Рабочая программа по ФГОС 0 2021 Математика пролонгировано
MI4HI4CTEPCTBOIIPOCBETTIEHVLfl,pOCCr4fr CKOr;t@EAEpAUT{tr
Muuucrcpcmo
o
6pas o BaHLIfl , HayKr{ }r MoJroAeNuofi rroJrr4Tr.rKr{ Kpacno4apcKoro Kpa,
Mynz quu anru o e o 6p as o B aHr.r e Tyan cu ucrc uit p aiton
MBOy COIII
Il! 14 uu. f.K. Xyxona
PACCMOTPEHO
CO|JIACOBAHO
MeroArrqecKI4u o6:seArzueuueu
3auecrure,ru Ar4peKropa no YBP
yunrelefi
or"31"
yTBEPxtAEHO
,{upexrop MEOy COtil
i\!
14
rarra.
f.K.
Xyxona C, Kpuneuxoncxoe
pyxoBoArzrerrr IIIMO Cy66oruua
llporoxor
c. KpuneuxoBcKoe
A.III.
l
3au.4upexrpa no YBP AaeArrH 3.A.
,(npexrop MEOY COIII
llporoxon Nl1
.ltlrl4 fpuroprena 11.B.
.#-
J\!1
ov2n2W
or "31" 082022
&rcor/
flpuxa.:
J,{b2
or "31" 082022 r.
PAEOIIA.g TIPOTPAMMA
(rD 2s01lse)
yue6noro [peAMera
Aly- 5 KJracca ocHoBHoro o6ruero o6pasonauu.a
sa 2022-2023 yue6w;fi roA
Cocrasarem: Kauaesa AnercaHgpa flanroeHa
yql4Tenb MaTeMaTllKr4
TI O.fl C
HI4TE JIbHA-fl 3ATIPIC KA
oEIIIA-fl XAPAKTEPI4CTI4KA yTIEEHOIO IIPEAMETA " MATEMATI{KA "
Pa6oqax rporpaMMa no MareMaruKe Anfl o6yuaroquxcs 5 xlaccon pa:pa6oraHa Ha ocHoBe @e4epa:mHoro
rocyAapcrBeHHoro o6pasonareJlbHoro craHAapra ocHoBHoro o6ulero o6pasonauur c yuerou u
coBpeMeHHbIX MI4poBbIx rpe6onaHufi. npe4t.f,Brr:{eMbrx K MareMarprLrecKoMy o6pa:onaur4roo14rpap,lluit
poccaficxoro o6pa:oeaHtlfl., Koropble o6ecnequearor
oBJraAeHr4e KJrroqeBbrMr4 KoMnereHulz.flMll,
cocraBJlflIotul4Mll OCHOBy Anq HelpepbrBHoro o6:a:oeaHzfl H caMopa3Br'tlrfl, a raKlr(e rleJlocrHocrb
o6rqexylrrypHoto, rplr{HocrHoro r4 no3HaBareJrr,Horo pa3Bktrvfl. o6yuarorqzxcq. B pa6ovefi npotpaMMe
yqreHbl uilev v IroJro)I(eHLI[ Konqenquu pa3BLrrns. MareMararrecKoto o6pasoaanus e Poccv iicrofi
Oelepauuu. B snoxy uur|lponofi rpancrfopnaaur{14 Bcex cSep ue:rone.recxofi AesreJrbHocrr4 HeBo3Mo}r(Ho
crarb o6pa:oaauublM coBpeMeHHbIM r{erloBeKoM 6es 6asosofi uarenaarrzqecxofi [oAtoroBr(u. Yxre B urxoJre
MaTeMaral(a cny)I(I4T orropHblM npeAMeToM Anq E3yqeHafl cMelr(Hbrx ArrcqrrnJrrrH, a rrocJle [IKoJrbr pea-truofi
ueo6xo4uuocrlro craHoBl4Tcfl He[pepbrBHoe o6pasonaHHe, uro rpe6yer rroJrHorlenuofi 6a:osofi
o6qeo6pasonaremuofi noAroroBKrr, B ToM rrr,rcre rr MareMarr4qecrofi.
3ro o6yc:roB:reHo reM, rrro B Harrrr4 gHrz pacrer qucno uporpecczii, cBr3aHHbrx c HenocpeAcrBeHHbrM
IlpaMeHeHIreM MareMarvKr4'. u n c$epe SKoHoMr4-{r4,
v z 6uzuece, a B TexHonor}IqecKr,rx o6,racr.ax,
}r Aa}r(e
B
ryMaHaTapnr,Ix c(repax, Tarant o6pasou, Kpyf rxKonbHlil(oB, Anfl r(oTopbrx MaTeMaTaKa Mo)KeT cTaTb
3Harrr4MbrM
npeIMeroM, pacurr4pqeTcr.
llpaxru.recxa, [orle3HocrL, MareMarvKzr o6ycroueHa reM, .{ro ed npeAMeroM .rBJlgrorcg
t|lyu4aueuraJrbHbre crpyr(Typbr Haruero Mr4pa: flpocrpaHcrBeHHbre $opl,ru u r(oJrrrLrecrBeHHbre orHor]reHrzrt o'f
npocreiiruux, ycBaI4BaeMLIx B HenocpeAcrBeHHoM orrblTe, Ao AocraroLrHo cJro)r(Hsrx, ueo6xoAr4Mbrx Arrr.fl
pasBtrrLlfl. HayrrHbrx r4 npuKnaAurx u4efi. Bes rouxperHbrx MareMarr4rrecKr.rx:uauufi 3arpy4HeHo rroHr{MaHi4e
rpuHqanoB ycrpoficrna r4 acrroJrb3oBar:ztr coBpeMeHHofi rexuuru, BocnpH.f,Tr4e r4 vHTepnperaurrfl
pa:uoo6pa:uofi couuaruuofi, gKoHoMr4qecrofi, nonr.rrr4rrecxofi uu$opMaril4v, rraanoscf$exruBHa
noBceAHeBHafl rrpar(Tr4rrecxarr AeflTeJrbHocrr. Kaxc4oMy qenoBeKy n cnoefi )I(H3HI4 [p].IxoAarcq BblrorHqrb
pac.rdru 14 cocraBJrrrrb anropr4TMbr, HaxoArrrs 14 [przMeHrrrb Sopiraylsl, BJIaAerb flpaKTl4qecxul,tu npueMaMI4
reoMerpr4qecxr4x llsuepeuafi 14 rrocrpoeHuit,uutau, aHrpoprraqarc, npeAcraBneHHyrc B Br.{Ae ra6rug,
AaarpaMM z rpa$uxoB, )nrrrb B ycnoBprflx HeorrpeAenennocru u rroHuMarb Bepo.[THocttrfi xapar(Tep
clyuafiuux co6tstui,t.
O4uonpertreHHo c pacurr4peHr4ela crfep npr4MeHeHr.r, MareMarvKrz B coBpeMeHHoM o6ulecree ece 6oree
Ba)KHbrM craHoBr4Tc.f,
HaBErr(ax.
