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8/7/2019 MATHS SPM PAPER 2 QUESTIONS
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TILUS
TILUS 2/9441
2/9441 MPJatpiCkaH0102 halebesnamalahtahiL[
SARALESNAASKIREPEP NUHATNAHAGNETREP
02AISYALAMNARAJALEPLIJIS 01
2fostsisnocrepapnoitseuqsihT 1 .segapdetnirp
SCITAMEHTAM2repaP
setunimytrihtdnasruohowT
SIHTNEPOTONOD ERAUOYLITNUREPAPNOITSEUQ
OSODOTDLOT
.1 noitcesowttsisnocrepapnoitseuqsihT : noitceS A dna noitceS B .
nisnoitseuqllarewsnA AnoitceS nidna .BnoitceS
.2 .laugnilibsirepapnoitseuqsihT
.3 psecapsehtnisrewsnaruoyetirW .repapnoitseuqehtnidedivor
.4 .ylraelcnettirwebtsumpetsgnikroW
.5 .detatssselnuelacsotgnidroccatonsinevigmargaiD
.6 .tekcarbninevigeranoitseuqhcaerofskraM
.7 .3dna2segapninevigsiealumroffotsilA
.8 ccifitneicselbammargorpnoN .dewollaerarotalucla
.maxeehtfodneehttapudnahebtsumrepapnoitseuqsihT9
noitceS noitseuQ lluFkram
skraMdeniatbo
1 3
2 4
3 4
4 3
5 4
6 5
7 6
8 6
9 6
01 5
A
11 6
21 21
31 21
41 21B
51 21
latoT
2/9441
scitamehtaM
2repaP
yaM
0102
AKALEMNARAJALEPNATABAJ
...:EMAN
5:MROF
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8/7/2019 MATHS SPM PAPER 2 QUESTIONS
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TILUS 2 2/9441
2/9441 MPJatpiCkaH0102 halebesnamalahtahiL[
TILUS
EALUMROFLACITAMEHTAM
noitseuqehtgnirewsnanilufplehebyamealumrofgniwollofehT ehteranevigslobmysehT.s
.desuylnommocseno .
SNOITALER
1 nmnm aaa
2nmnm aaa
3nmnm aa )(
4
ac
bd
cbdaA
11
5
Sn
AnAP
)()(
6 )(1)'( APAP
72
12
2
12 )()(ecnatsiD yyxx
8 ,tniopdiM
2,
2),( 2121
yyxxyx
9 =deepsegarevAnekatemit
dellevartecnatsid
01 =naeMatadforebmun
atadfomus
11 naeMseicneuqerffomus
)ycneuqerfkramssalc(fomus
21 meroehTsarogahtyP222 bac
31 12
12
xx
yy
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41tpecretni
tpecretni
x
ym
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8/7/2019 MATHS SPM PAPER 2 QUESTIONS
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
3
ECAPSDNASEPAHS
1 =muizepartfoaerA2
1 sedislellarapfomus thgieh
2 =elcricfoecnerefmucriC rd 2
3 =elcricfoaerA 2r
4 =rednilycfoaeraecafrusdevruC hr2
5 aeraecafruS =erehpsfo 24 r
6 aeralanoitcesssorc=msirpthgirfoemuloV htgnel
7 =rednilycfoemuloV hr2
8 =enocfoemuloV hr2
3
1
9 =erehpsfoemuloV 3
3
4r
01 =dimarypthgirfoemuloV 3
1aeraesab thgieh
11 (=nogylopafoselgnaroiretnifomuS n )2 081
21 o063
retnectadednetbuselgna
elcricfoecnerefmucric
htgnelcra
31 o063
ertnectadednetbuselgna
elcricfoaera
rotcesfoaera
41 ,rotcafelacS k=AP
AP '
51 =egamifoaerA k2 tcejbofoaera
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
4
AnoitceS25[ skram ]
rewsnA lla .noitcessihtnisnoitseuq
1 nO seitilauqenieerhtehtyfsitashcihwnoigerehtedahs,ecapsrewsnaehtnihpargeht
y x , x 2 na d y < 5 [3 skram ]
