PACCMOTPEHO
I4 PEKOMEHAOBAHO
K
yrBepxAeHr{ro
Ha 3aceAaHr.r[
IleAarolfiqecKoro coBeTa
flpororol Nel
or
<<29>>
aBrycra 2025r.
or
<0 1 > eewrx1px
2Q254
PAEOtIA.fl TIPOIPAMMA
CIIEIIKYPCA (MATEMATITKA B 3AAAIIAX II TECTAX>
Knacc:
7X
OZO frzreJrr-co craBlrrels : Marcr4MrryK O.II.
.t
Konra.recrso qacoB B He,ueJIIo: 1 .racos
Kofft.Iecrso qacoB B roA: 34.racon
r. Eepesnurcu,2025 r.
floqcHlIreJbHar 3anIIcKa
Tleur
''
"ililffi:"HJ,1"#H*".#l:.
Kypcy Mare
rort,r.{ecroft
3a.qa'ru:
.
.
ycrreugofo I{H
pactufipegfle gnanuft
CosAaHue ycnonufi AJUI
Yrny6nelvre
v
o
3aHllMaTenbHbx' HecTaHAapTHbIX 3aAarr
. flpusrarue I'IHTepeca K MareMarI'IKe'
o flo4Aepxra r{HTepeca K . AOIIOIIH}ITeIbHbIM
3aHuMarbc"
I
3aHflTLISM MaTeMaTI',IKOit
aatoo6P*onanueu'
:
u
xeJIaH}Ie
.
o(DopullpoBaHI,Ie?IccjIeAoBaTeJIbcKlIXyrr,rerrnfio6yvatouuxcr...l
.@opl,rupoBaHlleKoMMyHI,lKarusHoftKyJIbTypbIo6yuaror{uxcr.
KoJrlrqecrBo qa
B
cBr3arr c I{3yqeHI'Iet *utt*u' uxu'Hauzy
' Igpc
BxoALIr
n yue6nrdi llaH
AefireJrbHocrrl' recuo
HeAenIo' Bcero B roA -
34 \aca.
o
O6rqafl xapaKTeprrcrl{Ka yue6noro npoqecca
i
(Doptwttopz&Hu3aquuo6pazoe&meJ'bHozonpoqecca ' :
Kyp ca (nexuuounufi uetog)'
r,r3 Jloxeuue y3rloBbrx
"o,,po"ou
co6ecerosauur (AracrYccrara),
TeMarllqecroe rou6uHl'IpoBaHHoe 3aHflTI4e'
coo6qenus o6Yraroquxcx,
a
perlreHl,Ie HecraHAaprHblx 3aAarr;
a
3HaKoMcTBocHayqHo-IIoIIyJUIpHofirrureparypofi,csggaHHoficMaTeMaTuKo}I'
pa6ota B fiapax'
TBopqecKue flpaKTI',IqecKHe paoorbl'
:
Moxuo BbIAeJrr{Tb cJIeAyIoqI4 e Q optwtt KoHmp oiln
a
a
a
o
a
o
t'j l'r' Iil
coo6uleHvs.v'AoKJIaAbI (rvrnnu),
.3alrlllra[poeKroB;pe3ynbTarblMaTeT:rI'It{ecK}IxBLIKTOpIIH'KOHKypcoB
.trtr
eKc
[peAnoxl'ITr oqeiiftr 3aHtrue
ucx (uoxno
B JII'Icre caMoKo
r{ npeAMerHbre pe3yJlbrarbr ocBoeHns
lllannpyeMbre JrrrrrHocrHbre, MerarrpeAMerHbre
yue6uoro KYPca
Jlllqnocrnble Pe3yabrarbl
1) nampuomuqecKoe
:
locnumaHue;
oK
K
K
,
M
TMOTOM&Tr(K
I't Poccuftcr<
rI'Ix
HaYKax
ilPllKJIaAHbrx cQePax;
2) eparcdaHcKo e u dyxoeuo-HpalcmoeH
.
