matematica clasa 5 - culegere de exercitii si probleme ... clasa 5 - culegere de... · rnergoud rs...

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rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U . ncsou !]ue]suoC uelnelcg- n tn t'l poulq eueol . ncsedo6 ecrcnl . nru16-ning olll ceioC preuoo'I-urluelsuo3 . ncsolncu;g 5o6e.rg . eqe.4ez leql6

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Page 1: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

rnergoud rS uircu=xe aq ruectlnc

V-N V VSV.IC NUINfd

vclrvl lrrvl,u

ee[u3g eu llslr C-EreouEI/U . ncsou !]ue]suoC uelnelcg- n tn t'lpoulq eueol . ncsedo6 ecrcnl . nru16-ning olll

ceioC preuoo'I-urluelsuo3 . ncsolncu;g 5o6e.rg . eqe.4ez leql6

Mtlflllfiulflfl

Page 2: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

Se6ly'pnf 'r1Sa1so3 gCrl I

29""""""' """ (ercnPae) eayelrydecd e$el69 """"""' esnduoc oJotunu ieuud oJotunN ?'Z'l99 """"""' 6 m ls e nc olellllqlzl^lp op llroluc e'z'l99 """"""' '0J'

'9 'Z"nc olellllqlzl/\lp op llJoilJC Z'Z'I?g """"""""""" tunuoc t;dr11nu ltunuuoc uoztntp lnldtllntu itozrxq y'7'1

t9 """"""' """"' oletnleu toptotunu eapyilqlzl^lo z'l29 """"""' ezelodt tesle1 Bpole17\ I'Z't'l6? """"""', sJo^ul lnlnsJotu epoloy\ g'L'l'lLn.".."""" "' p^qern6u Bpoloy\ t'L't'l9V""""""' tetiereduoc epolo17\ t'L'l'lt, """"""' """ olellun el luocnper epolar! z'L'l'l2t """"""' lolauelqoJd e elen;ozoJ op octlotulue opoloy\ l.'Z't'l

ezelodtlosplepoJow 'sJoAu! npsJow epopw 'ga14enbg epolew 'rcrtercdwoc epolew 'eJeJ

-!un q uocnpoJ epoJow :Jopwolqud e ercalozd op octJowrye opolory 1'L'l69 """"""' """ opelocel{eletlpA 'opunlo) ropzoJuued eerczt14n jtoltrtercdo qr?nlcole eoup)O g'L'l

Lt,"'"""'"' " Zezeq uleeroucs9'9't'lge """"""' jLezeq uleoroucs 9'9't'lgt """"""' .ro;r.re1nd eerereduoC r'9't'ltt """"""' """" uelnd nc Inclec ep lln6ey t'g'['l00 """"""' ""' lernleu rPunu lnun lnlerlpdz'9'1,'lL2 """"""" "' lernleu Jpunu tnun e leJnleu lueuodxe nc BoJolnd L'9'1,'l

(fiercdo ??l) Z ezeq u! eoroucs!61, ezeq u! edeucs lto1ue1nd eerctedwoc lue1nd nc pqec ep pbu lptn4euJ?unu lnun ruul?d iptnpu r?urnu lnun e pJnJeu yeuodxe no edond 9'L'l12""""""' olernleu)olo)-eunu e JSaJ nc eoJiJQdw! lelenpu nluownu e uez JSaJ nc ee$tpdu1?'L'l.,2 """""""""" unwoc p)opeJ !fip4epdotd 'ap)nJeu Jolueutnu eefi1nwu1t'L't

L|""""""' ' oleJnleu Jolorounu eoJoppcs z'z'L'ltt """"""' tlpleudord 'olernleu JoloJorunu eoJeunpv VZ'l'let """""' """ olunl-eu rop)ewnu euepgcs llfp4epdotd 'eletnpu Jop)outnu eueunpv Z'L'lO t

" " " " " " " " " " " oleJnleu Jolelounu eoJeutlse t6 eeletutxolde'eoJeuopJo'eoJ-ereduuoc lro;ereuunu exe ed olernleu JoloJorunu eoJeluozoJdeU Z'1,'1,'l

L"""""""', """' eleJnleu JoloJoLunu eoJl1c t6 eeleuca L'L'r'lg """""""' y?wgso'ugturxotde le1en4eu nloJounu edeuopJo E eerctedwoclto1ercwnu exe ed eoJeJuezeJdet lelenpu top)ewnu edryc E eercucg i'i'19 """""""' op)ryeu otownu nc yfetedg y'1