nakaidesidgnayfargadaP napawajnagnaurid agiteknaksaumemgnayuatnarnakkerol, - agitnaamaskatek :
y x , x 2 dna y < 5
rewsnA :
2 foeulavehtetaluclaC p fodna q raenilsuoenatlumisgniwollofehtyfsitastaht
snoitauqe :
irebkatneresraenilnaamasrepnaksaumemgnayqialinnadpialingnutiH tuk :
524
1 qp
84 qp [4 skram ]rewsnA :
y = x
x 2=
0
1
2
3
4
5
6
y
1 2 3 4 x
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
5
3 S :noitauqecitardauqehtevloS amasrepnakiasele tukirebkitardaukna :
x
xx
)4(23
4[ skram ]
rewsnA :
4 margaiD 4 htiwdiobucaswohs WVUT as latnoziroheht esab . M,L dna N ehterafostniopdim ,SP QR dna VU .ylevitcepser
hajaR 4 kapatnagneddiobukhaubesnakkujnunem kufugnem WVUT . hagnetkitithaladaNnadM,L
,SPigab QR gnisamVUnad - .gnisam
neviG TW ,mc8= WV namc21= d UQ .mc4=
cdnayfitnedI enalpehtneewtebelgnaehtetalucla L UV enalpehtdna UVRQ .
[3 skram ]=TWirebiD 8 =VW,mc 21 =UQnadmc 4 mc .
naditsaplaneK h hatasaratnaidtudusnakgnuti UVL hatasnagned UVRQ .
rewsnA :
4margaiDhajaR 4
Q
S
P
TU
VW
L M
N
R
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
6
5 margaiD 5 aswohs dilos afoepahsehtni thgir dimaryp . V acitrevsi erauqsehtevobayll
esab MLKJ . rednilycA .dilosehtfotuonekatsimc6thgiehdnamc3suidarhtiwhajaR 5 ajepephaubesnakkujnunem l kutnebreb haubes pi dimar .kaget idkagetkatelretV sata kapat iges
amastapme MLKJ . haubeS ejrebgnayrednilis iraj 3 iggnitnadmc 6 dmc .utilajepepadapiradnakrauleki
neviG KJ ehtdnamc8= mc21sidimarypehtfothgieh mcni,emulovehtetaluclac,3
,
ehtfo gniniamer .dilos ( esU = 241.3 ) 4[ skram ]=KJirebiD 8 nadmc piggnit i halaidimar 21 ,mc h mcmalad,udapisinakgnuti
3lajepep, laggnitgnay .uti
( anuG = 241.3 )
rewsnA :
J K
LM
V
5margaiDlaudaJ 5
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
7
6 nI D 6margai , O enilthgiartS.nigiroehtsi RS si otlellarap enilthgiarts QP . itauqeehT no
enilthgiartsfo RS si 24
3 xy .
malaD R haja 6 .nalasahalaiO, surulsiraG RS siragnaamasreP.QPsurulsiragnagnediraleshalada
RSsurul halai 24
3 xy .
dniFiraC
)a eht tniopfosetanidrooc Rkitittanidrook R
)b itauqeeht no enilthgiartsehtfo PQsiragnaamasrep Psurul Q.
5[ skram ]
rewsnA :
)a(
)b(
R
6margaiDhajaR 6
x
P
S
O
y Q ( 9,8 )
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
8
7 rotcesswohs7margaiD M QP , rotces TSM dna elcricimes RQP htiw ertnec M.hajaR 7 aubesnakkujnunem natalubimesnadTSMrotkes,QPMrotkesh PQ .MidtasuprebR
tahtneviG =SP 3 ,MP QM dnamc7= RMQ 021= o . gnisU =722 etaluclac,
=SPawahabirebiD 3 =QM,MP 7 nadmc =RMQ 021o . nakanuggnemnagneD =
7
22gnutih,
)a( margaidelohwehtfo,mcni,retemirepeht.hajarhurules,mcmalad,retemirep
)b( mcni,aeraeht 2 noigerdedahsehtfo,mcmalad,saul
2kerolrebnasawak,
6[ skram ]
rewsnA :
)a(
)b(
S
T
P
Q
M R
7margaiD7hajaR
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
9
8 )a( I foxirtamesrevn
24
31si
14
31 n
m.
