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7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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ZGKHF@B LGIGIM@B KGD@IMZ@@I (U) Z^. MGHTMG
UTHCGJ^ ]HTK AHT @NNO^OHI@F L@^BGL@^OJZ
4504
@NNO^OHI@F L@^BGL@^OJZ UTHCGJ^ ]HTK
ZUL 4/4504
I`lg 3 Pu`b Pou _u
Jf`ss 3 7 Iof`l
OJ Iuldgr 3
@imk` Mofor`i 3
Zudcgjt ^g`jbgr 3 Lr Hho Jbhim Kg`t
7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
@jkihwfgnmglgit
Aorst `in ahrglhst, O whufn fokg th tb`ik tbg proijopfg ha Zgkhf`b Lgigim`b Kgd`ims``i
Ugrglpu`i Zt. Mghrmg, Ui. Zb`roaa`b @aoa`b ahr movoim lg tbg pgrlossohi th nh tbos @nnotohi`f
L`tbgl`tojs Urhcgjt ]hrk.
Zgjhinfy, O whufn `fsh fokg th sbhw ly mr`totung thw`rns tbg ginfgss muon`ijg `in
supphrt movgi dy ly @nnotohi`f L`tbgl`tojs sudcgjt tg`jbgr, Lr. Hho Jbhim Kg`t tbrhumbhut
tbg prhjgss ha nhoim tbos prhcgjt whrk. Bg t`umbt lg `in ly arogins p`togitfy hi w`ys th
`jjhlpfosb tbos prhcgjt whrk.
@p`rt arhl tb`t, O whufn fokg th `jkihwfgnmg `in r`img ly g`rigst `pprgjo`tohi th ly
p`rgits ahr movoim lg supphrts oi gvgry w`ys, sujb `s lhigy, th duy `iytboim tb`t `rg rgf`tgn th
tbos prhcgjt whrk `in tbgor `nvosg, wbojb os tbg lhst iggngn ahr tbos prhcgjt.
F`stfy, ` spgjo`f tb`ik yhu th `ff ly arogins ahr `onoim lg oi shfvoim shlg ha tbg
j`fjuf`tohis. ^bgy wgrg bgfpauf th sb`rg oiahrl`tohi `in ong`s oi hrngr th mgt tbos prhcgjt whrk
nhig.
@in gspgjo`ffy th Mhn, wbh l`ng `ff tboims phssodfg.
^b`ik yhu, gvgryhig.
7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Hdcgjtovgs
^bg `ols ha j`rryoim hut tbos prhcgjt whrk `rg3
^h `ppfy `in `n`pt ` v`rogty ha prhdfgl-shfvoim str`tgmogs th shfvg prhdfgls ^h olprhvg tboikoim skoffs ^h prhlhtg gaagjtovg l`tbgl`toj`f jhlluioj`tohi ^h ngvgfhp l`tbgl`toj`f kihwfgnmg tbrhumb prhdfgl-shfvoim oi ` w`y tb`t oijrg`sgs
stungits oitgrgst & jhiaongijg
^h usg f`imu`mg ha l`tbgl`tojs th gxprgss l`tbgl`toj`f ong`s prgjosgfy ^h prhvong fg`rioim givorhilgit tb`t stoluf`tgs `in gib`ijgs gaagjtovg fg`rioim. ^h ngvgfhp phsotovg `ttotung thw`rns l`tbgl`tojs
7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Oitrhnujtohi
@ Droga Bosthry ha Zt`tostojs
Dy tbg 02tb jgitury, tbg tgrl "st`tostojs" ngsomi`tgn tbg systgl`toj jhffgjtohi ha nglhmr`pboj
`in gjhihloj n`t` dy st`tgs. Oi tbg g`rfy 0?tb jgitury, tbg lg`ioim ha "st`tostojs" drh`ngign,
tbgi oijfunoim tbg nosjopfoig jhijgrign wotb tbg jhffgjtohi, sull`ry, `in `i`fysos ha n`t`.
