material de preparacion - segunda fase onem 2012 - nivel iii_2012

7/31/2019 Material de Preparacion - Segunda Fase ONEM 2012 - Nivel III_2012

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yyy*lntmnjdnvt *fkaiurat*eal

Jos`k7 OOO Dae`jt`7@voeh Su~p`w Kknjau EPVUA7 AJ@L62>6

LOUE@KJ@N 2>

>* @k rntoa d` lo enun+ ~p` ù epndvnda+ to`j` pj rawa* ut`

doutn d` tvùd` knu ù~pojnu d` lo rntoa7 62+52+42 l`tvauvùrètosnl`jt`* Epkù

uaj knu dol`juoajù d` lo rntoa***1

6* @jeajtvnv pjn cpjeoj epndvtoen c-}/+ tnk ~p` uo V ù pjjl`va cavlnda`}ekpuosnl`jt` rav pjau -`j fnu` >2/+ c-V/ tnlfoj ùt`

cavlnda

`}ekpuosnl`jt` rav pjau*

5* @jeajtvnv pj jl`va tnk ~p` up lotnd u`n `k loula jl`vaeaj upu eocvnu r`vlptndnu*

4* J r`vuajnu u` mne`j vìnkau `jtv u+ d` cavln ~p` jndoùnf` kn rvae`d`jeon d`k vìnka ~p` vèof`* Eala ja to`jjojipjn ivneon vìnknvu` n u loula+ u` rvadpe`j nkipjnu

docoepktndù rnvn v`nkownv kn nuoijneoj d` ~poj vìnkn n~poj* Ka mnfotpnk ù ojtvadpeov J rnr`kotau eaj kau jalfvùd` kau rnvtoeornjtù+ `j pjn fakun+ y v`rnvtovkau nk nwnv* @j

enua d` ~p` n nkipja k` ta~p` up rvaroa jalfv`+ u` njpkn `kv`rnvta y mny ~p` saks`v n v`r`tovka mnutn eajuìpov ~p`

jndo` u` vìnk` n u loula*Epk ù ùtn rvafnfokodnd `j cpjeoj d` J+ y uo ù rauofk`+eajae`v up t`jd`jeon nk npl`jtnv `k snkav d` J1

0* &@j pj ùt`vn mny pjau >22 moiau* U` eai` pja+ ~p` ùtnipg`v`nda+ ja u` d`sp`ks` n kn ùt`vn8 u` unen atva+ tnlfoj

ka ùt+ ja u` d`sp`ks`* Epk ù kn rvafnfokodnd d` ~p` kaùt `k t`ve`va1&

3* Pjn ealrnn to`j` 0 dovètosau* Knu vìknu d` kn ealrnnv`~po`v`j ~p` epnk~po`v lnyavn -tvù a lu/ d` dovètosaurp`dnj nfvov kn engn cp`vt`+ r`va ~p` jojipjn lojavn -dau a

l`jau/ d` dovètosau kn rp`dnj nfvov* U` rvaraj` `~pornv nkn engn cp`vt` eaj >2 e`vvndpvnu d` lnj`vn ~p` uka u`

rp`dn nfvov epnjda ùtj dourajofkù knu kknsù d` tadnu knue`vvndpvnu+ y dnv n endn dovètosa pj eajgpjta d` kknsù d`&j&

e`vvndpvnu doutojtnu*

9* @jeajtvnv tadau kau snkavù d` &j& rnvn kau ~p` `}out` pjn

cavln d`v`rnvtov knu kknsù d` nep`vda eaj knu vìknu d` kn ealrnn*

=* Olnioj`lau pj `}nl`j tora tùt d` >2 rvìpjtnu+ dajd`

uaka u` dnj 6 uakpeoajùy uaka pjn d` `kknu ù eavvètn* Ne`vtnv ep`jtn > rpjta ycnkknv ja vùtn y u` nrvp`fn eaj 0 rpjtau*

