Matemáticas 2º RIEB Alumno 2011-2012

8/6/2019 Matemticas 2 RIEB Alumno 2011-2012

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Liphlpjmi}

]hgxe`ag

ri`a


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Liphlpjmi}% ]hgxeà griàxh `h}irrannià var ni @jrhmmje Ghehrin `h Liphrjinh} H`xmipjsa} "@GLH*.`h ni ]xo}hmrhpiri `h H`xmimje O}jmi. ]hmrhpiri `h H`xmimje Vonjmi%

]hmrhpiri `h H`xmimje Vonjmi

Inae}a Nxdiloja Jritoin

]xo}hmrhpiri `h H`xmimje O}jmiDa} Chreieà Gaetnht ]embht

@jrhmmje Ghehrin `h Liphrjinh} H`xmipjsa}Liri H`jpb Ohren`ht _hzh}

Maar`jeimje pmejma,vhìggjmiLiri Mrj}pjei LIrpeht Lhrmià. Iei Njnji _alhraStyxht. Inhj} Gaetnh} @xntij`h}

Ixparh}

Dh}} Liexhn Bhree`ht ]apa. Smpar Liexhn GirmiLaeph}. @jiei Kirjei Bhree`ht Mi}pra. Hnsji

Vhrrx}yxi Ljla. Ljgxhn eghn Nhe Bhree`ht.Vjnir @aeid Mi}pjnna Insirià. H`jpb Styxht Timiri}.Inli _a}i Miepe Nadhra. Liri Phrh}i A}arja Girmi

_hsj}je pmejma,vhìggjmi

eghn @iejhn sjni Lxdjmi. @iejhni I}hrhp ArpjtLirpjeht. Lirgirjpi ]apa Lh`jei

I}h}arh}

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Inhdie`ra Varpjnni `h Oxhe. Viona Lirpeht Natiì

Mxjìà h`jparjin

H`wje _adi} Giloai. Mjpninj Zimiviepnj ]hrsjeLirpeht

Vra`xmmje h`jparjin

Lirpe Igxjnir Ginnhga}

Carlimje

Liri hn ]igrirja sjni Lirmjin

Varpiì@j}ha `h manhmmje4 Mirna} VinnhjraJnx}primje h varpiì4 _ama Vi`jnni

Vrjlhri h`jmje. ?696]hgxeì h`jmje. ?699 "mjmna h}manir ?699,?69?*

@%_% ]hmrhpiri `h H`xmimje Vonjmi. ?699Irghepjei ?2. Mhepra.636?6. Ljma. @%C%

J]OE4 :72,367,03:,

Jlvrh}a he Ljma@j}prjoxmjegripxjpi,Vrabjoj@i}xshepi

]hrsjmja} h`jparjinh} "?696*Mbiepj H`jparh}

@j}ha z `jigrilimje

Igx}pe Itxhni `h ni Mxhsi

Jnx}primje

]iepjiga _a}inh}. Hnsji Nhpjmji Glht _a`rgxht.Criemj}ma @h Ieì. Mba Vi`jnni. Bhrheji Gaetnht

Jmaeagrici

Herjyxh Lirpeht. Irlieà Insirià.Irmbjsa Jmaeagrcma @GLH! ]HV

Igri`hmjljhepa}Ni ]hmrhpiri `h H`xmimje Vonjmi igri`hmh i na} l} `h 06 ?20 lih}pra}

z lih}pri}. i ni} ixparjì`h} h`xmipjsi} `h paà hn vi}. in ]je`jmipaEimjaein `h Prioidiàrh} `h ni H`xmimje. i hvhrpa} imi`ljma}. i na}Maar`jeiàrh} H}pipinh} `h I}h}ari z ]hgxjljhepa viri ni Irpjmxnimje`h ni H`xmimje O}jmi. i na} Maar`jeiàrh} H}pipinh} `h I}h}ari z]hgxjljhepa viri ni _harli `h ni H`xmimje Vrjlirji. i laejparh}.i}h}arh} z àmheph} `h h}mxhni} earlinh}. var manioarir he ni rhsj}je`h ni} `jhrheph} shr}jaeh} `h na} njora} `h phpa nnhsiì i mioa `xriephni} Dareiì} Eimjaeinh} z H}pipinh} `h Hvnarimje `h na} Liphrjinh}H`xmipjsa} z ni} _hxejaeh} _hgjaeinh}. rhinjtiì} he ?662 z ?66:% I}mala i ni @jrhmmje Ghehrin `h H`xmimje Je`ghei z @jrhmmje Ghehrin `h@h}irranna `h ni Gh}pje h Jeeasimje H`xmipjsi%

Ni ]HV hpjhe`h }x xe h}vhmjin igri`hmjljhepa i ni Argiejtimje `hH}pià} Johrailhrjmiea} viri ni H`xmimje. ni Mjhemji z ni Mxnpxri "AHJ* z inMhepra `h Jesh}pjgimje z `h H}px`ja} Isietià} `hn Je}pjpxpa VanjpmejmaEimjaein var }x virpjmjvimje he hn `h}irranna `h h}pi h`jmje% I} malai ni @jrhmmje Ghehrin `h @h}irranna Mxrrjmxnir `h ni ]xo}hmrhpiri `hH`xmimje O}jmi var biohr ixparjtià viri h}ph njora hn x}a `h ingxei}vravxh}pi} h j`hi} `h liphrjinh} hnioarià} var }pi%

Piloje }h igri`hmh hn ivaza `h ni} }jgxjheph} je}pjpxmjaeh}4Xejshr}jì` Eimjaein Ixpeali `h Ljma. Mhepra `h H`xmimje zMivimjpimje viri hn @h}irranna ]x}phepionh `h ni ]hmrhpiri `hn Lh`jaIlojheph z _hmxr}a} Eipxrinh}. ]amjhì` Liphlpjmi Lhjmiei. ]% M%.]hmrhpiri `hn Prioida z Vrhsj}je ]amjin. Ljej}phrja `h H`xmimje `h ni_hvonjmi `h Mxoi% I}jlj}la. ni ]hmrhpiri `h H`xmimje Vonjmi hpjhe`h}x igri`hmjljhepa i paì} iyxhnni} vhr}aei} h je}pjpxmjaeh} yxh `hliehri `jrhmpi h je`jrhmpi maeprjoxzhrae i ni rhinjtimje `hn vrh}hephnjora `h phpa%


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yxh rhinjtiri} he hyxjva

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0909

7Jephgra na ivrhe`jà

Ao}hrsi ni jlighe z rhinjti na yxh }h ph je`jmi%

?? 90 ?0 ?3

?9

9=

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9:

?= 98 92 ?6

Miì grxva `h cjgxri} pjheh xei }injì%]je iprish}ir na}

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yxh biz he miì xea `h hnna}%He hn }jgxjheph h}vimja `h}mrjoh

mxinyxjhri `h na} prh} `h}vnitiljhepa} yxh }hgxj}ph mae hn nvjt

"vxh`h} vi}ir var hemjli h na} elhra}*%

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89 8? 8= 80 88 87 82 36

39 3? 3= 33 37 32 3: 76

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29 2= 20 23 27 22 2: :6

:9 :? := :0 :8 :3 :2 :: 966

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viri h}mxmbir l}jmi%Mala yxjhrhe she`hr 966 elhra}.hn

grxva }h jsj`j he hyxjva} z miì xea hoh she`hr 96 elhra}%

Na} elhra} yxh ea ivirhmhe he ni pioni }ae na} yxh zi }h

she`jhrae%

9%He hyxjva maeph}phe ni} vrhgxepi}%

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Mxnh} }ae na} a} elhra} yxh zi she`j hn hyxjva Gisjapi}1

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hyxjva%H}mrjoh h}a} elhra}4

Mae yx elhra phrljei hn vrjlhr oanhpa yxh miì hyxjva pjheh yxh

she`hr1

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she`hr1

PH Onayx 9z Qv669 6 %je`` 9 6 !63!99 684= V

0808

7Ixpahsinximje

Maephejà} vramh`jlhepinh}]jhlvrh na

biga

Na biga i

shmh}

@jcmjnlheph

na biga

_h}xhnsa `jchrheph} pjva} `h

vraonhli} `h }xli z rh}pi%

Jephrvrhpa ni jecarlimjevrh}hepiì he jlgheh}%

_hmaeatma yxh hn vh}a z hn pilia

`h `jchrheph} aodhpa} `hvhe`h `hn

liphrjin mae hn yxh h}pe bhmba}%

Vxhà malxejmir `h}vnitiljhepa}

`h}`h inge vxepa `hn nxgir àe`h

sjsa i pris} `h xe mrayxj}%

Maephejà} impjpx`jeinh}]jhlvrh na

biga

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shmh}

@jcmjnlheph

na biga

Mxieà prioida he hyxjva.ivrheà

`h lj} malvihra}%

Mxieà prioida he hyxjva.hchmpa

lhdar ni} ma}i} yxh }j ni} nnhsa i

mioa je`jsj`xinlheph%

He ni} mi}jnni} marrh}vae`jheph}.lirmi mae xei vinali "* na

yxh lhdar rhcnhdh na yxh vjhe}a%

PH Onayx 9z Qv669 6 %je`` 08 =6!68!99 63466 V

0=0=

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maeamjljhepa} ivrhe`j a} he hn onayxh%

Je}prxmmjaeh}%Hemjhrri ni nhpri yxh marrh}vaeì i ni rh}vxh}pimarrhmpi%

He hn }jgxjheph h}yxhli h}pe rhvrh}hepià} na} inxlea} h

}hgxeà grià yxh carlie hn mara h ni h}mxhni%Na} h manar

shr`h }ae hn grxva I. na} itxnh} hn O z na} ilirjnna} hn M%

9% Mxepa} inxlea} marrh}vae`he in grxva I z in M1

i* 3 z 92 o*3 z 9? m* 9? z 92 `* 92 z ?0

?% Mxepa} inxlea} biz he hn mara1

i*9? o* 92 m* ?0 `* =3

=% ]h yxjhrh yxh he hn mara bizi ni lj}li miepjì` `h inxlea} `h

na} grxva} M z O% Mxepa} inxlea} hn M }h pjhehe yxh igrhgir1

i* 3 o* 9? m* 92 `* ?0

0% Viri yxh bizi 96 inxlea} hn grxva I.mxepa} inxlea} cinpie1

i* 0 o* = m* ? `* 9

PH Onayx 9z Qv669 6 %je`` 0= =6!68!99 6848 V


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Miì nhmmje jemnxzh4

Ingxei} }hmmjaeh}4

Piloje hemaeprir} xe jmaea yxh je`jmi yxh px njora

pjheh liphrjin rhmarpionh in cjein `hn njora%

@jsjrphph z ivrhe`h mae px njora `h Liphlpjmi})

@ipa jephrh}ieph

Yxh ph lxh}pri ma}i} mxrja}i}

z i shmh} vama maeamjì}%

_hpa

Mae vraonhli} jephrh}ieph}

yxh ph bire vhe}ir%

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ilvnh} z hdhrmjph} px}

maeamjljhepa}% Hn jmaea yxh

na} `j}pjegxh ph rhmxhrì yxh

ni o}yxhì he Jephrehp ni

rhinjmh} mae xe i`xnpa%

Na yxh maeatma

Mae impjsjì`h} viri yxh

rhmxhr`h} maeamjljhepa}

i`yxjrjà}%

Hdhrmjmja} mae na} mxinh}

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h}priphgji} viri ìrnh}

}anxmje%Vraonhli} rhnimjaeià}

mae ni sjì `jirji%

908

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Mxepa lj`h ni oinnhei itxn1

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Hvnjmi px} rh}vxh}pi}%

Yx iejlin vh}i lhea} yxh ni armi1

Mxepa} kjnagrila} vh}i he vralh`ja xe hnhcieph1

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Mxn `h na} iejlinh} rhgj}prià} he ni pioni h} hn l}

vh}ià1 Z hn yxh vh}i lhea}1

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ia}1

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ia}1

PH Onayx =z0Qv626 98=%je`` 908 =6!68!99 63468 V

9898

9% _iyxhn cxh i xe milvilhepa he hn h}pià `h Gxhrrhra z

sj}jp xe mrji`hra h parpxgi} lirjei}. àe`h izx` i njohrir

i ni} mri}% Nh hvnjmirae yxh i} }h vxh`h }insir xei `h ni}

h}vhmjh} `h iejlinh} lhjmiei} he vhnjgra `h `h}ivirhmhr%

Viri maepir.igrxv ni} parpxgi} yxh biz he hn mrji`hra%

Mxepi} parpxgi} biz he hn mrji`hra1

Yx bjmj}ph viri }iohr mxepi} bioi1

@ipa jephrh}iephXei parpxgi ni` i`xnpi nnhgi i vh}ir bi}pi386 kjnagrila}%Ni} bhlori} i`xnpi} nnhgiei vaehr 966 bxhsa} a l}; }x jemxoimje`xri `h 86 i 76 ì}%

PH Onayx 9z Qv669 6 %je`` 98 =6!68!99 63460 V

:

= 3? ?3 =8 8

8 ?7 =? 2= 00 := 3? 80 ?