MareMarurlecxail crl4Jrb Mr,nrrJreHrr.s, npoflBJrsrolJvtitcr a orpe4ereHHblx yMcrBeHIrblx
B npoqecce
v3y.ueHlafl. MareMarur(H B E.pceHan npaeiraon
ecrecrBeHHrru o6pa:oM Brsrroqarorcfl rrHAyKrIVfl
v
14
MeroAoB MbIrrIreHHl
LreJroBeKa
Ae4yKrrlrs, o6o6rue:a:ae A KoHKperI4 r]at\l4fl, aHutu3 v
x.raccutfuxa\yrfl, H cucreMarr43ar\ktr,, a6c'rparrzpoBaHI4e h aHaJrotLtfl. O6r,exru MareMaraqecKltx
yMo3arolrcqeuufr,, npaBr4Jra rrx r(oHcrpyLlpoBaH:zfl pacr(pbrBaror MexaHH3M rorarrecKux nocrpoeuuil,
cr4HTe3,
cnoco6crnyrcr nrrpa6orr(e yMeHHr rpoplrynupoBarb, o6ocuoerrsarb [I Aol(a3blBarb cyx(AeHl4q, TeM caMbIM
pa3BrrBaror iroraqecKoe MErrrrJreHrre. Begyrqar ponb npITIraAJIero{T MareMarLIKe u n Sopnar4poBaHW
antoprrrMr.r.recxofi r(oMnoHeHTbr MbrrrrJreH:zfl.vBoailLrrauurr yrraeuufi 4eficrnonarb rro 3aAaHI{bIM antop}ITMaM,
ocHoeofi yue6uofi
coBepueHcrBoBarb r{3BecrHbre r{ KoHcrpyr{poBarb HoBbre. B npoqecce perrreHplf, 3aAaLI
AerrTenbHocru Ha ypoKax MareMaTr4Kpr
MbIIUICH},Iq,
-
pa3BlrBaroTcrr Tar()Ke TBoprIecKa.fl
14
-
IlpIrKnaAHaq cTopoHbl
O6yuenue NrareMarr4Ke Aaer Bo3Mo)r(Hocrb pa:Br4Barr y o6yuarouluxcfl ToLIHyIo, paquoHanbHyio I4
au$opuarraBHyro pelrb, yMeHue orl6upars nau6oree noAxoArlullle fl3blKoBbIe, cI{MBoJII{qecI(ue, rpa$u'lecrue
cpe/xcrBa ArL BblpaxeHl4fl cy)I(.qesuit u HatJrrIAHoto
ax [peAcraBrIeHLIr.
Heo6xo4url,rbrM KoMrroHeHToM o6uteii Kynbrypbr B coBpeMeHHoM Tor'II(oBaHVr4 qBJr.sercrt o6ulee 3HaI(oMCTBO
c MeToAaMI{ [O3HaHI4S AefiCTBI4TeJ]bHOCTI.,I, npeACTaBneHVe
or MeroAoB Apyrr4x ecrecrBeHHbrx
peueHLI[ HayqHblx u [paKnaAHbIX
O npe,4MeTe I4 MeTO,4aX MaTeMaTI,IKLI,UX OTrptqLtir.
o6 oco6euuocrflx rrpr4MeueHli.f, MareMarr4Ku Anq
3aAar{. Taxurra o6parou, MareMarurrecxoe o6pasonanue sHocIar csofi
r4 ryMaHraTapHbrx HayK,
BKnaA n $opnrupoBaHue o6uteft Kynbrypbr r{enoBeKa.
I4syueune MareMarllrlz TaKx(e cnoco6crsyer gcrerr{rrecKoMy BoclruraHr4ro qenoBeKa, rroH}rMaH}r}o
Kpacorbl Iz I{3.rlqecrBa MareMarr.rqecKr4x paccy}rt4eHraft, nocnpzflTr4ro teoMerpr.rqecKr4x &oprur, ycBoeHr{ro
r4Aer4 cr4MMeTpytu.
IIEJII,I pI3yrIEHAfl yqEEHOTO KypCA
IlpuopurerHbrMu uenflMr4 o6yreuux MareMarr,rKe e 5 xracce flBJrrrrorcf,:
[poAon)I(eHae SopnruponaHafl ocHoBHbrx MareMarnqecKr.rx nouqrufi (.rucno, BeJrlrqaHa,
reoMerpl4rrecKas $urypa), o6ecne.{usarcxlrrx ilpeeMcrBeHHocrb r{ nepcneKTr4BHocrb MareMarr4r{ecKoto
-
o6pasonaHua o6yualorqvxcfl.;
pa3Brrrlre r{HTeJrJreKTyanbHErx rr rBoprrecKzx cuoco6socrefi o6yuarorquxcs, [o3HaearemHoft
-
aKTI.{BHocrH, HccJIeAoBareJlbcKrrx yueurzfi, r4HTepeca K r,r3freHr4ro MareMarr,rKr4;
-pr
[oABeAeuue o6yuarcquxc, Ha AocrylHoM Anrr HHx ypoBHe K oco3HaHr4ro B3ar4MocBfl3r4 MareMarur(r4
oKpyr(arculefo MHpa;
$opuzpoBaHkre Synrquouamuoft MareMarr4qecrofi rpaMorHocrr.r: )"laeHrz.f, paclo3HaBarb
MareMarr4rrecKpre o6rexrur B peanbHblx xr43HeHHbrx cr,rryaur4sx, ilpprMeHsrb ocBoeHHble yMeHIif, An.,I
-
perrreHr'Ifl rrpaKTr4Ko-opr4eHTr4poBaHHbrx 3al.aq, r4HTepnpeTl{poBaTi, flonyrleHHble pe3ynbTaTll u
orIeHr4B
arb r.rx H a
co
orBercrBu e rtp arTllqecrofi cvry a\vkr.
OcHonurre rruHkrr4 coAepxaHu, Kypca MareMarr4Ku s 5 xracce
apu$uerl4qecKa,
-
Koropbre pa3Bl,IBalorc{ rrapanJreJrbHo, KaxAafl B coorBercrBr,ra c co6crneHHofi
He3aBrrcr{Mo oAHa
or 4pyrofi,
a B TecHoM KoHTaKTe
r.r
14
roruxofi,
reoMerpl4qecKafl,
oAHaKo, He
B3ar,rMoAeficrsuu. TaxNe B Kypce npol4cxoAuT
3HaKoMcrBo c oJreMeHrauu ame6pbl Ir onucaremHofi crarucruKu.
Irlsyueuue apa$rraeruuecKoro Marepr4ana Harrr,rHaerc.f, co cr{creMarrga\uLl u pa3Burva, sHaHufi o
HarypaJrbHrIX rrlzcJlax, noryrreHHblx B Har{amuofi
rurore. flpra
3ToM coBeprueHcrBoBaHlle
Bblrrl4clzrelrgofi
u QopuzpoBaHr4e HoBbIx reoperr4qecKux 3HaHr{fi co.{eraercq c pa3BIzTI4eM Bllqvclurelruofi
Kynbrypbr, B qacrHocrz c o6yueupreM flpocrefiruuu upueuart npLIKI4AKI{ I4 oIIeHKLI pe3ynbraroB
TexHr,rKI{
nsrqracrenufi.