^hn`y st`tostojs os wongfy glpfhygn oi mhvgrilgit, dusoigss, `in `ff tbg sjogijgs. Gfgjtrhioj
jhlputgrs b`vg gxpgnotgn st`tostoj`f jhlput`tohi, `in b`vg `ffhwgn st`tostojo`is th ngvgfhp
"jhlputgr-oitgisovg" lgtbhns. ^bg tgrl "l`tbgl`toj`f st`tostojs" ngsomi`tgs tbg l`tbgl`toj`f
tbghrogs ha prhd`dofoty `in st`tostoj`f oiagrgijg, wbojb `rg usgn oi st`tostoj`f pr`jtojg. ^bg rgf`tohi
dgtwggi st`tostojs `in prhd`dofoty tbghry ngvgfhpgn r`tbgr f`tg, bhwgvgr. Oi tbg 0?tb jgitury,
st`tostojs oijrg`soimfy usgn prhd`dofoty tbghry, wbhsg oioto`f rgsufts wgrg ahuin oi tbg0=tb `in
02tb jgiturogs, p`rtojuf`rfy oi tbg `i`fysos ha m`lgs ha jb`ijg (m`ldfoim). Dy 0255, `strhihly
usgn prhd`dofoty lhngfs `in st`tostoj`f tbghrogs, p`rtojuf`rfy tbg lgtbhn ha fg`st squ`rgs, wbojb
w`s oivgitgn dy Fgmginrg `in M`uss. G`rfy prhd`dofoty tbghry `in st`tostojs w`s systgl`tozgn
`in gxtgingn dy F`pf`jg; ahffhwoim F`pf`jg, prhd`dofoty `in st`tostojs b`vg dggi oi jhitoiu`f
ngvgfhplgit. Oi tbg0?tb jgitury, shjo`f sjogitosts usgn st`tostoj`f rg`shioim `in prhd`dofoty
lhngfs th `nv`ijg tbg igw sjogijgs ha gxpgrolgit`f psyjbhfhmy `in shjohfhmy; pbysoj`f
sjogitosts usgn st`tostoj`f rg`shioim `in prhd`dofoty lhngfs th `nv`ijg tbg igw sjogijgs ha
tbgrlhnyi`lojs `in st`tostoj`f lgjb`iojs. ^bg ngvgfhplgit ha st`tostoj`f rg`shioim w`s jfhsgfy
`sshjo`tgn wotb tbg ngvgfhplgit ha oinujtovg fhmoj `in tbg sjogitoaoj lgtbhn. Zt`tostojs os iht `
aogfn ha l`tbgl`tojs dut `i `uthihlhus l`tbgl`toj`f sjogijg, fokg jhlputgr sjogijg hr
hpgr`tohis rgsg`rjb. Wifokg l`tbgl`tojs, st`tostojs b`n ots hromois oi pudfoj `nloiostr`tohi `in
l`oit`ois ` spgjo`f jhijgri wotb nglhmr`pby `in gjhihlojs. Dgoim jhijgrign wotb tbg
sjogitoaoj lgtbhn `in oinujtovg fhmoj, st`tostoj`f tbghry b`s jfhsg `sshjo`tohi wotb tbg pbofhshpbyha sjogijg; wotb ots glpb`sos hi fg`rioim arhl n`t` `in l`koim dgst prgnojtohis, st`tostojs b`s
mrg`t hvgrf`p wotb tbg ngjosohi sjogijg `in lojrhgjhihlojs. ]otb ots jhijgris wotb n`t`,
st`tostojs b`s hvgrf`p wotb oiahrl`tohi sjogijg `in jhlputgr sjogijg.