SlvunrvN =lu3runN'l

sulJdnc

tGZZgZg lt} r08rl 3r

- "" 'ceio3 pleuca---leue;qo.ld lS r rf rc.raxa

flflflmnnfll

Page 3: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

:efieafie :plewnez efice4Teynzot nc eprnJeu oJewnu ?nop e eetfugdutlg.z.tl89 t ' opuou apwpez ep llull r?wnu un nc oputcoz rotttlce4 eefi1nwi1 p.7.11

09t """""'" afiuouqewpoz ep lluA Jpwnu un nc opwpez rcphe4 eoJoppos 6 eercunpv fz.ilLVr """""' onuou opwtcoz ep ilutJJputnu un nc epwpoz lfice4 Joun eoJeuop)o E eerctedutoC Z.Z.Z.al9?L """"" ' epueu opwtcoz ap WTr?unu un no opurr-ez ficet1rcun e roprewnu exe ed eercluezedey jUpuitxotdV

l.Z.Z.llWL """"" epuou opwtcoz ep lu4Jgunu un nc eleupez fice4roun eJOpJeWnU eXe ed eeJeluozoJdet $ eeleuoplo 'eetercduoc lugwtxotdy 7.7-118tl, """""' "" prewpro efice4 u! opuou epupoz op llullJ?unu un nc eleutnez nlce4 loun eaneuao$ue4 laleuoez yJcetl ep puuoJ gns0L !ry e1e yelnd yoilwnu nc oreupro to11fice4 eoJotrcs lelewtcez ltlcery L.Z.ltLtt """"" "" apwpoz 1fice4 7'112t1""""" """ (ercn1eae) ea11e1n11A-ecet elidilzt

-' prewpto ofical o-4u!p nes prnpu reunu un-4u!p e4uecotd 1IceU I Lit221"""""' " .rolrrie.redo rupnlcoJo eoutpro Z'g't'll8tt """""' "' eJeurpro tol;;fceg ee.rrJ.rpdul g'g'l'll9t1, """""' e.repd elee.recrprlig'g't'1ZtL """""' "" oJeurpro ro111ice4 ee.rrf;nuu; 7'g't'll60! """" oreurpro ro11;ice4 eoropErcs rS ee.reunpe nc euralqorj g.g.l..ii90t """"" ""' oJeurpro rolrflce4 BoropgJs Z'g'L'll1.01 """""' "" aJeutpJorollfce4 eoJeunpv t'g'l,'ll66 """"""' "' oreuvro tice4 nc fiercdg 9.1.1186 """"""' ' unuoo Joltunu un e; ro;rrfce4 eoJocnpv Z.g.r.ll96 """"" eleJnleu oJorunu pnop e unruqJ npqnu cLu teu loC l,.g.t.ll96 """"""' """,""""' unuoc roilunu un e1n1ulce4 eoroc-npe !(u4uo61e prpl oprnleu orounu pnop e unuoc np41nu cila rcu pC g.L.ll2G """" elqncnpol !fice4 tottfice4 eercagdutrs E eerccrypwv Z.?.L.llt6 """"" opJnJeu arcunu ?nop e unuoc JoztAtp oJew Eu loc L.t l.al16 """""""" olqncnpq !.Ice4 tolrfice4eerccEputs E eerccryldwe!(ut11to61e gg) elenleu erounu pnop e unuoc roztAtp ereu lew pC f.L.tt88 """"""' " eice4o-4urpto16e4u!eoroleocs E eerccnpoqq tiit78 """"""' aewpto rrhe4 loun e JopJounu exeed eercTuezetdet lo\ptpwnu loyunu Eelece nc nlfice4 eercteduog 7.1.1108 """"""' 'oluele^qce;1fcer3 V'l'1,'ll92 """"""' oluocord t'r't'll2,1""""""' eleluneldns 'oJelruntqce ,e.lepunqns rrlce.l3 Z.L.t ll89 """"""' """ oreulpro;;fcel1 L't'L't89 """"""' (ug4uezedu uud) e4uelearyca IIce4leluecad larcyunedns'ercyuruqce ,orelunqns ylcetl lercu1pto ltlcery f it 99 """"""' "" erculpto lficeU L.tt99 """"""' f'rvuulcfz tflcvuJ .:ruvNtouo tfl3vul

