@EAEPAJIbHOE f OCYAAPCTBEHHOE OBPA3OBATEJIbHOE EIOA-XETHOE yI{PEXAEHI4E BbICIIE|O OBPA3OBAHI4TI

(or,rHAHCOBbrfr yHT,TBEPCIITET |IPI4 |IPABT4TEJTbCTBE pOCCmz-CKOI4 OEAEPAII4A)

K OnnEAX I4H@OPMATVIKI4 U IIp Of PAMMI,IP OB AHI4rl

YTBEPXIAIO3alrecrurear aupexropa no yve6-

aa<t dl > Af zo/d',.

PAE OrrA-g IIPOI PAMMA AI,IC qI4[IJII,IHbIOYA.lf Maremarura

Kog, cnequa.nbHocrb 09.02.03 flporpaN.rNraponaHue e xoNanbrorepurrx cucreN{ax

Mocxea2018

Pa6o.ra, nporpaMMa AxcrlunJrr.tHbr pa:pa6orana Ha ocHoBe @e.qepalruoro rocy-AapcrBeHHoro o6paaorare:uHoro craHAapra no cneuutrJrbHocrr,r cpeAHero npo-$eccnonaaruoro o6pa:oaauua

09. 02. 03_ flDorpalarrauposaHr.re s rolanrrcrepHrtx crcreN,raxxoa. HaHMeHoaafl re cneuualrtHofi H

Paspa6orvzrn : 3opr.rHa O. A, npenogaBare,rrb MareMarr.rKr,r

Peueu:esr: r Eozr<cTeneH6.3BaIMe.

ru/fal6ry gnyede "1.2Pa6oqas nporpaMMa Ar4cur4nJrr.rHEr paccMorpena r.r peKoMeHAoBaHa K yrBepxAe-Huro Ha 3ace4atvLr npeluerHofi (qux,rorofi) KoMr4cclurMaTeMaTI4r{eCKI,IX X eCTeCTBeHHO - HaytIHbIX IUCUUnJ'II4H

flpororon Np 'h o-, n y') ir^'"*Zt'1"'"' 204r.

flpe4ce4arear npeglaernofi (qrrnonoft) KoMrrccrir4

/A. B. Ceuenu *rrut ---431nornxcE / O.H.O.

PEIIEH3UgHA PAEOIIYIO NPOTPAMMY

no .urcqurunHe__QY4-!.1_MareuauxacnequaJrBHocru 09.02.03 llporparrruupoBaHr.re B KoMnbxlrepHhrx cr{creMaxcocraBJreHHyro npeno.[aBareneru MareMatuxri lKK 3ooxxofi Ortrrofi A.nexcanapos]rofi .

flpegcranreun€u sa peqeH3xrc pa6ovax nporpaMMa o6qeo6pasoaaremnoi yre6uoftAucuu[JruHhr r<Mareuarrxa>> npeAHa3HaqeHa Mt peanr.r3arluu cpeAHero o6qeroo6paroaauur, ,Birf,erc, qacrblo flporpaMMbr [oAroroBxr.r cneq]raJr]rcroB cpeAHero 3BeHa

(aaaee - IIICC3) B coorBercrBuu c <DIOC no cnelluanbnocru r.r npr{Mepnofi nporpan,tr"rofio6ueo6parorarearrofi yve6Hofi AucqlrnJrxHrr <Marelrarnxa: a.nre6pa H Haquura

MareMarr.rqecKono aHaJrn3a, reoMerpnr> c f{eroM TexHuqecroro rtpoapnrt, noJryqaeMononpoQeccraoHamHoro o6pasoaaxua.

Pa6oqas [porpaMMa o6qeo6paeonatelsnofi AI,Icq[nnHHhr <<Mareuamxa> BxoAxr B

o6uleo6pasonaremnui fre6xbrft uux;r r{ cocraBJreHa Ha ocHoBe npurr,repnofi nporpaMMbro6qeo6pa3oBarearsofi yre6rofi Ar{cunflnr4HLr <Mareuarlrxa: ame6pa r.r HaqalaMareMarrqecKoro aHaJrr.r3a, reoMerpruI)) aarop M.IzI. Eatuuaron, ogo6penHofi @fAY(OIIPO) Mnno6puayru Poccnu, 2015 u OegepamHoro rocyAapcrBeHHoroo6patoaareruroro cranAapra no creql{aJlbHocrtM cpeAHero npoQeccuouaarxoroo6pasoaanur.

Pa6oqas nporpaMMa oao6peHa Ha 3aceAaur{r{ unxnosoft KoMr,tccr{H <<Mareuamqecxrxr.r ecTecTBeHHo-HayqHhrx AIrcq!rIIJIIlH>.

Pa6o.ra, [porpaMM4 paccql-rraHa sa 351 qaca, B r.q.l68qaca - TeoperrqecKllxtaunruEt,66 qaca - npaKTuqecrxx tar.xruir, 117 .{acog - caMocrof,TeJrrHa, pa6ora.

Ilporparralra co,qepxlrr pa3Aenhr: nacnopr pa6ovefi nporpar.{MEr o6ueo6pa3oBarenrnofiyre6nofi Aucuurrruubr, crpyrffypa u coAepxaHr,re o6ueo6pasoaaremuofi yre6uofi,(Hcu nrrlrHbr, ycnoBx, pezrnu3arrurr pa6ovefi [porpaMMhr o6uleo6pasorarenrnofi yre6uofiAr{cul.rflnr,rHBr, KoHT ponE n orIeHKa pe3ynbraroB ocBoeHr.r, o6qeo6paronatennrofi yve6uofiAr.rcuunJrnHEr.

B nacnopre nporpaMMrr o6osHaqeHrt o6namr trpHMeHeHHr pa6ovefi fiporpaMMbl,Mecro Ar4crIH[JruHrr B crpyKrype nnCC3, uen[ l,t sagauu yre6nofi Arcqunlmt -Tpe6oBaxr,r, K pe3ynbraraM ocBoeHI,L yre6uofi AllcurrrrnuHrl, KoJIHqecrBo r{acoB Ha

ocBoeHHe yre6Hor .u4crunirllHEr.PasAer (Crpyrcrypa u coAepxaxfie o6ueo6paroratelrsoft yqe6Hof AncqE[nuHLI)

npeAcTaBJreH:

- o6reuolr yre6noft ArcqlI[nI,IHbI u BuAaMu fre6Hofi pa6oru o6yraroqerocr;- teMarr.rqecKlrM nJIaHoM ll coAepxaHuenr yre6noi ArlcqunJluHbl, B KoropoM

pacKpErTa [ocneAoBaTenBHocTb Ll3yqeHns pa3AenoB H TeM nporpaMMll, coAepxaH[eyuebnoro MarepI,IaJIa, BEIAeJIeHII Teoperl{qecKl{e 3aHtrut, ypoBHIa ocBoexlrc

AHAaKTT,FTeCKHX eALIHI,Iq, O6teM ayAHTOpHbIX qaCOB.

B parAene <Ycttogur peanx3allllu nPorPaMMbI o6qeo6paroaarelruofi yve6Hofi

ALrCqxn fiHhD) O6O3Ha.I9HEI rpe6Oratru-n K MIHI,IMaJIrHOMy MaTepHanbHO - TexHrqecKoMy H

uuSopuaquoruouy o6ecne.reHl{rc perull{3alruu axcuIrJII{HbI.B paeAere <Kourpoar H oueHKa pe3ynbraroB ocBoeHr.r, o6ueo6paronarelsnofi

yre6Hofi ,qlrcquflnl{H6l)) onpeAenegll p$ynbTarbl o6f{eH14, (ocaoennue )rMeH?lt'ycBoeHHEre ruanur), Qopr"ru lr MeToAbr KoHTpoJrs r oueHKr{ pe3ynbTaToB o6yrenur.

Teuarnxa reoperr{qecxux lanmrfi, Qopnarr H MerorEI KoHTpon s oueHKLr pe3yilbraroBo6yuexua o6ecneqlrsarcr .qocrnxexue ueaefi n 3aAaq fre6Hofi AxcrlunJrnHrr<rMateuatuxa>.

Pa6o.{a, nporpaMMa no .q[cIIH[nIrHe <<Mareuaruxar> paspa6oranxanlpenoraBareneMMareMarxxr IKK 3opunofi Omrofi A.nexcaHgpoaxofi perouerAyerc, AJIIucnoJrb3oBaHr.rf, a yre6xou flpoqecce.

