GM EMAT 3 ESP - 22 23 Fusionado
July 15, 2022 | Author: Anonymous | Category: N/A
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lln ou nss o uggvvnnss a annttggss
Iuán `gl angstrd 3.º Vrkanrkn / uok`n`gs >-2 Iuán `g augstrn
antgaîtkcns cns bnsn`d GANP gs uo prdirnan pnrn ln gosgþnozn `g lns antgaîtk go agtd`dldiáns koodvn`drns qug pgraktgo uo nprgo`kznjg skiokekcntkvd. Irnckns nl jugid, ln anokpulnckóo y lns nctkvk`n`gs cdotgxtunlkzn`ns, antgaîtkcnss. tus nluaods `kserutnrîo `g lns antgaîtkcn
N`gaîs, ag`knotg ln sgcugocknckóo cáclkcn `g lds cdotgok`ds y ln `kvgrsk`n` `g gxpgrkgockns `g nprgo`kznjg cdosgiukrîs uo nprgo`kznjg prdeuo`d y `urn`grd `gs`g g`n`gs tgaprnons, rgspgtno`d td`ds lds rktads `g nprgo`kznjg. N cdotkounckóo, gocdotrnrîs uon sglgcckóo `g pîikons `g ln Iuán `gl angstrd, gl `dcuagotd go gl qug sg `gsnrrdllno td`ns lns nctkvk`n`gs nl `gtnllg y lds nspgctds pg`nióikcds clnvgs pnrn prdirnanr tu `án n `án. [ td`d gl prdirnan gstî `ksgþn`d pnrn `nr rgspugstn n ln ougvn lgy `g g`ucnckóo LDALDG:
@gsnrrdlld `g lns cdapgtgockns gspgcáekcns
Gvnlunckóo cdapgtgocknl y cdotkoun
Gstrntgikns `g g`ucnckóo kocluskvn
Pgcodldián nl sgrvkckd `gl nprgo`kznjg CkbgrGANP gs ln nplkcnckóo pnrn ln prîctkcn sganonl `g GANP `g anogrn nutóodan y pgrsdonlkzn`n. CkbgrGANP CkbgrGANP pgraktg uo nprgo`kznjg n`nptntkvd, cdo nctkvk`n`gs qug sg njustno nl prdirgsd `gl nluaod.
Cdo egg`bnch koag`kntd pnrn encklktnr ln nutdodaán.
´Cóad usnrld4 Go ln Iuán `gl angstrd gocdotrnrîs `gtnlln`ds lds cdotgok`ds qug sg trnbnjno go cn`n sgskóo `g CkbgrGANP.
Pu igstdr `g nuln, `án n `án Go ayrdda, gl igstdr `g nuln dolkog `g tghano, gocdotrnrîs td`d ld qug ogcgsktns pnrn prgpnrnr y `nr tus clnsgs, cdo td`ds lds rgcursds ogcgsnrkds `gl `án, pnrn rgnlkznr lns nctkvk`n`gs ¡go uo sdld clkc!
P u i g s t d r ` g n u l n , ` á n n ` á n
¡Gl Lkbrd `gl nluaod tnabkëo gs `kiktnl!
Cdoiurn GANP @kiktnl `gscnrino`d ln nplkcnckóo pnrn kDS d No`rdk`, d gotrn go www.gant`kiktnl.cda, y igstkdon tus irupds.
Gvnlún `g edran cdapgtgocknl Vnrn rgnlkznr uon gvnlunckóo cdotkoun y cdapgtgocknl tg ko`kcnads quë nctkvk`n`gs pug`gs rgnlkznr, cuîo`d y cdo quë kostruagotds cugotns.
Dbsgrvnr gl `gsgapgþd
Rgnlkznr uo `knioóstkcd
Nskionr uo okvgl
Wtklkzn lds ko`kcn`drgs `g cn`n sgskóo nsdckn`ds n cn`n uon `g lns cdapgtgockns, pnrn dbsgrvnr gl prdirgsd `g lds nluaods.
Go sgskdogs gspgcácns, utklkzn `kegrgotgs kostruagotds pnrn rgnlkznr uo `knioóstkcd `gl okvgl `g lds nluaods.
Nl onlkznr ln uok`n` d cursd, utklkzn td`n ln gvnlunckóo rgnlkzn`n pnrn sgþnlnr go quë okvgl `g ldird `g ln cdapgtgockn antgaîtkcn sg gocugotrn cn`n nluaod.
• Rgikstrd `g gvnlunckóo.
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l n k c o g t g p a d c n a r d e g ` n ú l n v G
• Gvnlunckóo `g vgldck`n` `g cîlculd agotnl. • Ekcmn cdad prugbn. • Vdotg n prugbn. • Vrugbn `g ln uok`n`.
• Rúbrkcns `g cdapgtgockn antgaîtkcn pdr ckcld.
Vnrn uon gvnlunckóo aîs îikl, pdogads n tu `kspdskckóo gl Rgikstrd `g gvnlunckóo y gl rgstd `g kostruagotds go N``ktkd edr scmddls. Vd`rîs gvnlunr `gs`g cunlqukgr `kspdsktkvd cdo uo sdld clkc y cdapnrtkr lds rgsultn`ds go tkgapd rgnl cdo lns enaklkns. Nccg`g n trnvës `g ayrdda y `kserutn `g td`ns sus vgotnjns. vgotnjns.
Vnrn rgnlkznr uon gvnlunckóo cdapnrtk`n cdo tus nluaods, qug lgs pgraktn tdanr cdockgockn `g sus nprgo`kznjgs, n ld lnrid `g ln uok`n` gocdotrnrîs:
Nctkvk`n`gs `g nutdgvnlunckóo Nctkvk`n`gs qug pgraktgo nl nluaod rgflgxkdonr sdbrg su nprgo`kznjg y nutdrrgiulnrsg. • • • • • •
Gscnlgrn `g agtncdiokckóo @knrkd `g antgaîtkcns Vlnotklln `g rgsdluckóo `g prdblgans Rúbrkcn `g rgsdluckóo `g prdblgans Nutdgvnlunckóo onl `g cdotgok`ds Vdredlkd `g nprgo`kznjg
Nctkvk`n`gs `g gvnlunckóo `gl nprgo`kznjg cddpgrntkvd Nctkvk`n`gs qug pgraktgo nl nluaod gvnlunr cóad mn trnbnjn`d go gqukpd, cóad trnbnjno sus cdapnþgrds y cóad trnbnjno gllds. • • • •
Rúbrkcn `g cdgvnlunckóo Irîcn `g gvnlunckóo `gl trnbnjd cddpgrntkvd Pglnrnþn `g gvnlunckóo `gl trnbnjd cddpgrntkvd Ktkogrnrkd `g gvnlunckóo `gl trnbnjd cddpgrntkvd
l n k c o g t g p a d c n a r d e g ` n ú l n v G
Rgcdodcg lds adagotds `g nprgo`kznjg Lns uok`n`gs `g GANP gstîo kotgrcdogctn`ns gotrg sá, `g edran qug lds cdotgok`ds skiugo uon prdirnanckóo cáclkcn y sg rgtdano pgrkó`kcnagotg `gs`g uon irno `kvgrsk`n` `g gxpgrkgockns `g nprgo`kznjg. Ln skstganskiokcntkvd y gl `gsnrrdlld `g lns tkznckóo y sgcugocknckóo `g gstns nctkvk`n`gs mncgo pdskblg gl nprgo`kznjg skiokcntkvd mnbklk`n`gs antgaîtkcns `g edran prdeuo`n y `urn`grn, `gs`g koenotkl mnstn prkanrkn. Cdad snbgads qug lns dpgrnckdogs bîskcns, suan, rgstn, aultkplkcnckóo y `kvkskóo, sdo cdotgok`ds clnvg go ln gtnpn `g prkanrkn, tg ko`kcnads gl prdcgsd `g nprgo`kznjg. Vnrn mncgrld, gocdotrnrîs lds skiukgotgs kcdods go lns nctkvk`n`gs, sgþnlno`d lds skiukgotgs adagotds, qug sdo skgaprg ncuaulntkvds:
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R g c d o d c g l d s a d a g o t d s ` g n p r g o ` k z n j g
Cdaprgoskóo
Kotrd`ucckóo
Vrîctkcn
Cdosdlk`nckóo
`gl cdocgptd
`gl nlidrktad
`gl nlidrktad
`gl nlidrktad
Nctkvk`n`gs qug pgraktgo cdodcgr g kotgrkdrkznr gl cdocgptd.
Nctkvk`n`gs goedcn`ns n `gscubrkr gl nlidrktad y cóad utklkznrld.
Nctkvk`n`gs pnrn prnctkcnr gl usd `gl nlidrktad, `g anogrn prd`uctkvn d skstgaîtkcn.
Nctkvk`n`gs `krkik`ns n utklkznr gl nlidrktad go `kvgrsk`n` `g sktunckdogs pnrn nnoznr.
´^uë pug`gs mncgr cdo gstn koedranckóo4 •
Sgiukr ln ildbnlk`n` `gl prdcgsd `g nprgo`kznjg `g lns dpgrnckdogs bîskcns.
•
@gtgctnr go quë adagotd sg gocugotrn cn`n nluaod, pnrn dergcgrlg lns nctkvk`n`gs qug ogcgsktn.
•
Vrkdrkzn r, `gotrd `g ln nctkvk`n`, gl dbjgtkvd rglnckdon`d Vrkdrkznr cdo gl adagotd `g nprgo`kznjg.
g j n z k ` o g r p n g ` s d t o g a d a s d l g c d o d c g R
Dbjgtkvds `g nprgo`kznjg Notgs `g prdeuo`kznr go cn`n uod `g lds `áns, cdapnrtkads lds dbjgtkvds `g nprgo`kznjg `g td`d gl cursd pnrn tgogr uon vkskóo cdaplgtn. Lds dbjgtkvds rgsnltn`ds sdo lds qug sg trnbnjno cdo anydr kotgosk`n` n ld lnrid `g cn`n uok`n`.
WOK@N@ >
WOK@N@ 2
• Lggr, Lggr, gscrkbkr y dr`gonr oúagrds
• Cdaprgo`gr ln aultkplkcnckóo.
mnstn gl >6 666. • Crgnr g kotgrprgtnr ktkogrnrkds.
• Agadrkznr lns tnblns `g aultkplkcnr.
• K`gotkcnr gl pgráagtrd `g pdláidods.
• Wtklkznr ln prdpkg`n` cdoautntkvn
• K`gotkcnr gl vnldr `g cn`n ckern.
• Aultkplkcnr pdr >6, >66 y >666.
• Vgsnr cdo ln bîsculn go irnads
• Cdapnrnr uok`n`gs `g tkgapd tkgapd.. • Rgcdodcgr cugrpds igdaëtrkcds.
• @gckr ln mdrn.
• Nprdxkanr n uok`n`gs `g akllnr akllnr..
• K`gotkcnr îoiulds rgctds.
• Gotgo`gr ln `kvkskóo.
• Suanr y rgstnr cdo vnrkns ckerns.
• Gstkanr y cnlculnr îrgns.
• K`gotkcnr lds glgagotds `g ln
• Gstkanr prd`uctds.
ckrcuoegrgockn y `gl cárculd. • Rglnckdonr lns cnpnck`n`gs cdo lns erncckdogs: ag`kds, tgrckds y cunrtds.
g j n z k ` o g r p n g ` s d v k t g j b D
`g ln aultkplkcnckóo.
• Cnlculnr îrgns `g cun`rn`ds y rgctîoiulds.
y hkldirnads.
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• Wtklkznr lds dr`konlgs.
• Lggr g kotgrprgtnr irîcds lkognlgs, `knirnans `g bnrrns y pkctdirnans. • Drinokznr `ntds go tnblns.
• Mncgr gstkanckdogs.
• Wsnr ln aîqukon `g euockdo euockdogs gs pnrn
• Rgnlkznr rgpnrtds gquktntkvds. • Lggr g kotgrprgtnr `knirnans `g bnrrns.
aultkplkcnr. • Rglnckdonr ln aultkplkcnckóo y ln `kvkskóo.
• K`gotkcnr kiunl`n`gs y `gskiunl`n`gs.
• Wtklkznr ln cnlculn`drn.
• Cdodcgr lds oúagrds ogintkvds go
• Gscdigr ln dpgrnckóo cdrrgctn pnrn rgsdlvgr
cdotgxtds cdtk`knods.
uo prdblgan.
• Nprdxkanr lds rgsultn`ds `g suans y rgstns.
WOK@N@ 3
WOK@N@ 0
• Clnskcnr îoiulds niu`ds, rgctds
• Nplkcnr lds oúagrds `gckanlgs.
y dbtusds. • @kvk`kr pdr uon ckern y cdo rgstd. • Lggr pkctdirnans, `knirnans `g bnrrns y irîcns lkognlgs.
• Clnskcnr iurns skaëtrkcns y nskaëtrkcns. • Cdaprgo`gr lns erncckdogs y lds oúagrds akxtds. • Aultkplkcnr oúagrds `g vnrkns ckerns.
• Gscrkbkr kiunl`n`gs y `gskiunl`n`gs.
• Gstkanr y ag`kr îrgns, ldoiktu`gs y pgsds.
• Clnskcnr rgctns pnrnlglns y sgcnotgs.
• Cdodcgr lns erncckdogs `g m mdrn. drn.
• Cdodcgr lds oúagrds `gckanlgs.
• Cdostrukr ckrcuoegrgockns.
• Cnlculnr îrgns go uok`n`gs cun`rn`ns.
• Lggr y gscrkbkr lds oúagrds rdanods
• Mncgr gstkanckdogs `g pgsd y ldoiktu`.
`gl K nl ]].
• Suanr y rgstnr `gckanlgs.
• Rgcdodcgr lns erncckdogs gqukvnlgotgs.
• Rgcdodcgr pdlkg`rds y cugrpds rg`do`ds.
• Mncgr prg`kcckdogs.
• Rgcdodcgr ln plnotn, gl pgrl y gl nlzn`d
• Aultkplkcnr uo oúagrd gotgrd pdr uo
`g cugrpds igdaëtrkcds. • Clnskcnr trkîoiulds sgiúo sus ln`ds y sus îoiulds.
oúagrd `gckanl. • Cdodcgr oúagrds dr`konlgs mnstn gl 06. • Nprdxkanr aultkplkcnckdogs y `kvkskdo `kvkskdogs. gs.
• Clnskcnr cun`rklîtgrds y pnrnlgldirnads.
• Rgcdodcgr iurns cdoirugotgs.
• Prnosedranr uok`n`gs `g ag`k`n.
• K`gotkcnr `kbujds n gscnln.
• Cdodcgr lds oúagrds cun`rn`ds.
• Gxpldrnr lds gxpdogotgs.
• Lggr tgraóagtrds. • Cdodcgr gl vdluago.
g j n k z ` o g r p n g ` s d v k t g j b D
Cdotgok`ds WOK@N@ > GUNLWNCKÓO Ko`kcn`dr `g gvnlunckóo
VNRN GAVGZNR • Cîlculd agotnl
GOSGÞNO@D -NVRGO@KGO@D • Pnrjgtns ouagrnlgs
VNRN NCNBNR @knrkd `g antgaîtkcns
Vrdpdog `kvgrsns dpckdogs pnrn
K`gotkcnckóo `gl notgrkdr `g
K`gotkcnckóo y lgcturn
Vugstn go prîctkcn
cdostrukr gl oúagrd n`gcun`d go gl jugid `gadstrnckóo.
oúagrds `g mnstn trgs ckerns.
`g oúagrds `gl 7666 nl >6 666.
`g gstrntgikns y prdcg`kakgotds.
• Vrdblgans drnlgs Dpgrnckdogs `g suan y rgstn.
> • Vrdblgan `gl `án Cdaprgoskóo y rgsdluckóo `g prdblgans.
Ko`kcn`dr `g gvnlunckóo K`gotkcn gl gspnckd cgrcnod n trnvës `g uo crdquks.
• Cîlculd agotnl K`gotkcnckóo `gl pdstgrkdr `g oúagrds `g mnstn cuntrd ckerns.
• Vrdblgans drnlgs Dpgrnckdogs `g suan y rgstn. Cîlculd `g ln aktn`.
2
• Vrdblgan `gl `án
• Jugid `gadstrnckóo cddpgrntkvd y cmns Dr`gonckóo `g oúagrds onturnlgs mnstn >6 666. Rgcdodckakgotd `gl vnldr pdskckdonl `g lns ckerns mnstn lns uok`n`gs `g akllnr. akllnr.
• Jugid `gadstrnckóo cddpgrntkvd y >.ª cmn Kotgrprgtnckóo y `gscrkpckóo `g ktkogrnrkds. Drkgotnckóo go gl gspnckd n pnrtkr `g uo crdquks.
Rgflgxkóo drnl Rgflgxkóo sdbrg gl prdcgsd sgiuk`d go uon nctkvk`n` d prdblgan.
• 2.ª cmn Lgcturn `g anpns.
Vugstn go prîctkcn `g gstrntgikns y prdcg`kakgotds. Rgsdluckóo `g prdblgans cdo dpgrnckdogs cdabkon`ns.
C D O P G O K @ D S
Ko`kcn`dr `g gvnlunckóo Gxtrng cdocluskdogs ncgrtn`ns `g ln nctkvk`n` anokpulntkvn.
• Cîlculd agotnl K`gotkcnckóo `gl notgrkdr y pdstgrkdr `g oúagrds `g mnstn cuntrd ckerns.
• Pnrjgtns igdaëtrkcns K`gotkcnckóo `g iurns plnons.
@knrkd `g antgaîtkcns Gxprgskóo y cdauokcnckóo go lgoiunjg antgaîtkcd.
• Nctkvk`n` anokpulntkvn • Vrdblgans drnlgs Cîlculd `gl pgráagtrd `g iurns plnons. Dpgrnckdogs `g suan y rgstn.
• Vrdblgan `gl `án
3
Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans. @gscdapdskckóo `g iurns plnons.
Cdocgptd `g pgráagtrd `g uon iurn. Nctktu`gs pgrsdonlgs `gl qugmncgr antgaîtkcd: rgflgxkóo y nriuagotnckóo.
• Aurnl `g antgaîtkcns • Mkstdrkns pnrn pgosnr Gstkanckóo y ag`k`n `g ldoiktu`gs. K`gotkcnckóo `g iurns plnons.
• Ekcmns K`gotkcnckóo `g lns cnrnctgrástkcns `g lns iurns plnons. Cîlculd `gl pgráagtrd `g iurns plnons.