3ro Apo6u. Ha.Iano v3yteHur
o6brKHoseHHbrx r{,4ec{Tr.rrrHbrx gpo6efi orHeceHo x 5 rnaccy. 3ro nepnufi sran B ocBoeHLIu Apo6efi, KolAa
rrpor4cxoArzr 3HaKoMcrBo c ocHoBHbrMrl vlesMvt, [oHgrl4qMu reMbl. IIpu eronr paccMorpeHae
o6rrxHoeeHurx 4po6eft s norHoN4 o6renre npeArrrecrByer LI3yqeHIrIo Aecsrl4rrHblx Apo6efi, vro
-{Llcronofi ilLrHvrlr, KotAa ilpar,rna Eefic;rsufi c
uenecoo6pa3Ho c ror{KLI 3peH[rs irorl,IKlr vt3roxeHplq
lpyrofi rpyuHufi 6lox
n coAeplr(aHuu apu(fvrerz.Iecxofi ItvHlrr4
AecflTr.rr{Hbrura 4po6aur4 Mo)r(Ho o6ocuosarb
yxe
-
pr3BecrHbIMpI aJItopI4TMaMH BbInoJIHeHu.f, refi.ctsuia c
o6ru 5 KJIacca [peAcraBneHa Harrlf,AHa, reoMerpvrfl,
KAqCCTBE (3AMECTHTCJIfl
HartpaBreHHaq Ha pa3Byrrue
o6pasuoro MLIrIrJreHHr, npocrpaHcrBeHHoro noo6paxeuux, uzolpasrrreJrbHbrx yueuufi. 3ro eaxHtrfi oral s
vr3yqerrLl reoMerpl{H, xoropufi ocyulecrBnfl.ercfl. Ha HarnsAHo-npaKTuqecKoM ypoBHe, onupaercq Ha
HatnrIAHo-o6pa:uoe MbIIxJIeHIre o6yuarorquxcs. Eomruafl ponr orBoAr,rrcrr npaKTurrecxofi 4eare:rbHocrrr,
onblTy, grcilepl4MeHTy, MoAerrr4poBanlilo, O6yqarorur4ecrr 3HaKoMflTc.f, c reoMerpprqecKr4Mr4 rfurypanrra ua
IrJrocttocrl4 Ir B npocrpaHcrBe, c ux flpocrefiururru rcouSuryparil4qMr4,yqa'rcfl, raso6paxrau, r4x Ha
HeJII4H0BaHuoi,tu
Krer.Iarofi 6yrvtare, paccMarprrBaror
narl.a4uofi reoMerprra
r4x
npocreilurze csoficrsa. B npoqecce r43yqeHus
3:uaHLrs, nonyrreHHrre o6yuarorqt4Mztcfl B HaqaJrbHofi
urxore, clrcreMarr43rrpyrorcJ{
r.{
pacurr4p,IroTc_s.
MECTO YTIEEHOTO KYPCA B YqEEHOM TIJIAHE
Cor:racso yue6uorvry nnaHy e 5 Kracce u3yrraerc-fi r4HTerpupoeauurrfi [peAMer <, xoroprtfi
Br(Jrroqaer apzcfueruuecrrzfi Mareprzan
r.r
HarnqAHyro reoMerpLrro, a raKlr(e [porreAeBTurrecKue cBeAeHH-s
arre6pu. Y.re6Hsrfi [JraH Ha r.r3yqeHr.re MareMaruKra e 5 xracce orBoA].rr
rleAeJrro, Bcero 170 yue6usx qacoB,
He MeHee 5
yue6nux qacoB
B
r43
COAEPXAHpIE yTIEEHOIO KyPCA "MATEMATI{KA"
Harypa.nnHbre qrrcJra rr HyJrb
Haryparsuoe r{Hcro. Pxg uaryparbHbrx quceJr. r{ucro 0. Irlso6paNeHrae HarypaJrbHbrx rrlrceJr ror{KaMr,r Ha
KoopAl4HarHofi (urac:ronofi) nprrraofi. IloszquoHHa, crcreMa
crrrzcJreHr.r.f,.
Plrucxas HyMeparrr4f, KaK rpr4Mep
Heno3lllll4ounofi cracreMbl cqlrcJIeHnx. [ecxruLrnas. clrcreMa cqucJleHl4q. CpaeueHue HarypanbHblx rILIceJI,
cpaBHeHI4e HarypanbHbrx rruceJr c uyneru. Cnoco6rr cpaBHeHr.rr. Orpyueurre HarypiubHbrx qzcel. Clo>xesue
HarypanbHbrx r{ucen; csoftcreo Hynfl npu cJroxeHr4r.r. Bsr.rr4raHl4e xax Aeftcrnue, o6parHoe cnoxeHr4}o.
Yuuoxesue HarypanbHblx rrflceJl; cnoftcrna Hyllfl, t4 eIr4Hr{rlbr
yMHoxeHvilt.,{enenue xar 4eficrnue,
o6pauroe yMHolr(eHr.rrc. Korr,rnoneurrr Aeficreuit, cB.,r3b Mexry Hr4Mrz. llponepra pe3ynbrara
apu$nreruuecKoro Aefic'rnug. flepenrec'rureJrbHoe r4 coqerareJrbHoe cnoficrna (saronrr) cJroxeHr.rrr r4
npr4
yMHolr(eHr{fl, pacnpeAerrr,rrenbHoe ceoficrso (:axon) yMHo}r(eHr4.s. Zcuoru:oBaHr4e 6yxa
4rr
o6o:Haqeuuq
leitctsuia...{erurera r4 KparHEIe qvcra)
Ha MHolr(r4relu. flpocrbre r4 cocraBHbre Lrvcna. llpusuaxu AeJII4MocrI,I ua2,5,10,3,9.,{eleuze
Her,r3BecrHoro KoMrIoHeHTa I4 3anr4clI cBoficrn apra$uerr4rrecKr4x
pa3no)I(eHr4e
c ocrarKoM. Crenenr c HarypaJrbHbrM nora3areJreM. 3auucr rrrzcJra B Br4Ae cyMMLI pa3psAHblx cJlaraeMblx.
9ucroeoe Bbrpax(eHr,re. Brr.rl4creHr4e 3Haqenrafi .rucroBblx Bbrpax(euuit; noprrAor BbIrIoJIHeHHs, Leitclsuit.
I4cuomsoeaHr4e rrpr4 BbrrrlrcJleHr,rsx nepgMecrr.rreJrbHoro I4 corlerareJlbHoro ceoficre (:axouon) cJlo)I(eHa.f, Iz
yMHo)r(enr.rr, paclpeAeJIHTeJIbHoro ceofi crea yMHoxeHI4.tL
[po6u
llpe,4cranleHrre o apo6u rar cnoco6e 3arrlacla qacrLr BeJrr4qr,rHbr. O6rmuoseHHble 4po6n. Ilpanulrnrte u
HenpaBr{nburre gpo6u. Crrreuraunat gpo6u; npeAcraBJreHne cMerrrauuofi apo6w B BI4Ae HerlpaBl,Inbnofi gpo6z
-uacrLtttvcna rr3 HenpaBr{mnofi
r4 BErAeJreHue qelofi
Apo6u. I4so6paNeuue 4po6efi TorrKaMLI ua.{ucrosofi
npxvrofi. OcHosHoe csoficreo Apo6u. Coxpaqeurae gpo6efi. flpune4eHze apo6ra K HoBoMy 3HaMeHare,rlo.
Cpaeueuue apo6eil. CloNenue r4 Bbrr{r4TaHue 4po6efi. Ynrsoxesue II Ae,'IeHHe 4po6efi; B3aaMHo-o6parurte
Apo6u. HaxoxAeuple qaeru rlenoro r4 rleroro no ero qacru. fiecttuuuan 3a[acb apo6efi. flpe4craueHue
Aecsrvrruofi apo6u B Br{.qe o6HxnoeeHnofi. Zso6paxeHr{e AecrrurlHblx gpo6efi ToqKaMI4 na qracrosofi
nprmofi. CpanHeHue Aecsrr.rrrHbrx apo6efi. ApuSnreruqecKue geitcrnun c Aec.f,TutrHuuz gpo6ruu.
Oxpyrnenze Aecsrr.rrrHslx gpo6efi .