PeueHrenr: no yve6noi pa6ore KlITr.r3 KEFY

?ryega 3.X.

coAEPxtAHT4E

crp.l. rIACtIopr pAEorrEIZ [pofpAMMbr yrrEEHoit [uc- 4

UIITIJII,IHbI2. CTPyKTyPA I,r COAEPXAHTTE OEITIEOEPA3OBATEJTb- g

nofi vrrEEHo it guctlufrJrlrHbr

3. ycJloBl,rfl pEAJI[I3Arilrrr panoqul [porpAMMbI oE- 17IUEoEpA3oBATEJIruofr yrrEnHoit[wc\urIJII,IHbI

4. KOHTPOJIb I4 OIIEHKA PE3yJIbTATOB OCBOEHI,Ifl l gyrrEEH o it lucularrJr r.r Hbr

r. rIACrIopr pAEorrEir uporpAMMhl o B rrl E o E PA3 OB,trUrrn O fry[IEEHOII AUC{IIIIJII,IHbI MareMarlr Ka

1.1. O6"racrb rrpr,rMeHeHIlq pa6ovefi [porpaMM[,r: pea[krcaw; cpeAHero o6ue-ro o6pa:oBannfl B npeAenax fIfICC3 ilo crequarbHocrr4

09.02.03 llporpanaMr4poBaHue B KoMrrbrorepHbrx cracreMax B coorBercrBl4l4 c

O|OC, npr4MepHofi nporpalruofi Baurrr,rar<oea M. VI., MareMarrrKa, c yr{eroM rex-Hr4rrecKoro npo$ranq ronyqaeMoro npoQ eccr,roHarbHoro o6pa:o n aHVr.

1.2. Mecro yue6uofi Aucuun,'rHHbr B crpyKType o6paroBareJrbHofi uporpaMMbl:Ar{crlr4[nuua MareuarHxa npvHaAnexuT K rpynne o6ueo6pa3oBarenbHblx trI4cII]I-r.rrrrH cpeAHero o6ulero o6pasonauux.

1.3. I{e.nu u 3aAaqu o6qeo6pa3oBareJrunofi yue6nofi ArrcrlurrJruHbr - rpe6o-BaHHf K pe3yJrbTaTaM ocBoeHIIq AHculrrrJrlrHbr:I-{enr yue6uofi Ar4clll4rrn}rHbrIracTvr ToTIHbIX HayK

Mareuaruxa c$opllrnpoBarb 3HaHkrfl I,I yMeHI,L s o6-

B pesynrrare ocBoeHkrfl y.re6uofi Aprcqlz.ilnunrr o6y.raroquficq AonxeH:

rHarr/noHr{Marb:3HarreHr,re MareMara.{ecxofr HayKr{ An;t perueHurfl 3a4arl, Bo3Hr4Karoqr4x B Teo-pw v [paKTr4Ke; [rr4poTy r4 B To xe BpeM{ orpaHr4r{eHHocTb npr{MeHeHl,4fl il.la-

TeMarrrqecKr4x MeroAoB K aH€Lrrr43y Lr vccne[oBaHr4ro [poqeccon u -ssreHufi srpr4poAe z o6ulecrne;3HarreHrre npaKTr4Kr4 H BorrpocoB, Bo3Hr4Karoqr4x e caNaofi MareMaruKe An,$opvrzpoBaHufl. v pa3Bvrrtrq MareMaru.recxofi HayKLl; r4cropurc pa3Br{Tr4, rro-IlflTkrfl rtkrcJla, co3AaHI4q MaTeMaTl4r{ecKofo aHaJrv3a, Bo3HI,IKHoBeHI4q 14 pa3BI,I-

TH, feoMerpvkr;yHr{BepcaJmuufi xapaKTep 3aKoHoB Jrorr4Klr MareMarnr{ecKr4x paccyx4eHufi,I4x rIpI4MeHI{Mocrb Bo Bcex o6rac'rqx r{eroBer{ecxofi AeflTenbHocru;Bep ofl THocrsstfi xapaKTep pa3nr4rrHbrx [poqe c co B oKpyxarcqero Mr{pa.

AJTTEEPA

yMeTb:BbrIroJIHf,Tb apra$rraeruqecKr4e Aeitcteus HaL .u:acralr^n, coqera.f, ycrHble v[HcbMeHHbre flplreMbr; HaxoAuts rtpu1nr4xeHHble 3HarIeHWfl BeIrvqrIH H rlo-rperuHocra Bbrr{[cJreswi,t (a6conrorHafl, Lt orHocr4Tenruax); cpaBHr,rBarb r{r,rc-

JroBbre BbrpaxeHuq;HaxoAarb 3HarIeHI,L KopHfl, cre[eHu, norapu$nra, Tpl4foHoMerpr4r{ecK}rx Bbr-

paxeunfr Ha ocHoBe oflpeAe r,ele.rs.) r{cnonb3yfl rrpn ueo6xo4uMocrr{ HHCTpy-MeHT€LIIbHbIe cpeACTBa; nonb3oBarbc, npu6nnxesuofi ouesxoft [pu [paKTr4-I{CCKIIX

PACI{CTAX;

. BbI[oJIH-flTb [peo6pa3oBa{hfl BblpaxeHui,t, npvtxre]Hflfl Sopuynu, cBf,3aHHbreco ceoft crBaMH creneuefi , norapu$MoB, Tpr4roHoMerpur{ec Kr4x QyH rcrlufi ;

ucuoJlb3oBarb upno6pereHHble 3HaHHq H yMeHHfl B rrparcTu.recrcofi ger-TeJrbHocrrr rr rroBceAnennofi ?KIr3Hrr :

Artx rrpaKTr4rrecKrdx pacqeroB no QopuyJraM, BKJrro.rar QopuyJrbr, coAepxaqr4ecrerreHl4, paAI4KanbI, norapuoMbr r4 Tpr4roHoMerpurrecKue QyHxqvrz^, uclJioJrb3yflnpu neo6xoAl,IMocrl4 crlpaBor{Hble Marepl4anbr H rrpocrefi mue Bbrrrucnr{TeJrbHbreycrpoficrna.

@yHrcquu u rpaQurcn

yMeTb:. Bbrr{r4cJrrrb 3HarreHr.re synxquu no 3aAaHHoMy 3HarreHuro apfyMeHTa rrpLr

pa3nl4qHbrx cnoco6 ax 3ailanpra Qynxuuu ;

. olpeAenrrb ocHoBHbre csoficrea r{r4cJroBbrx synxqufi, HJrJrrocrptrpoBarb r4x

Ha fpaolrKax;o crPourr rpa$vK]a v3yqeHHbrx synxqufi, r.rJrJrrocrpr4poBarb uo rpasnxy cnofi-

crBa 3JreMeHTapHbrx @ynxqnfi;. I4cfloJlb3oBarb iloHqrue Qynxquu .qn, orll4ca:e.Lrfl v aHaIru3a 3aB:.,cr4ruocrefi

BENI4qI4H;

lrcrroJrb3oBarb upuo6pereHHbre 3HaHrrfl tl yMeHHq B rrpaKTuqecrcofi Aefl-TeJrbHocrr.r H rroBceAHeeHofi ?KII3HH :

. Arrfl orrtrcaHnfl, c rroMorrrro Qyuxqnfi pa:nuqHbrx 3aBr4caMocrefi, [peAcraB-retnfl, rax rp aQ uq e c KH, r{ HTep tr p e r arJptv rp aQ u xo n.

