7° Libro en Digital F Prima

 

7 ZFELZIC ICTFIÃTOKC

KL[TC ZOKC

 e ' GZVRL FDOTLZOCN

Fdokoû` fspfkocn

 

Klpyrogmt :236

 e ' Grupl Fdotlrocn  Dosfól, cricdl y plrtcdc

 e ' Grupl Fdotlrocn 

Rrlmojodc nc rfprldukkoû` tltcn l pcrkocn df fstc ljrc,  plr kucnquofr ifdol, so` cutlrozckoû` fskrotc df

 e 'Grupl Fdotlrocn.

vf`tcsBeproicgruplfdotlrocn.kli Tfnïel`ls8 :444-3;;2 =534-4:4: . . .

632 R?46i 7

E'Rroic Grupl Fdotlrocn Ictfiãkc 78 mckoc nc rfslnukoû` df prljnfics / E'Rroic Grupl Fdotlrocn . -- 3c fd. -- Cnchufnc, Klstc Zokc8 E'Rroic Grupl Fdotlrocn, :234 352 p. 1 :7 ] :3 ki. O[J@ ?7=-??;2-63;-22-: 3. ICTFIÃTOKC - F[TVDOL _ F@[FÓC@XC. F@[FÓC@XC. :. ICTFIÃTOKC - F@[FÓC@XC F@[FÓC@XC DOUFZ[OE DOUFZ[OEOKCDC. OKCDC. O. Tétunl.

 

O@TZLDVKKOÛ@ Rcrc rfspl`dfr c nc iufstrc df rfspftl, klrtfséc y cdiorckoû` df tc`tls dlkf`tfs kl` fstc Fdotlrocn, plr eo` nlgrcils dfscrrlnncr kl` ïxotl nc tltcnodcd dfn `ufvl prlgrcic df fstudol o`knuyf`dl proicroc. Mc` sodl iukmls cóls, dfsdf fn cól :23:, kuc`dl cpf`cs sf gfstcjc nc rfelric df nc fdukckoû` ictfiãtokc f` Klstc Zokc, quf mfils fstcdl o`vfstogc`dl y rfcnoif`tã`dl`ls kl` cplrtfs df iukmésoils dlkf`tfs df tldl fn pcés, pcrc krfcr  u`c klnfkkoû` df nojrls kl` fstã`dcrfs o`tfr`ckol`cnfs pfrl pnf`cif`tf cdcptcdls c nc rfcnodcd `ckol`cn. Cdlptc`dl fn f`el Cdlptc`dl f`elquf quf pro`kop pro`kopcn cn dfn prlgrcic df fstu fstudol dol df Ictfiã Ictfiãtokcs tokcs,, nc Zfslnukoû` df Rrljnfics kl` ï`ecsos f` kl`tfxtls rfcnfs, rfcnfs , cprljcdl fn :3 df icyl df :23: plr fn Kl`sfhl [upfrolr df Fdukckoû` df Klstc Zokc. C kl`to`uckoû` sf prfsf`tc nc dostrojukoû` df mcjonodcdfs y nfkkol`fs plr pfroldl df lktcvl cól , usc`dl nc fstrctfgoc sugfrodc f` fn Dlkuif`tl df o`tfgrckoû` df mcjonodcdfs pcrc Lktcvl cól ( Fncjlrcdl plr fn Rrlyfktl  Zfelric df nc Fdukckoû` Fdukckoû` Ictfiãtokc f` Klstc Klstc Zokc). DO[TZOJVKOÛ@ DF MCJONODCDF[ _ NFKKOL@F[ RCZC [ÏTOIL CÓL Rroifr pfroldl @ØIFZL [

[fgu`dl pfroldl

Tfrkfr pfroldl

F[TCDÉ[TOK C

GFLIFTZÉ C

Mcjonodcdfs

Nfkkol`fs

Mcjonodcdfs

Nfkkol`fs

Mcjonodcdfs

Nfkkol`fs

M-3 y M-:

?

M3, M:, M;, M4, M-6 y M-5

7

M3, M:, M;, M4 y M-6

6

M-;, M-4, M-6 y M-5

7

M7, M= y M?

3:

M-5 y M-7

6

M-7, M-= y M-?

7

ZFNCKOL@F[ _ ÃNGFJZC

M=, M? y M32

4

M-32, M-33, M-3: y M-3;

5

M-3 y M-:

5

M-33 y M-3:

6

M-34 y M-36

32

M-; y M-4

7

M-3; , M-34 y M-36

6

M-35 y M-37

6

M-3= y M-3?

6

M-:2 y :3

4

6;

M-35 , M-37, M-3= y M-3? M-:2 , M-:3 y M-::

[uic tltcn df nfkkol`fs plr pfroldl ;: „Fn vfmékunl pcrc trc`sotcr plr fn iu`dl df nc rczû` fs nc ictfiãtokc’

 e ' Grupl Fdotlrocn 

;6

5 6

 

É@DOKF KCROTVNL 38 @ØIFZL[ @øifrls `cturcnfs 3. :.