? ?8 33 70 8

:

]jgejcjmià z x}a h na} elhra}

79

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@h shr`h.na} mrmxna} yxh phegie hn lj}la`gjpa z yxh }xlhe 93%

@h itxn.na} yxh phegie hn lj}la gjpa z yxh }xlhe =6% @h ilirjnna.na} yxh phegie hn lj}la gjpa z yxh }xlhe 98%

Elhra `h bxhsa}he hn ginnjehra

Elhra} eipxrinh}

_h}xhnshvraonhli}%

Ghrirà cxh h simimjaeh} in riemba h }x} ioxhna}% Nh gx}p

sj}jpir hn ginnjehra paà} na} i} z maepir na} bxhsa} yxh

vx}jhrae ni} ginnjei}%

9%He hyxjva}.ao}hrshe hn ginnjehra h ni vgjei iephrjar zmaeph}phe ni} vrhgxepi}%

Mxepa} bxhsa} biz he hn ginnjehra1

]j Ghrirà rhmagj 2 bxhsa} viri hn h}izxea.mxepa}

bxhsa} yxhìrae1

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Mxepa} manam he miì oan}i1

Malvirhe }x} rh}vxh}pi} z vramh`jljhepa} mae na} h apra

hyxjva z h}mroiena} hepra hn rhmxi`ra%

PH Onayx 9zQv6696 %je ` =6 !68!99 68 482 V

9292

9%He virhdi}.ao}hrshe ni jnx}primje h ni vgjei iephrjar zmaeph}phe ni} vrhgxepi}%

Lirgirjpi vig in she`hàr 98 vh}a}.mxepa}

z mxnh} vhmh} vxà malvrir1

Ghrirà pjheh ?8 vh}a}%Nh inmietir hn jehra viri xe vht

ehe.xe gxvvz z xe ohpi1

Var yx1

Mla aopxsjhrae ni rh}vxh}pi i ni vrhgxepi iephrjar1

Malvirhe }x} rh}xnpià} mae na} h apri virhdi%

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Mxepa hoh} vigir var mxipra vhmh} lannz1

Mxepa `hoh} vigir var xe vht mhori z à} vhmh} ohpi1

Mxepa pjheh} yxh vigir var prh} oaph} `h injlhepa1

]j malvri} xe vht ohpi z ph }aorie 98 vh}a}.mxepa jehra

phei}1

Vrhgxephe i apra} h }x} malvihra} mxnh} }ae }x} rh}xnpià};

he mi}a h yxh phegie rh}vxh}pi} jchrheph}.hvnjyxhe mla

ni} aopxsjhrae z.mae izxì h }x vrach}ar.`hmjìe mxn h} ni

marrhmpi%

Vgjei}:,96

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PH Onayx 9z Qv669 6 %je`` 92 =6!68!99 6346= V


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V r h } h e p i m j e % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % =Maeamh px njora % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 0

Onayxh JIvrhe`jtidh} h}vhrià} % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 2 9 Elhra} h bxhsa} he hn ginnjehra % % % % % % % % % % % % % % % % % % % % % % % % % % % % : ? Ni rjci z ni} rhgxnirjì`h} h na} elhra}% % % % % % % % % % % % % % % % % % % % % 99 = Manhmmjaeh} `h aodhpa} % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 90 0 Igrhga. yxjpa z malvira% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 97 8 ]xli} z rh}pi} viri malvnhpir i 96% % % % % % % % % % % % % % % % % % % % % % % % % % % 9: 3 Vniea} a mxrsa}1% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?? 7 _hmarrjà} % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?8 2 Yx vh}i l}1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?2 : Yx xri l}1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % =9 96 Mni}jcjma. ar`hea z argiejta aodhpa} % % % % % % % % % % % % % % % % % % % % % % % % % % % =0 99 _hxejla} ipa}% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % =7

Jephgra na ivrhe`jà % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 09Hsinximje % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 0=I x p a h s i n x i m j e % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %08

Onayxh JJIvrhe`jtidh} h}vhrià} % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 03

9? Mxepi} hmhei} }ae1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %07

9= Yx elhra h}1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 86 90 Mxhepi h 96 he 96 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 80 98 I h}malvaehr elhra})% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 82 93 Mxepa lh }aor1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 39 97 Cjgxri} viri }hnnir % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 30 92 H} vniei ni miri1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 37 9: Yx lh jmh ni jlighe1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 76 ?6 _hvrh}hepimjaeh} gricjmi}% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 7=

Jephgra na ivrhe`jà % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 78Hsinximje % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 72I x p a h s i n x i m j e % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %7:

Onayxh JJJIvrhe`jtidh} h}vhrià} % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 26 ?9 Yx elhra }h carli1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 29 ?? Yx elhra} cinpie1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 28 ?= Mxepi} cjgxri} }ae1 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 2:

?0 Hn lj}la }xlieà% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % :9

Je`jmh


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Ivrhe`jtidh} h}vhrià}

@hphrljeinimir`jeinjì``hmanhmmjaeh}

rhvrh}hepiì}grcjmilheph%

_h}xhnshvraonhli}`h}xlizrh}pimae`j}pjepa}

}jgejcjmià}%

Minmxnilhepinlheph}xli}zrh}pi}maeelhra}

`hn9in96%

Malxejmi`h}vnitiljhepa}arinlhephaipris}

`hxemrayxj}%

_hnimjaeihnvh}azhnpilia`hà}al}aodhpa}.

}hie}pa}`hnlj}laliphrjinaea%

ayxhJ


11/210

:

= 3? ?3 =8 8

8 ?7 =? 2= 0

0 := 3? 80 ?

? ?8 33 70 8

:

]jgejcjmiàzx}a`hna}elhra}

79

Na yxh maeatma% Ao}hrsi na} elhra} yxh bizhe na} mrmxna} z manarina} `h imxhrà mae nayxh }h ph je`jmi% @h shr`h. na} mrmxna} yxh phegie hn lj}la

`gjpa z yxh }xlhe 93% @h itxn. na} yxh phegie hn lj}la `gjpa z yxh }xlhe =6% @h ilirjnna. na} yxh phegie hn lj}la `gjpa z yxh }xlhe 98%

Elhra `h bxhsa}

he hn ginnjehra

Elhra}eipxrinh}

_h}xhnsh vraonhli}%

Ghrirà cxh `h simimjaeh} in riemba `h }x} ioxhna}% Nh gx}p

sj}jpir hn ginnjehra paà} na} ì} z maepir na} bxhsa} yxh

vx}jhrae ni} ginnjei}%

9%He hyxjva}. ao}hrshe hn ginnjehra `h ni vgjei iephrjar z

maeph}phe ni} vrhgxepi}% Mxepa} bxhsa} biz he hn ginnjehra1 ]j Ghrirà rhmagj 2 bxhsa} viri hn `h}izxea. mxepa}

bxhsa} yxhìrae1 Ghrirà gxir` na} bxhsa} yxh nh yxhìrae he ? oan}i}%

Mxepa} manam he miì oan}i1 Malvirhe }x} rh}vxh}pi} z vramh`jljhepa} mae na} `h apra

hyxjva z h}mroiena} `hepra `hn rhmxi`ra%


12/210

9696

?%Paà} na} ì} Ghrirà nnhe sirji} oan}i} mae bxhsa}% He miìxei gxir` 8 bxhsa}% Malvnhpi hn }jgxjheph mxi`ra viri }iohr

mxepi} oan}i} z mxepa} bxhsa} dxep `jirjilheph%

@i Elhra`hoan}i} Papin`hbxhsa}

Nxeh} 2 06

Lirph} 98

Ljrmanh} 3

Dxhsh} 7

Sjhreh} 86

]oià 99

@aljega 38

=%Na} ioxhna} `h Ghrirà nh `jhrae ? oan}i} mae97 `xnmh} miì xei% n ni} yxjhrh rhvirpjr i 8 iljga}%

Inmietire ni} gana}jei} viri ìrnh 8 `xnmh} i miì

eja1 Hvnjmi mla nnhgi}ph i ni rh}vxh}pi%

]j }h jemnxzh Ghrirà he ni rhvirpjmje `h `xnmh}.

