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

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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.

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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

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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.

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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

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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,

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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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    @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