Rltf`kocs Kl Klij ijo` o`ck ckoû oû` ` df lpfr lpfrck ckol ol`f `fss

;. 4. 6. 5. 7. =.

Cn Cngl glro roti til ld df f nc d dov ovos osoû oû` ` Kl`kfptl df dovosojonodcd y dovoslr @ @ø øifrls proils y klipufstls @øifrls klipufstls y sus ecktlrfs proils Ié`oil kliø` iøntopnl Iãxoil kliø` dovoslr

? 3; Tflréc df `øifrls 3= 3? :: :; :6 :5 @øifrls f`tfrls

?.2. Z@ø @øif fd`tfr `f tovl vlss 3 fncifrl kolrls `fss f`t ffrls lrls df`fgc ` gcto 33. Zfktc `uiïrokc 3:. Ucnlr cjslnutl df u` `øifrl f`tfrl 3;. Lpufstl df u` `øifrl f`tfrl 34. 36. 35. 37. 3=. 3?. :2. :3. ::. :;.

;; ;6 ;5 ;? 43

Lpfrckol`fs, kãnkunls y fstoickol`fs Kl`iutctovodcd y cslkoctovodcd df nc suic y nc iuntopnokckoû` [uic df `øifrls f`tfrls Zfstc df `øifrls f`tfrls Iuntopnokckoû` df `øifrls f`tfrls Dovosoû` df `øifrls f`tfrls Rltf`kocs kl` jcsf f`tfrc y fxpl`f`tf `cturcn Rrlpofdcdfs df pltf`kocs Rltf`kocs y rcékfs Zcéz df u` `øifrl f`tfrl Klijo`ckoû` df lpfrckol`fs KCROTVNL :8 GFLIFTZÉC

:4. Ru`tls, sfgif`tl, rfktc, sfiorrfktc, rcyl y pnc`l :6. Zfktcs pcrcnfncs, pfrpf`dokuncrfs y kl`kurrf`tfs

Kl`lkoiof`tls jãsokls

44 46 45 47 4= 63 6: 66 65 6= 72 73

Uosucnozckoû` fspckocn :5. E Eoogurcs trodoif`sol`cnfs y sus fnfif`tls :7. :=. :?. ;2. ;3. ;:. ;;. ;4. ;6.

74

Ã`gunls Ã`gunls nnc`ls, cdyckf`tfs, nls quf elric` pcr no`fcn y nls lpufstls plr fn vïrtokf Ã`gunls kl`gruf`tfs, klipnfif`tcrols, supnfif`tcrols Ã`gunls dftfrio`cdls plr dls rfktcs pcrcnfncs y u`c trc`svfrscn Troã`gunls Dfsogucndcd troc`guncr [uic df ncs ifdodcs df nls ã`gunls o`tfr`ls df u` troã`gunl [uic df ncs ifdodcs df nls ã`gunls fxtfr`ls df u` troã`gunl Kucdronãtfrls [uic df nls ã`gunls o`tfr`ls df u` kucdronãtfrl [uic df nls ã`gunls fxtfr`ls df u` kucdronãtfrl Rcrcnfnlgrcils

77 7= =3 =6 =7 == ?3 ?: ?;

;5. @l pcrcnfnlgrcils

?4

;7. ;=. ;?.

322 32: 324

42. 43. 4:. 4;. 44. 46. 45.

Gfliftréc c`cnétokc Ru`tls y eogurcs gfliïtrokcs f` u` pnc`l kl` u` sostfic df fhfs kcrtfsoc`ls Ru`tl ifdol df u` sfgif`tl Ru`tls f` fn o`tfrolr y f` fn fxtfrolr df eogurcs kfrrcdcs f` u` sostfic df fhfs kcrtfsoc`ls KCROTVNL ;8 ZFNCKOL@F[ _ ÃNGFJZC [ukfsol`fs Nfy df elrickoû` df u`c sukfsoû` utonozc`dl nf`guchf `cturcn, tcjuncr y cngfjrcokl Zfnckol`fs Rrlplrkol`cnodcd o`vfrsc Rrlplrkol`cnodcd dorfktc f o`vfrsc KCROTVNL 48 F[TCDÉ[TOKC _ RZLJCJONODCD Kl`kfptls jãsokls Nc fstcdéstokc Kl`lkoiof`tls jãsokls fstcdéstokls Ucrocjonodcd Dostrojukoû` df erfkuf`koc

47. 47. Iãx If Ifdo dodc dcss i df rf rfsu suif 4=. Iãxoil oil ié`o é`oil il yif` rfklr rf`klrrod rodl l

332 334 33; 3:; 3:= 3;6 342 344 347

KCROTVNL 68 ZF[RVF[ ZF[RVF[TC[ TC[ 4?. 4?. Zfsp Zfspuf ufst stcs cs

362

 