Adagotd `g nprgo`kznjg
GUNLWNCKÓO Ko`kcn`dr `g gvnlunckóo Rgprgsgotn ln ergcugockn `g lds `ntds go uo `knirnan `g bnrrns.
VNRN GAVGZNR • Cîlculd agotnl K`gotkcnckóo `gl notgrkdr y pdstgrkdr `g oúagrds `g mnstn `ds ckerns.
GOSGÞNO@D-NVRGO@KGO@D • Jugid `gadstrnckóo y cmns Rgikstrd `g `ntds go tnblns `g `dblg gotrn`n. Kotgrprgtnckóo y glnbdrnckóo `g `knirnans `g bnrrns.
VNRN NCNBNR Rgflgxkóo drnl Gxprgskóo y cdauokcnckóo go lgoiunjg antgaîtkcd.
• Vrdblgans drnlgs Dpgrnckdogs `g suan, rgstn y aultkplkcnckóo.
0
• Vrdblgan `gl `án
• Antkjugids Drkgotnckóo gspncknl. Rgprgsgotnckóo `g `ntds go `knirnans `g bnrrns.
Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans. Cdodckakgotd `gl cnlgo`nrkd.
Ko`kcn`dr `g gvnlunckóo Cdostruyg oúagrds `g cuntrd ckerns sgiúo gl vnldr nskion`d pdr lds bldqugs.
• Cîlculd agotnl K`gotkcnckóo `g vnldrgs pgr`k`ds go suans y rgstns mnstn >6.
Ekcmn cdad prugbn
• Pnrjgtns ouagrnlgs Dr`gonckóo `g oúagrds go ln rgctn ouaërkcn mnstn 366.
@knrkd `g antgaîtkcns Nctktu`gs pgrsdonlgs `gl qugmncgr antgaîtkcd: rgflgxkóo y nriuagotnckóo.
• Jugid `gadstrnckóo y cmns • Vrdblgans drnlgs Unldr pdskckdonl `g lns ckerns.
7
Rgcdodckakgotd `gl vnldr pdskckdonl `g lns ckerns mnstn lns uok`n`gs `g akllnr.
CkbgrGANP
• Vrdblgan `gl `án Cdaprgoskóo `g gouockn`ds `g edran drnl.
Ko`kcn`dr `g gvnlunckóo Cdostruyg uon dpgrnckóo n pnrtkr `gl rgsultn`d go gl jugid `gadstrnckóo.
• Cîlculd agotnl Suans y rgstns mnstn 26.
• Vrdblgans drnlgs Dpgrnckdogs `g suan, rgstn y aultkplkcnckóo.
5
• Antkjugids Suan `g `ds suano`ds `gl 6 nl 7 y `gl 7 nl >6 go cun`rd `g `dblg gotrn`n.
• Jugid `gadstrnckóo y cmn Dpgrnckdogs `g suan y rgstn cdo oúagrds onturnlgs. Nlidrktad `g ln suan y `g ln rgstn.
Rgflgxkóo drnl @gsnrrdlld `g ln rgflgxkóo sdbrg lns gstrntgikns utklkzn`ns.
• Jugid `g cubds • Vrdblgan `gl `án Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans. Cdodckakgotd `gl cnlgo`nrkd.
Ko`kcn`dr `g gvnlunckóo Glkig gotrg lds `ds aëtd`ds `kstkotds `g cnlculnr gl îrgn.
• Cîlculd agotnl Dpgrnckdogs cdabkon`ns `g suans y rgstns mnstn 26.
Rgstn mnstn 26.
• Ekcmn Noîlksks y cdaprgoskóo `gl gouockn`d `g prdblgans `g suan y rgstn.
• Nctkvk`n` anokpulntkvn y 2.ª cmn
Rgflgxkóo drnl
Kotrd`ucckóo nl cîlculd
Wsd `g lds nprgo`kznjgs n`qukrk`ds go sktunckdogs
`g îrgns.
cdtk`knons.
• Vrdblgans drnlgs Cîlculd `gl `dblg y ln aktn`. Dpgrnckdogs `g suan y aultkplkcnckóo.
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• Rutkon `g pgosnakgotd @gsnrrdlld `g ln rgflgxkóo sdbrg lns gstrntgikns utklkzn`ns.
• Vrdblgan `gl `án Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans.
Ko`kcn`dr `g gvnlunckóo Nirupn `gcgons cdo antgrknl anokpulntkvd pnrn rgsdlvgr suans.
• Cîlculd agotnl Suans y rgstns mnstn 26.
• Vrdblgans drnlgs
=
Dpgrnckdogs `g suan y rgstn. Wsd `g erncckdogs: ag`kds.
• Vrdblgan `gl `án
Rgsdluckóo `g prdblgans sgockllds `g suan.
• Nctkvk`n` anokpulntkvn y cmn Nirupnckóo y `gsnirupnckóo `g oúagrds go cgotgons, `gcgons y uok`n`gs. Dpgrnckdogs `g suan cdo antgrknl anokpulntkvd.
• Jugid `g cubds Suan `g mnstn cuntrd oúagrds `g uon ckern.
Rgflgxkóo drnl Ugrbnlkznckóo `gl prdcgsd sgiuk`d go uon nctkvk`n` d prdblgan.
Vrugbn `g vgldck`n` (suan)
S D @ K O G P O D C
GUNLWNCKÓO Ko`kcn`dr `g gvnlunckóo Dr`gon cdrrgctnagotg pgsds utklkzno`d irnads y hkldirnads.
VNRN GAVGZNR • Cîlculd agotnl Suans mnstn 26.
• Vrdblgans drnlgs Dpgrnckdogs `g suan y rgstn.
GOSGÞNO@D-NVRGO@KGO@D • Nctkvk`n` anokpulntkvn cddpgrntkvn y cmns Lgcturn, dr`gonckóo, cdapnrnckóo y suan `g pgsds go hkldirnads y irnads.
VNRN NCNBNR Rgflgxkóo drnl Vugstn go prîctkcn `g gstrntgikns y prdcg`kakgotds. Wsd `g ln bîsculn.
; • Vrdblgan `gl `án
• Aurnl `g antgaîtkcns
Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans.
Ko`kcn`dr `g gvnlunckóo Rgprgsgotn prdblgans antgaîtkcds cdo `kegrgotgs gstrntgikns `urnotg gl jugid `gadstrnckóo.
>6
• Cîlculd agotnl Suans mnstn 26.
• Vrdblgans drnlgs Dpgrnckdogs `g suan y rgstn. Wsd `g erncckdogs: cunrtds.
• Vrdblgan `gl `án N`qukskckóo `g prdcgsds `g rnzdonakgotd y gstrntgikns `g rgsdluckóo `g prdblgans.
Ekcmn cdad prugbn
• Jugid `gadstrnckóo y cmns Lgcturn, noîlksks y cdaprgoskóo `gl gouockn`d `g prdblgans. Vugstn go prîctkcn `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans: mncgr uo `kbujd, uon tnbln, uo gsqugan `g ln sktunckóo, gosnyd y grrdr rnzdon`d, dpgrnckdogs antgaîtkcns n`gcun`ns, gtc.
@knrkd `g antgaîtkcns Crgnckóo y rgsdluckóo `g prdblgans.
CkbgrGANP
• Jugid `g cubds Rgstn mnstn 26.
Ko`kcn`dr `g gvnlunckóo Rgcdodcg ln mdrn go gl rgldj nonlóikcd.
• Cîlculd agotnl Suans mnstn 26.
• Vrdblgans drnlgs
C D O P G O K @ D S
Dpgrnckdogs `g suan. Rgsdluckóo `g prdblgans cdo ag`k`ns `g tkgapd.
>>
• Jugid `gadstrnckóo y cmns Lgcturn y rgprgsgotnckóo `g ln mdrn go gl rgldj nonlóikcd y `kiktnl.
Rgflgxkóo drnl @gsnrrdlld `g mnbklk`n`gs `g rgcdodckakgotd `g lds nprgo`kznjgs n`qukrk`ds.
• Antkjugids Lgcturn `gl rgldj nonlóikcd `g 7 go 7 akoutds.
• Vrdblgan `gl `án Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans. Cîlculd `g dpgrnckdogs cdabkon`ns.
Ko`kcn`dr `g gvnlunckóo K`gotkcn `kegrgotgs tkpds `g îoiulds go gl gotdrod `urnotg ln nctkvk`n` anokpulntkvn.
>2
• Cîlculd agotnl Rgstns mnstn >6.
• Vrdblgans drnlgs Wsd `g erncckdogs: aktn`gs. Cdodckakgotd `gl rgldj. K`gotkcnckóo `g îoiulds rgctds.
• 2.ª cmn Nprdxkanckóo n lns mdrns go puotd y lns ag`kns mdrns.
• Nctkvk`n` anokpulntkvn y cmns K`gotkcnckóo `g îoiulds rgctds, niu`ds y dbtusds.
@knrkd `g antgaîtkcns Rgprgsgotnckóo `g cdocgptds antgaîtkcds.
• Antkjugids Cîlculd `g vnldrgs pgr`k`ds go suans mnstn >6.
• Vrdblgan `gl `án Noîlksks y cdaprgoskóo `gl gouockn`d `g prdblgans. Cdodckakgotd `gl cnlgo`nrkd. Wsd `g lds oúagrds dr`konlgs go cdotgxtds cdtk`knods.
Vdotg n prugbn >
GUNLWNCKÓO Ko`kcn`dr `g gvnlunckóo Vnrtkckpn nctkvnagotg go gl rnzdonakgotd `gl prdblgan `gl `án.
VNRN GAVGZNR • Cîlculd agotnl Rgstns mnstn >6.
• Vrdblgans drnlgs
GOSGÞNO@D-NVRGO@KGO@D • Jugid `gadstrnckóo y cmn Suans llgvno`d `g `ds y trgs oúagrds `g `ds ckerns (nirupno`d `gcgons). Suans vgrtkcnlgs `g oúagrds `g `ds ckerns.
VNRN NCNBNR Rgflgxkóo drnl Ugrbnlkznckóo `gl prdcgsd sgiuk`d go uon nctkvk`n` d prdblgan.
Wsd `g erncckdogs: aktn`gs. Dpgrnckdogs `g rgstn. Cdotgd `g `kogrd y gqukvnlgockns gotrg lns `kegrgotgs adog`ns • Jugid `g cubds `gl skstgan adogtnrkd Suan `g `ds oúagrds `g ln Wokóo Gurdpgn. `g `ds ckerns.
>3
• Vrdblgan `gl `án K`gotkcnckóo `g pntrdogs go sgrkgs ouaërkcns. Vnrtkckpnckóo nctkvn go gl kotgrcnabkd `g dpkokdogs, rgflgxkdogs y rgspugstns n prgiuotns.
Ko`kcn`dr `g gvnlunckóo Vrdpdog anogrns `g rgsdlvgr gl prdblgan `gl `án.
• Cîlculd agotnl Suans y rgstns mnstn 26.
• Jugid `gadstrnckóo y cmn @gsnirupnckóo `g cgotgons y `gcgons pnrn rgstnr.
• Vrdblgans drnlgs Dpgrnckdogs `g suan y rgstn. Wsd `g erncckdogs: aktn`gs.
>0
Rgflgxkóo drnl Wsd `g lds nprgo`kznjgs n`qukrk`ds go sktunckdogs cdtk`knons.
• Jugid `g cubds Rgstn `g `ds oúagrds `g `ds ckerns.
• Vrdblgan `gl `án Wsd `g gstrntgikns pnrn ln rgsdluckóo `g prdblgans cdo adog`ns.
Ko`kcn`dr `g gvnlunckóo Rglnckdon ln aultkplkcnckóo cdo suans `g suano`ds kiunlgs.
• Cîlculd agotnl Dpgrnckdogs cdabkon`ns `g suans y rgstns mnstn 26.
• Vrdblgans drnlgs Dpgrnckdogs `g suan, rgstn y aultkplkcnckóo. Wsd `g erncckdogs: ag`kds.
>7
• Jugid `gadstrnckóo y cmns Aultkplkcnckóo cdad suan `g suano`ds kiunlgs.
Rgflgxkóo drnl Ugrbnlkznckóo `gl prdcgsd sgiuk`d go uon nctkvk`n` d prdblgan.
• Mkstdrkns pnrn pgosnr Rgsdluckóo `g prdblgans `g aultkplkcnckóo y rgpnrtd gquktntkvd. Cîlculd `gl `dblg y ln aktn`.
CkbgrGANP
• Vrdblgan `gl `án Wsd `g ln aultkplkcnckóo go prdblgans cdotgxtunlkzn`ds.
Ko`kcn`dr `g gvnlunckóo Rgprgsgotn ln nirupnckóo `g uok`n`gs, `gcgons y cgotgons cdo antgrknl anokpulntkvd.
• Cîlculd agotnl Suans y rgstns mnstn 26.
• Vrdblgans drnlgs Dpgrnckdogs `g suan y rgstn. Wsd `g erncckdogs: aktn`gs.
>5
• Vrdblgan `gl `án Cdapdskckóo y `gscdapdskckóo `g cnotk`n`gs `g `kogrd cdo adog`ns.
• Nctkvk`n` anokpulntkvn Nirupnckóo y `gsnirupnckóo `g oúagrds go cgotgons, `gcgons y uok`n`gs. Suans llgvno`d cdo antgrknl anokpulntkvd.
Rgflgxkóo drnl K`gotkcnckóo `g grrdrgs go ln rgsdluckóo `g prdblgans.
• Ekcmns Rgsdluckóo `g prdblgans. Suans llgvno`d `g `ds oúagrds `g trgs ckerns go vgrtkcnl.
• Antkjugids Suan `g `ds suano`ds `gl 6 nl 7 y `gl 7 nl >6 go cun`rd `g `dblg gotrn`n.
Ekcmn cdad prugbn
S D @ K O G P O D C
WSD LN SWAN VNRN AWLPKVLKCNR
WSD LN SWAN VNRN AWLPKVLKCNR
Wtklkzn lds `kbujds pnrn rgsdlvgr lns skiukgotgs dpgrnckdogs.
DBJGPKUD Aultkplkcnr utklkzno`d suano`ds kiunlgs.
>.
CDAVGPGOCKNS Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián K`gotkekcnr lns antgaîtkcns go sktunckdogs cdtk`knons y gscdlnrgs y buscnr sktunckdogs qug sg pug`no rglnckdonr cdo k`gns antgaîtkcns cdocrgtns. Sgotk`d `g ln kokckntkvn y gspárktu gaprgo`g`dr Pgogr kokckntkvn pnrn trnosedranr lns k`gns go ncckdogs: plnokekcnr y rgnlkznr prdygctds vknblgs.
0Ù71
26
5Ù01
20
0Ù01
>5
2.
>7 W >
3.
; 0
| 0.
3 .º V R K A N R K N
=Ù21
>5
|
3=
GOSGÞNO@D-NVRGO@KGO@D
VNRN GAVGZNR - 7 akoutds Cîlculd agotnl
Vrdblgan `gl `án
Jugid `gadstrnckóo
@gbgo adstrnr lds rgsultn`ds cdo lns rug`ns ouagrn`ns. n. 3 + 5. ;. `. 9 + 9 – >6. 0. b. >> – 9. 0. g. 7 + >6 – >>. 0. c. 9 + 3 – ;. ;. >.
«Go ln tkgo`n `g ln gsqukon sdld qug`no trgs mugvgrns `g ag`kn `dcgon `g mugvds. Won mugvgrn sg cng nl sugld y `ds `g lds mugvds sg rdapgo. ´Cuîotds mugvds qug`no go ln tkgo`n4¸. >5 mugvds. Vd`gads cnlculnr prkagrd cuîotds mugvds cdotkgogo trgs mugvgrns: aultkplkcnads 5 Ù 3 d suanads lds mugvds `g uod go uod, `g `ds go `ds, `g trgs go trgs d `g sgks go sgks. Sk `g lds >= mugvds kokcknlgs sg rdapgo `ds, qug`no qug`no:: >= ‒ 2 1 >5.
Juinads n cdapdogr rgctîoiulds. Sk gs ogcgsnrkd, gapgznads cdo uon `gadstrnckóo. Rgpnrtkads uon mdjn cun`rkculn`n y lîpkcgs `g `ds cdldrgs n cn`n pnrgjn. Vdr turods, lds juin`drgs lnozno `ds cubds (6-7) y `kbujno, sdbrg uo úokcd pnpgl cun`rkculn`d cun`rkculn`d,, uo rgctîoiuld cdo ln bnsg y ln nlturn qug `gtgrakogo lds cubds. Cn`n juin`dr pkotn sus rgctîoiulds `g uo cdldr `kstkotd y sko supgrpdogrlds n okoiuod `g lds rgctîoiulds gxkstgotgs. @gotrd `g cn`n rgctîoiuld `gbgrî nodtnr gl oúagrd `g cnskllns qug cdotkgog. Gl rgtd qug sg plnotgn nl juin`dr gs cóad cdotnr gl
Vrdblgans drnlgs >. Pgrgsn, Juno y Akiugl tkgogo cuntrd cnrnaglds cn`n uod. ´Cuîotds cnrnaglds tkgogo go tdtnl4 >2 cnrnaglds. 2. ´Cuîotns ag`kns onrnojns mny go uon onrnojn y ag`kn4 3 ag`kns onrnojns. 3. Pgoid cuntrd ildbds. ´Cuîotds ag enltno pnrn tgogr >24 = ildbds.
7 > n á @ ¹ > W ¹ º . 3
oúagrd `g cnskllns: pug`g cdotnrlns `g uon go uon, cdotnr lns `g uon ekln y aultkplkcnrlns aultkplkcnrl ns pdr gl oúagrd `g eklns (nirupnckóo `g glgagotds pdr eklns) d cdotnr gl oúagrd `g lns cnskllns c nskllns `g uon cdluaon y aultkplkcnr gl rgsultn`d pdr gl
s d o a u l n s d l g ` l g v k o l g o ú i g s > ` n ` k o u n l g ` s g o d k s g s s n l n o d k c c g l g S
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
WSD LN SWAN VNRN AWLPKVLKCNR AWLPKVLKCNR
Go gl jugid `gadstrnckóo, utklkzno uod `g lds cubds (6-7) y `kbujno cun`rn`ds `g ln`d ld qug ko`kqug gl cubd.
Gscrkbg gl gouockn`d antgaîtkcd y mnlln gl rgsultn`d. Eájntg go gl gjgapld.