IOTOBHOCTbIO
K
BbITIOJIHEHPIIO
[peACTaBneHI'IeM o MareMarllqecK
crpyrryp, flnltenuir, rpolleAyp rpaxAa
^
npo6reira' cBs3aHHbIX ',c [paKTI',IqecK]
roToBHOCTbrO K O6CyNgeuuo ,r""atnt*
npHMeHeHueM Aocrl{xeHl4fi HayKLI, oco3HaHr.reM BarKHocrr.r MopanrHo-gTl,rqecKr
[pIaHUI{rroB B AerreJrbHocru
3) mpydoeoe
o
nocnumaHue:
,,
;
,
,,
ycraHonxoft na aKTrIBHoe yqacrlre B peIxeHr4LI npaKTllarecKltx 3aAaar Mar'eMaru.recKc
HaIpaBJIeHHOoTLI' OCo3HaHI4eM BaXHocTII MaTeMaTI4qeCKOrO O6paSOnaUux r
lporsxeHHl4 sceft xPI3HLt !.ils ycneruuofi npo(fecczonalrnoft 4e-arelruocrra:
pa:]BI'ITI{eM Heo6xo4zurx ylteHufi, oco3HaHHbrM nu6oporvt r pocrpoeHl,Ie
I{HAIIBI'IAy€rnrnofi rpaeKTopl{I4 o6pa:onauzr tr xrr3HeHHbx rrJraHoB c yu€rou rgrrHb,
uHTepecoB u o6ulecrneHHbrx norpe6uocrefi;
4) ecmemwtecKoe
o
yu€uoro;
locnLtmeHue;
,
l
cuoco6Hocrblo K SMoIII4oHanbHoMy r.r 3crerLrqecKoMy Bocrrpr{rrr{ro MareMarrrqecKra
o6rerron, 3aAaq, peruenufi; paccyxgeHufi, yMeHrilo Br4Aerb MareMarr.rqecKn
3aKOHOMepHOCTr,r B r.rcKyccTBe;
5) qeuuocmu HayqHozo no3HaHufl:
' opzsHTa\ueft B AetreJlbHocrlz Ha coBpeMeuHyro clrcreMy HafrHbrx upe.4craBnenzfi o
ocHoBHbIX 3aKoHoMepHocrtx pa3BrTprfl. qeJroBeKa, rrptlpoAbr I,r o6rqecrna, rIoHI,IMaHI,Ie
.
'MareMarrrecKoft HayKH Itax cQeprr qeroBerrecKoft Aegrelruocrr.r, grarroB ee pasnnirar
3HaIII{MOCTI{ EIrfl pa3BuTkrfr r\nBuItLlaar\kru, oBJraAeHr.IeM f,3brKOM MareMarr.IKtr
rynrrypofi KaK cpeAcrBoM rro3HaHr4s Mr4pa, oBJraAeHr{e
upocrefi ruuMr4 HaBbrKaMr.r r4ccneAoBatem crcofi Aef renbHo crr.r ;
6) Qusuuecrcoe BocnumqHue, Qopuupoeauue Kynbmypbt sdopoeua u oMoquoHanbHoe
6nazononyvun:
' loroBHocrbro rlprlMeHgrb MareMarr4rrecKlre gHailufl. B HHTepeCax cBoero 3AopoBbj
BeAeHI{t 3AopoBol'o o6pa:a XI,I3HI{ (saopoeoe rrr4Talne, c6alaucuponauuuft pe*",
zanxT]uit lI orAbxa, perynflpHaf, Qusr,ruecxaa aKTr.rBHocTb), c(foprraupoBaHHocrbro HaBbr(
pe(pnexcrau, npIr3HaHI{eM cBoero npaBa ua ouu6ry r.r raKoro xe [paBa
Apyror
MareMarlzqecrcoft
qenoBeKa;
7) erconoeuuecKoe socnumaHue
'
;
opueHTaIluefi Ha [pI4MeHeHve MareMarr,rqecKrax gnanuft AJrs pelxeHvr sa4aq n o6nacr