mxepa} nh pamire i miì xea1

@ipa jephrh}iephXe bxhsa `h ish}prxt vh}i heprh 9%? z 9%2 kjnagrila}.z hyxjsinh ivrajliìlheph i ?0 bxhsa} `h ginnjei%


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16/210

9090

Elhra}eipxrinh}

Argiejti xei manhmmje exlhra}i. he apri} h lhearmiepjì`. viri maepirni a malvirirni%7=

]jgejcjmiàzx}a`hna}elhra}

Na yxh maeatma% H}mrjoh he hn rhmxi`ra mxepi} cjgxri} biz hemiì mi}a z. `h}vx}. maeph}pi ni} vrhgxepi}%

Manhmmjaeh}

`h aodhpa}

]j }h ar`heie na} mxi`ra} `h lizar i lhear miepjì` `h

cjgxri}. mxn rhmxi`ra h}piri he vrjlhr nxgir1

Z mxn. he npjla1


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18/210

9393

=%Carlhe hyxjva}. he miì xea lhpie sirja} aodhpa} he xeioan}i. }je `hmjr ni miepjì` `h aodhpa}. jephrmlojheni mae

apra hyxjva% Maeph}phe ni} vrhgxepi}% Mxepa} aodhpa} biz he ni oan}i1

Mla aopxsjhrae hn papin `h aodhpa}1 Biz inge apra hyxjva yxh phegi ni lj}li miepjì` `h

aodhpa} yxh hn pxza1 Mxn h} ni oan}i mae lizar miepjì` `h aodhpa}1

Vgjei}9,2

?%_hmarpi ni} pirdhpi} Mla maepir l} rvjà1% }ini malaivaza viri nnhsir i mioa ni} impjsjì`h}%

_iyxhn njohr ingxei} parpxgi} he hn lir% Viri bimhrnamae rivj`ht pal i ni} parpxgi} `h ? he ? z cxh 3 shmh} i

`hva}jpirni} he ni vnizi%

Mae izxì `h px} pirdhpi}. maeph}pi%

Mxepi} parpxgi} njohr1 Mxepa} sjidh} phe`ri yxh bimhr }j yxj}jhri njohrir

08 parpxgi} `h = he =1 Mxepi} parpxgi} njohriri }j `jhri 3 sxhnpi} nnhsieà

i ni} parpxgi} `h 8 he 81 Ibari h}mrjoh à} vrhgxepi} mala ni} iephrjarh} z

rh}xnshni}%


19/210

9797

_iyxhn nh} maep i Ghrirà. Nanjpi z Lirgirjpi }x ishepxri he hn milvilhepa

àe`h biz xe mrji`hra `h parpxgi}; h}pa na} lapjs i malvrir ingxea} vhmh}.i} yxh cxhrae in imxirja viri i`yxjrjr na ehmh}irja viri }x vhmhri%

Na yxh maeatma% @h miì manhmmje. manarhi `h itxn hn grxva `hpirdhpi} mxzi }xli h} jgxin i ?0%

Igrhga. yxjpa z malvira

]jgejcjmiàzx}a`hna}elhra} Vraonhli}i`jpjsa}Vraonhli} `h }xli z rh}pi%70

Manhmmje ?Manhmmje 9

Yx pirdhpi cinpi viri yxh he ni vrjlhri manhmmje ni }xlipapin }hi jgxin i 061

Yx pirdhpi igrhgiri} viri yxh ni }xli `h ni} à}manhmmjaeh} }hi jgxin i 966. maepieà ni pirdhpi yxh bi}

igrhgià1

Vhtohpi$8

Vhtgxvvz$96

Vhtlannz$98

Vhtmhori$96

Vhtehe$?6

Injlhepavirivht$

8

0 9? 8 : 3 0 2 3 8 = 7


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21/210

9:9:

Vgjei}9,2

Na yxh maeatma% Argiejtià} he hyxjva}xpjnjmhe ni} pirdhpi} `hn rhmarpionh4 ni} parpxgi}%

Miì dxgiàr }hnhmmjaeir xei pirdhpi `h miì

elhra `hn 9 in :% Va}phrjarlheph. paà} na}

dxgiàrh} dxepire z rhsanshre }x} pirdhpi}%

Xe jephgrieph pali paì} ni} pirdhpi} he

`h}ar`he. rhvirph 8 i miì malvihra z }h

yxhì mae hn rh}pa% Hn hemirgià `h rhvirpjr

ni} pirdhpi} pali xei `h ni} }xzi}. lhemjaei

elhra z ni lxh}pri% Na} `hl} dxgiàrh}

`hohe ox}mir heprh }x} pirdhpi} xei yxh }xlh

96 mae ni yxh la}pr }x malvihra% Hn yxh nilxh}prh vrjlhra z `jgi4 Nnhgx in 96). }h yxhì

mae iloi} pirdhpi}%

Giei hn yxh dxeph l} pirdhpi} `h}vx} `h

8 raeì}%

Mnmxnalhepin

78]xli} z rh}pi} viri

malvnhpir i 96

Vraonhli}i`jpjsa}%

Xpjnjti mnmxna} lhlarjtià} `h }xli}z rh}pi} mala malvnhlhepa} i 96%


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?=?=

9%Viri h}ph dxhga ehmh}jpire xei midi z aodhpa} mae carli`h ìà. vhnapi a pxoa. z vxh`he }hr }njà} a bxhma}% Miì

xea `h na} aodhpa} pjheh yxh heprir he ni midi `h pin liehri

yxh }h vxhì lashr njorhlheph he hn jephrjar in jemnjeirni a

ni`hirni%

Dxhgxhe he hyxjva}% Xea `h na} jephgrieph} lhphr xe aodhpa

i ni midi }je yxh na} `hl} na shie z ni mhrrir%

Var pxrea}. na} `hl} jephgrieph} lashre ni midi

}xishlheph ljhepri} ni }a}pjhehe mae iloi} liea}. z `jre

}j hn aodhpa }h `h}njti a rxhì. }j pjheh miri} vniei} a mxrsi}%

@h}vx}. joxdire he }x mxi`hrea hn aodhpa yxh }xvaehe h}p

gxirìà% Cjeinlheph. iorjre ni midi viri malvirir hn aodhpa

mae hn `joxda z nnheire ni pioni% He apri raeì. milojire `h

nxgir mae hn hemirgià `h gxirìr hn aodhpa he ni midi%

Ealorh`hnaodhpa

]h`h}njti

_xhì ]njà Bxhma

Var yx ingxea} aodhpa} }h `h}njtie1

Var yx ingxea} apra} rxhìe1


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?%_heie ingxea} `h na} aodhpa} yxh pridhrae%