Kcpétunl 3

 @øifrls

' Grupl  eFdotlrocn 

 

KL@LKOI OIOF OF@ @TL[

MCJONOD ODC CDF[ F[RFKÉEOK ÉEOKC C[

@øifrls @cturcnfs Lpfrckol`fs [uic Zfstc iuntopnokckoû` Dovosoû` Rltf`kocs

3. Kcnkuncr fxprfsol`fs `uiïrokcs cpnokc`dl fn kl`kfptl df pltf`koc y nc `ltckoû` fxpl`f`kocn. :. Zfslnvfr Zfslnvfr u`c klijo` klijo`ckoû ckoû`` df lpfrckol` lpfrckol`fs fs quf o`vlnuk o`vlnukrf rf l `l fn usl df df pcrï`tfso pcrï`tfsoss ;. Cpnokcr Cpnokcr fn cnglr cnglrotil otil df df nc dovoso dovosoû` û` f` nc rfslnu rfslnukoû` koû` df df prljnfic prljnfics. s. 4. Cpnokc Cpnokcrr nls kl`kfpt kl`kfptls ls df dovoso dovosojo jonod nodcd, cd, dovoslr dovoslr,, eck ecktlr tlr y iøntop iøntopnl nl df u` `øifrl `øifrl `cturcn f` nc rfslnukoû` df prljnfics f` doefrf`tfs kl`tfxtls. 6. Odf`to Odf`toeok eokcr cr `øifrl `øifrlss proils proils y klipu klipufst fstls. ls.

 

 

 

 

 

Klijo`ckoû` lpfrckol`fs Tflréc df `øifrls Cnglrotil df dovosoû` Dovosojonodcd Ecktlr  Iøntopnl  @øifrls proils  @øifrls  

 

df

nc

 

 

 

 

 

klipufstls  

Dfskliplsokoû`

 proic @øifrls F`tfrls F`tfrls `fgctovls Kl`kfptl df `øifrl f`tfrl Zfnckol`fs df lrdf` Zfktc `uiïrokc Ucnlr cjslnutl  @øifrl lpufstl Lpfrckol`fs, kãnkunls y fstoickol`fs [uic Zfstc Iuntopnokckoû` Dovosoû` Rltf`kocs Zcékfs Klijo`ckoû` df lpfrckol`fs  

 

 

 

 

 

5. Dfskl ipl`fr uu`` `øifrl `øKliø` ifrl klip ufstl f` dls sus ecktlrfs eckt proi ls. 7. Dfsklipl`f Ljtf`fr Ljtf`fr fn Ié`oil Iér `oil Kl iø`klipufstl Iøntopn Iøntopnl l df `øifrls `øilrfs frls proils. cpnokc cpnokc`dl `dl fn cnglrot cnglrotil il klrrfspl`dof`tf. =. Ljtf`fr Ljtf`fr fn Iãxoi Iãxoill Kliø` Kliø` Dovoslr Dovoslr df dls dls `øifrls `øifrls cpnok cpnokc`dl c`dl fn cnglrotil cnglrotil klrrfspl`dof`tf. ?. Rnc`tfcr Rnc`tfcr y rfslnvfr rfslnvfr prljnfi prljnfics cs dl`df dl`df sf utonokf utonokf fn Ié`oil Ié`oil Kliø` Kliø` Iøntop Iøntopnl nl y fn Iãxoil Kliø` Dovoslr. 32. Odf`toeokcr `øifrls f`tfrls f`tfrls `fgctovls `fgctovls f` kl`tfxtls kl`tfxtls rfcnfs. rfcnfs. 33. Rnc`tfcr y rfslnvfr lpfrckol`fs lpfrckol`fs y prljnfics prljnfics utonozc`dl utonozc`dl ncs rfnckol`fs rfnckol`fs df lrdf` f` nls `øifrls f`tfrls. 3:. Vjokcr Vjokcr `øifrls `øifrls f`tfrls f`tfrls f` nc rfktc rfktc `uiïrokc. `uiïrokc. 3;. Dftfrio`cr fn fn lpufstl y fn vcnlr cjslnutl cjslnutl df u` `øifrl f`tfrl. f`tfrl. 34. [oipnoeokcr kãnkunls ifdoc`tf ifdoc`tf fn usl df ncs prlpofdcdfs df kl`iutctovodcd y cslkoctovodcd df nc cdokoû` y iuntopnokckoû` 36. Zfslnvfr prljnfics prljnfics cpnokc`dl suics, rfstcs, rfstcs, iuntopnokckol`fs iuntopnokckol`fs y dovosol`fs df `øifrls f`tfrls. 35. Kcnkuncr pltf`kocs pltf`kocs kuyc jcsf sfc u` `øifrl `øifrl f`tfrl y fn fxpl`f`tf sfc u` `øifrl `øifrl `cturcn. 37. Vtonozcr ncs ncs prlpofdcdfs df pltf`kocs pcrc rfprfsf`tcr rfprfsf`tcr fn rfsuntcdl rfsuntcdl df lpfrckol`fs kl` pltf`kocs df ogucn jcsf. 3=. Odf`toeokcr nc rfnckoû` rfnckoû` f`trf pltf`kocs pltf`kocs y rcékfs rcékfs klil lpfrckol`fs lpfrckol`fs o`vfrscs. o`vfrscs. 3?. Kcnkuncr nc rcéz df u` `øifrl f`tfrl f`tfrl kuyl rfsuntcdl rfsuntcdl sfc f`tfrl. f`tfrl. :2. Kcnkun Kcnkuncr cr rfs rfsunt untcdl cdlss df lpfrck lpfrckol` ol`fs fs kl` `øifrl `øifrlss f`t f`tfrl frlss f` fxprfs fxprfsol` ol`fs fs quf o`klrplrf` nc klijo`ckoû` df lpfrckol`fs kl` pcrï`tfsos l so` fnnls. :3. Zfslnvfr prljnfics prljnfics f` nls quf sf cpnoquf` cpnoquf` ncs lpfrckol`fs kl` `øifrls f`tfrls. f`tfrls.