.il

Page 4: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

Ltz :: ::::: : firyosfi7"""""' ""' (ercnpae) eagelnydecar oJsel

6tZ """""' ""' (lo;esen eeleycedec)ctq6unldelp ln;nped-rdr;e;ered pe rS rn;nqnc Inunlo^:unlo n.4ued PrnsPU ep llPllun t'g'lllgtz"" rn;nrq6unldorp/nlnlerlpd eue :eue ru1ued PrnsPU op liPilun Z'9'lllLt7"""""' e4euued :eut6unl ru1ued PrnsPU op llPUUn t'g'llltt'"""""' """""" Hns-pw op to11jg11un op UPw)oJSuul luqbun4dery p1nped1dp1ercd p $ plnqnc

nwryo^:wnp^ ru1ued ?ns,ut ep fig11un ip1ryqburydeq1ryn1e4?d eue :oue

ru1ued grns?w ep fipyun le4ewued :ewbunl ru1ued Uns?w ep rtruun y'ilt822""""', "'(eteu-ndedns uyd) e14eu1s op exe !(ercundetdns uyd) epentbuoc pn617 9'111

122"""""' elewrse5exesolnulw $ epefi ul elewudxe yryq1un op Uns?ur nc epqeC 'y6unp y.16un 'pug6un lzn4qo gbun 'lincse ry6un '4deq ry6un :unrq6un ep u7c1sep !(ruoyodetnc eficrupuoc ri eerctnspw) e1ueru6uoc yryqbun 'gbun nun eJnsQW '1t46un

lnun pJotle1xe 'ry6un lnun nro4e4u le1uewe1e 'fie1ou 'efiugep 4.16u11 7'115

022"""""' Tcundun op glel pund lnun pc4Jetus lluewbes nun pcol[1w !(eficrupuoc) eluentb-uoc eluewbes lyeuios nun eewbunl lelcund ?nop o4ulp elueplg t'tttg12"""""' "" e1e1ercd eldeq'oJualncLtoc e1dery:e1dery

?nop e eAlplil e1fizod !,,eun rcLunu $ p4deery o ecdJ olcultslp elcund pnop

uud" lercrw1oc elcund lp1deery o ep PIel Tcund lnun ep o^!lep) epfizo4 7'111

2t2"""""' (Lfiepu'erc1uez-efiu'ercucsep) Tuew1es'g4deerynues'ueldtwes'ue1d'p4deaq'lcund L'lllnz"' """' YUnSYU!| =o

IlYJNn ls ilHrf l lo3e =o frNf t l]'I:t'lll

n02"""""' """ (ercnpae) ea14e1ry1decor olso1

n6t "' octlsqeJs olep op Jos mun elpow !11u11 nc nes76 oruq nc ecgefi 'opqeJ uJ

elezuebto ecqsqels elep leluencetg Tole4ep e arczuebto op owalqoJd OL'Z'ttO6t """""' oreleuow tiryun$ du17'psetu 'e4eycedec 'LilnpA'aue 'euttbunl ru1ued ?JnsQut ep igllun $ u1n

-Jarut dec ul !!ice4 nc rolowopod eercnlozet n4ued ac7owlue opolery 6'Z'ltLgV " eanrzod eleuortet ereLunu nc rcilrtercdo l7gnpolo eowpo Z'B'Z'llV1L """""' """ eNlzod eleuortet deunN t'8'Z'!l

earyzod eleu-ortet ercwnu nc rcprtetedo upn4coJo eewpo lea4rzod eleuofiet oJownN g'Z'lt

6L1""" g.tewpJo efice4 u! octpouod elewoez lice4 rcun eoteu)olsueL [Z'tltLL"""""' efiuou eleutoozep ilulJ )Qwnu un nc eleunez fice4 Qnop e eetfugdwl lpueu pJnJeu )?wnu unel epueu epwpez op tlull )?unu Ltn no epwooz fioe4 rcun eefi.tgdw! g'Z'ttggt """""" """" elelctpoued lpptutcez eficetl o-rlul oteupro lfice4rcun eeJeuttoJsuu] le1en4eu eJownu )oilnw Ew nes Qnop e QcqowyJe epew

:efiea1de lglewoez fu)89t '. epueu opuffi,zq09t. """""'qeupoz op lluu ryua tAVL """""',

J?UoU Un nc qeuxm I9t1 """""-ez ficetltoun e)ore,xttw\. """"" qtEuJopJeunu exe d aEf,8t1 """""'J?UIU Un nC qeum fi0L !ry e1e yeyd Wtt r.t,Let'-""""'2t1 """""'?ZL" ?euproffi4o422t """""'8D """""'9!t """""'zLt'-""""'60t """" oreulpJoro;iE90t """""1.0t """""'66 """"""'86 """"""""""""'-""'- trt96 """"" olernleu ararrl96 """"""'-npe !(uyto61e gg) rya26"""" elqncnpt tfu41,6 """"" oPrnpu a.Erurat6 """"""""""""""""" q!(a1uo61e gp1) eletr4an a