Nhsiephe xei lh}i `h xe nià `h liehri yxh yxh`h

njghrilheph jemnjeiì% Manayxhe xea var xea na} aodhpa} yxh pridhrae }aorh ni

lh}i z ao}hrshe }j vhrliehmhe he }x }jpja a }j }h `h}njtie%

Yx amxrrh1 @joxdhe he }x mxi`hrea miì aodhpa z h}mrjoie ni} cri}h}

rxhì a }h `h}njti. }hge marrh}vaeì% Manayxhe ni lh}i he va}jmje earlin z sxhnsie i vaehr

na} aodhpa}% Ao}hrshe yx }xmh`h z malephena mae }x}

malvihra}% Mla manamirie xe si}a mjne`rjma he ni lh}i viri yxh ea

rxh`h1

Malvirhe }x} rh}vxh}pi} mae paà hn grxva z nnhgxhe i xei

maemnx}je%

Na}aodhpa}maemiri}mxrsi}rxhìezna}aodhpa}yxhpjhehe

miri}vniei}}na}h`h}njtieaea}hlxhshe%


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?7?7

=%Argiemhe}h he hyxjva}% Ao}hrshe ni mxi`rmxni la`hnaz plheni mala hdhlvna% He ni} apri} mxi`rmxni}

`joxdhe na yxh cinpi he hn nxgir yxh nh} marrh}vae`i%

@h}vx}. primhe hn miljea yxh xeh na} `joxda}. mala }hlxh}pri he hn la`hna%


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?2?2

Maemhvpxinjtimje

Ieinjti ni rhnimje vh}a sanlhe%Lh`jì

72Yx vh}i

l}1Na yxh maeatma% He hyxjva}. rheie aodhpa} mala nvjmh}.}imivxepi}. gali} z marmbanipi}% @h na} aodhpa} rhxejà}.palhe xe vir `h hnna} z h}pjlhe mxn vh}i l} z mxn lhea}.z rhg}prhena% He ni pioni }jgxjheph h}mrjoie }x ealorh z }x}h}pjlimjaeh}%

Ealorh

Aodhpayxh

vh}il}

Aodhpayxh

vh}ilhea}

Majemj`he paà} na} jephgrieph} `hn hyxjva he ni}

h}pjlimjaeh}1

Var yx1

9%He hyxjva}. rheie hn }jgxjheph liphrjin4 xe vina `h h}maoi. à} vnipa}lh`jiea} `h mirpe. h}pilorh z prh} oirri} `h vni}pjnjei `hn lj}la pilia%

Mae}prxzie xei oinieti mala ni `h ni jnx}primje%


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33/210

=9=9

7:Maemhvpxinjtimje

Malviri ni `xrimje `h à} a l}impjsjì`h}% Lj`h ni xrimje h xei impjsjì`

mae jchrheph} xejì`h} irojprirji}%

Lh`jì

Yx `xri

l}1Na yxh maeatma% H}pjli mxn`h ni} à} impjsjì`h} `xri l}%@h}vx} h}mrjoh px rh}vxh}pi%Hn rhmrha a ni mni}h `h

liphlpjmi}%Oiirph a `h}izxeir%

9%He hyxjva} `h prh} jephgrieph} rhinjmhe h}pi impjsjì`% He hn vipja `h nih}mxhni liryxhe à} }hglhepa} `h rhmpi virinhna} z `hn lj}la nirga mala }h

lxh}pri he ni jlighe% Xea `h x}ph`h} miljeir }aorh hn vrjlhr }hglhepa mae

vi}a} nirga}; z hn apra. }aorh hn }hgxeà }hglhepa. mae vi}a} marpa}% Hn phrmhr

jephgrieph `hn hyxjva ìr vinliì} i xe rjpla mae}pieph `h pin carli yxhmae vinliì miì xea isietir xe vi}a in lj}la pjhlva% _hgj}prhe mxepi}

vinliì} pirìe he nnhgir in hprhla `hn }hglhepa%

Yxje nnhg vrjlhra1 Var yx1 Yxje nnhg `h}vx}1 Var yx1

Mxepa pjhlva pir` miì xea1


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=?=?

?%@h liehri je`jsj`xinar`hei ni} jlgheh} `h

imxhrà mae hn lalhepa `hn

ì he yxh }h rhinjtie%

H}mrjoh xe elhra i miì

xei `h ni} jlgheh}

hlvhtieà var hn xea%

Malviri px} rh}vxh}pi} mae

px} malvihra} z malhepi

hn varyx `h px rh}vxh}pi%


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====

@ipa jephrh}iephIepjgxilheph }h lhì hnpjhlva mae rhnadh} `h igxi.irhei a `h }an%

=%He hyxjva} prijgie na} }jgxjheph} liphrjinh}4 xei oaphnni `h vn}pjma`h xe njpra a l}. xei mxohpi z vnxlaeh}% He ni oi}h `h ni oaphnni bigie

xei vhrcarimje vhyxhi%

]ingie in vipja he grxva. imxhr`he xe rhmarrjà i rhinjtir% Var hdhlvna4

iprish}ir hn vipja miljeieà z rhgrh}ir marrjheà in vxepa `h rhxeje% H}

jlvarpieph yxh miì jephgrieph `hn hyxjva nnhsh i mioa hn lj}la rhmarrjà%

Viri lh`jr ni `xrimje `h miì rhmarrjà. he hyxjva} nnhehe ni oaphnni mae igxi.

manyxheni mae hn arjcjmja bimji ioida mxorjeàna mae xe `hà% He mxiepa }ingi

hn vrjlhra `h x}ph`h}. `h}pvhena. `hdieà mihr hn igxi }aorh xei mxohpi z na

pivire `h exhsa mxieà }x malvihra bizi sxhnpa% Hepaemh}. liryxhe maevnxle hn ejshn `hn igxi yxh bi yxhìà he ni oaphnni%

_hvjpie na iephrjar mae na} `hl}

jephgrieph} z `hphrljehe yxje bjta l}

rvjà hn rhmarrjà% Yxje pir` l} pjhlva1

Mla na }xvjhrae1 ]j he nxgir `h ni oaphnni x}iri} xei miemje

viri lh`jr hn pjhlva yxh pirìe he }injr

z rhgrh}ir in }ine. mla malviriri} na}

pjhlva}1


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=0=0

796O}yxhìzargiejtimje`hnijecarlimje

Mni}jcjmi. ar`hei z `h}mrjoh manhmmjaeh}%Ienj}j}`hnijecarlimje

Mni}jcma. ar`hea

z argiejta aodhpa}Na yxh maeatma% Nnhsi in }ine `h mni}h} ingxei manhmmje yxhphegi} he px mi}i. var hdhlvna. h}pilvi}. vjh`ri} a miejmi}.heprh apra}% _hehph mae apra} malvihra} z ao}hrshe ni}manhmmjaeh}%

Mni}jcjyxhe miì xei `h imxhrà mae mxipra `jchrheph}

mirimphr}pjmi}%

H}mrjoh i maepjeximje miì xei `h ni} mirimphr}pjmi} yxh

xpjnjtirae viri mni}jcjmir ni} manhmmjaeh}%

Malvirhe mae apra hyxjva }x mni}jcjmimje% Yx apri}

mirimphr}pjmi} xpjnjtirae na} `hl} hyxjva} viri mni}jcjmir }x}

manhmmjaeh}1

@ipa jephrh}iephAo}hrsi he px njora Hvnarimje `h ni Eipxrinhti z ni]amjhì`hn Vnipa `hn ojhe malhr z shrjcjmi mla h}pemni}jcjmià} na} injlhepa}%


