AP CALCULUS AB/CALCULUS BC 15 SCORING GUIDELINES Quesion 1 The rae a which rainwaer flows ino a drainpipe is modeled by he funcion R, where R ( ) = sin 5 cubic fee per hour, is measured in hours, and 8. The pipe is parially blocked, allowing waer o drain ou he oher end of he pipe a a rae modeled by D ( ) =.4 +.4 +.96 cubic fee per hour, for 8. There are cubic fee of waer in he pipe a ime =. (a) How many cubic fee of rainwaer flow ino he pipe during he 8-hour ime inerval 8? (b) Is he amoun of waer in he pipe increasing or decreasing a ime = hours? Give a reason for your answer. (c) A wha ime, 8, is he amoun of waer in he pipe a a minimum? Jusify your answer. (d) The pipe can hold 5 cubic fee of waer before overflowing. For > 8, waer coninues o flow ino and ou of he pipe a he given raes unil he pipe begins o overflow. Wrie, bu do no solve, an equaion involving one or more inegrals ha gives he ime w when he pipe will begin o overflow. 8 : { 1 : inegrand (a) R( ) d = 76.57 (b) R( ) D( ) =.16 < Since R( ) < D(, ) he amoun of waer in he pipe is decreasing a ime = hours. (c) The amoun of waer in he pipe a ime, 8, is + [ R( x) D( x) ] dx. 1 : considers R( ) and D( ) : and reason 1 : considers R ( ) D ( ) = : 1 : jusificaion R ( ) D ( ) = =,.71658 Amoun of waer in he pipe.71658 7.964561 8 48.54686 The amoun of waer in he pipe is a minimum a ime =.7 (or.71) hours. w (d) + [ R ( ) D ( )] d = 5 : { 1 : inegral 1 : equaion 15 The College Board. Visi he College Board on he Web: www.collegeboard.org.
AP CALCULUS AB/CALCULUS BC 14 SCORING GUIDELINES Quesion 1 Grass clippings are placed in a bin, where hey decompose. For, he amoun of grass clippings remaining in he bin is modeled by A ( ) = 6.687(.91 ), where A () is measured in pounds and is measured in days. (a) Find he average rae of change of A ( ) over he inerval. Indicae unis of measure. (b) Find he value of A ( 15 ). Using correc unis, inerpre he meaning of he value in he conex of he problem. (c) Find he ime for which he amoun of grass clippings in he bin is equal o he average amoun of grass clippings in he bin over he inerval. (d) For >, L ( ), he linear approximaion o A a =, is a beer model for he amoun of grass clippings remaining in he bin. Use L ( ) o predic he ime a which here will be.5 pound of grass clippings remaining in he bin. Show he work ha leads o your answer. (a) A( ) A( ) =.197 (or.196) lbs/day wih unis (b) A ( 15 ) = 1. 64 (or.16) The amoun of grass clippings in he bin is decreasing a a rae of.164 (or.16) lbs/day a ime = 15 days. 1 : A ( 15) : 1 : inerpreaion (c) 1 A ( ) = A ( ) d 1.415 (or 1. 414) = 1 1 : A( ) d : (d) L ( ) = A( ) + A ( ) ( ) A ( ) =.55976 A( ) =.7898 : expression for L ( ) 4 : 1 : L ( ) =.5 L ( ) =.5 = 5.54 14 The College Board. Visi he College Board on he Web: www.collegeboard.org.