Haqa.na MareMarlrqecKofo aHaJrrr3a

yMeTb:. HaxoAr,rrbrrpor43BoAHbre3JreMeHTapHbrxSyuxqufi;. r4crroJrb3oBarb rrpou3BoAHyro An, la3yY,etus, csoftcrn oynxuuft u [ocrpoe]ts.],1,fl,

rpaQr.rron;. rpul,reHrrb rlpor43BoAHylo Anq rrpoBeAeHlrfl npra6nraxeHHbrx nrrvucreuufi,

perxarb 3a1a.tv rrpuKnaAHofo xapaKTepa Ha HaxoxAeHue nau6orrruero r4

HAUMCHbIUC|O 3HAqCHHq ;

. BbrrrIacJr.rrrb B rrpocrefiurux cnyqaqx [noqaAr4 u o6rerru c HcrroJrb3oBaHr4eM

orrpeAeneHHofo I4HTerpana;

HcrroJrb3oBarb npuo6pereHHbre 3HaHHfl H yMeHHfl B rrpaKTlrqecrcofi Aer-TeJrbHocru H rroBceAHeeHofi xu3Hrr Anfl:

o petue:ang. npr4KnaAHbrx 3aAaq, B ToM rIHcJre coq[€LrlbHo-3KoHoMlaqecKlrx u bw-3I4rIecKI4x, ua uau1oJlblur,re 14 HaIzMeHb[II4e 3Har{eHl4tr, Ha HaxoxAeHne cKopo-cTId V yCKOpeHHf.

Ypannen ufl kt HepaBeHcrBa

yMeTb:o peuaTb parlr{oHurrrbHbre, froKa3aTeJrbHbre, JrorapzsMr,rqecKpre, TpHroHoMerprr-

rrecKrre ypaBHeHr4r, cBoArrrlhecfl K nr4HefiHbrM r{ KBaAparHbIM, a TaKxe aHa-

JIOrI4rrHbre HepaBeHcTBa 14 cLIcTeMbI ;

. r4cfroJrb3oBarb rpaor4.{ecKufi MeroA perxeHHq ypaBHeHvrir pr HepaBeHcrB;

. r43o6paxarb Ha KoopAr4HarHofi rrJrocKocrr4 perxeHlrq ypaBHeHl4fi, HepaBeHcrB

r4 clrcTeM c AByM, HeI43BeCTHbIMI4;

cocTaBJrf,Tb r4 perxaTb ypaBHelJr4fr 14 HepaBeHcTBa, cB.rI3bIBaIoqI4e HeI43BecTHbIe Be-

JII4IIIIHbI B TCKCTOBbIX (B TOM qI4CJIC IPI4KNAAHbIX) 3AAAI{AX.

HcrroJrb3oBaTb [p[oopeTeHHbre 3HaHrrfl rr yMeHr{fl B flpaKTlrrrecKofi Aefl-TeJrbHocrH Ir rroBceAHeBHofi r(rr3Hlr :

. Arrfl nocrpoeHl]1lfl Lr LtccreAoBaHr4.f, rrpocrefirxprx MaTeMaTr4qecKr,rx MoAenefi.

K O MBI{HATO PI4KA, C TATI4 C TI,IKA 14 TE OPfig, BE P Ofl TH O -CTEfryMeTb:

. peuarb [pocrefiruue xou6zuaropHbre 3a4aqv MeroAoM nepe6opa, a raKxe cr4crroJrb3oBaHueM r,r3BecrHbrx Sopuyn ;

o Bbrrrucrqrb B npocrertutux cnyqarx BepoqrHocrn co6srtuit sa ocHoBe rIoA-cr{eTa rll4cra ucxoAoB;

rrcrroJrb3oBarb npuo6pereHHbre 3HaHrrfl r.r yMeHHfl B rrpaKTuqecKofi Aeq-TeJIbHocrH I{ rloBceAHeeHofi }Klr3Hrr :

o AL aljanv3a pe€LnbHblx qlrcJroBblx AaHHbrx, npeAcTaBJreHHbrx B Bl]ile Ar4a-rpaMM, rpa$uron;

. aHaJru:a unSopMarlr4u crarvcrurrecKoro xapaKTepa.

IEOMETPYTfl

yMeTb:o pacno3HaBarb Ha r{eprexax H MoAeJrqx [pocrpaHcrBeHHbre Sopurr; coorHo-

cprrb rpexMepHrre o6rerrbl c ktx ormcarnfllau, vtso6palKet:aflvla;. orrucbrBarb B3ar4MHoe pac[onoxeHr4e rrprMbrx Lr rrJrocKocrefi n npocrpaHcrBe,

apzyMeHmuponamb c6ou cycrcdeuua o6 emou pocnolo)tceHuu;. aHa-[r,r3r4poBarb B rrpocrefiruux cnyr{aflx B3ar{MHoe pacnonoxeHr4e o6rerros s

rrpocTpaHcTBe;o uso6paxarb ocHoBHbre MHorolpaHHr4Kpr H Kpyrnbre rena; Bbr[orHqrb qepre-

xr4 rro ycnoBr4qM 3a4al{;. cmpoumb npocmeilu,tue ceueHufl tq6a, npu3Jvtbt) nupattuda4o peuarb rrJraHr4Merpr4r{ecKrre rr [pocrefimue crepeoMerpnqecKr4e 3a4.auu Ha

HaxoxAeHlre reoMerpur{ecKr4x BeJrr4qr4H (Anuu, yrJroB, [noqaAefi, o6rerraon);. HCIIOJIb3OBATb NPI4 PEIXEHI,II4 CTEPEOMETPI4IIECKI4X 3AAAI{ IIJIAHI,IMCTPLIqCCKUC

Qaxru r4 MeroAbr;. upoeoAl4Tb AoKa3areJrbHbre paccyxAeHEfl B xoAe pemeHns 3aIaq:'

HcrroJrb3oBaTb nprroopeTeHHbre 3HaHHs r.r yMeHrrfl B rrpaKTurrecKofi Aefl-TeJrbHocrlr H rroBceAHeBHofi XH3HH:

. Alfl HccneAoBaHr4fl. (nao4enrEpoaaHur) HecJroxHbrx rrpaKTr4r{ecKr4x cutyatlttitHa ocHoBe r,I3yqeHHux Soplayr u ceoficrn Snryp;

o Bblrrl4eilenr4fl o6rerraoe r4 rrnouaAefi nonepxuocrefi npocrpaHcrBeHHbrx reJrnpr4 perxeHLrv [paKTlrqecKrrx 3a1aq, vcnoJrb3yfl. rrpar ueo6xo4uMocrr4 crrpa-BOrrHr.IKr4 r4 BbIt{ r4CJI HTeJrbHbre yCrpOfi Crna.

1.4. Ko.nuqecrBo qacoB, orBeAeHHoe Ha ocBoeHne rrporpaMprrr o6uleo6paro-BareJrbHofi yue6nofi AucrlunJrHHbr, B ToM qHcJre:

MaKcr,rMaJmHofi yve6nofi Harpy3KH 351 .racoe, B ToM r{r4cre:

o6qsaremuoft ayAr.rropHofi yue6uofr Harpy:xra o6yuarcrleroc, 234 tacon;caMocro.sremsofi pa6oru o6yraroqerocq I 17 qacoe.

2. CTpr/KTvPA pr COAEPXAHLTE OETTIEOEPA3OBATETbHOfrr/rrnsHofr AucqlrfrJrlrHbr

2,1, Oiltena o6uleo6paronarelrnoil yue6uofi AlrcqrrrJruHbl kr BrrAbI yue6uofipa6orsl

Bug yue6nofi pa6oru O6oen uoco6

MarccuvraJrbHafl y.re6Haq Harpy3Ka (ncero) 351

O6qrarerbHafl ayArlTopHaq yqe6uaq Harpysrca (ncero) 234B TOM I{I4CJIE:

npaKTzqecKrle 3a}lflTldfl 66KoHTpoJrburre pa6oru 2

Cauocrofl TeJrbHaq pa6ora o6yqaroluerocq (ncero) 117

B TOM III4CIE:

lorraaurHue 3an^aunfl Anf, cryAeHToB 49

Bneay4raropHaf, (cauocrorrerbHa.s) pa6ora,yrny6nenue v pacruI,IpeHlle zsawuitt rro reMaM,

ocBoeHr4q OIIOI (DIOC

HanpaBneHHaf Ha

ueo6xo4uMbrM Anfl

6B

Pe$epar 34CoctaereHr,re onopHoro KoHcrIeKTa rlo :aAauHofi TeMarI,IKe 24Coc:rasreu[e orqera o6 u:yreuuoM Mareplrane 14flo4roronra coo6rqeuux n Qopnae npe3eHTauuu 27Peueune 3aAaq 18

flpolaexyrorrHa.f, arrecraur4x n Sopue AeI$. 3arrera, nucbweHHozo sK3auteHe

2.2. T ewarurrecKufi nrran H coAep)KaHue yue6uofi AHcrIn[Jr[rHbr Mareprarurca

HaurreHonanuepa3AeJIOB rr TeM

Cogepxcauue yve6Horo Marepua,rar,ra6oparopHr,re pa6orr,r r,r [paKTuqecxrre 3aHflTrtrfl,caMocroqreJrsHafl pa6ora o6yvarorquxcn