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=3=3

?%Ioida ivirhmhe ni} vjhti} }hviriì} `h xe ralvhmiohti}%Argiejtià} he hyxjva}. }je gjrirni}. bigie na }jgxjheph%

J`hepjcjyxhe ni} vjhti} yxh sie he ni} h}yxjei} z iephenh}hn elhra xea% Ox}yxhe ni} vjhti} yxh sie he ni arjnni `h irrjoi z iephenh}

hn elhra à}% I ni} vjhti} yxh sie he ni arjnni `h ioida iephenh} hn

elhra prh}% Ieaphe hn elhra mxipra i ni} vjhti} yxh sie he ni arjnni `h

ni `hrhmbi% Ieaphe hn elhra mjema i ni} vjhti} yxh sie he ni arjnni `h

ni jtyxjhrì% Mxepi} vjhti} yxhìrae viri ni virph `h he lh`ja1 Mae mxepi} vjhti} }h carli hn ralvhmiohti}1


39/210

=7=7

799O}yxhìzargiejtimje`hnijecarlimje

_hmavjni ipa} viri aophehr exhsi jecarlimje%Ienj}j}`hnijecarlimje

_hxejla}

ìpa}Na yxh maeatma% Vrhgxepi i mjema `h px} malvihra} yx crxpinh} gx}pi malhr he hn rhmrha% Miì sht yxh h}madie xei crxpi.ieapi xei vinali "* he ni cjni i ni yxh vhrphehmh% Vxh`h}igrhgir ealorh} `h crxpi}%

EalorhLiega Mama

Vji Vnpiea @xritea

Mxn h} ni crxpi yxh l} nh} gx}pi malhr i px} malvihra}1

Mxn h} ni crxpi yxh lhea} nh} gx}pi1

I mxepa} malvihra} nh} gx}pi ni vji1 I mxepa} malvihra} nh} gx}pi hn liega1

@ipa jephrh}iephNi} shr`xri} z crxpi} crh}mi} ph izxìe i liephehrph}iea% _hmxhrì yxh viri malhrni} `hohe h}pir nisiì}z `h}jechmpiì}%

Xei pioniea}vhrljphargiejtirni

jecarlimjeaophejìhexeihemxh}pi%


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=2=2

9% I virpjr `h ni }jgxjheph jecarlimje rh}vae`h ni} vrhgxepi}%

@hvarph}4

Cxpoan. oi}yxhpoan. ipnhpj}la. ohj}oan. sanhjoan z eipimje%

Nxgirh}4

H}mxhni. milva. mhepra `hvarpjsa. mnxo. mi}i x apra nxgir%

i* Yx `hvarph ph gx}pi l}1

o* Yx `hvarph vrimpjmi} l}1

m* @e`h vrimpjmi} malelheph h}ph `hvarph1

`* Mae yxje vrmpjmi} h}h `hvarph1

_hgj}pri na} rh}xnpi`a} `h pa`a hn grxva he ni} pioni} `h ni

}jgxjheph vgjei%


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=:=:

@ipa jephrh}iephVrimpjmir xe `hvarph prh} shmh} i ni }hliei ohehcjmjipx }inx`% Malvrxoina)

@hvarph Gx}pil} Nxgir`ae`h}hvrimpjmiCxpoan

Oi}yxhpoan

Ipnhpj}la

Ohj}oan

Sanhjoan

Eipimje

Hehngrxvamalhepheni}rh}vxh}pi}yxhaopxsjhraehenihemxh}pi%

@hphrljehena}jgxjheph4

@hvarphyxh}hvrimpjmil}% @hvarphyxhgx}pil}%

Hn`hvarphyxhgx}pil}.h}pilojehnyxh}hvrimpjmil}1

He`e`h}hvrimpjmihn`hvarphl}crhmxhephlheph1


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0909

7Jephgra na ivrhe`jà

Ao}hrsi ni jlighe z rhinjti na yxh }h ph je`jmi%

?? 90 ?0 ?3

?9

9=

?8

9:

?= 98 92 ?6

Miì grxva `h cjgxri} pjheh xei }injì% ]je iprish}ir na}

rhmpegxna} oniema}. mae px nvjt priti xe rhmarrjà viri xejr hn

rhmxi`ra mae hn elhra yxh rhvrh}heph ni miepjì` `h dxgxhph}

yxh biz he miì xea `h hnna}% He hn }jgxjheph h}vimja `h}mrjoh

mxinyxjhri `h na} prh} `h}vnitiljhepa} yxh }hgxj}ph mae hn nvjt

"vxh`h} vi}ir var hemjli `h na} elhra}*%

Ibari ivnjmir} na} maeamjljhepa} mae}prxjà} he hn onayxh%

_h}xhnsh na} vraonhli} }jgxjheph}%


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0=0=

7HsinximjeI maepjeximje rh}anshr} vraonhli} he na} yxh ivnjmir} na}

maeamjljhepa} ivrhe`jà} he hn onayxh%

Je}prxmmjaeh}% Hemjhrri ni nhpri yxh marrh}vaeì i ni rh}vxh}pi

marrhmpi%

He hn }jgxjheph h}yxhli h}pe rhvrh}hepià} na} inxlea} `h

}hgxeà grià yxh carlie hn mara `h ni h}mxhni% Na} `h manar

shr`h }ae `hn grxva I. na} itxnh} `hn O z na} ilirjnna} `hn M%

9%Mxepa} inxlea} marrh}vae`he in grxva I z in M1i* 3 z 92 o*3 z 9? m* 9? z 92 `* 92 z ?0

?%Mxepa} inxlea} biz he hn mara1

i*9? o* 92 m* ?0 `* =3

=%]h yxjhrh yxh he hn mara bizi ni lj}li miepjì` `h inxlea} `h

na} grxva} M z O% Mxepa} inxlea} `hn M }h pjhehe yxh igrhgir1

i* 3 o* 9? m* 92 `* ?0

0%Viri yxh bizi 96 inxlea} `hn grxva I. mxepa} inxlea} cinpie1

i* 0 o* = m* ? `* 9


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0000

He hn 9 `hn }jgxjheph mrayxj} }h xojmi ni mi}i `h I`rjiei z he hn =. ni `h _jmirà%

Lirpe nnhg i ni mi}i `h _jmirà z yxjhrh sj}jpir i I`rjiei. vhra _jmirà ea na

vxh`h imalviir }je hloirga. nh hvnjmi mla nnhgir%

9

?