Rgtd Go gl jugid `gadstrnckóo, prnctkcno lns tnblns `gl 5 nl >6 usno`d lds cubds (6-7) y (7->6) y uon cun`ráculn `g anydr tnanþd.
2 Ù315 7.
5.
> W
>7
7 Ù 2 1 >6 9.
2 Ù 7 1 >6 =.
Gvnlunckóo koedranl Dbsgrvnckóo
0 Ù 3 1 >2 ;.
|
Rglnckdon ln aultkplkcnckóo cdo suans `g suano`ds kiunlgs. Augstrn kokckntkvn go gl jugid `gadstrnckóo.
3 Ù 0 1 >2
Gvnlunckóo edranl
Anrcds tkgog uon cubktgrn cdo >2 cubktds `g mkgld y cuntrd vnsds. ^ukgrg pdogr gl aksad oúagrd `g cubk tds go cn`n vnsd. ´Cuîotds cubktds pdo`rî go cn`n vnsd4
Ekcmns
3 .º ¹ W > ¹ @ á n > 7
3;
|
VNRN NCNBNR - 7 akoutds
7 6
S g l g c c k d o n l n s s g s k d o g s ` g l n u o k ` n ` > s g i ú o g l o k v g l ` g l d s n l u a o d s
Rgsuglvg cdrrgctnagotg 9 `g lds ; gjgrckckds prdpugstds go lns ekcmns.
Vug`g pdogr >, 2 d 3 cubktds go cn`n vnsd.
Jugid `gadstrnckóo
Mkstdrkn pnrn pgosnr
oúagrd `g cdluaons (nirupnckóo `g glgagotds pdr cdluaons). Vdr gjgapld, uo juin`dr lnozn lds cubds, dbtkgog uo 3 y uo 0, y `kbujn uo rgctîoiuld `g >2 cnskllns (3 Ù 0, 0 Ù 38 d lns suans qug cdrrgspdo`no 3 + 3 + 3 + 3…). Gl jugid ncnbn cuno`d uo juin`dr od tkgog gspnckd pnrn `kbujnr su rgctîoiuld. Inon gl juin`dr qug mnyn pkotn`d aîs cnskllns cnskllns `g ln cun`ráculn.
Lggads ln mkstdrkn pnrn pgosnr
Buscno`d
uo odabrg.
Ekcmn `gl nluaod Ekcmns `gl `án >7 Lds nluaods rgsuglvgo `g edran ko`kvk`unl lds gjgrckckds `g lns ekcmns. Rgvksnads lds rgsultn`ds gotrg td`ds.
Vg`kads n lds nluaods qug gxplkqugo cóad mno cnlculn`d lns îrgns `g lds rgctîoiulds: cdotno`d cnskllns, aultkplkcno`d aultkplkcno` d eklns pdr cdluaons d cdluaons pdr eklns.
CkbgrGANP - Sgskóo 3 @gscdapdskckóo `g `gcgons go uok`n`gs. K`gotkekcnckóo `g îoiulds niu`ds, rgctds y dbtusds. Suans cdo oúagrds `g `ds ckerns nirupno`d `gcgons y uok`n`gs. K`gotkekcnckóo `g lns mdrns go rgldj nonlóikcd y `kiktnl. Rgstns llgvno`d `g oúagrds `g `ds ckerns `gsnirupno`d `gcgons. Aultkplkcnckóo cdad suan `g suano`ds kiunlgs.
•
•
•
•
•
•
N K R N A K R V º . 3
GOPKGO@D LN AWLPKVLKCNCKÓO
GOPKGO@D LN AWL AWLPKVLKCNCKÓO PKVLKCNCKÓO >.
DBJGPKUD Cdaprgo`gr ln aultkplkcnckóo cdad uon suan `g suano`ds kiunlgs.
Cdldrgn `g nanrklld lns cnskllns n lns qug llgins cuno`d nvnozns `g `ds go `ds. Mnz uo cárculd vgr`g go lns cnskllns n lns qug llgins cuno`d nvnozns `g ckocd go ckocd. @kbujn uon ] rdjn go lns cnskllns n lns qug llgins cuno`d nvnozns `g >6 go >6. Go td`ds lds cnsds, ln c nsklln `g snlk`n gs gl 6.
6
>
2
3
0
7
5
9
=
;
>6 >> >2 >3 >0 >7 >5 >9 >= >;
ANPGRKNL
26 2> 22 23 20 27 25 29 2= 2;
Rgcursds nuln
36 3> 32 33 30 37 35 39 3= 3; 06 0> 02 03 00 07 05 09 0= 0;
•
Vrdygctnblgs: Pnrjgtns ouagrnlgs `g sgrkg `gl 2, 3, 7 y >6
76 7> 72 73 70 77 75 79 7= 7; 56 5> 52 53 50 57 55 59 5= 5 ; 96 9> 92 93 90 97 95 99
CDAVGPGOCKNS Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián Gstnblgcgr rglnckdogs gotrg `kegrgotgs cdocgptds, nsá cdad gotrg lds `kvgrsds skiokekcn`ds `g uo aksad cdocgptd.
9= 9;
=6 => =2 =3 =0 =7 =5 =9 == =; ;6 ;> ;2 ;3 ;0 ;7 ;5 ;9 ;= ; ;
37 W 2
2.
Cdldrgn `g nzul lns cnskllns n lns qug llgins cuno`d nvnozns `g dcmd go dcmd. Rd`gn cdo uo cárculd onrnojn gl oúagrd nl qug llgins cuno`d nvnozns `g ougvg go ougvg. @kbujn uon ] rdjn go lns cnskllns n lns qug llgins cuno`d nvnozns `g skgtg go skgtg. Go td`ds lds cnsds, ln cnsklln `g snlk`n gs gl 6.
6
Sgotk`d `g ln kokckntkvn y gspárktu gaprgo`g`dr Pgogr kokckntkvn pnrn trnosedranr lns k`gns go ncckdogs: plnokekcnr y rgnlkznr prdygctds
>
2
3
0
7
5
9
=
;
>6 >> >2 >3 >0 >7 >5 >9 >= >; 26 2> 22 23 20 27 25 29 2= 2; 36 3> 32 33 30 37 35 39 3= 3; 06 0> 02 03 00 07 05 09 0= 0;
vknblgs.
76 7> 72 73 70 77 75 79 7= 7; 56 5> 52 53 50 57 55 59 5= 5; 96 9> 92 93 90 97 95 99 9= 9; =6 => =2 =3 =0 =7 =5 =9 == =;
3 .º V R K A N R K N
;6 ;> ;2 ;3 ;0 ;7 ;5 ;9 ;= ; ;
GOSGÞNO@D-NVRGO@KGO@D
Cîlculd agotnl
Vrdblgan `gl `án
Pnrjgtns ouagrnlgs
@gbgo adstrnr gl rgsultn`d `g ln dpgrnckóo cdo lds cubds ouaërkcds. n. > – >. 6. b. 0 + 3. 9. c. = – 3. 7. `. >6 + 7. >7. g. > – 6. >.
«Nlbgrtd tkgog ougvg nþds8 Rnúl tkgog ougvg nþds aîs qug Nlbgrtd8 y Cnrdlkon, ln an`rg `g Nlbgrtd, tkgog gl `dblg `g ln g`n` `g Rnúl. ´Cuîotds nþds tkgogo Rnúl y Cnrdlkon4¸. Rnúl tkgog >= nþds y, Cnrdlkon, 35. 35. Vrkagrd `gbgads cnlculnr ln g`n` `g Rnúl. Vnrn glld, suanads ; nþds n ln g`n` `g Nlbgrtd: ; + ; 1 >=. Vnrn cnlculnr ln g`n` `g Cnrdlkon, pd`gads suanr d aultkplkcnr. Lns dpgrnckdogs sgráno: >= + >= 1 35 d >= Ù 2 1 35.
Vrdygctnads lds prkagrds oúagrds Vrdygctnads cdosgcutkvds `g lns tnrjgtns ouagrnlgs `g uon sgrkg, ln `gl 2, gl 3, gl 7 d gl >6. Vg`kads n lds nluaods qug gocugotrgo gl suano`d qug sg rgpktg skgaprg. Vd`gads prgiuotnrlgs sk snbráno `gckrods lds trgs oúagrds skiukgotgs `g ln sgrkg.
Vrdblgans drnlgs >. Ag lnvd lds `kgotgs tr trgs gs vgcgs nl `án `urnotg `ds akoutds. ´Cuîotd tkgapd kovkgrtd go lnvnrag lds `kgotgs cn`n `án4 5 akoutds. 2. Okcdlîs y Skaóo tkgogo ckocd pgldtns `g erdotóo, pgrd mno cdln`d trgs. ´Cuîotns pgldtns lgs qug`no nmdrn4
2 pgldtns.
3. Cnrlds cdckoó sgks gapnon`kllns y mn mgcmd skgtg aîs. ´Cuîotns gapnon`kllnss tkgog nmdrn4 gapnon`klln
>3 gapnon`kllns. gapnon`kllns.
|
7 3 n á
@ ¹ 2 W ¹ º . 3 |
;0
VNRN GAVGZNR - 7 akoutds
; =
Jugid `gadstrnckóo Ods `gsplnznads n uo luinr `gl cdlgikd `do`g tgoinads suekckgotg gspnckd pnrn cdrrgr. @gckads n lds nluaods qug juinrgads n mncgr pnqugtgs. Sk gs ogcgsnrkd, juinads odsdtrds tnabkëo. Gxplkcnads qug `gbgo cdrrgr pdr gl gspnckd y, cuno`d `kinads «Vnqugtgs `g TTTTT (oúagrd)¸, `gbgrîo edranr irupds cdo tnotds nluaods cdad ko`kqug gl oúagrd. Vdr gjgapld, sk go ln clnsg mny 36 nluaods, pd`gads pg`krlgs qug edrago pnqugtgs `g ckocd y, cuno`d
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
GOPKGO@D LN AWL AWLPKVLKCNCKÓO PKVLKCNCKÓO
Vug`go usnr antgrknl anokpulntkvd pnrn rgsdlvgr lds gjgrckckds `g ln sgiuo`n ekcmn.
Rgsuglvg.
3.
Rgtd Mny `ds dbjgtds go cn`n pdrtnlîpkcg s. ´Cuîotds dbjgtds mny4
2Ù71 2
+
2
+
2
+
2
+
Vnrn ln sgiuo`n ekcmn, pd`gads pg`kr n lds nluaods qug tnpgo lns kaîigogs cdo uo pnpgl y qug rgnlkcgo lns dpgrnckdogs agotnlagotg.
>6
2
0. Mny cuntrd fldrgs go cn`n ancgtn. ´Cuîotns fldrgs mny4 2 W
0Ù71 0
+
0
+
0
+
0
+
26 37
0
Gvnlunckóo koedranl
7. Cn`n pnch tkgog trgs ydiurgs. ´Cuîotds ydiurgs mny go tdtnl4
Dbsgrvnckóo
3Ù51 3 + 3 + 3 + 3 + 3
Rglnckdon ln n`kckóo `g suano`ds kiunlgs cdo ln aultkplkcnckóo. Augstrn kokckntkvn pnrn crgnr lds
>=
+ 3
| 3 .º ¹ W 2 ¹ @ á n 3 7
pnqugtgs `urnotg gl jugid `gadstrnckóo. 5. Cn`n cnjn cdotkgog sgks onrnojns. ´Cuîotns onrnojns mny go tdtnl4
Gvnlunckóo edranl 5Ù31 5
+
5
+
Ekcmns
>=
5
| ; 6
;7
Rgsuglvg cdrrgctnagotg 0 `g lds 5 gjgrckckds prdpugstds go lns ekcmns.
VNRN NCNBNR - 7 akoutds Jugid `gadstrnckóo gstëo drinokzn`ds, `gbgrîo snlkr sgks pnqugtgs cdo ckocd nluaods cn`n uod. Won vgz edran`ds lds pnqugtgs, mncgads uon pugstn go cdaúo. Vg`kads n lds nluaods qug cugotgo lds pnqugtgs qug mno snlk`d (sgks), cuîotds nluaods cdapdogo cn`n pnqugtg (ckocd) y cuîotds nluaods sdads go tdtnl (36). Vnrn gstn rdo`n `gl jugid, lgs prgiuotnads cuîotns vgcgs sg vn rgpktkgo`d gl ckocd pnrn llginr n lds 36 nluaods (sgks) y cóad ld pd`ránads gxprgsnr go edran `g aultkplkcnckóo (7 Ù 5 1 36). Vdogads dtrd gjgapld cdo lns aksans rgelgxkdogs. Nsá, pnrn uon clnsg `g 36 nluaods, pd`gads prdpdogr dtrn rdo`n cdo pnqugtgs `g `ds, trgs, sgks d `kgz.
Ekcmn `gl nluaod Ekcmns `gl `án 37 Lds nluaods rgsuglvgo lds gjgrckckds `g lns ekcmns ko`kvk`unlagotg.
Vrdpdogads uon suan `g suano`ds kiunlgs y ln gscrkbkads go ln pkznrrn. Vg`kads n lds nluaods qug, go vdz nltn, `kino cóad sg gxprgsn go edran `g aultkplkcnckóo aultkplkcnck óo y quë mno mgcmd pnrn pnsnr `g ln suan n ln gxprgskóo go edran `g aultkplkcnckó aultkplkcnckóo. o.
Go cnsn Lds nluaods gscrkbgo go sgks pnpglgs oúagrds `gl > nl ;, lds cdldcno bdcn nbnjd y prgpnrno uo puþn`d `g inrbnozds. Cdigo `ds oúagrds: gl prkagrd ko`kcn ln cnotk`n` `g nirupnckdogs `g inrbnozds qug `gbgo mncgr y, gl sgiuo`d, lds inrbnozds qug `gbg mnbgr go cn`n irupd. Ekonlagotg, ld gscrkbgo go uo pnpgl go edran `g aultkplkcnckó aultkplkcnckóo. o.
N K R N A K R V º . 3
CDODZCD GL ÎRGN DBJGPKUD Cnlculnr gl îrgn `g `kstkotns ekiurns.
J W G I D @ G C W B D S
@kbujn gl îrgn
Juin`drgs @ds
ANPGRKNL
Antgrknl
Dbjgtkvd
• @ds cubds ouaërkcds (6-7) @kbujnr iurns cuyn îrgn • Won mdjn cun`rkculn`n sgn gl prd`uctd • Bdláirned `gl rgsultn`d `g lds cubds.
Cnrtulkon Vóskts
•
•
Rgcursds `dcgotg
Odrans
Rúbrkcn `g cdgvnlunckóo
>. Wo juin`dr lnozn lds `ds cubds. Sk go nliuod snlg uo cgrd, vuglvg n lnoz lnoznr nr..
•
2. Gotrg lds `ds juin`drgs, cnlculno gl prd`uctd `g lns puotunckdogs. puotunckdogs.
CDAVGPGOCKNS Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián Wtklkznr `kegrgotgs aëtd`ds `g `gadstrnckóo `gadstrnckó o pnrn nriuagotnr lns nekranckdogss y lds prdcgsds antgaîtkcds nekranckdog rgnlkzn`ds go cdotgxtds cgrcnods.
35 0 W 2
3. Cn`n juin`dr `kbujn go ln mdjn cun`rkculn`n uon iurn cuyn îrgn sgn kiunl nl rgsultn`d `g ln aultkplkcnckóo notgrkdr notgrkdr,, tdano`d uo cun`rn`d `g ln mdjn cdad uok`n`. 0. Gl sgiuo`d juin`dr lnozn lds cubds y rgpktgo rgpktgo ln aksan `koîakcn. `koîakcn. @gbgo kotgotnr `kbujnr iurns `kstkotns go cn`n juin`n. 7. @gspuës `g trgs lnoznakgotds lnoznakgotds `g cn`n juin`dr, juin`dr, inon gl qug cdoskin aîs iurns `kstkotns.
Gjgapld:
Cdapgtgockns sdcknlgs y cávkcns Sgr cnpnz `g gvnlunr gl prdcgsd irupnl.
Lnoznakgotd:
2
Ekiurns `g cn`n juin`dr:
0
> ;
|
Aultkplkcnckóo: 5 3 n á
2Ù01=
@ ¹ 2 W ¹ º . 3
3 .º V R K A N R K N
|
;5
VNRN GAVGZNR - 7 akoutds Cîlculd agotnl agotnl
Vrdblgans drnlgs drnlgs
Vrdblgan `gl `án
Lds nluaods `gbgo rgspdo`gr drnlagotg n ln skiukgotg prgiuotn: «´Cuîl `g lds dbjgtds `g cn`n pnrgjn tkgog gl îrgn anydr4¸. n. Wo plntd `g pnpgl d uon pîikon `g pgrkó`kcd. Won pîikon `g pgrkó`kcd. b. Won adog`n `g > € d uon adog`n `g > cëotkad. Won adog`n `g > €. c. Won rgbnon`n `g pno d uon inllgtn. Won rgbnon`n `g pno. `. Wo tglgvksdr d uon cnjn `g znpntds.
>. Gldy mn cdaprn`d dcmd ildbds y, `g cnakod, sg lg mno rgvgotn`d ln aktn`. ´Cuîotds ildbds lg qug`no4 0 ildbds. 2. Ckocd nakids tkgogo trgs ani`nlgons cn`n uod. ´Cuîotns ani`nlgons tkgogo go tdtnl4 >7 an`nlgons. 3. ´Cuîotns ag`kns onrnojns mny go `ds onrnojns y ag`kn4 7 ag`kns onrnojns.
«Go ln pkznrrn, `kbujnads >2 cun`rn`ds. ´@g cuîotns anogrns `kstkotns sg pug`go cdldcnr gstds cun`rn`ds pnrn qug edrago rgctîoiulds4¸. @g sgks anogrns `kstkotns. Won ekln `g >2 cun`rn`ds, cuntrd eklns `g trgs cun`rn`ds, sgks eklns `g `ds cun`rn`ds y lns rgsultnotgs `g ikrnr lns ekiurns notgrkdrgs.
Wo tglgvksdr. g. Won agsn `gl cdlgikd d uon cnan `g antrkadokd. Won cnan `g
antrkadokd.
CDODZCD GL ÎRGN Cdosk`grno`d qug
gs uon uok`n` `g supgrckg, cnlcul cnlculn n gl îrgn `g lns iurns:
>.
2. >
0
uok`n`.
3.
uok`n`gs.
0.
2 W
=
uok`n`gs.
>2
uok`n`gs.
>6
uok`n`gs.
35
7.
| 3 .º ¹ W 2 ¹ @ á n 3 5
5.
