Matemáticas 4º RIEB Alumno 2011-2012

8/6/2019 Matemticas 4 RIEB Alumno 2011-2012

1/202

Getmgtioes

O}e|tha

|edh


2/202


3/202

O}

e|t

ha|e

dh


4/202

Getmgtioes. O}e|th a|edhn}m dmse||hjjedh vh| je Di|mooi` Am`m|ej dm Getm|iejms Md}oeti~hs "dagm)* dm je _}lsmo|mte|e dmMd}oeoi` Lsioe* _mo|mte|e dm Md}oeoi` Vljioe.

_mo|mte|e dm Md}oeoi` VljioeEjh`sh J}keglih I|e{lej

_}lsmo|mte|e dm Md}oeoi` LsioeKhs Nm|è`dh Ah`{jm{ _òbm{

Di|mooi` Am`m|ej dm Getm|iejms Md}oeti~hsGe|e Mditb Lm|`jdm{ \myms

Ohh|dièoi` toìoh'vmdeaaioeGe|e O|istiè Ge|t`m{ Gm|oedhEè Jijie \hgm|h {u}m{Ejmris Ah`{jm{ D}j{eidms

E}th|msVije| Dhèk Oestijjh Ej~e|edh* oth| Ge`}mj Ae|oe Gh`tms*Mj~ie Vm||}su}e Grigh* Gia}mj àmj Jm` Bm|``dm{*Dieè Ce|iè Bm|``dm{ Oest|h* Kmss Ge`}mj Bm|``dm{ _hth*Ejge \hse Oe`t` Jhkm|h* Ob|istie` E||mdh`dh De{

\m~isi` toìoh'vmdeaaioe

àmj Deìmj ~ije G}kioe* Deìmje Esm|mt H|ti{ Ge|ti`m{*Ge|ae|ite _hth Gmdiè

Esmsh|msJh}|dms Ege|h Gh|m`hJmtioie Ge|e dm jhs àmjms Ah`{jm{ E||mdh`dhsoe| Vejeoihs Omlejjhs

Ohh|dièoi` mdith|iejDi|mooi` Mdith|iej* dagm(smvEjmke`d|h Vh|tijje dm L}m`

O}idedh mdith|iejMdqi` \hkes AeglheOitjeji Yeoeve`tji _m|~i` Ge|ti`m{

V|hd}ooi` mdith|iejGe|t` Ea}ije| Aejjmahs

Nh|geoi`Kssioe Lm|mìom Aì{ \eg|m{* El|ebeg Gm`ms @m{*Ge|e dmj _ea|e|ih ~ije Ge|oiej* Geaeji Aejjmahs {u}m{

Vh|tedeDismh dm ohjmooi`; Oe|jhs Vejjmi|hIj}st|eoi` dm vh|tede; \hoh Vedijje

_ma}`de mdioi`*


5/202

Je _mo|mte|e dm Md}oeoi` Vljioe* m` mj ge|oh dm je \mnh|ge I`tma|ej dm je Md}oeoi`Lsioe* vje`tme }` `}m~h m`nhu}m dm jil|hs dm tmrth* u}m beom `nesis m` mj t|elekh yjes eoti~idedms dm jhs ej}g`hs ve|e mj dmse||hjjh dm jes ohgvmtmòies lsioes ve|e je

~ide y mj t|elekh. Mstm m`nhu}m iòh|vh|e ohgh evhyh Tmo`hjhaes dm je I`nh|geoi`

y Ohg}ìoeoi` "TIO)* getm|iejms y mu}ivegim`ths e}dih~is}ejms m i`nh|gtiohs*

u}m k}`th oh` jes liljihtmoes dm e}je y msohje|ms* m`|iu}mom` mj oh`hoigim`th m` jes

mso}mjes gmrioeès.

Mstm jil|h dm tmrth i`tma|e mst|etmaies i``h~edh|es ve|e mj t|elekh m` mj e}je*

dmge`de`dh ohgvmtmòies dhom`tms u}m ev|h~mobm` disti`tes n}m`tms dm

i`nh|geoi`* }sh i`tm`si~h dm je tmo`hjhae* y ohgv|m`si` dm jes bm||egim`tes y jhs

jmà}ekms u}m ìhs y k~m`ms }tiji{e` m` je shoimded dmj oh`hoigim`th. Ej gisgh

timgvh sm l}soe u}m jhs mst}die`tms edu}im|e` belijidedms ve|e ev|m`dm| vh| s}

o}m`te y u}m jhs ved|ms dm negijie ~ejh|m` y eohgvem` mj oeglih beoie je mso}mje

gmrioeè dmj n}t}|h.

_} mjelh|eoi` ms mj |ms}jtedh dm }è sm|im dm eooih`ms dm ohjelh|eoi` oh` gjtivjms

eoth|ms* ohgh je Ejie`{e vh| je Oejided dm je Md}oeoi`* eshoieoih`ms dm ved|ms dm

negijie* i`~mstiaedh|ms dmj oegvh dm je md}oeoi`* h|aeìsghs m~ej}edh|ms* gemst|hs

y ohjelh|edh|ms dm di~m|ses disoivjiès* es ohgh mrvm|ths m` dismh y mdioi`. Thdhs

mjjhs be` m`|iu}moidh mj oh`tmìdh dm mstm jil|h dmsdm disti`tes vjetenh|ges y e

t|e~s dm s} mrvm|imòie. Je _mo|mte|e dm Md}oeoi` Vljioe jms mrtim`dm }` sm`tidh

ea|edmoigim`th vh| mj ohgv|hgish dmghst|edh oh` oede ìh |msidm`tm m` mj

tm||ith|ih gmrioe`h y oh` eu}mjjhs u}m sm mò}m`t|e`

n}m|e dm j.