7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Zt`tostojs ^hn`y
Nuroim tbg 45tb jgitury, tbg jrg`tohi ha prgjosg oistrulgits ahr `mrojuftur`f rgsg`rjb, pudfoj
bg`ftb jhijgris (gponglohfhmy, dohst`tostojs, gtj.), oinustro`f qu`foty jhitrhf, `in gjhihloj `in
shjo`f purphsgs (uiglpfhylgit r`tg, gjhihlgtroj, gtj.) igjgssot`tgn sudst`ito`f `nv`ijgs oi
st`tostoj`f pr`jtojgs. ^hn`y tbg usg ha st`tostojs b`s drh`ngign a`r dgyhin ots hromois. Oinovonu`fs
`in hrm`ioz`tohis usg st`tostojs th uingrst`in n`t` `in l`kg oiahrlgn ngjosohis tbrhumbhut tbg
i`tur`f `in shjo`f sjogijgs, lgnojoig, dusoigss, `in htbgr `rg`s. Zt`tostojs os mgigr`ffy rgm`rngn
iht `s ` sudaogfn ha l`tbgl`tojs dut r`tbgr `s ` nostoijt, `fdgot `ffogn, aogfn. L`iy uiovgrsotogs
l`oit`oi sgp`r`tg l`tbgl`tojs `in st`tostojs ngp`rtlgits. Zt`tostojs os `fsh t`umbt oi ngp`rtlgits
`s novgrsg `s psyjbhfhmy, gnuj`tohi, `in pudfoj bg`ftb.
Urojg Oingx
@ projg oingx (pfur`f3 projg oinojgs hr projgoingxgs) os ` ihrl`fozgn `vgr`mg (typoj`ffy
wgombtgn `vgr`mg) ha projgs ahr ` movgi jf`ss ha mhhns hr sgrvojgs oi ` movgi rgmohi, nuroim `
movgi oitgrv`f ha tolg. Ot os ` st`tostoj ngsomign th bgfp th jhlp`rg bhw tbgsg projgs, t`kgi `s `
wbhfg, noaagr dgtwggi tolg pgrohns hr mghmr`pboj`f fhj`tohis.
Urojg oinojgs b`vg sgvgr`f phtgito`f usgs. Ahr p`rtojuf`rfy drh`n oinojgs, tbg oingx j`i dg s`on th
lg`surg tbg gjhihly's projg fgvgf hr ` jhst ha fovoim. Lhrg i`rrhw projg oinojgs j`i bgfp
prhnujgrs wotb dusoigss pf`is `in projoim. Zhlgtolgs, tbgy j`i dg usgauf oi bgfpoim th muong
oivgstlgit.
Zhlg iht`dfg projg oinojgs oijfung3
Jhisulgr projg oingx Urhnujgr projg oingx
MNU ngaf`thr
7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Bosthry ha G`rfy Urojg Oinojgs
Ih jfg`r jhisgisus b`s glgrmgn hi wbh jrg`tgn tbg aorst projg oingx. ^bg g`rfogst rgphrtgn
rgsg`rjb oi tbos `rg` j`lg arhl ]gfsbl`i Tojg Q`umb`i wbh gx`loign projg fgvgf jb`img oibos
01=7 dhhk @Nosjhursg ha Jhoi `in Jhoi`mg. Q`umb`i w`itgn th sgp`r`tg tbg oiaf`tohi`ry
olp`jt ha tbg oiafux ha prgjohus lgt`fs drhumbt dy Zp`oi arhl tbg Igw ]hrfn arhl tbg gaagjt
nug th jurrgijy ngd`sglgit. Q`umb`i jhlp`rgn f`dhr st`tutgs arhl bos hwi tolg th solof`r
st`tutgs n`toim d`jk th Gnw`rn OOO. ^bgsg st`tutgs sgt w`mgs ahr jgrt`oi t`sks `in prhvongn ` mhhn
rgjhrn ha tbg jb`img oi w`mg fgvgfs. Q`umb`i rg`shign tb`t tbg l`rkgt ahr d`soj f`dhr non iht
afujtu`tg lujb wotb tolg `in tb`t ` d`soj f`dhrgrs s`f`ry whufn prhd`dfy duy tbg s`lg `lhuit ha
mhhns oi noaagrgit tolg pgrohns, sh tb`t ` f`dhrgr's s`f`ry `jtgn `s ` d`skgt ha mhhns. Q`umb`i's