1 SCORING GUIDELINES Quesion 1 On a cerain workday, he rae, in ons per hour, a which unprocessed gravel arrives a a gravel processing plan is modeled by G ( ) = 9 + 45cos, 18 where is measured in hours and 8. A he beginning of he workday ( =, ) he plan has 5 ons of unprocessed gravel. During he hours of operaion, 8, he plan processes gravel a a consan rae of 1 ons per hour. (a) Find G ( 5. ) Using correc unis, inerpre your answer in he conex of he problem. (b) Find he oal amoun of unprocessed gravel ha arrives a he plan during he hours of operaion on his workday. (c) Is he amoun of unprocessed gravel a he plan increasing or decreasing a ime = 5 hours? Show he work ha leads o your answer. (d) Wha is he maximum amoun of unprocessed gravel a he plan during he hours of operaion on his workday? Jusify your answer. (a) G ( 5) = 4.588 (or 4. 587) The rae a which gravel is arriving is decreasing by 4.588 (or 4.587) ons per hour per hour a ime = 5 hours. 1 : G ( 5) : 1 : inerpreaion wih unis 8 ons : { 1 : inegral (b) G( ) d = 85.551 (c) G ( 5) = 98.14764 < 1 A ime = 5, he rae a which unprocessed gravel is arriving is less han he rae a which i is being processed. Therefore, he amoun of unprocessed gravel a he plan is decreasing a ime = 5. (d) The amoun of unprocessed gravel a ime is given by A ( ) = 5 + ( Gs ( ) 1 ) ds. A ( ) = G ( ) 1 = = 4.948 1 : compares G( 5 ) o 1 : 1 : conclusion : 1 : considers A ( ) = 1 : jusificaion A ( ) 5 4.948 65.761 8 55.55189 The maximum amoun of unprocessed gravel a he plan during his workday is 65.76 ons. 1 The College Board. Visi he College Board on he Web: www.collegeboard.org.
11 SCORING GUIDELINES (Form B) Quesion 1 A cylindrical can of radius 1 millimeers is used o measure rainfall in Sormville. The can is iniially empy, and rain eners he can during a 6-day period. The heigh of waer in he can is modeled by he funcion S, where S () is measured in millimeers and is measured in days for 6. The rae a which he heigh of he waer is rising in he can is given by S ( ) = sin(.) + 1.5. (a) According o he model, wha is he heigh of he waer in he can a he end of he 6-day period? (b) According o he model, wha is he average rae of change in he heigh of waer in he can over he 6-day period? Show he compuaions ha lead o your answer. Indicae unis of measure. (c) Assuming no evaporaion occurs, a wha rae is he volume of waer in he can changing a ime = 7? Indicae unis of measure. (d) During he same 6-day period, rain on Monsoon Mounain accumulaes in a can idenical o he one in Sormville. The heigh of he waer in he can on Monsoon Mounain is modeled by he funcion M, where 1 M () = ( + ). The heigh M ( ) is measured in millimeers, and is measured in days 4 for 6. Le D ( ) = M ( ) S ( ). Apply he Inermediae Value Theorem o he funcion D on he inerval 6 o jusify ha here exiss a ime, < < 6, a which he heighs of waer in he wo cans are changing a he same rae. 6 (a) S( 6) = S ( ) d = 171.81 mm : 1 : limis 1 : inegrand (b) S( 6) S( ) 6 =.86 or.864 mm day (c) V() = 1π S() V ( 7) = 1π S ( 7) = 6.18 The volume of waer in he can is increasing a a rae of 6.18 mm day. 1 : relaionship beween V and S : { (d) D ( ) =.675 < and D ( 6) = 69.77 > Because D is coninuous, he Inermediae Value Theorem implies ha here is a ime, < < 6, a which D ( ) =. A his ime, he heighs of waer in he wo cans are changing a he same rae. 1 : considers D( ) and D( 6) : 1 : jusificaion 1 : unis in (b) or (c) 11 The College Board. Visi he College Board on he Web: www.collegeboard.org.