_mo|mte|e dm Md}oeoi` Vljioe

aV|msm`teoi`


6/202

aOh`hom t} jil|h

5=5

aI`tma|h jh ev|m`didhEbh|e evjioe|s jhs oh`hoigim`ths oh`st|}idhs m` mj ljhu}m.\ms}mj~ m jhs sia}im`tms

v|hljmges.

Hlsm|~e mj sia}im`tm teljm|h y oh`tmste jes v|ma}`tes.

5. U} n|eooi` dmj teljm|h |mv|msm`te`

jhs o}ed|hs |hkhs8

d)56 666 # 9 666 # 466 # =6 # >

dm $ 5.O}`th di`m|h

tim`m m` thtej8

e) $ 4 52>

l)$ 4

o) $ 4

d)$ 4 5

?. Oe|jhs tim`m ? le||es dm ege|e`th.

U}im|m |mve|ti|jes m`t|m j y s}s t|ms egiahs. U} n|eooi` dm jes

le||es dm ege|e`th jm oh||msvh`dm e oede }`h8

e) 5 . .

Mj ev|m`di{ekm u}m edu}im|es ej t|eleke| oh` t} jil|h dm Getmgtioes tm l|i`de|bm||egim`tes ve|e de| shj}oi` e v|hljmges dm t} ~ide die|ie |mjeoihèdhs oh` jes

getmgtioes.

T} jil|h dm Getmgtioes oh`ste dm oiòh ljhu}ms u}m* gmdie`tm jes eoti~idedms v|hv}mstes* tml|i`de` mst|etmaies ve|e dmse||hjje| t} vm`segim`th getmgtioh.

Oede ljhu}m oh`tim`m;

I`tma|h jh ev|m`didh

Dh`dm |mshj~m|s v|hljmgesevjioe`dh jh ev|m`didh m` mjljhu}m.

E}thm~ej}eoi`

Ve|e u}m ~ejh|msjhs ev|m`di{ekms yeotit}dms u}m besjha|edh d}|e`tm mj

ljhu}m.

Jmooih`ms

Oh` ~e|ies eoti~idedmsu}m jjm~e|s e oelh m`mu}ivh h dm ge`m|ei`di~id}ej.

M~ej}eoi`

M` je u}m tm de|s o}m`te dmj e~eòmdm t} ev|m`di{ekm d}|e`tm mj ljhu}mmjiaim`dh }è |msv}mste oh||mote dm

o}et|h hvoih`ms.

99

@gm|hs èt}|ejms

\ms}mj~mv|hljmgesm`dh`dmsm}tijiommj~ejh| vhsioih ejdmjhs

daithsm` mjsistmgedmoigej.a5êjh| vhsioihèj

_iaìnioedh y }sh dm jhs gm|hs

Jh u}m oh`h{oh.

\ms}mj~m jhs v|hljmgessia}im`tms;

Mj th dm _mlesti` u}im|m ohgv|e| }`h dm msths jil|m|hs. O}j dm jhs t|ms jil|m|hs tim`m geyh| dmso}m`th8

Dm eo}m|dh oh` je i`nh|geoi` u}m bey m` jhs oe|tmjms*mj ohsth sm

v}mdm o}l|i| m` veahs smgeèjms.O}`ths veahs smgeèjms tm`d|e

u}m beom| mj th dm _mlesti` ve|e ohgv|e| mj jil|m|h E8

Dm o}`th sm|e mj jtigh veah8

Oh` o}j dm jhs t|ms jil|m|hs tm`d|e u}m beom| gs veahs smgeèjms8

Mj th dm _mlesti` ~ih u}m vhde disgi`}i| mj `gm|h dm veahs

smgeèjms si oede smgeè veaele jh mu}i~ejm`tm e dhs* t|ms h beste

o}et|h veahs k}`ths.Mso|ilm mj ghdmjh dm jil|m|h u}m oh||msvh`dm e

oede }è dm jes o}m`tes u}m bi{h mj th dm _mlesti`.

4veahs dm$466?veahs dm$665ve ahdm$4=65ve ahdm$5=6

Jil|m|h

=veahs dm$466?veahs dm$


7/202

(55 55;=? . .

Oede jmooi` iòj}ym;

Oh`tiè di~i|ti`dhtm ej timgvh u}m ev|m`dms m iòh|vh|es `}m~es belijidedms u}m tm

vm|giti|` |mshj~m| v|hljmges e` gs i`tm|mse`tms%

Eja}ès ~moms mòh`t|e|s jes smooih`ms sia}im`tms;

Deth i`tm|mse`tm

Tm v|msm`te i`nh|geoi`sh|v|m`dm`tm y e ~momsvhoh oh`hoide.

\mth

Oh` v|hljmgesi`tm|mse`tms u}mtim`m` }` geyh|a|edh dm dino}jted.