N K R N A K R V º . 3
9.
5
uok`n`gs.
2
uok`n`gs. ;9
| ; 2
GOSGÞNO@D-NVRGO@KGO@D Nctkvk`n` anokpulntkvn cddpgrntkvn @kvk`kads ln clnsg go irupds `g cuntrd, lgs nskionads lds rdlgs cnrnctgrástkcds `gl trnbnjd cddpgrntkvd y lgs gotrginads uon cnrtulkon y lds póskts. Cn`n irupd `gbg `kbujnr uo rgctîoiuld go ln cnrtulkon. Lgs prgiuotnads cuîotds póskts ogcgsktno pnrn cubrkr td`n ln supgrekckg `gl rgctîoiuld `g ln cnrtulkon. Lugid, cdagotnads koskstkgo`d go qug `gbgo dergcgr gl rgsultn`d `no`d gl oúagrd y lns uok`n`gs. Vdr gjgapld, >5 póskts. Sk gl oúagrd `g póskts od gs gxnctd, pug`go `nr uo rgsultn`d nprdxkan`d. N cdotkounckóo, dr`gonads lds rgctîoiulds `g agodr n anydr îrgn. Gl dbjgtkvd gs qug lds nluaods vgno qug pd`gads usnr ln aksan uok`n` `g supgrekckg pnrn cnlculnr gl îrgn `g `kstkotns ekiurns y qug mncgrld pgraktg cdapnrnr lns îrgns. Won vgz tgrakon`n ln nctkvk`n`, pd`gads pnsnr gl kostruagotd pnrn ln cdgvnlunckóo.
Aurnl `g antgaîtkcns Go gl gspnckd `g antgaîtkcns `g ln clnsg pd`gads cdlinr lds `kstkotds rgctîoiulds `kbujn`ds pdr lds irupds.
Jugid `g cubds @kbujn gl îrgn
CDODZCD GL ÎRGN Sk cn`n uod `g lds cun`rn`ds tkgog uo îrgn `g > ca², cnlculn gl îrgn `g lns skiukgotgs iurns plnons.
=.
;.
0
>7
ca²
>6.
ca²
>>.
35 W 2
>5
>0
ca²
>2.
ca²
>3.
3 ;
|
5 3 n á
3 .º V R K A N R K N
26
ca²
>2
@ ¹ 2 W ¹ º . 3
ca²
|
;=
VNRN NCNBNR - 7 akoutds
Ekcmn `gl nluaod
@knrkd `g antgaîtkcns
>.ª ekcmn `gl `án 35
Vg`kads n lds nluaods qug gscrkbno go su `knrkd quë gs pnrn gllds gl îrgn `g uon ekiurn plnon.
Cdaplgtno ln ekcmn ko`kvk`unlagotg. Go lds `ds últkads gjgrckckds `gbgo gstkanr gl oúagrd `g cun`rn`ds qug edrano lns ekiurns. 2.ª ekcmn `gl `án 35
Rgsdlvgads gl prkagr gjgrckckd go ln pkznrrn, n ad`d `g gjgapld, y cdaplgtno gl rgstd `g ln ekcmn go pnrgjns. Lds nokanads n utklkznr `kstkotns gstrntgikns go gl cîlculd `g lns îrgns. 3.ª ekcmn `gl `án 35
Rgsuglvgo ln ekcmn go pgqugþds irupds. Vug`go rgpnrtkrsg lns dpgrnckdogs y cdaprdbnr lds rgsultn`ds td`ds juotds.
Go cnsn
@gbgo npdynr uo pkg sdbrg uo pnpgl cun`rkculn`d y, cdo uo lîpkz, trnznr gl cdotdrod `g ln sugln `g su znpntd. N cdotkounckóo,, tkgogo qug cdotkounckóo nvgrkiunr su îrgn nprdxkan`n (go uok`n`gs cun`rn`ns).
CDODZCD GL ÎRGN Rgsuglvg lns skiukgotgs dpgrnckdogs.
>0.
>3 7 + 270
>7.
3=;
>9.
57=9 + 2=50
=37 + 0;5
> 5.
>33>
>=.
;07>
27=0 + ;=7
2790 + >227
39;;
> ;.
375;
5= 5=99 – 375
33>
2 W
35
26.
5> 5>3 3 – 0=9
2>.
>25
23. | 3 .º ¹ W 2 ¹ @ á n 3 5
=666
9=5; – 2037
22.
7030
20.
;527
=725 – 05;=
3=2=
27.
>253
– >5> >
– ;7=;
+ =93 9
53=;
35
>6666
N K R N A K R V º . 3
@knrkd `g antgaîtkcns
@gscrkbg cdo tus pnlnbrns quë gs gl îrgn `g uon iurn plnon. ;;
| ; 0
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
Rgtd
Vd`gads rgedrznr lds cdotgok`ds cdo ln ekcmn `gl `án 35 `g AyRDDA.
Vd`gads naplknr lds cdotgok`ds cdo ln ekcmn `gl `án 35 `g AyRDDA.
Gvnlunckóo koedranl Dbsgrvnckóo
Justkekcn ln kapdrtnockn `g lns uok`n`gs `g ag`k`n go gl cîlculd `g îrgns `urnotg ln nctkvk`n` anokpulntkvn. Gvnlún nl cdapnþgrd cdo bugo crktgrkd y dbjgtkvk`n`.
Gvnlunckóo edranl Rúbrkcn `g cdgvnlunckóo
Wtklkznads gstg kostruagotd pnrn qug lds nluaods sg gvnlúgo autunagotg. @knrkd `g antgaîtkcns Ekcmns
Rgsuglvg cdrrgctnagotg >6 `g lds >3 gjgrckckds prdpugstds go lns `ds prkagrns ekcmns.
VRNCPKCD LN VRDVKG@N@ CDOAWPNPKUN @G LN AWLPKVLKCNCKÓO
VRNCPKCD LN VRDVKG@N@ CDOAWPNPKUN @G LN AWLPKVLKCNCKÓO Aultkplkcn.
DBJGPKUD Vrnctkcnr ln prdpkg`n` cdoautntkvn `g ln aultkplkcnck aultkplkcnckóo. óo.
ANPGRKNL Rgilgtns Cuksgonkrg
•
Rgcursds nuln Vrdygctnblgs: Pnrjgtns ouagrnlgs `g aultkplkcnckdogs Antkjugids: Suans ilub-ilub 3
•
•
>.
9
Ù
7
1
37
2.
7
Ù
9
1
37
3.
0
Ù
; 1
35
0.
;
Ù
0 1
35
7.
>6 Ù 5 1
56
5.
5 Ù >6 1
56
9.
3
20
=.
=
20
Ù
= 1
Ù
3 1
02 W 2
;.
= Ù;
>6.
92
= Ù9
>>.
75
7 Ù=
>2.
06
9 Ù5 02
CDAVGPGOCKNS Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián Rgprgsgotnr uo prdblgan
>3.
; Ù=
>0.
92
= Ù7
>7.
06
5 Ù9
>5.
02
9 Ù= 75
antgaîtkcnagotg y rgsdlvgrld pdr ag`kd antgaîtkcnagotg `g gstrntgikns y `gstrgzns. >9.
3 .º V R K A N R K N
Sgotk`d `g ln kokckntkvn y gspárktu gaprgo`g`dr @gsnrrdllnr mnbklk`n`gs pnrn mncgr ergotg n lds cnabkds y lns `kekcultn`gs cdo nutdgstkan,, cdostnockn y gspárktu `g nutdgstkan supgrnckóo.
5 Ù= 0=
>=.
; Ù5 70
>;.
= Ù5
26.
0=
5 Ù; 70
GOSGÞNO@D-NVRGO@KGO@D
Cîlculd agotnl
Vrdblgan `gl `án
Pnrjgtns ouagrnlgs
@gbgo rgspdo`gr drnlagotg. Vug`go usnr ln tnbln `g aultkplkcnr, sk ld ogcgsktno. n. 5 Ù =. 0=. b. 0 Ù >6. 06. c. = Ù 5. 0=. `. >6 Ù 0. 06. g. ; Ù 3. 29.
«Skgtg pgrsdons tkgogo ; € cn`n uon. Ougvg pgrsdons tkgogo 9 € cn`n uon. ´^uë irupd `g pgrsdons tkgog aîs `kogrd4¸. Pkgogo ln aksan cnotk`n` `g `kogrd. Vnrn nvgrkiunr quë cnotk`n` `g `kogrd tkgog gl prkagr irupd, pd`gads suanr td`ns lns cnotk`n`gs `g `kogrd (; + ; + ; + ; + ; + ; + ;) d aultkplkcnr ln cnotk`n` `g `kogrd pdr gl oúagrd `g pgrsdons qug mny (; Ù 9 1 53 €). Rgpgtkads ln dpgrnckóo pnrn gl sgiuo`d irupd (9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 d 9 Ù ; 1 53 €). Vdr tnotd, tkgogo ln aksan cnotk`n`. Pnabkëo pd`gads rgprgsgotnrld cdo `kogrd.
Vnsnads lns tnrjgtns ouagrnlgs `g aultkplkcnckdogs aultkplkcnck dogs qug kaplkqugo ln prdpkg`n` cdoautntkvn.
Vrdblgans drnlgs >. Cnrkon tkgog `kgz bkllgtgs `g 7 €. ´Cuîotds gurds tkgog4 76 €. 2. G`inr mn mgcmd ckocd pnogckllds y, su mgranod, ougvg. ´Cuîotds mno mgcmd gotrg lds `ds4 >0 pnogckllds. 3. Cnrlds mn nmdrrn`d ckocd bkllgt bkllgtgs gs `g >6 €. ´Cuîotds gurds mn nmdrrn`d4 76 €.
2 0 n á
@ ¹ 2 W ¹ º . 3 |
>>5
VNRN GAVGZNR - 7 akoutds
9 6 > |
Nctkvk`n` anokpulntkvn @kbujnads go ln pkznrrn uo rgctîoiuld `g cuntrd uok`n`gs pdr ougvg uok`n`gs sdbrg uon cun`ráculn, pnrn cdotnr cuîotds cun`rktds mny `gotrd. Gxplkcnads qug pd`gads cdotnrlds d aultkplkcnr ; Ù 0, pdrqug sdo cuntrd eklns `g ougvg cun`rn`ds. @gspuës, `kbujnads uo rgctîoiuld `g ougvg uok`n`gs pdr cuntrd uok`n`gs y sgiukads gl aksad rnzdonakgotd rnzdonak gotd pnrn qug cdaprugbgo qug nmdrn mny 0 Ù ; cun`rktds. Gs `gckr, gl rgsultn`d gs gl aksad. N cdotkounckóo, `kvk`kads ln clnsg go irupds `g cuntrd nluaods y lgs pg`kads qug, usno`d lns rgilgtns Cuksgonkrg cdad eklns, cdostruyno rgctîoiulds `g `kegrgotgs ag`k`ns y qug
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
VRNCPKCD LN VRDVKG@N@ CDOAWPNPKUN @G LN AWL AWLPKVLKCNCKÓO PKVLKCNCKÓO 2>.
Ontnlkn tkgog `kgz adog`ns `g 7 cts. ´Cuîotds cëotkads tkgog4
Vrdpdogads qug jugiugo n Crgn `gskiunl`n`gs, gl jugid `g cubds `gl `án 27.
76 cts.
Rgtd 22. Vg`rd tkgog ckocd adog`ns `g >6 cts.
Vrdpdogads qug jugiugo n Crgn aultkplkcnckóo. o. `gskiunl`n`gs sdld cdo ln aultkplkcnckó
76 cts.
´Cuîotds cëotkads tkgog4
´Cuîl gs gl îrgn4
3 ca
23.
20.
0 ca
0 ca 3 ca
2 W
02
>2
27.
>2
ca²
2 ca
ca²
7 ca
25.
2 ca
Gvnlunckóo koedranl 7 ca
>6
Dbsgrvnckóo Nplkcn ln prdpkg`n` cdoautntkvn
ca²
| 3 .º ¹ W 2 ¹ @ á n 0 2
pnrn cnlculnr îrgns. Augstrn sgiurk`n` go ln cdostrucckóo `g rgctîoiulds.
>6
ca²
Gvnlunckóo edranl Ekcmns Rgsuglvg cdrrgctnagotg 22 `g lds 25 gjgrckckds `g lns ekcmns.
Antkjugids
Suans ilub-ilub 3 >>9
| > 6 =
VNRN NCNBNR - 7 akoutds Nctkvk`n` anokpulntkvn
Antkjugids
cdaprugbgo cuîlgs tkgogo ln aksan îrgn. Vnrn gapgznr, cdostrukads, pdr gjgapld, uo rgctîoiuld cdo ckocd rgilgtns `g 3 y dtrd cdo trgs rgilgtns `g 7, y lugid lds drkgotnads pnrn cdaprdbnr qug gl îrgn gs ln aksan. Rgpgtkads gl prdcgsd cdo sgks rgilgtns `g 2 y `ds rgilgtns `g 58 cuntrd rgilgtns `g 3 y trgs rgilgtns `g 0. ´Gs suekckgotg rgdrkgotnrlns pnrn cdaprdbnr qug gl îrgn gs ln aksan4
Suans ilub-ilub 3 Mncgads uon `gadstrnckóo `gl jugid pnrn qug pug`no prnctkcnr lns suans.
Vrgiuotnads go quë sg `kegrgockno gl rgctîoiuld `g 5 Ù 2 y gl `g 2 Ù 5: cnabknads d «cdoautnads¸ ln pdskckóo `g lns rgilgtns y ln pdskckóo `g lds enctdrgs (aultkplkcn`dr y aultkplkcno`d aultkplkcno`d). ).
Ekcmn `gl nluaod Ekcmns `gl `án 02 Rgsuglvgo ko`kvk`unlagotg lds gjgrckckds `g lns ekcmns. Nl ncnbnr, cdaprugbno lds rgsultn`ds go pnrgjns.
CkbgrGANP - Sgskóo ; Búsqug`n `g gstrntgikns g strntgikns pnrn aultkplkcnr oúagrds `g uon ckern. Gstkanckóo `gl rgsultn`d `g aultkplkcnckdogs. Wsd `g ln prdpkg`n` cdoautntkvn `g ln aultkplkcnckó aultkplkcnckóo. o. K`gotkekcnckóo `g oúagrds dr`konlgs mnstn gl 36.º. Wsd `g ln aultkplkcnckóo go sktunckdogs cdtk`knons.
•
•
•
•
•
N K R N A K R V º . 3
CDODZCD LDS GLGAGOPDS @G LN CKRCWOEGRGOCKN [ @GL CÁRCWLD
CDODZCD LDS GLGAGOPDS @G LN CKRCWOEGRGOCKN [ @GL CÁRCWLD Jugid `gadstrnckóo
Sdogtd rg`do`d
>.
Subrnyn ln `gokckóo `g cn`n glgagotd sgiúo gl cdldr ko`kcn`d go ln lgygo`n. Ckrcuoegrgockn
DBJGPKUD
Sdy uon curvn, cgrrn`n, pgregctn8
Cdapnrnr ln ckrcuoegrgockn y gl cárculd.
tgoid uo puotd qug anrcn ak `gstkod. Vdr ël pnsn ln láogn rgctn
Cárculd
ANPGRKNL
qug uog puotds `g dpugstd cnakod. Ln aktn` `g gstn láogn cdogctn,
Vnlktd `g 3 ca
•
Cgotrd
Rgcursds nuln Antkjugids: ´Go quë ag`k`n4
cdo `kstnockn cdostnotg y auy bugo tkod, cn`n akgabrd `g gstn curvn sglgctn cdo gl puotd qug ag jn `kvkod.
•
Rgcursds `dcgotg Ktkogrnrkd `g gvnlunckóo `gl trnbnjd cddpgrntkvd
•
Sdy ln aîs bglln iurn plnon
22
@kîagtrd
rd`gn`n pdr ln yn agockdon`n curvn cgrrn`n.
W >
Ods cdodcgs, gstdy sgiurd. ´Akgotd4 Aîs `g akl cdsns tkgog gstn gikg. Rn`kd
CDAVGPGOCKNS
¡Prnoqukld! @gjn n uo ln`d gl lnagotd, qug pdr o tgrakon gstg gspgrpgotd.
Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián
2.
Gxprgsnr k`gns y prdcgsds antgaîtkcds `g anogrn cdaprgoskblg utklkzno`d gl lgoiunjg vgrbnl (drnl y gscrktd).
@kbujn lds glgagotds qug npnrgcgo go gl pdgan `gl cdldr ko`kcn`d go ln lgygo`n. 3 5
| 2 2 n á @ ¹ > W ¹ º . 3
Cdockgockn y gxprgskdogs culturnlgs 3 .º V R K A N R K N
Pgogr kokckntkvn, kanikonckóo y crgntkvk`n` pnrn gxprgsnrsg n trnvës `g có`kids nrtástkcds.
|
75
GOSGÞNO@D-NVRGO@KGO@D
VNRN GAVGZNR - 7 akoutds Cîlculd agotnl
Vrdblgan `gl `án
@gbgo rgspdo`gr cdo lns rug`ns ouagrn`ns. n. 2066 + 3666. 7066. b. =666 – 5666. 2666. c. 2266 – >>66. >>66. `. >376 + 576. 2666. 2666. 7766. g. 3666 + 2766. 7766.
«Óscnr `gbán rgckbkr 0 € `g cnabkd nl cdaprnrsg uo vk`gdjugid, pgrd cuno`d snlán `g ln tkgo`n sg `kd cugotn `g qug gl gaplgn`d lg mnbán `n`d >6 € `g cnabkd. Go rgcdapgosn pdr `gvdlvgr gl gxcgsd `g cnabkd, gl `ugþd lg `kd n Óscnr ckocd vgcgs aîs ln cnotk`n` `g cnabkd qug `gbán `gvdlvgrlg rgnlagotg. ´@g cuîotd eug ln rgcdapgosn4¸. 26 €. Gl cnabkd cdrrgctd gs `g 0 €8 ckocd vgcgs aîs `g gsn cnotk`n` gs 7 Ù 0 1 26.
Vrdblgans drnlgs >. Pgoid `ds pkzzns pnrn rgpnrtkr gotrg dcmd nakids. ´^uë pnrtg lg tdcn n cn`n uod4 Won cunrtn pnrtg. 2. Cnrlds tkgog trgs cugotns `g cdrrgd glgctróokcd. Go uon tkgog trgs agosnjgs y ckocd go cn`n uon `g lns dtrns `ds. ´Cuîotds agosnjgs tkgog go tdtnl4 >3 agosnjgs. 3. Anrtn instn 3 € go inllgtns, 7 € go vgr`urns y 5 € go bgbk`ns. ´Cuîotd `kogrd mn instn`d4 >0 €.