1 SCORING GUIDELINES Quesion 1 There is no snow on Jane s driveway when snow begins o fall a midnigh. From midnigh o 9 A.M., snow cos accumulaes on he driveway a a rae modeled by f() = 7e cubic fee per hour, where is measured in hours since midnigh. Jane sars removing snow a 6 A.M. ( = 6. ) The rae g (), in cubic fee per hour, a which Jane removes snow from he driveway a ime hours afer midnigh is modeled by for < 6 g () = 15 for 6 < 7 18 for 7 9. (a) How many cubic fee of snow have accumulaed on he driveway by 6 A.M.? (b) Find he rae of change of he volume of snow on he driveway a 8 A.M. (c) Le h () represen he oal amoun of snow, in cubic fee, ha Jane has removed from he driveway a ime hours afer midnigh. Express h as a piecewise-defined funcion wih domain 9. (d) How many cubic fee of snow are on he driveway a 9 A.M.? 6 or 14.75 cubic fee : { 1 : inegral (a) f() d = 14.74 (b) Rae of change is f( 8) g( 8) = 59.58 or 59.58 cubic fee per hour. (c) h ( ) = For < 6, h () = h( ) + gs ( ) ds= + ds=. For 6 7, < h () = h( 6) + gs ( ) ds= + 15 ds= 15( 6 ). For 7 9, 6 6 < h () = h( 7) + g( s) ds = 15 + 18 ds = 15 + 18( 7 ). 7 7 for 6 Thus, h () = 15( 6) for 6 < 7 15 + 18( 7) for 7 < 9 : 1 : h () for 6 1 : h () for 6 < 7 1 : h () for 7 < 9 1 : inegral 9 (d) Amoun of snow is f() d h( 9) = 6.4 or 6.5 cubic fee. : 1 : h( 9) 1 The College Board. Visi he College Board on he Web: www.collegeboard.com.
9 SCORING GUIDELINES (Form B) Quesion A sorm washed away sand from a beach, causing he edge of he waer o ge closer o a nearby road. The rae a which he disance beween he road and he edge of he waer was changing during he sorm is modeled by f() = + cos meers per hour, hours afer he sorm began. The edge of he waer was 5 meers from he road when he sorm began, and he sorm lased 5 hours. The derivaive of f () 1 is f () = sin. (a) Wha was he disance beween he road and he edge of he waer a he end of he sorm? (b) Using correc unis, inerpre he value f ( 4) = 1.7 in erms of he disance beween he road and he edge of he waer. (c) A wha ime during he 5 hours of he sorm was he disance beween he road and he edge of he waer decreasing mos rapidly? Jusify your answer. (d) Afer he sorm, a machine pumped sand back ono he beach so ha he disance beween he road and he edge of he waer was growing a a rae of g( p ) meers per day, where p is he number of days since pumping began. Wrie an equaion involving an inegral expression whose soluion would give he number of days ha sand mus be pumped o resore he original disance beween he road and he edge of he waer. 5 or 6.495 meers : { 1 : inegral (a) 5 + f() d = 6.494 (b) Four hours afer he sorm began, he rae of change of he disance beween he road and he edge of he waer is increasing a a rae of 1.7 meers hours. (c) f () = when =.66187 and =.848 The minimum of f for 5 may occur a,.66187,.848, or 5. f ( ) = f (.66187) = 1.976 f (.848) =.696 f ( 5) =.487 1 : inerpreaion of f ( 4) : 1 : unis : 1 : considers f () = 1 : jusificaion The disance beween he road and he edge of he waer was decreasing mos rapidly a ime =.84 hours afer he sorm began. 5 x : { (d) f () d = g( p) dp 1 : inegral of g 9 The College Board. All righs reserved. Visi he College Board on he Web: www.collegeboard.com.
