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7/30/2019 ST Math and RTI
1/2
ZX EBXO BGH VXCMYCHMGJM%FBZMH CGXMVYMGXCKGZ XOBX CE^VKYM VMZ]LXZ
Hbtb%Hrcvmg Vmpkrts
tk Cgikre CgstrujtckgXom VXC rmpkrts brm bvbclbflm bt tom
stuhmgt, jlbss bgh sjokkl lmvml,
bgh omlp tmbjomrs chmgtciy stuhmgt
hmjcmgjcms cg ebstmrcga stbghbrhs
bgh ceplmemgt tcemly cgtmrvmgtckgs'
B gmurksjcmgjm bgh mhujbtckgrmsmbrjo%fbsmh gkg%prkit jkrpkrbtckg
llllllllllllll
Ikr ekrm cgkrebtckg, jkgtbjt us0???'1=2'=88: | cgkNecghrmsmbrjo'gmt
www'ecghrmsmbrjo'gmtECGHVmsmbrjo Cgstctutm
@c@c cs tom pmgaucg
imbturmh cg tom ZX Ebto skitwbrm
abems' Gkt kgly hkms tom
jkeputmr%bgcebtmh @c@c ektcvbtm bgh mgabam
joclhrmg cg sklvcga tom ebtomebtcjs cg tom
abems, @c@c kiimrs tmbjomrs pkwmriul wbys tk
jkggmjt ebto jkgjmpts tk
jlbssrkke cgstrujtckg'
ECGH Vmsmbrjo Cgstctutms
Zpbtcbl%Xmepkrbl /ZX# Ebto
sktwbrm prkarbes prkvchm
rmsmbrjo%fbsmh bpprkbjo kr f/Xcmr 2# bgh cgtmrvmgtckg /Xc
Flmghcga cghcvchublczmh, 202 st
cg tom ugcqumly bjjmsscflm hcact
jkgvmgtckgbl tmbjomr%bjclctbt
cgstrujtckg, ZX Ebto mgabams s
lmvml k ebto kr lbgaubam prk
prkarmssckg k ebto ughmrstbg
Cg tom ZX Ebto0 D%= abem Xua Fkbt,
stuhmgts mgjkugtmr b vcsubl puzzlm
womrm tomy eust rmbrrbgam tom fkbts
sk tobt tom frcham wcll kpmg' Xocs abem
tmbjoms bhhctckg, suftrbjtckg bgh tom
jkgjmpt ki mqubl bekugts'
Xom abem Fcrh Mxprmssckgs cg ZX
Ebto0 Ilumgjy cgtrkhujms stuhmgts
tk bhhctckg bgh suftrbjtckg up tk 2>'
Ztuhmgts mgjkugtmrcga tocs puzzlm obvm
ebstmrmh tom vcsubl rmprmsmgtbtckg
ki tom ebtomebtcjs, bgh brm gkw
mgjkugtmrcga tom kvmrlby ki guefmrs
bgh syefkls kgtk tom ebto'
Qm wmgt sokppcga ikr bg
cgtmrvmgtckg ikr b suf%pkpulbtckg
ki kur dchs wok struaalm wcto ebto,
fut wm gkw rmjkagczm
cts ikr mvmrykgm'
%Hbvm Zbwtmllm, D%26 ebto ibjclctbtkr,
Jklkrbhk Zprcgas Zjokkl Hcstrcjt 22
QOBX CZ Z^BXCBL XME^KVBL /ZX# VMBZKGCGA;
Fkrg kut ki gmurksjcmgjm rmsmbrjo bt tom ]gcvmrscty ki
Jblcikrgcb, Crvcgm, ECGHs ugcqum bpprkbjo bjjmssms tom
frbcgs cggbtm spbtcbl%tmepkrbl rmbskgcga bfclcty' Xocs bfclcty,
wocjo lcms bt tom jkrm ki cggkvbtcvm tocgdcga bgh skpocstcjbt%
mh prkflme%sklvcga, bllkws tom frbcg tk oklh vcsubl, emgtbl
rmprmsmgtbtckgs cg sokrt%tmre emekry bgh tk mvklvm tome cg
fkto spbjm bgh tcem, tocgdcga eultcplm stmps bombh' ECGHs
bpprkbjo jkgscsts ki lbgaubam%cghmpmghmgt, bgcebtmh
rmprmsmgtbtckgs ki ebto jkgjmpts hmlcvmrmh vcb jkeputmr
skitwbrm abems'
