libro zaculeu matemática 1er. semestre
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3² Içsncm - Arupm Rgcuj`uVrnh`r s`h`str` - NA@Y
Hgt`hçtncg >
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Hgt`hçtncg >Vrnh`r s`h`str`
Y`s`rvgems tmems jms e`r`clms. Wu`eg rnaurmsgh`ot` prmlnineg jg r`prmeuccnóo tmtgj m pgrcngje` `st` hgt`rngj `eucgtnvm, pmr cugjqun`r h`enm m prmc`enhn`otm, sno jg gutmrnzgcnóo e`j NostntutmAugt`hgjt`cm e` @eucgcnóo Ygenmdóoncg, NA@Y. S`aòo grtècujm 59 e` jg Cmostntucnóo Vmjètncg e`Augt`hgjg qu` s` r`d`r` g jg gutmrèg.
© Nostntutm Augt`hgjt`cm e` @eucgcnóo Ygenmdóoncg, NA@Y.@s uog mirg prmeucneg pmr ̀ j E`pgrtgh`otm e` Y`egccnóo y Ens`÷m, pgrg ̀ j
Nostntutm Augt`hgjt`cm e` @eucgcnóo Ygenmdóoncg, NA@Y.
77 gv`oneg 765967
NSIO >1>9>47561>
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Èoenc`Èoenc ̀ ..........................................................................................................................................
¡In`ov`oneg y in`ov`onem! ..........................................................................................................
S`hgog 7Suhg y r`stg cmo oòh`rms hgygs NN ....................................................................
¡Vgrg cmh`ozgr!@st`jgs hgygs .................................................................................................................@j huoem e` jg hgt`hçtncg
7. Ouh`rgcnóo hgyg........................................................................................................................... 7.7 Cmov`rsnóo e` ouh`rgcnóo hgyg gj snst`hg e`cnhgj ............................................................. 9. Suhg cmo oòh`rms hgygs .............................................................................................................3. Y`stg cmo oòh`rms hgygs .............................................................................................................
Y`suh`o ..................................................................................................................................................Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................Ygzmoghn`otm jóancm.............................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
S`hgog 9Hujtnpjncgcnóo y envnsnóo cmo oòh`rms hgygs ...................................... 91
¡Vgrg cmh`ozgr! @j c`rm hgyg ..................................................................................................................@j huoem e` jg hgt`hçtncg
7. Hujtnpjncgcnóo cmo oòh`rms hgygs ............................................................................................9. Envnsnóo cmo oòh`rms hgygs ......................................................................................................
Y`suh`o ..................................................................................................................................................Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................Ygzmoghn`otm jóancm.............................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
NHgt`hçtncg · Èoenc`
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S`hgog 3Jóancg e` prmpmsncnmo`s ............................................................................................................
¡Vgrg cmh`ozgr! Po prmij`hg e` jóancg .............................................................................................................@j huoem e` jg hgt`hçtncg
7. Jg jóancg ............................................................................................................................................... 7.7 Jgs prmpmsncnmo`s y su r`pr`s`otgcnóo ....................................................................................... 7.9 O`agcnóo e` prmpmsncnmo`s ........................................................................................................
9. Cjgsndcgcnóo e` jgs prmpmsncnmo`s ............................................................................................................. 9.7 Vrmpmsncnóo snhpj` c`rrgeg ........................................................................................................ 9.9 Vrmpmsncnóo snhpj` gin`rtg ........................................................................................................
Y`suh`o ..........................................................................................................................................................Nov`stnau` `o jg r`e... ......................................................................................................................................
Gutmcmotrmj .....................................................................................................................................................Ganjnege e` cçjcujm h`otgj ..............................................................................................................................Ygzmoghn`otm jóancm .......................................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .........................................................................................................................
S`hgog 5 Cmo`ctnvms jóancms y tgijgs e` v`rege ............................................................ 07
¡Vgrg cmh`ozgr! Vrçctncg e` uo j`oaugb` ou`vm ..............................................................................................
@j huoem e` jg hgt`hçtncg7. Vrmpmsncnóo cmhpu`stg .....................................................................................................................9. Cmo`ctnvms jóancms ............................................................................................................................ 9.7 Cmobuocnóo2 (/ ) ................................................................................................................................ 9.9 Ensyuocnóo2 (6 ) ................................................................................................................................
9.3 Cmoencnmogj2 (↙) ..............................................................................................................................
9.5 Incmoencnmogj2 (↕) ............................................................................................................................3. Tgjmr`s e` v`rege (v, d)..........................................................................................................................
3.7 Ugijgs e` v`rege .............................................................................................................................Y`suh`o ..........................................................................................................................................................Nov`stnau` `o jg r`e... ......................................................................................................................................Gutmcmotrmj .....................................................................................................................................................Ganjnege e` cçjcujm h`otgj ..............................................................................................................................Ygzmoghn`otm jóancm .......................................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .........................................................................................................................
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S`hgog 0Y`ajgs e` jms cmo`ctnvms jóancms ..............................................................................
¡Vgrg cmh`ozgr! Vgr`bgs e` ignj` ..............................................................................................................@j huoem e` jg hgt`hçtncg
7. Y`ajgs e` jms cmo`ctnvms jóancms .............................................................................................. 7.7 Y`ajg e` jg cmobuocnóo (/ ) ....................................................................................................... 7.9 Y`ajg e` jg ensyuocnóo (6 ) ........................................................................................................
7.3 Y`ajg e`j cmoencnmogj (↙) .........................................................................................................
7.5 Y`ajg e`j incmoencnmogj (↕) ......................................................................................................Y`suh`o .................................................................................................................................................Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................
Ygzmoghn`otm jóancm ..............................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
S`hgog 4H`enegs e` ensp`rsnóo ........................................................................................................
¡Vgrg cmh`ozgr! Jg h`eng grnthîtncg .........................................................................................................@j huoem e` jg hgt`hçtncg
7. H`enegs e` ensp`rsnóo ..................................................................................................................
7.7 Ygoam m ghpjntue (Y) ........................................................................................................ 7.9 E`svngcnóo (e) ..................................................................................................................... 7.3 E`svngcnóo h`eng (EH) ........................................................................................................
Y`suh`o ..................................................................................................................................................Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................Ygzmoghn`otm jóancm ..............................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
S`hgog 1Vrmiginjnege`s ............................................................................................................................
¡Vgrg cmh`ozgr! Lnstmrng e` jg prmiginjnege ..............................................................................................@j huoem e` jg hgt`hçtncg
7. Jg prmiginjnege ............................................................................................................................9. ½Cóhm h`enhms jg prmiginjnege= ..............................................................................................
NNHgt`hçtncg · Èoenc`
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Y`suh`o ..........................................................................................................................................................Gutmcmotrmj .....................................................................................................................................................Ganjnege e` cçjcujm h`otgj ..............................................................................................................................Ygzmoghn`otm jóancm .......................................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .........................................................................................................................
S`hgog <Y`pgsm2 s`hgogs 7 g 1 ................................................................................................................
@j huoem e` jg hgt`hçtncgSuhg y r`stg cmo oòh`rms hgygs NN..........................................................................................................Hujtnpjncgcnóo y envnsnóo cmo oòh`rms hgygs .......................................................................................Jóancg e` prmpmsncnmo`s ..........................................................................................................................Cmo`ctnvms jóancms y tgijgs e` v`rege ......................................................................................................
Y`ajgs e` jms cmo`ctnvms jóancms ............................................................................................................H`enegs e` ensp`rsnóo ................................................................................................................................Vrmiginjnegè s ............................................................................................................................................Ganjnege e` cçjcujm h`otgj .........................................................................................................................
Mrn`otgcnmo`s smir` jg pru`ig pgrcngj ..............................................................................................................
S`hgog >Vrmar`snóo grnthîtncg ...................................................................................................................
¡Vgrg cmh`ozgr! Jgs dgs`s e` jg Juog .................................................................................................................@j huoem e` jg hgt`hçtncg
7. Vrmar`snóo grnthîtncg .......................................................................................................................... 7.7 @j òjtnhm tîrhnom e` uog prmar`snóo grnthîtncg ....................................................................... 7.9 @j prnh`r tîrhnom, `j oòh`rm e` tîrhnoms y jg end`r`ocng e` tîrhnoms ........................... 736 7.3 Suhg e` jms tîrhnoms `o uog prmar`snóo grnthîtncg .............................................................. 73
Y`suh`o ..........................................................................................................................................................Nov`stnau` `o jg r`e... ......................................................................................................................................
Gutmcmotrmj .....................................................................................................................................................Ganjnege e` cçjcujm h`otgj ..............................................................................................................................Ygzmoghn`otm jóancm .......................................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .........................................................................................................................
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S`hgog 76Vrmar`snóo a`mhîtrncg .......................................................................................................
¡Vgrg cmh`ozgr! Jg r`prmeuccnóo e` jgs cîjujgs ..........................................................................................@j huoem e` jg hgt`hçtncg
7. Vrmar`snóo a`mhîtrncg ................................................................................................................. 7.7 Òjtnhm tîrhnom e` uog prmar`snóo a`mhîtrncg..................................................................... 7.9 Vrnh`r tîrhnom e` uog prmar`snóo a`mhîtrncg ...................................................................... 7.3 Suhg e` jms tîrhnoms e` uog prmar`snóo ..............................................................................
Y`suh`o ..................................................................................................................................................Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................Ygzmoghn`otm jóancm ..............................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
S`hgog 77Not`rîs snhpj` .............................................................................................................................
¡Vgrg cmh`ozgr! Y`pgsm e` pmrc`otgb` .......................................................................................................@j huoem e` jg hgt`hçtncg
7. Not`rîs (n) ..................................................................................................................................... 7.7 Cçjcujm e`j not`rîs snhpj` ..................................................................................................... 7.9 Cgpntgj, tgsg y uonege e` tn`hpm...............................................................................................
Y`suh`o .................................................................................................................................................Nov`stnau` `o jg r`e... ..............................................................................................................................Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................Ygzmoghn`otm jóancm ..............................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
S`hgog 79Y`pgrtm prmpmrcnmogj ...........................................................................................................
¡Vgrg cmh`ozgr! Jms r`pr`s`otgot`s e`j pu`ijm ...........................................................................................@j huoem e` jg hgt`hçtncg
7. Y`pgrtm prmpmrcnmogj .............................................................................................................. 7.7 Y`pgrtm enr`ctgh`ot̀ prmpmrcnmogj ................................................................................... 7.9 Y`pgrtm nov`rsgh`ot` prmpmrcnmogj ..................................................................................
THgt`hçtncg · Èoenc`
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Y`suh`o ..........................................................................................................................................................Gutmcmotrmj .....................................................................................................................................................Ganjnege e` cçjcujm h`otgj ..............................................................................................................................Ygzmoghn`otm jóancm .......................................................................................................................................E`sgrrmjj` ou`vgs lginjnege`s .........................................................................................................................
S`hgog 73Y`ajg e` tr`s snhpj` y cmhpu`stg ......................................................................... 71>¡Vgrg cmh`ozgr! Y`pgsm e` jg prmpmrcnmogjnege enr`ctg ` nov`rsg ............................................................. 7
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S`hgog 70@j prnshg .........................................................................................................................................
¡Vgrg cmh`ozgr! Jg e`scmhpmsncnóo e` jg juz y `j prnshg e` O`wtmo ..................................................... 9
@j huoem e` jg hgt`hçtncg
7. @j prnshg ..................................................................................................................................... 7.7 @j`h`otms e`j prnshg...............................................................................................................
7.9 Cjgsndcgcnóo e` jms prnshgs ......................................................................................................
9. Çr`g e`j prnshg .............................................................................................................................
g. Çr`g e` jg igs` (Gi ) ...........................................................................................................
i. Çr`g jgt`rgj (Gj) .................................................................................................................
c. Çr`g tmtgj (Gt) ...................................................................................................................
3. Tmjuh`o e`j prnshg .......................................................................................................................
Y`suh`o .................................................................................................................................................
Nov`stnau` `o jg r`e... ..............................................................................................................................
Gutmcmotrmj .............................................................................................................................................
Ganjnege e` cçjcujm h`otgj ......................................................................................................................
Ygzmoghn`otm jóancm ..............................................................................................................................
E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
S`hgog 74Cu`rpms a`mhîtrncms cmhpu`stms ..........................................................................
¡Vgrg cmh`ozgr! @j hmogst`rnm e` Aj`oegjmual ..............................................................................................995
@j huoem e` jg hgt`hçtncg
7. Cu`rpms a`mhîtrncms cmhpu`stms ...............................................................................................
9. Çr`g e` cu`rpms cmhpu`stms ........................................................................................................
3. Tmjuh`o e` cu`rpms cmhpu`stms ..................................................................................................
Y`suh`o .................................................................................................................................................
Gutmcmotrmj .............................................................................................................................................Ganjnege e` cçjcujm h`otgj ......................................................................................................................
Ygzmoghn`otm jóancm ..............................................................................................................................