O6r€pr qacoB YponenrycBoeHr{fl

ParAe.r l. BneAeuue )

Tema l. Parslrrue troHqrufl o rrucre 10flpu6.nnNeHHoe 3Har{esue. A6corlorHiul [I orHocureJrbHiur trorpemHocru. I-{elue r{ pauvo-HaJrbHbre r{ucna.,(po6n. fieficrnut c 4po6ruufleficrnureJlbHble qvcra. Crau4apruarl 3anllcr, r{Hcra. [eitcrsur. c rrrrcJraMr4 B craHIaprHoMBr4Ae. floHqrr,re KoMrrJreKcHoro rrucra

3

[Iparclu.recrcue 3aHflTrrfl 2

1 fieitc -'nux ua,4 npu6nuxeHHbrMr.r 3HaqeHr.rrMu r{r.rceJr. Irlso6paxenpre KoMrrJreKcHr,rxqLICCJI

2

CaMocroqreJr[,rrbre pa6orsr 6Pe$epar Ha reMy: <.{po6u>, <flpoqeHrsr>Peuresue 3a4aq no o6pasqy, tro reMe: <fleficrnzr na4 npu6nuxeHHbrMu 3HaqeHr4flMvttwt-CCJI )Pe$epar Ha reMy: <Cuoco6u yflpoureHu, MareMarur{ecKr.rx sbrpaxeHufi ).

)1

)

3

Teua 2. KopHlr, crerreHu lr .norapuQvru 30

Perueuze cplcreMbl lznefinrrx ypannenufi I,I HepaBeucre. CreneHb c HarypanbHbrM 14 rrenbrM

rroKa3areJleM. Csoficrea crenesefi. Kopeur n-ofi creueuu. Cnoficrna xopnefi. CreueHs c pa-IIt4oHiInbHbIIvl z AeficrBI,ITeJIbHbIM rloKirareJlerra. Jlorapr.r$Mbr u rrx cnoficrea. flpanu:ra,rora-purfrrauponanvs..llorasarerbuas, kr norapurprrauqecKiur $yuxqur.r, vx csoficrsa u rparfuxu.lloxa-raleLtbHble ypaBHeHar. Ilorcasa'r'e.lrbHble HepaBeHcrBa. JlorapnSnlzqecKr4e ypaBHeHr.rq.

Jlorapu$rraHqecKr4e HepaBeHcrBa.

Peuresue cplcreM [oKa3areJlbHblx ypaBHesui,t.l4ppaquonaJrbHr,re ypaBHeHr.rr. Peureur.re up-paqrroHaJrbHbrx ypaBHesrafi .

3

Caprocrosre,'rr,HLIe pa6orrl t2

Pe$epar Ha reMy: <<llonqrr.re BzxeagparHoe ypaBHeuue. Cuoco6u pemeuux.>CocrasreHr.re onopHoro KoHcrreKTa Ha reMy: <[ecrrzuubre rr HarypiIJIbHbIe rorapzSurr>flpereHraq ufl Ha reMy : < Pauuosa,rsuue Synxquu >

CocrasreHr.re orropHoro KoHcrreKTa rro reMe: <Peurenue I4ppau[IoHilnbHblx ypannenufi>Cocranneuue onopHoro KoHcneKTa rro reMe: <<Peurenue vpparluoHanbHrrx HepaBeHcrB)Cocranneuze orqera o6 usyueuuofi reue: <<Pelrenne HppauuoHaJ'rbHbrx ypanneurafi, crrcreMr,IDDarII{oHiInbHbrx ypaeHeHu fi I,I H epaBeHcrB ))

))

)22)

2

Ilparcru.recnrre 3aufl Trrfl t2

2J

4

5

6

7

Peurenne 3aAarr ua 4eficrnu, co crerreHflv.rrpr KopHrMIr.Peurenpre 3aAarr na csoficrsa IloKa3arelruofi (pyurqzu.Peueuue 3aAarr ua ceoficrsa norapuQnaraqecxofi $ynxquu.lloxa:arerbHbre ypaBHeHl{fl 14 HepaBeHcrBa.

Peurenue cflcreM norapn$lruqecKplx ypanneuufi .

Berroprr B [pocrpaHcrne. flefic^tBvtfl. Har, BeKTopaMLL

2

Tepra 3. flnqrvrrre u rrJrocKocrrr B rlpocrllaHcrBe 18

Axcuousr crepeoMerpuu. BaauuHoe pacnonoxeHl4e flpqMblx B npocrpaHcree. BsaIaMHoe

pacnonoxeHr4e nprMbrx rr rrJrocKocrefi s npocrpaHcrne. llapa,uleJlbHocrb nprMbrx Ir rlJroc-

xocrefi. Ceqenus xy6a rrocrcocrbro. Yror uexAy np{MbrMr.r. flepueugaxynqpHocrr. llep-neHAr.rKynqpHocrb upruofi r4 [JrocKocru. Yror MexAy nprlrofi I4 rlJlocKocrrro. Yror MexAy

AByMfl rr Jrocrocrfl rr,ru. flepueHAl,IKynqpHocrb n JIocKo crefi .

J

CaprocroqreJrbHbre pa6orbl 8

Pe$epar rro reMe: <Kpumre BToporo ropflAKa. OrpyxHocrr>flpe:eHraqvrs.HareMy: <flpoexqus BeKTopa Ha rlprMylo ocb, II csoficrna upoerqufi>Pe$epar Ha reMy: <CeoficrBa qerr,rpexyroJrbHrrKa, naparnenorpaMMa, KBaApara, porr.r6a>

Cocraerenrae orqdra o6 u:yvennofi reue: <Ilpxuue h [JIocKocrLI B npocrpaHcrBe)

2

2.,

2

I

flparruuecrcHe 3aHfl Trrfl 6

8. Peurenue 3aAar{ Ha rrapi}nneJrbHocrb nprMbrx r,r nJrocKocrefi n npocrpaHcrBe.9. Pemeuue 3aAar{ Ha HaxoxAeHlze yrna MexAy AByM, [rocKocrqMl410. Peureuze 3aAarl Ha nepneHAl,IKynrp LI HaKnoHHyIo.

2

Tena 4. 3reprenrrr rconr6unaroDlrKlr 4 2

flepecranosxz. Pa3N{errIeHA.f,. llpanu:ra xovr6unaroprrrr4. Coqeranra-s. (Dopuyna 6unouaHsroroua.

2

CaMocroqre!'IlH[,Ie Da6orsr 2

CocraereHue or.rdra o6 usy.IeHHofi reue : <3:reuenrr,r xou6uuaropl{Kl,I ) ) 2

flparru.recKrre 3aHsrufl 2

I 1. Peurenue rcorr.r6unaropHbrx 3aAarr. )Terua 5. Koolrnusarbr rr BercTopr,r 16

.(exaprona clrcreMa KoopAI,IHar Ha rrJrocKocru. Bexropbr Ha rrJrocKocrr,r.

Csqsr MexAy KoopAr4HaraMV14 BeKTopaMr.r. Ypanueuue npxlaofi 14 ypaBHeHr.re oKpyxHocrr,r.YpanueurEe rrpot43BonbHofi rcpunofi. .{eraproBa cr{creMa KoopAr.rHar B npocrpaHcrne. Bex-Topbr B lpocrpaHcrse. CrargpHoe rlporr3BeAeHrre BeKTopoB B npocrpaHcrse. Paccro.rrHaeMexAy AByM, ToqKaMV B rrpocrpaHcrne. YpanHeHr,re flJrocKocrr{. Ypanueuxe c$epsr. Teo-peMa o rpex nepleHAr,rKynqpax. llpu:naru nepfleH.4r.rKynqpHocrr.r nprMbrx ra nlocxocrefi.