Peurenue reKcroBblx 3aAaq
Pemeuue reKcroBbrx 3a1aq apu$naeruuecKkrM cnoco6ou. Peueuue JIorI4qecKLIx 3aAarl Peureuue 3aI.a.u
uepe6oporra Bcex Bo3MolxHr,rx BaprraHToB. ZcuomsoBaHl,Ie npu petrreHvrh sal.aq ra6maq u cxeM. Peurenze
3AAAI9., COAepX(aqI4x 3aBHCHMOCTI4, CBg3bIBaIOlII4e BeJIIzI[II4HbI: CKOpOCTb, BpeMg, paCCTOqHI4e; IIeHa,
KoJIHrlecrBo, crol4Mocm. EAunuqbr I43MepeHr,r.,I: Maccbl, o6t€rua, IIeHbI; paccroflHl4.f,, BpeMeHIa, cKopocrl4'
Cessr MexAy eAHHHuaMr,r r{3MepeHprfl raNAofi BeJrlrqrrHbr. Peruesue ocHoBHbIX 3al:aq ua 4po6a.
llpe4cran"neHr4e AaHHbIx B BLIAe ta6tut1, cron6'rarsrx IIIatpaMM.
Har.usgsas reoM erpr,rq
HausAuue npeAcraBneHrrfl o (fnrypax Ha nJrocKocrl4: TolIKa, rlpflv,afl, orpe3oK, JIf{, yroJl, JIoMaHafl,
MHoroyronrrHtrK, oKpyxuocrb, Kpyr. Yrol. flpxvrofi, ocrprtfi, ryuoft u pasnepuyrutfi yrrtrt. fitmua orpe3Ka,
firmuarouauofi, nepuMerp MHotoytonbHl{Ka. I4snaepeuze a flocrpoeH]Ie
yrnoB c rroMotrlbro rpaHcnoprupa.Hartr.AHbre rrpeAcraBneHl{fl o Szrypax Ha rlrocKocru: MHoroyroJIbHIrK;
npflMoyronbHr.rK, KBaApar; Tpeyronr,HprK, o paBeHcrne Suryp. I4so6paxtenue @aryp, B ToM r{ucre Ha
xlerqarofi 6ynare. flocrpoenue xon$nryp a\uir. us.racrefi npatrofi, oKpyxHocrll Ha HeJILIHosaHHofi u
rlerqarofi 6yuare. Irlcno6sosanue cnoficrB cropoH Ir yrnoB [p.uMoyronbHl{Ka, KBaApara, flloulaAs
Merpr4qecKr4e eAr4Hrrubr AJrrrHr,r.
npqMoyronbHl4Ka
14
MHoroyroJIbHIrKoB, cocraBJreHHblx r{3 npflMoyronbHHr(ots, B ToM
Lrr.rcJre
rpzryp,
xrer.raroft 6ylaare. EAIlHuuu r.r3MepeHr4s nnoqaAr4. Har:rqAHrIe [peACTaBreHI,Iq o
rrpocrpaHcrBeHHbrx dlurypax: npflMoyronruufi rapannenerurreA, xy6, ntuororpaHHI4KI4. 14:o6paxteuue
npocrefiuux MHororpaHHr4KoB. Pa:eeprnra xy6au [apanneneflflneAa. CosAaHue uoAerefi MHororpaHHI4KoB
uso6paxr4aHr4Hau peanr{3arlrlr4 ero rrpaB, npeAcraBneHIzeM o
MareN4arr.rqecro4x ocHoBax rpynrqaoHupoBaHz.fl pa3nr4rrHbrx crpyKTyp, sereHLrfi, flpoueA)/p rpa)r(AaHCI(ol o
o6ulecrna (nsr6opu, onpocbl u np.);
roroBHocrr,ro
r
o6cylnAeHlzro 3Tr4qecr(r4x npo6rena, cBrr3aHH6Ix c [paKTuqecKaM rIpI4MeHeHI4eM
Aocrr4)r(eHr{fi uayxl.t, oco3HaHr4eM Ba)I(Hocrlr MopanbHo-3TI4qecKI4x rIpIrHUIrnoB B AerITeJrbHocrH yueuoro.
Tpy4onoe BocrlrrraHIre:
ycraHoBr(ofi na aKrueHoe yqacrrze B peureHr4r4 npaKTr4qecKux 3aAar{ MareMarurrecrofi HarlpaBneHHocrIt,
oco3r{aHueM Ba}r(Hocrr{ MareMarrTqecKoro o6pasoeatrvfl Ha rlporfl}I(eHl4u ecefr
)KL13HI4
4,u ycneruHofi
ueo6xo4uurtx yueuufi; oco3HaHHula art6oponl u
nocrpoeHr{eM aHAr4BuAya,lruofi TpaeKToprru o6pasoeaHuflu )Iflz3HeHHLIX tIJIaHoB c yuerou rI4rrHbIX
r4HrepecoB u o6urecrseHHblx norpe6Hocrefi .
npo(teccrzosalrsofi Ae-rrrenbHocrLr
3creru.recKoe BocnuTaHrre
kr pa3BHTrreM
:
croco6gocrbro K gMourroHarTbHoMy a ocrerlrLrecKoMy BocrIpI4tITLIIo MareMarttqecKLIx o6't,eKloB, 3aAatt,
peureuufi, paccy)r(Aer{ufi; yueuuro BHAerb MareMar}ILIecI(Ire 3aKoHoMepFIocrli B lrcxyccrBe.
Ileuuocru HayqHoro [o3HaHIrl:
opveHraqr4efi n 4eme.rbHocrrr Ha coBpeMeHHyro c[IcreMy HayqHblx npeICTaBne:nufi. o6 ocHoBHEIx
3aKoHoMepHocrqx pasBprrr4s. qeJroBeKa, npr4poAbr u o6rqecrna, ToFIIIMaHHeM MareMaruqecxofi HayKH I(aK
c( eprr qeJroBerrecKofi 4exrelrHocra,
3TarroB ee pasnara.f, LI 3HarIIrMocrI4 Anq pa3BttrLts.
oBJraAeHraeM .s3brKoM MareMarr4Kr4 r.r MareMarlaqecxofi
rylrrypofi
\LrBr4nv3a\w;
KaK cpeAcrBoM Ilo3HaHkrfl MVpa;
oBrraAeHr4ena upocrefiuruMr4 HaBbrr(aMr4 accne.qoBareJrbcl(ofi
AerlremHocra.
Cru:uqecrcoe BocrrrrraHr.re, QopuuponaHrre KyJr[,TypLI 3AopoBLfl tr 3MoIIIroHa,'Iblroro 6larouo.nyuun:
toToBHocTl,Io [pr{MeHtTb MaTeMa'tHrrecKrle 3]IIaH]dfl B LtI-ITepeCaX CBOelo 3AOpOBE.[, BeAeHklg 3AOpOBOIO
o6pasa xr.r3Hrr (s4opoeoe fivlalne, c6a,rancupoeaHHrIfi pexLIM za:r^sruit 14 orABIxa, perynqpHax cpuszvecrax
artruBHocrr); ccfopuupoBaHHocrr,ro HaBbrKa pesnexcuu, tIpI43HaHI{eM cBoeto flpaBa ua ouru6xy
I4
TaKoro )I(e
IIpaBa Apyf of o qeJroBel(a.
SKo,rorHqecKoe BocrIHTaHIre :
opr.regraur4efi sa npuNreHeHr.re Mal'eMarr4LrecKl{x :Hasait AntI perrreH:afl 3a\a\ e o6racrll coxpaHHocrl4
o6pyr(arcUefi cpe4u, nnaHr4poBaH[rr flocryrrKoB rr oqeHKI4 I{x Bo3Mo)I(HbIx nocregcroufr. AnrI oKpyr(aroUefi
cpeAbr; oco3lraHlrelr rrto6alrnoro xapar(Tepa 3KoJlotl,rLlecKux npo6:relt u nyrefi ?Ix peu]eHlrr.