Oh`s}jte m`

Oh` i`nh|geoi` dh`dmvhd|s egvjie| y mkm|oite|t}s oh`hoigim`ths. Mjioh`h u}m jhs distià}mtm |mo}m|de mnmot}e| jelsu}mde m` i`tm|`mteohgveedh dm }` ed}jth.

Jh u}m oh`h{oh

Oh` eoti~idedmsve|e u}m |mo}m|dmsoh`hoigim`thsedu}i|idhs m` jmooih`ms*ljhu}ms h a|edhse`tm|ih|ms.

Mkm|oioihs y v|hljmgesoh` jhs o}ejmsdmse||hjje|s mst|etmaies yv|homdigim`ths ve|e de|shj}oi` e v|hljmges u}msm tm v|msm`te` te`th m` jemso}mje ohgh m` je ~idedie|ie.


8/202

a`diomLjhu}m I

V | m s m ` t e o i ` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?Oh`hom t jil|h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Ev|m`di{ekms msvm|edhs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

5 êjh| vhsioihèj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 < Ohgve|h gmdides dm tevmtms y jisth`ms. . . . . . . . . . . . . . . . . . . . . . . . 54 ? O e ` t i d e d m s m u } i ~ e j m ` t m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Aeè| h vm|dm| oh` je edioi` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Oejo}je n|eooih`ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5< Jhs v|moihs oh` om`te~hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . =6 5? _ } o m s i h ` m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . =? 54 G}jtivjioh vh| 56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . => 5= _}ge h |mste dm n|eooih`ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . =2 5> \ms}mj~h v|hljmges y }tiji{h je di~isi` . . . . . . . . . . . . . . . . . . . . . . . . >5 51 Nia}|es y o}m|vhs amhgt|iohs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >? 52 Idm`tinioh o}m|vhs amhgt|iohs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >= 59 à}jhs m` }` o|o}jh8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >9


9/202

?9 Dm }` gmt|h vh| }` gmt|h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5?2 46 Jedh vh| jedh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 45 Jh gs v|hleljm ms u}m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 4< Jhs {eveths dm ghde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

I`tma|h jh ev|m`didh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5=5M~ej}eoi` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5= 4? Mj |mve|th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5=1 44 Mj ohoim`tm ms8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>6 4= O}`th u}mde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>? 4> N|eooih`ms dm gmt|hs ohgvjmths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>= 41 O}`ths v}mdh ohgv|e|8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>2 42 O}`th nejte ve|e 568 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

49 Jhs t|ià}jhs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51? =6 J e s | m o t e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 =5 Jes ohglièoih`ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

I`tma|h jh ev|m`didh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525M~ej}eoi` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5266) # " ) # " ) 7

" ) # " ) # " ) # " ) 7

5. Nh|gm` mu}ivhs.

Jme` jes sit}eoih`ms v|hv}mstes m` oede }`h dm jhs iòishs. Dmsv}s* eèjiom` jes mrv|msih`ms u}m sm mò}m`t|e` m` mj sia}im`tm

|mo}ed|h. \mjeoih`m` je mrv|msi` u}m si|~m ve|e |mshj~m| oede }è dm jes sit}eoih`ms

v|hv}mstes. Mso|ile` dmlekh dm oede mrv|msi` mj iòish u}m jm oh||msvh`dm. Oejo}jm` mj |ms}jtedh dm oede mrv|msi`. E`htm` mj |ms}jtedh oh||moth ej nièj dm oede iòish.

5


13/202

5555

l) Nm|è`dh t|e`svh|te ohstejms dm è|e`kes m` s}oegi`. Jjm~e }` ohstej oh` 5 smooih`ms dm 266esim`ths oede }è3 4 oh` 466 esim`ths oede }è y }è

oh` lhjhs |hkhs* 5 lhjh eè|e`kedh y > dm ohjh|

~m|dm* o}`ths v}`ths sm aeè`8

n) M` }è vevmjm|e sm m`t|mae|h` jhs sia}im`tmse|to}jhs; 4 oekes oh` 266 ahges oede }è3 = veu}mtms

oh` lhjses oh`


14/202

5


15/202

5?5?

?. \meji{e jes dmsohgvhsioih`ms dm jhs sia}im`tms gm|hs.e) 1 2


16/202

5454

@gm|hs n|eooihè|ihs\ms}mj~m v|hljmges m` jhs u}m sm |mu}im|e mrv|mse| y ohgve|e|gmdides dm jhàit}d* oeveoided* }tiji{e`dh n|eooih`ms* m` nh|ge

`}g|ioe y a|nioe.

_iaìnioedh y }sh dm jhs `gm|hs

a>5>

Jmm jes v|ma}`tes y s}l|eye je |msv}mste oh||mote. Mgvjme jes ti|es dmj

\moh|teljm 5 ve|e ey}de|tm e |mshj~m| h ~m|inioe| t} |msv}mste.

Dm jes sia}im`tms ti|es o}j ms je smooi` gs oh|te8

_mooi` oh` 5< _mooi` oh`

Dm thdes jes sia}im`tms ti|es o}j ms je smooi` gs je|ae8

_mooi` oh`


19/202

5151

Jh u}m oh`h{oh. \ms}mj~m mjv|hljmge sia}im`tm.

