGE.
lalculus AB
Theradiusof a circle is increasingat a constantrateof 0.2 metersper second.What is the rate of increasein the
areaof the circle at the instantwhen the circumferenceof the circle is 20a meters?
(A) 0.042m2lsec
(B) 0.4n m2lsec
(C) an m2lsec
(D) 20r.o2ls"c
(E) 1002m2lsec
-9.
For whichof the following does lim /(_r) exist?
II.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
@
rny part of this pago ir illegal.
I
GO ON TO THE NEXTPAGE.
37
Calculus AB
80.Thefunction/iscontinuousfor*2<xSlanddifferentiablefor-2<x<l.lff(-2)=-5andf(l)=4,
whichof thefollowingstatements
couldbefalse?
(A) Thereexistsc, where-2 < c < l, suchthat (c) = 0.
"f
'(c) = 0.
(B) Thereexists
c,where-2 < c < l, suchthat
f
(C) Thereexists
c, where-2 < c < 1,suchthatf (c) = 3.
(D) Thereexists
c, where-2 < c < 1,suchthatf '(c) = 3.
(E) Thereexistsc, where-2 ( c ( 1, suchthatf (c) >-/(;) for all .r ontheclosedinterval-2 < x < l.
81. Let / be the function with derivative given by f '(x) = sin(x2 + l). How many relative extremadoes / have
ontheinterval2 < x < 4?
(A) One
3B
(B) Two
Unauthorlzodcopylng or Fu..
any p.rt ot thlr p.g€ b lllcgtl,
(C) Three
(D) Four
(E) Five
GO ON TO THE NEXTPAGE.
Calculus AB
( r s 8' whichof
82.Therateofchangeofthealtitudeofahot-airballoonisgivenbyr(r) = t3 4tz +6 for0
the following expressionsgives the changein altitude of the balloon during the time the dtitude is decreasing?
(A)
(s)
(c)
8.514
J,.r,
r(t)dt
r8
dt
Jor(t)
12-661
Jo
r(t)dt
@)13# r'Q)dt
*,
ffi
@
f'*'r'(t)dt
GO ONTO THENEXTPAGE.
Calculus AB
g3.Thevelocity,in ft/sec,of a particlemovingalongthe.r-axisis givenby thefunctionv(t) = e' + te'' Whatis the
averagevelocityof theparticlefrom time t = 0 to time t = 3 ?
(A) 20.086ff/sec
(B) 26.447ftlsec
(C) 32.809ff/sec
(D) 40.671fflsec
(E) 79.342ftJsec
g4. Apizza,heated to a temperatureof 350 degreesFahrenheit(oF), is taken out of an oven and placed in a 75oF
-110e-0'a' degreesFahrenheit
room at time t = 0 minutes. The temperatureof the pizza is changing at a rate of
= 5 minutes?
per minute. To the nearestdegree,what is the temperatureof thepizza at time t
(A) 112'F
40
(B) 119"F
rtr.d copylng or r.ux
ol thl! D.o. l. llLg.l.
(c) 147"F
(D) 238"F
(E) 335'F
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Calculus AB
85.If a trapezoidal
sumoverapproximates <Odr, anda rightRiemannsumunderapproximates *,
[if
fitOl
whichof thefollowingcouldbethegraphof y = f (x) ?
Un uthorlz.d copylng or r.u.. ol
.nY D.rl ot thl. Dro. lr lllooel.
GO ONTO THENEXTPAGE.
A1
= I
Calculus AB
86. The baseof a solid is the region in the first quadrantboundedby the y-axis, the graph of y = tan-l x, the
horizontalline y = 3, and the vertical line ;r = 1. For this solid, eachcrosssectionperpendicularto the -r-axisis
a square.What is the volume of the solid?
(A) 2.s61
(B) 6.612
(C) 8.M6
(D) 8.7s5
87. The function / has first derivative given by f '(x) =
pointofthegraphof/ ?
(A) r.008
+z
(B) 0.473
Unauthorizodcopylng or ?€u3. ot
any part ot thli pago b lll.gal.