igabgnasgnosskirtaM
24
31halai
14
31 n
m.
foeulavehtdniF m dna fo n..nialinnadmialiniraC
)b( etaluclac,secirtamgnisU foeulaveht x dna fo y gniwollofehtyfsitastaht
suoenatlumis enil :snoitauqeraraenilnaamasrepnaksaumemgnayyialinnadxialingnutih,kirtamhadeaknakanuggneM
katneres :tukireb
x 3y = 5
4 x 2y = 01 6[ skram ]
rewsnA :
)a(
)b(
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8/7/2019 MATHS SPM PAPER 2 QUESTIONS
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
01
9 )a( etatS eerht seitilauqeni .wolebnoigerdedahsehtyfsitashcihwnakatayN agit kerolrebuatnarihunememgnaynaamaskatek .hawabid
3[ skram ]
rewsnA :
)a( )i( ..
)ii(
)iii( .
)b( margaidnneVehT s teswohsecapsrewsnaehtni A, tes B dna tes C tahthcus,
teslasrevinueht CBA .G ,AtesnakkujnunemnapawajgnauridnneVhajarrabma tes nadB tes tesnaadaeknagnedC
atsemes CBA .
tesehtedahs,ecapsrewsnaehtnismargaidehtnO 3[ skram ]teskerol,napawajgnauridhajaradaP
)i( AB')ii( CBA )(
rewsnA :
)i(
)ii(
y
x0
=y 2 +x 1
2 x=y 4
A
B C
A
B C
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
11
01 )a( margaiD 01 wohs s neetriht nidecalperahcihwsdracdelebal xoba .hajaR 01 maladeknakkusamidgnaylebalrebdaksalebagitnakkujnunem haubes .katok
A c ra amorfmodnartanesohcsid xob yB. ehtfosemoctuoelbissopehtgnitsil
,tneve dnif tahtytilibaborpeht.utikatokiradkawararaceshilipiddakutaS nakiaraneynemnagneD nahadusekaumes gnay
nikgnum nailakgnarabekirac, awahab
)i( eht delebaldrac eralewovhtiw .nesohchilipidlakovnagnedlebalrebdak
)ii( eht delebaldrac htiw R si .nesohclebalrebdak R .hilipid
stneduts041ybderocsskramehtswohs01elbaT)b( ani scitamehtaM .stsetlaudaJ 01 naijumaladdirum041heloihelorepidgnayhakramnakkujnunem kitametaM .
skraM stnedutSforebmuN
15 55 11
65 06 54
16 56 76
66 07 71
A essistneduts .puorgehtmorfmodnartadetcelipiddirumgnaroeS .utinalupmukadapiradkawararaceshil
tahtytilibaborpehtdniF krameht :sinailakgnarabekiraC awahab halaiaynhakram :
)i( 16lavretnissalcehtni 56salekgnalesmalad 16 56
)ii( .skram16nahtssel iradgnaruk 16
[ 5 skram ]
rewsnA :
)a( )i(
)ii(
)b( )i(
)ii(
D margai 01ajaR h 01
P PE R E C
I LDN U A R
01elbaTlaudaJ 01
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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21
11 )a( btnemetatsehtetelpmoC llareifitnauqehtgnisuwole otemosro amrof eurt
.tnemetats
nagnedtukirebnaataynrepnakpakgneL nagnalibesuataaumesititnaukgnepnakanuggnem kutnu,
gnaynaataynreputauskutnebmem raneb .
(b) ugragniwollofehtniesimerpehtetelpmoC :tnem
tukirebhajuhmaladsimerpnakpakgneL :
1esimerP : tesfI P tesfotesbusasi Q neht, PQP .
1simerP : tesigabtesbushaladaPtesakiJ Q akam, PQP .
2esimerP / simerP 2 : .
noisulcnoC : teS P tesbusatonsi tesfo Q.
nalupmiseK : teS P tesbusnakub tesigab Q.