Mrv|mse dm t|ms ge`m|es disti`tes

ogh veae|es je oe`tided smejede

m` oede e`}`oih si t}~im|es gh`mdes

dm 56*


20/202

52252

5. M` }è tim`de dm d}joms tviohs gmrioe`hs* dh` J}is* mj d}mh* s}mjm vmdi| e s}sojim`tms u}m jm vea}m` mj igvh|tm mreoth dm s} ohgv|e* v}ms `}òe tim`m oeglih.

\m`mtm oh` }` ohgvem|h y oh`tmstm` jes v|ma}`tes sia}im`tms.

O}`th sm bel| dm veae| vh| }è ohoede y }` oeghtm8 Oh` u} gh`mdes h lijjmtms veae|e` si u}im|m` }se| mj gìgh `gm|h dm

gh`mdes8 _i Ge`}mj u}im|m ohgv|e| dhs geoe||h`ms y }è è|e`ke* o}`th bel| dm

veae|8

Ogh beom ve|e veae| oh` mj gìgh `gm|h dm gh`mdes8

_i sjh o}m`te oh` dhs gh`mdes dm 56 vmshs* o}`th jm nejte ve|e ohgvjmte|8 Oh` o}`tes gh`mdes dm 56 vmshs y dm 56 om`te~hs v}mdm Ge`}mj |meji{e| s}

veah8 Keigm ohgv|e smis oeje~m|es dm e{oe| y smis vejeù}mtes* vm|h ve|e veae| sjh

tim`m }` lijjmtm dm =6 vmshs. O}`th di`m|h jm shl|e h jm nejte8

@e|e`kes$2.=6 o(}

Ohoedes

$?.=6 o(}

Geoe||h`ms

$1.66 o(}

Oeghtms

$=.=6 o(}

Vejeù}mtes

$4.=6 o(}

Oeje~m|es

$


21/202

5959

Oe|gm` tim`m $9=.=6 y oh` mjjhs u}im|m ohgv|e| d}joms. O}`ths y dm o}jms d}joms dm

je vai`e e`tm|ih| v}mdm ohgv|e| ve|e aeste| mreotegm`tm mse oe`tided dm di`m|h8

U} tivh dm d}joms v}mdm ohgv|e| Nm|`e`de si u}im|m aeste| mreotegm`tm $5


22/202


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25/202

6 cijgmt|hs*

o}`th di`m|h aeste| m` ohgl}stiljm8

Ebh|e ohgvjmte je sia}im`tm telje y ~m|inioe si t} |ms}jtedh ms oh||moth.

Jit|hs Ohsth Cijgmt|hs

5 $9.9> 5

5= 526


26/202


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28/202

>

Jh u}m oh`h{oh. ]tiji{e mj \moh|teljm < ve|e nh|ge| jhso}m|vhs amhgt|iohs. Dmsv}s* mso|ilm s} `hgl|m m` mjjhs.

O}m|vhsMrvjh|e o}m|vhs amhgt|iohs

ve|e eèji{e| dinm|m`tms v|hvimdedms.

Oh`st|}ooi` dm o}m|vhs

amhgt|iohs

a>Nia}|es

Ebh|e* m` je sia}im`tm telje* mso|ilm jhs deths u}m nejte`.

O}m|vh amhgt|ioh@gm|hdm oe|es

@gm|hdm ~|tioms

@gm|hdm e|istes

V|isget|ieà}je|

V|isge|moteà}je|

O}lh

V|isgevm`teahèj

V|isgebmreahèj

Vi|gidmo}ed|eà}je|

Hotemd|h

Oh`sm|~e y a}e|de t}s o}m|vhs amhgt|iohs3 jhs }tiji{e|s m` je sia}im`tm jmooi`.

Vaiès 595'599


29/202


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32/202

?66?6

M`t|m mj o}lh y mj v|isge o}ed|eà}je|* o}j tim`m geyh| `gm|h dm oe|es8

O}`tes oe|es |moteà}je|ms tim`m mj v|isge vm`teahèj8 O}`tes oe|es m` nh|ge dm vm`tah`h tim`m mstm v|isge8


33/202

?5?5

U} tim`m` m` ohg` jes oe|es dm msths o}m|vhs amhgt|iohs8

O}`ths oe|es |moteà}je|ms tim`m` jhs sia}im`tms o}m|vhsamhgt|iohs8 V|isge t|ieà}je| V|isge |moteà}je|

V|isge vm`teahèj V|isge bmreahèj M` jhs o}m|vhs e`tm|ih|ms* o} tes oe|es h sh` |moteà}je|ms8

\mthO}`tes oe|es |moteà}je|ms tim`m }` v|isge hoteahèj8

O}e`dh dhs nia}|es tim`m` jes gisges

jhàit}dms* jhs gisghs à}jhs y je

gisge nh|ge sh` ohà|}m`tms.

]` vhjah`h |ma}je| ms }è nia}|e vjeèo}yhs jedhs tim`m` je gisge jhàit}d y s}s

à}jhs i`tm|`hs tim`m` je gisge gmdide.

Oh` evhyh dm s} v|hnmsh| dmsoe|a}m` mj v|ha|ege Vhjy u}msm mò}m`t|e m` je sia}im`tm di|mooi`;bttv;((qqq.vmde.ohg(dhq`jhed(Oh` mstm v|ha|ege* mrvjh|m` jhs sjidhs vjetìohs u}msm iòj}ym`* es ohgh s}s dmse||hjjhs vje`hs. M` mu}ivhs*smjmooih`m` }`h dm jhs dmse||hjjhs vje`hs ve|e oh`st|}i| mjo}m|vh amhgt|ioh m` vevmj.