Jugid `gadstrnckóo cddpgrntkvd Sdogtd rg`do`d Gscrkbkads go ln pkznrrn lns pnlnbrns «ckrcuoegrgockn¸, «cárculd¸, «cgotrd¸, «`kîagtrd¸ y «rn`kd¸, cn`n uon `gl cdldr cdrrgspdo`kgotg n ln lgygo`n `g ln prkagrn ekcmn `gl Lkbrd `gl nluaod. N cdotkounckóo, `kvk`kads ln clnsg go irupds `g cuntrd. Lggads uon vgz gl pdgan go vdz nltn y lgs `gckads qug, ag`knotg ln tëcokcn `g trnbnjd cddpgrntkvd lgcturn cdapnrtk`n, ld vuglvno n lggr gllds. Go ël gstîo `gekok`ds lds cdocgptds qug mny go ln lgygo`n y `gbgo subrnynr cdo gl cdldr cdrrgspdo`kgotg lds vgrsds qug mnino rgegrgockn n cn`n uod `g lds tërakods. Won vgz mnyno tgrakon`d, gotrg td`ds mnrgads uon pugstn go cdaúo `g lds rgsultn`ds y, sk gs ogcgsnrkd, rgcdr`nrgads ln `gekokckóo `g cn`n glgagotd. Vdr últkad, pg`kads qug cn`n irupd cdostruyn uo cnlkirnan `do`g
s d o a u l n s d l g ` l g v k o l g o ú i g s > ` n ` k o u n l g ` s g o d k s g s s n l n o d k c c g l g S
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
CDODZCD LDS GLGAGOPDS @G LN CKRCWOEGRGOCKN [ @GL CÁRCWLD Dbsgrvn ln `knon y rgspdo`g n lns prgiuotns.
Mncgo uo cárculd pnsd n pnsd. Cdldcno gl pnlktd go mdrkzdotnl y uo gxtrgad sgrî gl cgotrd, qug qug`nrî ekjd. @gspuës mnrîo ikrnr gl dtrd gxtrgad nlrg`g`dr. @gbgrîo k`gotkekcnr cn`n uod `g lds glgagotds.
27 76 97
Rgtd
>66
@gbgo `kbujnr uon ckrcuoegrgockn, ckrcuoegrgockn, koscrkbkr uo rdabdk`g y trnznr lns `knidonlgs.. @gbgo gocdotrnr gl puotd `g `knidonlgs cdrtg, gl cgotrd g ko`kcnr lds dtrds glgagotds.
3. ´^uë glgagotd tkgogo go cdaúo td`ns lns ckrcuoegrgockns4 Gl cgotrd.
0. ´Cuîotd ak`g gl rn`kd `gl cárculd anydr4
> W
29 aa 22
7. ´Cuîotd ak`g gl `kîagtrd `gl cárculd agodr4 >2 aa Dbsgrvn gl `kbujd y rgspdo`g n lns prgiuotns.
5. Gl sgiagotd NB gs uo `kîagtrd. N
9.
Gvnlunckóo edranl
rn`kd.
Gvnlunckóo:: Ktkogrnrkd `g Gvnlunckóo
D
=. Lds `kîagtrds sg cdrtno go gl puotd cgotrnl (puotd D). B
C
`gl sgiagotd C@ |
G
Antkjugids
´Go quë ag`k`n4
3 .º ¹ W > ¹ @ á n 2 2
79
|
l g ` g l d s n l u a o d s
gvnlunckóo `gl trnbnjd cddpgrntkvd. Wtklkznads gstg kostruagotd pnrn qug gvnlúgo gl trnbnjd `gl irupd `urnotg gl jugid `gadstrnckóo. Ekcmn Rgsuglvg cdrrgctnagotg 7 `g lds 9 gjgrckckds `g ln sgiuo`n ekcmn.
VNRN NCNBNR - 7 akoutds
5 0
S g l g c c k d o n l n s s g s k d o g s ` g l n u o k ` n ` > s g i ú o g l o k v
Dbsgrvnckóo K`gotkekcn lds `kstkotds glgagotds `g ln ckrcuoegrgockn y `gl cárculd go gl pdgan `gl jugid `gadstrnckóo. Vlnsan lds `kstkotds glgagotds `gl cárculd y ln ckrcuoegrgockn go uo cnlkirnan. c nlkirnan.
@
Gl sgiagotd DG gs uo
;. Gl sgiagotd DC gs ln aktn`.
Gvnlunckóo koedranl
Jugid `gadstrnckóo cddpgrntkvd
Antkjugids
npnrgzcno lds glgagotds `gl cárculd y `g ln ckrcuoegrgockn. Lgs rgcdr`nads qug uo cnlkirnan gs uon cdapdskckóo `do`g ln `kspdskckóo `gl tgxtd kotgotn rgprgsgotnr gl cdotgok`d `gl aksad. Won vgz tgrakon`ds lds cnlkirnans, pd`gads pnsnr gl kostruagotd `g gvnlunckóo.
´Go quë ag`k`n4 ag`k`n4 Mncgads uon `gadstrnckóo `gl jugid, go gl qug prnctkcno ln gstkanckóo `g ag`k`ns.
Aurnl `g antgaîtkcns Nl tgrakonr gl jugid `gadstrnckóo, pd`gads cdlinr go gl gspnckd `g antgaîtkcns lds cnlkirnans `g lds nluaods.
Vg`kads n lds nluaods qug rgelgxkdogo sdbrg quë glgagotds cdapnrtgo ln ckrcuoegrgockn ckrcuoegrg ockn y gl cárculd y pdr quë.
Ekcmn `gl nluaod >.ª ekcmn `gl `án 22 Cdaplgtno ln ekcmn `urnotg gl jugid `gadstrnckóo.
2.ª ekcmn `gl `án 22 Rgsuglvgo ln ekcmn ko`kvk`unlagotg. Vug`go pdogr go cdaúo lns rgspugstns cdo gl irupd clnsg.
Go cnsn @gbgo buscnr go cnsn uo dbjgtd ckrculnr, sktunr gl cgotrd g ko`kcnr uo rn`kd y uo `kîagtrd.
N K R N A K R V º . 3
RGLNCKDOD LN AWLPKVLKCNCKÓO [ LN @KUKSKÓO
G S P R N P G I K N @ G V G O S N A K G O P D
DBJGPKUD Rglnckdonr ln aultkplkcnckóo y ln `kvkskóo.
Ekcmns d pnlktds
Aultkplkcn`dr
5
Ù
0
Aultkplkcno`d
1
@kvksdr
ù
20
20
Vrd`uctd
@kvk`go`d
5
1
0
Cdckgotg S G @ W P K L K A K S
´Go qug sg pnrgcgo4
Sdo `ds dpgrnckdogs, tkgogo lds aksads oúagrds.
ANPGRKNL •
Skaklktu`gs CDOSKIWGyGL `kegrgockns @DBLG
CDAVGPGOCKNS
Aultkplkcnckóo
Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián Nonlkznr y gvnlunr nriuagotds (gocdotrnr rnzdogs y cdocluskdogs y `gscubrkr supdskckdogs).
> 79 W > 2
Cdapgtgockn go cdauokcnckóo lkoiüástkcn Gxprgsnr drnlagotg agosnjgs, pgosnakgotds, vkvgockns, dpkokdogs y sgotkakgotds `g anogrn sgocklln.
´Go qug sg `kegrgockno4 Cdo rgspgctd n ...
• Gl skiod gs Ù. • Lns pnrtgs `g ln aultkplkcnckóo sdo gl aultkplkcno`d, gl aultkplkcn`dr y gl prd`uctd. • Ln aultkplkcnckóo aultkplkcnckóo gs uon anogrn aîs rîpk`n `g mncgr uon suan `g suano`ds kiunlgs. • Lds oúagrds oúagrds gstîo go `kegrgotgs pdskckdogs.
Pgrakodldián
Wtklkznckóo
@kvkskóo • Gl skiod gs ù. • Lns pnrtgs `g ln `kvkskóo sdo gl `kvk`go`d, gl `kvksdr y gl cdckgotg. • Ln `kvkskóo `kvkskóo skrvg pnrn rgpnrtkr go pnrtgs kiunlgs d `kstrkbukr go irupds uon cnotk`n`. • Lds oúagrds oúagrds gstîo go `kegrgotgs pdskckdogs.
• Cdo lds aksads oúagrds oúagrds sg rgprgsgotno sktunckdogs `kstkotns.
S G O D R P
• Won dpgrnckóo gs ln kovgrsn kovgrsn `g ln dtrn.
N V
• Ln `kvkskóo gs ln dpgrnckóo cdotrnrkn cdotrnrkn `g ln aultkplkcnckóo. 3 .º V R K A N R K N
S N K C O G R G E K @
• Vnrn sdluckdonr uon `kvkskóo, utklkzd utklkzd ln aultkplkcnckóo.
S G O D K S W L C O D C
VNRN GAVGZNR - 7 akoutds Vrdblgan `gl `án
Lds nluaods `gbgo adstrnr lds rgsultn`ds cdo lns rug`ns ouagrn`ns. n. 06 ù =. 7. `. 35 ù 0. ;. b. 0; ù 9. 9. g. ; ù ;. >. c. 75 ù =. 9.
«Cdpknads go ln pkznrrn ln skiukgotg kanigo:
Vrdblgans drnlgs >. Sk `gbd agzclnr 266 aL ` `gg lgcmg y 276 aL `g ontn láquk`n, ´quë cnpnck`n` `gbgrî tgogr, cdad aáokad, gl rgckpkgotg `g agzcln4 076 aL. 2. Vg`rd bnjn trgs vgcgs pdr gl tdbdiîo go uo akoutd. ´Cuîotns vgcgs pd`rî bnjnr go cuntrd akoutds4 >2 vgcgs. 3. Sdeán mncg ougvg edtdcdpkn edtdcdpkns. s. Sk cn`n uon `g gllns cugstn 3 cts, ´cuîotd `gbg cts. pninr Sdeán4 29 cts.
@g gstds oúagrds, sdld sg pug`go suanr lds qug cuaplno lns skiukgotgs cdo`kckdogs: Sg gocugotrno go uon zdon `g supgrpdskckóo `g, nl agods, `ds ekiurns. Pd`ds lds oúagrds qug sg gocugotrno go ln zdon `g supgrpdskckóo sdo rgsultn`ds `g ln tnbln `gl 2.
•
•
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9 7 n á @ ¹ 2 W ¹ º . 3 |
>52
Cîlculd agotnl
> 0 >
´^uë `ds ekiurns supgrpugstns cdotkgogo lds oúagrds qug sg pug`go suanr4 ´Cuîl gs gl rgsultn`d `g ln suan `g `kcmds oúagrds4¸. Prkîoiuld y cárculd, 3=. Mny trgs zdons `g supgrpdskckóo: trkîoiuld-cárculd,, cun`rn`d-cárculd y trkîoiuld-cárculd trkîoiuld-cárculd-cun`rn`d. trkîoiuld-cárculd-cun `rn`d. @g gstns, ln qug cdotkgog lds rgsultn`ds `g ln tnbln `g aultkplkcnr `gl 2 (>6, >2 y >5) gs ln prkagrn.
CDOSKIWG @DBLG N`kvkon glGLcubd
Juin`drgs Prgs n ckocd
Antgrknl • @ds cubds ouaërkcds (6-7) • @ds cubds ouaërkcds (7->6)
S D B W C G @ D I G W J
Dbjgtkvd N`kvkonr gl oúagrd `gl dtrd juin`dr
Odrans >. @ds nluaods sgrîo gl irupd `g lds enctdrgs y, y, lds `gaîs, gl `g lds lds prd`uctds. 2. Cn`n cdapdogotg `gl irupd `g enctdrgs gscdig uo cubd y ld lnozn. Augstrn Augstrn n lds prd`uctds gl oúagrd qug lg mn s nlk`d sko qug gl dtrd enctdr ld vgn. 3. Gl irupd `g lds prd`uctds prd`uctds aultkplkcn lds `ds oúagrds oúagrds y `kcg gl rgsultn`d nl irupd `g lds enctdrgs. 0. Lds enctdrgs `gbgo n`kvkonr quë oúagrd mn snlk`d go gl cubd `gl dtrd cdapdogotg `gl irupd n pnrtkr `gl rgsultn`d `g ln aultkplkcnckóo.
> 2 W
79 >
7. Sg turono pnrn kotgrcnabknrsg kotgrcnabknrsg lds rdlgs. rdlgs.
Enctdrgs Non
Akrgyn
Lnozn gl cubd (6-7) sko qug ld vgn Akrgyn
Lnozn gl cubd (7->6) sko qug ld vgn Non
0 | 3 .º ¹ W 2 ¹ @ á n
;
Gl irupd `g lds prd`uctds aultkplkcn lds `ds oúagrds (0 x ; 1 35) y lgs `kcg gl rgsultn`d n Non y Akrgyn. Non n`kvkon qug gl enctdr qug lg enltn gs gl ;.
N K R N A K R V º . 3
Akrgyn n`kvkon qug gl enctdr qug lg enltn gs gl 0.
7 9
|
>53
> 0 2
GOSGÞNO@D-NVRGO@KGO@D Gstrntgikn `g pgosnakgotd Skaklktu`gs y `kegrgockns Vnrtkads `g lns dpgrnckdogs gscrktns go ln pkznrrn d `gl gjgapld `gl Lkbrd `gl nluaod. Lgs prgiuotnads sk rgcugr`no lns pnrtgs `g ln aultkplkcnck aultkplkcnckóo óo (enctdrgs y prd`uctd), pgrd nmdrn `kegrgocknads lds enctdrgs gotrg aultkplkcno`d y aultkplkcn`dr, lds gscrkbkads go ln pkznrrn cdad go gl gjgapld y nodtnads tnabkëo lns pnrtgs `g ln `kvkskóo. Vg`kads n lds nluaods qug ods `kino quë skaklktu`gs vgo gotrg nabns dpgrnckdogs y lns gscrkbkads go ln pkznrrn. Lugid lgs pg`kads qug ods `kino lns `kegrgockns qug dbsgrvno, y pd`gads nyu`nrlgs cdo prgiuotns: «´Cóad sg llnano lns pnrtgs `g cn`n dpgrnckóo4¸8 «´^uë mncgads cuno`d `kvk`kads4¸.. `kvk`kads4¸.... Ekonlagotg, dbtgogads lns cdocluskdogs. Vnrn nyu`nrlgs n dbsgrvnr qug uon dpgrnckóo gs ln kovgrsn `g ln dtrn, pd`gads gscrkbkr ln `kvkskóo bnjd ln
aultkplkcnckóo, mncgr ln lgcturn `g aultkplkcnckóo, kzqukgr`n n `grgcmn (sgks pdr cuntrd kiunl n vgkotkcuntrd) y rgnlkznr ln aksan lgcturn `g `grgcmn n kzqukgr`n go ln `kvkskóo (cuntrd pdr sgks kiunl n vgkotkcuntrd).
Jugid `g cubds N`kvkon gl cubd
RGLNCKDOD LN AWL AWLPKVLKCNCKÓO PKVLKCNCKÓO [ LN @KUKSKÓO Rgsuglvg.
>.
Mny >5 dr`gon`drgs y go cn`n agsn pd`gads cdldcnr cuntrd. ´Cuîotns agsns ogcgsktnads pnrn td`ds lds dr`gon`drgs4
0 agsns
2. Pgogads cuntrd agsns y go cn`n uon pd`gads cdldcnr cuntrd dr`gon`drgs. ´Cuîotds dr`gon`drgs pd`gads cdldcnr go tdtnl4
>5 dr`gon`drgs
Vlnotgn `ds prdblgans cdo sus rgspgctkvns sdluckdogs qug cdotgoino lds skiukgotgs `ntds: dcmd pkakgotds, >5 pkakgotds y `ds cgstns. Rgspugstn nbkgrtn. N ad`d `g gjgapld:
3. 79
Kzno y Jkagon vno n rgcdigr pkakgotds nl mugrtd y, gotrg lds `ds, rgcdigo >5 pkakgotds. Sk go cn`n cgstn cnbgo dcmd pkakgotds,
W 2
´cuîotns cgstns llgonrdo4 2 cgstns
0. Gotrg Kzno y Jkagon mno llgon`d `ds cgstns cdo >5 pkakgotds. Sk lds mno rgpnrtk`d pdr kiunl gotrg nabns cgstns, ´cuîotds pkakgotds mno cdldcn`d go cn`n uon4 = pkakgotds 3 0 >
7. Sg mn prgpnrn`d uon clnsg pnrn 70 gstu`knotgs. Sg mno pugstd sgks lns `g agsns.
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´Cuîotns agsns mny go cn`n ln4
; agsns
5. 3 .º V R K A N R K N
9 7 n á
@ ¹ 2 W ¹ º . 3
Lds cnanrgrds `g uo rgstnurnotg cdapnrtgo sus prdpkons gquktntkvnagotg. Nodcmg rgcdikgrdo =6 €. ´ Cuîotd inoó cn`n cnanrgrd4
Od mny suekckgotgs `ntds, ogcgsktnads snbgr cuîotds cnanrgrds sdo.
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>50
VNRN NCNBNR - 7 akoutds
Ekcmn `gl nluaod
@knrkd `g antgaîtkcns
>.ª ekcmn `gl `án 79
Vg`kads n lds nluaods qug kovgotgo uon aultkplkcnckóo y sgþnlgo cn`n uod `g sus tërakods. Nl ln`d, `gbgo rgnlkznr ln kovgrsn `g ln aultkplkcnckóo gscrkbkgo`d ln `kvkskóo. @g ougvd, sgþnlno cn`n tërakod `g ln `kvkskóo.
Lds nluaods rgsuglvgo ln ekcmn `urnotg ln gstrntgikn `g pgosnakgotd pgosnakgotd.. 2.ª ekcmn `gl `án 79
Lds nluaods rgsuglvgo ko`kvk`unlagotg lds gjgrckckds `g ln ekcmn. Cdaprugbno lds rgsultn`ds go irupd. 3.ª ekcmn `gl `án 79
Lds nluaods rgsuglvgo lds gjgrckckds `g ln ekcmn go irupds `g trgs (cn`n irupd rgsuglvg uon cdluaon). Cdaprugbno lds rgsultn`ds cdo ln cnlculn`drn.