,llu.ruocrubre pe3yJu,Tarr,r, o6ecnequsarculue aAarlTaulrrc o6yuaroulerocrt K lr3MeHrIrcurrMcfl
yc,'r o B rrl M couu a,'I bH o ii ll up upoAu oii cpeA['I :
toroBHocrbro x AeficrBrrrrM B ycnoBr.{flx HeonpeAeneHHocru, rroBbrrreHl{Io ypoBH.[ cnoefi KoMIIereHTHocrI4
qepe3 rrpaKTuLreorylo AeflTeJrbHocrb, B ToM rrl4cre yMeHpIe ytll4Tbcq y ApyfHX lro4efi, upuo6perarr n
coBMecrHofi Aeqre6Hocrl{ HoBLIe 3HaHHfl, HaB[,II(I4
I4
I(oMrIereH\PlLl
113
oIIbITa ApyfHx;
ueo6xo4rarraocrbro n cpopr..aapoBaHr4v HoBbIx 3uauufi, B ToM tll{cre t|lopruy.nupoBarb v[ev, roHqrl4fl,
tr4IIore36l o6 o6r,exrax H .rrBreHprqx, B'r'oM r{I4cre paHee HeLI3BecrHbIx, oco3HaBa$ .qe$aqarrl co6creeHHblx
zsasufr. Ir KoMII ereHruocrefi , nrlaHr{po Barl ceo e pa3Blrrlz
e;
cnoco6HocTblo oco3HaBaTb cTpeccoByro cr.rTyarlurc, Boclpr4Hr,rMarb crpeccoByro cr4Tyaqr4ro KaK Bbr3oB,
Tpe6yloqflfi xourpuep, KoppeKTr4poBarb
pucKr4
r.r
npr4Hr{MaeMbre perxeH}rs u Aeficrsraa, SopiraynrrpoBarb kr orleHzBarb
flocJre4crnux, $opunpoBarb orrbrr.
METATTPEAMETHbIE PE3yJIbTATbI
Meraupe4nrerHble pe3yJlbrarbl ocBoeHr4.f, nporpaMMbr yue6uoro npeAMera
xapaKTepr{3yrorcq oBJraAeHheM yHulepcanbHbuwtt no3HarameltbHbrJ}ru deilcmaunuu, yHulepcanbHbuvtu
KoMJt yHuKamusHblrwu
deilcmsuauu
u yHusepcailbHbttutu
pezynflmarHutuu deilcmlunltu.
l)
VuuaepcailbHbte no3HanameilbHbrc deilcmsun o6ecnequaanm QopuupolqHue 6asoautx KozHumuzHbtx
npoqeccor o1yuanu4uxcn (ocooeuue uemodor nosHaHufl oKpyacanu4ezo A4upq,' npuu4eHeHue flozurtecKLtx,
uc c n e d o e am e nb c Kux o ne p at4uit,
Eatosrre Jrorr{qecKue
-
Aefi
uru (t opu
yue uuil p a6 o mamu c
crsurt
aquefi).
:
BbIflBJrflTb LI xapaKTeppr3oBarb cyrqecrBeHHbre rrpu3HaKr.r MareMarvqecKzx
orsoureuufi Melr(Ay
rroHfl Trdf,Mr4
o6rerron, uonmuft,
;
Sop,urynupoBarb orrpeAeneHnfl, ll.otfl"tr4it; ycratatJrr4Barb cyqecrBeHnrrfi upusHar tcraccuQLrKar\rtv,
ocHoBaHr4q lns o6o6qeHnfl.lr cpaBHeHr.rfl, Kpr.rrepr{u npoBoAr4Moto ananla3a;
-
Boclp[HzMarb, SopuynzpoBarb a npeo6pasoBbrBarb cyxAeHus: yrBepAI{TeJIbHbIe
orplrrlarenbHbre, eAI4HLtqHbIe, llacrnble u o6qae;
-
-
ycnoBHrle; BbrqBrrrb MareMarlrqecK[e 3aKoHoMepHocrr{, B3alrMocBr3u
I4
I4
flporplBoper{Hfl n Saxrax,
AaHHbrx, Ha6moAeuu.fl x I,I yrBepxAeHnfl x ;
-
npeAnararb Kpr{Tephkr 4rrfl BburBJreHrzs 3aKoHoMepnocrefi u rrporaBopeuuit;
AenaTb BbrBoAbr c r{cnonb3oBaHr4eM 3aKoHoB JrolI4KI4, AeAyKTI4BH['IX A [IHAyKTI4BHbIX
-yMo3aKnloq
-
eHufi., yMo3aKnloqeuufi uo aHaJIorHI{;
paz6uparb AoKa3areJrbcrBa MareMarr.rqecKr.rx yrBep)r(AeHufi (npm,rue
LI
or nporl4BHoto), nponogurr
caMocrosrenbHo HecJroxHbre AoKa3arenbcrBa MareMarrzqecxl4x Sarron, BblcrpaflBarb apfyMeHTaul{}o,
[pr4 BoArrrb nplrMepbl LI KoHTplpI4MepbI;
o6ocsoBbrBarb co6crnesnbre paccyx(lenrrfl;
-(cpanHranarb
HecKoJrbKo Bapr{aHToB perrreHprfl,
nu6zparr cnoco6 pelxeHl{fl yue6Hofi
3an.aqv
nm6uparr Hau6olee noAxoArlrlufi c y.rerotvt
caMocro.nreJlbHo BbIAeJIeHHbx Itpurepnen).
Easonue uccJreAoBareJrbcKue gefi crnun
-
:
ucrroJrb3oBarb Borrpocbr KaK r.rccneAoBareJrEcKr,Ifi uucrpyueHT rlo3HaHlzfl;
Borrpocbr, Quxcupyroullre nporr4Bopeqve,
Sop*ynupoBarb
-ycraHaBnl{Barb
cKoMoe u
I't
apryMeHT[Ipo
-
B
aTb
cB
upo6leuy, caMocrorreJlbHo
AaHHoe, $opnaupoBarb rl4rlore3y,
olo rlo3
Ll
IdI4]O, MHoHI'I e ;
srcnepzueur, ne6olblrloe
no ycraHoBJreuuro oco6euuocrefi MareMarl4tlecxoto o6rerra, 3aBl'Icl4Mocrefi o6t,exros
npoBoAr{Tb rro caMocro.f,TeJrbHo cocraBJIeHHoMy rlnaHy HecJIoxHbIft
r4ccJIeAoBaHI,Ie
Mex(Ay co6ofi;
-
caMocroflTeJrbHo (popnlynupoBarb o6o6qeuufl I,I BbIBo,4bI no pe3yJIE'TaraM rlpoBeAenuoro
Ha6lrcAeHrzfl,ktccreryoBanyrfl, orleHlrBarb AocroBepHocrb rlonf{eHHblx pe3ynbraroB, BbIBoAoB LI
o6o61lesnfi; nporno:r4poBarb Bo3MoxHoe pa3Br.rrl4e rlpoqecca, a raKx(e BL'IABI'Ilarb npeAnonolKeHl4fl o
elo
pa3BI'ITI4I4 B HOBbTX yCnoBI'Iqx'
Pa6ora c uu$opuaquefi:
BbrrBJrrrb HeAocraroqHocrb
-
ra
zs6rno.rHocrb ran(fopuaqlz,u) ranrbtx, ueo6xo4r,rMbrx Anf, pelxeHlafl
3AAaqU;
nu6uparb, a*aJtlr3ptpoBarb, cr4creMarr43r4poBarb
-
BHAoB
r4
r4HTepnperr4poBarb uIr(popuauxlo pa3nl4rIHblx
u $opr'.r rpeAcraBJrenufl;
nrr6uparr Sopvry rrpeAcraBneHrar unSopMarluu t4 prnnrocrpr4poBarB pemaeMbre 3a4aril4
Ar4arpaMMaMu, uuoit rpaQuxoft u ux rcon6uHarlu.[Mr4;
-
cxeMaMr4,
orleHr4Bars ua4eNuocrr uuSopMar1url no KprrrepusM, npeAnox(eHHbrM yrII4TereM I,Inu
-
c(poprrryruapoBaHHbrM caMocroflreJrbHo.