9 SCORING GUIDELINES Quesion The rae a which people ener an audiorium for a rock concer is modeled by he funcion R given by R() = 18 675 for hours; R() is measured in people per hour. No one is in he audiorium a ime =, when he doors open. The doors close and he concer begins a ime =. (a) How many people are in he audiorium when he concer begins? (b) Find he ime when he rae a which people ener he audiorium is a maximum. Jusify your answer. (c) The oal wai ime for all he people in he audiorium is found by adding he ime each person wais, saring a he ime he person eners he audiorium and ending when he concer begins. The funcion w models he oal wai ime for all he people who ener he audiorium before ime. The derivaive of w is given by w () = ( ) R(). Find w( ) w( 1 ), he oal wai ime for hose who ener he audiorium afer ime = 1. (d) On average, how long does a person wai in he audiorium for he concer o begin? Consider all people who ener he audiorium afer he doors open, and use he model for oal wai ime from par (c). people : { 1 : inegral (a) R () d= 98 (b) R () = when = and = 1.696 The maximum rae may occur a, a = 1.696, or. R ( ) = Ra ( ) = 854.57 R ( ) = 1 : 1 : considers R () = 1 : inerior criical poin and jusificaion The maximum rae occurs when = 1.6 or 1.6. (c) w( ) w() 1 = w () d = ( ) R() d = 87.5 1 1 The oal wai ime for hose who ener he audiorium afer ime = 1 is 87.5 hours. : { 1 : inegral 1 1 (d) w( ) = ( ) R( ) d.77551 98 98 = On average, a person wais.775 or.776 hour. : { 1 : inegral 9 The College Board. All righs reserved. Visi he College Board on he Web: www.collegeboard.com.
For ime AP CALCULUS BC 8 SCORING GUIDELINES (Form B) 1 hours, le r () 1( 1 e ) Quesion = represen he speed, in kilomeers per hour, a which a car ravels along a sraigh road. The number of liers of gasoline used by he car o ravel x kilomeers is g x =.5x 1 e x. modeled by ( ) ( ) (a) How many kilomeers does he car ravel during he firs hours? (b) Find he rae of change wih respec o ime of he number of liers of gasoline used by he car when = hours. Indicae unis of measure. (c) How many liers of gasoline have been used by he car when i reaches a speed of 8 kilomeers per hour? kilomeers : { 1 : inegral (a) r() d = 6.7 dg dg dx dx (b) = ; = r () d dx d d dg dg r( ) d = dx = x= 6.7 = (.5)( 1) = 6 liers hour : uses chain rule : { wih unis (c) Le T be he ime a which he car s speed reaches 8 kilomeers per hour. Then, rt ( ) = 8 or T =.145 hours. 4 : 1 : equaion r () = 8 : disance inegral A ime T, he car has gone T xt ( ) = r( ) d= 1.79497 kilomeers and has consumed g( x( T )) =.57 liers of gasoline. 8 The College Board. All righs reserved. Visi he College Board on he Web: www.collegeboard.com.
7 SCORING GUIDELINES (Form B) Quesion The wind chill is he emperaure, in degrees Fahrenhei ( F, ) a human feels based on he air emperaure, in degrees Fahrenhei, and he wind velociy v, in miles per hour ( mph ). If he air emperaure is F, hen he.16 wind chill is given by W( v) = 55.6.1v and is valid for 5 v 6. (a) Find W ( ). Using correc unis, explain he meaning of W ( ) in erms of he wind chill. (b) Find he average rae of change of W over he inerval 5 v 6. Find he value of v a which he insananeous rae of change of W is equal o he average rae of change of W over he inerval 5 v 6. (c) Over he ime inerval 4 hours, he air emperaure is a consan F. A ime =, he wind velociy is v = mph. If he wind velociy increases a a consan rae of 5 mph per hour, wha is he rae of change of he wind chill wih respec o ime a = hours? Indicae unis of measure. (a).84 W ( ) =.1.16 =.85 or.86 When v = mph, he wind chill is decreasing a.86 F mph. : { 1 : value 1 : explanaion (b) The average rae of change of W over he inerval W( 6) W( 5) 5 v 6 is =.5 or.54. 6 5 W( 6) W( 5) W ( v) = when v =.11. 6 5 1 : average rae of change : 1 : W ( v) = average rae of change 1 : value of v dw dw dv = = 5 5 =.89 F hr d dv d (c) ( ) W ( ) = = OR W = 55.6.1( + 5).16 dw =.89 F hr d = dv 1 : = 5 d 1 : uses v( ) = 5, : or uses v () = + 5 Unis of F mph in (a) and F hr in (c) 1 : unis in (a) and (c) 7 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and www.collegeboard.com/apsudens (for sudens and parens).
