teknik menjawab matematik upsr 2016
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GM\BGMNKNH @JBE ? LMKARQ@HA ]MLK ]MD
Cbhakbj Wbkhmk Dbhonwnc
Dntbdntmk F`rdnt CnenruRY\S
Rhtuk Durmg-durmg Wneuh6
YYG Ybhndpnha
3!6
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Msm knhguhanh cbhakbj tbkhmkdbhonwnc s`njnh dntbdntmk
cbrf`rdnt cnenru RY\S 39>6>. YBHABHNJNH
3. \@NJNH KCNW GNJND K> GNH K3
GNH K3
7. SRDR\NH KBJBDNENH DRSMG GNJND KBSWN\ > GNH KBSWN\ 3 2. NYN ]NHA YBSJR \N]N JNKRKNH \BDN\N DBHONQNC KBSWN\ 3.
6. F@SDNW JNDN V\ F@SDNW CNENSR
1. NYNKNE \@NJNH KCNW GNH L@HW@E \@NJNH KCNW.
. L@HW@E JNWMENH KBSWN\ > GNH KBSWN\ 3 GNH \KBDN
ONQNYNH ! 3" \@NJNH GMRCNE\RNM GNSM \@NJNH GNJND CRKRWBK\ DNWBDNWMK WNERH 6 DBHAMKRW W@YMK # 3$>6%
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YBHABHNJNH
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• Dntbdntmk wnomc gnjnd RY\S.
• Dbdpuhynm 3 kbrtns ( k> gnh k3)
• Kbrtns >
- Romnh cobktm! ( nhbkn pmjm"nh)
- > ond
- #$ snjnh
- #$ dnrkn"
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Kbrtns 3
- uomnh sucobktm! ( pbjcn%nm cbhtuk
rbsphg tbr"ng)
- > ond
- >& snjnh
- '$ dnrkn"Ybdnrkn"nh dntbdntmk
K> k3 * >$$ +
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\@NJNH KCNW GNJND K> GNH K3
• \,/ K9 < \,/ 97S26K6S S\ 6/116.
• K> / K3 D7/1/R/16 \,/ K9.
• 5RD< \,/ K9 6K D7/7/R\76Y
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YBDNSKNENH KBSWN\ DNWBDNWMK K> GNH K3
2,SD 9 > \,/ ( > DSK > \,/ ( > DSK D = 3 D / ? D
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SRDR\NH KBJBDNENH KBSWN\ >SRDR\NH KBJBDNENH KBSWN\ >
"Cbrnhaanpnh dntbdntmk sbhnha.Cbrnhaanpnh dntbdntmk sbhnha.
"Ap! dbh"n#n$ sn%nh.Ap! dbh"n#n$ sn%nh.
"&m'nk dbh$n(n sn%nh 'bhanh tb%mtm.&m'nk dbh$n(n sn%nh 'bhanh tb%mtm."&m'nk )n!nd kbdn!mrnh nsns sbs*nt*&m'nk )n!nd kbdn!mrnh nsns sbs*nt*
tn"*k.tn"*k.
"&m'nk )n!nd sn%nh +nha 'm$n(n.&m'nk )n!nd sn%nh +nha 'm$n(n.
"Ap! dbh"n#n$ sn%nh.Ap! dbh"n#n$ sn%nh.
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SRDR\NH KBJBDNENH KBSWN\ 3SRDR\NH KBJBDNENH KBSWN\ 3
"Cbrnhaanpnh dntbdntmk sbhnha.Cbrnhaanpnh dntbdntmk sbhnha.
"Ap! dbh"n#n$ sn%nh.Ap! dbh"n#n$ sn%nh.
"&m'nk )n!nd khsbp sbs*nt* tn"*k.&m'nk )n!nd khsbp sbs*nt* tn"*k."&m'nk )n!nd kbdn!mrnh nsns sbs*nt*&m'nk )n!nd kbdn!mrnh nsns sbs*nt*
tn"*k.tn"*k.
"&*%msnh +nha tm'nk kbdns.&*%msnh +nha tm'nk kbdns.