=

8%Mxn }hri ni hvnjmimje marrhmpi yxh phe`ri yxh ìrnh _jmirà1

i* Prh} mxi`ri} in h}ph z à} bimji hn }xr%

o* @a} mxi`ri} in h}ph z à} in earph%

m* @a} mxi`ri} in h}ph z à} in }xr%

`* Mxipra mxi`ri} in h}ph z à} bimji hn earph%

Ao}hrsi ni} }jgxjheph} oinieti}%

3%Mxn aodhpa h} hn l} vh}ià1

i* Hn a}a% o* Ni nipi% m* Ni midi% `* Ni vhnapi%


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0808

7Ixpahsinximje

Maephejà}vramh`jlhepinh}]jhlvrhna

bigaNa biga i

shmh}@jcmjnlheph

na biga

_h}xhnsa `jchrheph} pjva} `hvraonhli} `h }xli z rh}pi%

Jephrvrhpa ni jecarlimjevrh}hepiì he jlgheh}%

_hmaeatma yxh hn vh}a z hn pilia`h `jchrheph} aodhpa} `hvhe`h `hn

liphrjin mae hn yxh h}pe bhmba}%

Vxhà malxejmir h}vnitiljhepa}`h}`h inge vxepa `hn nxgir àe`hsjsa i pris} `h xe mrayxj}%

Maephejà} impjpx`jeinh}]jhlvrhna

bigaNa biga i

shmh}@jcmjnlheph

na biga

Mxieà prioida he hyxjva. ivrheà

`h lj} malvihra}%

Mxieà prioida he hyxjva. hchmpalhdar ni} ma}i} yxh }j ni} nnhsa imioa je`jsj`xinlheph%

He ni} mi}jnni} marrh}vae`jheph}. lirmi mae xei vinali "* na

yxh lhdar rhcnhdh na yxh vjhe}a%


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Ivrhe`jtidh} h}vhrià}

Jephrvrhpizmalvirielhra}`hà}mjcri}%

Xpjnjtihnmnmxnalhepinvirirh}anshr}xli}`hà}mjcri}%

Malhepihj`hepjcjmimirimphr}pjmi}`hmxhrva}ghalprjma}%

_h}xhnshvraonhli}àe`hxpjnjtinioinieti%

I

OayxhJJ


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07

9%Hemjhrri mae xe manar. manhmmjaeh} `h 96 cjmbi} `hn grxva Iz mae apra manar ni} `hn grxva O% I h}pi} manhmmjaeh} `h 96

hnhlhepa} }h nh} nnili `hmhei}%

9`hmhei`hcjmbi}


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02

?%Malvnhpi ni pioni% H}mrjoh hn elhra `h `hmhei} yxh }hcarlie. ni miepjì` `h cjmbi} a hn manar yxh marrh}vaeì%

Cjmbi}Manar Itxn Larià _ada

Miepjì``hcjmbi}

: ?6 99

Miepjì``h `hmhei}

9 ? =

Malviri px} rh}xnpià} mae na} `h apra malvihra% ]j

}pa} ea majemj`he. shrjcjyxhe }x} rh}vxh}pi}%

=%He virhdi}. rh}xhnsie na} }jgxjheph} vraonhli}%

i* @jiei pjheh =0 cjmbi} z Ie`r} 0=% Mxepi} `hmhei} `h

cjmbi} pjheh miì xea1 z Yxje pjheh

l} cjmbi}1o* _aohrpa pjheh == cjmbi} z Nh}njh ?3% Ar`heirae }x} cjmbi}

carlieà `hmhei}% Yxje pjheh l} `hmhei}1

m* Laep}hrrip pjheh 08 cjmbi}. Vh`ra 80% @h}vx} `h igrxvirni}

he `hmhei}. yxje pjheh l} `hmhei}1

Yxje pjheh lhea} cjmbi}1

`* @h}vx} `h maepir }x} cjmbi} z carlir `hmhei}. Lirpepjheh 0 `hmhei} z = cjmbi} l}. Bmpar pjheh = `hmhei}

z 8 cjmbi} l}. ]jnsji 0 `hmhei} z 2 l}% ]j }h ar`heie `hn

yxh pjheh l} cjmbi} in yxh pjheh lhea}. yxje yxhì he

phrmhr nxgir1 Var yx1


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0:

He hn rhmxi`ra }jgxjheph h}mrjoie xe vramh`jljhepa viri `hphrljeir yxje

pjheh l} cjmbi} z yxje lhea}%

Viri}iohr}jxeimiepjì h}lizaryxhaprimxieàpjhehe

hnlj}laelhra`hmjcri}.ao}hrsiheni} a}miepjì`h}

hn`gjpayxhh}pinijtyxjhrì%Nimiepjì`lizar}hrni

yxhphegihn`gjpa`hlizarsinar;}jh}hnlj}la`gjpa.

malvirihn}jgxjheph`gjpa`hni`hrhmbi%

Lirpe Bmpar ]jnsji


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89

9%]jgxh ni} vj}pi}. maeph}pi ni} vrhgxepi}%

Yx elhra h}p heprh hn 76 z hn 7: z phrljei he 8% Yx elhra phrljei he = z h}p heprh 98 z =6% H}p heprh 00 z 22. h} lizar yxh 76 z phrljei he :% Yx

elhra h}1 ]ae lizarh} yxh 98. lhearh} yxh 08 z phrljeie he 7% Yx

elhra} }ae1 ]ae lhearh} yxh ::. lizarh} yxh 76 z phrljeie he 0% Yx

elhra} }ae1

?%Ao}hrsi mi`i grxva `h elhra} z ar`eina} `h lhear i lizar%

i* =2. :?. 37. 96. 0:%

o* 9:. 27. 88. 29. ?0. 03%m* 72. 9?. 08. 37. ?=. 80. :=%

`* 0:. 88. 79. 9?. 06. ??. 78. 0%


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8?

=%He virhdi}. h}mrjoie na} elhra} yxh malvnhphe mi`i }xmh}je%

Malvirhe }x} rh}xnpi`a} mae apri virhdi%

@h}mrjoie na yxh bjmjhrae viri malvnhpir ni }xmh}je 7. 9?. 97.

He yx elhra} phrljei ni }xmh}je `hn manar ilirjnna1

He yx elhra} phrljei ni }xmh}je `hn manar eiriedi1

Hn 07 carlir virph `h ni }xmh}je `hn manar ra}i1

Var yx1

Hn 77 carlir virph `h ni }xmh}je `hn manar eiriedi1

Var yx1

?7 97 9? 96 9=

2?7

37

96

97

=7


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8=

0%H}mrjoh }aorh ni nehi }j hnelhra `h ni jtyxjhrì h}

lizar. lhear a jgxin yxh hn

elhra `h ni `hrhmbi%

8%_h}xhnsh ni} avhrimjaeh} z h}mrjoh }aorh ni nehi hn }jgeai`hmxià viri je`jmir }j hn rh}xnpià `h ni }xli `h ni

jtyxjhrì h} lizar. lhear a jgxin yxh hn rh}xnpià `h ni }xli

`h ni `hrhmbi%

?= + 98 87 + 96

=2 + 96 0? + ?6

=0 + 2 : + 06

87 + =8 =6 + 2

7= + 9= 8: + 96

00 + 98 26 + ?6

?= + ?8 9= + 08

36 + 9? =2 + =0

00 + ?8 =: + =6

?3 lhear yxh 0?