E`sgrrmjj` ou`vgs lginjnege`s .................................................................................................................
TNHgt`hçtncg · Èoenc`
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S`hgog 71Y`pgsm2 s`hgogs > g 74 .............................................................................................................
@j huoem e` jg hgt`hçtncgVrmar`snóo grnthîtncg ................................................................................................................................
Vrmar`snóo a`mhîtrncg ...............................................................................................................................Not`rîs snhpj` ..............................................................................................................................................Y`pgrtm prmpmrcnmogj .............................................................................................................................Y`ajg e` tr`s snhpj` y cmhpu`stg ..................................................................................................................@j cmom ....................................................................................................................................................@j prnshg ...................................................................................................................................................Cu`rpms a`mhîtrncms cmhpu`stms .............................................................................................................Ganjnege e` cçjcujm h`otgj .........................................................................................................................
Mrn`otgcnmo`s smir` jg pru`ig pgrcngj ..............................................................................................................
Cjgv`s .................................................................................................................................................94>
Inijnmargdèg.........................................................................................................................................9>0
TNNNNA@Y · Rgcuj`u
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7Hgt`hçtncg · ¡In`ov`oneg y in`ov`onem!
¡In`ov`oneg y in`ov`onem!Lmy cmotnoòg su r`cmrrnem pmr ̀ j dgscnogot` huoem e` jgs hgt`hçtncgs ̀ o ̀ j arupm Rgcuj`u.G jm jgram e` tr`notg y cugtrm s`hgogs e`sgrrmjjgrç jgs cmhp`t`ocngs hgrcgegs pmr `jCurrècujm Ogcnmogj Igs` (COI ) y qu` r`spmoe`o g `stg cmhp`t`ocng sup`rnmr2
E`sgrrmjj` su lginjnege pgrg utnjnzgr y r`jgcnmogr jms oòh`rms, susmp`rgcnmo`s içsncgs, jms sèhimjms y ̀ j rgzmoghn`otm hgt`hçtncmtgotm pgrg prmeucnr ` not`rpr`tgr enstnotms tnpms e` nodmrhgcnóo,cmhm pgrg ghpjngr su cmomcnhn`otm y gpjncgrjms g jg r`gjnege e`su vneg cmtnengog.
Got`s e` s`aunr prmduoenzgoem ̀ o jgs cmhp`t`ocngs qu` e`sgrrmjjgrç eurgot` ̀ st` g÷m e``stuenm, pjgtnqu`hms smir` jg pmrtgeg e` su jnirm. ½Wuî v`=
@j mib`tnvm `s qu` `stg nhga`o oms trgoshntg gjauogs ne`gs, s`otnhn`otms y su`÷ms qu`e`i`hms t`o`r pr`s`ot`s. Vmr `b`hpjm2
@j huoem e` jg pmrtgeg oms r`cu`reg qu` smhms pgrt` e`j pjgo`tg Un`rrg y qu` `o îj, jghgt`hçtncg ̀ s uog l`rrghn`otg qu` oms gyueg g e`scuirnr, gpr`oe`r y sgimr`gr jgs cn`ocngs,jgs grt`s y jg cujturg.
Jms oòh`rms hgygs oms r`cu`rego qu` p`rt`o`c`hms g uo pu`ijm hujtnîtoncm `not`rcujturgj, cmo uo cmomcnhn`otm hgt`hçtncm qu` e`i`hms vgjmrgr y cmos`rvgr.
Jg hgom egoem uo cjnc oms novntg g `xpjmrgr,e`scuirnr y cmhpgrtnr cmomcnhn`otms cmo `jr`stm e`j huoem g trgvîs e` not`ro`t.
Jg nhga`o e` uo arupm e` hgoms gjr`e`emre` uo cmrgzóo oms lgijg e` `stgij`c`r r` -jgcnmo`s cmo jgs p`rsmogs qu` oms rme`go.Not`rcghinghms dmrhgs e` s`otnr, p`osgr yv`r jg vneg. Jg rnqu`zg e` `stgs r`jgcnmo`sy jg hgo`rg `o qu` gpr`oe`hms g r`smj -v`r ou`strgs end`r`ocngs oms cmovn`rt`o`o h`bmr`s p`rsmogs.
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9 NA@Y · Rgcuj`u
½Cóhm gjcgozgrç `sg cmhp`t`ocng hgt`hçtncg=Oms `odmcgr`hms `o cnocm cmhp`t`ocngs `sp`cè cgs. Vgrg sgi`r sn jgs lg gjcgozgoem, `j Currècu -jm Ogcnmogj Igs` prmpmo` noencgemr`s e` jmarm , `stms crnt`rnms smo cmhm uo t`rhóh`trm qu`hne` su e`s`hp`÷m `o cgeg cmhp`t`ocng. Nr`hms gvgozgoem pgsm g pgsm.
Tgyg bçoems` quî s`ccnmo`s e`j jnirm lgc`o pmsnij` qu` ust`e e`sgrrmjj` cgeg cmhp`t`ocng qu`pr`s`otghms g cmotnougcnóo.
Cmhp`t`ocng e` argem Noencgemr e` jmarm S`ccnóo e`j jnirm
7. Vrmeuc` pgtrmo`sgrnthîtncms, gja`irgncmsy a`mhîtrncms, gpjncgoemprmpn`ege`s y r`jgcnmo`s.
7.7 Gpjncg jg dgctmrnzgcnóo e`pmjnomhnms gj snhpjn cgrdrgccnmo`s gja`irgncgs y envnenrpmjnomhnms.
7.9 Y`su`jv` prmij`hgs qu`novmjucrgo cçjcujm e` h`enegsy gpjncgcnóo e` prmpn`ege`se` aurgs pjgogs y cu`rpmssójnems.
7.3 Gpjncg jg trnamomh`trèg g jgr`smjucnóo e` prmij`hgs.
@j huoem e`jg hgt`hçtncg
Ygzmoghn`otmjóancm
Ganjnege e`cçjcujm h`otgj
E`sgrrmjj` ou`vgslginjnege`s
9. Cmostruy` hme`jmshgt`hçtncms qu` j` p`r -hnt`o jg r`pr`s`otgcnóoy goçjnsns e` r`jgcnmo`scugotntgtnvgs.
9.7 @hnt` buncnms `o enscusnmo`smdr`cn`oem grauh`otms y bustn -
cgoem sus pgsms y r`sujtgems.
9.9 Y`cmomc` jgs ne`gs hgt`hçtn -cgs gistrgctgs qu` snhimjnzg,arg cg ` not`rpr`tg.
9.3 Ptnjnzg end r̀`ot`s hîtmems ̀ ojg r`smjucnóo e` `cugcnmo`s,no`cugcnmo`s y snst`hgs e``cugcnmo`s.
@j huoem e`jg hgt`hçtncg
Ygzmoghn`otmjóancm
Ganjnege e`cçjcujm h`otgj
Gutmcmotrmj
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3Hgt`hçtncg · ¡In`ov`oneg y in`ov`onem!
Cmhp`t`ocng e` argem Noencgemr e` jmarm S`ccnóo e`j jnirm
3. Ptnjnzg jms end`r`ot s̀tnpms e` mp`rgcnmo`s ̀ o
`j cmobuotm e` oòh`rmsr`gj`s, gpjncgoem sus prm -pn`ege`s y mit`on`oemr`sujtgems cmrr`ctms.
3.7 Ptnjnzg ` cn òt`h`ot` jms end` -r`ot`s tnpms e` mp`rgcnmo`s ̀ o
`j cmobuotm e` oòh`rms r`gj`s,gpjncgoem sus prmpn`ege`s yv`rn cgoem qu` sus r`sujtgemssmo cmrr`ctms.
3.9 Ptnjnzg ` cn`ot`h`ot̀ jgscugtrm mp`rgcnmo`s içsncgs`o ̀ j cmobuotm e` oòh`rmscmhpj`bms, v`rn cgoem qu`sus r`sujtgems smo cmrr`ctms yr`pr`s`otçoemjms ̀ o ̀ j pjgomcgrt`sngom.
@j huoem e`jg hgt`hçtncg
Ygzmoghn`otmjóancm
Ganjnege e`cçjcujm h`otgj
Gutmcmotrmj
5. @hnt` buncnms r`d`r`ot̀ sg pr`auotgs qu` s` lgpjgot`gem iuscgoem,r`pr`s`otgoem ` not`r -pr`tgoem nodmrhgcnóo e`end`r`ot`s du`ot`s.
5.7 Gogjnzg cmobuotms e` egtmsgpjncgoem h`enegs e` t`o -e`ocng c`otrgj, pmsncnóo yensp`rsnóo.
5.9 Ptnjnzg cmoc`ptms prmiginjèstn-cms gj r`smjv`r prmij`hgs.
¡Vgrgcmh`ozgr!
@j huoem e`jg hgt`hçtncg
Nov`stnau` ̀ ojg r`e
Ygzmoghn`otmjóancm
E`sgrrmjj` ou`vgs
lginjnege`sGutmcmotrmj
0. Gpjncg hîtmems e` rgzm -oghn`otm, ̀ j j`oaugb` y jgsnhimjmaèg hgt`hçtncg`o jg not`rpr`tgcnóo e`sntugcnmo`s e` su ̀ otmrom.
0.7 Y`gjnzg mp`rgcnmo`s ̀ osnst`hgs end`r`ot`s gj e`cnhgjcmovnrtn`oem e` uo snst`hg gmtrm.
0.9 Vrmpmo` hmen cgcnmo`s ̀ o j̀h`bmrghn`otm e` `strgt`angs
e` r`smjucnóo e` prmij`hgs.
¡Vgrgcmh`ozgr!
@j huoem e`jg hgt`hçtncg
Ygzmoghn`otmjóancm
Ganjnege e`cçjcujm h`otgj
E`sgrrmjj` ou`vgslginjnege`s
Gutmcmotrmj
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5 NA@Y · Rgcuj`u
Cmo su `sdu`rzm, pmerç cmoqunstgr `stgs cmhp`t`ocngs g trgvîs e` tr`s tnpms e` cmot`onems2
E`cjgrgtnvms2 Jms cmot`onems e`cjgrgtnvms j` gpmrtgrço `j cmomcnhn`otm e` jmsenstnotms gsp`ctms t`órncms, cmoc`ptugj`s y cn`otèdncms e`j çr`g.
Vrmc`enh`otgj`s2 Cmhm noencg su omhir`, jms cmot`onems prmc`enhn`otgj`s s`
e`sgrrmjjgrço g igs` e` `b`rcncnms, prmc`enhn`otms m goçjnsns e` prmij`hgs `o jmscugj`s pu`eg e`hmstrgr `j emhnonm y jg pu`stg `o prçctncg e` jms cmomcnhn`otmse`cjgrgtnvms.
Gctntuenogj`s2 Jms cmot`onems gctntuenogj`s smo tmem gqu`jjm qu` tn`o` qu` v`rcmo su gctntue got` `j `stuenm y got` jg vneg, `o a`o`rgj. @o `j jnirm `ocmotrgrçgctnvnege`s y r`dj`xnmo`s smir` sntugcnmo`s cmtnengogs emoe` not`rvn`o` jg hgt` -hçtncg.
Ou`strm pjgot`ghn`otmJg hgt`hçtncg `stç pr`s`ot` `o tmegs jgs çr`gs e` jg vneg. G engrnm lgc`hms cu`otgs,pgaghms pgsgb`s, r`cninhms `j vu`jtm y h`enhms `j tn`hpm. @stg hgt`rng oms gyueg gcmhpr`oe`r `j j`oaugb` y jms cmomcnhn`otms cn`otèdncms `o a`o`rgj.
• Tgjmrgroms g omsmtrms hnshms Tgjmrgrs` g sè hnshm nhpjncg r`cmomc`r jgs lginjnege`s prmpngs y sgi`r gpr`cngr
jgs e` jms mtrms. Y`gjnzgr`hms gctnvnege`s pgrg cmhprmigr ou`strms cmomcnhn`o-tms y `ornqu`c`rjms cmo jms e` jg cmhuonege `eucgtnvg.
• Tgjmrgr g jms e`hçs Jgs ne`gs e` jms mtrms oms p`rhnt`o cmomc`r puotms e` vnstg enstnotms, ghpjngrou`strgs p`rsp`ctnvgs e` vneg y `ocmotrgr smjucnmo`s cml`r`ot`s g jg r`gjnege.Gpjncgr`hms jms cmomcnhn`otms hgt`hçtncms g sntugcnmo`s cmtnengogs e` ou`strmpgès y gpr`oe`r`hms g r`smjv`rjms r`sp`tgoem jg env`rsnege e` jms pu`ijms qu`cmovnv`o `o Augt`hgjg.
• Cmovnvnr `o smcn`ege @j cmomcnhn`otm smjm tn`o` snaondncgem sn s` gpjncg g jg r`gjnege y s` cmhpgrt`cmo jms e`hçs. Vrmpmo`hms cmot`onems y gctnvnege`s qu` j` gyuegrço g e`sg-rrmjjgr su r`spmosginjnege cnuegegog y cmov`rtnrs` `o uo ga`ot` e` cghinm `osu cmhuonege.