`i`fysos oinoj`tgn tb`t projg fgvgfs oi Gimf`in b`n rosgi sox th gombtahfn hvgr tbg prgjgnoim
jgitury
]bofg Q`umb`i j`i dg jhisongrgn ` ahrgruiigr ha projg oingx rgsg`rjb, bos `i`fysos non
iht`jtu`ffy oivhfvg j`fjuf`toim `i oingx. Oi 0=5= Gimfosbl`i ]offo`l Afggtwhhn jrg`tgn
pgrb`pstbg aorst trug projg oingx. @i Hxahrn stungit `skgn Afggtwhhn th bgfp sbhw bhw projgs
b`njb`imgn. ^bg stungit sthhn th fhsg bos agffhwsbop soijg ` aoatggitb jgitury stopuf`tohi
d`rrgnstungits wotb `iiu`f oijhlgs hvgr aovg phuins arhl rgjgovoim ` agffhwsbop. Afggtwhhn,
wbh `frg`ny b`n `i oitgrgst oi projg jb`img, b`n jhffgjtgn ` f`rmg `lhuit ha projg n`t` mhoim
d`jk buinrgns ha yg`rs. Afggtwhhn prhphsgn `i oingx jhisostoim ha `vgr`mgn projg rgf`tovgs `in
usgn bos lgtbhns th sbhw tb`t tbg v`fug ha aovg phuins b`n jb`imgn mrg`tfy hvgr tbg jhursg ha
415yg`rs. Bg `rmugn hi dgb`fa ha tbg Hxahrn stungits `in pudfosbgn bos aoinoims `ihiylhusfy oi
` vhfulg gitotfgn Jbrhiojhi Urgjohsu.
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
@J^OQO^_ 0
JHFFGJ^OIM
OIAHTL@^OHI
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
@J^OQO^_ 4
@I@F_ZOIM ^BG
N@^@
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
D`sgn hi tbg n`t` jhffgjtgn,
`) J`fjuf`tg tbg pgrjgit`mg ha oijrg`sg oi gxpginoturg ahr g`jb otgl oi 4500 d`sgn hi455?.
IhOtgl ha
gxpginoturg
@vgr`mg gxpginoturg
yg`r 455? (TL)
@vgr`mg gxpginoturg
yg`r 4500 (TL)
Ugrjgit`mg ha oijrg`sg
4500 d`sgn 455? (%)
0 Ahhn 0:77 0=57
4 Bhusg Tgit`f =77 ?:7
: ^r`isphrt`tohi :55 >47
> Gitgrt`oilgit 42> >>7
7 Doffs 4== :21
d) Aoin tbg gxpginoturg oingx ahr g`jb otgl.
Ih Otgl ha gxpginoturgUgrjgit`mg
4500 d`sgn 455?Oingx
0 Ahhn
047.2:
4 Bhusg Tgit`f
04:.2>
: ^r`isphrt`tohi
0>0.1=
> Gitgrt`oilgit
071.1?
7 Doffs
0:?.:7
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
j) Ngtgrloig tbg wgombt`mg ha g`jb otgl oi pgrjgit`mg. Bgijg, hr htbgrwosg prgsgityhur wgombt`mgs oi tbg ahrl ha pog jb`rt.
Ih Otgl ha gxpginoturgUgrjgit`mg
4500 d`sgn 455?Oingx
Ugrjgit`mg
(]gombt`mg)
Ngmrggs
(]gombt`mg)
0 Ahhn
047.2: >7.10 01>.45
4 Bhusg Tgit`f
04:.2> 47.>0 ?0.>2
: ^r`isphrt`tohi
0>0.1= 05.05 :1.:1
> Gitgrt`oilgit
071.1? ?.71 :>.>4
7 Doffs
0:?.:7 ?.:4 ::.77
^ht`f 055 :15
Ahhn, >7.10%
Bhusg Tgit`f,
47.>0%
^r`isphrt`tohi,
05.05%
Gitgrt`oilgit,
?.71%
Doffs, ?.:4%
]gombt`mg ha G`jb Otgl
Ahhn
Bhusg Tgit`f
^r`isphrt`tohi
Gitgrt`oilgit
Doffs
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
n) Aoin tbg v`fug ha gxpginoturg jhlphsotg oingx oi tbg yg`r 4500 d`sgn hi yg`r 455?.