3

C avrocrosreJr[,H [,re p a6orr,r 8

Pe$epar Ha reMy: <Kpunue BToporo ropflAKa . funep6ona>CocrasreHrre olopHoro KoHcneKTa no reMe: <florxpnar crrcreMa KoopAraHar))

flpeseuraqvfl. Ha reMy: <Yron MexAy npruofi u rrJrocKocrbro)KoopAuuarbr H BeKTopu. Cocrauenrae or.{€ra o6 usyvesnofi reue: <Koop.u,ruarbr u BeKTo-pbl))

2

2,,

2

I

fIDaxrnqecKHe 3aHfl Trrs 2

12. I)emerrue 3aAaq rro 'rcMc

Teua 6. Ocrrossr rprrroHoMerpur.l 26PaAuaHsas Mepa yrna. Onpe.uelenue cvryca, Kocr.rHyca, TaHreHca 14 KoraHreHca. 3uaxprTpr.r ro H oMerpr,rqecKr4 x Syn rqnfi n o rrerBeprrM.

@opnaynu [pr,rBeAeHlal. <Doprraynbl cJIoxeHLIr. Ooprraynbr rroJroBr.rHHoro yrna. <DyHrquuy:sin x v y:cos x, r4x ocHosHsre csoficrBa H rpaSraxra.

@ynxquu y:tg x u y:ctg.tr, Hx ocHosHlre cnoficrBa rr rpa$uru. flpocrefiurr4e rpr.rroHoMer-puqecKr{e ypaBHeHHr. OlHopolHbre rpr,rroHoMerp[r{ecKne ypaBHeHr.rr. TpuroHouerpaqe-cKr4e HepaBeHcTBa.

3

[IrrarcrnqecKrle 3aHqruq 8

1 3. llpeo6pa3oBaHne rpprroHoMerpr,rqecKux nupaNeuufi .

I 4. llpeo6pa3oBaHr.re rpa$uxon rpr.rroHoMerpr.rqecKux $yHxqufi .

15. Peurenpre rpr,rroHoMerpr{qecKplx ypaBHeHHfi c ucuonr3oBaHzeM Tpr,rroHoMerpuqecKr.rx

$opr'ayr.16. Peurenue rpr.rroHoMerpurrecK[x ypaBHeHr.rfi, upuno4uMbrx K KBaAparHbrM.

2

CarrocrosreJrbHbre pa6orrr t2Cocrasreur.re otropHoro KoHcleKTa rro reMe: <flocrpoeHue rpa$axoB Tpr.rroHoMerpr.rqecKux

Syuxqufi>CocrasreHue orropHoro KoHcleKTa rro reMe: <flepuo4zqHocrb rpr.rroHoMerpuqecKlrx Syr*-qufi)Pe$epar Ha reMy: <CeoftcrBa o6parnr,rx tpyurqrafi>Peruenue rprzroHoMerpr,rqecKl,Ix ypasHeHufi no o6pasqy.

2

2

2)

3

CocraereHue onopHoro KoHcneKTa no reMe: <BupaxeHlle rpr,rroHoMerpuqecKax (fyuxqnfir{epe3 TaHreHc rroJroBr,rHHoro apryMeHTa))

Peuresue rpr,rroHoMerpr{qecKr4x HepaBeHcre no o6pa3uy

2

2

Teua 7. @yurcquu r.r llx csoficrBa H rpa0urcu t4Orpe4eneuue tfyuxqua. O6racrr, oflpeAeneHrr.rr r4 MHoxecrBo gHa.renzfi $ynrcqnu. Cnoco-6rr :aAanuq SyHxur.ru. Cxerraa rrccneAoBalrus fr yHxIIuu.

2

flparru.recKrle 3aHqrrlq .,

7J .I4ccrctoBaHrre rfyuxqrafi no cxeMe. -)

CaprocroqreJrbHbre pa6orrr t5Cocrauenpre onopHoro KoHcleKTa rro reMe: <<Eecroneqno 6onrurue u 6ecrouer{Ho Miurbre

BEJIPIqI,IHbI)

Pe$epar Ha reMy: <Apu$HleruqecKarr Il reoMerpar{ecKarr nporpeccr4ra. Y6rrnaroular reoMer-pr4qecKarr nporpecclr, ))

I4cc te govanue (f yur<q uir ro cxeM e

CocrasreHze orq€ra o6 u:yreuuofi relre: <I4ccreAosariue Qyurquu>flpe:eHraqvfl, Ha reMy: <IrlccreAosanue rfynxr\vrv Ha rrerHocrb r{ HeqerHocrb, 3KcrpeMyMbr)PeSepar Ha reMy: <Haupan:reHue Br,rnyKJrocrr.r rpa$r.rxa>Pe$epar Ha reMy: <Bsrnog rpraroHoMerpllqecKl4x ($opuyr croxeuux)>flpeseHrauvrfl. Ha reMy r.rccneAoBarenbcxofi pa6orsr: <Tpaexropuq ABHxeHlr.,r ror{Kr,r))

2)2

2)I

2

Kournomnaq Da6ora 2

2 Cetwecmp

Tepra 8. MuororrraHHrrKrr 26flpocrpancrBeHHbre rera. flpl.I:ua. flpruar rpLI3Ma. Csoficrea npxuofi rpLI3MbI.

flaparrenerprneA r.r ero csoftcrsa.f Iup at.,z.u aa. fI o crp o eu z e c e.r e H u ii n Iap aM LIArI.

Peureuue 3aAaq Ha HaxoxAeHr{e 3JreMeHToB nI{paMI4AbI.

flpanumuax [upaMr.rAa. YceqeHnas nupaMLIAa.

Penresue 3aAarr Ha HaxoxAeHrre 3JreMeHToB yceveuuofi [rrpaMlrAbl.llpanunrsrre MHororpaHH[Kt4.

3

flDarcruqecK[e 3auqrus 8

18. Peurenue 3aAaq

19. Peureuae 3aAaq

20. Peurenue 3aAaq

21. Peuresve3a\aq

Ha HaxoxAeHr,re sJreMeHToB npI,I3Mbr.

Ha HaxoxAeHr,re 3JreMeHToB napaJrnenenl4rleAa.

Ha HaxoxAeHr,re gJreMeHToB npaBr{nbHofi nuparraz4u.npo6umsofi uarpanleHHocrrr.

I

CaprocroqreJrbHbre pa6orr,r 10

flpereuraqus. Ha reMy HccneAoBareJrbcxoft pa6orsr: <<3nnunrprqecKaq op6ura>Perbepar Ha reMy: <IIpusHaKH paBeHcrBa rpeyronbHuKoB)

2)

llpereuraqvfl Ha reMy: <fpa$ravecxoe perxeHue ypaBHeHr.rf, ))

llpe:euraq vfl Ha reMy: <flpxrvroyro.nrurrfi TpeyronbHr,rK)CocraereHl,Ie onopHoro KoHcleKTa rlo reMe: <3reuenmr cr,rMMerpur{ npaBr.rnbHbrx MHoro-rpaHHr4KoB))

)2)

Teua 9. Te.na rl rroBepxHocru BparrleHrrfl 8IIIap u c$epa.I[unuu4p.Konyc.

3

CaruocrosreJrr,Hble pa6orsr 4Pe$epar Ha reMy: <llpocrpancrBeHHuur reopeMa flu$aropa>flpeseuraqufl HareMy: <<Bsauuuoe pacloJroxeuue c$eprr u npxuofi >

)2

[Ipaxruvecrue 3aHqruq 422. Peuesrre 3aAaq23. Peurenue 3aAaq

HaxoxAeHr,re SJIeMeHTOB

HaxoxAeHr,re 3JreMeHToB

KOHyCa.

uapa, ur4nrrHApa.

HA

HA

Tenra 10. Haqarra MareMaruqecKoro aItaJIlr3a 26MareuaruqecKue MoAeJrr,r pa3nur{Hbrx flpoqeccoB.flocreAo eareJrbHocrr,r r,r u x cnofi crna. flpe4en rrocJreAo BareJrbH ocrr4.flouqrtae [pou3BoAHofi. feouerpuuecrcufi r,r MexaHr.rqecxprfi cMbrcJr npou:noguofi.Ypanueuue KacarenbHofi x rpa$uxy Qynxqrau.(Doprraynu auQSepenuprpoBaHr,rq.llpou:no.qnbre sJreMeHrapHbrx $ynrquft .

flpuvreueur4e rpor43BoAsofi x uccJreAoBaHuro Qyurcqr,rfi .