Go cnsn
Sgpnrno >= inrbnozds. @gbgo rgpnrtkrlds `g anogrn gquktntkvn go `ds irupds, lugid go trgs irupds y, ekonlagotg, go sgks. Vnrn tgrakonr, `gbgo gxprgsnr gl rgsultn`d dbtgok`d cdo lds inrbnozds go edran `g `kvkskóo y `g aultkplkcnckóo. aultkplkcnckóo.
RGLNCKDOD LN AWL AWLPKVLKCNCKÓO PKVLKCNCKÓO [ LN @KUKSKÓO Rgsuglvg lns dpgrnckdogs. Eájntg go lds skiods.
;
=. 5 Ù 2 1
>2
;. 7 Ù 2 1
>6
>6. 35 ù ; 1 0
>>. = Ù 9 1
75
>2. = Ù 2 1
>5
>3. >7 ù 7 1
3
>0. ; Ù 2 1
>=
>7. ; Ù 3 1
29
>5. 32 ù 0 1
=
>9. 0= ù 5 1 =
>=. 5 ù 2 1
3
0;
26.>6 ù 2 1
7
2>. ; Ù 0 1
35
22. 36 ù 5 1
7
23. 3 Ù 0 1
>2
20. >2 ù 3 1
0
27. >5 ù 0 1
0
25. 7 Ù 0 1
26
29. 26 ù 7 1 0
2=. 3 Ù 7 1
>7
2;. 9 Ù 2 1
>0
36.75 ù = 1
3>. 5 Ù 7 1
36
32. ; Ù 5 1
70
33. >6 Ù 2 1 26
30. >6 ù 7 1
2
37. >2 ù 2 1
5
35. = ù 2 1
9.
>= ù 2 1
>;. 9 Ù 9 1
2 W
79
| 3 .º ¹ W 2 ¹ @ á n
9
0
N K R N A K R V º . 3
@knrkd `g antgaîtkcns
Kovgotn uon aultkplkcnckóo y sgþnln cn`n uon `g sus pnrtgs. Nl ln`d, rgnlkzn ln kovgrsn `g ln aultkplkcnckóo gscrkbkgo`d ln `kvkskóo. @g ougvd, sgþnln cn`n pnrtg.
7 9
|
>57
> 0 0
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
Rgtd
Go gl jugid `g cubds, pug`go utklkznr antgrknl anokpulntkvd pnrn n`kvkonr gl oúagrd.
@urnotg gl jugid `g cubds, pd`gads pg`kr n lds nluaods qug jugiugo n uon vgrskóo aîs cdaplkcn`n. Edrano irupds `g trgs. @ds nluaods `gl irupd lnozno cn`n uod uo cubd ouaërkcd y `kcgo gl prd`uctd `g aultkplkcnr lds `ds oúagrds nl tgrcgr cdapdogotg. Gstg `gbg n`kvkonr lds `ds pdskblgs oúagrds qug mno snlk`d. Vug`g pg`kr uon pkstn pnrn qug sus cdapnþgrds lg `kino uod `g lds oúagrds `g lds cubds ouaërkcds.
Gvnlunckóo koedranl Dbsgrvnckóo
Nonlkzn ln rglnckóo gotrg ln aultkplkcnckóo aultkplkcnck óo y ln `kvkskóo. Gxplkcn drnlagotg sus k`gns `urnotg ln gstrntgikn `g pgosnakgotd.
Gvnlunckóo edranl @knrkd `g antgaîtkcns Ekcmns
Vd`gads pnsnr ln sgiuo`n ekcmn cdad prugbn `g gvnlunckóo y gscrkbkr gl rgsultn`d go ln mdjn `g sgiukakgotd `gl nluaod. Rgsuglvg cdrrgctnagotg 36 `g lds 35 gjgrckckds prdpugstds go lns ekcmns.
JWGID CDO GL PKGAVD
JWGID CDO GL PKGAVD N Cnrdlkon lg gocnotn ln aúskcn. Lds anrtgs c notn go uon cdrnl, lds vkgrogs vn n clnsgs `g iuktnrrn y cn`n >0 `áns (cdotno`d n pnrtkr `gl `án > `gl ags), sg gocugotrn cdo su irupd `g aúskcn.
DBJGPKUD Rgsdlvgr prdblgans `g ag`k`ns `g tkgapd.
>.
Rd`gn sdbrg gl cnlgo`nrkd y cdo lds cdl drgs ko`kcn`ds, lds `áns qug Cnrdlkon vn n cdrnl, lds `áns qug tkgog clnsg `g iuktnrrn y lds `áns qug s g gocugotrn cdo su irupd `g aúskcn.
ANPGRKNL Cdrnl
Bldqugs lóikcds: trkîoiulds vgr`gs,
•
Iuktnrrn
nanrkllds y nzulgs Cnlgo`nrkd Rdtuln`dr bdrrnblg
•
Irupd `g aúskcn
•
Rgcursds nuln Vrdygctnblgs: Gl trkvknl `gl tkgapd8 tkgapd 8 Gl trkvknl `gl tkgapd (sdluckóo) (sdluckóo)
•
52 W 2
CDAVGPGOCKNS Cdapgtgockn antgaîtkcn y cdapgtgockns bîskcns go ckgockn y tgcodldián K`gotkekcnr lns antgaîtkcns go sktunckdogs cdtk`knons y gscdlnrgs y buscnr sktunckdogs qug sg pug`no rglnckdonr cdo k`gns antgaîtk antgaîtkcns cns cdocrgtns.
2.
´^uë `áns `gl ags `g nbrkl qug`nrî cdo su irupd4
Lds `áns >0 y 2=
3.
Gstg ags, ´tkgog aîs `áns `g cdrnl d `g iuktnrrn4
@g iuktnrrn
0.
´Cuîotds `áns `g`kcnrî gstg ags Cnrdlkon n ln aúskcn4
>> `áns
7.
´Cuîotds `áns `g `kegrgockn mny, gstg ags, gotrg lds qug vn n ln cdrnl y lds qug tkgog clnsg `g iuktnrrn4
2 `áns
5.
Ln clnsg `g iuktnrrn gapkgzn n lns >=:36 m y `urn 07 ako. ´N quë mdrn tgrakon ln clnsg4
Nprgo`gr n nprgo`gr 3 .º V R K A N R K N
Sgr cdosckgotg `g lds prdpkds cdodckakgotds y lns prdpkns cnrgockns. >=2
GOSGÞNO@D-NVRGO@KGO@D
VNRN GAVGZNR - 7 akoutds Cîlculd agotnl
Vrdblgan `gl `án
Jugid `gadstrnckóo
Lds nluaods `gbgo adstrnr lds rgsultn`ds cdo lns rug`ns ouagrn`ns. n. 7 Ù 7. 27. `. 0 Ù 0. >5. b. ; Ù ;. =>. g. 3 Ù 3. ;. c. 6 Ù 6. 6.
«Wo rgerîo pdpulnr `kcg “Prgk “ Prgkotn otn `áns tkgog odvkgabrg, cdo nbrkl, juokd y sgptkgabrg, `g vgkotkdcmd sdld mny uod y lds `gaîs `g trgkotn y uod‑. ´@óo`g mny aîs `áns, go lds prkagrds sgks agsgs d go lds últkads sgks agsgs `gl nþd4¸. Go lds sgks últkads agsgs. Lds sgks prkagrds agsgs sdo gogrd, egbrgrd, anrzd, nbrkl, anyd y juokd. Sk akrnads lds `áns `g cn`n ags y lds suanads, dbtgogads gl tdtnl `g `áns (3> + 2= + 3> + 36 + 3> + 36 1 >=>). Lds nluaods pug`go mncgr ln suan cdo ln nyu`n `g ln rug`n ouagrn`n. Sk mncgads ld aksad cdo julkd, nidstd, sgptkgabrg, dctubrg, odvkgabrg y `kckgabrg,
Notgs `g cdagoznr ln sgskóo, prdygctnads uo cnlgo`nrkd cdo td`ds lds agsgs `gl nþd go ln aksan mdjn y `kbujnads go ln pkznrrn `ds rgldjgs nonlóikcds sko anogckllns. Edranads irupds `g cuntrd. Vrdpdrckdonads n cn`n irupd rdtuln`drgs `g pkznrrn blnocn, cuntrd ekcmns `g cn`n cdldr y `ds trkîoiulds `g cn`n cdldr. N`gaîs, cn`n nluaod cdig gl rgldj `g su gstucmg. Unads n juinr n uo cdocursd `g prgiuotns. Vrdygctnads lns prgiuotns `gl rgcursd Gl trkvknl `gl tkgapd, tkgapd, qug sdo `g trgs tkpds: Mkstdrkn (nzulgs), Ckgockns onturnlgs (vgr`gs) y Uk`n cdtk`knon
snbrgads gl tdtnl `g `áns (3> + 3> + 36 + 3> + 36 + 3> 1 >=0).
(nanrkllns). Lds cdocursnotgs `gbgo (nanrkllns). cdotgstnrlns utklkzno`d utklkzno`d gl gspnckd go blnocd qug tkgogo `gbnjd `g su rgldj d ko`kcno`d ln rgspugstn cdo lns anogckllns. Cuno`d tgoino ln rgspugstn prgpnrn`n, `gbgo cdldcnr rîpk`nagotg lns anods go
Vrdblgans drnlgs drnlgs >. Pgoid dcmd nþds y ak mgranon anydr tkgog trgs aîs qug yd. ´Cuîotds nþds tkgog ak mgranon4 >> nþds. 2. Mdy gs `án 2. ´^uë `án sgrî `gotrd `g >7 `áns4 @án >9. 3. Gstg ags, trgs nakids cuaplgo nþds, y gl ags qug vkgog, `ds aîs. ´Cuîotds nakids cuaplgo nþds gstds `ds agsgs4 7 nakids.
NPGOCKÓO N LN @KUGRSK@N@ Dxáigod
JWGID CDO GL PKGAVD
@urnotg gl jugid `gadstrnckóo, pg`kads n lds nluaods qug sg kovgotgo uon gqukvnlgockn `g mdrns y akoutds.
Anrtn y Rubëo qukgrgo kr n pnsnr uo o `g sganon n Sgvklln. Ukvgo go An`rk` y pug`go `gsplnznrsg go `kegrgotgs ag`kds `g trnospdrtg.
9.
Rgtd
Cdaplgtn lds gspnckds go blnocd.
NUG
@urnotg gl jugid `gadstrnckóo, pg`kads n lds nluaods qug sg kovgotgo uon gqukvnlgockn `g nþds y `áns.
Nvkóo
Snlk`n
Llgin`n
Prnygctd
Snlk`n
Llgin`n
Prnygctd
>0:66 m
>5:37 m
2 m 37 ako
>0:66 m
>7:67 m
> m 7 ako
>5:66 m
>=:36 m
2 m 36 ako
>5:36 m
>9:37 m
> m 7 ako
26:37 m
23:>7 m
2 m 06 ako
>9:66 m
>=:67 m
> m 7 ako
Nutdbús Snlk`n
Llgin`n
Prnygctd
>7:66 m
2>:27 m
5 m 27 ako
>5 >5:6 :66 6m
23 :6 :6 6 m
9m
2 W
52
=.
@g td`ds lds trnospdrtgs qug pug`go cdigr, ´cuîl gs gl aîs lgotd4
;.
Sk cdigo gl nutdbús y qukgrgo llginr notgs `g lns >6 `g ln odcmg, ´n quë mdrn `gbgo cdigrld4
Gl nutdbús
>6. ´Cuîotds akoutds `urn gl trnygctd go nvkóo4
N lns >7 m
Gvnlunckóo koedranl
57 ako
Dbsgrvnckóo
>>.
Sk qukgrgo snlkr notgs `g lns >7 m y llginr notgs `g lns >5 m, ´quë trnospdrtg `gbgo cdigr4
Gl nvkóo
>2.
´Cuîotds akoutds `urn gl prkagr trnygctd go NUG4
>77 ako
Cdotgstn n lns prgiuotns `gl trkvknl `urnotg gl jugid `gadstrnckóo.
| 3 .º ¹ W 2 ¹ @ á n
>3.
Unldrn lns gstrntgikns utklkzn`ns go gl Vnrn ncnbnr . ´Cuîlgs sdo lns mdrns `g snlk`n y `g llgin`n `gl sgiuo`d nutdbús4
Gvnlunckóo edranl Ekcmns
5 2
>=3
|
Rgsuglvg cdrrgctnagotg >6 `g lds >3 gjgrckckds prdpugstds go lns ekcmns.
> 7 =
VNRN NCNBNR - 7 akoutds Jugid `gadstrnckóo gl cgotrd (uons gockan `g lns dtrns). Gl nluaod qug cdldqug prkagrd ln anod y qug cdotgstg cdrrgctnagotg n ln prgiuotn pug`g cdigr ekcmn, nzul sk mn ncgrtn`d uon prgiuotn `g Mkstdrkn, vgr`g sk gs pnrn uon prgiuotn `g Onturnlgzn d nanrklln sk gs `g Uk`n cdtk`knon. Cuno`d sg tgoino `ds ekcmns `g uo aksad cdldr sg cnabkno pdr uo trkîoiuld (nzul, vgr`g d nanrklld). Inon ln pnrtk`n gl nluaod qug tgoin aîs trkîoiulds.
Ekcmn `gl nluaod Ekcmns `gl `án 52 Lds nluaods rgsuglvgo ko`kvk`unlagotg lds gjgrckckds `g lns ekcmns. Lugid, lns cdrrkigo go pnrgjns.
Vg`kads n lds nluaods qug gxplkqugo quë gstrntgikn mno sgiuk`d pnrn rgspdo`gr n lns prgiuotns `gl trkvknl.
Go cnsn Lds nluaods npuotno go uon mdjn ln egcmn nctunl y trgs cuaplgnþds. @gbgo cnlculnr gl tkgapd qug enltn d gl tkgapd qug mn pnsn`d `gs`g ln egcmn nctunl mnstn ln `g lds cuaplgnþds.
N K R N A K R V º . 3
Antgaîtkcns rgnlgs y anokpulntkvns N`gaîs, tgo`rîs td`d gl antgrknl ogcgsnrkd pnrn qug tus nluaods nprgo`no anokpulno`d: jugids `g agsn, tnrjgtns, rgctns ouaërkcns, uo gstucmg pnrn cn`n nluaod cdo cmns, cubds, tnblns `g aultkplkcnr...
¡pnrn nprgo`gr mnckgo`d y `kserutno`d!
@gscubrg aîs go www.tghanog`ucntkdo.cda
Ncdapnþnakgotd pgrsdonlkzn`d Gosgþnr cdo lds prdirnans tghano gs uon nutëotkcn npugstn pdr ln koodvnckóo g`ucntkvn y pdr gl cdaprdaksd cdo tus nluaods. Wo `gsneád gadckdonotg g kospkrn`dr qug nbdr`nads juotd n tk, cdo kluskóo y rkidr. Vnrn glld, pdogads n tu `kspdskckóo rgcursds, edranckdogs y uo plno `g ncdapnþnakgotd pgrsdonlkzn`d `urnotg td`d gl cursd. Gocdotrnrîs td`ds gstds rgcursds y sgrvkckds skgaprg go
ayrdda, tu plntnedran dolkog `dcgotg.
thlgnrokoi
Ygbkonrs
Vlntnedran edrantkvn cdo td`d ld ogcgsnrkd pnrn gspgcknlkznrtg go ougstrds prdirnans.
Cdovgrsnckdogs y tnllgrgs Cdovgrsnckdogs cdo rgegrgotgs y gxpgrtds go g`ucnckóo.
Ncdapnþnakgotd go gl nuln
Rguokdogs pg`nióikcns
Pg ncdapnþnads
Rgsuglvg tus `u`ns
`gs`g ln plnokcnckóo `g ln sgskóo mnstn ln rgnlkznckóo go gl nuln.
cdo uo pg`nidid skgaprg n tu `kspdskckóo `kspdskckóo..
Lnbs
Cgotrd `g nyu`n
Gocugotrds edrantkvds y gxpgrkgocknlgs cdo dtrds `dcgotgs cdad tú.
Won bnsg `g cdodckakgot cdodckakgotd d pnrn rgsdlvgr tus cdosultns `g anogrn koag`kntn.
Gxpgrkagotnr, nonlkznr, gvnlunr, crgnr. Bnjd gstns prgaksns y `gs`g lns kotglkigockns aúltkplgs, GANP prdpdog n lds nluaods uo nprgo`kznjg kotgirnl `g lns antgaîtkcns. Cdosckgotg `g ln ogcgsk`n` `g snbgr trnbnjnr `g edran cddpgrntkvn y ln kapdrtnockn `gl jugid go gl nprgo`kznjg, GANP drinokzn sus cdotgok`ds pnrn qug lds nluaods pug`no goergotnrsg y n`nptnrsg n `kstkotds cdotgxtds `g ln vk`n `knrkn. Cdo GANP lns antgaîtkcns sg nprgo`go y sg `kserutno.
> ; > 6 6 6 A H P
7 > > 6 6 > 6 > 6 0 = > 2 K ] ]
7 > 6 6 6 7 6 > 6 0 = > 2
llnnss o ou annttggss uggvvnnss a
3.º Vrkanrkn / uok`n`gs >-2
Lkbrd `g augstrn
GANP gs aîs qug uo lkbrd Go GANP sg nprgo`g n trnvës `g uon irno `kvgrsk`n` `g gxpgrkgockns anokpulntkvns, lú`kcns y cdotgxtunlkzn`ns qug nsgiurno gl `gsnrrdlld `g ln cdapgtgo cdapgtgockn ckn antgaîtkcn. Ln sgskóo go gl nuln sg gstructurn go trgs adagotds clnvg. Lns cmns `g gstg lkbrd sdo sdld uon pnrtg `gl prdcgsd `g nprgo`kznjg `g GANP. GANP.
Vnrn gapgznr 7 akoutds Edagotnads ln niklk`n` agotnl, ln gscucmn nctkvn y gl rnzdonakgotd lóikcd. Gs gl adagotd pnrn gl cîlculd agotnl, lds prdblgans drnlgs y lds prdblgans `gl `án.
VRDBLGAN @GL @ÁN
VRDBLGANS DRNLGS
CÎLCWLD AGOPNL
C D O D C G L N S O W G U N S A N P G S
n n r
V
@KNRKD ANPGAÎPKCD
7 a k o
zn r r
g a pg
ANPKJWGIDS
.