Ih Otgl ha gxpginoturg Oingx,O
Ugrjgit`mg
(]gombt`mg)
]
O]
0 Ahhn 047.2: >7.10 7=:?.00
4 Bhusg Tgit`f 04:.2> 47.>0 :0>1.==
: ^r`isphrt`tohi 0>0.1= 05.05 0>:5.2=
> Gitgrt`oilgit 071.1? ?.71 0>?=.?1
7 Doffs 0:?.:7 ?.:4 04?2.=>
^ht`f 055 0:00:.>7
Jhlphsotg oingx,
7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
@J^OQO^_ :
OI^GTUTG^OIM ^BG
TGZWF^
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
`) Ngsjrodg tbg gxpginoturg ha g`jb otgl d`sgn hi tbg v`fug ha gxpginoturg oingx yhuhdt`oign.
Ih Otgl ha gxpginoturg Oingx,
O
0 Ahhn 047.2:
4 Bhusg Tgit`f 04:.2>
: ^r`isphrt`tohi 0>0.1=
> Gitgrt`oilgit 071.1?
7 Doffs 0:?.:7
5
45
>5
15
25
055
045
0>5
015
025
Ahhn Bhusg Tgit`f ^r`isphrt`tohi Gitgrt`oilgit Doffs
Oingx
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Ih Otgl ha gxpginoturg Ngsjroptohis
0 AhhnAhhn oingx iuldgr os 047.2:. Ahhn b`s oijrg`sgn 47.2:%
jhlp`rgn th yg`r 455?.
4 Bhusg Tgit`f
Bhusg Tgit`f oingx iuldgr 04:.2> os tbg fhwgst v`fug `lhim
tbg htbgr otgls wotb tbg oijrg`sg ha 4:.2>% arhl tbg d`sgn
yg`r 455?.
: ^r`isphrt`tohi^r`isphrt`tohi oingx iuldgr os 0>0.1=,wbojb os >0.1=% ha
oijrg`sg d`sgn 455?.
> Gitgrt`oilgit
Gitgrt`oilgit b`s tbg f`rmgst v`fug ha oingx iuldgr wbojb os
071.1? oi tbg fost ha otgl. ^bg pgrjgit`mg ha oijrg`sg ha
gitgrt`oilgit jhlp`rgn th tbg yg`r 455? os 71.1?%.
7 Doffs
Doffs thhk up tborn f`rmgst v`fug ha oingx iuldgr oi tbg gitorg
otgl, `in tbg oingx iuldgr os 0:?.:7, oijrg`sgn wotb
pgrjgit`mg ha :?.:7%.
d) L`kg ` jhijfusohi d`sgn hi tbg jhlphsotg oingx ha gxpginoturg.
^bg jhlphsotg oingx ahr hvgr`ff gxpginoturg os 0:0.0:, tbg tht`f gxpginoturg oijrg`sg
:0.0:% oi tbg yg`r 4500 d`sgn hi tbg yg`r 455?.
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
@J^OQO^_ >
AWT^BGT
GRUFHT@^OHI
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
`) Oi tbg yg`r 450:, tbg jhst ha fovoim os gxpgjtgn th oijrg`sg dy 45% d`sgn hi yg`r4500. J`fjuf`tg tbg gxpginoturg oingx ha g`jb otgl oi yg`r 450: d`sgn hi yg`r 455?.
Ih Otgl ha gxpginoturg Oingx,O
4500 d`sgn 455?
Oingx,O
450: d`sgn 455?
0 Ahhn 047.2:
4 Bhusg Tgit`f 04:.2>
: ^r`isphrt`tohi 0>0.1=
> Gitgrt`oilgit 071.1?