(c) 0
^li
i;;;7
(D) -0.278
(E) 20.773
What is the .r-coordinate of the inflection
(E) The graph of / has no inflection point.
GO ONTO THENEXTPAGE.
lalculus AB
: S.On the closedinterval [2, 4], which of the following could be the graphof a function / with the propertythat
t
^:
_ _
e
"
z J
4
I f ( t )d t = l ?
2
4
J
2
I
O
l
(c) v.
- ^authorlzGdcopying or rcure of I
@
GOON TO THENEXTPAGE.
Calculus AB
'(2) = -5, andlet g bethefunctiondefinedby
89. Let,f beadifferentiablefuncrionwith
/(2) = 3 and f
g(x) = xf (x).Which of the following is an equationof the line tangentto the graphof g at the point where
x = 2 2
(A) Y = 3-r
( B ) y - 3 = -5(-r - 2)
( C )y - 6 =
-5(x - 2)
( D )y - 6 =
-7(x - 2)
( E )y - 6 =
- 1 0 ( x- 2 )
90. For all .r in the closedinterval [2, S], ttre function / hasa positive frst derivative and a negativesecond
derivative.Which of the followine could be a tableof valuesfor f ?
(A)
44
(B)
rlzod copylng or reusa
ot lhl. oaa6 lr llloqal.
(c)
(D)
(E)
GO ONTO THENEXTPAGE.
Cdculus AB
a(r) = tn(l + zt)' lf tne
t > 0, itsaccelerationisgivenby
91.Aparticlemovesalongthe.r-axissothatatanytime
= 2 \s
velocity of the particleis 2 at time t = 1,thenthe velocity of the particleat time t
G) r.60e
(A) 0.462
(c)2.sss
(D) 2.886
(E) 3.346
gZ. 1,etg be the function given by 8(r) =
sin(r'z)ar for -l < x < 3. On which of the following intervalsis g
f
decreasing?
(A)-l<x<0
( B )0 s x < 1 . 7 7 2
(C)1.253<
x<2.171
(D)1.772<x<2.507
@)2.802<x<3
ENDOF SECTIONI
AFTERTIMEHASBEENCALLED,TURNTO THE NEXT PAGEAND
93-96.
ANSWER
QUESTIONS
UnaulhorEcd coPylng ot ruua.
of thlr
Calculus AB
93. Whichgraphingcalculatordid you useduringtheexamination?
(A) Casio6300,Casio7300,Casio7400,Casio77ffi,T1-73,TI-80,or TI-81
q:00' fI-92: or TI-85
igi Cusio9700,Casio9800,Sharp9200,Sharp
Plus,or TI-86
iCi Curio9850,CasioFX 1.0,Sharp9600,Sharp9900,TLq3{I:83
48 series,Hp 49 series,or TI-89
I{P
40G,
HP
39c,
38G;IIP
I{p
i.o,
ini curio 9970,casio Algebrarx
(E) Someothergraphingcalculator
yourcalculatoruse?
94. Duringyour CalculusAB course,whichof thefollowingbestdescribes
(A) usedmy own graPhingcalculator.
(B) useda graphirigcalculatorfurnishedby my school,both in classand at home'
(c)
useda gtaphing calculatorfurnishedby my school only in class'
(D) useda it"itti"I calculatorfurnishedby -y schoolmostly in class,but occasionallyat home'
(E) did not use a graPhingcalculator.
9 5 . During your CalculusAB course,which of the following describesapproximately.howoften
u grupiing calculator was usedby you or your teacherin classroomlearningactivities?
(A)
(B)
(C)
(D)
(E)
Almost every class
About three-quartersof the classes
About one-halfof the classes
About one-quarterof the classes
Seldom or never
you
96. During your CalculusAB course,which of the following describesthe portion of testing time
were allowed to use a graphing calculator?