"&m'nk dbhaa*hnknh pbd$nrms *ht*k&m'nk dbhaa*hnknh pbd$nrms *ht*kdbd$*nt anrmsnh.dbd$*nt anrmsnh.
"&m'nk dbd$mhn n+nt dntbdntmk.&m'nk dbd$mhn n+nt dntbdntmk.
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" Dbh*%ms sn%nh ntn* nhakn +nha sn%n!.Dbh*%ms sn%nh ntn* nhakn +nha sn%n!.
" Lbpnt p*t*s nsn $m%n sn%n! dbhamrn.Lbpnt p*t*s nsn $m%n sn%n! dbhamrn.
" &m'nk t*%ms *hmt pn'n "n#npnh.&m'nk t*%ms *hmt pn'n "n#npnh.
" &m'nk dbh*h"*kknh "n%nh dbhamrn +nha&m'nk dbh*h"*kknh "n%nh dbhamrn +nhasbdp*rhn.sbdp*rhn.
" \n%n! dbhamrn 'nh sn%n! pm%m! pbrnsm.\n%n! dbhamrn 'nh sn%n! pm%m! pbrnsm.
" K*rnha dbd$brm pbr!ntmnh kbpn'nK*rnha dbd$brm pbr!ntmnh kbpn'nsn%nh , dnrkn!.sn%nh , dnrkn!.
" &m'nk )n!nd sn%nh.&m'nk )n!nd sn%nh." &m'nk dn!* sbdnk "n#npnh.&m'nk dn!* sbdnk "n#npnh.
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#nrn dbhonwnc kbrtn$ 3$bdn$n RY\S
!%Dbdcn&n gnh dbdnendm $`njnh gbhanhtbjmtm%
3% 'nwnc $`njnh dbhamkut urutnh &`ht`e gnrm
(m) kb (mm) gnh kb (mmm)%*%Fmkmr dbhgnjnd tbrengnp $`njnh +nha
gm$`nj tbrutndnh+n $`njnh ,CW%
.% Wuhoukknh pbhamrnnh/ uhmt gnh n+nt
dntbdntmk $bkmrnh+n gmpbrjuknh%
9% Wujm$nh h`dc`r db$tm objn$ gnh tmgnk kncur%
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#nrn dbhonwnc kbrtn$ ! gnh 3$bdn$n RY\S
9; 2)
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F`rdnt jndn >$ F`rdntcnenru 3!6
2rdnt jndn
/yntnknh gun rntus rmcu tm%n rntus jmdn puju" gnjnd pbrkntnnh. : > dnrkn"4
2rdnt cnru
3$$ ?&$
m) /yntnknh gnjnd pbrkntnnh. : > dnrkn"4
mm) /yntnknh gm%mt ynh% tbrjbtnk pngn hmjnm tbdpnt rmcu. : > dnrkn" 4
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\`njnh ,CW
YK< 6R \,/ K9 8888888
K< \,/ K9 6R \/1 \R\
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\`njnh ,CW
\,/ 0/1 D7/1R56 D6/ DRS6 /
D7D7SRK/ Y7D6K6S/ S\ 6/116.
6K \R\< 7Y6 Y7SR D7D6K6S \7;S D7/D
7S
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#`ht`e $`njnh ,CW
ukmsknh sbcun" sb%mbdpnt tbpnt ynh% dbdpuhynm juns
3# Cd L
>3Cd
3Cd
' Cd
# Cd
G Cd
? Cd
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#`ht`e jntmenh gnh tbkhmkdbhonwnc $`njnh dntbdntmk
`rdnt cnenru RY\S
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,
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#nrn dbhonwnc kbrtn$ ! gnh 3$bdn$n RY\S
9; 2)
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!%
htnrn ynh% cbrmkut= ynh% dnhnkn" dbdpuhynm hmjnm ynh% sndn
gbh%nh ' B&$ $$$8
.'B& 5utn
9.'B.& 5utn
;.'.B& 5utn
.$.'B& 5utn
3% 4ñ3>
7>7
.
9.
;.
.