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4 NA@Y · Rgcuj`u
¡Vgrg cmh`ozgr!Vgrg `otrgr `o `j t`hgPo trghpmjèo gyueg g jms cjgvgenstgs g tmhgr gjturg y`otrgr cmo sugvnege `o `j gaug.
Jg s`ccnóo ¡Vgrg cmh`ozgr! oms prmpmo`2• r`cmregr cmomcnhn`otms pr`vnms,
• cmomc`r egtms curnmsms r`jgcnmogems cmo `j t`hg,
• pr`s`otgr jg vneg e` hgt`hçtncms e`stgcgems.
@stgs gctnvnege`s s`rvnrço "e` gcc`sm" y omsgyuegrço g `otrgr cmo sugvnege `o `j t`hg.
@j huoem e` jg hgt`hçtncg@j prmpósntm e` ̀ stg s`ccnóo ̀ s gpr`oe`r, prgctncgr ygpjncgr jms duoegh`otms e` jg hgt`hçtncg. Cmomc` -r`hms `sp`cngjh`ot` jms prnocnpnms e` jg jóancg, jg
`stgeèstncg, `j çja`irg y jg a`mh`trèg.
Y`su`jvg jms `b`rcncnms y r`pètgjms, gsè bgrç `o suh`hmrng jms cmoc`ptms ou`vms y j` egrç s`aurnege`o jm qu` gpr`oe`.
Ughinîo ̀ ocmotrgrç r`cugerms cmo r`cmregtmrnmsm `xpjncgcnmo`s qu` `ornqu`c`o `j cmot`onem y`spgcnms vgcèms pgrg lgc`r gomtgcnmo`s, `scrninrne`gs nhpmrtgot`s, pr`auotgs, `tc.
Gomt` sus euegs y r`sgjt` jm qu` e`i` r`cmregr m pr`stgr gt`ocnóo.
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76 NA@Y · Rgcuj`u
Jnirm, cjgs` rgengj y cèrcujm e` `stuenm¡Su `qunpm e` trgigbm!
@j jnirm, cmo s`r uog iu`og l`rrghn`otg, om jm `s tmem. Vgrg qu` ust`e gjcgoc` `j onv`j e`cmhp`t`ocng e`s`gem, ou`strm snst`hg pmo` g su enspmsncnóo2 `j jnirm, jg cjgs` rgengj y jgnovntgcnóo g pgrtncnpgr `o uo cèrcujm e` `stuenm.
• Jg cjgs` rgengj tn`o` cmhm duocnóo prnocnpgj`xpjncgr y dgcnjntgr jg cmhpr`osnóo e` jms t`hgstrgtgems `o `j jnirm.
Vu`e` `scuclgr jg cjgs` rgengj `o uog `hnsmrge` su jmcgjnege, e`scgragrjgs `o ou`strg pç -anog www.na`r.`eu.at m gequnrnrjgs `o CE `o jgcmmrenogcnóo r`anmogj.
• @j cèrcujm e` `stuenm `s `j juagrpgrg cmhpgrtnr y gpr`oe`r buotms.
Gprmv`cl` ̀ stms r`cursms y gpóy`s` ̀ o p`rsmogs e` su cmhuonege pgrg r`smjv`r sus euegs.
• @jjnirm cuhpj` cugtrm duocnmo`s2
g. U`xtm, `o `j qu` `ocu`otrg jg nodmrhgcnóo y `je`sgrrmjjm e` jms cmot`onems g `stuengr.
i. Vnzgrróo, pgrg qu` eurgot` jg cjgs` rgengjsuirgy` ne`gs nhpmrtgot`s m r`gjnc` enstnotgsgctnvnege`s.
c. Cuge`rom e` trgigbm, cmo `b`rcncnms pgrg prgc -tncgr jm gpr`oenem.
e. L`rrghn`otg e` gutm`vgjugcnóo, cugoem r` -su`jv` su gutmcmotrmj cgeg s`hgog.
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77Hgt`hçtncg · ¡In`ov`oneg y in`ov`onem!
Ou`strg h`tmemjmaèg pgsm g pgsm
Vgrg dgcnjntgr su gpr`oenzgb` y gprmv`clgr hçs y h`bmr `j `stuenm cgeg s`hgog, snag `stmspgsms. ¡Om s` sgjt` onoauom!
J`g `j cmot`onem e` jg s`hgogJ``r `j cmot`onem oms p`rhnt` t`o`r uog ne`g a`o`rgj e`j t`hg2 quî sg-i`hms, cmo quî jm r`jgcnmoghms, `tc. @st` prnh`r cmotgctm tghinîo omslgrç cg`r ̀ o jg cu`otg e`j `sdu`rzm g r`gjnzgr pgrg gpr`oe`r jm ou`vm y omspmoerç "`o moeg" pgrg jg cjgs` rgengj.
7
@scucl` jg cjgs` rgengjCmo jms 0 s`otnemsJg cjgs` rgengj `s ou`strg hg`strg. E` glè qu` `j prmarghg s` jjgh` "@jHg`strm `o Cgsg". Jgs hg`strgs y hg`strms jmcutmr`s `xpjncgo `j cmot`on-em, prmpmo`o `b`rcncnms y mtrms `b`hpjms pgrg ghpjngr `j t`hg.
9
E`spuîs e` jg cjgs` rgengj, su trgigbm p`rsmogj @stuenm y gutmcmotrmjDnogjnzgeg jg cjgs` rgengj `s `j hmh`otm e` su trgigbm p`rsmogj. Enstrniuygsu tn`hpm2 `s h`bmr uo pmcm cgeg eèg, qu` tmem jg vèsp`rg.
3
Cmosujt` sus euegsPo `stuengot` not`jna`ot` sgi` cuçoem p`enr gyuegCmosujt` jms t`hgs qu` om j` lgo qu`egem cjgrms ̀ o mtrms jnirms, ̀ o not`r-o`t, cmo dghnjngr`s m ghnams. S`aurm qu` ̀ ocmotrgrç p`rsmogs enspu`stgsg gyuegrj`.
5
Vgrtncnp` `o uo cèrcujm e` `stuenm
Gpr`oe`r buotmsVóoags` e` gcu`rem cmo mtrms ̀ stuengot`s y mragonc`o uo cèrcujm e` ̀ stu-enm. Smjncnt`o jg gyueg e` gjauog p`rsmog vmjuotgrng e` jg cmhuonege. @smj`s gyuegrç g r`smjv`r euegs y r`dmrzgr jm gpr`oenem. Ge`hçs, t`oerço jgmpmrtuonege e` not`rcghingr gpr`oenzgb`s, ne`gs y s`otnhn`otms.
Y`cu`re` qu` sn`hpr` pu`e` gcuenr g su tutmr gsnaogem.
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79 NA@Y · Rgcuj`u
½Cóhm gprmv`clgr h`bmr su `stuenm=• Iusqu` uo juagr cóhmem y cmo iu`og njuhnogcnóo. @s nhpmrtgot` qu` s`
gj`b` e`j runem y e` jgs enstrgccnmo`s.
• @jnbg uo lmrgrnm pgrg trgigbgr y `stuengr. Jg cmostgocng y jg enscnpjnog smosus h`bmr`s cmhpg÷`rgs e` `stuenm.
• J`g cmo gt`ocnóo jgs nostruccnmo`s e` jms `b`rcncnms got`s e` r`smjv`rjms.
• Cmosujt` sus euegs cmo mtrgs p`rsmogs e` su cmhuonege qu` pu`egogyuegrj`.
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7
Suhg y r`stg cmooòh`rms hgygs NN
½Wuî `ocmotrgrç `stg s`hgog=
@st`jgs hgygs
Ouh`rgcnóo hgyg
Ugijgs e` hujtnpjncgr e`j 7 gj 76
Çr`g smhir`geg e` dnaurgs a`mhîtrncgs
@stg s`hgog jmargrç2 E`scndrgr jg d`clg noscrntg `o uog `st̀ jg hgyg. Cmov`rtnr oòh`rms e`j snst`hg hgyg gj snst̀ hg e`cnhgj.
Suhgr y r`stgr oòh`rms `o ̀ j snst`hg e` ouh`rgcnóo hgyg. Vrgctncgr jg ganjnege e` cçjcujm h`otgj cmo jg hujtnpjncgcnóo. Cgjcujgr `j çr`g e` jg r`anóo smhir`geg `o dnaurgs a`mhîtrncgs. Ne`otndncgr `j ̀ j`h`otm qu` om augreg r`jgcnóo `o uog s`rn` e` dnaurgs.
73Hgt`hçtncg · S`hgog 7
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¡Vgrg cmh`ozgr!@st`jgs hgygs
Jgs `st`jgs smo hmouh`otms qu` jms gotnaums hgygs `jgimrgigo pgrgcmoh`hmrgr `v`otms nhpmrtgot`s cmhm jg jj`ageg e` uo ou`vm r`y m jgvnctmrng e` gjaòo au`rr`rm nhpmrtgot`.
Jg j`cturg e` uog `st`jg s` cmhn`ozg `o jg pgrt` sup`rnmr cmo uo ajndmnotrmeuctmrnm qu` gouocng2 ‚gquè vn`o` uog d`clg nhpmrtgot`‘. Sn`hpr` ̀ s`j hnshm, smjm cghing jg cgi`zg e`j c`otrm, qu` vgrèg s`aòo `j h`s.
Ju`am, j`y`oem e` grrnig lgcng gigbm y e` nzqun`reg g e`r`clg, cgeg ajndmr`pr`s`otg uo p`rnmem e` tn`hpm ̀ o ̀ st` mre`o2 7 igk'tuo (755 666 eègs),7 k'gtuo (1966 eègs), 7 tuo (346 eègs), 7 wnogj (96 eègs) y 7 k'no (7 eèg).Cgeg uom e` `stms ajndms jj`vg pmr e`jgot` uo oòh`rm hgyg qu` e`omtg
cuçotms p`rnmems s` cmosne`rgo `o cgeg dnjg. Sn uo ajndm om tn`o` oòh`rm,s` tmhg cmhm c`rm.
E` `stg hgo`rg jg d`clg qu` v`hms `o jg `st`jg 7 s` j`` gsè2
> igk'tuo + 70 k'gtuo + 76 tuo + 6 wnogj + 6 k'no
@stg d`clg noencg `j oòh`rm e` eègs qu` lg trgoscurrnem e`se` `j noncnm e`jg `rg Hgyg, 79 e` gamstm e` 3775 g.C.
Dnogjh`ot`, su`j`o gpgr`c`r mtrms ajndms qu` e`scrni`o egtms e`j cgj`oeg-rnm juogr, cncjms rntugj`s, omhir` e`j ou`vm smi`rgom, `tc. @j òjtnhm ajndm
e` jg `st`jg 7 `s 3 gbgw qu` noencg `j t`rc`r p`rnmem gbgw e`j cgj`oegrnme` jg cu`otg jgrag.
¡G trgigbgr!
Cmo jg nodmrhgcnóo qu` gcgig e` j``r e`scuirg jg d`clg qu` s` e`scrni` `ojg `st`jg 9. @scrnig smir` jg jèo`g `j oòh`rm qu` cmrr`spmoe` g cgeg p`rèmeme` tn`hpm. Snag `j mre`o noencgem pmr jgs jèo`gs puot`gegs.
igk'tuo + k'gtuotuo + wnogj
k'no
½Wuî d`clg `s= Huy in`o, `s `j 73 igk'tuo qu` mcurrnó `j 97 e` encn`hir`e` 9679.
@st`jg 7
n o t r m
e u c c
n ó o
@st`jg 9
75NA@Y · Rgcuj`u
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7. Ouh`rgcnóo hgygCmh`oc`hms ̀ st` ou`vm cursm r`cmregoem jg ouh`rgcnóo hgyg qu` ̀ stuenghms
`o `j arupm Ptgtjço. @stg s`hgog r`pgsgr`hms jg suhg y jg r`stg.Y`cu`re` qu` jg ouh`rgcnóo hgyg s` igsg `o uo snst`hg vna`snhgj (igs` 96) y`hpj`g tr`s sèhimjms pgrg r`pr`s`otgr tmegs jgs cgotnege`s.
• Jg cmoclg m cgpgrgzóo r`pr`s`otg ̀ j c`rm.
• @j puotm r`pr`s`otg gj uom.
• Jg igrrg lmrnzmotgj r`pr`s`otg `j cnocm.
Jms prnh`rms 7> oòh`rms smo2
8 7 9 3 5 0 4 1 < >6 7 9 3 5 0 4 1 < >
6 ! " # $ % & / ( )76 77 79 73 75 70 74 71 7< 7>
@j snst`hg e` ouh`rgcnóo hgyg, ge`hçs e` vna`snhgj, tghinîo `s pmsncnmogj.@sm qun`r` e`cnr qu` `j vgjmr e` uo oòh`rm e`p`oe` e` su pmsncnóo v`rtncgj. Jgspmsncnmo`s snau`o `jmre`o e` gigbm lgcng grrnig .