(A)
(B)
(C)
(D)
(E)
46
All or almost all of the time
About three-quartersof the time
About one-half of the time
About one-quarterof the time
Seldomor never
uthorlzod copylng or rlu36
prrt ot thlt pege lt lllogal.
section I Answer Key and Percent Answering correctly
Calculus BC Part A
Calculus AB Part A
2
3
Correct
Answer
E
D
E
4
l)
Item
No.
l
5
D
{-)
C
7
B
B
ts
9
0
B
C
z
3
E
5
E
t)
6
C
4
Percent Correct by Grade
5
4
3
2
1
75
94
97
98
99
L2
23
40
62
84
22
30
47
37
65
79
55
B6
92
96
?,3
43
57
72
B6
76
55
85
92
97
18
42
69
87
95
47
22
6'/
84
95
23
9
40
60
82
35
61
79
93
98
I4
25
35
46
62
3
83
5B
82,
s
D
!)4
96
76
59
34
5
C
8e
69
'i1
6
C
'i-/
D
34
91
ri1
c4
7:3
25
B]
80
42
38
62
2a
77
68
32
3i
35
46
19
64
54
?.5
24
?.3
30
1.4
39
29
15
t9
TJ
95
90
85
90
li
96
66
73
2?,
?-5
55
13
13
59
ac
5
1
65
I
44
9
75
l0
96
B9
92
74
6B
78
83
55
52
41
69
36
40
39
16
tr6
30
5ii
58
34
18
11
52
31
37
31
34
24
4L
2,7
69
4D
20
21
'22
D
II
7B
79
B0
2.3
?.4
?.5
2€)
E
55
()
u
95
94
90
52
35
87
84
76
B
4b
18
7
53
il4
2
4
23
29
'ta
3
18
AE
1ti
I
3!
2?,
1.7
1?'
T2
2,4
2.4
2A
13
4L
1
32
57
51
38
9
I
2
42
5?,
3B
?.6
68
3
1
F
J7
65
29
66
67
58
18
6
2.
3
C
B
84
6
L
9,1
61
'd2-
7
,1
63
?,2
1u
6
44
l8
10
I
L)
/,J
6rl
17
5
36
20
?,1.
22
23
24
25
'26
D
43
I9
i_1
11
2,4
i0
b
5:i
?.?,
2,0
1.4
14
F]
4fl
1.4
I
4
IJ
fl8
2.4
-/5
61
49
?,8
20
33
18
27
28
tl
I
l)
D
B
B
88
B9
90
91
92
92
il
D
B
E
D
1.4
2.?,
15
9
Total
Percent
Correst
23
7-/
8fl
74
64
t;/
54
65
95
61
4l
37
18
t,7
-t1
t5
52
25
55
36
2A
78
3J
J/
LT
54
7?
79
80
81
39
s2
50
2.6
83
34
1()
33
51.
4 1
43
26
44
42
30
60
17
49
t1
13
15
33
7 9 6
19
30
14
1.2
30
19
1.2
24
13
i7
37
T2
I
1g
32
Correct
Answer
U
Percent Correct by Grade
5
4
3
2
1
'/1
'/8
61
44
3B
33
23
l'r
D
B
D
B6
87
2.2.
36
19
57
45
79
80
A
46
07
3
63
81
94
69
B6
63
38
83
68
73
52
79
66
6 5 3
77
57
79
50
79
61
82
62
84
56
B0
92
26
54
70
B8
85
79
79
C
A
4t)
',10
78
83
B4
26
ll li
g
55
'd2
:lS
B6
t0
13
C
bt
(l:r
/1
(i2,
LJ
4
Item
No.
76
C,'
26
45
66
Total
Percent
Correct
96
67
88
79
65
69
29
tJl
74
43
44
87
86
q3
58
78
36
1A
59
26
33
28
70
62
75
47
39
Calculus BC Part B
Percent Correct by Grade
5
4
3
2
1
38
B'7 73
97
94
Correct
Answer
'.ig
34
33
43
72
Calculus AB Part B
Item
No.
76
77
Percent Correct by Grade
5
4
3
2
7
84
94
98
97
99
'10
33
60
49
51
76
94
B8
98
4i
b4
49
61
F
C
41.