7 SCORING GUIDELINES Quesion The amoun of waer in a sorage ank, in gallons, is modeled by a coninuous funcion on he ime inerval 7, where is measured in hours. In his model, raes are given as follows: (i) The rae a which waer eners he ank is f () = 1 sin ( ) gallons per hour for 7. (ii) The rae a which waer leaves he ank is 5 for < g () = gallons per hour. for < 7 The graphs of f and g, which inersec a = 1.617 and = 5.76, are shown in he figure above. A ime =, he amoun of waer in he ank is 5 gallons. (a) How many gallons of waer ener he ank during he ime inerval 7? Round your answer o he neares gallon. (b) For 7, find he ime inervals during which he amoun of waer in he ank is decreasing. Give a reason for each answer. (c) For 7, a wha ime is he amoun of waer in he ank greaes? To he neares gallon, compue he amoun of waer a his ime. Jusify your answer. 7 gallons : { 1 : inegral (a) f() d 864 (b) The amoun of waer in he ank is decreasing on he inervals 1.617 and 5.76 because f () < g() for < 1.617 and < < 5.76. (c) Since f () g() changes sign from posiive o negaive only a =, he candidaes for he absolue maximum are a =,, and 7. (hours) gallons of waer 5 5 + f() d 5( ) = 516.591 7 7 516.591 + f() d ( 4) = 451.87 : { 1 : inervals 1 : reason 1 : idenifies = as a candidae 1 : inegrand 5 : 1 : amoun of waer a = 1 : amoun of waer a = 7 1 : conclusion The amoun of waer in he ank is greaes a hours. A ha ime, he amoun of waer in he ank, rounded o he neares gallon, is 517 gallons. 7 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and www.collegeboard.com/apsudens (for sudens and parens).
6 SCORING GUIDELINES Quesion A an inersecion in Thomasville, Oregon, cars urn lef a he rae L () = 6 sin ( ) cars per hour over he ime inerval 18 hours. The graph of y = L() is shown above. (a) To he neares whole number, find he oal number of cars urning lef a he inersecion over he ime inerval 18 hours. (b) Traffic engineers will consider urn resricions when L () 15 cars per hour. Find all values of for which L () 15 and compue he average value of L over his ime inerval. Indicae unis of measure. (c) Traffic engineers will insall a signal if here is any wo-hour ime inerval during which he produc of he oal number of cars urning lef and he oal number of oncoming cars raveling sraigh hrough he inersecion is greaer han,. In every wo-hour ime inerval, 5 oncoming cars ravel sraigh hrough he inersecion. Does his inersecion require a raffic signal? Explain he reasoning ha leads o your conclusion. 18 (a) L () d 1658 cars (b) L () = 15 when = 1.481, 16.1166 Le R = 1.481 and S = 16.1166 L () 15 for in he inerval [ R, S ] 1 S L () d= 199.46 S R cars per hour R (c) For he produc o exceed,, he number of cars urning lef in a wo-hour inerval mus be greaer han 4. 15 1 OR L () d= 41.91 > 4 The number of cars urning lef will be greaer han 4 on a wo-hour inerval if L () on ha inerval. L () on any wo-hour subinerval of [ 1.54, 15.86 ]. : { 1 : seup : 1 : -inerval when L() 15 1 : average value inegral wih unis 1 : considers 4 cars 1 : valid inerval [ h, h ] + 4 : h+ 1 : value of L () d h and explanaion 4 : OR 1 : considers cars per hour 1 : solves L () 1 : discusses hour inerval and explanaion Yes, a raffic signal is required. 6 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and www.collegeboard.com/apsudens (for AP sudens and parens).