Hau6orsuree r,r Har.rMeHbrrree 3HaqeHr,r.fl SyuxquftHa AaHHOM OTpe3Ke.

floHsrue uepnoo6pasnofi . Csofi crBa nepBoo6pa:uofi . Heonpegelesuufi vHTerpan.OcHosHrre npaBr4na Haxox.(eHux uepnoo6pzr3Hbrx.flepnoo6pasHffr cnoxHofi Synxqur.r.

2

Cauoc'rogreJrlH[,re pa60rr,r t6Cocran:reHllc ofiopHoro KoHorreKTa Iro reMe: <Cpanueuue 6ecxoseqHo MiL'Ibrx BeJrrar{raH)

Ilpe:eHraq ufl. Ha reMy : < Bercropurre ArratpaMMbr ))

Pe$epar Ha reMy: <flu$SepeHuvan Qynrqnn>PeSepar Ha reMy: <<Brr.rucneHr{e npou3BoAubrx or cJroxHr,rx Synxqnfi>PerueHue 3araq no o6pa:qy no reMe: <Haxox4eHr4e npou3BoAHbrx or 3neMeHTapHbrx (byux-ur4fi)Perueuue 3a!'a'u no o6pasqy no reMe: <Bsr.{[cneHae rrpo]r3BoAHbx or cJroxHbrx $ynrqzfi>Pe$epar Ha reMy: <<@r.rgra.recKr,re rrpunoxeHz.s HeolpeleneHHoro r,rHTetpaJra)Perueuue 3aAaq no o6pasqy rlo reMe: <lIccre4oaanze fiynxqufi c rroMorrlbro [por.r3BoAHbrx))

2))2

2

).,

flDarcruqecKue 3aHqrufl 4

24 . Bt t'tuqrreHr.re [por{3BoAHsrx $ynrcqufi .

25. Peuresfie 3aAar{ Ha HaxoxAeHI,Ie HeollpeAeneHHoto IrHTerpaJIa.

Tevra 11. Llnrernal rr ero nDIrMeHeHI,Ie 18

Irlsrraepenue uoulaAefi rrJrocKr4x 0uryp.(Doprr,ryra Hrrorona-Jleft 6nuua. flloruaAr xpanolznefi nofiIrlnrerpa-uruar Soprvryra o6rerua.Brr.rncreHpre o6reuoB [pocrpaHcrBeHHblx reJI.

flnorua.{u noBepxHocrefi npocrpaHcrBeHHblx reJI.

Peureuue 3a.qaq [oBLIrrIeHHofi cnoxnocru.

TpaIIequu.2

CaNrocroqreJrbHble pa6oru 10

PeQepar Ha reMy: <[uQSepeHrlr,ran Lr ero npprMeHeHrre x upu6nuxeHHblM BbIqI4cJIeHI4.rIM))

Cocrannenue olopHoro KoHcrreKTa rro reMe: <<@r,rgraqecrue rrpunoxeHl.Il{ o[peAeJleHHoro

r.rHTerpaJra))

Cocraueuze orqera o6 usyreHnofi relre: <<BrrqacreHlle nnoqaAll Kpl{Bonl{nefinofi Tpale-qI,II,I.)

Peuresue 3araq no o6pa:uy, tlo reMe: <I,Iurerpal ll ero [pLIMeHeHLte)

flpe:enraq vr. Ha reMy: <Ce.IeHI,L KoHl4rrecrofi nonepxuocrl4 )

)

)

)

22

flnarcruqecmue 3aHflTuq 6

26. Peureuve 3a4ar+.

27 . Pemeruve 3a!.a,s.

28. peurenue 3aAaq

HA

HA

HA

BbIrrI{cJIeHI4e finoua.[uBrIrIpIcJreHrde o6reNa osBbrr{ucreHI,Ie nnouaAlr

Kpr.r Bonr.rH efi u o ft rpan er\r4r4.

npocTpaHcTBeHHbrx TeJr.

npocrpaHcTBeHHbrx TeJr

Tena 12. Sletrenrr,r reopuu BeporrHocrefi. 3lerueHTbl MareMarlr.recrcofi crarlrcrrrKrr 10

Bepoxruocrb u ee cnoficrea. Klaccuqecxoe onpeAeJIeHLIe BepoqrHocrl,I.

I4cnrrraunr -f, . Eepnynnu.Cnyvafi nue B eJILIqtl HbI. MareuaruqecKo e o xI,IAaH I{e v rLtcilep cufl.Hopnaanrnoe pacnpeAeJreHl'Ie.

1

flnarcruqecK[e 3aHsr[fl 4

29. Peruenlre BeporrHocrHblx 3aAar{.

30. Penrenve 3a4aq Ha HaxoxAeHr.re MareMarrrr{ecKoro oxI4AaHLIfl vI lr4cr:epcvr.1

CavrocrosreJrlHr,Ie pa6orsr 6

floeseHrau:afl. Ha reMy: <@opuyla Eafieca> 2

Pe$epar Ha reMy: <3naqenze cnyuaftnofi BeJII{qIIHII

CocraereHr.re orropHoro KoHcneKTa rro reMe: <3aronHbI. )

B 3aBHCr.rMOCTr,r OT XapaKTepa 3ailaql,4>>

pacnpeAeneHufl cnyqafinofi seruqpr-2

)Tepra 13. YnaeHeHrlq r.r HeDaBeHcrBa t4

PannoczlrHocrb ypaeneurfi. flpurrleneHr,re MareMaru.{ecxofi TepMI,IHonotpru vt oI,IMBoJI}IKI,I.

KnaccuSurarru, ypaBH e:r,uit. OcHosHsIe nppleMbl peIxeHLIfl ypannennfi .

Cucreurr ypanuenrafi. PaeHocllrbHocrb cLIcreM ypanueunfi .

Peureuue clrcreM MeroAoM noAcraHoBKI{.Cu crerrr,r rrEHeft nrrx ypanueHlaft c AB)'tvL He[I3BecrHbIMLI.

Hepaneucrso: o6racrb Aorrycrr,rMbrx 3HaqeHufi uepaneucrBa, pelreHl,Ie HepaBeHcrBa, ocHoB-

Hbre MeroAbr perueHr,rf, HepaBeHcre. MeroA I,IHTepBiInos. Texcrosble 3aAaqz.

Tpurouorraerpr.rqecKr4e ypaBHeHufl H HepaBeHcrBa floragarerbHbre r.r norapu(fuuqecKlleYPABHEHI,I' I,I HEPABEHCTBA V CHCTCMbI.

3

CavrocrosreJrb HbIe rra6orrt 8

flpereuraqve, Ha reMy: <KraccuqecKpre MeroAsr npu6ruxeHHoro BbIqI4cJIeHLIr xopuefiKBaAparHoro ypaBHeHIr, )Peuresue HeKoropbrx noKa3areJrbHbrx u norapuSMlrqecKlrx ypanuenzfi uo o6pasqyIlpe:euraqvfl HareMy: <O6sop sneMeHrapnsrx $yuxquft . >

Cocraereuue or.{€ra o6 usyqeHuofi relre: <MuororpaHHLIK[I z Tela BpaIrIeHI{t.>

2)2

2

fIDarrrl.recKrre 3arrflTHs 6

31. Peurenue 3aAar{ rlo reMe.32. Peruenue cr{creM rpaSu.recrcI,IM MeroAoM.

33. Peruenue 3aAaq IIoBbIIrIeHHofi cloxsocru.Terua 14. fIrreAersaMeHaIrIroHHoe rroBTopeHIre l0

Tercrosrre 3aAarr[. TpnrouoMeTpHqecKr.re ypaBHeHilf, H HepaBeHcTBa. floxasarelbHble, JIo-

rapuSN{u.recKr.re u uppauuoHanbHbre ypaBHeHr.r.s H HepaBeHcrsa. IrIccreAoBaH}Ie $yurcqau.BCEIO 351 qac

3. y c JI O B,utfl, p E AJII,I3A rI [I U II p O f pA M M bI O E III E O B pA3 O BAT E JI b H OIzApICq[fIJII,IHbI

3.1. Tpe6oBaHr{fl K Mr{HlrMaJrbHoMy MarepuaJrbHo-TexHI{rlecKoMy o6ecuerreHHIoP e arus aq ut y te1uoit Aucr\wrrJr HH br rp e6yer :naJrurv.vfl, yu e 6 n o ro x a6 us eraHa 28 uocaAo.rurrx N{ecr