.
o k a 7
RGELG]KDOGS DRNLGS
VBL
r n b n
c
n n
r
n V
MKSPDRKNS VNRN VGOSNR CKBGRGANP
d `
o k g
EKCMNS
`
JWGIDS @G CWBDS
G osg þ n o ` d
p n
-
NCPKUK@N@GS ANOKVWLNPKUNS
Vnrn ncnbnr 7 akoutds Rgflgxkdonads sdbrg ld nprgo`k`d y llgvnads n cnbd `koîakcns qug pgraktgo n lds nluaods nnoznr lds nprgo`kznjgs.
o r g
JWGIDS @GADSPRNCKÓO GSPRNPGIKNS [ RWPKONS @G VGOSNAKGOPD
Gosgþno`d-nprgo`kgo`d Go ln pnrtg cgotrnl `g cn`n sgskóo nprgo`gads lds cdotgok`ds antgaîtkcds cdabkono`d nliuons `g gstns nctkvk`n`gs gxpgrkgocknlgs y anokpulntkvns.
2
Won irno `kvgrsk`n` `g gxpgrkgockns GANP dergcg nctkvk`n`gs pnrn nprgo`gr lds cdotgok`ds `gs`g td`ns lns kotglkigockns, pnrn qug td`ds lds nluaods cdogctgo cdo lns antgaîtkcns.
Lóikcd-antgaîtkcn
Lkoiüástkcd-vgrbnl
Cdrpdrnl-ckogstëskcn
Onturnlkstn
Kotrnpgrsdonl
Uksunl-gspncknl
Auskcnl
Kotgrpgrsdonl
Nctkvk`n`gs pnrn `gsnrrdllnr ln cdapgtgockn Ln Pnxdodaán Pnxdodaán `g Bldda clnskcn clnskc n lds okvglgs `g pgosnakgotd qug sg pdogo go prîctkcn go lds prdcgsds `g nprgo`kznjg. Wo nluaod cdapgtgotg gs nqugl cnpnz `g utklkznr lds okvglgs `g ` g pgosnakgotd supgrkdr. supgrkdr. Vdr glld, go GANP sg sgcugockno nctkvk`n`gs `g nprgo`kznjg `g`uctkvd qug pgraktgo nplkcnr, nonlkznr, gvnlunr y crgnr, pnrn nprgo`gr n trnosegrkr Lds nprgo`kznjgs n sktunckdogs `gl `án n `án.
Go GANP sg edagotno lds okvglgs `g pgosnakgotd `g dr`go supgrkdr. L K Z
R
¹
O N
NR
¹
G U N
L W N
N
R
N
C
C
¹
R
K L
G
V
N
R
N
R G @
R G
C D
R @ N N R
¹
G O
C D A V R
S G P N A S N U G W O S N L G C D O D C
3
WSD LN L N SWAN VNRN AWLPKVLKCNR AWLPKVLKCNR
Wtklkzn lds `kbujds pnrn rgsdlvgr lns skiukgotgs dpgrnckdogs.
>.
0Ù71
2.
>7 5Ù01 W >
3.
0Ù01
0.
=Ù21
3=
M K S P D R K N S
>7 V N R N V G O S N R
Buscno`d uo odabrg Npdstn`d go ln pugrtn `g ln cnsktn `gl jnr`áo y cdo gl flnsm pnrnlkzn`dr go ln anod, cdad sk eugrn uon pkstdln y gstuvkgrn rd`no`d uon pgláculn `g ncckóo, gl nbugld Antáns susurró: ‐Inln, n ln `g trgs, nctkvn gl komkbk`dr glëctrkcd pnrn qug sg npniug ln luz, yd gotrnrë y pkllnrë nl kotrusd `gsprgvgok`d: uod... `ds... ¡trgs! Gl nbugld snltó `gotrd `g ln cnsktn `no`d `no` d uo gapujóo n ln pugrtn, justd cuno`d sg eug ln luz. Cdo uon puotgrán nsdabrdsn, ncgrtó n `kspnrnr cdo gl flnsm pnrnlkzn`dr n uon iurn qug sg adván y… ¡ELNSM! Mubd uo `gstglld y gl kotrusd qug`ó `g pkg, tkgsd cdad uon gstntun. Inln `gsnctkvó gl komkbk`dr y nl vdlvgr ln luz, Antáns sg mnbán qug`n`d `g pkg`rn cdo ln bdcn nbkgrtn y lds djds cdad plntds. ‐´Gs ln `dctdrn Eldp4 ‐prgiuotó Iukllg `gs`g gl qukckd `g ln pugrtn, `do`g td`ds sg npkþnbno pdr gotrnr. ‐Od... ‐rgspdo`kó Antáns‐. Aîs bkgo pnrgcg... pnrgcg... ‐¡Ak nbugld! ‐irktó Lgado `g rgpgotg.
>7 R N S O G V N R N V S N K R D P S K M
06
06
Pd`ds akrnrdo n Lgado y `gspuës nl nlkgoáigon qug tgoáno goergotg. Od cnbán `u`n: grno enaklkn. ‐¡Mny qug `gsmncgr gl gegctd pnrnlkzn`dr! ‐gxclnaó Antáns‐. Ogcgsktnads mkgld. Rîpk`d, k` nl cdoigln`dr y trng`, pdr ld agods, dcmd cubktds. Inln y Iukllg cdrrkgrdo n buscnrlds. Lds cubktds vgoáno gapnqugtn`ds `g `ds go `ds. Cdikgrdo ckocd pnqugtgs y snlkgrdo pktno`d.
´Mno cdik`d ln cnotk`n` cdrrgctn `g pnqugtgs4 ‐´Mnbëks trná`d cuntrd pnqugtgs cdad aáokad4 ‐prgiuotó gl nbugld. ‐Sá ‐`kjd Inln‐, mgads cdik`d ckocd, td`ds lds qug mnbán. ‐Vgregctd ‐sg nlgiró gl nbugld‐, nsá krî aîs rîpk`d. Gl nbugld nadotdoó lds `kgz cubktds go ln cnbgzn `gl nlkgoáigon rgcnlgotn`d. Ld qug od nirn`ó `ganskn`d n Lgado, qug rgdrinokzó lds cubktds edrano`d uon pkrîak`g cdo cuntrd, trgs, `ds y uo cubktd go cn`n pksd. M K S P D R K N S
>7
‐´N qug qug`n aîs bdoktd4 ‐cdagotó. ‐Nl o tg gocugotrd, Z30/Nb… ‐cdoskiukó `gckr gl nbugld `g Lgado trns uods sgiuo`ds‐. ´N tk ttnabkëo nabkëo tg mno pnrn pnrnlkzn`d4 lkzn`d4 ‐Vgr`don ‐sg `ksculpó gl nbugld Antáns‐ ‐Vgr`don Antáns‐.. Mn sk`d uon lnagotnblg cdoeuskóo. Skëotntg, pdr envdr, prdotd gstnrîs bkgo. Prng`lg uo vnsd `g niun. ‐Agjdr uons inllgtns ‐rgplkcó gl nlkgoáigon‐, qug sg gstnbn `gspgjno`d rîpk`nagotg.
V N R N V G O S N R
‐[d tnabkëo qukgrd ‐`kjd Lgado. Iukllg snlkó n td`n vgldck`n`. ‐¡Inllgtns pnrn td`ds! ‐`kjd nl rgirgsnr n ln cnsktn. ‐¡Vgrd sk sdld mns trná`d uon! ‐gxclnaó Lgado.
´Vdr quë crggs qug sg pug`g cdoeuo`kr Lgado4 ‐Oddd. Mg trná`d uo pnqugtg. Mny uon `dcgon. ‐¡^uë bkgo! Vd`rga Vd`rgads ds rgpgtkr ‐`kjd gl nbugld Antáns Antáns,, qug grn auy idldsd.
´Cuîotns inllgtns lg tdcno n cn`n uod4 ‐Bugod, pugs cdo gl pnr `g inllgtns qug ods tdcn n cn`n uod, od së sk sg ag quktnrî gl mnabrg qug tgoid ‐`kjd Iukllg‐. ´Vdr quë od vns n pdr ag`kn `dcgon aîs4 ‐[ uo zuaktd `g onrnojn ‐`kjd gl nbugld `g Lgado qug… sg mnbán gspnbkln`d `gl td`d. ‐Sá, sá ‐`kjd Iukllg‐8 uo zuad pnrn td`ds. ‐¡Unnnnlg! ‐`kjd Lgado, rgskion`d‐ pgrd od ds cdaîks aks inllgtns, ´gm4
´Cuîotns inllgtns trngrî Lgado4, ´y zuads4
R N S O G V N R N V
>7 S N K R D P S K M
0>
0>
Lgado vdlvkó n td`n vgldck`n` cdo sgks inllgtn inllgtnss y uo vnsd `g zuad. ‐Vgrd, ´sdld mns trná`d uo zuad4 ‐sg qugjó Iukllg nl vgr n Lgado.
´Vdr quë crggs qug sdld mn trná`d uo zuad4 ‐Vugs clnrd, Iukllg ‐rgspdo`kó Lgado, cdoeuo`k`d‐. Gs ld qug ag mns pg`k`d: «uo zuad pnrn td`ds¸. ‐Gs pgrd crgd Iukllg‐nclnró pg`án uoln zuadvgr`n`, pnrn cn`n uod `gqug o dsdtrds odsdtrds nbugln Non‐. Od tg prgdcupgs, Lgado, yd krë n buscnr zuad pnrn td`ds. ‐Ag sdrprgo`gs, Z30/Nb... ‐`kjd gl nbugld `g Lgado‐. Wo sdld vknjg y yn mns mgcmd cuntrd nakids. ´Snbgs cuîotds nakids mg mgcmd yd go ln cnotk`n` `g vknjgs qug llgvd n lns gspnl`ns…4 Cgrd. M K S P D R K N S
>7 V N R N V G O S N R
N gstg rktad, ´cunotds nakids tgo`rî gl nbugld go gl `dblg `g vknjgs4 ´[ Lgado nl cnbd `g `ds4
‐Od së pdr quë ag ld kanikonbn ‐lg rgspdo`kó Lgado‐. Mncgr nakids od `gpgo`g `g lds vknjgs qug uod mnin, sk od `g ld iruþóo qug uod sgn, y tú… ‐Sá, pdskblgagotg tgoins rnzóo, pgrd ¡pdr td`ds lds niujgrds `g iusnod mkpgrgspncknlgs!, mkpgrgspnckn lgs!, yn sdy `ganskn` `ganskn`d d vkgjd pnrn cnabknr cnabknr.. Go o, vnads nl irnod: mg vgok`d pnrn llgvnrtg n cnsn, nsá qug rgcdig tus cdsns qug ods vnads. ‐¡Nmdrn4... gs qug gstdy nprgo`kgo`d uo adotóo `g cdsns. ´Od pug`d qug`nrag uo pdcd aîs4 ‐Bugod, ag pnrgcg qug, `g adagotd, od vnks n rgirgsnr n cnsn okoiuod `g lds `ds ‐dbsgrvó Inln. ‐¡^ug od vnads n rgirgsnr n cnsn! ‐gxclnaó gl vkgjd nlkgoáigon gapgzno`d n cdigr uo cdldrcklld onrnojn «qukëo-dsn-llgvnrag-ln-cdotrnrkn «qukëo-dsn-llgvnrag-ln-cdotrnrkn¸‐. ¸‐. ´[ sg pug`g snbgr qukëo vn n kapg`árodsld4
´Vdr quë crggs qug tkgogo qug qug`nrsg4 ‐Bugod, ln prgiuotn od gs qukëo sk od quë ‐`kjd Antáns kotgotn kotgotno`d o`d trnoquklkznr nl rgeuoeuþóo nbugld `g Lgado‐. Ln onvg `g Lgado gstî rdtn y ln tuyn sg ncnbn `g mncgr nþkcds go gl ntgrrkznjg. Od tgoëks trnospdrtg. ‐¡Rgcdotrnrrnyds cósakcds, ak onvg! ‐gxclnaó gl nbugld `g Lgado‐ ¡Ld ‐¡Rgcdotrnrrnyds mnbán dlvk`n`d! ‐Vgr`don,, nbugld `g Lgado ‐kotgrvkod Inln‐, ´cóad tg llnans4 ‐Vgr`don ‐Wy, pgrd sk od ds mg prgsgotn`d ‐sg `ksculpó Lgado‐. Ds prgsgotd n ]yp30/sgt. Ak nbugld aîs enadsd.
R N S O G V N R N V
>7 S N K R D P S K M
02
02
‐Vugs cdad od lg pdoinads uo odabrg aîs eîckl…. ‐suikrkó Antáns. @gck`kgrdo qug Inln, Iukllg y Lgado prdpdo`ráno ckocd odabrgs od abrgs cn`n uod y qug gl nbugld `g Lgado glgikrán gl qug aîs lg iustnrn.
´Cuîotds odabrgs prdpdo`rîo gotrg lds trgs4 Nrturktd, Bnbu, Bnonod, Bgrry, Bgrry, Cktrdokd, Cktrus, Lkan, Ano`nrkod, Agldo, Ononbua, Drnoig, Vnsn, Vdaglóo, Vrdagtgd y Sdrbgtg eugrdo lds qukocg odabrgs prdpugstds pdr ln enaklkn. ‐Sdo uods odabrgs egáskads‐rgeuoeuþó gl vkgjd gxtrntgrrgstrg gxtrntgrrgstrg.. ‐Od sgns tno iruþóo, cmü` ‐lg rginþó Lgado. ‐´Cóad ld mns llnan`d4 ‐prgiuotó Antáns. Antáns. M K S P D R K N S V N R N V G O S N R
>7
‐Cmü`‐cdotgstó ‐Cmü`‐cdotgst ó Lgado‐. Go ougstrd k`kdan, cmü` skiokcn «nbugld¸. VNRN VGOSNR
‐¡Gotdocgs tg llnanrgads Cmü`! ‐`kjgrdo lds igaglds n ln vgz. ‐Gs uo bugo odabrg ‐ncgptó Cmü`‐ N`gaîs, tgoid ln g`n` suckgotg pnrn sgr gl cmü` `g td`ds vdsdtrds.
EkO
R N S O G V R N V
>7 S N K R D P S K M
WSD LN SWAN VNRN AWLPKVLKCNR Gscrkbg gl gouockn`d antgaîtkcd y mnlln gl rgsultn`d. Eájntg go gl gjgapld.
2 Ù 315
7.
5.
> W
>7
9.
;.
=.
Anrcds tkgog uon cubktgrn cdo >2 cubktds `g mkgld y cuntrd vnsds. ^ukgrg pdogr gl aksad oúagrd `g cubktds go cn`n vnsd. ´Cuîotds cubktds pdo`rî go cn`n vnsd4
3;
GOPKGO@D LN AWLPKVLKCNCKÓO >.
Cdldrgn `g nanrklld lns cnskllns n lns qug llgins cuno`d nvnozns `g `ds go `ds. Mnz uo cárculd vgr`g go lns cnskllns n lns qug llgins cuno`d nvnozns `g ckocd go ckocd. @kbujn @kbujn uon ] rdjn go lns cnskllns n lns qug llgins cuno`d nvnozns `g >6 go >6. Go td`ds lds cnsds, ln cnsklln `g snlk`n gs gl 6.
6
>
2
3
0
7
5
9
=
;
>6 >> >2 >3 >0 >7 >5 >9 >= >; 26 2> 22 23 20 27 25 29 2= 2; 36 3> 32 33 30 37 35 39 3= 3; 06 0> 02 03 00 07 05 09 0= 0; 76 7> 72 73 70 77 75 79 7= 7; 56 5> 52 53 50 57 55 59 5= 5; 96 9>
92 93 90 97 95
99
9= 9;
=6 => =2 =3 =0 =7 =5 =9 == =; ;6 ;> ;2 ;3 ;0 ;7 ;5 ;9 ;= ;;
37 W 2
2.
Cdldrgn `g nzul lns cnskllns n lns qug llgins cuno`d nvnozns `g dcmd go dcmd. Rd`gn cdo uo cárculd onrnojn gl oúagrd nl qug llgins cuno`d nvnozns `g ougvg go ougvg. @kbujn @kbujn uon ] rdjn go lns cnskllns n lns qug llgins cuno`d nvnozns `g skgtg go skgtg. Go td`ds lds cnsds, ln cnsklln `g snlk`n gs gl 6.
6 > 2 3 0 7 5 9 = ; >6 >> >2 >3 >0 >7 >5 >9 >= >; 26 2> 22 23 20 27 25 29 2= 2; 36 3> 32 33 30 37 35 39 3= 3; 06 0> 02 03 00 07 05 09 0= 0; 76 7> 72 73 70 77 75 79 7= 7; 56 5> 52 53 50 57 55 59 5= 5; 96 9>
92 93 90 97 95
99
9= 9;
=6 => =2 =3 =0 =7 =5 =9 == =; ;6 ;> ;2 ;3 ;0 ;7 ;5 ;9 ;= ;;
;0
GOPKGO@D LN AWLPKVLKCNCKÓO Rgsuglvg.
3.
Mny `ds dbjgtds go cn`n pdrtnlîpkcgs. ´Cuîotds dbjgtds mny4
2Ù71 2
+
2
+
2
+
2
+
2
0. Mny cuntrd fldrgs go cn`n ancgtn. ´Cuîotns fldrgs mny4 2 W
0Ù71 0
+
0
+
0
+
0
+
0
7. Cn`n pnch tkgog trgs ydiurgs. ´Cuîotds ydiurgs mny go tdtnl4
3Ù51 3 + 3 + 3 + 3 + 3
+ 3
5. Cn`n cnjn cdotkgog sgks onrnojns. ´Cuîotns onrnojns mny go tdtnl4
5Ù31 5
+
5
+
5
37
;7
J W G I D @ G C W B D S
@kbujn gl îrgn
Juin`drgs @ds
Antgrknl Dbjgtkvd • @ds cubds ouaërkcds (6-7) @kbujnr iurns cuyn îrgn • Won mdjn cun`rkculn`n sgn gl prd`uctd • Bdláirned `gl rgsultn`d `g lds cubds.
Odrans >. Wo juin`dr lnozn lds `ds cubds. Sk go nliuod snlg uo cgrd, vuglvg n lnoznr. lnoznr. 2. Gotrg lds `ds juin`drgs, cnlculno gl prd`uctd `g lns puo puotunckdogs. tunckdogs.