2: :2

=2 ?3

80 809?8 966

930 92:

Inmalvirirà}elhra}}hvxh`hex}irna}}jgxjheph}}jgea}4

>mxieàhn`hnijtyxjhrìh}lhearyxhhn`hni`hrhmbi% 5mxieàhn`hnijtyxjhrìh}lizaryxhhn`hni`hrhmbi%


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80

Na yxh maeatma% Ao}hrsi na} sigaeh} `h xe lj}la manar;h}mrjoh }aorh ni nehi na} elhra} ar`hei`a} `h lhear i

lizar z maeph}pi%

Sigaeh} eiriedi}4

Sigaeh} itxnh}4

Sigaeh} lari`a}4

Sigaeh} ilirjnna}4

Yx apra elhra vhrphehmh i ni }xmh}je yxh }h carli maena} sigaeh} ilirjnna}1

Yx apra elhra vhrphehmh i ni }xmh}je yxh }h carli maena} sigaeh} itxnh}1

790Elhra}eipxrinh}

Vra`xmh }xmh}jaeh} arinh} z h}mrjpi}. i}mhe`heph} z`h}mhe`heph} `h 96 he 96. `h 8 he 8 z `h 966 he 966%

H}pjlimjezmnmxnalhepin

Mxhepi `h 96

he 96?:

0?

=0

:

0=

8090

00=0 90

00 ?0

?0

09

0

9:70

:0


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88

9%He hyxjva. miì jephgrieph `hoh phehr in lhea} 98 aodhpa}vhyxha} "vjh`ri} a oanjpi} `h vivhn*% X}he hn rhmarpionh4

Mla maepir l} rvjà1 z hn pionhra viri nnhsir i mioa hn

}jgxjheph dxhga%

Carlhe à} laepaeh}. hn vrjlhra mae ni} pirdhpi} `h 8 z 96.

z hn }hgxeà mae hn rh}pa% _hsxhnsie ni} pirdhpi} `h miì laepe% Var pxrea}. palire xei pirdhpi `h miì laepe% Ni}

pirdhpi} 8 z 96 nh} je`jmire `h mxepa he mxepa }h carlir

ni }xmh}je; ni apri pirdhpi nh} je`jmir i virpjr `h mxn

elhra ni malhetire% He hn pionhra manayxhe }x} 98 aodhpa}. }aorh miì elhra

yxh carlie virph `h ni }xmh}je yxh }h mrh z lhemjaehe

}pa} he sat inpi%

Jejmja

Vgjei9,2


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83

H}mrjoie he }x mxi`hrea ni} }xmh}jaeh} yxh }h sie carlieà he miì pxrea `hn

dxhga% Xpjnjmhe xe manar viri ni }xmh}je `h 8 he 8 z apra manar viri h}mrjojr ni

}xmh}je `h 96 he 96%

Nxj} }im ni} pirdhpi} 8 z =% Yx elhra} carlie ni }xmh}je1

Ie`rhi }im 96 z ?% Yx elhra} carlie ni }xmh}je1

@iejhn h}mrjoj4 2. 9=. 92. ?=. ?2. ==. =2 z 0=% Yx pirdhpi} pal `h miì laepe1

I`rjiei h}mrjoj4 ?. 7. 9?. 97. ??. ?7. =?. =7 z 0?% Yx pirdhpi} pal1

Shrejmi }im hn 8 z hn 0 z h}mrjoj4 0. :. 90. ?6. ?0. ?:. =8 z =:% @h na} elhra} yxhh}mrjoj. mxnh} ea vhrphehmhe i h}pi }xmh}je1

Njtohpb }im hn 96 z hn 7 z h}mrjoj4 7. 97. ?7. =7. 87. 27 z 967% Viri yxh ni }xmh}je

h}p marrhmpi. yx elhra} nh cinp h}mrjojr1

Xei }xmh}je h} i}mhe`heph}jna}elhra}

yxhnicarliesie`hnlhearinlizar%Hemiloja.}jna}elhra}sie`hnlizarin

lhearni}xmh}je h} `h}mhe`heph%


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87

?%H}mrjoie na} elhra} yxh carlie ni }xmh}je `h}mhe`heph% Palhe hemxhepi ni} mirimphr}pjmi} h}vhmjcjmi`i} he ni pioni%

Mirimphr}pjmi}`hni}xmh}je ]xmh}jeexlrjmiJejmji he4 @hmxepahemxepasi:2 96 he 96 :2. 22.

37 8 he 8 37. 3?.

23 96 he 96

79 96 he 96

00 8 he 8

96= 96 he 96

:: 8 he 8

=%Malvnhphe ni} }jgxjheph} }xmh}jaeh} z maeph}phe ni} vrhgxepi}%

9=

73

=7

2?

96?

92

79

07

7?

?6?

Mxnh} `h ni} }xmh}jaeh} iephrjarh} sie `h 8 he 81 z @a} `h ni} }xmh}jaeh} iephrjarh} sie `hn lizar in lhear "carli

`h}mhe`heph*. mxnh} }ae1 z @h mxepa he mxepa si ni }xmh}je h*1 `h he

i*

o*

m*

`*

h*


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82

798Elhra}eipxrinh}

Hemxhepri rh}xnpià} h }xli}xpjnjtieà jshr}a} vramh`jljhepa}%

H}pjlimjezmnmxnalhepin

Na yxh maeatma% _hmarpi na} }jgea} `hn rhmarpionh Viri }hgxjrdxgieà% Xpjnjti na} elhra} `h ni} pirdhpi} `h ni} parpxgi} z na}

}jgea} viri rhvrh}hepir }xli} yxh ph `he mala rh}xnpià 96%Vgjei 98

9%He virhdi}. niemhe xe ìà z h}mrjoie ni miepjì` `h vxepa}

}aorh ni nehi itxn; he ni apri. h}mrjoie hn elhra yxh }xliàin `h ni nehi itxn ` mala rh}xnpià hn yxh }h je`jmi viri

miì mi}a%i* QQQQQ + QQQQQ < 96

o* QQQQQ + QQQQQ < ?6

m* QQQQQ + QQQQQ < 96

`* QQQQQ + QQQQQ < ?6

h* QQQQQ + QQQQQ < 96

c* QQQQQ + QQQQQ < ?6

Malvirhe }x} rh}xnpià} mae na} `h apra} malvihra}%Aopxsjhrae na} lj}la}1 Var yx1

H}mrjoie à} }xli} `jchrheph} mxza rh}xnpià }hi jgxin i =6%

z H}mrjoie à} }xli} `jchrheph} yxh }hie jgxinh} i 86%

z

Malvirhe }x} rh}vxh}pi} mae ni} `h apra} hyxjva} z

rhcnhjaehe mla h} va}jonh aophehr xe lj}la elhra

mala rh}xnpià `h }xlir virh} `h elhra} `jchrheph}%

I `h}malvaehr

elhra})


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8:

=%Argiejtià} he hyxjva}. h}mrjoie ni} }jgxjheph} }xli} `h prh} liehri}`j}pjepi} viri yxh }h mxlvnie ni} mae`jmjaeh}4 yxh hn rh}xnpià ea

milojh z yxh hn mnmxna }h bigi l} rvjà%He ni npjli nehi h}mrjoh hn rh}xnpià%

9: + 99 < < < < =8 + ?8 < < < < =6 + 03 < < < < ?: + =2 < <

Matemáticas 2º RIEB Alumno 2011-2012

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Transcript of Matemáticas 2º RIEB Alumno 2011-2012