2)
H
VuueepcanuHbte KomJvtyHuKamurHote deilcmeun o1ecneraulanm cfuopuupolaHHocmb coqualtbHbtx
albtKo 6 o 6yu atou4uxcn.
O6qenue:
-
BocnpuHuMarb
$opnrynzpoBarb cyxAeHpu B coorBercrBlru c ycnoBusMli h uen.,IMI4 o6Iqeuua;
ra
,cHo, TorIHo, tpaMoTHo B6rpa)I(aTb cBolo TorIKy 3peHa{ B ycTH},Ix
I4 IrI{CbMeHHbIX TeKCTaX, AaBaTb
pesyrsrar; B xoAe o6cyxgeuul
npo6reur,t, peruaeuofi 3aryaqu, BEIcKa3bIBarb
rrotrcHeHas rro xoAy perxeHr,rs 3ap;a,4pr, KoMMeHTVpoBarb rronyqeHHbtfi
3aAaBarb Bonpocbr rro
cyqecrny o6cyN4aeuoft TeMbI,
u4ert, HarleJreHHbre Ha [oI4cK pelreHl4g;
colocraBJrflTb cBor.r cylr(AeHr4.f, c cyx(AeHr4flMr4 Apyrux yqacrHpIKoB AHaJIora, o6HapyxIt4am npoqecc LI pe3ynbrar pa6orrr;
rrprrHr.rMarb ueJrb coBMecrHofi Ae.srelrsocrr4, rrJraHl4poBarb
o6o6qarb
Br.rAbr
MHeHHs HecKoJrbKHx nro4efi; )rqacrBoBarr B
rpynnoerrx Sopuax pa6oru (o6cyx4enux,
o6ueu MHeHHflMI,I, Mo3toBble urypMbl I{ Ap.);
-
BbrrloJrH.f,Tb cBoro
qacrb pa6orrr
r,r
KoopAr,tHl,IpoBarb cnolz 4eficrBl4g c ApyrI,IMH TIJIeHaMI'I KoMaHAbI;
oueHr4Barb KarrecrBo cBoeto BKnaAa s
o6u[fi
[poAyKT no KpLITepI4xrvr, cSopvtynl4poBaHHblM
yqacrHI4KaMI{ B3avMoAefi crnns.
3)
YwuaepcanuHbte pezynnmunHbrc deilcmaun o1ecnequaanm QopuupoaaHue ctvtbtcttorbtx ycmaHo9oK u
acu3HeHHblx HaBdKoq fluqHocmu.
CanroopraHLI3aIII{fl:
caMocro.rlTeJrbHo cocraBr.f,Tb rrrraH, aJITopLITM pelxeHl{s galLaqv
-perxeHr4s
(ulu ero uacrr), art6upars cnoco6
c yverou r4Merorlr4xcs pecypcoB u co6crseHHblx Bo3Mo>ruocrefi, apryMeHTnpoBarb
KoppeKTr{poBarb Bapr.raHTbr peurenuft c yudrou noeofi nuooprvraquu.
Iz
CaruoxonrpoJrb:
BnaAerr cnoco6aur4 caMonpoBepxr4, caMoKouTponr [poqecca u pe3ynbrara pelxeHl4fl
-MareM
-
arr4arecxo
fi 3 ap.aqv.
npeABr{Aerb rpyAHocrr4, Koropbre
Moryr
Bo3Hr4KHyrb rrpu peixeHr{r{ 3a4aqt4, BHocr.{Tb KoppeKTI4Bbr B
Ae.greJIbHocrb Ha ocHoBe HoBbrx o6crogr:emcrn, uafi4eHHbx oruz6ox, BbrqBreHHbrx rpyAnocrefi;
-
oIIeHI,IBarb coorBercrBl4e pe3ynbrara AesrenbHocrr4 rrocraBreusoft qenr4
r4
ycJroBr.r{M, o6r.scH.f,rr
ilpr4r{uHbl Aocrrr}r(eHlrs.vryr Herocrr4xeHr{.f, rleJrr.r, HaxoAr4Tb ouru6xy, AaBarb orIeHKy npuo6pereHHoMy
onbrTy.
IPEAMETHbTE PE3yJrbTATbr
rluc.ra I{ BblrrrrcJreHr{fl
flonnuars u npaBr4JlbHo ynorpe6nsrb
14
repMr4Hbr, cBr3aHHbre c HarypaJrbHErMr.r qr{cJraMr4, o6rmnoseHHLIMI4
Aecfl Tr.rr{Hsnrz 4po6xrr,tu.
Cpannunarb
r,r
yflopflAorrr,rBarb HarypanbHbre qr{cJra, cpaBHr4Bars n npocrefiurux cnyqasx o6rrxnoBeHHble
4po6z.
CoorsocurE, ToqKy Ha KoopArrsarHofi (uucronofi) npmr,rofi c coorBercrByrorul{M efi quclorra
HarypanbHbre r{ucra roqKaMr.r Ha KoopAusaruofi (uucnonofi) nprrraofi.
Apo6u,
Aec.f,
THrrHbIe
r.I
u:o6paxtarr
apu$rraerruecKze Aeitc:rsufl. c HarypanbHbrMr.r -rtr4cralr.kr, c o6rmnoseHHblMt4 Apo6xuu n
npocrefiruux cnyqaqx.
Brnolssrr
Brrnomlsrb rpoBepKy, npIrK[IAKy pe3ynbrara srr.{ucreHl4fi
.
Oxpyrnxrn HarypanbHble qHcJIa.
Peruenue reKcroBbrx 3aAaq
Peruarr reKcroBbre 3a1a:tv apu(puerrzuecKuM cnoco6orr
I4
c [oMolrlbro opraHu3oBaHHoro KoHeqHoro
nepe6opa Bcex Bo3MoxHLIx BapIraHToB.
Peurars 3aila.uv, coAepxaqne3aBlraul.rrocrr4, cBq3brBaro4l4e BeJIIzrrIzHbI: cKopocrb, BpeMg, paccrogHze;
IIeHa, KOnVqeCTBO, CTOI{MOCTb.
Irlcuomsosarr, KparKa e 3artt4ckr, cxeMbr, ra6ruqrr, o6osHa.{eHus, ilpv pemeHlll4 3aAaq.
flo6gosarbcq ocHoBHbrMr4 eArzHr.rrlaMr4 t43Mepeuvrfl'. I{eHbI, Maccbl; paccrosHrlr, BpeMeHIa, cKopocrl{;
Bbrpaxarb oAHr4 eAUHI4IIbI BenLI- rrI4HbI rlepe3 Apyrl4e.
Zgsreram, auaJrv3upoBarb, orleHr,rBarb raH$opuaql4lo, [peAcraBneHHyro s ra6raue, Ha cror6'{arofi
Ar4arpaMMe, r4HTeplpeTr4poBaTb rrpeAcTaBneHHbre AaHHbIe, I4CIIOJIb3OBaTb AaHHbIe npu peIxeHI,II4 3aIlAq.