5 SCORING GUIDELINES (Form B) Quesion A waer ank a Camp Newon holds 1 gallons of waer a ime =. During he ime inerval 18 hours, waer is pumped ino he ank a he rae () 95 sin ( ) W = gallons per hour. 6 During he same ime inerval, waer is removed from he ank a he rae () 75sin ( ) R = gallons per hour. (a) Is he amoun of waer in he ank increasing a ime = 15? Why or why no? (b) To he neares whole number, how many gallons of waer are in he ank a ime = 18? (c) A wha ime, for 18, is he amoun of waer in he ank a an absolue minimum? Show he work ha leads o your conclusion. (d) For > 18, no waer is pumped ino he ank, bu waer coninues o be removed a he rae R() unil he ank becomes empy. Le k be he ime a which he ank becomes empy. Wrie, bu do no solve, an equaion involving an inegral expression ha can be used o find he value of k. (a) No; he amoun of waer is no increasing a = 15 since W( 15) R( 15) = 11.9 <. wih reason 18 (b) 1 + ( W() R() ) d = 19.788 11 gallons : 1 : limis 1 : inegrand (c) W() R() = =, 6.4948, 1.9748 (hours) gallons of waer 1 6.495 55 1.975 1697 18 11 1 : inerior criical poins 1 : amoun of waer is leas a : = 6.494 or 6.495 1 : analysis for absolue minimum The values a he endpoins and he criical poins show ha he absolue minimum occurs when = 6.494 or 6.495. k (d) R () d= 11 18 1 : limis : 1 : equaion Copyrigh 5 by College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and www.collegeboard.com/apsudens (for AP sudens and parens).
4 SCORING GUIDELINES Quesion 1 Traffic flow is defined as he rae a which cars pass hrough an inersecion, measured in cars per minue. The raffic flow a a paricular inersecion is modeled by he funcion F defined by () 8 4sin ( ) F = + for, where F() is measured in cars per minue and is measured in minues. (a) To he neares whole number, how many cars pass hrough he inersecion over he -minue period? (b) Is he raffic flow increasing or decreasing a = 7? Give a reason for your answer. (c) Wha is he average value of he raffic flow over he ime inerval 1 15? Indicae unis of measure. (d) Wha is he average rae of change of he raffic flow over he ime inerval 1 15? Indicae unis of measure. (a) F () d= 474 cars : 1 : limis 1 : inegrand (b) F ( 7) = 1.87 or 1.87 Since F ( 7) <, he raffic flow is decreasing a = 7. wih reason 1 15 (c) () 81.899 cars min 5 F d= 1 : 1 : limis 1 : inegrand (d) F( 15) F( 1) 15 1 = 1.517 or 1.518 cars min Unis of cars min in (c) and cars min in (d) 1 : unis in (c) and (d) Copyrigh 4 by College Enrance Examinaion Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and www.collegeboard.com/apsudens (for AP sudens and parens).
SCORING GUIDELINES (Form B) Quesion J 6DAK>AHBC=IJ B=FKJ=JE==A?D=CAI=JJDAH=JA= J Г! A Г C=IFAH@=OMDAHAJEIA=IKHA@E@=OI6DAHA=HA#C=IBJDAFKJ=JEJDA=A=J JEAJ6DA=AEI?IE@AHA@J>AI=BAMDAEJ?J=EI"C=IHAIIBFKJ=J = 1IJDA=KJBFKJ=JE?HA=IEC=JJEAJ'9DOHMDOJ >.HMD=JL=KABJMEJDAK>AHBC=IBFKJ=J>A=JEJIEEKKIJEBOOKH =IMAH? 1IJDA=AI=BAMDAJDAK>AHBC=IBFKJ=JEI=JEJIEEKKIJEBOOKH =IMAH @ )ELAIJEC=JHKIAIJDAJ=CAJEA=FFHNE=JEJJ =JJ=I=@ABHJDA =KJBFKJ=JEJDA=A)JMD=JJEAJ@AIJDEI@AFHA@E?JJD=JJDA=A >A?AII=BA =IMAHMEJDHA=I $ = = ' Г! A Г Г$"$ IJDA=KJEIJE?HA=IEC=JJDEIJEA > = J Г! A Г J IAJI= J J #!!%"! ILAIBHJ = J EIAC=JELABHJ #! =@FIEJELA KIJEBE?=JE BHJ #! 6DAHABHAJDAHAEI=EEK=J J #!!%" Г J?!%" # Г! A @J EJACH=@ EEJI!#""IJDA=AEII=BA!??KIEMEJDHA=I >=IA@EJACH=B= J @ = Г! Г 6DA=AME>A?AI=BA IFABJ=CAJEA MDAJDA=KJ@A?HA=IAI>O)EA=H@A =IMAH FHA@E?JIJDEIMED=FFAMDAJ# Copyrigh by College Enrance Examinaion Board. All righs reserved. Advanced Placemen Program and AP are regisered rademarks of he College Enrance Examinaion Board.