Oh`s}jte m`...


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?


35/202

????

5. \m`mtm oh` }` ohgvem|h. Jmm m` ~h{ ejte jes i`st|}ooih`msu}m s}am|istm ve|e jjmae| e }`h dm jhs j}ae|ms smjmooihèdhs* si`

gmòihè| dm u} j}ae| sm t|ete. T} ohgvem|h di| e u} j}ae| tm

|mnm|istm. N}m oh||moth mj j}ae| u}m gmòih` t} ohgvem|h8 Ebh|e ms mj t}|`h dm t} ohgvem|h. Ejt|`m sm m` je jmot}|e*

dm ge`m|e u}m jhs dhs v}mde` jmm| jes t|eymoth|ies e t|ms jhs

j}ae|ms smjmooihèdhs.

_}vhàeghs u}m ~i~ms m` je oese `gm|h 562. Mso|ilm e

oh`ti`}eoi` ogh jjmae|es e oede }`h dm t}s j}ae|ms v|mnm|idhs.

Je |hse dm jhs

~im`ths `hs vm|gitm

jhoeji{e| m` }`

geve jhs v}`ths

oe|dièjms; @h|tm*

_}|* Mstm y Hmstm.

O}e`dh sm de` i`st|}ooih`ms ve|e jjmae| e }` j}ae| dmlm

beom|sm oh` oje|ided y v|moisi`. Ms `momse|ih i`dioe|mj `hgl|m dm jes oejjms* `gm|h dm o}ed|es u}m tim`m`

u}m |moh||m|sm beoie mj @h|tm h _}|* Mstm } Hmstm. E ~moms

|ms}jte tij gmòihè| j}ae|ms oh`hoidhs ohgh |mnm|mòie*

vh| mkmgvjh* je iajmsie h mj gm|oedh.

Deth i tm|mse`tmJe |hse dm jhs ~im`ths tegli` msoh`hoide ohgh je |hse `}tioe3 ejMstm sm jm oh`hom tegli` ohghH|im`tm h Jm~e`tm y ej Hmstm*ohgh Hooidm`tm h Vhìm`tm.


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?4?4


37/202

?=?=

_i mst` m` je mso}mje* ogh be|e` ve|e jjmae| ej Oestijjh dm

Obev}jtmvmo8

_hl|m mj vje`h dm je vaiè e`tm|ih|* smejm` oh` }è j`me dmohjh| |hkh o}j sm|e mj |moh||idh u}m |meji{e|e` ve|e t|esjede|sm

dmsdm je mso}mje beste mj Oestijjh dm Obev}jtmvmo. Ohgve|m` s} |moh||idh oh` mj u}m bioim|h` ht|es ve|mkes. O}j n}m je hvoi` gs oh|te ve|e jjmae|8

]` a|}vh dm smis ej}g`hs dmoidi ~isite| mj G}smh @eoihèj dm

E`t|hvhjhae. Es u}m hlsm|~e|h` mj vje`h y t|e{e|h` }è |}te.

Ogh bioim|h` ve|e jjmae| si ve|tim|h` dm je mso}mje8

G}mst|m` s} |msv}mste e thdh mj a|}vh y dmsv}s dmoide` o}j

ms mj oegi`h gs oh|th ve|e jjmae| ej g}smh. G|u}m`jh m` mj

vje`h.

Ve|tim`dh dmj E}dith|ih @eoihèj* dmso|ilm vh| jh gm`hs dhs

t|eymoths e sitihs igvh|te`tms u}m `h sm beye` gmòihèdh e`.

Dm jhs t|eymoths u}m mjmaistm* o}j ms mj gs je|ah8

O}j ms mj gs oh|th8

\mthE ve|ti| dmj vje`h dmtm|giè m`t|m u} oejjms

sm mò}m`t|e je msteoi` dmj Gmt|h E}dith|ih.


38/202

?>>?>

\mjeoih`ms dm v|hvh|oihèjided\ms}mj~m v|hljmges dm ~ejh| nejte`tm m` jhs u}m sm de mj ~ejh|

}ìte|ih* h sm v|ma}`te vh| j* gmdie`tm disti`ths v|homdigim`ths.

E`jisis dm je i`nh|geoi`

a9Mj~ejh|

nejte`tmJh u}m oh`h{oh. \ms}mj~m jhssia}im`tms v|hljmges.e) J}ise t|eleke m` }è nl|ioe dm

oegises. Ve|e oede oegise dm

ed}jth sm `momsite` 5= lhth`ms.

Ey}de e J}ise e mòh`t|e|

jes oe`tidedms u}m nejte` m`je sia}im`tm telje. Dmsv}s*

oh`tmste jes v|ma}`tes.

Oegises dm geàe je|ae ve|e ed}jth

Oe`tidedms dm oegises 5 > 54 1= 5>6

Oe`tidedms dm lhth`ms 5=

O}`ths lhth`ms sm momsite` ve|e oh`nmooihè| 56 oegises8 O}`ths lhth`ms sm `momsite` ve|e lhth`ms ve|e 2 oegises.Ey}de e J}ise e mòh`t|e| jes oe`tidedms u}m nejte` m` je sia}im`tm

telje. Dmsv}s* oh`tmste je v|ma}`te.