Jg tgijg snaun`ot` hu`strg jms vgjmr`s pmsncnmogj`s lgstg jg cugrtg pmsncnóo.
pmsncnóo vgjmr pmsncnmogj
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7.7 Cmov`rsnóo e` ouh`rgcnóo hgyg gj snst`hge`cnhgj
E` igs` 96 g igs` 76
@o `j arupm Ptgtjço gpr`oenhms g cmov`rtnr jms oòh`rms hgygs gj snst`hg
e`cnhgj. Jm lncnhms cmo oòh`rms qu` mcupgigo lgstg jg t`rc`rg pmsncnóo. @stgs`hgog g÷genr`hms uo onv`j hçs, mp`rgr`hms cmo oòh`rms lgstg jg cugrtgpmsncnóo. Vgrg mp`rgr e`i`hms s`aunr jms hnshms pgsms qu` gpr`oenhms.
Y`cmreîhmsjms.
• Hujtnpjncghms `j vgjmr pmsncnmogj pmr `j oòh`rm e`cnhgj qu` r`pr`s`otgjg cndrg hgyg.
• Suhghms jms r`sujtgems.
Dèb`s` `o jms `b`hpjms.
@b`rcncnm 9Cmovn`rtg jms oòh`rms hgygs g snst`hg e`cnhgj. Auè`s` pmr `j `b`hpjm.
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9. Suhg cmo oòh`rms hgygsCmhm j` noencghms ̀ o ̀ j gpgrtgem got`rnmr, ̀ stg v`z vghms g mp`rgr cmo uo onv`jhçs `o jg ouh`rgcnóo hgyg. Suhgr`hms cmo oòh`rms lgstg jg cugrtg pmsncnóo.Y`cmre`hms jms pgsms2
• @scrninr jms suhgoems `o uog tgijg `o su pmsncnóo cmrr`spmoen`ot`.• Suhgr sèhimjms naugj`s, e`se` jg prnh`rg pmsncnóo lgcng grrnig.
• Y`gjnzgr jgs trgosdmrhgcnmo`s o`c`sgrngs. Y`cu`re`2
– Cnocm puotms dmrhgo m s` cmovn`rt`o ̀ o uog igrrg ̀ o jg hnshg pmsncnóo.
– Cugtrm igrrgs dmrhgo uo puotm `o jg pmsncnóo noh`engtg sup`rnmr.
Y`dr`squ`hms ou`strg h`hmrng cmo uo `b`hpjm e` jg suhg e` ems oòh`rmslgstg jg t`rc`rg pmsncnóo cmhm vnhms `o `j arupm Ptgtjço. @stg v`z lgr`hmsjgs trgosdmrhgcnmo`s o`c`sgrngs `o jg hnshg tgijg g÷gen`oem uog cmjuhog g jg
e`r`clg.Suh`hms 9
16
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• @scrninhms jms suhgoems `o uogtgijg y suhghms jms oòh`rms `ojg cugrtg cmjuhog.
• Jms cnocm puotms s` cmovn`rt`o `ouog igrrg `o jg hnshg pmsncnóo.
T`ghms glmrg `j `b`hpjm e` uog suhg e` oòh`rms lgstg jg cugrtg pmsncnóo.Vr`st` gt`ocnóo g jgs cugtrm igrrgs qu` s` cmovn`rt`o ̀ o uo puotm ̀ o jg pmsncnóonoh`engtg sup`rnmr.
Suh`hms 0
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• @scrninhms jms suhgoems `o uogtgijg y suhghms jms oòh`rms `ojg cugrtg cmjuhog.
• Cugtrm igrrgs s` cmovn`rt`o `o uopuotm `o jg pmsncnóo noh`engtgsup`rnmr.
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T`ghms mtrm `b`hpjm.
Suh`hms 7
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• @scrninhms jms suhgoems `o uogtgijg y suhghms jms oòh`rms `ojg cugrtg cmjuhog.
• Cnocm puotms s` cmovn`rt`o `o uogigrrg `o jg hnshg pmsncnóo.
> >
7 0 5 > >
@b`rcncnm 3
Gpjnqu` `j prmc`enhn`otm qu` gpr`oenó pgrg r`smjv`r jgs suhgs cmo oòh`rms hgygs.
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• @scrnig jms suhgoems `o uog tgijg y suh`jms oòh`rms `o jg cugrtg cmjuhog.
• Cnocm puotms s` cmovn`rt`o `o uog igrrg`o jg hnshg pmsncnóo.
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• @scrnig jms suhgoems `o uog tgijg y suh`jms oòh`rms `o jg cugrtg cmjuhog.
• Cugtrm igrrgs s` cmovn`rt`o `o uo puotm`o jg pmsncnóo noh`engtg sup`rnmr.
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3. Y`stg cmo oòh`rms hgygs@j s`otnem e` jg r`stg ̀ s quntgr uog cgotnege h`omr e` mtrg hgymr. Vgrg r`stgr ̀ oouh`rgcnóo hgyg, s`aunhms jms pgsms qu` l`hms gpr`oenem. T`ghms2
• @scrninr `o uog tgijg hnou`oem y sustrg`oem.
• Y`stgr sèhimjms naugj`s `o cgeg pmsncnóo, e` gigbm lgcng grrnig.• Sn jg cgotnege e` puotms `o ̀ j hnou`oem `s h`omr qu` ̀ o `j sustrg`oem,
lgy qu` trgosdmrhgr uog igrrg `o cnocm puotms.
Cmhm `j prmc`enhn`otm `s igstgot` s`ocnjjm, `stg v`z cmh`ozgr`hms `j prnh`r`b`hpjm e` jg r`stg cmo oòh`rms lgstg jg cugrtg pmsncnóo. Dèb`s`2
Y`st`hms 3
<
54
9
4
70
–
• @scrninhms hnou`oem y sustrg`oem `ouog tgijg y r`stghms oòh`rms naugj`s`o ghigs pgrt`s.
• @scrninhms `o jg òjtnhg cmjuhog jms oò -h`rms qu` om s` `jnhnogrmo y `s` `s `jr`sujtgem.
T`ghms uo `b`hpjm e` cugoem jg cgotnege e` puotms `o `j hnou`oem `s h`omrqu` `o `j sustrg`oem. Vr`st` gt`ocnóo.
Y`st`hms 0
6
1
"
3
4
9
6
–
• @scrninhms hnou`oem y sustrg`oem `ouog tgijg. Lgy qu` trgosdmrhgr `o jms
ems onv`j`s sup`rnmr`s uog igrrg ̀ o cnocmpuotms.
• @scrninhms `o jg òjtnhg cmjuhog jms oò -h`rms qu` om s` `jnhnogrmo y `s` `s `jr`sujtgem.
Mis`rv` qu` `o jg t`rc`rg y cugrtg pmsncnóo `scrninhms cnocm puotms `o `j hn-ou`oem, ̀ o v`z e` jg igrrg lmrnzmotgj, pgrg r`stgr jg cgotnege e` puotms qu` lgy`o `j sustrg`oem.
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@b`rcncnm 5Gpjnqu` `j prmc`enhn`otm qu` gpr`oenó y r`su`jvg jgs r`stgs cmo oòh`rms hgygs qu` s` pr`s`otgo gcmotnougcnóo. Un`o` uo `b`hpjm.
6) 0
3<6
3
700
–
• @scrnig hnou`oem y sustrg`oem `o uogtgijg. Y`st` `o ghigs pgrt`s.
• @scrnig `o jg òjtnhg cmjuhog jms oòh`rmsqu` om s` ̀ jnhnogrmo y ̀ s` ̀ s ̀ j r`sujtgem.
7) %01
3
0
3
43
–
• @scrnig hnou`oem y sustrg`oem `o uogtgijg, trgosdmrhgoem uog igrrg `o cnocmpuotms pgrg r`stgr.
• @scrnig `o jg òjtnhg cmjuhog jms oòh`rmsqu` om s` ̀ jnhnogrmo y ̀ s` ̀ s ̀ j r`sujtgem.
9) 0
1
3
"
5
9
80
–
• @scrnig hnou`oem y sustrg`oem `o uogtgijg, trgosdmrhgoem uog igrrg `o cnocmpuotms pgrg r`stgr.
• @scrnig `o jg òjtnhg cmjuhog jms oòh`rmsqu` om s` ̀ jnhnogrmo y ̀ s` ̀ s ̀ j r`sujtgem.
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7. @j snst`hg e` ouh`rgcnóo hgyg s` igsg `o uo snst`hg vna`snhgj qu` utnjnzg tr`s sèhimjms pgrgr`pr`s`otgr tmegs jgs cgotnege`s.
• Jg cmoclg m cgpgrgzóo r`pr`s`otg `j c`rm.• @j puotm r`pr`s`otg ̀ j uom.
• Jg igrrg lmrnzmotgj r`pr`s`otg ̀ j cnocm.
Ge`hçs e` vna`snhgj, `j snst`hg e` ouh`rgcnóo hgyg tghinîo `s pmsncnmogj. @stm qun`r` equ` `j vgjmr e` uo oòh`rm e`p`oe` e`j juagr qu` mcupg `o jg tgijg e` pmsncnmo`s.
pmsncnóo vgjmr pmsncnmogj
5 963 8
0
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Gctnvnege 7. E`hu`str` jm gpr`oenem@scrnig jms oòh`rms hgygs `o oòh`rms e`j snst`hg e`cnhgj. Un`o` uo `b`hpjm.
6) 3 8 5) # 8 ) 1 8
9) 4 8 4) < 8 76) & 8
3) > 8 1) ! 8 77) 0 8
Gctnvnege 9. Vrgctnqu` jm gpr`oenemG. Cmovn`rtg jms oòh`rms hgygs g snst`hg e`cnhgj. Un`o` uo ̀ b`hpjm.
6) 4 6
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+ 09 37>
7) 94
6
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9) 65
1
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8
6
$
I. Y`gjnc` jgs suhgs cmo oòh`rms hgygs. Un`o` uo ̀ b`hpjm.
6) 0
9
4
0
0
9
3
1
+
7) 3
9
0
8
7
0
7
5
+
7 0 1 "
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9) 7
6
3
5
9
3+
3) 6
8
"
0
7
#+
566
967
566
967
5) 5
8
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%
4
%
0
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9
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3
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¡G pmo`rs` `o dmrhg! Y`cup`r` jg v`jmcnege e` cçjcujm h`otgj. @scrnig `j r`sujtgem e` jgs hujtnpjncgcnmo`s jm hçs rçpnem qu` pu`eg, om utnjnc` cgjcujgemrg on tgijgs.
G.6) 4 x 3 8
7) 9 x 5 8
9) 1 x 0 8
3) 5 x > 8
5) 3 x < 8
0) 4 x 9 8
4) > x 4 8
1) < x 1 8
) 4 x 5 8
76) 3 x 0 8
77) 9 x > 8
79) 5 x 3 8
73) 1 x 7 8
75) > x 0 8
70) 0 x 1 8
74) 1 x 1 8
71) 5 x < 8
7 x > 8
7>) < x 9 8
96) 0 x 4 8
97) 5 x 5 8
99) 3 x 1 8
93) > x 3 8
7<
6) 4 x 8 95
7) 3 x 8 97
9) > x 8 91
3) 1 x 8 9<
5) 0 x 8 36
0) < x 8 56
4) 5 x 8 34
1) 3 x 8 95
) < x 8 45
76) > x 8 34
77) 5 x 8 74
79) 4 x 8 7<
73) > x 8 >
75) 1 x 8 1
70) > x 8 x 8 50
97) 9 x 8 74
99) 0 x 8 30
93) < x 8 5<
I.5
6) x 1 8 30
7) x 4 8 34
9) x 5 8 963) x < 8 5<
5) x 5 8 95
0) x 0 8 50
4) x > 8 34
1) x 1 8 04
8 91
>) x 3 8 79
76) x > 8 8 05
99) x 4 8 46
93) x 7 8 06
C.0
95NA@Y · Rgcuj`u
Ganjnege e` cçjcujm h`otgj
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G. Cgjcuj`hms `j çr`g e` dnaurgs smhir`gegs . @st` tnpm e` `b`rcncnms smo cmhuo`s `o jgs prue`j H NO@EPC. Y`smjv`rjgs j` gyuegrç g e`sgrrmjjgr su lginjnege `spgcngj. J`g jg nodmrhgcnóo y mis`r -v` cmo gt`ocnóo jg dnaurg. Ju`am, r`spmoeg g jg pr`auotg.
Sn `j cugergem e` jg dnaurg hne` 5 chpmr jgem, ½cuçotm hne` `j çr`g e` jgr`anóo smhir`geg=
Vgrg r`smjv`r `j prmij`hg snag `stms pgsms2
7) @scrnig cuçotms trnçoaujms dmrhgo jg dnaurg.