Har.[qAHafl reoMerprrfl
flog,soearbc.f, teoMerpl4qecK[Ml4 tIoH.urLItMLI: TorIKa, ltp.aMarl, orpe3oK, JIyr{, yroJl, MHoroylonbHuK,
oKpy)rGocTb, Kpyr.
flpuao4zm nplrMepbr o6rerroe oKpyxaroqero
MI,Ipa, uMelorUux
Sop*y
I43yr{eHHbIx leoMerpl4qecKlax
S,a.yp.
Zcno6sosarb repMlrHoJrotr4ro, cBr3aHHyro c yrnaMl{: BepIlIrHa cropoHa; c MHoloyloJIbHHKaMI{: yloJI,
BeprII{Ha, CTOpOHa, ALIaIOHaJIb; c oKpyxHocTbro: pa vyc, [ua}.leTp,IIeHTp.
I4so6paxiM
F
o
tr -!t .g
F
6<;
tNi
Es
i:
I
I
o:,bi
o
qt
o
!e>,c
>=
>b6
I
so
<6
G
do
L
d
!?N
>,i
>,u
\1;
v)=
d9
Jo
!d>
^c
(t
s>
AE
(z
=
t
d
iics.+
ii
dq
6t
B
E
!2N
tr
-26tr
L:
KP
t
gs
5d
ON
E$
:.:r
>d
,,2
*,itr
!! >.
^c
a6
rsE
fsEeg
i=i
;;v
;e
6
3€o>
-b
a o
EU
EO
4d
*F
tso
)o
E9
,
o
L
o
<6
6a
az
,i!
\\:
>6
I
Ed
\z
!(5
do
o>
AE
,{,
<
i6
> -$
( !*
\s
5d
o
>:
\€
E
9d
<6
ET
i6
ON
ii+
6i
i;
6A
B
d
E+
p
a
q
t
d;
+!
!o
d!
cu
:N
;:
5.j
qo
tso
70
I
Pd
5i
trv
v
)s
40
tso
i5.
o
p
o
o
60x
o.ox
?tr;,
F65
t
E F\a
3qH
5
h
f!t
o
E
od
o.
JE
.^
o4
@I
FO
OE
tso
.9X
o2
tr),
8e
.9X
a
oz
tr)'
o
-o
IO
,, . *
F--4
3599
3599
JOtro
= H & A\6
E6otrOr
NN
Nd
OO
dN
66
OO
N
N
O
6l
6
O
N
N
O
N
-oi
OO
NN
N c]
OO
c'l .l
60
rn9
OO
O
O
O
o
r
O
9pEp
y
4 5 s 6 5."
Itsoq>o
oi
O
F
,^
;
a
E
o
o
o
=b
-v
6
4srO
o
!t >>o
trF90
i so
5
,^
oisUl
a
d
L
@
=uof
4tr e-i
j-
;=s
o
q9
I
tr
si
ts
< or
o9E
4
a 5."
I OX q
H
o
tr
o
a
."
4
E
"i;
sE9
X
=
r5
Ef
39
ea
Q o cio
!?>ox
JPO6
]ovr
iI
NN
NN
OO
NN
NN
NN
OO
dN
oi
o
OO
@
O
6ri
o*
O
o
O
O
o
O
oo
OO
=:
H
xu
i o
o ,^
,s=2
s:r6
ts:
i
at
Is
I x
e;
_-
I>T O
o
pX5
58
i >
= xo
d!E "dEE
NN
Nd
OO
NN
oo
OC
oci
+N
o
I
=
o
qF
d
Fb
Ero
o6
o
F
t
O
q
v
N
m
!
a
ri
!.
a
)\
ce
0r
a
t
F
i
ii
I
a
a
!
o
F
d
E
E
d
2
r{
o
U
o
o
hl
F
IJ]
F
i
E
o.
z,
7'
o
F
o
a
F
Z
f
I
trt
E
z,=
6*
d
o
7
o
\
5
E
4
5
o
a
f;
I
3
I
s
2
T
!
a
a_
E
o
3
o
Z
I
o
r:t
I
c
c
o
5
i
o
a
h
5
E
4
c-
.1
$.
v]
o
o.
N
5
tr{
(
o
sQ
m._
ir
!5
EE
-
xY
b
o
5
i
I
>2
tr
9
q'.r
ia
-L9
g2
o>t
E>
=o
EC
o!q
dtl
.i,
oo
oo
o
i
oN
J6
UE
=o
troo
.deb
Jt(iX>ts
9;:i
ts*->
r9; t
>+6
>sv
Ef,L
-. I
,!!o
-3F
;Hq
::Y:
Ll_
'l
,a .i
oo
,'9
NC
bEz.
.=oo
\a 3i
"
i-r
I
o
::<
N
5d
N
si
i:
d
o
)s
ELi
IO
FO
>5
5
o
F
o
o
HCO
-.oo
o
..
FEEY
)s
Fts
*o
v
v
h
E9
o:
d2ro
S o
E q
:
H
-I
4cX
F O
:.
U
St:s
iijg6
=
4
,^
o
F
.^
=5
x6
FP OXX
8.q
E 5 ;E5V
=ukgoE
! > tr i
d^
YobY
trY
JOOZ6Z
] E o > .- O >
N
N
o
N
6
NN
NN
-.!i!r .^ o
a
q
@o
oo
c'l c'!
oo
OO
N
9@
NN
O
O
o
H
x
H
FO
>6
j
tJ5
E
:i.^
Eg
E
H
3
i
l:.^
g
oroH:ro E,"iS E,.iT
E
;;sE
;,iEE
;FXtr
*f,EE
:Htr EileF
EFFs xEEE
EF+9
9
-d)^
^UOI
E
ssisioFx
E
i
a
4 t'iJ
6v
o
s48
Siab
b9P*
F:I::4S
;XkXsdF
ci:lrY
5D.a
:xo
-
I A
E+
>6
Xr
sv
OYE
."
5
Ll
TO
Fo
oi
>o
FO
oi
i5.
)s
_5!
:N
:N
r"3fU
7830
s _ oH
s
o\
-
9d
E
A
3,,
(o ;
5F
:H
a
Eo
9..io
€
EEgH
jEgE
.,Eg.lE
oE E
_
=
Ei:S*
I
ido
os
5A
>F
EO
AF
;o
IF
FO
sl:
Od
v<9
i=L
6
o65:
E8
9 " "I
-iQOS
'5
PuEEb
9
;iisAFso
*EueF;
i..
E
9€
so
6
C
E
o
s
o60='Yd
dL-5q;
P;T9
o(6o
N(\
Nd
OO
NN
6l N
Nd
OO
.l cl
6V
NO
'^9
OO
rO
O
o
o
O
O
O
oi
o
OF
o=
E
N
N
O
..1
I
d
EE
x
zi
>rc
jci
==
hio
J.
5
a
qo
o;
ilF
ro5
oXr
af.u
Ei*
LF
d >'*
Fe'^'
R=E
6
s
!l*
o
o
ro
6
5
a
o
i
ts
F
N
a
tr
t ;l
o
0
I
ts
o
o
:-B
z
D
vB
da
urs
5r
YO
p
T
N
6iBBE
(t
otsY
E
6
BE93q
6F
!x
o^'
{
otrr-5"roo
iIidEE
=geRE
s
o
5o:i
{!ao
o=
6\
o
NN
NN
I *96
e=9
= ";S
6
sp
o4
NX^>
o
b
=
"H
g
PX
dil
I
s(
o5
ot
3i
a6
os
9A
UT
EI
oF
\(
s:
@
N
>!'