(c .ecnetnesgniwollofehtnodesabsnoitacilpmiowtnwodetirW)
.hawabidtayanakrasadrebisakipmiaudnaksiluT
(d) ekaM a reneg la ecneuqesrebmunehtrofnoitcudniybnoisulcnoc hcihw...,42,01,2
:nrettapehtswollofrobmonnaturuigabnahuraaracesmumunalupmisekutastauB ,2 42,01 ebaloptukignemgnay.., r :tuki
)2(3=71
1+
)2(3=412
2+
)2(3=723
3+
=... ........... ]skram6[
:rewsnA
)a(
)b( ...:2esimerP ..........)c( .:1noitacilpmI
:2noitacilpmI ... .
.)d(
stoortnereffidevahsnoitauqecitardauq . aynupmemkitardauknaamasrep acnupi - nanialrebgnayacnup .
x3
siylnodnafi521= x 5=
x3
= 521 =xakijaynahnadakij 5
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TILUS 2/9441
2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
TILUS
31
BnoitceS
84[ skram ]
rewsnA lla .noitcessihtmorfsnoitseuq
12. )a( eulavehtswohsecapsrewsnaehtni21elbaT s fo x fodna y noitauqeehtrof
xy
4 .
foeulavehtdniF p fodna q. 2[ skram ]
laudaJ 21 ialinnakkujnunemnapawajgnaurid igabynadxialin naamasrepx
y4
.
.qnadpigabialiniraC
)b( esu,noitseuqehtfotrapsihtroF egapnodedivorphpargeht 15 aesuyamuoY.
.elurevrucelbixelf
namalahadapnakaidesidgnayfargsatreknakanug,ininalaosnaiareckutnU 15. helobadnA
.elbiskelfsirabmepnakanuggnem
uyB ehtnotinu1otmc2foelacsagnis htob xa e rgehtward,s fohpax
y4
rof
65.0 x .
alaksnakanuggnemnagneD 2 adapekmc 1 adaptinu audek aud ,iskap isgnufigabfargsikul
xy
4 kutnu 65.0 x . 4[ skram ]
)c( isU 21ninwardhpargehtgn )b( dnif,idsikulidgnayfargnakanuggneM )b(21 irac, nak
)i( foeulaveht x nehw y = 4.5n iali x alibapa y = 4.5
)ii( foeulaveht y nehw x = 5.4
alibapayialin x = 5.4 2[ skram ]
)d( foseulavehtlladnifothpargruoynoenilthgiartselbatiusawarD x hcihw
s fsita y noitauqeeht 427 2 xx rof 65.0 x .
ehtetatS es foseulav x [4 skram ]L siku nak surulsiragutas gnay es iracnemkutnuadnafargadapiaus ialin ialin gnayx
naamasrepnaksaumem 4272 xx igab 65.0 x .
ialinnakatayN - xialin tubesret .
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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41
rewsnA :
)a(
x 5.0 1 5.1 2 5.2 3 4 5 6
y 8 4 76.2 2 p 1 33. 1 q 76.0
1elbaT 2laudaJ 21
p =
q =
)b( egapnohpargrefeR 1 .5)c( )i( x .=
)ii( y ..=
)d( x .= , .
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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51
fhparG 21noitseuQro
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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61
13 )a( noitamrofsnarT T noitalsnartasi
2
3noitamrofsnartdna P nasi itna esiwkcolc
(ertnecehttuoba09fonoitator 1 , 2 .)
naamlejneP T isalsnarthalai
2
3naamlejnepnad P naratuphalai 09 atuki adapmajnawalhar
tasup ( 2,1 .)
(tniopfoegamiehtfosetanidroocehtetatS 0 , 6 gniwollofehtfohcaerednu)
:snoitamrofsnart
kititigabjemitanidrooknakatayN ( 0, 6 ) :tukirebnaamlejneppaiteshawabid
)i( P,)ii( TP ,
( )iii T2. [5 skram ]
)b( margaiD 31 ,slaretalirdauqeerhtswohs DCBA , HGFE dna MLKJ , anonward
.enalpnaisetraC
hajaR 31 agitnakkujnunem isis tapme , ,MLKJnadHGFE,DCBA nasetraChatasutausadapsikulid .