Pj nkplja eajtùtn nk nwnv tadnu `kknu* Uo kn rvafnfokodnd d`ne`vtnv pjn vùrpùtn ù d`k 02%+kpìa ne`vtnvn 0

rvìpjtnu+ `jtajeù unenv pj 0 y kn rvafnfokodnd d` nrvafnvu`von pj >22%*

?* Pjn rknwn d` tavau nfnjdajndn u` `jep`jtvn epfo`vtn d`

mo`vfn* Kn enfvn mnlfvo`jtn ` ojuneonfk` u` ntn n pj rpjtaepnk~po`vn d` kn eovepjc`v`jeon eaj pjn ep`vdn d` kajiotpd

tnk ~p k` r`vlotn eal`vu` `}netnl`jt` kn lotnd d` knmo`vfn ~p` mny `j kn rknwn* ^p kajiotpd d`f` t`j`v knep`vdn1

>2* Mnkknv epntva ojt`vsnkau doutojtau `j kau epnkù kn èpneoj}4 >6} ( >4} > < 2 t`jin pjn uakn uakpeoj*

>>* T`jo`jda pj tvojipka `~pokt`va d` nktpvn m+ epk u`vn `kvndoa d`k evepka ojuevota `j `k loula1*

>6* Pjn m`v`jeon u` v`rnvt` d` nep`vda eaj ka ùtorpknda `j `k

eavvùrajdo`jt`tùtnl`jta* Uìj `k loula+ `k moga lnyav vèof` >22*222rtu lu kn ~pojtn

rnvt` d` ka ~p` ~p`dn `j ù` lal`jta* @k ~p` uoip` `j `dndvèof` 622*222rtu y kn ~pojtn rnvt` d`k vùta* @k t`ve`va 522*222 rtu y kn

~pojtn rnvt`d`k vùta **** y nu upeùosnl`jt`+ endn pja d` kau mogauvèof` d` `jtvndn

>22*222 rtu lu ~p` `k njt`voav y >!0 d`k vùta* Ka epvoauaù ~p` jojipjad` kau mogau rvatùtn rav~p` tadau vèof`j kn louln enjtodnd*

Epjtaumogau uaj1

>5* U` to`j`j >6 faknu d`k loula tnlna y eakav* Tadnuto`j`j `k loula rùa+ `}e`rta pjn epya rùa ù doc`v`jt` nk

d` knu d`lu-r`va ja unf`lau uo ù lnyav a l`jav/* U` douraj` d` pjnfnknjwn

ealrnvntosn -ùta ù+ uaka jau uovs` rnvn unf`v uo pj afg`tarùn lnu~p` atva+ r`va ja jau dn `k snkav d`k rùa/* U` tvntn d`+ eaj
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uaka TV@U r undnu+ ns`voipnv epnk ù kn fakn doc v`jt`+ kn~p` to`j` pj rùa doutojta

nk d` knu d`lu* Nd`lu+ d`fou dèov uo ùtn fakn rùn lnua l`jau

~p` knu atvnu*>4* Dau r`vuajnu dèod`j gpinvu` pjn laj`dn n &rnvù a

jajù&7 uo unk` &rnv& injn `k gpindav >+ y uo unk` &olrnv&

injn `k gpindav 6*Nd`lu+ raj`j pjn eajdoeoj7 kau dau ùtj afkoindau nunenv+ nk l`jau+ pj d`da* Rnvn ùt` gpìa+ dèolau ~p` pj

gpindav ù &kouta& uo `koi` gpinv &rnv& eaj pjn rvafnfokodndtnk ~p` ln}oloe` up f`j`coeoa ùr`vnda+ y &tajta& uo unen kaud`dau nk nwnv* Uprajo jda ~p` kau dau gpindavù uaj