9) @scrnig cuçotms trnçoaujms `stço smhir`gems.3) Cgjcuj` jg rgzóo `otr` `j oòh`rm e` trnçoaujms smhir`gems y `j tmtgj e` trnçoaujms . (@j
t`hg e` rgzmo`s y prmpmrcnmo`s jm `stuenó `o jg s`hgog 9> e`j arupm Wunrnauç). @xpr`s` sur`spu`stg cmhm uog drgccnóo y snhpjndèqu`jg lgstg su hèonhg `xpr`snóo.
5) Cgjcuj` `j çr`g tmtgj e`j cugergem. Y`cu`re` G 8, 9.
0) Hujtnpjnqu` `j r`sujtgem e`j nocnsm 5 pmr jg drgccnóo qu` mituvm `o ̀ j nocnsm 3. @j r̀ smit`oag s`rç `j çr`g e` jg r`anóo smhir`geg e` jg dnaurg.
I. Snag jms pgsms qu` gpr̀ oenó `o `j `b`rcncnm got`rnmr pgrg cgjcujgr `j çr`g e` jg r`anóo smhe` cgeg dnaurg. Lçagjm `o su cuge`rom.
76 ch
aurg 7
< ch
aurg 9
79 ch
aurg 3
76 ch
aurg 5
5 ch
90Hgt`hçtncg · S`hgog 7
Ygzmoghn`otm jóancm
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Hgrqu` cmo uo cl`qu` jg cgsnjjg qu` h`bmr noenqu` su r`oenhn`otm. jmargem `oprmc`sm omjmargem
E ` s p u
î s
e ` ` s t u
e n g r . . .
E`scndrm jg d`clg noscrntg `o uog `st`jg hgyg.Cmovn`rtm oòh`rms e`j snst`hg hgyg gj snst`hg e`cnhgj.
Suhm y r`stm oòh`rms `o `j snst`hg e` ouh`rgcnóo hgyg.
Vrgctncm jg ganjnege e` cçjcujm h`otgj cmo jg hujtnpjncgcnóo.
Cgjcujm `j çr`g e` jg r`anóo smhir`geg `o aurgs a`mhîtrncgs.
Ne`otn cm `j `j`h`otm qu` om augreg r`jgcnóo `o uog s`rn` e` aurgs.
E`sgrrmjj` ou`vgs lginjnege`sY`jgcnmo` daurgs . @stg gctnvnege j` gyuegrç g e`sgrrmjjgr su cgpgcnege e` mis`rvgcnóo. Jgs aurgs e` cgeg s`rn` augrego uog r`jgcnóo `otr` sè. Pst`e e`i`enstnoaunr jg qu` om cuhpj` cmo `sg r`jgcnóo.
Hgrqu` cmo uog `quns (x) jg aurg qu` om s` r`jgcnmog cmo jgs e`hçs. @j nocnsm6 `s uo `b`hpjm.
6)g. i. c. e.
Umegs jgs aurgs e` jg s`rn` tn`o`o uog `clg qu` gpuotg g jgs `squnogs e`jcugerm. Jg aurg e`j nocnsm c om cuhpj` cmo `stg cmoencnóo, pmrqu` jg `clggpuotg lgcng `j c`otrm e` uom e` jms jgems.
7)g. i. c. e.
9)g. i. c. e.
3)g. i. c. e.
5)g. i. c. e.
0)g. i. c. e.
4)g. i. c. e.
94NA@Y · Rgcuj`u
Y`vns` su gpr`oenzgb`
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9
Hujtnpjncgcnóo y envnsnóo cmooòh`rms hgygs
½Wuî `ocmotrgrç `stg s`hgog=
@j c`rm hgyg
Hujtnpjncgcnóo y envnsnóo cmo oòh`rms hgygs
Envnsnmo`s `xgctgs
Gc`rtnbms hgt`hçtncms
@stg s`hgog jmargrç2
Cgjcujgr `j vgjmr pmsncnmogj e` jgs cndrgs ̀ o jms oòh`rms hgygs.
Hujtnpjncgr y envnenr cmo `xgctntue oòh`rms hgygs.
Vrgctncgr `j cçjcujm h`otgj r`smjvn`oem envnsnmo`s `xgctgs.
Hujtnpjncgr cmo `j hîtmem Uz`jtgj.
91Hgt`hçtncg · S`hgog 9
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¡Vgrg cmh`ozgr!@j c`rm hgyg
Po puotm e` pgrtneg
Sno eueg, uom e` jms gpmrt`s hçs nhpmrtgot`s e` jms hgygs du` `j e`scu-irnhn`otm e`j vgjmr e`j c`rm. @st` oòh`rm s` pu`e` r`pr`s`otgr e` hgo`rgsenstnotgs. Jg hçs cmomcneg ̀ s jg dnaurg e` jg cmoclg qu` l`hms ̀ hpj`gem lgstgglmrg `o ou`strm cursm.
Mtrg dmrhg e` r`pr`s`otgrjm `s h`engot` jg dnaurg e` uog djmr qu` snaondncg uopuotm e` pgrtneg, uo mrna`o cmhòo. @stm `s pmrqu`, gj cmotrgrnm e`j cmoc`ptmmccne`otgj e` c`rm cmhm vgcèm, `o jg hgt`hçtncg hgyg s` `otn`oe` cmhm `jtmem, jg pj`ontue, `j prnocnpnm, `j cn`rr` e` uo cncjm.
Mis`rv` `o jg njustrgcnóo jms snaoms y ajndms cmo jms qu` jms hgygs `xpr`sgigo
`j vgjmr e`j c`rm. Jgs dnaurgs e` jg dnjg sup`rnmr smo cmhuo`s `o jms cóenc`s, jgse` jg dnjg nod`rnmr s` mis`rvgo hçs `o jgs `st`jgs y `o jms `endncnms.
¡G trgigbgr!
@o jg ̀ st`jg C e` Wunrnauç lgy ajndms qu` noencgo ̀ j noncnm e` jg cu`otg jgrag e`j 73 igk'tòo. J` hmstrg-hms gjauoms `o jgs nhça`o`s e` gigbm. ½Vu`e` ne`otn cgr jg aurg qu` r`pr`s`otg gj c`rm= Ymeî`jgcmo uog jèo`g.
9<NA@Y · Rgcuj`u
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7. Hujtnpjncgcnóo cmo oòh`rms hgygs½Y`cu`reg cóhm s` j``o jgs `st`jgs hgygs= @o jg s`hgog 7 vnhms qu` `stms
hmouh`otms r`pr`s`otgo d`clgs nhpmrtgot`s qu` s` not`rpr`tgo hujtnpjncgoemoòh`rms pmr b`rmajè cms qu` snhimjnzgo enstnotms p`rnmems e` tn`hpm.
Gpr`oeghms g hujtnpjncgr, cmhm jm lgcègo jms gotnaums hgygs. T`ghms uo ̀ b`h-pjm y snaghms jms pgsms pgrg r`smjv`rjm2
Hujtnpjnqu`hms 7
3
7
9x
• @scrninhms jms dgctmr`s `o jg pgrt``xt`rog e` jg tgijg. @j hujtnpjncgoem
gj jgem nzqun`rem `o pmsncnóo v`rtncgjy r`sp`tgoem `j mre`o pmsncnmogj2 jgv`not`og smir` jg uonege.
• @scrninhms `j hujtnpjncgemr `o jg pgr -t` sup`rnmr `o pmsncnóo lmrnzmotgj. Jgv`not`og s` cmjmcg g jg nzqun`reg sm-ir` jg prnh`rg cmjuhog. Jg uonege s`cmjmcg g jg e`r`clg smir` jg s`auoegcmjuhog.
• Hujtnpjncghms cgeg oòh`rm e`j huj -tnpjncgoem pmr jg v`not`og e`j hujtn-pjncgemr. @scrninhms jms r`sujtgems e`gigbm lgcng grrnig.
• Ju`am, hujtnpjncghms cgeg oòh`rme`j hujtnpjncgoem pmr jg uonege e`jhujtnpjncgemr. @scrninhms jms r`sujtg-ems e` gigbm lgcng grrnig.
• Suhghms jms r`sujtgems e` dmrhgengamogj y `scrninhms `j tmtgj `o jgtgijg e` pmsncnmo`s.
Jg hujtnpjncgcnóo cmooòh`rms hgygs s`mp`rg naugj qu` `o `jsnst`hg e`cnhgj. 7 x 7 8 7 x 8
7 x 3 8 3 x 8
7 9
7 7
3 3
7 9
7 7 9
3 3 4
7
3Hujtnpjncgoem
7 9 7
7 7 9 0
3 3 4 4
Y`sujtgem mprmeuctm
7 9
7
3
Hujtnpjncgemr
9>Hgt`hçtncg · S`hgog 9
@j huoem e` jg hgt`hçtncg
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Po cgsm `sp`cngj
G v`c`s jg hujtnpjncgcnóo s` r`gjnzg cmo oòh`rms qu` smjm tn`o`o cndrgs `o jgpmsncnóo e` jg uonege.
Hujtnpjnqu`hms 9
03x
• Vgrg hgot`o`r `j mre`o s` cmjmcg uo c`rm`o jg pmsncnóo e` jg v`not`og qu` `stçe`smcupgeg. Ju`am, s` snau`o jms pgsmspgrg hujtnpjncgr qu` vnhms `o `j `b`hpjmgot`rnmr. Dèb`s`.
• Hujtnpjncghms cgeg oòh`rm e`j hujtnpjn -cgoem pmr jg v`not`og e`j hujtnpjncgemr.
@scrninhms jms r`sujtgems e` gigbm lgcnggrrnig.
• Ju`am, hujtnpjncghms cgeg oòh`rm e`jhujtnpjncgoem pmr jg uonege e`j hujtnpjn-cgemr. @scrninhms jms r`sujtgems e` gigbmlgcng grrnig.
• Suhghms jms r`sujtgems e` dmrhg eng -amogj y `scrninhms `j tmtgj `o jg tgijg e`pmsncnmo`s.
@b`rcncnm 77) Hujtnpjnqu` 7
1
9
7x
• @scrnig jms dgctmr`s `o jg pgrt` `xt`rog e` jg tgijg.
• Hujtnpjnqu` cgeg oòh`rm e` jg cmjuhog pmr cgegoòh`rm e` jg dnjg, e` gigbm lgcng grrnig.
• Suh` jms prmeuctms `o dmrhg engamogj y `scrnig `jr`sujtgem `o jg tgijg e` pmsncnmo`s.
8 3
9
0
8 3
9 8
0 8
8 3
9 8 4
0 8 %
8 3 8
9 8 4 4
0 8 % %
9 7
7
1
36NA@Y · Rgcuj`u
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9) Hujtnpjnqu` 7
3
7
7x
• @scrnig jms dgctmr`s `o jg pgrt` `xt`rog e` jg tgijg.
• Hujtnpjnqu` cgeg oòh`rm e` jg cmjuhog pmr cgegoòh`rm e` jg dnjg, e` gigbm lgcng grrnig.
• Suh` jms prmeuctms `o dmrhg engamogj y `scrnig `jr`sujtgem `o jg tgijg e` pmsncnmo`s.
3) Hujtnpjnqu` 00
9x
• @scrnig jms dgctmr`s `o jg pgrt` `xt`rog e` jg tgijg.
• Hujtnpjnqu` cgeg oòh`rm e` jg cmjuhog pmr cgegoòh`rm e` jg dnjg, e` gigbm lgcng grrnig.
• Suh` jms prmeuctms ̀ o dmrhg engamogj y `scrnig jmsr`sujtgems `o jg tgijg e` pmsncnmo`s.
5) Hujtnpjnqu` 73
0
3
7x
• @scrnig jms dgctmr`s `o jg pgrt` `xt`rog e` jg tgijg.• Hujtnpjnqu` cgeg oòh`rm e` jg cmjuhog pmr cgeg
oòh`rm e` jg dnjg, e` gigbm lgcng grrnig.
• Suh` jms prmeuctms `o dmrhg engamogj y `scrnig `jr`sujtgem `o jg tgijg e` pmsncnmo`s.
0) Hujtnpjnqu` 7
3
7
3
0x
• @scrnig jms dgctmr`s `o jg pgrt` `xt`rog e` jg tgijg.
• Hujtnpjnqu` cgeg oòh`rm e` jg cmjuhog pmr cgegoòh`rm e` jg dnjg, e` gigbm lgcng grrnig.
• Suh` jms prmeuctms `o dmrhg engamogj y `scrnig `jr`sujtgem `o jg tgijg e` pmsncnmo`s.
37Hgt`hçtncg · S`hgog 9
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9. Envnsnóo cmo oòh`rms hgygs@j s`otnem e` jg envnsnóo ̀ s r`pgrtnr uog cgotnege ̀ o mtrg. Snaghms jms pgsms pgrgenvnenr cmhm jm lgcègo jms hgygs. Jms hgygs mp`rgigo jg envnsnóo snaun`oem ̀ st`prmc`enhn`otm2
Envneghms 99
9ñ
• @scrninhms `o jg tgijg `j envne`oem ydu`rg e` `jjg `j envnsmr.