 

 

 

 

 

 

 

@ltc8 F` proicroc nc nc iuntopnokckoû` iuntopnokckoû` sf rfprfsf`tc rfprfsf`tc kl` u`c " x " , f` sfku`dcroc sf sf rfprfsf`tc kl` u`  pu`tl "  ".

Fhfipnl :  6  32

 

KCROTVNL 38 @ØIFZL[ 7

 @ØIFZL[ @CTVZCNF[ Rrljnfic o`trlduktlrol 3 Zlsy prliftf rfgcncr c Df`zfn : klnl`fs fn 3 df hunol, 4 klnl`fs fn : df hunol, = klnl`fs fn ; df hunol, 35 klnl`fs fn 4 df hunol, y csé sukfsovcif`tf mcstc klipnftcr fn ifs. Fs dfkor, kcdc déc dfn ifs, Zlsy

sf kliprliftf c rfgcncr fn dljnf df nl quf rfgcnû fn déc c`tfrolr. c) ¼Kuã`tl dfjf pcgcr Zlsy fn ;3 df Hunol< j) ¼Tf pcrfkf quf pldrã kuipnor su prlifsc<

Rrljnfic o`trlduktlrol : 3) Dftfri Dftfrio`f o`f nl quf sf slnoko slnokotc tc f` nnls ls soguof`tf soguof`tfss f`u`kocdls8 f`u`kocdls8 c) [o u`c pltf`koc fquovcnf c

32 y su jcsf fs 32 ¼Kuãn fs fn fxpl`f`tf<

j) [o u`c pltf`koc fquovcnf c

322 y su jcsf fs 32 ¼Kuãn fs fn fxpl`f`tf<

k) [o u`c pltf`koc fquovcnf c

3222 y su jcsf fs 32 ¼Kuãn fs fn fxpl`f`tf<

d) [o u`c pltf`koc fquovcnf c

:7 y su jcsf fs

f) [o u`c pltf`koc fquovcnf c

= y su jcsf fs

; ¼Kuãn fs fn fxpl`f`tf< : ¼Kuãn fs fn fxpl`f`tf<

Rrljnfic o`trlduktlrol ; Fskrojc f` elric df pltf`koc nls soguof`tfs `øifrls. 3)

4 4)

:)

?

;)

;5 

6)

4?  :7 

7)

=3 

=) 3 4 4 

5) 3:6 

?)

 e ' GZVRL FDOTLZOCN

;4; 

 

= KCROTVNL 38 @ØIFZL[

 @ØIFZL[ @CTVZCNF[ Rrljnfic o`trlduktlrol 4 Ioroci vc c nc efroc kl` su pcdrf pcrc kliprcr ncs erutcs quf nnfvcrã` klil ifrof`dc durc`tf nc sfic`c. F`kuf`trc` quf fn K@R sugofrf, pcrc fsc sfic`c, nls prfkols quf jro`dc f` nc soguof`tf tcjnc8 Rrlduktls efroc dfn cgrokuntlr V. Klnl`fs Rrlduktl V. ifdodc R. Klnl`fs Rrlduktl ifdodc Cpol vfrdf Ag Noiû` V`l 522 62 Cyltf sczû` Ag Ic`gc Ag 422 562 Cyltf tofr`l V`l Icrckuyã Ag 422 =62 Jc`c`l V`l Ilrc Ag :7 3;22 Jrûklno Ag Ifnû` Ag ;22 562 Kciltf Ag  @crc`hc V`l 3222 46 Kfjlnnc sfkc Ag  Ócipo Ag 522 =:6 Kfjlnnc trf` Ag Rcpc Ag =:6 472 Klnoenlr Klkl Kunc`trl Kmcyltf sczû` Kmcyltf tofr`l