&koutau&+ ns`voipnvn/ ~poj injnv uo endn pja ev`` ~p` `k atva ù &tajta&*f/ eaj ~p rvafnfokodnd gpinv &rnv& endn pja d` kau

gpindavù+ uo kau dau unf`j ~p` `k atva ù &kouta&*

>0* -n/@jeajtvnv `k rvol`v `jt`va rauotosa epya epndvndat`vlojn `j tvù epntvau*-f/@jeajtvnv tadau kau `jt`vau rauotosau epyau epndvndau

t`vlojnj `j tvù epntvau*-e/D`lautvnv ~p` ja `}out` jojij epndvnda r`vcètat`vlojnda `j epntva epntvau*

>3* Epk ù kn k` d` cavlneoj d` ùtn uèp`jeon4+ 3 + ? + >2 + >4 + >0 + 6> + 66 + 60+ 63+ 55+ 54+ **1

>9* U`nj }+ y+ w knu uakpeoajù d` kn epneoj >59 ( 690} (>?3}6 ( }5 < 2

Epjta snk` kn enjtodndw

w

y

y

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>=* T`j`lau pj fokknv eovepknv d` vndoa V `j `k epnk raj`lau knfakn fknjen ndoutnjeon v d`k e`jtva* U` rod` mnkknv iàltvoenl`jt`-njnktoenl`jt` ùlu ceok/ kn dovèeoj `j kn ~p` mnfv`lau d` iakr`nv kn faknrnvn ~p`dùrpu d` v`fatnv dau sèù `j kn fnjdn rnu` rav `k loularpjta `j `k ~pù` `jeajtvnfn ojoeonkl`jt`*

>?* &Pj nptalsok u` dovoi` eaj vplfa javt` eaj pjn s`kaeodndd` 0 l!u+ y atvasn mneon `k ùt` n >0 l!u* Epnjda nlfau ùtj nkoj`ndau eajvùrèta n pj`g` s`vtoenk+ kn doutnjeon ~p` kau u`rnvn ù d` 40 l* Eaj ~ps`kaeodnd u`nk`gnj kpìa d` 5 uìpjdau1&

62* Mnkknv kau `jt`vau rauotosau n+ f+ y e tnkù ~p

506=2>6322>22=26>?efn *

6>* Mkkù` pjn cpjeoj ~p` rnvn }:2 u`n eajtojpn+ d`vosnfk` ys`voco~p` knv`kneoj c-6}/ < } c-}/ 8 c->/ < >

66* &Pjn unjdn rùn >2 hokaivnlau+ d` kau epnkù `k ??% ùnipn* Dùrpu dèo`vta to`lra nk uak+ u` `snrav rnvt` d`k nipn+ uo`jda nmavn`k rave`jtng`d` nipn d`k ?=%* Epnjta rùn nmavn kn unjdn1*&

65* Mnkknv `k jl`va d` pjau `j kn v`rvù`jtneoj fojnvon d`7-66 6 ( >/-63 65 ( >/-6>= 6? ( >/-604 669 ( >/-6>36 6=>

( >/-6

4=3

6

645

(>/64* Uprajinlau ~p` `k rvaeùa ojcojota lautvnda eajdpe` n pj

jl`va v`nkrauotosa fo`j d`cojoda* Mnkknvka* @}rvùnv l`donjt` pjncvlpkn d`vèpvv`jeon endn rnua d`k rvaeùa `j cpjeoj d`k njt`voav *

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60* Mnkknv kn upln d` kau epfau d` knu vneù d` } >2 ( }? ( }= ( ***( }6 ( } ( > < 2

63* Kn cpjeoj V-n/ taln `k jl`va v`nk n y ka v`dajd`n nk`jt`va lnu rv}ola* Uo u` talnj } ` y nk`ntavonl`jt` d`cavln ~p` V-}/ y V-y/+mnkknv kn rvafnfokodnd d` ~p`7n/V-}/(V-y/