3.2. Y\e6Ho-MeroAuqecrcufi KoMrrJreKc o6uleo6pa3oBare.nrsofi y.re6uofi AlrculluJrHHbI,crrcreMaru3rrpoBaHuufi no KoMrroHeHTaM.1 . Hoprraar[sHHfi KoMTTJIeKT:

Y.re6Hrrfi rJraH, @fOC, flacnopr xa6uuera, Pa6ouar rporpaMMa, KT[I;2. Meroluqecxufi:Mero4rauecKr4e parpa6orKr4 ypoKoB, TexHoJrorur{ecKl4e Kaprbl, cIIeHapI4}I orKpblTblx Mepo-rrpuxrufi.;3. Mero4nqecrufi KoMrrJreKT TeM:

3a4lasws An-s caMocrosreJrbHofi pa6orbr, peKoMeHAauI4x x na6oparopHblM I4 rIpaKTI,IqecKI4M

pa6orau, Marepnanbr Anq 3aKpennernfl, u rIpoBepKI4 zsa:auitt rlo reMaM;4. KounneKr KoHTporq 3HaHI4it uyverrfi cryAeHror:KoHrponrHue pa6orrr, Tecru, llepeveHb BorrpocoB 14 TrrrroBbrx 3aAar{, BKnroqaeMblx B 3K3a-

MeHarlr4oHHrre 6nrerbr, rrepeqeHb nr4Teparypbr, HopMarr4BHo-TexHr,rqecKux r.a6r,vr:q, AoKy-MeHTauur4, HarJrrAHux noco6uit, texruuqecKr4x cpeAcrB, AorrycKaeMbrx npu [poBeAeHI4H 3K-

3aMeHa.

3.3. I4uQopMaur{oHHoe - KoMMyHHKaur{oHHoe o6ecneqeulre o6yueHrrflllepeueub peKoMeHAyeMbrx yue6nux uzgalatait, Hurepner-pecypcoB, Aorloruurelrnofirrr.rTepaTypbrOcuoeuate ucmoqHuKu:

1. Y.re6Hux MareMarprKa M.VI. Eauruaxos VIzA. <Axa4euws>> 2017

2. C6opnur 3a1a.t upo$ransuofi nanpaBJreHHocrt4 MareMarl4Ka M. 14. Eauruaros VlzI..<<Axa4euus>> 2017

,{ o noauum erbHbt e uc mo uHuKu :

1. floypounue paspa6orKrr rro reoMerpw VI. A. -flponeHro <BAKO> 20142. Yporu rro Kypcy <Anre6pa vt HaqaJra aHarrr43a>> M. lI. He.{aes OOO (5 3a 3Ha-

le^prfl>> 2017

1. 3nerrpouuufi pecypc <E4ranoe oKHo Aocryna x o6pa":onareJlbHblM pecypcaM>. @op-

Ma Aocryna: http://window.edu.ru2. 3nerrpounrrfi pecypc <(De4epalrHufi rleHrp unQoprvraqlaoHHo-o6pasonarenbHblx pe-

cypc oB). (Doprvra Aocryna : http ://fc ior. edu. ru

3. Eguruat KoJrJreKrIr4,

collection.edu.ru/

qnSponux o6pasonareJrbHbrx pecypcoB: http://school-

4. Kararor yue6uuxon, o6opyAoBa:aktfl,3neKTpoHHbrx pecypcoB: http://ndce.edu.ru

5. 1 .http://www.bookomania.ru/unhebniki-i-posobij.ru/wikipedia.org/wiki

4. KOHTPOJIb lI OUEHKA PE3vJrbrATOB OCBOEIJVTfl OEIqEOEPA3OBA-TE Jr b H o fr yqn ns o ir Alr c rlr4frJrr,rH bt

Kourpolr I4 oIIeHKa pe3ynbraroB ocBoeHufl Aprctfr4nJrr4Hbr ocyqecrBrqerc, npe[oAaBareJreMB npoqecce npoBeAeHnfl [paKTur{ecKr4x zaurr:rzit, TecrnpoBaHptr, a raKxe BbrnoJrHeHut o6y-

frq alo rrlr4 M kl c fl r4H AI,IB[4 ly aJlbHbrx 3 aAaHLrH, I p o e KTo B, H c c Jr e A o B aH r4

Pe:y,rsraru o6yveuua(ocroennue yMeHrrr, ycBoeHHrre ruaHun)

@opur,r rr Mero-Abr KoHTpoJrfl rr

oIIeHKIT pe3y,'Ib-TaroB odyqenus

ocBoeHu, yue6Hofi Aacultrurr,rHbr o6yrarcutnfi c, AoJrxeH rHarr/noHuprars :.3Har{eHlre MareMarl4qecrofi uayxn an, perxeHxrl 3aaaq, Bo3HlrKarouux B Teopl4r4 u [paKTHXe;uLIpoTy I4 B TO )(e BpeMt OIpaHLIqeHHOCTb IIpI4MeHeHH' MareMaTr,rqecKlrx MeToAoB K aHilrlr3yr,r r4ccJreAoBaHr,[o flpoueccos u ssretui4 B [pxpoae u o6ulecree;3HalteHI,Ie [paKTI,IKIl 14 BonpocoB, Bo3HuKaroulux s cal.roi MareMarr.rKe anr SopuupoBaHr{, r{

pa3BWTt4A MareMarlrqecxofi uayru; rlcroplrrc pa3BLfivu floHrrrl, .tttcila, co3aaHu, MareMarllqe-cKoro aHzulI,I3a, Bo3HlrKHoBeHUfl U pA3BU'tLtA reOMeTpt4r,r;

yH[Bepc€InbHbtft xapamep 3aKoHoB Jrorr.rKrr MareMarrrqecKxx paccyxae:aui,r, ux npr,rMeHUMocrbBo Bcex o6racrqx qeJroBerrecKoft neqrerrHocrlr;Bepof,rHocrHbrfi xapaxrep pil:nrl.rHbrx npoueccoB or(pyxarcuero Mflpa.

AJIIEBPA

yMerb:BIITIoJIHTITI apuQueruuecxne Aeficrs[, HaA r{rlcnaMu, coqerur ycrHbre [i [rrcbMeHHrre fiplte-MBI; HaxoArITr npu6ruxeuHble 3HaqeHru Be,'rriq[H r.r lorperxHocrr4 BbrqrrcJreHufi (a6co,rrornarI4 orHocr4TeJrb nax) ; cpaa uu Barb r{ I4cnoBbre BLIpaxe Hltr ;

HaxoAlrrr 3HaqeHI4{ KopHt, creleHr{, norapuQua, TpuroHoMe'rpur{ecKrx nrrpaxeunfi Ha ocHo-Be orIpeAeneHI,IrI, ucnon63yr npu ueo6xoAr4Mocru r,rHcrpyMeHrulnbHbre cpeacrBa; [oJrb3oBarbc,npra6nr,rNe uno fi oue sxofi flpu rparour{ecKr,rx pacqerax ;

BbInoJIHrITb upeo6pa:oeaHl,It Bblpaxeuufi, npuueuar Soprrlynu, cBr3aHHbre co cnoftcrsaNrr,rcreueuefi , norapuQuoa, Tpr,rroHoMerpr{qecKr,rx Synxuufi ;

IrcrloJlb3oBaru upuo6pereHHble 3HaHHfl H yMeHrrs B npaKT[qecroil reqre,'rbuocrrr H rro-sceAHesHofi xu3Hrr:

Arq npaKrlrqecKl{x pacqeroa no SopuyJIaM, BKJIIoqEuI Sopuynu, coAepxau[e crefleHr.r, paAH-K€IJIII, Jlorapla$rr.ru u rpxroHoMerp[qecKlre Qynxuulr, Hcnonb3y, npu neo6xonrrMocru cnpa-Bor{ Hbre M arep r,ranbr u npocre ft ru ue BLrq }rcJrr.rrerbHLre ycrpo fi craa.