Oegises ve|e ìh

Oe`tidedms dm oegises 5 2 56 5 446

U} v}mdm beom| J}ise ve|e selm| o}`ths lhth`ms sm `momsite` ve|e

546 oegises dm ìh8


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?1?1

5. M` mu}ivh* |ms}mj~e` mj v|hljmge sia}im`tm.

Je ohoiè dm dh` Lmth ms neghse vh| s}s |iohs teohs dm ohobiìte vilij.

E`htm` mj deth u}m nejte m` oede }è dm jes sia}im`tms te|kmtes.

H|dm` dm ? teohs

vh| $


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?22?2

\mthJhs ej}g`hs dm o}e|th a|edh ohgv|e|h` n|}te. Eydm`jms e ohgvjmte|

mj sia}im`tm o}ed|h ve|e selm| o}`th ohgv|e|h`;

\m`e`sm m` mu}ivhs y

|ms}mj~e` mj v|hljmge sia}im`tm.

A|}vhCijha|eghs vh|

oeke

Vim{es m` thtej

Ge`{e`es Vm|es D}|e{`hs

4h. E 56 =6

4h. L 2 42 26

4h. O 5< >6


41/202

?9?9

Oh` lesm m` je i`nh|geoi`dmj e`}òih |msvh`de` jes

v|ma}`tes;

O}`th o}mste` t|ms oekes dm

vish jegièdh dm > gg dm

a|hsh|8

O}`tes oekes dm vish

jegièdh dm > gg o}l|m` }`

vish dm 5> g


42/202

46646

5. \m`mtm oh` }` ohgvem|h y |mejiom` jh u}m smi`dioe m` oede oesh e ve|ti| dm je i`nh|geoi` dm je

igeam`.

U} oe`tided dm ea}e oh`tim`m je lhtmjje8 O}`ths gijia|eghs "ga) dm shdih oh`tim`m8

E u} oe`tided dm ea}e oh||msvh`dm je

i`nh|geoi` `}t|igm`tej dm je mtiu}mte8

M` je igeam` dm je i{u}im|de eve|mom je mtiu}mte

dm }` o}edm|`h* hls|~eje y oh`tmste jesv|ma}`tes;

EA]E _IGVJM VHTELJM

OH@T. @MTH 5.= J

I@NH\GEOI@ @]T\IGM@TEJ

Vh| 566 gJ;

Oh`tm`idh m`m|atioh 6 coej

Oe|lhbid|eths 6 a

V|htm`es 6 a

A|eses "jvidhs) 6 a

_hdih = ga

O]EDM\@HN5

566BHKE_

O]ED\H1gg

VevmjLh d=>a

(g66 gs oe|e. O}`th jm

ohst je lioiojmte e _e`d|e8


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4 ms;

e) 56 666 # 966 # 4= # >

l) 56 666 # 9 666 # 4= # >

o) 56 666 # 966 # 466 # =6 # >

d) 56 666 # 9 666 # 466 # =6 # >

dm $ 5. O}`th di`m|h

tim`m m` thtej8

e)$ 4 52>l)$ 4 o)$ 4 d) $ 4 5

?. Oe|jhs tim`m ? le||es dm ege|e`th.

U}im|m |mve|ti|jes m`t|m j y s}s t|ms egiahs. U} n|eooi` dm jes

le||es dm ege|e`th jm oh||msvh`dm e oede }`h8

e) 5


45/202

4?4?

4. \hd|iah ~m`dm m` s} vevmjm|e jhs

hlkmths sia}im`tms;

Ohgvjmte je telje dil}ke`dh m` mj jtigh|mo}ed|h mj di`m|h u}m jm shl|e h jm nejte e

oede u}im` ve|e ohgv|e| mj hlkmth.

Di`m|h u}mtim`m oede

`ih

Hlkmthu}m dmsmeohgv|e|

Jm nejte h jm shl|e

Gia}mj; $5>1 Oeke dm ohjh|ms

\}tb; $1< Jil|h

Mstbm|; $


46/202

4444

=. _mjmooihè je

nia}|e u}m tim`m

shjegm`tm }` ve|

dm jedhs ve|ejmjhs.

e)

o)

l)

d)

>. Dhe J}vite }tiji{e jhs sia}im`tms ià|mdim`tms ve|e v|mve|e| }` ve`.

U} oe`tided dm ià|mdim`tms `momsite|e ve|e v|mve|e| ? ve`ms8

Oe`tided Ià|mdim`tm

< te{es E{oe|

566 a|eghs Ge`tmu}ijje

4 vim{es B}m~h

? vim{es @e|e`kes

5 cijha|egh Be|iè

e) > te{es dm e{oe|

?66 a dm ge`tmu}ijje

9 vim{es dm b}m~h

5< e|e`kes

4 ca dm be|iè

l) > te{es dm e{oe|

?66 a dm ge`tmu}ijje

5< vim{es dm b}m~h

9 è|e`kes

? ca dm be|iè

o) > te{es dm e{oe|

526 a dm ge`tmu}ijje

9 vim{es dm b}m~h

9 è|e`kes

? ca dm be|iè

d) > te{es dm e{oe|

526 a dm ge`tmu}ijje

5< vim{es dm b}m~h

5< e|e`kes

4 ca dm be|iè


47/202

4=4=

aE}thm~ej}eoi`M` jes oesijjes oh||msvh`dim`tms* ge|oe oh` }è vejhge jh u}m gmkh||mnjmkm jh u}m vim`ses.