7 Doffs 0:?.:7
d) Arhl tbg oiahrl`tohi oi prgvohus `jtovoty (>`), usg `t fg`st twh lgtbhns th aoin tbgjhlphsotg oingx ha gxpginoturg oi tbg yg`r 450: d`sgn hi yg`r 455?.
Lgtbhn 0
455? 4500 450:
0:0.0: 045
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7/23/2019 Project Work for Additional Mathematics 2012 (Penang)
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Gitgrt`oilgit - oistg`n ha mhoim th joigl`s ahr lhvogs. Lhvog NQNs wg`tbgr otshromoi`f hr por`tgn j`i dg dhumbt `in w`tjb `t bhlg. ^bg jhst ha NQN os r`tbgr
jbg`pgr tb`i lhvog tojkgts ahr ` a`lofy.
DoffsDoffs jhsts fokg gfgjtrojoty `in w`tgr j`i dg rgnujgn dy s`voim tbg `lhuitha gfgjtrojoty `in w`tgr us`mg. Hig a`lofy sbhufn usg tbgsg shurjgs wosgfy fokg
turioim fombts haa nuroim n`ytolg, `vhon b`voim ` fhim sbhwgr tolg `in gtj.
n) Zbhw tbg olp`jt ha yhur summgstohi hi tbg jhlphsotg oingx ha gxpginoturg. Dy `ssuloim tbg oingx iuldgr ahr 4500 d`sgn hi 455? os 055 ahr tbgsg otgls
^r`isphrt`tohi, Gitgrt`oilgit `in Doffs.
Ih Otgl ha gxpginoturgOingx,
450: d`sgn 455?]gombt`mg
0 Ahhn
>7.10 122=.00
4 Bhusg Tgit`f
47.>0 :==1.02
: ^r`isphrt`tohi
05.05 0404.55
> Gitgrt`oilgit
?.71 00>=.45
7 Doffs
?.:4 0002.>5
^ht`f 055 0>0>5.2?
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
@J^OQO^_ 7
JHIJFWZOHI
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
D`sgn hi tbg rgsuft ha stuny,
`) Fost tbrgg (:) olphrt`it otgls oi ` a`lofy gxpginoturg. Gxpf`oi bhw yhu sgfgjt tbgsgolphrt`it otgls.
o. AhhnAhhn os tbg gssgito`f iggn ha `ff fovoim tboims gspgjo`ffy bul`is `in `iol`fs.
]otbhut ahhn, hig j`i igvgr hdt`oi iutrogits iggngn ahr dhny th auijtohi wgff.
Ahhn pf`ys ` vot`f rhfg oi tbg survov`f ha l`ikoin `in ot os prhvgi th dg tbg shurjg
ha foag. ^bus, ot os hig ha tbg olphrt`it otgls oi ` a`lofy gxpginoturg.
oo. Bhusg Tgit`fB`voim ` bhusg os vgry olphrt`it oi gvgry bul`is foag dgj`usg gvgryhig iggns `
sbgftgr. Hig j`i dg prhtgjtgn `in sgjurgn dgoim oi bhlg. Aurtbgrlhrg, ot gi`dfgs
us th fg`n ` ngagisovg foagstyfg `s ot haagrs sgfa-`ssur`ijg `in sgjuroty th l`ikoin.
Oi hrngr th b`vg ` bhusg, wg iggn th p`y lhrtm`mg gvgry lhitb uitof tbg ngdts `rg
sgttfgn (oi tbg ahrl ha bhusoim fh`is) th ` spgjoaoj p`rty, fokg d`iks. ]bofg bhusg
rgit`f os p`on gvgry lhitb ahr rgitgn bhusgs.
ooo. ^r`isphrt`tohi^r`isphrt`tohi b`s dgjhlg ` d`sos ha bul`is n`ofy foag oi tbos gr`. Ughpfg iggn
tr`isphrt`tohi fokg j`rs, lhthrjyjfgs, dusgs `in gtj th tr`vgf th ` ngstoi`tohi.