coxpaHHocrll oKpy)Katoqeft cpeAbl, nnaHzpoBaHr.rr ilocryrrKoB r,r orIeHKLr rrx Bo3MoxHbr
uocle4croufi Ant oxpyxaroulefi cpeAbr, oco3HaHr{eM uo6anrnoro
gKoJrorrrqecrcux npo6JreM lr
xapaKTep
nyrefi ux perueHrzr;
8) adanmaqun K u3weHtntquwtcfl ycttorufiw coquqJtuuotj u npupoduoil cpedu:
o roroBHocrblo tc 4eficrnuxM B ycnoBlltx HeorrpeAen€Hnocrra, rroBbr[reHnro ypoBHr
cBoe:
KOMTIeTeHTHOCTTI qepe3 npaKTurlecKyro Ae.rrTeJrbHocTb,
B TOM rrr{CJre yMeHr4e yqr,rTbcfl
ruoAefi,
npzo6petarb
B coBMecrnofi Ae.sreJrbHocrr,r HoBhre 3*a:rrtrs.. HaBbrKr{
ApyrLIX
o
l
KOMrreTeHrI4r4 r43 OrrbrTa .4pyr-rrx ;
neo6xoAlzuocrrto n SoprraupoBaluu HoBbrx 3nauufi, B ToM qr.rcfle (foprraynrzpoBarb LrAev
IIoH.[TpIt, fl{rlore3bl o6 o6rertax rI sBJreHurx, B ToM qI,IcJre paHee HelrsBecrHhu
oco3HaBarb ge(pzqnrrr co6crseuHrrx sHaHuft rr KoMuereuruocreft, nJraHr.rpoBarb cBo
prI3Br4Tr,re;
o
cuoco6Hocrblo oco3HaBarb crpeccoByro cr.rryarlrfio, Bocnpr.rHr.rMaTb crpeccoByrr
cHTyaIII4Io KaK BbI3oB, rpe6yroqnft roHrpuep, KoppeKTr.rpoBarb rrptrHr.rMaeMbre perreHr.rr
u geitcrvut, QoprvrynupoBarb I,I orleHrrBarb pr.rcKLr u nocneAcrnur, (popunpoBa-rb onqr.l
MeranpeqMerHbre p eryJrbrarbr :
flosaasamenbHue yHusepc&nbHwe yveflnue deficmeun
o
Easoearc roeuqecKue deilcmeun :
BbuIBJItrb 14 xapaKTepl,I3oBarb cyrqecrBeHHbre npu3HaKr4 MareMarr4qecKr.rx o6rer
Bo3MoxHocreft, apryueHTr,rpoBaTb r.r KoppeKTr,rpoBarb BaprraHTbl peureuuft c y.r€rot
Hosoft un(fopuaquu.
C auoxo u mp oJtb, gwoqLtou atauuit uHm e rn eKm :
BJraAerr cnoco6aMr.r caMonpoBepKr,r, caMoKoHTpont rpoqecca lr pe3ynbrara pemeHuj
MareMar[qecxoft 3aAaqld;
IPEABI,IAETb TPYAHOCTKI, KOTOPbIE MOTYT BO3HI{KHYTb NPI,I PEUIEHI,II 3AAAqIl, BHOCLIT]
KoppeKTr{Bbr B AesreJrbHocrb Ha ocHoBe HoBbrx o6crosremctn, HaftAeHHbIx ouru6ox
BbrflBJreHHbrx rpy4Hocrefi ;
olleHr.rBarb coorBercrBr{e pe3ynbrara AerrenrHocrl4 rlocraBnenuoft qentl lI ycnoBlasM
o6rscHs6 npuquHbr Aocrl{xeHr4flvIrv He Aocrl4xeHrar IIeJIV, HaxoAI4Tb orun6ry, AaBarI
oIIeHKy npuo6per€HHoMy oIIbIry.