(Dyurcuuu u rpaQuru

yMeTb:

BbIqI,IcJIflTb 3HaqeHI4e $yr*Uull no 3aAaHHoMy 3HaqeHaro apryMeHTa rrptr puBn[rrHbrx cnoco6ax3aLaHWfl Qynxur,ru;onpeAenrrb ocHoBHbIe cnoftcrna rIflcJIoBbIx $ynxuufi, [nJr]ocrpr{poBarb r4x na rpaourax;crporlrb rpa$r'Ixu [r3) {eHHbtx Synrurafi, r.nJrrocrp}rpoBarb rro rpa$ury ceoftcrea 3JreMeHrap-Hux Qynxuufi;r.rcnoJlb3oBarb [oHrrr]re $ynxuull AJrt on[caHLIfl v aHar.v3a 3aBrcuMocrefi neluvttu;

HcnoJrb3oBaru npro6pereHHbre 3HaHrrq t,r yMeHHc B npaKT[qecroil treqrerbHocrn r{ tro_sceAHeaHoI xH3HH:

Mfl onvcaH'u'. c lloMoulblo OyHrqHI pa3nruHbtx 3aBllcuMocre[, npeacrau el:afl vrx rpa0uue-cKrl, lrHrepnperaur,rx rpaQuxon.

Haqa,ra MareMarrrqecKoro aHa!.Il,r3a

yMeTb:Haxoar,rrr rrpotr3BoaHbre lneMeHrapHbrx Qynxu[fi ;ucrronb3oBar' npor.r3BoaHy|o wrs, v3].,,e*ilu caoicrs oyn*urfi u rrocrpoe'u, rpaQuxoa;trpl4MeHtrb npoII3BoAHylo Affl npoBeAeuut npulm'txeHHblx srt,rl,tcreHtafi, peurarb 3anaqvrIpLI KJIaAHo ro xapaKTepa Ha HaxoxAe H ue aau6olrrue ro r,r Har,rMeHbrxero 3Har{eH[r ;ast'{}icrsrr s npocrefiurHx crrtiux nnouaafi n o6rerrlu c flcrroJlb3oEaHueM orrpereJeHHofo

l.Bxoanofi KoHTponbzsauuit o6yrarorqux-c, 3a Kypc ocHoBHoroo6ruero o6pa:onanu-rlpeAMeTa MaTeMarH-Ka, BbIflBneHlIe MOTII-

BAqTI4 K I,I3)^{EHI4IO

Ar,tcqurrJrrrHr,r <Ma-TEMATUKA) B

ovcI]o2. Texyutuft rou-rponb B Sopue:- Tecrlrpoeauue

cpera:uauufi noreMaM pa3aenoB

IUCUUIUITIHbI.

- flpoeepxa 4o-MarrrHux pa6or.

- llpoaepxa orrre-ra no npoAenaH-

Hoi eueayau-ropHofi calro-crorrerrHofi pa-6ore.

3. Py6exnlrfi xon-Tponb B $opr'le ron-rpor*rofi pa6oru.4. I4roroeas arrecra-uua n $opue axsa-MEHA.

IrHTerpana;

IICIIOJIb3OBaTb [p[OopeTeHHbre 3HaHIrq u yMeHuf B fipaKTflqecKofi AesTe,'IbHocTIr u no-BCeAHeBHOfi 1(r{3HU Anr:

. perueHr4, [pr{KnaAHr,tx 3aAaq, B TOM r{I4CJre COq}r€1,'rbHO-3KOHOMUqeCKI4X h sLI3[rrreCKI4X, Ha

HAI46ONbTIIE 14 HAI4MEHbIIII{E 3HAI{CHI4fl, HA HAXOXAEHUE CKOPOCTII T'I YCKOPEHU'.

Ypaeneuua n HepaBeHcrBa

yMeTb:. peuarb paur{oHanbHbre, rroKa3arelrbHr,re, aoraprzrpnaravecxlre, TpI,IroHoMe'Ip[qecKLIe ypaBne-

Hrrs, cBoA.f,Illllecq x rnHefiHbrM lr KBaAparHbrM, a raKxe aHaJlor[qHbte HepaBeHcrBa I4 cpIcreMbl;

. ncrroJrb3oBarb rpaQrvecrnfi MeroA peIueHIlJI ypaBHeHI4[ Iz uepareucrr;

. uso6paxarb Ha KoopAnHarHofi n,rocxocrl perreHxr yparueuuft, HepaBeHcrB tI cl4creM c AB)'Ivtf,

HEI{3BCCTHbIMH;

. COCTABJIflTs I'I PEUATb YPABHCHI,I' 14 HEPABCHCTBA, CBfl3bIBA}OUI[E HCI43BECTHbIC BCJII4I]I4HI'I B

TeKCTOBbTX (n rou t{Ilcne npuKraAHblx) 3aAaqax.

HcnoJrb3oBarb rrpuo6pereHHbre 3HaHr,rq ri yMeHI.rq B npaKTl{qecrcofi Aeqre,'Ibuocrl{ u rro-

BceAHeBHofi xu3HLI:. Ntt nocTpoeHr4, r{ [rccJIeAoBaHI{fl npocrerlxllx MareMaTl'tqecKlrx MoAenefi.

KOMEI4HATOPHKA, CTATI,ICTI'IKA 14 TEOP VIfl BEPOflTHOCTEfr

yMeTb:. perxarb flpocrefirune rou6usaropHbre 3aAaqr.r MeroAoM nepe6opa, a raKxe c ucrIoJIb3oBaHIteM

r.r3BecrHbrx Sopuy,r;. Bbtr{ucrqrb B npocreftrulrx cn)qarx BepoqrHocrx co6blTrlil Ha ocHoBe roAcrlera qucra [cxo-

AOB;

ucloJrb3oBaru npno6pereHHbre 3HaHrrq l,r yMeHUq B [paKTuqecKof aefre,lbHocrl{ Ir tlo-eceAHeeHo[ xH3HLt:

. lJrA aHurJru3a pe€rnbHbtx qlrcnoBbrx .qaHHbrx, [peAcraBneHHbrx B BI{ae AL{alpaMM, rpa$uxon;

. algiarvsannSopuaul{}Icrar}'rcrl{tlecKoroxapaKTepa.

I-EOMETPI4-g

yMeTb:. pacno3HaBarb Ha qeprexax r,r MoAeJr{x npocrpaHcrBeuHble $oprrasl; coorHocl4Tb rpexMepHble

o6beKTbI c rrx IDVIaHVAMII, x3o6paxeHunM:a;. orrrcbrBaTb B3arrMHoe pacnonoxeHl,Ie flpflMblx u ruIocKocreil r npocrpaHcrBe, apzy,MeHmupo-

Bamb c6ou cycrcdeuun o6 emou pacnonocteHuu;. aHiur[3r.rpoBarb n npocreilruux cJ.ryqaflx B3aI,IMHoe pacnonoxeHl,Ie o6rexroe B npoc'IpaHcrBe;

. ra:o6paxarb ocHoBHbre MHororpaHHlrxr4 rI Kpyrnble rena; BbInoJIHrrb qeprexl{ [o ycnoBI'IrM

3aAar{;. cmpoumt npocmeilwue ceueHufl rcy6a, npusuot, nupauudoq. peurarb ruraHr,rMe'rpr.rqecKr.re u npocreftruue crepeoMerplrqecKl.Ie 3aIaqv Ha HaxoxAeHrle reo-

Merp[qec KI4x BeJIIrq I{H (A,luu, yruIoB, IrJIoIrraAe fi , o6teuo a) ;

. trcrroJrb3oBarb npu peueHr{r,r crepeoMerpr{tlecK}Ix 3aAaq rulaHuMerp[qecKl4e oaKTbI I'I MeroAbl,

. nponoAr4Tb aoKa3aTeJrbHbre paccyxAeH[, B xoAe peueHlu 3aaar{;

r{crroJrb3oBars upro6pereHHbre 3HaHHq l,r yMeHHfl B rlpaKTl'rqecrcofi Aesre.rbHocrE Il IIo-

BCEAHEBHOT XI,I3HII:. D.1,r lrccJreAoBaHlrr (ruoaelrponanlrr) HecJloxHbtx flpaxrxqecKux cliryauufi Ha ocHoBe I43y-

qeHHbIx QoPrr,tYn n csoftcrs QnrYP;. Bbrquclesus o6reuoB r{ flnoulaAefi [oBepxHocrefi upocrpaHcrBeHHblx ren npH peIxeHI.IlI

[paKTur{ecKlrx 3aaaq, ucronb3yf ttpr{ Heo6xoAl.{Mocru crtpaBorlr.llcu Ll Bblql4cJlflTenbHble

ycrpoficrea.