Dgsongs, tbgy iggn th tr`vgf th m`oi oijhlg thh. L`iy a`lofogs hwi `t fg`st `
vgbojfg `in bgijg, tbgy iggn th spgin ahr tbg augf projg. ]bofg tbg htbgrs wbh
tr`vgfs dy pudfoj tr`isphrt`tohi, ot os stoff oi iggn th p`y ahr tbg dus hr j`d a`rg. @s
` jhijfusohi, tr`isphrt`tohi os ` igjgssoty ahr ` pgrshi th tr`vgf arhl hig pf`jg th
`ihtbgr.
^bg tbrgg olphrt`it otgls gxpginoturg `rg sgfgjtgn dy rgagrroim th tbgor rgspgjtovg
wgombt`mgs.
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
d) ]b`t os tbg jhst ha fovoim ahr ` a`lofy oi tbg yg`r 4500 wbgi jhlp`rgn th yg`r 455?8Jhst ha fovoim oi tbg yg`r 4500 os :0.0:% lhrg tb`i yg`r 455?.
j) ]b`t `rg tbg olp`jts hi ` a`lofy oa tbg jhst ha fovoim oijrg`sgs dy 45% oi 450:8^bg olp`jts hi ` a`lofy oa tbg jhst ha fovoim oijrg`sgs dy 45% oi 450: whufn v`ry
d`sgn hi tbg oijhlg ha tbg a`lofy.^bg rosoim jhst ha fovoim wbofg tbg oijhlg ha
a`lofy rgl`ois tbg s`lg woff droim ollgisg b`rnsbop th ` a`lofy `s tbgy jhufn iht
spgin gihumb hi ahhn, bhusg rgit`f, tr`isphrt`tohi, gitgrt`oilgit `in doffs
`jjhrnoimfy. ^bg phssodfg olp`jt hi ` a`lofy oa tbg jhst ha fovoim oijrg`sgs dy 45% oi
450: os tbgy lombt dg dgfhw phvgrty foig. ^bg oijrg`sg oi tbg mgigr`f fgvgf ha projgs
olpfogs ` ngjrg`sg oi tbg purjb`soim phwgr ha tbg jurrgijy. ^bus, oiaf`tohi hjjurs.
Hig a`lofy woff a`jg prhdfgl fokg sbhrt`mg ha ahhn `in gvgitu`ffy, tbgy woff suaagr
arhl l`fiutrotohi. @p`rt arhl tb`t, tbg a`lofy woff b`vg noaaojuftogs oi p`yoim up tbgor
ngdts ahr bhusg fh`is/rgit`f `s tbg oijrg`sg ha jhst fovoim gaagjts tbg gjhihly `in
j`usoim tbg bhusg rgit`f th dg lhrg gxpgisovg. Lg`iwbofg, a`lofogs woff `fsh dg
aoi`ijo`ffy uist`dfg `s tbgrg woff dg ` 45% bokg oi tbg augf projg.
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
n) Oa yhur summgstohis `rg `dfg th rgnujg tbg jhst ha fovoim, bhw nhgs ot `aagjt tbgjhlphsotg oingx8
Dy `ssuloim tbg oingx iuldgr ahr 4500 d`sgn hi 455? os 055 ahr tbgsg otgls
^r`isphrt`tohi, Gitgrt`oilgit `in Doffs.
Ih Otgl ha gxpginoturgOingx,
450: d`sgn 455?]gombt`mg
0 Ahhn
>7.10 122=.00
4 Bhusg Tgit`f
47.>0 :==1.02
: ^r`isphrt`tohi
05.05 0404.55
> Gitgrt`oilgit
?.71 00>=.45
7 Doffs
?.:4 0002.>5
^ht`f 055 0>0>5.2?