rlp egrreruble pe3yJrbrarbl :
yqaulr4ecr Ilonyqar Bo3MoxHocrb Hayql,ITbct :
. caMocrorreJrbHo npuo6perarb r,r [pvMeHrrb 3HaHI,It B ptr]flI4qgbrx cllTyallurflx AII:
peluenr,rfl pa:lu.ruofi cJloxHocrr{ npaKTr.rqecKl{x 3aAaq, B ToM qucre c I{crIoJIb3oBaHI,Ie\
npu neo6xoAr,rMocrr,r c[paBoqHbrx MarepuanoB, KaJIbKyJItropa LI KoMnblorepa;
. rroJrb3oBarbcr rrpeAMerHbrM yKa3areneM euIlurnoueAufi kr cIrpaBoqH[KoB AJr
HaxoxAeHr.rr un(fopuarruLr; yr!(erb perrrarb 3aglaqv c lroMoulbrc nepe6opa Bo3Mo)KHbx
Bapr{aHToB;
o
BbrrroJrHrrr apllrfrraerr.rqecKue npeo6pa:oBaHLrfr. BbIpaxeHLIft, npuuentrb I'Ix Ans peureHll
y.re6nrrx MareMarr,rqecKllx 3a$aqtv salLaq, Bo3HlIKarouII4x
B
cMexHbIX yte6Hlr
npeAMerax;
o
ilpr,rMeHrrb u3yqeHHbre lloHrTr.rfl, pe3ynbTaTbl I{ MeTOAbI npu pellleH'r4v 3ilall u
pa3nr4qHbx peanbHbx cutya'4ui1 He cBoAsrquxct K He[ocpeAcrBeHuoMy [puMeHeHI'IF
n3BeoTHbE(\aJI|OpI,ITMOB;
.
!: -
cvrryar\vrr4 HeoupeAeJl€nnoctra rrpIl peuIeHI'I]
aKTy€rnbHbrx Anfl Hux upo6leu, a raKxe caMocrotreJlbHo llHTeprlperl'IpoBar
pe3yJrbTaTbr perrreHflr 3a4Aqvr C y.r€tOtvt OrpaHuUeuuft, CBt3aHHbD( C peanbHblM]
csofi crsaMI,I pac cMarpHB aeMblx npo qecco B u ts renvrfi
caMocroqrelbHo Aeficrsonarr
retua
n
r. oreueuru "!r"S?fTffi#:xl:' flulflr".r,,","
3HaKu',
*ur.rur"n
[pennero Bocrora. ,{penuuft Eruner (luac)
3ausrue 1. IrlcroplluecKarr cnpaBKa. Ka.recrsa neo6xoAI,ttuble npu Lgyqenr4r4 MareMarI{K
(nnuuauue, noo6paxeHlle, na6moAateJrbHocrb, yMeHI{e 6ucrpo cql,ITarb, Ir€IMtrb' BOJL
HecTaHAapTHOe MbtIIIJreHLIe, yM eHrre npI,IMeHf, Tb 3HaHI,It B TB OpqecKrax yclonuxx)
Tena 2. MeroA paBHbrx rpeyronbHuKoB - r,rcropl,ItlecKl,I fiepBblft reolterp[qecK?I
MeroA. (luac)
3
au.srue 2. Vlct opuuecKafl cnpaBKa. 3aAa'M c rpeyrolbHl'IKaMll.
Ooprrra KoHTpons : KoHcrpyI'IpoBaHI'Ie.
I
gncloBble Bblpax(enut'(4 uaca)
.'
I'
.---Tetwa.l. gucna lr Bblrrl4crtesus.
qu(fpu
apa6crue
r'r
Pulracxue
crpaBKa.
WcropuqecKas
3-6.
3a;rsrus.
"1111, III{CnOBIIX
q14CIOBOIO BbIpaXeH1aS' CpanneHUe'
BbrpalKeHI,IS. BnqUClenne 3HaqeHI'Ig
qucna r,r
ylopfAoql'IBaHl{e qficeJl' Harypalruble
Bbrpa6eHl{fi. guclOnafl llpf,Maf, CpaBHeHlIe ll
o6uter"rY 3HaMeHaretry: n:1111:
gpo6u. OcnosHoe cnoftcrso .Upo6la. npr".A."te 4po6efi
I{] yMHoXeHI4e
LI BbIqI'ITaHvIe liecflTz4qHblx Apo6efi'.'{eneuue
AecsTr,rr{Hofi Apo6er. CnOxenue
creneHb q:lruta 10' YrutroxenkIe.AecflT:uHblx A!:9?1!
Aecsrr,rtrHoir. gpo6u Ha HaTypanbHylo
I'I
flpeo6pa:oBaHrlg Aec.f,TrIqHbI < 4po6efi I o6ruICeHIafl. BrrqrtcreHlle 3HaqeHI'It
3
BbrpaxeHllr. Cpaanenue qrIcJIoBbIx Bblpaxeuuft' 9ucrosas
rlprMaf, , cpaBHeHrle u ynopgAo'{uBaHl4e'{UCer'
gpo6ra. Ouronnoe cnoftcrso Apo6u'
ffutypun""ur.