• Envnenhms ̀ j oòh`rm e` jg v`not`og y`scrninhms `j r`sujtgem g jg e`r`clg.
• Envnenhms jg uonege y `scrninhms `jr`sujtgem g jg e`r`clg.
• Jms r`sujtgems e` jg e`r`clg dmrhgo`j cmcn`ot` e` jg envnsnóo.
Envneghms 66
0ñ
• @scrninhms `o jg tgijg `j envne`oem ydu`rg e` `jjg `j envnsmr.
• Envnenhms ̀ j oòh`rm e` jg v`not`og y`scrninhms `j r`sujtgem g jg e`r`clg.
• Envnenhms jg uonege y `scrninhms `jr`sujtgem g jg e`r`clg.
• Jms r`sujtgems e` jg e`r`clg dmrhgo`j cmcn`ot` e` jg envnsnóo.
Envnsmr
9
9
9
Envne`oem
6
6
0
9 7
9
9
6 9
6
0
9 7
9 7
9
9 7
9 7
9
6 9
6 9
0
6 9
6 9
0
Cmcn`ot`
39NA@Y · Rgcuj`u
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@b`rcncnm 9Y`su`jvg jgs envnsnmo`s e` oòh`rms hgygs.
7) Envneg 0
%0ñ
• @scrnig `o jg tgijg `j envne`oem y du`rg e` `jjg `j envnsmr.
• Envneg ̀ j oòh`rm e` jg v`not`og y ̀ scrnig ̀ j r`sujtgem g jge`r`clg.
• Envneg jg uonege y `scrnig `j r`sujtgem g jg e`r`clg.
9) Envneg 5
<5ñ
• @scrnig `o jg tgijg `j envne`oem y du`rg e` `jjg `j envnsmr.
• Envneg ̀ j oòh`rm e` jg v`not`og y ̀ scrnig ̀ j r`sujtgem g jge`r`clg.
• Envneg jg uonege y `scrnig `j r`sujtgem g jg e`r`clg.
0
%
0
5
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5
7. Hujtnpjncgcnóo cmo oòh`rms hgygs
Vgrg hujtnpjncgr oòh`rms hgygs, `scrninhms jms dgctmr`s `o jgpgrt` `xt`rog e` jg tgijg, hujtnpjncghms `j oòh`rm e` jg cmjuhogpmr cgeg oòh`rm e` jg dnjg, suhghms jms prmeuctms `o dmrhg
engamogj, `scrninhms `j r`sujtgem `o uog tgijg e` pmsncnmo`s.
9. Envnsnóo cmo oòh`rms hgygs
Vgrg envnenr oòh`rms hgygs, ̀ scrninhms `o uog tgijg ̀ j envne`oemy e`igbm e`j envne`oem, du`rg e` jg tgijg, `j envnsmr. Envnenhms `joòh`rm e` jg v`not`og y `scrninhms `j r`sujtgem `o jg tgijg e`pmsncnmo`s, envnenhms jg uonege y `scrninhms `j r`sujtgem `o jgtgijg e` pmsncnmo`s.
8 0 8
7 8 0 0
9 8 6 6
% 3
6 9
0
33Hgt`hçtncg · S`hgog 9
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Gctnvnege 7. E`hu`str` jm gpr`oenemG. Gpjnqu` `j prmc`enhn`otm qu` gpr`oenó pgrg hujtnpjncgr cmo oòh`rms hgygs y r`su`jvg cgeg
mp`rgcnóo. Un`o` uo `b`hpjm.
6) 7
19x
7) 7
91x
8 9 8
7 8 9 9
1 8 $ $
8 1
7
9
9) 93
5x 3) 0
59
7x
5) 75
59x
0) 97
30x
4) 07
93x
1) 59
39x
35NA@Y · Rgcuj`u
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I. Gpjnqu` `j prmc`enhn`otm qu` gpr`oenó pgrg envnenr cmo oòh`rms hgygs y r`su`jvg cgeg mp`rgcnóo.Un`o` uo `b`hpjm.
6) 3>
3ñ 7) "
43ñ
3 7
> 3
3
9) %6
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5) 6
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Jms `b`rcncnms e` cçjcujm h`otgj j` gyuego g h`bmrgr sus cgpgcnege`s e` h`hmrng, cmoc`otrgcnóo ygt`ocnóo. G cmotnougcnóo j` prmpmo`hms ems s`rn`s e` mp`rgcnmo`s hgt`hçtncgs2 jg prnh`rg e` huj-tnpjncgcnmo`s y jg s`auoeg e` envnsnmo`s. Y`suîjvgjgs `o `j h`omr tn`hpm pmsnij`. ¡Cmhn`oc` glmrg!
G.
6) < x < 8
7) 5 x > 8
9) 0 x 4 8
3) 9 x > 8
5) 3 x < 8
0) 4 x 7 8
4) < x 5 8
1) 6 x 4 8
) > x > 8
76) 4 x 5 8
77) 1 x > 8
79) 0 x 3 8
73) < x 1 8
75) 4 x 9 8
70) 1 x 1 8
74) 0 x > 8
71) 4 x 1 8
7) < x 0 8
96) > x 3 8
97) 9 x < 8
99) 1 x 5 8
93) > x 4 8
95) 5 x 77 8
90) < x 4 8
94) 4 x 76 8
91) 5 x 79 8
9) 76 x 76 8
36) 90 x 76 8
37) 46 x 76 8
39) 34 x 76 8
33) 79 x 76 8
35) 5< x 76 8
30) 06 x 76 8
45
6) 90 ñ 0 8
7) 59 ñ 1 8
9) 7< ñ 9 8
3) 70 ñ 0 8
5) 97 ñ 1 8
0) 5> ñ 1 8
4) 40 ñ 7 81) 19 ñ > 8
) 45 ñ < 8
76) 39 ñ 5 8
77) 05 ñ > 8
79) 50 ñ 0 8
73) 8
75) 34 ñ 4 8
70) 43 ñ 1 8
74) 56 ñ 0 8
71) 70 ñ 3 8
7) 34 ñ > 8
96) 91 ñ 3 8
97) 43 ñ > 8
99) 06 ñ 0 8
93) 74 ñ < 8
95) 46 ñ 76 8
90) 55 ñ 77 8
94) 50 ñ 70 8
91) 46 ñ 96 8
96 ñ 36 8
9>) 5< ñ 79 8
36) 90 ñ 90 837) 50 ñ 0 8
39) 766 ñ 76 8
33) 766 ñ 90 8
35) 566 ñ 56 8
30)
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G cmotnougcnóo j` prmpmo`hms uog s`rn` e` gc`rtnbms hgt`hçtncms. Y`smjv`rjms j` gyuegrç g e`sgrrm -jjgr `j p`osghn`otm jóancm y g h`bmrgr jg cgpgcnege e` rgzmogr.
E`t`rhno` `j oòh`rm qu` cuhpj` cmo jgs cmoencnmo`s qu` s` ego `o cgeg nocnsm.6) g. @j oòh`rm `s h`omr qu` 06 c. @j oòh`rm `s uo hòjtnpjm e` <
i. @j oòh`rm `s hgymr qu` 39 e. @s envnsnij` `otr` 76
@j oòh`rm `s2
Jg prnh`rg y jg s`auoeg pr`hnsgs noencgo qu` `j oòh`rm `stç `otr` 06 y 39
Jg t̀ rc`rg y cugrtg, s`÷gjgo qu` jms hòjtnpjms `o `st` rgoam smo 56 y 5
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Hgrqu` cmo uo cl`qu` jg cgsnjjg qu` h`bmr noenqu` su r`oenhn`otm. jmargem `oprmc`sm omjmargem
E ` s p u
î s
e `
` s t u
e n g r . . .
Cgjcujm `j vgjmr pmsncnmogj e` jgs cndrgs `o jms oòh`rms hgygs.
Hujtnpjncm y envnenem cmo `xgctntue oòh`rms hgygs.
Vrgctncm `j cçjcujm h`otgj r`smjvn`oem envnsnmo`s `xgctgs.
Hujtnpjncm cmo `j hîtmem Uz`jtgj.
E`sgrrmjj` ou`vgs lginjnege`sHîtmem Uz`jtgj e` hujtnpjncgcnóo
@j hîtmem Uz`jtgj e` hujtnpjncgcnóo mdr`c` uog hgo`rg dçcnj e` hujtnpjncgr utnjn-zgoem uog r`e e` rgygs y puotms qu` dgcnjntgo `j prmc`enhn`otm.
Gpr`oeghms `st` hîtmem hujtnpjncgoem 3 x 9 . Vr`st` gt`ocnóo.
• Urgzghms 3 jèo`gs lmrnzmotgj`s pgrg r`pr`s`o -tgr `j hujtnpjncgoem. Mis`rv` jg dnaurg.
• Urgzghms 9 jèo`gs v`rtncgj`s pgrg r`pr`s`otgr`j hujtnpjncgemr.
• Cmotghms jms puotms e` jg not`rs`ccnóopgrg mit`o`r `j r`sujtgem 4.
Glmrg j` tmcg g ust`e. Hujtnpjnqu` 5 x 3 . J` gyueghms cmo jgs r`ctgs qu` r`pr`-
s`otgo gj oòh`rm 5.
4
3<NA@Y · Rgcuj`u
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3
Jóancg e` prmpmsncnmo`s
½Wuî `ocmotrgrç `stg s`hgog=
Po prmij`hg e` jóancg
Jg jóancg, jgs prmpmsncnmo`s y su r`pr`s`otgcnóo, cjgsndncgcnóo e` jgs prmpms
Ugijgs e` hujtnpjncgr e`j 7 gj 76
Vrmij`hgs e` jóancg
@stg s`hgog jmargrç2 Cmomc`r `j cghpm e` `stuenm e` jg jóancg. Enstnoaunr uog prmpmsncnóo e` uog `xpr̀ snóo qu` om `s prmpmsncnóo.
Ptnjnzgr `j j`oaugb` snhiójncm e` jg jóancg pgrg r`pr`s`otgr nodmrhgcnóo. Y`pr`s`otgr prmpmsncnmo`s `o dmrhg snhiójncg y r`gjnzgr su o`agcnóo. Ptnjnzgr `j p`osghn`otm jóancm pgrg e`t`rhnogr `j vgjmr e` v`rege e` sntugcnmo`s
cmtnengogs. Vrgctncgr `j cçjcujm h`otgj.
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¡Vgrg cmh`ozgr!Po prmij`hg e` jóancg
Po iu`o rgzmoghn`otm g trgvîs e` jg jóancg, oms p`rhnt` tmhgr jg e`cnsnóo
cmrr`ctg. Vgrg `otrgr gj huoem e`j rgzmoghn`otm, vghms g prgctncgr. J`g cmogt`ocnóo.
Cugtrm ghnams, Hgrtg, Susgog, Cgrjms y Ymi`rtm, dmrhgo `j cmhntîe` v`cnoms. Jms cgrams ̀ o ̀ j cmhntî smo2 pr`sne`ot̀ , vnc`pr`sne`ot`,s`cr`tgrnm y t`smr`rm.
Sgi`hms qu`2
7. Jg p`rsmog qu` `stç s`otgeg dr`ot` g Cgrjms `s s`cr`tgrnm.
9. G jg e`r`clg e` Cgrjms `stç sntugeg jg p`rsmog qu` `s pr`sne`ot`.
3. Ymi`rtm y Hgrtg `stço s`otgems uom gj jgem e`j mtrm y onoauom e`jms ems tn`o` cgram `o jg pr`sne`ocng.
5. @j t`smr`rm `s hub`r.
E`t`rhno` cmhm ̀ stço s`otgems ̀ noenqu` quî cgram tn`o` cgeg uome` `jjms.
Tghms g mre`ogr ou`strm p`osghn`otm. Cmo jg nodmrhgcnóo qu` oms eg ̀ j prmij`-hg y `j `squ`hg, pme`hms `ocmotrgr jg smjucnóo.
@o jg jèo`g sup`rnmr e`i`hms `scrninr `j omhir` y `o jg jèo`g e` gigbm `j cgramqu` mcupg cgeg p`rsmog.
J` gyueghms cmo uo `b`hpjm.
Cgrjms
Cmo jg nodmrhgcnóo e`j `squ`hg, pme`hms v`r cóhm `stço uincgems.
7. Jg p`rsmog qu` tn`o` ̀ j cgram e` pr`sne`ot` ̀ s2
9. Jg p`rsmog qu` tn`o` ̀ j cgram e` vnc`pr`sne`ot̀ `s2
3. Dr`ot` g Cgrjms `stç s`otgem2
5. Hgrtg mcupg `j cgram e`2
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7. Jg jóancg Ygzmoghn`otm cmrr`ctm
Sn `o `j tntujgr e` uog omtncng j`y`rg2Jms s`r`s luhgoms p`rt`o`c`o g jg dghnjnge` jgs gv`s , su s`otnem e` jg jóancg j` gev`rtnrèg noh`engtgh`ot` e` qu` `s uogg rhgcnóo dgjsg.