N'
I
gJ
x
k€
6i a ii
-+?
Ot
:.\
o
S
o
-c
r!
o
<5
!
t=
fP
,i vj
5'
{{
o
@
ul
s
E
E
5
ts
-)
=<
=.6
ui
@6
3
p
e6
N
A
N
N
!e
-
l"
!"
;*
<+
o
t
;
(c
E
a
a
ar
N
;
N
Eti
p
E
O
:1
i
t
o
c
.P
q
I
!
@
a
O
O
o
O
9
O
I
o
I
O
:J
ie
ie
ie
iJ
O
N
N
o
f.)
839ts=9XE=ns
B99BE3BE:5F
EEeHgETSTIi
iD6EitS6ii!l=
r=Fri==.irj59
+=e*-=E+!=g
di'8iE
E;EE
9'c9.
Ti9E3S
d9B.;'i:;sE8
;oqr.
ao9i
',
q<-*do
naSx €sEi=EEEg
EEEH aEH;5$
EiqI53
r i; r
x
i, rJ *
; o!
;
? q s
iri,2F
E
_a;x "iiiaF = E
_6;5
l;.
J4HE E:X,
E
E:*.
<
;
*v <
!o!s
ps(.i
*uEd
*LUP
q=
\dj
il
o
-
Jl.
o
S
o
o
{{
!
o,
a-
I
I
!
f,t
o
36a='il
6aS
=a<
6E:
+s;
p
€':
o
6E
Nr!
o
!
t
NOb
!
=q
9<
jo
O-
Ie
g
H€
5@3
o
o
Er
g
N=
AE
.tr s4
o
8
-/.
x
E
n6
{{{
o
;
r
!qo.p =
lr'P
uo!
Ez
xi
I
Ti90!$
- *iJ o
EtsEN-
:a'
N
6
o
o
o
o
o
o
5
{n
0a
(rc
o
d
o
Fo
g
UJ:
:D
3
EU-l
o
,AE
-o
a:
N
o
o9x-
ix
r.E ETd5
*d
E;
iZ
;FJ
io
a5
qR>
==IB
"i":!,e
XE,
X +
!=
r5
YB
os=Ndic
o i X -"
B
<6
5(
oaP
r3
€EFIEIE
6'
o=
a@
a.a
@r
- <
oS(qs
o14
iia
s =:
5b;9
rir@u
A!
EX}
E
Ex,
iE
i i 0 id
@E*'<
E6;
I S(r
a
QEE
6s9,
5
o
;
sQ^
t
EEga:'X:
5?8XEB: SEasEEE
il:E= ;ts
d
S O i
e
,98
3
S;
xho
=raro
{5S@
E
o
B
tr
$:o
Eig
b
o
6'o
-
B
x
tv
u = ^
$.4:o@
:ir]
5€ x:5
H g,: A
6F9'
E'
I
.6
"=,E
ED
OO
NN
OO
NN
NN
xooooaa
o o 6@
!PEOH
p!!
o:i
H
h
+
i
e 6'PE
X
=:E E
Xtro
x=5
6tsq
x
o
r
P
rC
5i X'x, : i
q_EY'
O
i
$H" ai
r
=*truN
Xoo*tu
I;
o
J
ci
5F
I6
5a
EA
>*>
;.::
<5'
d
3r6
;on
AdY
>?
{='
o\B
o
F
+o
oB
a+
dp
9.G
iD
o
r
6
r,
s+
CE
E
6
bq
6J
e{
air
g5
.9<
{
6o
\o
?
F>-
9:.>
1,3
o;-:p
D .F3
5 b-d
E
!i,!
N
wN
O
o
Ja'
P
oood
flE i 5 H E
;iYEi:
T;
o^
dO
olr
ho
oul
ol
A
w
o
)ioxorT
E@O-ti
o*X
{
>
pe.ijg
Qq 3q
-dF
F
: @:
E
f
e=
o=
E
{
o
ia
o
r
(
E
oo
o@
oo
f3
--l
{@
9O
.g':
{
o
-..1
!
O
6
<;!
ad
?.ya
Ii7<
*{
Y.<<
5\
xo
NJ
Bq
N=
6:
I5=
o:
=
P
5<
3 6-s
N {O
{{
i tJ
o
5a
o
o
a
!
e5
e
:[
: ?!
!4I
r
o
ol
o
o
=I:
z.'., 7a a
oEt
o
P
!)E
YP
o :l
.2
i.6
_!=
rn*
I
U)
t'J
--=i
I
a
!
UT
*i
*i
uo
;c
c
=
v
o5I
D=
tr
p
6<
J
a
e
al
lD
'Y
;I
N
o
O
O
O
O
pE:
ou'
o!
PP
NN
5Q
B;
EO
oo
OO
NN
a r o E < O "' = o g
ol
!oooopridx
! !,
s ol5
=
3C 9 E E E E E X
,. ? B E E B F X S
aPrr;r=
oiEx-
$-to
),3
oolJ
Ov
$J=:
.FOE
3;
c6
"I'
,! r,
o
ol
s
4
o
N
?C
L^
=;
xI!
3
g
r
E
!Y
+
-<
o
H
60
oo
OrE
Ew
g
s(
!
\o
?
o
o-
i
€:
o
o
{
!
6
9'
Ie
OO
N
.N
^
OO
NN
O
N
O
N
pE
O
F 3 ! = =(r::
Eooa*t
pxSJ:s
FSud+:r
,r
5I3
O
H<
oQ?;:
o=
ro
b@
6=
1o
i9
9a
"FEg
\
O\B
pc
a ::\d
d6
'Os
6--
ito
o
o
(
F
Nia
uro
6:
NJ
€.
g
g
F
o
:t
o
o
oni
@
o
S
o
o
o
5
o
!
o
{o
@
!N
a
E€
X; S X;
!gE{
5
g
Jl
9:r
OO
ie
P
E
p
@
iEtr
" 6I
,o
.{:
I
Yd
!
E3X
o
o
6F
s(
A
;< OED
k=
E;A<9
:;.E@E
sryaL
oi=3!
i3
b
EEE'
x<5,
O
O
IJP
NN
OO
NN
E
,;=E
o
O
l:E
!o
aP€"E=6
6!
.6q
FD^
!o
od
!@
OX
=d
itr
O
I"<=OOEE
on p o 6l'
xs r5<<.aH
O E o tr:s 5
O
g-c
E
46 s
F "9;g j;{3 =
I
E : '' a
E
o
XrO
Sdi
:,
E;#
d -
"'
b
oi
o!
io
69
d<
trE
so
OE
o/
lo
9<
-nis(
Pss(
Or
*
r b:
u6E
i_hip
.aoliP
E
P!c
9'
:J
OO
OO
ie i)
OO
iJ i.)
OO
NU
NP
65
OY
s6
E!
oa
.x;
!!
o
i-i
6H
o=
=s9
or
909
o@rsot
i;
O
OO
5AH-'Eg
E*9P€E
l6c
x;
6FO
Pa
;
E
O
NO
:- :o
OO
!D 9J
NN
OO
PN
=
!g@ho
at
P
O
;
E
co
-o
o
O
!@)rH
:9io
::?e
8P
.YO
s a!+
3J ts
X
rd
Io
5.e
s'
o
I
aa
=o
Qr,
a
o
a
tr
fl3
6;
1o
o5
o=
:o
x<
EO
;o
q
=E
E
!^6;!
U P(;. S
!o<
pI<