3
>3
3
>7
3
>6
3
>5
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*%
#&.>3 >& F ?.3 *
.#3.$B
9.&'.$3
;.&'.A3
.'$.>3
.% htnrn ynh% cbrmkut= ynh% dnhnkn" dbdpuhynm hmjnm ynh% pnjmh%kbCmj8
.3$+ gnrmpngn >?$$
9.?$+ gnrmpngn >G$
;.'$+ gnrmpngn A$.G$+ gnrmpngn ?$
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9%
Snon" > dbhuhoukknh "nr%n cn%m gun obhms cun"-cun"nh
tbdpntnh.
Dnry dbdcbjm 3 cmom hbhns= # cmom gurmnh gnh sbcmom tbdcmknm
gbh%nh "nr%n SD 3$$. 9brnpnkn" "nr%n sbcmom tbdcmknm mtu8
.SD >#.'$
9.SD >&.'$;.SD 3&.#$
.SD ?$.#$
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6%
Snon" 3 dbhuhoukknh wnktu cbrdujn kbjns tndcn"nh Dhn gm
sbkjn"hyn.
Snon" 3
Dhn dbh%"ngmrm kbjns dntbdntmk sbjndn #& dmhmt gnh 9n"nsn
Dnjnysmn sbjndn &$ dmhmt= gbh%nh wnktu rb"nt sbjndn 3$ dmhmt
gm nhtnrn kbgun-gun kbjns mtu. Yngn pukuj cbrnpnkn" kbjns
tumsybh Dhn tndnt8
.3.#& p.d
9.?.>$ p.d
;.?.#& p.d
.#.>& p.d
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7%
Snon" ? dbhuhoukknh msm pngu sntu pnkbt susu .
Snon" ?
Yunh \mtm tbjn" dbdcbjm ? pbkbt susu sb%nr ynh% sndn. mn
dbh%%uhnknh 3$?& dj gnrmpngn susu sb%nr tbrsbcut uhtuk
dbdcunt kbk. 9nkmhyn tbjn" gmtunh%knh sndn cnhynk kb gnjnd
& cmom ctj. 9brnpnknh msm pngu = gnjnd dj = susu gm gnjnd sbtmnp
ctj8
.>A?
9.3&?
;.??#
.&?3
> mtbr
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2%
Snon" # dbhuhoukknh sbcmom kbk cbrcbhtuk kucmg
Snon" #
Kbk tbrsbcut gmpth% kbpngn 3& kbpmh% ynh% sndn cbsnr.
9brnpnkn" msm pngu= gnjnd Cd E= sbpth% kbk8
.3#
9.?3;.?G
.#'
G Cd
3$ Cd
& Cd
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%
Snon" & dbhuhoukknh tmtmk Y gnh M ynh% gmjukms pngn sntn" ;nrtbs.
Snon" &
-
>
3
?
#
&'
B
y
$> 3 ? # &
'
B
G
A
O
mtmk Y= M gnh S dbdcbhtuk sntu sb%m tm%n sndn smsm./yntnknh krgmhnt ynh% duh%kmh cn%m tmtmk S mtu.
. ( &=>)
9.( &=?)
;.( &=')
.( '=&)
M Y
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!% Snon" ' dbhuhoukknh 3 obhms cun"-cun"nh .
Snon" '
Ynk Sndjm dbhybgmnknh #G cmom cun" tbdcmknm gnh #$ cmom hbhns
uhtuk gmounj gm %brnm cun"-cun"nhhyn. \bcnhynk #& cmom tbdcmknm
gnh ?G cmom hbhns tbjn" gmounj. 9brnpnkn" hmscn" cun" tbdcmknm
gnh cun" hbhns ynh% tmh%%nj8
.3 ?9.? 3
;.# >
.# 3
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!!% Ymkt%rn! dbhuhoukknh oudjn" kutmpnh gbrdn ynh% tbjn" gmnhourknhjb" Ybrsntunh 9ujnh \ncmt Dbrn" gm sbcun" sbkjn" dbhbh%n".
Cht"
Cht"
Cht"
Cht"
Dbwnkmjm > rnh%
/yntnknh dmh cn%m kutmpnh gbrdn mtu .