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52* n/ U`nj n+ f y e+ y tvù `jt`vau rauotosau doutojtau tnkù ~p`7n ( =f ( 60e < 6224+ f ù lktorka d` n + y e ù lktorka d`f * @jep`jtvntadau kau rauofkù snkavù d` n + f y e *f/ Pj eakèeoajoutn to`j` eo`vtn enjtodnd d` ro`dvnurvèoaunu+ tadnud` rùau doutojtau* Uo v`tovn knu 5 ro`dvnu lu rùndnu+ `krùa tatnk

d` tadnu knu ro`dvnu ~p` t`jn doulojpy` `j 50%* Uo v`tovn+d` knuro`dvnu vùtnjtù+ knu 5 lu kosonjnu+ `k rùa tatnk d` doemnuro`dvnuvùtnjtù doulojpy` `j upu 0!>5* Epjtnu ro`dvnu t`jnavoiojnkl`jt``k eakèeoajoutn1e/*@jep`jtvn `k lnyav jl`va d` 9 diotau doutojtau ~p` ulktorka dèndn pja d` upu diotau*

5>* NFED ù pj epndvnda eaj doniajnkù ~p` u` eavtnj `j A*Kn fouètvow d`k jipka FNA eavtn n FA y FE `j J y R

vùrètosnl`jt`* Uo kn kajiotpd d` JA u 64+ mnkknv knkajiotpd d` RE*

56* U` tvntn d` mnkknv pjn `}rvùoj e`vvndn rnvnU-}/ < eau5-}/ eau5-5}/!5 ( eau5-?}/!? eau5-69}/!69 (

***

55* Kn cpjeoj c-}+y/ s`vocoenc-2+y/ < y(> 8 c-}(>+2// 8 c-}(>+y(>/ +y//rnvn tadau kau }+y `jt`vau rauotosau* Mkkù` c-4+>?=>/

54* Kau Jl`vau @pk`vonjau s`vocoenj kn v`kneoj d` vèpvv`jeon@-j+>/ < >@-j+h/ < ->(j,h/ @-j,>+h,>/ ( h @-j,>+h/

@utnu v`kneoajù uaj uoloknvù n knu ~p` d`coj`j kau jl`vauealfojntavoau

E-j+2/ < >E-j+h/ < E-j,>+h,>/ ( E-j,>+h/eaj ka ~p` kau jl`vau `pk`vonjau u` rp`d`j eajuod`vnv pjn

i`j`vnkowneoj d` ùtau*Rav up ùtvpetpvn+ tnlfoj u` rp`d`j douraj`v `j pjtvojipka uoloknv nk d` Tnvtnikon+ ~p` u`vn

>> >

> 4 >

> >> >> >> 63 33 63 >

Kn rvìpjtn u `}out` pjn cpjeoj i`j`vntvow uolrk` rnvn

ùtau jl`vau1Kau jl`vau ealfojntavoau to`j`j rav cpjeoj i`j`vntvow

C < >!-> , y->(}//

y+ rav ka ~p` m` `jeajtvnda+ kau jl`vau `pk`vonjau rp`d`jaft`j`vu` `lrk`njda knu cpjeoajù Uh ~p` yn eajae`lau+ ka

~p` olrkoen nndov cnetavù }!->,}/h* Lo rvìpjtn u`vn ravpjn cavln lu uolrk`+ d`k tora

C < > ( y-> ( }/ ( y6-> ( 4} ( }6/ ( y5-> ( >> } ( >>}6 (}5/ ( *** < 11

50* U`n R-}/ pj rakojaloa d` ivnda 9*Mnkknv R-?/+ uo R->/+

R-6/!6+ R-5/!5+R-4/!4+R-0/!0+R-3/!3+R-9/!9+R-=/!=*

53* R-}/ù pj rakojaloa d` ivnda 5j tnk ~p`7R-2/

material de preparacion - segunda fase onem 2012 - nivel iii_2012

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