)i( MLKJ foegamiehtsi DCBA noitamrofsnartdenibmocehtrednu UV .:snoitamrofsnartehtllufniebircseD
MLKJ igabjemihalai DCBA naamlejnepnagnubaghawabid UV .
:aynpakgnelesnakiaruH
)a( U,
)b( V.
)ii( laretalirdauqtahtnevigsitI DCBA aerafonoigerastneserper 23 mc2.
ni,aeraehtetaluclaC mc2
dedahsehtybdetneserpernoigerehtfo, noigerawahabirebiD isis tapme BA iaynupmemgnaynasawakutausilikawemDC ek saul na 23 mc
2.
mcmalad,saulnakgnutiH2
kerolrebuatnarheloilikawidgnaynasawak, .
7[ skram ]
24 42 86Ox
2
4
6
8K
M
A
B
D
C
6
y
E
F
H
G
J
31margaiDhajaR 31
L
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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71
rewsnA :
)a( )i(
)ii(
)iii(
)b( )i( U : ...
)ii( V .: ....
..
)c(
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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81
41 margaiDniatadehT 41 ydobehtswohs thgiew erdlihc23fo,gkni, .netragrednikaninhajaRmaladataD 41 igab,gkmalad,tarebnagnabmitnakkujnunem 23 kidathaubesmaladdirum a.
)a ehtnodesaB 41margaiDniatad uybdna gnis eht ssalc etelpmoc,3folavretni
T elba 41 .ecapsrewsnaehtni .nakrasadreB hajaRmaladatad 41 nad nakanuggnemnagned salekgnales 3, laudaJnakpakgnel
41 .napawajnagnaurid .
)b TnodesaB elba 41 ,)a(ni c naemehtetalucla thgiew .gkni,nakrasadreB J lauda 41 ,)a(id nimnakgnutih .gkmalad,tareb
)c otmc2foelacsagnisuyB ehtnodlihc1otmc2dnasixalatnozirohehtnogk3.atadehtrofmargotsihaward,sixalacitrev
alaksnakanuggnemnagneD 2 adapekmc 3 nadkufugnemiskapadapgk 2 adapekmc 1 dirumtubesretatadigabmargotsihutasnaksikul,gnacnacnemiskapadap
)d( S margotsihehtnodesabdeniatbonoitamrofnienoetat ni )c(41 .idmargotsihnakrasadrebtamulkamutasnakatayN )c(41
:rewsnA
)a(
lavretnissalC ycneuqerF tniopdiM
01 21
.
41elbaTlaudaJ 41
)b(
..........................................................................................................................................)d(
82 11 32 72 02 51 03 42
72 52 71 91 61 32 52 62
92 71 32 21 02 12 32 82
92 91 33 42 32 42 52 13
41margaiDhajaR 41
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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91
hparG f 41noitseuQro
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2/9441 MPJatpiCkaH0102 [ tahiL namalah halebes
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02
51 )a( tahtneviG m seirav yltcerid sa foebuceht n dna m nehw63= n 2= xe, sserp
m fomretni n . ehtdnif,ecneH evitisop foeulav n nehw m = 882 .awahabirebiD m gnusgnalaraceshabureb nagned nagitasauk nad m = 63 =nalibapa 2,
nakpakgnu m .nnatubesmalad ialinnakiracaynsureteS n ibapa al m = 882 .[3 skram ]
b( )elbaT 51 ,selbairaveerhtneewtebnoitalerehtswohs
p , qdna
r.laudaJ 51 habuhelobmepagitaratnanagnubuhnakkujnunem ,p q nad .r
p q r
3 6 2
8 52 y
6 w 3
elbaT 51laudaJ 51
tahtneviG2r
qp foseulavehtetaluclac, w dna fo y.
awahabirebiD2r
qp , ialinnakgnutih - .ynadwialin 5[ skram ]
)c( ,51margaiDnI SRQ .enilthgiartsasihajaRmalaD ,51 rulsiraghaladaSRQ .su
dniFiraC
)i( foeulaveht soc ?
ialin sok
)ii( SRP 4[ skram ]
Q P
R
S
mc3
mc4
o
51margaiD
hajaR 51
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12
rewsnA :
)a(
(b)
(c) )i(
)ii(
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