.SD >$.&$ 9. SD >>.?$ ;. SD >3.&$ . SD >?.&$
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!3 /yntnknh ynh% dnhnkn" duh%kmh cbrjnku pngn pbrmstmwn gm cnwn"
. brgnpnt G "nrm gnjnd sbdmh%%u
9. 9uruh% pbh%umh ngn gm pnhtnm Dnjnysmn
;. \njom turuh gm hb%nrn Dnjnysmn. 1ncuh%nh gun sb%m tm%n dbhongm sntu sb%m bdpnt tbpnt
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,
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!% Snone ! dbhuhoukknh gun gmamt gnh 9gmamt +nha hmjnm tbdpnth+n gmcbrmknh gnjndkuruhanh%
G( Smcu) $ B( Sntus rmcu) $ '(sn) 3( Yuju") >( 5utn)
m) 9bhtukknh sntu hdcr B gm%mt gbh%nh dbh%%uhnknh sbdun gm%mt gnh hmjnm
tbdpnt ynh% gmcbrmknh gnjnd Snon" >. : > dnrkn"4
mm) 9uhgnrknh hdcr gm onwnpnh (m) kbpngn puju" rmcu ynh% tbrgbknt
: > dnrkn" 4
> B$G $3'
Snon" >
> B$G $3' * > B>$ $$$
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3% \bcnh+nk gnrmpngn $bcmjnhanh durmgdbh+brtnm
n&nrn jnrmnh 3 d% gnrmpngn durmg mtuturut tbrjmcnt gnjnd n&nrn j`dpnt onue %
m)
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*%
m) 3&k%
BG.# O & #
* AG
$.>3&k% O G *> k%
* >$$$ %
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.%Dhn = Jurnmgn" gnh 9mjjy cbrkh%sm sbcmjnh%nh %ujm. Dhn dbhgnpnt
3&+ gnrmpngn oudjn" %ujm mtu dnhnknjn Jurnmgn" dbhgnpnt #$+ gnh
cnkmhyn ngnjn" kbpuhynnh 9mjjy. 9mjnh%nh %ujm Dhn pbrjb" mnjn" >3$
cmom.
m)
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9%Dbm ;"mh% dbhgnpnt pmhondnh pbhgmgmknh cbroudjn" SD >G$ $$$
gbh%nh !nbgn" >+ sbtn"uh.
m)
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6%
S&'&( 6 )*+,+',--&+ )&& /*9&- 7,& /,&( /& 7&9 C&+7&9 7&+ )&& /&
7 C&+7&9 ]. W*)( )&& /&5 -*7,&=7,& /& 7&9 C&+7&9 -* C&+7&9 ]
&7&&( &)&.
9nhgnr 9nhgnr 0
9ns Y
9ns M
B.>& nd #.&$pd
G.>$ nd
Snon" '
mm% O-& /& ? /*9&- &;& 2 )+ 7&9&7& )&& :&+5 7*&-&+ *&
*9&+5-, 7 '&&+ 9&:& *&)& "$ )+ . Y&7& ,-, /*9&&-&( /& ? &-&+ /&
7 /&+7&9 ] 4 C*9-&+ '&;&&+ &+7& 7&&) *) >3 '&). 8 < )&9-&( 0
% E,+5 *)( *9'&&+&+ /& Y # 7&&) '&) 7&+ )+
8 > )&9-&(0>' ond &$ dmhmt F B ond >& dmhmt
* A ond ?& dmhmt
G ond >$ dmhmt F & dmhmt
* G ond $& dmhmt
G ond $& dmhmt A ond ?& dmhmt #$ dmhmt
* >G ond 3$ dmhmt
* '.3$ pd
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7%
S&'&( 1 )*+,+',--&+ *5,,+5 -&+ :&+5 7/* *( ,&+ N)+&( /*9(&95& SD 32$. K&+
, 7+5 -*&7& 2 /&(&5&+ :&+5 &)& &+'&+5. G& )*+55,+&-&+ < /&(&5&+ ,+,-
)*)/,& /&', &+&-+:&.
Snon" B
% C*9&&-&( &+'&+5 -&+# 7&&) )# :&+5 75,+&-&+ ,+,- )*)/,& /&', &+&-+:& .