Oh`tmìdhs v|homdigm`tejms

_imgv|m jh

beah

Jh beah e

~moms

Dinoijgm`tm

jh beah

\ms}mj~h v|hljmges u}m igvjioe`mòh`t|e| mj ~ejh| nejte`tm m`

|mjeoih`ms dm v|hvh|oihèjided.

Idm`tinioh jes ve|tms u}mohgvh`m` jhs o}m|vhs

amhgt|iohs.

Ohgv|m`dh je i`nh|geoi` u}m smv|msm`te m` di~m|shs vh|tedh|ms.

Oh`tmìdhs eotit}dièjms

_imgv|m jh

beah

Jh beah e

~moms

Dinoijgm`tm

jh beah

Gm a}ste t|eleke| m` mu}ivh.

O}e`dh gis ohgvem|hsve|tioive`* mso}obh oh` |msvmth

s}s hviìh`ms.

O}e`dh t|elekh m` mu}ivh*

ev|m`dh dm gis ohgvem|hs.

O}e`dh t|elekh m` mu}ivh* mnmothgmkh| jes ohses u}m si jes jjm~h e

oelh i`di~id}ejgm`tm.


48/202

hu}mII

Ev|m`di{ekms msvm|edhs \ms}mj~mv|hljmgesdh`dmdmtm|gi`m

u}n|eooi`ms}ève|tmdededm}è

geaìt}d Jmm*mso|ilmyohgve|e`gm|hsdmoigejms

besteom`tsighsmòh`tmrthsdmdi`m|h

ygmdioi`

\ms}mj~mv|hljmgesu}mmgvjme`s}ges

h|mstesdmn|eooih`ms

\ms}mj~mv|hljmgesu}mi`~hj}o|e`

disti`thssiaìnioedhsdmjedi~isi`dm

`gm|hsèt}|ejms

Idm`tinioeo}m|vhsamhgt|iohsgmdie`tmjedmso|ivoi`dms}soe|eotm|stioes

]tiji{emjt|e`svh|tedh|ve|egmdi|

à}jhs

\ms}mj~mv|hljmgesdm~ejh|nejte`tm

gmdie`tmmjojo}jhdmj~ejh|}ìte|ihh

evjioe`dhv|hvimdedmsdm}è|mjeoi`dm

v|hvh|oihèjided


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41

Igeaiè u}m mj |motà}jh

ms je o}e|te ve|tm dm }è

vejeù}mte dm oeoeb}etm.

Dil}ke je le||e ohgvjmte.

5. Hlsm|~e jes igam`msy oh`tmste jes v|ma}`tes.

Nia}|eE Nia}|eL

Nia}|eO Nia}|eD

M` u} nia}|e h nia}|es mst

ohjh|mede je gited dm je s}vm|nioim8

M` u} nia}|e h nia}|es mst

ohjh|mede je tm|om|e ve|tm dm je

s}vm|nioim8

M` u} nia}|e h nia}|es mst vi`tede

je o}e|te ve|tm dm je s}vm|nioim8

@gm|hsn|eooihè|ihs

Oejo}je n|eooih`ms dm geaìt}dms oh`ti`}es "jhàit}d*s}vm|nioim dm nia}|es) y* |mov|hoegm`tm* msteljmomu} n|eooi` ms }è ve|tm dede dm }è geaìt}d.

_iaìnioedhy}shdmjhs`gm|hs

a55Oejo}je

n|eooih`msJh u}m oh`h{oh. \meji{e je eoti~ided sia}im`tm.


50/202

42


51/202

49

?E oh`ti`}eoi` sm dmso|ilm` eja}ès dm jes ~m`teès dm jes oelees dmj|eòbh dh`dm ~i~m Ge}|ioih. Dil}ke m` jhs msveoihs }è |mv|msm`teoi`

dm oede ~m`teè.

]è ~m`teè |moteà}je| di~idide

bh|i{h`tejgm`tm m` ? ve|tms ia}ejms y

sjh }è tm|om|e ve|tm sm v}mdm gh~m|

ve|e el|i| h om||e|. Je ~m`teè gidm

4 g dm je|ah y 5 g dm ejth. O}`th

gidm je ve|tm u}m sm v}mdm el|i| h

om||e|8

]è ~m`teè u}m gidm 526 og dm je|ah y

=6 og dm ejth y tim`m nh|ge |moteà}je|

mst di~idide m` 9 ve|tms ia}ejms. O}`th

v}mdm gmdi| oede }è dm jes ve|tms* ve|e

u}m thdes sme` ia}ejms8

]è ~m`teè dm


52/202

=6

Ve|e

o}eju}im|

vm|sh`e

$


53/202


54/202

=

G}jtivjioh

vh|

56

G}jtivjioeoi`ydi~isi`

Dmtm|giè |majes v|otioes ve|e g}jtivjioe||videgm`tm vh| 56* 566* 5666* mtotm|e.a54

_iaìnioedhy}shdmjeshvm|eoih`ms

M` mj sej` dm _hne mst` h|aeì{e`dh }è |ine dm < veu}mtms

dm v|ha|eges dho}gm`tejms m` nh|geth D^D. Mj lhjmth ve|e

ve|tioive| m` je |ine dmj v|igm| veu}mtm o}mste $2.66 y mj dmj

sma}`dh* $5?.66. Jh u}m hltmàe` dm je ~m`te dm jhs lhjmths*

}è ~m{ u}m e mse oe`tided sm jm |mstm jh u}m ohste|h` jhs dhs

veu}mtms* sm }tiji{e| ve|e |meji{e| }` oh`~i~ih e ni` dm eh. M`

thtej sm igv|igim|h` =66 lhjmths ve|e oede }`h dm jhs veu}mtms.