7/30/2019 ST Math and RTI
2/2
^VKAVBE IMBX]VMZ
Zmli%plbjmh0Xom ZX Ebto sktwbrm stbrts mvmry stuhmgt wcto sujjmss, bgh qucjdly
frcgas tome tk tomcr pmrskgbl plbjmemgt womrm hmmp tocgdcga bgh
lmbrgcga cs rmqucrmh'
Vmsmbrjo%Fbsmh0Xom sktwbrms hmscag cgjkrpkrbtms tom lbtmst sjcmgtcijblly%fbsmh
rmsmbrjo cg jkagctcvm lmbrgcga, abem%fbsmh lmbrgcga bgh ektcvbtckg
tk dmmp mvmg lkw%jkgihmgjm stuhmgts mgabamh bgh prkhujtcvmlyjobllmgamh' Xom pksctcvm cepbjt k ZX Ebto kg stuhmgt ebto
bjocmvmemgt obs fmmg mxtmgscvmly sokwg torkuao b lbram%sjblm
rbghkeczmh jkgtrkl trcbl bgh eultcplm qubsc%mxpmrcemgtbl stuhcms'
Xbclkrmh Cgstrujtckg0Fbsmh kg tom cgkrebtckg cg tom rmpkrts, tmbjomrs jbg bsscag spmjcij
lmbrgcga kf`mjtcvms kr stuhmgts wok gmmh bhhctckgbl omlp cg bg
chmgtcimh brmb'
Cgstrujtcvm Immhfbjd0Ikr mvmry vcsubl puzzlm sklutckg pksmh fy tom stuhmgt, tom sktwbrm
bgcebtms tom vcsubl rmprmsmgtbtckgs k ebto tk prkvchm cgstrujtcvm
mmhfbjd' Qomtomr kr gkt tom sklutckg joksmg fy tom stuhmgt wkrdskr hkms gkt wkrd, bgcebtckg sokws woy ct wbs jkrrmjt kr cgjkrrmjt
bgh prkvchms cgkrebtcvm mmhfbjd tk stuhmgts'
Zmli%pbjmh0Ztuhmgts prkarmss torkuao tom sktwbrms amgtly sjbklhmh abems bt
tomcr kwg pbjm, bhvbgjcga tk tom gmxt jobllmgacga lmvml kgly torkuao
ebstmrcga tom prmvckus lmvml'
Fuclt%cg Vmpkrts0Xmbjomrs, ebto jkbjoms kr ktomr spmjcblczmh mhujbtckg prkmssckgbls
jbg bjjmss stuhmgt prkarmss hbtb cg rmbl%tcem' B fuclt%cg VXC rmpkrt
vcmwmh hbcly kr wmmdly sokws fkto jlbss bgh stuhmgt%lmvml hbtb,
cghcjbtcga lmvml k ebto stbghbrhs ebstmry bgh VXC arkwto'
Arkup Cgstrujtckg0Fy cgjkrpkrbtcga tom sktwbrms bgcebtmh vcsubl rmprmsmgtbtckgs k
ebto cg rmaulbr jlbssrkke kr arkup cgstrujtckg, tmbjomrs jbg omlp
stuhmgts ebdm tom jkggmjtckgs fmtwmmg wobt tomy obvm lmbrgmh
hurcga tomcr 202 ZX Ebto tcem wcto tom lbgaubam bgh syefkls tomy
mgjkugtmr cg trbhctckgbl jlbssrkke ebtmrcbls'
ZX EBXO
^VKAVBEZ
ZX Ebto0 D%=
arbhm%lmvmlmh cgstrujtckgblskitwbrm cs hmscagmh tk omlp bll
stuhmgts rmbjo ebto prkjcmgjy
torkuao smli%pbjmh, lbgaubam%
cghmpmghmgt, ebstmry fbsmh
kf`mjtcvms'
ZX Ebto0
Zmjkghbry Cgtmrvmgtckgcs hmscagmh ikr struaalcga echhlm
bgh ocao sjokkl stuhmgts
pmrikrecga wmll fmlkw arbhm
lmvml' Hcbagkstcj bssmssemgts
prmsjrcfm bg bpprkprcbtm
lmbrgcga pbto ikr mbjo stuhmgt'
Zmli%pbjmh bgh lbgaubam%
cghmpmghmgt, tom Zmjkghbry
Cgtmrvmgtckg skitwbrm prkvchms
cgstrujtckg kg ebto stbghbrhs
prmrmqucsctm tk ebstmrcga echhlm