88 """"""""' """"""" €f?8 """"""'ed eercTuezetdat bpryt

fifl|nilffifi$

Page 5: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

osnduoc olounu leuud eJelrnN .6 nc 16 t nc oleltltqlzl^lp op uloltro .,01 'g'z"nc eleltlrqtzt^tp op ilJolrJ3.

runuoc r;dr1;nu lrunuroc tJoztnrp lnldr1;nu llozrnr6 .

f 'IVU flIVN U O'I :lU f ru n N V=IIVI|'I I AEI AIO Z' I

ezelodr lesle] epoloru 'sJonut tnlnsJotu epolotu'pnriern6rl epolotu 'rerfeleduoc Bpoleu 'ole1un el lJocnp-oJ Bpolor.u :Jolol.uolqold e elen;ozd op octlorulue opolof! .

opBloce rS elellpd 'opunl-oJ :rolezelueled BoJeztltln llo;rrfe.redo lJpnlcoJo eoutpJo .

(tfer-edo prpl) Z ezeq uJ eoJoucs :Ot ezeq uJ eoJetJcs l.ro;r.re1ndeerereduoc luelnd nc lnclec ep rln6e.r l;elnleu Jptunu tnun1n1er1pd l;elnleu Jprunu tnun e leinleu lueuodxe nc eoJelnd .

oleJnleLl JoleJetunu e lsoJnc eerrfupdrul le;einleu Jolelounu e oJez lsoJ nc eelrfupdr-u1 .

unuoc Jolce1 lrjpleudold 'eleJnlBu toloJoulnu eelri;nuu; .oleJnleu JoloJ

-ounu eeJoppcs lripleudo.rd'oleJnleu JoleJotunu BeleunpV .rJpturlso' r.rpr-urxolde 1e1

-eJnleu JoloJounu eoJeuopJo rS eeleleduuoc llo;elounu exeed eeleluezeldel le;elnleu Jololounu eoJtltc rS eeleucg .

3'IVUnIVN 3Uf runN nC ltivu:tdo I'l

:e.rdsep eipnug lien ;olrdec lsoce ul

Page 6: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

'600 6 (p :ttz v @ :zog (q :u(e:rnlnJprunu InJosocopeld q6 InJosoccns oucs '?

LL'g 'g eloJJtc nc oucs riod er;tc leJl op eJounu elPC 't

'olcullsrp eJllc loJl op JPrunu cllu leu loc !s oJeu leu loc ollcs 'z

'rcozpnou llLU op elns nlled oueollltu tcutc (plrop rS tcozteJl Plns o llLu op rcezpnop (c

lre.r1 elns ese6 ttu.t ldo (qlrrur eldes eps pnoP (e

:oJounu oloJeolPt.uJn eqBte JoleJJlc ;ntolnfe nc olJcs 'L

)... o................. o.. o o...........$ iIClIdU

'Jprunu tnloce eeJolJcs ul rerilzod Pluolep ednl6 e1;e

op plpeJlp U eA 'lPunu un-Jlul PSlJcs 'PleuJoJ nou pdnr6 oJecell 'ol

-ledep reu e6e 16'etu pltunu 'olellun Pnou o Qzeew)ol olns ecoz'plns plrunu 'oleltun Pnou o PzeeuJoJ Jollcoz e ednl6 ecez'(ecezep) pdnr6 pnou oezeow)ollipUun ecez';euttcoz Inuolsls ul

'rolrqere pluolep tued

-oJno ep 1en;erd rs (erpul 'npulq) tuolpul op leluonul lsol B 'leuttcezgeuorirzod uolsrs ts lrunu 'etieleutnu op leLulcoz Inuolsls

"''o0L 0"" 'z 't '0 :olso oleJnleu Jololounu lnlls 'z

e4rcc'q'e'C + q. 0L + B. 001=CQE'0- ezeq uJ'oqBJe olJlc nc nlJcs es oleJnleu oloJerunN 'I

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .f iililUllt

SrvunrvN uo']=luf wnN vSulrlc 16 vru=lucs v'l't'l

3]VUnTVN 3U=lt/UnN nC llivufdo t'l

azq'pnrleln6g epolaJ-eJ epolout :Jopu

-oJ :JOlOZAlUered

-edo prpl) Z@eereleduoo lpey1n1e4pd llelnpu.q

nc eetrtrpdru!:aF.unuroo lopel:i

-ounu eoJopEcs:

-eJnleu JolaJaunued eeteluezaldar

f IVU NIVN

f.IVUNI

Page 7: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

:

I

B GIITJO Baplsrxo L = I + e nc 'Ltqe eruJoj op oloJerxnu elgC .9!,

lgq6 = gqe (q1q0 = /e

:e;rrie;e.r pcrJUoA eJec qB oleJorunu pBV .gt

'l,g'".'LZ'.gr ';.;, :;nlr6 ugcsesp6 es eledtul elgc 16 eled eleunu olgC '?1,

olounu OOO 6 = 666 - 666 6 :pcqe :e;dr-uex3'lep Jprunu rn;nurud Inrosocopeld plep eruJoJ

"p rprn, lnutlln

urp eoppcs ton 'eleltctlos JoloJounu InJE)tunu uedocsep e nJluod

). . . . . . . . o . . . . . . . . . . . o . . . . . . . . . o . . . . . .a4iilclffll

Lcqe erurol op reo aplslxo qB BruroJ ap ororunu elgc .01.

'81JOlO4tc euns nc o^tlncesuoc oJltc, utp leuJoJ InJprunu otrcs .z[

'gz roloJltc euns nc ecuuept orJts , utp leruJoj InJprunu oucs .H,

'-'zzzz' zzz'zz'z (c

-'oL 'g 'g 'v'z(q

;;;;;:;;;:":" :,1,'", o,'eqqe (e lpcqe (p:tot@:sg (q

I

;

ai

Z

L

:ue (e

:oleJnleu otounu JoloJeolptuJn ololeuJnlspJ otJcs

'q + e 'qeLee :etrJJoJ op rurxeu ts rututru JnJptunu otJcs

'eLe :ew)ol op lpunu cil.u leu le3 ts eJB[u tBu lec etJcs

100 LZ @ :eOO Z (c :Szt, Vg G :ggr s (e

6 + 01. L+ 001 . t + 000 l.Z= 6Lt,Z:lnlopotu pdnp'oJotunu eloJeolptuln eundutocso6

Lt' Z'0 eloJltc nc eruro1 riod ellrc toJl op oJounu olgC

.L

'9

'9

I

I

'6

'8

Page 8: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

'p'LU'e'6 t -001 = 66'L -01 = 6

:nrcrpul

94pJ!9L666"'666 *"""+ 666 + 66 + 6 =V

:lnrPrunu ore L op orlrc olgc PIJV '7

')0 etuJo, op Jpunu un lelBcJolur e-s o^rlncesuoc oJetunu Pnop erlul:e;iec;Iu1

'rrS urp rprunu eel-00 L le pUV

l, '? '6't'g'Z'0 't oleJnleu eJetunu ep gn.rrS [upJoprsuoC 'g

'L L JOIOJITC BUnS

PqlB PS oJec qeLZ eruJo] op olernleu roleJorunu InJPrunu PulLuJolocl 'z

'91/0= PQQ + cqqg :erie;er Pcuuo^ eres olorournu P[v 'I

'lep rPulnu lrryurp Boppcs lo^'ols$3tlc

e-\aa.a.aa.aa.o.at

acqe ar.r

'g L JOIOJIIC BtUnS n3 a

'gz Jolo4tc euJrxs

'eqqe (e

+. . . . . . . . . . o o . . . . . . . . . . . . . . . o . . . . . . . . .$iiuSl llt

L+6.V=o'l

'L+L'V='l'L+0.V=tl

:orJcs eleod es rn;n.rr6 le Jplunu eJEcuO:eriecrpul

("0'l) rn;n.rrS le uorurol eel - LLOZ p pUV (q

'ruoruJol nrled pcuJ nc ;nrrS pzeelduuo3 (e

L '6 'g'L olBJnlBU oJetunu ep;nrrS oll 'BL

'919 = e + ee + eee :Pc pullls e erllc PllV '/t

'q # e'qel

'ele teuuo)

LOO LZ (

6+0[.:lnlop(

Lt' z'a a

'l,g '"'' tz'.gl'!;, :;rur6 r,!

Page 9: Matematica Clasa 5 - Culegere de exercitii si probleme ... Clasa 5 - Culegere de... · rnergoud rS uircu=xe aq ruectlnc V-N V VSV.IC NUINfd vclrvl lrrvl,u ee[u3g eu llslr C-EreouEI/U

ll

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