SCORING GUIDELINES Quesion 6DAH=JA=JMDE?DFAFAAJAH==KIAAJF=H=CELA@=OEI@AA@>OJDABK?JE- @ABEA@>O - J #$ J Г " J $ 6DAH=JA=JMDE?DFAFAA=LAJDAI=A=KIAAJF=HJDAI=A@=OEI@AA@>OJDABK?JE @ABEA@>O J '&' J Г!& J!% *JD - J =@ J=HAA=IKHA@EFAFAFAHDKH=@JEA J EIA=IKHA@EDKHI=BJAHE@ECDJ6DAIA BK?JEI=HAL=E@BH ' > J >!JDADKHI@KHECMDE?DJDAF=HEIFA)JJEA J ' Copyrigh by College Enrance Examinaion Board. All righs reserved. Advanced Placemen Program and AP are regisered rademarks of he College Enrance Examinaion Board. JDAHA=HAFAFAE JDAF=H = M=OFAFAD=LAAJAHA@JDAF=H>O#J % 4K@=IMAHJJDAA=HAIJMDAK>AH > 6DAFHE?AB=@EIIEJJDAF=HEI#KJE#J % )BJAH#JDAFHE?AB=@EIIEJ JDAF=HEIM=O@=HI=HA?A?JA@BH=@EIIEIJJDAF=HJDACELA@=O4K@OKH =IMAHJJDAA=HAIJMDAK>AH J? AJ J -NГN @N BH ' > J >!6DAL=KAB % JJDAA=HAIJMDAK>AHEI!% # '.E@JDAL=KAB = % =@ANF=EJDAA=ECB % =@ = % EJDA?JANJBJDAF=H @ )JMD=JJEA JBH ' > J >!@AIJDA@AFHA@E?JJD=JJDAK>AHBFAFAEJDAF=HEI==NEK = > ' % -J@J $" % $"FAFAAJAHA@JDAF=H>O#F %! # -J@J -J@J ""&$# ' % 6DA=KJ?A?JA@M=I""& H! -J@J % &! % %FAFAAJAHA@JDAF=H>AJMAA#F=@ FIJDA=KJ?A?JA@M=I # $" % " "? = % -% Г% Г!& & 6DAHAMAHA!% #FAFAEJDAF=H=JJ% 6DAK>AHBFAFAEJDAF=HM=I@A?HA=IEC =JJDAH=JAB=FFHNE=JAO!&FAFADH=J JEAJ% @ = J -J ГJ J#%'"H#%'# EEJI! EJACH=@ =IMAH IAJKF L=KAB = % A=ECI! A=ECB % A=ECB = % Г EBHABAHA?AJJ % -J ГJ =IMAH
1998 Calculus BC Scoring Guidelines Copyrigh 1998 by College Enrance Examinaion Board. All righs reserved. Advanced Placemen Program and AP are regisered rademarks of he College Enrance Examinaion Board.