V`l V`l Zlnnl

=22 ;22 52

Rcpcyc Rfpo`l Roóc

Ag Ag V`l

;:6 422 576

V`l

;62

Rnãtc`l

V`l

3;6

V`l

;?2

Zfilnckmc

V`l

:62

3) [o fnnls kliprc` 3 poóc, 6 aonlgrcils df pcpcyc, = `crc`hcs y ifdol aonlgrcil df

ilrcs. ¼Kuã`tl pcgcrl` f` tltcn< :) [o fnnls kliprc` u` kucrtl df aonl df ócipé, 4 kmcyltfs y dls aonls df pcpcs.

¼Kuã`tl pcgcrl` f` tltcn<

;) [o Ioroc` kliprc dls aonls y ifdol df kfjlnncs, 6 jc`c`ls, y su pcpã kliprc

pcgcr l` f` tltcn< 4 pnãtc`ls y dls aonls df pcpcs. ¼Kuã`tl pcgcrl` 4) [o kliprcrl` dls klkls, trfs rlnnls df kunc`trl y aonl trfs kucrtls df kciltf.

¼Kuã`tl pcgcrl` f` tltcn<

 

KCROTVNL 38 @ØIFZL[ ?

 @ØIFZL[ @CTVZCNF[ M38 Kcnkuncr fxprfsol`fs `uiïrokcs cpnokc`dl fn kl`kfptl df pltf`koc y nc `ltckoû` fxpl`f`kocn M:8 Zfslnvfr u`c klijo`ckoû` df lpfrckol`fs quf o`vlnukrf l `l fn usl df pcrï`tfsos

Rltf`kocs

V`c pltf`koc fs u`c fxprfsoû` ictfiãtokc klipufstc plr u`c jcsf y u` fxpl`f`tf df `  . Dl`df " fs nc jcsf quf sf tlic c  nc elric c" c

c



 

   

c. ..c    c  j ` vfkfs

klil ecktlr tc`tcs vfkfs klil u`odcdfs tof`f fn fxpl`f`tf " ` " df nc lpfrckoû` "j" , fs nc pltf`koc.

y kuyl rfsuntcdl

Fhfipnl 3  @ltckoû` fxpl`f`kocn fxpl`f`kocn

@ltckoû` dfscrrlnncdc dfscrrlnncdc

; ;

:

;

: vfkfs

Fh f i pn l :  @ltckoû` fxpl`f`kocn fxpl`f`kocn

@ltckoû` dfscrrlnncdc dfscrrlnncdc

:

:4

Fhf ip nl ;

 :





 :

 

 :

 

35 4 vfkfs

 @ltckoû` fxpl`f`kocn fxpl`f`kocn dfscrrlnncdc ;

;



 4

;

@ltckoû`

;   

;  

 

KCROTVNL 38 @ØIFZL[ ?

 @ØIFZL[ @CTVZCNF[ =  )

F  hf r ko ko l d f i l vo

6 :

34)

=6  ;

36) 32

 

5 



:)

=)

3232323232323232

: : :

323232 



;) ;; 

;



;



4) 4  4  4  4 4

 33)

5)

5 6 

7)

73 

4 ;)

: :

 

7; 

J. Fskrojf f` f` `ltck `ltckoû` oû` fxpl`f`koc fxpl`f`kocnn ncs soguof`t soguof`tfs fs `ltcko `ltckol`fs l`fs dfscrrlnncdcs. 3) 6) 6  6  6  6  6  6  6  33 5) 5  5  5 5  5 5  3  7) = =  =  =  =  =  =  = 

4

4)

3;)

:

?  )

dfscrrlnncd c ncs soguof`tfs  pltf`kocs.

:  

32  )



C. Fskr Fskroj ojcc f` `ltckoû`

:) 3; 



;vfkfs

no z c ko û ` 3

3) 3: 

6; 

6)

4

; 



32 KCROTVNL 38 @ØIFZL[

 @ØIFZL[ @CTVZCNF[ M38 Kcnkuncr fxprfsol`fs `uiïrokcs cpnokc`dl fn kl`kfptl df pltf`koc y nc `ltckoû` fxpl`f`kocn M:8 Zfslnvfr u`c klijo`ckoû` df lpfrckol`fs quf o`vlnukrf l `l fn usl df pcrï`tfsos

Rrlpofdcdfs df ncs pltf`kocs Rrlpofdcd

Kcsl gf`frcn

Fhfipnl

Iuntopnokckoû` df pltf`kocs [fnls kl`sfrvc nc df ogucn  jcsf y sfjcsf suic` fxpl`f`tfs

c   c

Dovosoû` df pltf`kocs df ogucn jcsf [f kl`sfrvc nc jcsf y sf rfstc` nls fxpl`f`tfs

c

`

`

 6=  6 32=  63=

32



c) 6

32

 6=  632  =  6:

c)