sjokkl ebto bgh blamfrb'
ZX Ebto0 Ilumgjycs hmscagmh tk omlp arbhm
sjokkl stuhmgts fuclh umgjy
wcto bhhctckg bgh eultcplcjbtckg
ebto ibjts, fuclhcga spmmh bgh
bjjurbjy wcto ughmrstbghcga'
Mvchmgjm suaamsts tobt hmvmlkpcga rbpch bgh bjjurbtm rmspkgsms tk fbscj ebto ibjts, cgjluhcga scgalm%
suftrbjtckg, eultcplcjbtckg bgh hcvcsckg, eby prmvmgt bgh rmemhy lmbrgcga prkflmes' /Zdcfb, Ebagmus
) Mrcjdskg, 23?9#' Xom tmres umgjy bgh butkebtcjcty hmsjrcfm tocs lmvml ki sdcll hmvmlkpemgt' Cg
prkvmg usm ki bgcebtmh vcrtubl ebgcpulbtcvms mgbflm stuhmgts tk gkt `ust emekrczm fut blsk prkvm
ibjts' Xom stbtm%ki%tom%brt bhbptcvcty ebdms fbscj ebto ibjt rmjbll miikrtlmss bgh irmms stuhmgts wkrdcg
prkflme%sklvcga' Xom smli%pbjmh abems bllkw stuhmgts bt bgy bjbhmecj lmvml tk mgabam wcto tom jkgt
bpprkprcbtm ikr usm bt bll stbams ki VtC'
XCMV 2 XCMV 6 XCMV
^bcrmh wcto trbhctckgbl cgstrujtckg,
tom usm ki ZX Ebto obs fmmg
prkvmg bs b ocaoly miimjtcvm
prmvmgtckg prkarbe bhhrmsscga
tom amgmrbl pkpulbtckg kistuhmgts' Mbrly ceplmemgtbtckg
armbtly rmhujms tom cgjchmgjm
ki stuhmgts fmcga plbjmh cg Xcmr
6' Xom smli%pbjmh abems bllkw
stuhmgts bt bgy bjbhmecj lmvml
tk mgabam wcto tom jkgtmgt bgh
mxpmrcmgjm ceemhcbtm sujjmss,
mgjkurbacga pksctcvm fmobvckr'
Ikr stuhmgts wok hch gkt usm
ZX Ebto cg Xcmr 2, tom prkarbe
jbg fm cgtrkhujmh bt Xcmr 6
bgh cs mspmjcblly miimjtcvm cguglkjdcga ugrmblczmh lmbrgcga
pktmgtcbl' Cg bhhctckg tk omlpcga
amgmrbl stuhmgts wok brm gktpmrikrecga bt tomcr bjbhmecj
pktmgtcbl, tom prkarbe
suppkrts stuhmgts wok obvm
hcijulty wcto lbgaubam, kr wok
obvm eclh butcse, hyslmxcb kr
ktomr spmjcbl gmmhs' Xom fuclt%
cg rmpkrts bllkw tmbjomrs tkchmgtciy stuhmgt hmjcmgjcms tk
bhhrmss torkuao cgtmrvmgtckg'
Ztuhmgts wok obvm scagcjbgt
abps cg tomcr ebtomebtcjbl
dgkwlmham bgh prkflme%
sklvcga sdclls wcll fmgmt irke
tom usm ki ZX Ebto0 Zmjkghbry
Cgtmrvmgtckg' Xom ebtmrcbl jbg
fm jkvmrmh cg b vbrcmty ki jlbss
ekhmls cgjluhcga bhhctckgbl
ebto jlbssms, mxtmghmh
jlbss pmrckhs kr bhhctckgbl
tbramtmh cgtmrvmgtckg tcem' Xom
cgstrujtckgbl bpprkbjo kiimrs
stuhmgts tom ektcvbtckg tk
jkrrmjt prckr ecsjkgjmptckgs
bgh jkgstrujt b sklch
ebtomebtcjbl ikughbtckg'
Cg ocaoly cghcvchub
tocs cgtmgsm, mxpl
prkvchms jkgtmg
tom cghcvchubl
cgstrujtkrs bgb
tomy jbg mbscly ch
hmjcmgjcms fy
ebstmry bgh cep
cgtmrvmgtckgs' Xom
ibjtkr ki ZX Ebto
usmiul cg Xcmr : w
b gmmh ikr cgjr
bgh irmqumgjy bg
cgtmrvmg