"
"r.na
flpraeeAeHue apo6eft r o6uleuy gnanenaremo'
[o nsrne Aectrl'IrrHo fi 4po 6r'r. Ilpeo 6pa: oBaHI4e AectrI{qHbIX
14
,4po6eft B o6HrHoseHHrte 14 Hao6opor' Cuoxenue
BbrtrlrraHlle Aec.srlrtlHbrx apo6eft. r{eneuue rI yMHoxeH}Ie
10'
AecsrlttrHofi 4po6n Ha HarypamHyrc ctenenrrlacra
VunoNenue Aecflrur{nux APo6efi. .{eleuve 4ecflTvrqHbD(
4
5
6
nno6efr.
8
9
BogneAeune AByrrrteHa B 9lgngrlb.
10
Tpeyrolrnur flacrars.
Cnoxenue apo6efi. Blr.{[rauue apo6eft. Yllnoxenue
lpo6eft. ,{eleHlle apo6eft. CloNenue 14 BbrtI[TaHI'Ie
cMeIIraHHbIx 4Po6efi. YrrlnoNenrae
npo6efi.
12
Pauprottan"trrte rlucra.
I
I
I
I
I
llpeo6pasoBaHl4e 6yrcuennrtx srtpaNeHlau'
.Ilereuue MHororIJIeHa Ha MHoro'{neH qronK
11
I
1
I
I
14 AeJIeHI'Ie cMeIrIaHHbIx
I4ppaquoualrnue
qrIcJIa'
I
qu
,{efictnureJlbHble
pil|Hocrll. BuAeleune
13
t4
^qaunr.'ru PacHoc.l.T- KR
PagloNeritle MHoroqJIeHa Ha MHoxI4TerII{' IloHf,Tllc U
TOXrecTBax I'I MeroAax tIX AOKffiaTeffi
nePeueunofi' KoPeus
YParneuuft c oAsofi
uepelrenuoft.
15
t6
t7
18
ecuuil cMbIcJI MoAyJIt
Pettren"e ypannenufi' coAepxaulux HeI'I3BecrHoe rIoA
l-enn r ernwtr
Nf
croBblx 3 a.Ilaq c rIoMoIIIbIo yp aBHeHI{I'I'
perreHllr4
OnpeAeneulle ypaBHenufi ,{uo$aura' IlpaB}rna
P
errreu ue reK
tr-
t9
q
I
I
I
1
1
I
puellltfi
Ilpuueueur'le 4rao(faHToBblx ypaBHeHI'I[ K npaKrn'qeerr4M
I
3a.[aqaM.
20
2I
22
r [ara
CracreMu runefinrrx ypaeHeHuft c AsyMs lepeN'Ie{uHl"ur'
Dcrrrc'ne crrcreM vnasHeHufi Da3ruqHblMu cuoco6auu'
rII4cJIa
AaHHoM orHoIIreHI'II{'
Ot"o-atte. [enenue
B
u
flponopuHll, ocHoBHue ceoficrBa flponoptluia' flpwtax
^6-o-,ra c rnnn.rl.lrrrrnr{2
ITEI{ETe 3aBlIcI,IMOCTI',l.
1
1
I
wfl
KI
npoqeHTOB Or rrr,rcra
@eHr,re
r.r3BecrHoMy Konl'IqecrBy npoqeHToB
u
qucJra IIO
or uero' flpo[euTuoe
u yMeHbIIreHI'Ie tII'IcJra
orHoIrIeHlIe AByx ullcer. VserI'IqeHIae
Ha AaHHoe
Kqn4'reglle fl
Perueuue saAaq
[nuxenue
"a
IlpoueHrbl' Peruenue 3aAarl
HaBcrPeqY, BAofoHKy; ABI',IXeHI'Ie
IIo
Ha
TeqeHI',IIO rI
rlo reqeHI'IIo }I
finorxenr,re HaBcrpeqy, BAoroHKy; ABI'IxeHI{e
Peurenue HecraHAaprHblx 3aAaq' Peuenras
)'
3nuurnou srtrs. Ans'gereft "T' 1 1' MareMarI'IKa'
o
o
128 c'
Srer