Fase 1 - Matematicas

 

C@]K G2 @MZGSGJ@J GOJGSGJ[@A 0. A` kiprks` IO\ IO\ tgkok jes pa` pa`ot`s ot`s jk prejummg prejummgýo ýo (T0 y T>), uo `ai`mço (@), y jes tg tgkoj`s koj`s jk ikoujke (Z0 W Z>). Ko a`s sghugkotks t`na`s sk iukstr`2 ko a` prgikr` a` m`p`mgj`j jk a`s  pa`ot`s, a`s jki`oj`s jk a`s tgkoj`s jk ikoujke y aes mestes uogt`rges per Fi y ko a` skhuoj` t`na` a` jgst`omg` kotrk m`j` puote.

  `) Ceriua Ceriuakk uo iejka iejkaee jk Trehr` Trehr`i`mgý i`mgýoo Agok`a pp`r` `r` ig igogigz ogigz`r `r aes mest mestes es tet` tet`aks. aks. g 90,>,= b 9=,:,;

Cuomgýo Enbktgve2 R  Igo9:∘;4 x 0=+ 04∘: + 3∘34 x >; +

:∘;4 x =: + =∘:4 x =;

R  Igo9>44 x0= + :+ =34 x >; + >44 x=: + 0>4 x =;

^kstrgmmgeoks2  x 0=+ x 0: + x 0; ≪ :44  x >=+ x >: + x >; ≪ 344  x =:+ x=;9 >;4  x

 x

+

0:

>:

 x ≫ 8;4

+

=:

 x 0;+ x >; + x =; ≫ >;4  x 0=+ x >=∞ x =:∞ x =;9;44  x gb ≫ 4 T`r` teje g y tej` b

 n) ^ksukav` ka prenaki` p`r` jktkrigo`r a` seaumgýo ýptgi`.

 

]k gotrejumko aes j`tes ko ka Xgoqsn y sk entgkok a` sghugkotk hràcgm` jka prenaki` jk tr`ospertk.

Ko a` sghugkotk t`na` sk iukstr`o aes rksuat`jes jk a` seaumgýo jka prenaki`2

]k entgkok meie rksuat`je quk ka meste iéogie jka iejkae i`tkiàtgme ks jk $;=4.;44 kovg`oje >;4 ngkoks jk  T0 `  @  , 0;4 jk  T0 ` Z 0 , =;4 jk  T> ` Z 0, >;4 jk  T> ` Z > y >;4 jk  @ ` Z 0.

m) Puç m`ing m`ingee tkojré` quk kkckmtu` ckmtu`rsk rsk ko ka iejka iejkaee jk prehr`i prehr`i`mgýo `mgýo ag agok`a, ok`a, sg ka i iàxgie àxgie jk  ngkoks quk sk pukjko kovg`r jka j ka `ai`mço ` a` tgkoj` jk ikoujke 0 cukr` jk ;44. ;44 . Mýie m`ing`ré` ae `otkrger a` seaumgýo ýptgi`5

 

@a rk`agz`r ka m`inge ko aes v`aerks, sk entgkok meie rksuat`je quk ka meste iéogie jka iejkae i`tkiàtgme skré` jk $::;.;44 kovg`oje :44 ngkoks jk  T0 `  @  , 044 jk  T> `  @ , >;4 jk  T> ` Z 0, >;4 jk  T> ` Z > y ;44 jk  @ ` Z 0.

>. A` Kiprks` J Jgspa` gspa`yy ]. @. jkjgm jkjgm`j` `j` ` preykmt preykmtes es tgkok : ouk oukves ves magk magkotks. otks. ]k `sg `sgho`rào ho`rào aé aéjkrks jkrks jka preykmte ` m`j` uoe jk aes mu`tre magkotks. Meo n`sk ko jgckrkotks `otkmkjkotks y kxpkrgkomg`s jk aes aéjkrks, a`s v`rg`s `sgho`mgeoks aéjkr-magkotk jgcgkrko ko cuomgýo ` aes tgkipes jk tkrigo`mgýo preykmt`jes. A`s `sgho`mgeoks pesgnaks y aes tgkipes kstgi`jes jk tkrigo`mgýo ko jé`s, seo2

`. Ceriuak ka prenaki` g 90,>,=,:   b 90,>,=,:

Cuomgýo Enbktgve2 R  Igo904 x00+ 03 x 0> + => x 0= + >; x0: + 0: x >0 + >> x >>+ :4 x >=+ =4 x >: + >: x =0+ >> x =>+ >3 x ==+ >4 x =: + 0

^kstrgmmgeoks2  x 00+ x 0>+ x 0=+ x0: ≪ 0  x >0+ x >>+ x>= + x >: ≪ 0

 x 00+ x >0+ x =0+ x :0 ≫ 0  x 0>+ x >>+ x=> + x :> ≫ 0

 x =0+ x =>+ x== + x =: ≪ 0

 x 0=+ x >= + x ==+ x := ≫ 0

 x :0+ x :>+ x := + x :: ≪ 0

 x 0:+ x>: + x =: + x :: ≫ 0

 x gb ≫ 4 T`r` teje g y tej` b

 n. Muàa ks a` `sgho`mgýo ýptgi` y ka tgkipe tet`a p`r` kotrkh`r aes preykmtes5

 

@ meotgou`mgýo sk iukstr` a` hràcgm` jk `sgho`mgýo jk a`s pesgnaks `sgho`mgeoks jk aes aéjkrks ` aes : magkotks rk`agz`j` ko Xgoqsn.

Ko a` sghugkotk t`na` sk iukstr`o aes rksuat`jes jk a` seaumgýo jka prenaki`2

]k entgkok meie rksuat`je quk ka tgkipe iéogie jka iejkae i`tkiàtgme ks jk 83 jé`s `sgho`oje ` Bu`o ka magkotk >, ` Tkjre ka magkotk 0, ` ]kn`stgào ka magkotk : y ` @ojrk` ka magkotk =. m. ]upeoh` quk sk tgkok uo kipak`je `jgmgeo`a muyes tgkipes p`r` aes magkotks 0,>,= y : seo

rkspkmtgv`ikotk >>, =4, >< y >;, muàa skrà ̀  a` `sgho`mgýo ýptgi`5 ]k gohrks`o aes j`tes ko jks`rreaa` ko Xgoqsn jk a` sghugkotk i`okr`2

 

A` sghugkotk hràcgm` rkprkskot` a`s pesgnaks `sgho`mgeoks jk aes ; aéjkrks p`r` aes : magkotks.

@a seaumgeo`r ka prenaki` jk prehr`i`mgýo agok`a sk entgkok a` sghugkotk t`na` jk rksuat`jes2

Meo uo tgkipe tet`a jk 8: jé`s, Tkjre oe tkojré` `sgho`je ogohòo magkotk. A`s etr`s `sgho`mgeoks skré`o2 Bu`o meo ka magkotk 0, ]kn`stgào meo ka magkotk :, @ojrk` meo ka magkotk > y ka kipak`je `jgmgeo`a meo ka magkotk =. j. Puç aéjkr sk qukjý sgo preykmte5

Meo ka kipak`je `jgmgeo`a, Tkjre sk qukj`ré` sgo magkotk, ks jkmgr sgo preykmte.