Jg jóancg `s uog cn`ocng qu`̀ stueng hîtmems, prmc`enhn`otms y tîconcgspgrg enstnoaunr ̀ j rgzmoghn`otm cmrr`ctm m v`rege`rm e`j nocmrr`ctm m dgjsm .
@stg cn`ocng utnjnzg uo j`oaugb` prmpnm r`pr`s`otgem pmr `ouocngems jjghgemsprmpmsncnmo`s.
7.7 Jgs prmpmsncnmo`s y su r`pr`s`otgcnóoPog prmpmsncnóo `s uog mrgcnóo m `ouocngem qu` s` pu`e` cgjndcgr cmhmv`rege`rm m dgjsm . Cgeg prmpmsncnóo s` pu`e` r`pr`s`otgr cmo cugjqun`r j`trghnoòscujg, jgs hçs usgegs smo2 p, q, r , s, t …
Gjauoms `b`hpjms e` prmpmsncnmo`s smo2
q2 @j g÷m cmhn`ozg cmo `j h`s e` `o`rm. r 2 Po cugergem tn`o` cugtrm jgems naugj`s.
¡Gt`ocnóo! Om smo prmpmsncnmo`s jgs ̀ xpr`snmo`s cmhm2 ½Wuî tgj= , ¡Genós!, ½Wuîlmrg `s= , pmrqu` e` `jjgs om pme`hms sgcgr uog cmocjusnóo. Ughpmcm smo prm-
pmsncnmo`s jgs mrgcnmo`s nhp`rgtnvgs (qu` noencgo uog mre`o)2Cn`rr` jg pu`rtg ; onjgs e`sne`rgtnvgs (qu` `xpr`sgo uo e`s`m)2Mbgjç qu` jju`vg .
@b`rcncnm 7J`g gt`otgh`ot` cgeg `xpr`snóo y cjgsndèqu`jg cmhmprmpmsncnóo mom prmpmsncnóo. @scrnig uog`quns (x) `o jg cmjuhog cmrr`spmoen`ot`. Un`o` uo `b`hpjm.
@xpr`snóo Vrmpmsncnóo Om prmpmsncnóo
p2 @j hgogtè `s uo gonhgj gcuçtncm. x i2 ½J` austg jg hgt`hçtncg=
q2 Augt`hgjg `s uo pgès prmeuctmr e` gzòcgr.
h2 ¡Gyueg!
c2 Vgrg cunegr `j pjgo`tg `s o`c`sgrnm r`cncjgr jg igsurg.
e2 @j r`sp`tm `s uo vgjmr.
Jg pgjgirg jóancg prmvn`o` e` jg pgjg-irg arn`ag jmams, qu`snaon cg p`osghn`otmm rgzóo.
57Hgt`hçtncg · S`hgog 3
@j huoem e` jg hgt`hçtncg
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7.9 O`agcnóo e` prmpmsncnmo`sOm, `s dgjsm, om `s cn`rtm
@o jóancg pme`hms o`agr uog prmpmsncnóo. Jg o`agcnóo s` r`pr`s`otg `scrnin`oem `j snaomo`agemr ‚~‘ got`s e` jg j`trg hnoòscujg qu` r`pr`s`otg jgprmpmsncnóo.
@st` snaom s` pu`e` j``r cmhm2 "om", "̀s dgjsm qu` ", "om `s cn`rtm qu` ".
Mis`rv` jms `b`hpjms2
@b`rcncnm 9J`g cgeg prmpmsncnóo y ̀ scrèigjg e`igbm ̀ o dmrhg o`agtnvg. Y`cu`re` qu` pu`e` utnjnzgr cugjqun`rg e
jgs `xpr`snmo`s, "om", "̀s dgjsm qu` " y "om `s cn`rtm qu` ". @j nocnsm 6 j` snrv` e` `b`hpjm.
6) r2 Smjm jms on÷ms vgrmo`s tn`o`o e`r`clm g jg `eucgcnóo.
7) q2 Jg vntghnog G dmrtgj`c` jms lu`sms.
9) p2 Hnau`j Çoa`j Gsturngs agoó `j Vr`hnm Omi`j e` jg Vgz.
3) s2 3 gj cugergem `s >.
5) t2 G h`oms çrimj`s, hçs mxèa`om.
Vrmpmsncnóo O`agcnóo e` jgs prmpmsncnmo`s
p2Jms sgpms cgotgo. ~ p2Jms sgpmsom cgotgo.~ p2 @s dgjsm qu` jms sgpms cgotgo.~ p2 Om `s cn`rtm qu` jms sgpms cgotgo.
q2@j emij` e` < `s 70.~q2 @j emij` e`
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9. Cjgsndncgcnóo e` jgs prmpmsncnmo`sJgs prmpmsncnmo`s jóancgs s` cjgsn cgo `o snhpj`s y cmhpu`stgs. Umegs jgsprmpmsncnmo`s qu` l`hms vnstm lgstg glmrg smo snhpj`s. @stuengr`hms jgsprmpmsncnmo`s cmhpu`stgs jg próxnhg s`hgog.
9.7 Vrmpmsncnóo snhpj` c`rrgegPog prmpmsncnóo snhpj` c`rrgeg `s uo `ouocngem qu` s` cgjn cg enr`ctgh`ot`cmhm v`rege`rm m dgjsm. Vr`st` gt`ocnóo g jms `b`hpjms.
p2 Umems jms luhgoms smo hmrtgj`s. @s uog prmpmsncnóo v`rege`rg (v).s2 5 pmr < `s naugj g 79 . @s uog prmpmsncnóo dgjsg (d ).
9.9 Vrmpmsncnóo snhpj` gin`rtgPog prmpmsncnóo snhpj` gin`rtg `s uo `ouocngem qu` e`p`oe` e`j vgjmr gsna-ogem g jg vgrngij` pgrg cmov`rtnrs` `o v`rege`rm m dgjsm.Vmr `b`hpjm, jg `xpr`snóo2 x `s `j h`s qu` snau` g hgrzm , smjm s`rç v`rege`rg sn`j vgjmr e ̀x `s girnj, pmrqu` girnj `s `j h`s qu` snau` g hgrzm. S`rç dgjsg sn g x s` j` gsnaog uo vgjmr enstnotm, cmhm `o`rm m encn`hir`.
@o cmocjusnóo pme`hms e`cnr qu` uog prmpmsncnóo snhpj` gin`rtg s` trgos-dmrhg `o snhpj` c`rrgeg y v`rege`rg sn s` sustntuy` jg vgrngij` pmr `j vgjmrcmrr`ctm .
@b`rcncnm 3
Y`jj`o` `j cèrcujm e`j vgjmr qu` trgosdmrhg jgs prmpmsncnmo`s gin`rtgs `o prmpmsncnmo`s c`rv`rege`rgs. Ju`am, `scrèigjg smir` jg jèo`g. Dèb`s` `o `j `b`hpjm.
6) r2v `s uog `scrntmrg augt`hgjt`cg.
Ymsg Hmot`rm Anmcmoeg I`jjn Cgrh`o Hgtut`
r2
7) p2 x `s uo pgès e` C`otrmghîrncg.
Ntgjng Hîxncm Augt`hgjg
p2
9) q2 y `s uo eèg e` jg s`hgog.
@o`rm Hgrt`s Insn`stm
q2
Cgrh`o Hgtut` `s uog `scrntmrg augt`hgjt`cg.
53Hgt`hçtncg · S`hgog 3
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Nov`stnau` `o jg r`e...Noar`s` g ^muUui` y v`g `st` vne`m `o `j qu` vgrnms cn`otè cms `xpjncgo quî `s jg jóancg y sus gpjncgcnmo`s2
lttp2//www.ymutui`.cmh/wgtcl=v86^0a5>hmYr@
@o `j `ojgc` snaun`ot` pmerç env`rtnrs` cmo gjauoms bu`ams e` rgzmoghn`otm hgt`hçtncm.
www.gr`gcn`ocngs.cmh/Ygzmoghn`otm-hgt`hgtncm.lth
Smo2 Smo2
Vmr `b`hpjm2 Vmr `b`hpjm2
w2 @j trnam `s uo c`r`gj. p2 3 + x 8 1
@s2
S` `xpr`sg h`engot`2
Wu` smo2
S` cjgsndcgo `o2
Jg jóancg
prmpmsncnmo`s
mrgcnmo`s m `ouocngems qu` s` pu`e`o cjgsn cgrcmhm v`rege`rms m dgjsms. S` r`pr`s`otgo cmocugjqun`r j`trg hnoòscujg cmhm p, q, r , s…
jg cn`ocng qu` ̀ stueng hîtmems, prmc`enhn`otms y tîconcgs pgrg enstnoaunr ̀ jrgzmoghn`otm cmrr`ctm m v`rege`rm e`j nocmrr`ctm m dgjsm.
prmpmsncnmo`ssnhpj`s c`rrgegs
prmpmsncnmo`ssnhpj`s gin`rtgs
`ouocngems qu` s` cgjn cgo enr`ctgh`ot`cmhm v`rege`rms m dgjsms.
`ouocngems qu` e`p`oe`o e`j vgjmrgsnaogem g jg vgrngij` pgrg cmov`rtnrs``o v`rege`rms m dgjsms.
55NA@Y · Rgcuj`u
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Gctnvnege 7. E`hu`str` jm gpr`oenemG. Y`jj`o` ̀ j cèrcujm e` jg r`spu`stg cmrr̀ ctg g cgeg pr`auotg pgrg cmhprmigr sn cmomc` jgs e`dno
e` jóancg, prmpmsncnmo`s y su r`pr`s`otgcnóo. @j oòh`rm 6 j` snrv` e` `b`hpjm.
6) ½G cuçj e` jgs mpcnmo`s cmrr`spmoe` jg e`dnoncnóo2Mrgcnóo m `ouocngem qu` s` pu`e` cjgsndncgr cmhmv`rege`rm m dgjsm=
7) ½Cuçj e` jgs `xpr̀ snmo`s snaun`ot`s ̀ s uog prmpmsncnóo=
9) ½Cuçj e` jgs `xpr`snmo`s snaun`ot`som `s prmpmsncnóo=
3) ½Wuî sèhimjms utnjnzghms pgrg r`pr`s`otgr prmpmsncnmo`s=
5) ½Wuî cn`ocng s` `ocgrag e` ̀ stuengr hîtmems y prmc`enhn`o-tms pgrg e`t`rhnogr ̀ j rgzmoghn`otm cmrr`ctm e`j nocmrr`ctm=
0) ½Cuçj e` jgs `xpr`snmo`s snaun`ot`som `s prmpmsncnóo=
4) E` jgs mpcnmo`s snaun`ot̀ s, ½cuçj ̀ s uog prmpmsncnóodgjsg=
1) ½Cuçj e` jgs prmpmsncnmo`s snhpj`s `sgin`rtg =
j2 3 `s uo oòh`rm pgr h2 93 ̀ s uo oòh`rm nhpgr
r2 9 + 3 8 0 v2 1 x > 8 43 s2 (–x)3 8 –790
`2 x5 8 74 d2 7< ñ i 8 4 p2 755 8 79
50Hgt`hçtncg · S`hgog 3
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p Jms imsqu`s smo du`ot` e` mxèa`om.
r ¡Su`rt`!
I. J`g cgeg ̀ xpr`snóo y cjgsndèqu`jg cmhmprmpmsncnóo mom prmpmsncnóo. Auè`s` pmr `j `b`hpjm.
6) u2 Umem oòh`rm o`agtnvm `s envnsnij`.
7) s2 @j gotóonhm e` cjgrm `s mscurm.
9) b2 ½@scuclgst` jg cjgs` rgengj=
3) w2 Jg lmo`stnege `s uo vgjmr.5) r2 > `s envnsmr e` 34.
0) p2 Gpgag jg juz.
C. @scrnig cugtrm prmpmsncnmo`s. Un`o` uo ̀ b`hpjm.
6) 2
7) 2
9) 2 3) 2
5) 2
E. @scrnig cugtrm `xpr`snmo`s qu`om s`go prmpmsncnmo`s. J` gyueghms cmo jg prnh`rg.
6) 2
7) 2
9) 2
3) 2
5) 2
@. On`au` jgs prmpmsncnmo`s cmo cugjqun`rg e` jgs dmrhgs2 "om", "̀s dgjsm qu` ", "om `s cn`rtm qu` ".Un`o` uo `b`hpjm.
6) p2 Umems jms h`tgj`s smo r`cncjgij`s.
7) q2 Smjm jgs vntghnogs oms hgotn`o`o sgoms.
9) h2 Jms on÷ms e`i`o trgigbgr `o jgs cml`t`règs.
3) c2 36 `s hòjtnpjm e` 6.
Vr mpmsncnóo
~ p2Om `s cn`rtm qu` tmems jms h`tgj`s smo r`cncjgij`s.