O}`th di`m|h hltm`d|` dm je ~m`te dm jhs lhjmths8

Mrvjioe ogh hlt}~istm mj |ms}jtedh. Mj v|igm| de ~m`dim|h` 56 lhjmths ve|e mj v|igm| veu}mtm y 566

lhjmths ve|e mj sma}`dh veu}mtm. O}`th di`m|h k}`te|h` msm

de8

Jh u}m oh`h{oh. Dm nh|gei`di~id}ej* |ms}mj~m je

sia}im`tm eoti~ided.


59/202

=1

Ve|e mj u}i`th de sjh jms u}mdele` 56 lhjmths dmj sma}`dh veu}mtm

y 566 lhjmths dmj v|igm| veu}mtm. O}`th di`m|h k}`te|h` ve|e mj

u}i`th de8

Dmso|ilm dm u} ge`m|e hlt}~istm je |msv}mste.

_i mj v|igm| veu}mtm ohst $266.66 y mj sma}`dh* $5 ?66.66* o}`th

di`m|h u}md ve|e h|ae`i{e| mj oh`~i~ih8

\mth

V|igm|h dmoidi|` u}i` ohgim`{e je eoti~ided y oh`ti`}e| mj ohg'

vem|h dm je dm|mobe.

Oede k}aedh| je`{e| jhs dedhs y mj `gm|h u}m hltm`ae dm s}ge|

jhs v}`ths dm eglhs sm| g}jtivjioedh vh| mj `gm|h u}m sejae ej

ai|e| je vm|i`hje.

E`hte mj |ms}jtedh dm g}jtivjioe| msths dhs `gm|hs.

Mkmgvjh; Ej je`{e| jhs dedhs sm hltim`m < y ej ai|e| je vm|i`hje sm hl'

tim`m 56* vh| jh u}m mj |ms}jtedh ms


60/202

=2

V|hljmgesediti~hs

\ms}mj~m v|hljmges u}m igvjiu}m` s}ge h |mste dm n|eooih`ms* mòeshs smòijjhs* oh` disti`ths v|homdigim`ths. Mjelh|e m i`tm|v|mte

|mv|msm`teoih`ms a|nioes dm jes n|eooih`ms.

_iaìnioedhy}shdmjeshvm|eoih`ms

a5=_}ge h |mstedm

n|eooih`msJh u}m oh`h{oh. \meji{e je sia}im`tm eoti~ided ymso|ilm m` t} o}edm|`h jhs ojo}jhs u}m mnmot}estm.

Mj dmvh|tm ne~h|ith dm Geade ms mj n}tlhj y ohgh

thdhs m` s} negijie jh selm`* simgv|m jm |maeje`

lejh`ms y vmjhtes* u}m a}e|de m` s} oese. Ve|e

h|dmè|jhs jhs eohghd vh| ohjh|ms y tegehs. Ej

tm|giè| sm dih o}m`te dm u}m;

5= dmj thtej dm jhs lejh`ms* sh` dm ohjh| |hkh* sh` gs obioes u}m }` lej` dm

n}tlhj v|hnmsihèj y 5> ms gs a|e`dm. Mj |msth sh` dmj

gisgh tegeh u}m }` lej`.

U} n|eooi` |mv|msm`te` jhs lejh`ms dm ohjh|

ljeòh dmj thtej dm lejh`ms8 O}j ms je n|eooi` u}m |mv|msm`te jes vmjhtes u}m

sh` dmj gisgh tegeh u}m }` lej`8 U}m hvm|eoih`ms |meji{estm ve|e oh`tmste| jes

v|ma}`tes8 Dmso|ilm jh u}m beoms ve|e |meji{e| s}ges dm

n|eooih`ms.

Dmso|ilm jh u}m beoms ve|e |meji{e| |mstes dm

n|eooih`ms.


61/202

=9

5\ms}mj~m jhs mkm|oioihs sia}im`tms;

e) Ohjh|me jes s}ges u}m sh` ia}ejms e .

l) _i jh `momsites* }se jes ti|es dm je eoti~ided < ljhu}m 5 ve|eoh`tmste| mj sia}im`tm mkm|oioih. Hlsm|~e mj mkmgvjh;

E = ti|es dm 52 dm jhàit}d jm u}iteghs ? ti|es dm52 * m`thòms `hs

u}mde` < ti|es dm 52 * oede }è.

54 #

54 7

5? #

54 7

54 #

52 7

5> #

7

5? #

5> 7

?2 #

#

?> 7

?4 #

?4 7


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>6

7

Documents

Matemáticas 4º RIEB Alumno 2011-2012