 :  

c)

()c

 c`  i

c) 6

 ci  c`i

i

Rltf` Rl tf`ko kocc df u`c pltf`k pltf`koc oc [f kl`sfrvc nc jcsf y iuntopnokc` nls fxpl`f`tfs

sf

Rltf`koc df u` prlduktl [f fnfvc kcdc ecktlr cn

()c ` i  c `

 



;

i

()c j `  c` `  j

fxpl`f`tf o`dokcdl

6 

 x    x

  : ;  6    :36



 j  y y   4 

(:  j):

j)

` 

4



Rltf`koc kl` fxpl`f`tf kfrl Tldl Tl dl `øif `øifrl rl fn fnfv fvcd cdll c nc  pltf`koc kfrl fs ogucn c u`l c

Rltf`koc kl` fxpl`f`tf u`l Tldl Tl dl `øif `øifrl rl fn fnfv fvcd cdll c nc  pltf`koc u`l fs ogucn cn iosil `øifrl.

c

2

3

 3

 c

`  x    x 



 j`   y  y 

4

j

c) 72  3 j) j)   (: ;  ;6 )32 



3 c) 4   4

;

6

j) (:  ; ) 3

(:

 

 c

;; ): 6 ;

;



6

KCROTVNL 38 @ØIFZL[ 33

Cpnoquf f` kcdc kcsl nc  prlpofdcd df ncs  pltf`kocs ([ugfrf`koc8

Fhfrkokol df ilvonozckoû` :

 @l fs `fkfscrol dfscrrlnncr nc pltf`koc )

C. Iuntopnok Iuntopnokckoû` ckoû` df pltf`kocs pltf`kocs df ogucn jcsf 3)

;)

::  

=

:)

4 ;  

6)

4

32: 32 ; 



4)

5)

;7 

324 32 

J. Dovosoû` Dovosoû` df pltf`kocs pltf`kocs df oguc ogucnn  jcsf 3)

;)

6) 32

;4 

?

32 : 

4 

:)

32 

43= 436

K. R lt 3) f : ` : ko c ; d  f u ` c :)  p ; 6

lt f `

 

=

5) 32

4)

;6 

 e ' GZVRL FDOTLZOCN

5

:

koc



6) ;)

6)

  6 ; : 

 32 4)

5

  :  4 :



5)

32

32 7

32







D. Rltf` Rltf` koc df u`  prldu ktl 3)

4

5) ;)

32

  32     32 ;  :

6)

:

:

; 

32



; : 

;

:

; 



:)



4)

  32   32 6  :

5)





:





 

F. Fnfvf c nc pltf`koc pltf`koc o`dok o`dokcdc cdc ncs soguo soguof`tfs f`tfs fxprfsol`fs 3)

; 

:   ;

;)

7

;

3

:





2  :)

6 2 

4)

 e ' GZVRL FDOTLZOCN

 

3: KCROTVNL 38 @ØIFZL[

E. Zfsufnvc Zfsufnvc nls soguof soguof`tfs `tfs prl prljnfics jnfics.. 3) Dftfrio`f so ncs soguof`tfs ceorickol`fs sl` ecnscs l vfrdcdfrcs8 c) c)  

7

:   6  7 :  6  

:

j) j)  

:   ?  ;  :  ?  

 g)  g)  

6  6  ;  4 6  ;   4

;: m) m)  

: 

 5  : :  5  

4 

6  ;  6  4  ;  

:: k)  k) 

d)  d) 

f) f) 4  :  :  =  ;  :  =   ;

 e)

o)

5  5 322  32 5  322  32

;  4    ;:  35 ;  ;:  35

;     7  6 ;  7  

6;

:) Nls trcjchcdlrfs trcjchcdlrfs df u`c kl`strukkoû` kl`strukkoû` dfjf` klnlkcr u` pfdodl df ncdronnl ncdronnls, s, so nls klnlkc` f` 35

 posls y f` kcdc posl pl`f` 35 ncdron ncdronnls nls ¼Kuã`tls ncdronnl ncdronnlss mcjrã klnlkcdl klnlkcdl f` tltcn< Fxprfsf fn rfsuntcdl f` `ltckoû` df pltf`koc. ;) Kuc`tls nojrls mcjrã f` 3: kchcs so f` kcdc kchc mcy 3: dlkf`cs Fxprfsf fn rfsuntcdl f` `ltckoû`

df pltf`koc. 4) F` u` supfrifrkcdl nls rferfskls sf vf`df` f` pcquftfs df 4 nctcs. [o fn dfpf`dof`tf cponc ncs

p cquftfs df rferfskls, ¼Kuã`tcs nctcs mcjrã m cjrã klnlkcdl nctcs f` 4 posls y f` kcdc posl pl`f kuctrl pcquftfs f` tltcn< Fxprfsf fn rfsuntcdl f` elric df pltf`koc. 6) Icréc mc prfpcrcdl 6  jc`dfhcs df fipc`cdcs, kcdc jc`dfhc tof`f