54NA@Y · Rgcuj`u
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Gctnvnege 9. Vrgctnqu` jm gpr`oenemG. Cmhm l`hms `stuengem `stg s`hgog, tmeg `cugcnóo s` pu`e` cmosne`rgr uog prmpmsncnóo
gin`rtg. Y`su`jvg jgs `cugcnmo`s e` jg tgijg y gv`rnaú` `j vgjmr e` jg vgrngij` pgrg cmov`rtnprmpmsncnóo gin`rtg `o c`rrgeg v`rege`rg. Un`o` uo `b`hpjm.
Vrmpmsncnóo gin`rtg Tgjmr e` jg vgrngij` C`rrgeg v`rege`rg p2
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¡G pmo`rs` `o dmrhg! Y`cup`r` jg v`jmcnege e` cçjcujm h`otgj. @scrnig `j r`sujtgem e` jgs hujtnpjncgcnmo`s jm hçs rçpnem qu` pu`eg, om utnjnc` cgjcujgemrg on tgijgs.
G.
7) 9 x 5 8
9) 3 x > 8
3) 7 x 4 8
5) < x 9 8
0) 0 x 0 8
4) > x 7 8
1) 5 x 5 8) 1 x 3 8
76) 9 x < 8
77) 5 x 4 8
79) 4 x > 8
73) 0 x < 8
75) 7 x 6 8
70) 3 x 6 874) 3 x 1 8
71) < x 0 8
7 x 9 8
7>) 4 x < 8
96) 0 x 3 8
97) 7 x 9 8
99) 5 x > 8
93) 3 x 5 895) > x 4 8
7) x 0 8 56
9) x 4 8 46
3) x > 8 43
5) x 3 8 3
0) x 5 8 96
4) x 0 8 30
1) x 5 8 74
) x 4 8 36
76) x < 8 04
77) x 7 8 7
79) x 4 8 79
73) x 3 8 70
75) x < 8 39
70) x 76 8 ) x 76 8 96
96) x 76 8 16
97) x 76 8 766
C.
I.7) 9 x 8 7<
9) 0 x 8 0
3) > x 8 05
5) 7 x 8 76
0) 3 x 8 97
4) < x 8 45
1) 5 x 8 96
x 8 >6
>) 0 x 8 06
76) 3 x 8 >
77) > x 8 50
79) 5 x 8 74
73) > x 8 7<
75) 1 x 8 9<
70) 7 x 8 5
74) 9 x 8 74
71) > x 8 >
7) > x 8
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G. Y`su`jvg jms prmij`hgs snaun`ot`s utnjnzgoem jg jóancg y jgs mp`rgcnmo`s grnthîtncgs.
7) Cmo tr`s drutgs end`r`ot`s2 pgpgyg, sgoeèg y pn÷g s` pr`pgrgo buams e`jncnmsms.
sgimr`s end`r`ot`s e` buam s` pmerço pr`pgrgr cmo `stgs drutgs= Gyòe`s` cmhpj`tgoemtgijg.
7 drutg
9 drutgs
3 drutgs
@o tmtgj s` pu`e`o pr`pgrgr sgimr`s end`r`ot`s.
9) G uo s`÷mr s` j` pr`auotg jg lmrg y cmot`stg2 "e`otrm e` 96 hnoutms hn r`jmb hgrcg76236". Sn `j r`jmb `stç ge`jgotgem 0 hnoutms, ½quî lmrg du` lgc` 76 hnoutms `xgctgh`o
3) Goer`g, Irgujnm, I`rtg y Ymi`rtm `stço s`otgems gjr`e`emr e` uog h`sg. @o uog rmoegoòh`rms Goer`g enc` 09, Irgujnm 07, I`rtg 06, Ymi`rtm 5>; gsè suc`snvgh`ot`. ½Wunîo oòh`rm 7=
I. Cmhpj`t` jg tgijg e` 3 dnjgs pmr 3 cmjuhogs, cmo jms oòh`rms e`j 7 gj > y uo oòh`rm `o cugerm, t`on`oem `o cu`otg qu`2
g. 3, 4, , ̀ stço `o jg lmrnzmotgj nod`rnmr.
c. 7, 9, 3, 4, 1, >, om `stço ̀ o jg v`rtncgj nzqun`reg.
e. 7, 3, 5, 0, , om `stço ̀ o jg v`rtncgj e`r`clg.
C. @o `stg gctnvnege j` novntghms g env`rtnrs` r`smjvn`oem gjauoms gc`rtnbms jóancms. Jgr`su`jv`o gpjncgoem `j s`otnem cmhòo. Y`spmoeg jm hçs rçpnem qu` pu`eg.
7) Nhgano` qu` `stç `o uog cgrr`rg y ge`jgotg gj s`auoem juagr. ½@o quî pmsncnóo vg glmr
9) Noenqu` cuçotgs v`c`s s` pu`e` r̀ stgr 76 e` 766.
3) ½Vmr quî uog p`rsmog qu` vnv` `o @scunotjg om pu`e` s`r `ot`rrgeg `o V`tîo=
< 4
7
5>Hgt`hçtncg · S`hgog 3
Ygzmoghn`otm jóancm
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Hgrqu` cmo uo cl`qu` jg cgsnjjg qu` h`bmr noenqu` su r`oenhn`otm. jmargem `oprmc`sm omjmargem
E ` s p u
î s
e ` ` s
t u e n g r
. . . Cmomzcm `j cghpm e` `stuenm e` jg jóancg.
Enstnoam uog prmpmsncnóo e` uog `xpr`snóo qu` om `s prmpmsncnóo.
Ptnjnzm ̀ j j`oaugb` snhiójncm e` jg jóancg pgrg r`pr`s`otgr nodmrhgcnóo.
Y`pr`s`otm prmpmsncnmo`s `o dmrhg snhiójncg y r`gjnzm su o`agcnóo.
Ptnjnzm `j p`osghn`otm jóancm pgrg e`t`rhnogr `j vgjmr e` v`rege e`sntugcnmo`s cmtnengogs.
Vrgctncm `j cçjcujm h`otgj.
E`sgrrmjj` ou`vgs lginjnege`s@b`rcnt` su not`jna`ocng ̀ spgcngj, j` gyuegrç g ̀ stnhgr vmjòh`o`s g amjp` e` vnsVgrg `jjm e`i` cmotgr jm hçs rçpnem pmsnij` y `scrninr `j oòh`rm e` cuims `ocgeg pnjg. Un`o` uo `b`hpjm.
¡Gt`ocnóo! Gjauoms cuims e` ̀ odr`ot` tgpgo pgrcngj m tmtgjh`ot` g jms e` gtrçs.
7) 9)
Smjucnóo Smjucnóo
3) 5)
Smjucnóo Smjucnóo
0) 4)
Smjucnóo Smjucnóo
73
06NA@Y · Rgcuj`u
Y`vns` su gpr`oenzgb`
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5
Cmo`ctnvms jóancms ytgijgs e` v`rege
½Wuî `ocmotrgrç `stg s`hgog=
Vrgctncgr jms sèhimjms qu` r`pr`s`otgo jms cmo`ctnvms jóancms
Vrmpmsncnóo cmhpu`stg
Mp`rgcnmo`s cmhinogegs
S`cu`ocngs jóancgs
@stg s`hgog jmargrç2 Vrgctncgr jg `scrnturg e` jms cmo`ctnvms jóancms.
Enstnoaunr prmpmsncnmo`s snhpj`s y cmhpu`stgs.
@hpj`gr cmo`ctnvms jóancms pgrg cmostrunr prmpmsncnmo`s cmhpu`stgs.
Gogjnzgr nodmrhgcnóo pgrg è t`rhnogr `j vgjmr e` v`rege e` prmpmsncnmo`s.
Cmostrunr tgijgs e` v`rege.
Cmhpj`tgr s`cu`ocngs jóancgs.
07Hgt`hçtncg · S`hgog 5
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7. Vrmpmsncnóo cmhpu`stg Ems m hçs prmpmsncnmo`s
Jg s`hgog got`rnmr ̀ stuenghms jgs prmpmsncnmo`s snhpj`s. Tnhms qu` smo ̀ ouo-cngems qu` pu`e`o s`r v`rege`rms m dgjsms. @o j`oaugb` snhiójncm s` pu`e`or`pr`s`otgr cmo jgs j`trgs p y q.
p2 Jg Un`rrg `s uo pjgo`tg. v
q2 @j Smj `s uo sgtîjnt`. d
Sn s` bg, `stgs prmpmsncnmo`s smo noe`p`oen`ot`s, p`rm pu`e`o uonrs` pgrgdmrhgr uog prmpmsncnóo cmhpu`stg. Vmr `b`hpjm2
Jg Un`rrg `s uo pjgo`tg y `j Smj `s uo sgtîjnt`.
p o`xm q
@j o`xm "y" uo` jgs ems prmpmsncnmo`s got`rnmr`s. p y q
Pog prmpmsncnóo cmhpu`stg cmostg e` ems prmpmsncnmo`s snhpj`s qu` s` uo`oh`engot` cmo`ctnvms jóancms .
@stuengr`hms `stms cmo`ctnvms `o `j gpgrtgem snaun`ot`.
Y`cu`re` e`j cursme` Cmhuoncgcnóoy J`oaugb` qu`pgrg uonr ems m hçsmrgcnmo`s s` utnjnzgojms o`xms2 y , m, on…
@b`rcncnm 7J`g cgeg prmpmsncnóo e` jg nzqun`reg y `scrnig smir` jg jèo`g sn `s snhpj` m cmhpu`stg. Un`o` uo`b`hpjm.
6) Lgc` drèm m lgc` cgjmr.
7) U`oam uo lnbm e` s`ns g÷ms y uog lnbg e` tr`s.
9) T`ous ̀ s uog ̀ str`jjg vnsnij` e`se` jg Un`rrg.
3) @j bgaugr `s uo cgroèvmrm y `j v`ogem `s uo l`rièvmrm.
5) Jjghm pmr t`jîdmom m `ovèm uo h`osgb` e` t`xtm.
0) Jg jnhmogeg `stç l`clg cmo jnhóo.
4) Cmh` sgom y cr`c` in`o.
1) Jgs gi`bgs dgirncgo hn`j g pgrtnr e`j oîctgr e` jgs djmr`s.
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9. Cmo`ctnvms jóancms Vgrg uonr prmpmsncnmo`s
Jms o`xms qu` p`rhnt`o cmo`ctgr prmpmsncnmo`s snhpj`s pgrg dmrhgr prmpmsn-cnmo`s cmhpu`stgs smo jms cmo`ctnvms jóancms . S` jjghgo "cmo`ctnvms" pmrqu`
cmo`ctgo m uo`o prmpmsncnmo`s.Jms cmo`ctnvms jóancms hçs `hpj`gems smo2 cmobuocnóo, ensyuocnóo, cmoencnmogjy incmoencnmogj. S` jms pr`s`otghms g cmotnougcnóo.
9.7 Cmobuocnóo2 (/ )@o jóancg, jg cmobuocnóo cmrr`spmoe` g jg cmobuocnóo cmpujgtnvg "y", qu` `stu -enó `o jg s`hgog 9 e` Cmhuoncgcnóo y J`oaugb`. Un`o` cmhm duocnóo uonr emsprmpmsncnmo`s.
Mis`rv` `o jg tgijg cóhm s` cmostruy` uog prmpmsncnóo cmhpu`stg cmo `st`cmo`ctnvm. L`hms r`sgjtgem `o rmbm `j sèhimjm e` jg cmobuocnóo y cóhm s` j``.
Cmo`ctnvm Sèhimjm @b`hpjm S` ̀scrni` S` j``
Cmobuocnóo / Cgrh`o `stueng j`y`s y Gotmonm`stueng p`egamaèg. p
/ q p y q
9.9 Ensyuocnóo2 ( 6 )Jg ensyuocnóo s` cmhpmrtg cmhm jg cmobuocnóo "m" e` nenmhg `spg÷mj. Su duo-cnóo `s uonr prmpmsncnmo`s pgrg egrj`s uo s`otnem e` `j`ccnóo `otr` ems m hçs`j`h`otms.
T`g `o jg tgijg cóhm s` r`pr`s`otg y cóhm s` j`` `j sèhimjm e` jg ensyuocnóo.
Cmo`ctnvm Sèhimjm @b`hpjm S` ̀scrni` S` j``
Ensyuocnóo 6 Agirn`jg bu`ag dòtimj m bu`agigjmoc`stm. p 6 q p m q
@b`rcncnm 9@scrnig jg r`pr`s`otgcnóo snhiójncg e` cgeg prmpmsncnóo cmhm `stç `o `j `b`hpjm.6) Tmy gj cno ̀y e`spuîs vmy gj `stgenm.
7) Goerîs cmh`rç tghgj`s m cmh`rç cluclntms.
9) Vgrg cujtnvgr jg tn`rrg s` e`i` grgr y gimogr.
3) Ou`v` `s uo oòh`rm prnhm m ou`v` `s uo oòh`rm pgr.
p / q
05NA@Y · Rgcuj`u