^bg jhlphsotg oingx ngjrg`sgs arhl 07=.:1 th 0>0.>0.
g) ]b`t os tbg pgrjgit`mg ha rgnujtohi oi tbg jhst ha fovoim oi yg`r 450: oa yhursummgstohis `rg `jjgptgn8
^bg olp`jt dy jhitrhffoim tbg : otgls `dhvg, wg j`i rgnujg jhlphsotg oingx dy
00.42%
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
Tgafgjtohi
0. ]bofg yhu wgrg nhoim tbos prhcgjt, wb`t b`vg yhu fg`rign8^brhumbhut tbg prhcgjt wbofg O w`s jhinujtoim ot, O b`vg fg`rign l`iy tboims. O b`vg
jhlg th rg`fozg tbg olphrt`ijg ha l`tbgl`tojs oi n`ofy foag `p`rt arhl tbg rgmuf`r
j`fjuf`tohis ha solpfg iuldgrs. Lhrghvgr, O b`vg fg`rit th dg lhrg p`togit `in iht th
movg up g`sofy. ^bgsg `rg tbg phsotovg `ttotungs hig sbhufn b`vg th dg `dfg th nh
shlgtboim sujjgssauffy. Dgsongs, O fg`rign bhw th jhhpgr`tg wotb arogins. Ly arogins
`in O nosjussgn `dhut tbg prhcgjt `in wg sb`rgn ong`s `lhimst hursgfvgs. ^bos
nosjussohi b`s l`ng lg lhrg jhiaongit wbgi nhoim shlgtboim.
4. Fost hut sgvgr`f lhr`f v`fugs tb`t yhu pr`jtojg wbgi nhoim tbos prhcgjt.O b`vg pr`jtojgn sgvgr`f lhr`f v`fugs wbofg j`rryoim hut tbos prhcgjt whrk sujb `s
sgfa-nosjopfoig. O b`vg trogn ly vgry dgst th jhlpfgtg tbos prhcgjt whrk wotbhut
prhjr`stoi`toim `in bgijg, l`i`mgn th b`in ot oi hi tolg. ^bos prhcgjt b`n t`umbt lg
th rgsphisodfg hi tbg whrks tb`t `rg movgi th lg th dg jhlpfgtgn. Igvgrtbgfgss, O w`s
b`rnwhrkoim wbgi nhoim tbos prhcgjt `in b`n spgit lhst ha ly tolg shfvoim `ff tbg
j`fjuf`tohis p`togitfy. Dgsongs, O b`vg `fsh pr`jtojgn tg`lwhrk wotb ly agffhw
arogins dy sb`roim ong`s `in oiahrl`tohi tbrhumbhut tbg prhjgss ha nhoim tbos prhcgjt
whrk. Dy pr`jtojoim `ff tbgsg lhr`f v`fugs, O b`vg sujjggngn oi jhlpfgtoim tbos
prhcgjt whrk ha @nnotohi`f L`tbgl`tojs.
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@nnotohi`f L`tbgl`tojs Urhcgjt ]hrk 4 4504
:. Urgsgit yhur hpoiohis hr aggfoims jrg`tovgfy jhijgrioim tbos prhcgjt tbrhumb tbgus`mg ha syldhfs, offustr`tohis, nr`woims hr shims.
]bgi O kihw yhu ahr tbg aorst tolg,
O aggf sh st`r strujk,
O aggf jurohus `dhut yhu,
Hdsgssgn th kihw `ff `dhut yhu,
@in O gvgi st`fk yhu,
N`y `in Iombt,
O `l `fw`ys tboikoim `dhut yhu `in O rg`fozgn,
^bos os wb`t pghpfg j`ff a`ffoim oi FHQG
_hu `rg sh jfoimy `in `nnojtovg,
_hu l`kg lg turis th yhu 4>-bhurs ` n`y,
^gffoim lg fottfg dy fottfg `dhut ^bg Kihwgr ha @ff
Kihw, O aggf sh mr`tgauf
^b`t Bg b`s movgi lg tbg jb`ijg th mgt th kihw yhu
@nnotohi`f L`tbgl`tojs
O FHQG _HW