67
75
?-'e,
2
76
83
?-7
15
86
I
E
1
Correct
Answer
E
94
97
90
B6
D
Item
No.
76
75
77
I
19
Total
Percent
Correct
93
I)
it'a
A
9e,
94
79
'/6
6ij
,i7
87
52
42
28
58
28
1.7
E
!,16
A7
76
59
37
C
86
A
c3
3',7
86
(a
60
41
23
29
24
47
?7
88
39
90
C
C
84
42,
6B
47
60
32.
25
34
85
63
73
5e
41
22
D
;i
44
)t'
1?.
7
R
iio
6,1
49
32
i8
91
D
Ui
4',]
31
54
30
35
2A
18
13
13
55
31
.+t-l
39
59
24
53
92
'rl
41
Aq
27
13
I
Total
Percent
Correct
't5
74
80
66
B9
62
54
BO
62
69
44
4b
65
qo
59
42
53
Table .zAB-Calculus
AB Scoring Worksheet
Section I: MuttiPle Choice
)l t i . 2 0 0 0:
* (u4 x --Number Wrong
Number Correct
(out of 45)
Weighted
Sectton I Score
(lf iess than zero, enter
zero; clo not round)
Section II: Free ResPonse
x 1 C000
Ouestion 1
(Donot round)
(oul of 9)
x10000-
Ouestion 2
(Donot round)
(out of 9)
x 1 0000
Ouestion 3
(Doncrtlound)
(out of 9)
AP Grade Conversion Chart
x10000-
Ouestion 4
(Do no';round)
(oul of 9)
Composile
S c o r eR a n g e *
x10000:
Ouestion 5
(Donot round)
(out of 9)
x 1.0000-
Ouestion 6
(Donot round)
(out ol 9)
66-108
47-65
29-46
16-28
0- 15
AP Grade
5
4
3
2
1'
The stuc]enls' scores are welghteci accordlng [o
formulas cleterminetl in advance each year ily the
Development Colrinllllee to yielcl rtrw colrposrte
scores; the Chref Reader is resl:onsible for cot.tvertlng cornposiLe scores lo the s-polnt AP scale
Sum
Wetqhtecl
S e c i . i o nI I S c o r e
(Dorot, round)
Composite Score
Werghtecl
Seclron I Scoie
!"v'eigfrlrci
il Srrr,re
Se':ct:c;-,
Composite Score
(Rouncito nearesl
.r;hole number)
173
Table4.3AB_CalculusABGradeDistributions
grade of -3or above'
Nearly 66 percent 6f the AP studentswho took this exam earned a quaiiffing
Ex ;i,';rt."-|-
Grade
I
N"'*b";-f
P"'""* *
students
Grade
-f--------l
30032
I
,'t't
Extremeiy' weil quairfied
5
l
Weii qudified
4
1
3?.163
Ouaiified
,
|
:r:1,ie2
i
,).i).4:)|
'u'
:?!253 l,
t'e
Possiblv quahfrecl
No recommenclatlon
t
,
i
I
i
I
2rlu
|
tl+
|
i
L-,---.-.------
l
Mean Glacie
Standard Dq'vlatton
:
I
I
I
I
I
i
l
i i,,'.1
13lr
Total Number of iitud€rnts
I
:
___-_l
I
l
Table A.AAB_.Calculus AB Section tr Scores and AP Grades
ol-studentsreceivingeirchAP
For a given rangeof multiple-choiccscores,this tableshowsthc per!e ntage
by using the fbrmula
grud.. If yo., have calculatedthe multiple-choice scorc (Weighted Section I Score)
the studcntwould
that
grade
liLcly
most
the
shown in Table4.2AB,yoLlcan usethis tahlc to figure or-rt
receivebasedonly on that rnultiplc-choice score'
AP Grade
Multiple-Choice
46 to 54
37 to 45
28 ro 36
19 ro 2'/
1 0r o 1 8
0rog
Totai
174
Score