6 eoncs df fipc`cdcs kcdc

u`c ¼Kuã`tcs fipc`cdcs mcjrã f` tltcn< Fxprfsf fn rfsuntcdl f` `ltckoû` df pltf`koc. 5) Fxprfsf f` elric df pltf`koc ncs soguof`tfs sotuckol`fs8 

 @uifrl df doskls so sf kliprc` 6 pcquftfs kl` 6 kcdc u`l



 @uifrl df enlrfs so sf mckf` 37 rcils kl` 37 enlrfs kcdc u`l  @uifrl df trlzls df pc` so sf pcrtf` 5 pc`fs f` sfos pfdczls kcdc u`l



7) F` u`c urjc`ozckoû` mcy kuctrl f`trcdcs, kcdc f`trcdc tof`f 4 fskcnfrcs, kcdc fskcnfrc 4  posls, y

kcdc kcdc po posl sl 4  pufrtcs. [o f` kcdc pufrtc mcy

4  pfrsl`cs, ¼Kuã`tcs pfrsl`cs mcy f` fsc

urjc`ozckoû`< =) Dls pcrfhcs df fstudoc`tfs df sïtoil cól mc` prfpcrcdl u`c eofstc pcrc sus klipcófrls. [o kcdc

u`l nnfvc : ko`tcs df klnlrfs f` kcdc ic`l ¼Kuã`tcs ko`tcs nnfvc` f` tltcn<

 e 'GZVRL FDOTLZOCN  

KCROTVNL 38 @ØIFZL[ 3;

 @ØIFZL[ @CTVZCNF[ M38 Kcnkuncr fxprfsol`fs `uiïrokcs cpnokc`dl fn kl`kfptl df pltf`koc y nc `ltckoû` fxpl`f`kocn M:8 Zfslnvfr u`c klijo`ckoû` df lpfrckol`fs quf o`vlnukrf l `l fn usl df pcrï`tfsos

Klijo`ckoû` û` df lpfrckol`fs Klijo`cko 3) Fefktucr ncs lpfrckol`fs f`trf pcrï`tfsos    , :) Kcnkuncr ncs pltf`kocs y rcékfs. ;) Fefktucr nls prlduktls y klkof`tfs. 4) Zfcnozcr ncs suics y rfstcs.

Fhfipnl 3

Fhfipnl :

[oipnoeoquf nc fxprfsoû`

[oipnoeoquf nc fxprfsoû`

:4 =  6 ; 

7 ‛ (6 ‛ :  :) 

:4= 6



;

7 ‛   ‛  (6 ‛   ‛ 

 ;

36

4

7 ‛   ‛  (6

;  36 



:  :) 



3=

 4)  3

3=

7 3  5

Fhfipnl ;

Fhfipnl 4

[oipnoeoquf nc fxprfsoû` 6(:;  ‛ 6)‛  = ;  (7 ‛ : ;) 6(:  ‛ 6)‛= (7 ‛ : ;) 

=

5

6(= ‛ 6)‛ = (7 ‛ 5)   ;

6(;)‛ =

(3)  36  =  7

:

=





;



;:  (32 : ?)‛ ;(3: ; ): (7  ‛ ; ; :) ; (32   :   ?)‛   ;(3:   ; ): (7   ‛   ;  :)  ?

 6

 ;5

=

?(6    ?)‛  ;(;5 )=(7 ‛   ‛  5)    34

32=

3

?(34)‛  32= =  



3:5

3:5 32=  =  3=

3=  =  :5  e ' GZVRL FDOTLZOCN

 

 

3



36

[oipnoeoquf nc fxprfsoû`

 5

 



  

34 KCROTVNL 38 @ØIFZL[

Fhfrkokol df ilvonozckoû` ; C. Zfsufn Zfsufnvc vc ncs soguof soguof`tfs `tfs lpfrck lpfrckol`fs ol`fs ic`tf`of` ic`tf`of`dl dl fn lrdf` fstcjnf fstcjnfkodl kodl

=  6  

3)

 

: :)

 ‛ 3:  32 ‛ :  :   ;   ‛ 4   ‛ :

34) 34)   ;

34  ;  7

: 

 



36)

:  4  ‛ 5   3=   6? ‛ 32  6  

;) 33 5  ;

 5 7+3:  5

4)



 

37)

:6   : ;  ‛ ;   3:   7 ‛ :  :  

= ;+3=  ;

6)



3=)   7   3=)

;6 6  5  

5)

4

3?) ;

 ‛ 32     :   ‛ :  ;    :   ‛ :    ‛



4

:

4

:4  :  ;  = 34  : ‛ ;  : 

:2)   6 :2)

3= ‛ :; ‛ ;  6

=)



: 

:

:3) 6

 =  :  ;   ‛‛ :  7  ;   ; :   4 :  ‛ ;  ;  

:  : +6  :  ‛‛ 5 3:  5  ;; = ‛ ;  : 

  7  7  4  7

 32)

3: ‛32  : =

 33) 3;

6   

::)   ; ::)

: 

 ‛ 6  6 ;   4    35 ‛ :  4    :    :  ;   ‛

:;)   : :;)

4 

 ‛ ;  :    :   6   362 ‛ 3:     3:    ;  4   ‛

3:) 3:

;

;

:

;

:

:

‛ 37  ;  :4)  32 :4) 

2 

 55  :  ;;   =3   4 :   3  = :   6 :  ‛ :6  

 :4 ‛ ;  5  3;)

3;  

 e 'GZVRL FDOTLZOCN  

6

3: ‛ 32 ‛ 4  :

7)

?)

 3; 34 :  32  6;  6 

35) = 

;3‛ 6  5 

:6)

: :  35  :  =    6;   4 :   35   ? : 

6   ‛ :4   :

 e 'GZVRL FDOTLZOCN  

KCROTVNL 38 @ØIFZL[ 36

J. Zfsufnvc nls soguof`tfs prljnfics :222 plr déc kcdc u`l ¼Suï gc`c`koc 3) [o 37 fstudoc`tfs vochc` f` cutljøs tldc nc sfic`c y pcgc` ¢ :222 plr ljtof`f fn dufól dfn cutljøs so nf pcgc cn kmlefr ¢6= ion plr sfic`c<

:) [o Huc` rfkcrgc su tfnïel`l kl` ¢ :222 y rfcnozc ; nncicdcs df 4 io`utls, 6 nncicdcs df : io`utls y

ic`dc ;; if`schfs. ¼Kuã`tc rfkcrgc nf qufdc so kcdc io`utl df nncicdc kufstc ¢;2 y kcdc if`schf ¢6 <

;) Ko`kl ecionocs scnf` df pcsfl y mc` kliprcdl 5 aonls df kcr`f c ¢ 4 ion fn aonl,

¢3; ion f` fijutodls, y ¢43 ion f` rferfskls. ¼Kuã`tl dfjf pcgcr kcdc ecionoc<

V`cc iã iãqu quo` o`cc ft ftoq oquf uftc tc =6  jltfnncs plr io`utl. ¼Kuã`tcs jltfnncs ftoquftcrã f` tltcn so fstã 4) V` eu`kol`c`dl so` pcrcr durc`tf 6 décs plr sfic`c lkml mlrcs cn déc<

6) V`c eltlklpocdlrc mckf =2 klpocs kcdc io`utl. ¼Kuã`tl klstcrã` tldcs ncs eltlklpocs quf pufdf

mckfr durc`tf 6 mlrcs, so kcdc eltlklpoc kufstc ¢? kcdc u`c<

5) Kcrnls y Gcjrofnc vc` c nc nnojrfréc ojrfréc Kcrnls kliprc : ncpokfrls f` ¢?2 y u` elndfr f` ¢46 y Gcjrofnc

kliprc u` kucdfr`l f` ¢462 y trfs plstcnfs c ¢:2 kcdc u`c. ¼Kuã`tl do`frl pcgcrl` f`trf nls dls<

7) V`ls fstudoc`tfs dfkodf` rfcnozcr u`c cktovodcd pcrc ljtf`fr do`frl pcrc fn grupl plr nl quf

kliprc` 42 kmlklnctfs f` ¢;522 y nls vf`df` c ¢3;6 kcdc u`l. ¼Suï gc`c`koc ljtf`drã` plr nc vf`tc df tldls nls kmlklnctfs<

 e ' GZVRL FDOTLZOCN  

35 KCROTVNL 38 @ØIFZL[

 TFLZÉC DF @ØIFZL[ Rrljnfic o`trlduktlrol 3 Dl` Ic`ufn vc c pl`fr kfrãiokc f` fn posl df u`c mcjotckoû` quf iodf 4 iftrl iftrlss plr ; iftrls, ncs qu f fn ncdl icylr icylr df nc  pofzcs df kfrãiokc iodf` ;2 ki plr 36 ki . [f vc` c klnlkcr df elric tcn quf nlsftc sfc pcrcnfnc cn ncdl icylr df nc mcjotckoû`.

Ncs pofzcs df kfrãiokc pufdf` klrtcrsf pcrc quf f`kchf` f` nls fxtrfils df kcdc eonc df fnncs. Dl` Ic`ufn Ic` ufn nf dol ncs doi doif`so f`sol`f l`fss c su moh mohll y ïstf kliprû 3;6  pofzcs df kfrãiokc. [o `l sf quofjrc `o`gu`c. 3) ¼Nf cnkc`zcrã` fstcs pofzcs df kfrãiokc c dl` Ic`ufn< :) ¼Nf sljrcrã`