8 3 )&9-&( 0
% W,-&+ *I&(&+ -&+ :&+5 75,+&-&+ *( ,&+ N)+&( ,+,- )*)/,& /&',
&+&-+:&.
8 > )&9-&(0
3$ d
% C*9&&-&( (&95& -&+ :&+5 )&( +55&4 83 )&9-&(0
2
<
d
x
>3
2
69
392
<
4
d SD
d
SD
/29.>3
39
329
4
3$d->3d * Gd
Gd O SD >3.&$
*SD >$$
Y \>$Cd
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2%Y
M S
\
>$Cd
>'Cd
>3Cd'Cd
S&'&( )*+,+',--&+ 5&/,+5&+ 7,& *5 5& /*9,7, *5&-. Y&+'&+5 ?S
&7&&( 7,& -& */( &+'&+5 7&9&7& \W.
% H:&&-&+ &+'&+5 \W 7&&) I) 8 > )&9-&(0
% E,+5-&+ *9)**9# 7&&) I) # *,9,( 9&'&( *9*/, 8 3 )&9-&(0
% J,--&+ */,&( *55& /*9,7, *5&- 7*+5&+ *9)**9+:& &7&&( 3" I).
8 3 )&9-&(0
>'Cd 3 * G Cd
>3Cd >$Cd G Cd ' Cd >'Cd* &3Cd
5nwnpnh tbrcukn gbh%nh pbrmdbtbr 3# Cd
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A S&'&( )*+,+',--&+ - Q :&+5 7,- &7& &&( L&9*
y
O$ > 3 ? # & ' B G A
>3
?
#
&
B
'
w
Snon" A
m) /yntnknh krgmhnt tmtmk I. : > dnrkn"4
mm) mcbrmknh sntu tmtmk M dbdpuhynm krgmhnt (3 = ? ). nhgnknh tmtmk M.
: > dnrkn"4
( & = # )
M
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/ S&'&( >$ )*+,+',--&+ 7,& '*+ &-9) 7&&) */,&( -&- .
cbrpbrmsn
rbhcbrpbrmsnCkjnt
3& cntnh%
S&'&( >$
G/*9-&+ /&(&;& 3" 7&9&7& &-9) , /*9*9& 9*+ 7&+ **/(+:& /*9*9&I-&.
m) C*9&&-&( /&+5&+ &-9) /*9*9& 9*+ 4 83 )&9-&(0
mm) H:&&-&+ +/&( /&+5&+ &-9) /*9*9& 9*+ -*&7& /&+5&+ &-9)/*9*9& I-&4 8 3 )&9-&(0
6
>99
699
32>99
37
4
4
x
&-9) I-& 32 = 6 >@9*+ I-&
6 >
;nrtn pnjnh% dbhuhoukknh ounjnh ? obhms hnsm jbdnk gbh%nh jnuk
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>>;nrtn pnjnh% dbhuhoukknh ounjnh ? obhms hnsm jbdnk gbh%nh jnuk
ynh% cbrcbHn gm Sbstrnh \brm \nynh% gnjnd sbdmh%%u. Sbstrnh mhm
cbrpbrnsm sbtmnp "nrm sbjnmh "nrm "ng.
m) /yntnknh hnsm jbdnk ynh% dnhnkn" ngnjn" 3 knjm jbcm" cnhynk
gnrmpngn hnsm jbdnk gbh%nh gn%mh% jbdcu8 : > dnrkn"4
mm) & * A$
A$ ' * >&
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!3m) /yntnknh sntu pbrmstmwn ynh% nknh cbrjnku gm knwnsnh pnhtnm gm hb%nrn
Dnjnysmn.
n) brgnpnt rnh% cbrbhnh% gm pnhtnm
c) brgnpnt rnh% dbh%utmp smput @ kujmt smput .
C) brgnpnt rnh% cbrdnmh cjn gm pnhtnm
mm) Yngnhknh pbrmstmwn gbh%nh kbcjb"ongmnhhyn.
\untu enrm hnhtmku&mha cbrtnhguk
\btneuh dbdpuh+nm*66 enrm
$ntu enrm dbdpuh+nm39 ond
Duhakmh
cbrjnku
Wmgnk duhakmhcbrjnku
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