35 0 W 2
3. Cn`n juin`dr `kbujn go ln mdjn cun`rkculn`n u uon on iurn ccuyn uyn îrgn sgn kiunl nl rgsultn`d `g ln aultkplkcnckóo notgrkdr notgrkdr,, tdano`d uo cun`rn`d `g ln mdjn cdad uok`n`. 0. Gl sgiuo`d juin`dr lnozn lds cubds cubds y rgpktgo ln aksan `koî `koîakcn. akcn. @gbgo kotgo kotgotnr tnr `kbujnr iurns `kstkotns go cn`n juin`n. 7. @gspuës `g trgs lnoznakgotds lnoznakgotds `g cn`n juin`dr juin`dr,, inon gl qug cdoskin aîs iurns `kstkotns.
Gjgapld:
Lnoznakgotd:
2
0
Aultkplkcnckóo: 2Ù01=
Ekiurns `g cn`n juin`dr:
;5
CDODZCD GL ÎRGN
Cdosk`grno`d qug
>.
gs uon uok`n` `g supgrckg, cnlculn gl îrgn `g lns iurns:
2.
uok`n`gs.
uok`n`.
3.
0.
2 W
uok`n`gs.
uok`n`gs.
7.
uok`n`gs.
5.
9.
uok`n`gs.
uok`n`gs.
35
;9
CDODZCD GL ÎRGN Sk cn`n uod `g lds cun`rn`ds tkgog uo îrgn `g > ca², cnlculn gl îrgn `g lns skiukgotgs iurns plnons.
=.
;.
ca²
ca²
>6.
>>.
35 W 2
ca²
ca²
>2.
>3.
ca²
ca²
;=
CDODZCD GL ÎRGN Rgsuglvg lns skiukgotgs dpgrnckdogs.
>0.
>37
>7.
57=9 + 2=5 0
>5.
+ 0;5
+ 270
>9.
=37
>=.
27=0 + ;= 7
2790 + >22 7
>;.
5 =9 – 375 2 W
35
26.
5 >3 – 0= 9
2>.
9=5; – 203 7
22.
=725 – 05;=
23.
=666 – >5 >>
2 0.
;527 – ;7=;
27.
>253 + =9 39
@knrkd `g antgaîtkcns
@gscrkbg cdo tus pnlnbrns quë gs gl îrgn `g uon iurn plnon.
;;
VRNCPKCD LN VRDVKG@N@ CDOAWPNPKUN @G LN AWLPKVLKCNCKÓO Aultkplkcn.
>.
9
Ù
7
1
2.
7
Ù
9
3.
0
Ù
; 1
0.
;
Ù
0 1
7.
>6
Ù 5 1
5.
5 Ù >6 1
9.
3
Ù
=.
=
= 1
Ù
3
1
1
02 W 2
;.
= Ù;
>6.
= Ù9
>>.
7 Ù=
>2.
9 Ù5
>3.
; Ù=
>0.
= Ù7
>7.
5 Ù9
>5.
9 Ù=
>9.
5 Ù=
>=.
; Ù5
>;.
= Ù5
26.
5 Ù;
>>5
VRNCPKCD LN VRDVKG@N@ CDOAWPNPKUN @G LN AWLPKVLKCNCKÓO 2> 2>..
Ontnlkn tkgog `kgz adog`ns `g 7 cts. ´Cuîotds cëotkads tkgog4
tkgog ckocd adog`ns `g >6 cts. 22.. Vg`rd 22 ´Cuîotds cëotkads tkgog4
´Cuîl gs gl îrgn4
23.. 23
3 ca
20.. 20 0 ca 0 ca 3 ca
2 W
02 ca²
27.. 27
2 ca
ca²
25.. 25
7 ca 2 ca
7 ca ca²
ca²
Antkjugids
Suans ilub-ilub 3
>>9
CDODZCD LDS GLGAGOPDS @G LN CKRCWOEGRGOCKN [ @GL CÁRCWLD Jugid `gadstrnckó `gadstrnckóo o
Sdogtd rg`do`d
>.
Subrnyn ln `gokckóo `g cn`n glgagotd sgiúo gl cdldr ko`kcn`d go ln lgygo`n. Ckrcuoegrgockn
Sdy uon curvn, cgrrn`n, pgregctn8 tgoid uo puotd qug anrcn ak `gstkod.
Cárculd
Vdr ël pnsn ln láogn rgctn qug uog puotds `g dpugstd cnakod. Ln aktn` `g gstn láogn cdogctn,
Cgotrd
cdo `kstnockn cdostnotg y auy bugo tkod, cn`n akgabrd `g gstn curvn sglgctn cdo gl puotd qug ag jn `kvkod. Sdy ln aîs bglln iurn plnon
22
@kîagtrd
W >
rd`gn`n pdr ln yn agockdon`n curvn cgrrn`n. Ods cdodcgs, gstdy sgiurd. ´Akgotd4 Aîs `g akl cdsns tkgog gstn gikg.
Rn`kd
¡P ¡Prnoqukld! rnoqukld! @gjn n uo ln`d gl lnagotd, qug pdr o tgrakon gstg gspgrpgotd.
2.
@kbujn lds glgagotds qug npnrgcgo go gl pdgan `gl cdldr ko`kcn`d go ln lgygo`n.
75
CDODZCD LDS GLGAGOPDS @G LN CKRCWOEGRGOCKN [ @GL CÁRCWLD Dbsgrvn ln `knon y rgspdo`g n lns prgiuotns.
27 76 97 >66
3.
´^uë glgagotd tkgogo go cdaúo td`ns lns ckrcuoegrgockns4
0. ´Cuîotd ak`g gl rn`kd `gl cárculd anydr4
> W
22
7. ´Cuîotd ak`g gl `kîagtrd `gl cárculd agodr4
Dbsgrvn gl `kbujd y rgspdo`g n lns prgiuotns.
5. Gl sgiagotd NB gs uo N
9.
@
Gl sgiagotd DG gs uo
D
=. Lds `kîagtrds sg cdrtno go gl puotd
;. Gl sgiagotd DC gs
B
C
`gl sgiagotd C@ Antkjugids
´Go quë ag`k`n4
G
79
G S P R N P G I K N @ G V G O S N A K G O P D
Skaklktu`gs CDOSKIWGyGL `kegrgockns @DBLG Aultkplkcn`dr
5
Ù
0
Aultkplkcno`d
1
@kvksdr
ù
20
20
Vrd`uctd
@kvk`go`d
5
1
0
Cdckgotg S G @ W P K L K A K S
´Go qug sg pnrgcgo4
´Go qug sg `kegrgockno4 Aultkplkcnckóo
79 >
Cdo rgspgctd n ...
Pgrakodldián
W > 2
@kvkskóo
S N K C O G R G E K @
Wtklkznckóo
S G O D R P N V
S G O D K S W L C O D C
>52
CDOSKIWG @DBLG N`kvkon glGLcubd
Juin`drgs Prgs n ckocd
Antgrknl • @ds cubds ouaërkcds (6-7) • @ds cubds ouaërkcds (7->6)
S D B W C G @ D I G W J
Dbjgtkvd N`kvkonr gl oúagrd `gl dtrd juin`dr
Odrans >. @ds nluaods sgrîo gl irupd `g lds enctdrgs y, lds `gaîs, gl `g lds pr prd`uctds. d`uctds. 2. Cn`n cdapdogotg `gl irupd `g enctdrgs gscdig uo cu cubd bd y ld lnozn. Augstrn n lds prd`uctds gl oúagrd qug lg mn snlk`d sko qug gl dtrd enctdr ld vgn. 3. Gl irupd `g lds prd`uctds aultkplkcn lds `ds oúagrds y `kcg gl rgsultn`d nl irupd `g lds enctdrgs. 0. Lds enctdrgs `gbgo n`kvkonr quë oúagrd oúagrd mn snlk`d go gl cubd `gl dtrd cdapdogotg `gl irupd n pnrtkr `gl rgsultn`d `g ln aultkplkcnckóo. 7. Sg turono pnrn kotgrcnabknrsg lds rdlgs.
Enctdrgs Non
Akrgyn
Lnozn gl cubd (6-7) sko qug ld vgn Akrgyn
Lnozn gl cubd (7->6) sko qug ld vgn Non
0
;
Gl irupd `g lds prd`uctds aultkplkcn lds `ds oúagrds (0 x ; 1 35) y lgs `kcg gl rgsultn`d n Non y Akrgyn. Non n`kvkon qug gl enctdr qug lg enltn gs gl ;.
Akrgyn n`kvkon qug gl enctdr qug lg enltn gs gl 0.
> 2 W
> 79
>53
RGLNCKDOD LN L N AWL AWLPKVLKCNCKÓO PKVLKCNCKÓO [ LN @KUKSKÓO Rgsuglvg.
>.
Mny >5 dr`gon`drgs y go cn`n agsn pd`gads cdldcnr cuntrd. ´Cuîotns agsns ogcgsktnads pnrn td`ds lds dr`gon`drgs4
2. Pgogads cuntrd agsns y go cn`n uon pd`gads cdldcnr cuntrd ddr`gon`drgs. r`gon`drgs. ´Cuîotds dr`gon`drgs pd`gads cdldcnr go tdtnl4
Vlnotgn `ds prdblgans cdo sus rgspgctkvns sdluckdogs qug cdotgoino lds skiukgotgs `ntds: dcmd pkakgotds, >5 pkakgotds y `ds cgstns.
3. 79 W 2
0.
7. Sg mn prgpnrn`d uon clnsg pnrn 70 gstu`knotgs. Sg mno pugstd sgks lns `g agsns. ´Cuîotns agsns mny go cn`n ln4
cnanrgrds `g uo prdpkons gquktntkvnagotg. gquktn tkvnagotg. 5. Lds Nodcmg rgcdikgrdo =6rgstnurnotg €. ´Cuîotd cdapnrtgo inoó cn`n cnanrgrd4 csus nanrgrd4
>50
RGLNCKDOD LN AWLPKVLKCNCKÓO [ LN @KUKSKÓO Rgsuglvg lns dpgrnckdogs. Eájntg go lds skiods.
>= ù 2 1
5 Ù 2 1
7 Ù 2 1
9.
=.
;.
>6. 35 ù ; 1
>>. = Ù 9 1
>2. = Ù 2 1
>3. >7 ù 7 1
>0. ; Ù 2 1
>7. ; Ù 3 1
>5. 32 ù 0 1
>9. 0= ù 5 1
>=. 5 ù 2 1
>;. 9 Ù 9 1
26.>6 ù 2 1
2>. ; Ù 0 1
2 W
79
22. 36 ù 5 1
23. 3 Ù 0 1
20. >2 ù 3 1
27. >5 ù 0 1
25. 7 Ù 0 1
29. 26 ù 7 1
Ù 7 1 2=. 3 Ù 7
Ù 2 1 2;. 9 Ù 2
75 ù ù = = 1 36. 75
3>. 5 Ù 7 1
32. ; Ù 5 1
33. >6 Ù 2 1
30. >6 ù 7 1
37. >2 ù 2 1
35. = ù 2 1
@knrkd `g antgaîtkcns
Kovgotn uon aultkplkcnckóo y sgþnln cn`n uon `g sus pnrtgs. Nl ln`d, rgnlkzn ln kovgrsn `g ln aultkplkcnckóo gscrkbkgo`d ln `kvkskóo. @g ougvd, sgþnln cn`n pnrtg.
>57
JWGID CDO GL PKGAVD N Cnrdlkon lg gocnotn ln aúskcn. Lds anrtgs cnotn go uon cdrnl, lds vkgrogs vn n clnsgs `g iuktnrrn y cn`n >0 `áns (cdotno`d n pnrtkr `gl `án > `gl ags), sg gocugotrn cdo su irupd `g aúskcn.
>.
Rd`gn sdbrg gl cnlgo`nrkd y cdo lds cdldrgs ko`kcn`ds, lds `áns qug Cnrdlkon vn n cdrnl, lds `áns qug tkgog clnsg `g iuktnrrn y lds `áns qug sg gocugotrn cdo su irupd `g aúskcn.
Cdrnl Iuktnrrn Irupd `g aúskcn
52 W 2
2.
´^uë `áns `gl ags `g nbrkl n brkl qug`nrî cdo su irupd4
3.
Gstg ags, ´tkgog aîs `áns `g cdrnl d `g iuktnrrn4
0.
´Cuîotds `áns `g`kcnrî gstg ags Cnrdlkon n ln aúskcn4
7.
´Cuîotds `áns `g `kegrgockn mny, gstg ags, gotrg lds qug vn n ln cdrnl y lds qug tkgog clnsg `g iuktnrrn4
5.
Ln clnsg `g iuktnrrn gapkgzn n lns >=:36 m y `urn 07 ako. ´N quë mdrn tgrakon ln clnsg4
>=2
JWGID CDO GL PKGAVD Anrtn y Rubëo qukgrgo kr n pnsnr uo o `g sganon s ganon n Sgvklln. Ukvgo go An`rk` y pug`go `gsplnznrsg go `kegrgotgs ag`kds `g trnospdrtg.
9.
Cdaplgtn lds gspnckds go blnocd.
NUG
Nvkóo
Snlk`n
Llgin`n
Prnygctd
Snlk`n
>0:66 m
>5:37 m
2 m 37 ako
>0:66 m
2 m 36 ako
>5:36 m
>5:66 m 26:37 m
23:>7 m
Llgin`n
Prnygctd > m 7 ako
>9:37 m
> m 7 ako
>9:66 m
Nutdbús Snlk`n >7:66 m >5:66 m
Llgin`n
Prnygctd 5 m 27 ako
23:66 m
=.
@g td`ds lds trnospdrtgs qug pug`go cdigr cdigr,, ´cuîl gs gl aîs lgotd4
;.
Sk cdigo gl nutdbús y qukgrgo llginr notgs `g lns >6 `g ln odcmg, ´n quë mdrn `gbgo cdigrld4
>6. ´Cuîotds akoutds `urn gl trnygctd go nvkóo4 >>.
Sk qukgrgo snlkr notgs `g lns >7 m y llginr notgs `g lns >5 m, ´quë trnospdrtg `gbgo cdigr4
>2.
´Cuîotds akoutds `urn gl prkagr trnygctd go NUG4
>3.
´Cuîlgs sdo lns mdrns `g snlk`n y `g llgin`n `gl sgiuo`d nutdbús4
2 W
52
>=3
r g y N p s / l d d k c d l v p d g g l r r n g n s l c g k s p d r o t r d g n b s t l g g p i a n k n n r n s
` G g x l p p r g r d s b d l l g n a s n d l u c k ó o
r g S g d s g s p t l r d g r n g c l v n t c g g c k k i d r d o k g o n d l g s p s y n l r p / s d d b n r l g n a n
g K o l t p g r r d p b r l g g a t d n
k o O t g g c r g p s r k t g d t n n r y g u l ` r n g s p u n l r t n n ` d .
p n r n s g i u k r s u s p n s d s .
p G g k l r j d d o u g o c n g g s k s t t d r n n g y t u i ` k n n ,
c p p K ` d n g g o n r r o g s d t o k l l n g d b c c s g d . g r s l k d q t u d s ë n ` y n m u n ` t d c s g n , r
p p L n g g d r r d g n c o l d g a g c o g p s u o r t k c g k o d n ` n ` y d g u r , l ` d n .
g s c r k b
q ` S k u g i g n l d m g l d g s s p g r l t g n n i t s k g d ` i s d n . k
p p G n g l k r r j d d n ` o u g s g n o n c g g r s s r t k t d d r l l n n n r y t g l u i n k . ` n n ,
k o g C ` l d g g c g o g o a t s u p k r c o t k c o n d k g n r n y ` ` l u d d d s ` , p ` n g n p r t d n r d s n .
K o k c k n ` d
c c @ d d d r y r o g l n l n s p s s d u d o o u l ` ` k c k n k g o ` ó t g o g s s .
c q ` S d u g i k r g n l d r g u l c t g d t s s d k l z t s k r p . d n n t s l g d d s i k s ` n n y r d t s g v k s d
y G s l k j ë d c u ó o a n d g ` s g t r s n n t r r g k i l d l n n r l n .
p g C r g g k d l ` r a n d g c p o k o d r o d t g k o n s c ` r ë l d c d d l s ó d g . a s l d ` g o t n o d u c s , n k ` d
N v n o z n ` d
@ s k c d d l r n r y l r g s n g p s d s p d u o u l g ` c s k k t g o ó n t o g g s s c l y d o ó i c n l d s k c a n u . r p o k u ` g n b ` d g s
l ` c S d d i k s g j r d r ` d n o g l c d t s d k o t d s i s p c u y n d o r s r d g d r v s g , c k d c y s t d d q u q o s g l . u d u g s t o ` k l d n k t d d z a s g
n v s G l n ë l k l ` d p d j r g r d n s u b r n o l s r n g k r a r d g l s n g l t s n . p r r l n d n g o y t ` p i k g u n r , á n g ` d
l y K n o p t r g u g s g r p p ` r u d g g k t s a d t n g n l g i p k r s o p n d g r b r l n g ` a n n .
@ d y l n
k r d s l n l s u u c k o ó k ` o n s ` k o g s .
V r k o c k p k n o t g
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R ú b r k c n ` g
g r s d l u c k ó o ` g p r d b l g a n s
Pgcodldián nl sgrvkckd `gl nprgo`kznjg CkbgrGANP gs ln nplkcnckóo pnrn ln prîctkcn sganonl `g GANP `g anogrn nutóodan y pgrsdonlkzn`n. CkbgrGANP pgraktg uo nprgo`kznjg n`nptntkvd, cdo nctkvk`n`gs qug sg njustno nl prdirgsd `gl nluaod.
Cdo egg`bnch koag`kntd pnrn encklktnr ln nutdodaán.
Gxpgrkagotnr, nonlkznr, gvnlunr, crgnr. Bnjd gstns prgaksns y `gs`g lns kotglkigockns aúltkplgs, GANP prdpdog n lds nluaods uo nprgo`kznjg kotgirnl `g lns antgaîtkcns. Cdosckgotg `g ln ogcgsk`n` `g snbgr trnbnjnr `g edran cddpgrntkvn y ln kapdrtnockn `gl jugid go gl nprgo`kznjg, GANP drinokzn sus cdotgok`ds pnrn qug lds nluaods pug`no goergotnrsg y n`nptnrsg n `kstkotds cdotgxtds `g ln vk`n `knrkn. Cdo GANP lns antgaîtkcns sg nprgo`go y sg `kserutno.
> ; > 6 6 6 A H P
7 > > 6 6 > 6 > 6 0 = > 2 K ] ]
7 > 6 6 6 7 6 > 6 0 = > 2
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