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1) Brnomurr apnSrvreru.recKr4e Aeficrnus, coqera.r ycrHble u
rrlrcbMeHHbre rpueMbr, [pLrMeHeHLre BbrrrLrcJILITeJIbHbrx ycrpoficrn;
HaxoAltrb 3HarreHrrf, KopHtr narypanrHofi crelreHu, creleHl4 c
parlLloHzlJrbHbrM [oKa3aTeJreM,
r4crronb3yr rrplr
rorapzQua,
neo6xoAuMocrlt BbrrrLrcJrrzTeJrbHbre ycrpofi crBa; nonmoBarbct oqeHrofr z
npzKLrAKorr IIpn [paKTLrqecKlrx pacqeTax;
2) flponoArrrb upeo6pasoBaHus. qprcJroBbrx z 6yrneuHbrx Bblpaxerlri1
BKnroqarculLrx cren enkr, pa4uKaJrbr, rorapnQMbr 14 Tpl4roHoMerplrqecKlre
Qyrr qzu;
upaKrllqecKl{e pacqerbl Iro Qopruynau, BKrloqal
Qoprvryrn, coAep)Kalrllle crerreHrl, paALIKanbI, JlorapuQrvru Lr
3) BHuonnsrr
TpkTroHoMeTpLIqecKLIe Synrcqnn, nPU Heo6XoAtIMocTLI ucrronb3yr
clpaBoqHbre MaTepnarrbr r,r npocTefirrrr{e BbrrrkrcJlllTenbHble ycTpoitcrsa.
4) Oupe4erarn 3HaqeHue Qymquu ro 3HaqeHLIIo apryMeHra npn
pa3nr4qHbrx cno co6 ax 3allaHu'^ Qyurcqnu ;
5 ) Crpourr rpaQraKu LI3f{eHnrrx QyHrcIIufi , BbIroJIHflrb npeo6pas oBaHus
rpaQrErcon;
6) Ouucrrearr ro rpaQury il ilo
u
Qoprr,ryne noBeAeHve
cBoftcrBa
fiymqrafi;
7) Peruarb ypaBHeHLrs., evrcreMbl ypaBHeHl4ft, nepareHcrBa, ucnonb3yt
cBoficrBa Qynrcqufi u nx rpaQFIecKIfIe rlpeAcraBnenufl;
8) Onncrrsau u
r{ccJreAoBarb Qymqun peaJrbHblx 3aBI4cLIMocreiL,
rrpeAcraBJrrrb rzx rpaQzqecKu; LIHrepnperllpoBarb rpaQzrcll pe€uIbHbIX
[poqeccoB.
9) Peruam reoMerpl4qecKlle, Qzszuecrue, eKoHoMI4rIecKLIe u Apyrl4e
rrpnruraAHbre 3aILa'cIu, B ToM qLIcJIe 3Allarr]a Ha HaLI6OnbUrVe u
HarrMeHbIIIUe 3HaqeHnf, C npIIMeHeHVeM AnnapaTa MaTeMaTurlecKofo
aHarlu3a.
10) Peurarb reKcroBbre 3aAarrv c rroMorrlbro cocraBJIeHuA ypaBHelauit u
HepaBeHcTB, I4HTepnperllpyr pe3ynbraT c fIeToM olpaHl4rleHl{fi ycnoBl{.f,
3aAAqId;
11) I4:o6paxarb Ha KoopAlrHarHofi rrJrocKocrl4 MHox{ecrBa
ypaBHeHI4fi
z nepareHcrB, c AByMt
peIneHLIfi
rIepeMeHHbIMI4, LI I4x cvcreMbl
Lr upocrefiruze crepeoMerpuqecKue
3a$a'qu Ha Haxox{AeHve reoMerpr{rrecKl[x BerLttII4H (AnuH, yrJIoB,
nJrorrlaAefi, o6leuon);
12) Peruarr
13)
rrJraHuMerprrrrecKrre
I4cnomgosarn
rpz
pelxeHull
crepeoMeTpllqecKI4x 3aAarl
rrnaHVMerpLIqecKLIe Qarcru u MeroAbI;
Co4epxanue Qany.nrraTlrBa
IIOBbIIIIEHHOII
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1. Ypannenufl n HepaBencrna (11 uacon)
@oprvryru rcopHefi rrpocreLrIuux rpklroHoMerpllqecKrx ypaBHeHI4fi.
9acrnrre cnyqau perxeHrlrl rrpocTeI,IIxvx TprrfoHoMerpruecKI{x
ypanneuufi. Or6op rcopnefi, rpIIHaAne)ICaIIIt4x llpoMex(yrKy. Cuoco6rr
perueHLrrr rprrroHoMerpruecKl4x ypaBHeHLIu.
IrlppaquoH€lJlbHble ypaBHeHllt. MeroA paBHocI4JIbHocrI4.
I4ppa\noH€[JIbHbIe HepaBeHcrBa.
Alropnrrvr peilIeHl4t
HepaBeHcTB
MeTOAOM I4HTepB€UIOB.
)
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t
h
floragareJrbHbre ypaBHeHr4f,. MeroAu peIxeHLIt rIoK€BareJIbHbIX
ypaBHeHkI fi . floras areJlbHble HepaBeHcrBa, npl{Mepbl pelxeHl4fi .
JlorapuQMrrrrecKu e yp aBHeHLrx. Mero4 paBHocr{JrbHocrLr.
JloraprEQMr/rlrecKr4 e Hep aBeHcrBa.
2. BupaxeHrfl rr rrx npeo6pasoBaHrrfl (10 uacon)
CootuoureHvrs, Me)KAy rpr{roHoMerpuqecKuMr.,r Qyrrcqurnnra oAHoro
roro xe
14
apryMeHra. @oprr,rylu KparHbrx apryMeHToB. O6parnrre
rplroHoMerpr4qecKze QyHrquu.
Csoficrea crerleHl4 c IIeJIrIM rloKa3arereNa. Pa3noxeHlie MHororIJIeHa Ha
MHoxureJrLr. Corcparqeune 4po6u. Cyuna u p,zr3Hocrb 4po6efi.
llpozsne4eHLre u qacrHoe 4po6efi.
llpeo6pasoBaHue uppaqr4oH€rrrbHhrx nrrpaxeHzfi. Csoficrea creneHr4 c
paqv oHulJrbHbrM rroKa3aTeJreM.
JIorapvIQN,r. CsoficrBa norapraQrvror. flpeo6pasoBaHlrf, norapzQrr,u4qecKr4x
BbrpaxeHLru.
3. I4cc.neAoBaHue Qynnqnfi MerogaMrr MareMarr{qecKoro analnsa (5
uacon)
IrlccreAosaHue ynrcqnfi oJreMeHTapHbrMLr MeroAaMLr. flpozsBoAHat
Qyurquu, ee re Merpr,r.recrcufi u Qusu.recnufi cuucl. Zccle4onaHvre
@ynrqlrfi Ha oKcrpeMyMbr.
Zccle,qonaHue Q mqufi Ha Bo3pacraHLre u y6rrnaHue. l4cctreAoBaHr{e
Qynrcqufi sa nau(.oJlblrree r4 H€MMeHbrrree 3HarreHLre (r r.u. Ha orpe:re).
Zccne,4onaHpre Q nrqufi c rroMorrlbro rpaQzrca ed upozsno4nofi.
4. CrepeoMerpus (8 uacon)
Yrurr u paccro.l Hvrn, B rlpocrpaHcrBe. MHororpaHHkrKLr. Tela BpanleHr,rr.
llnorqa4r,r rroBepxHocrefi rel. O6renau ren.
Teivraru.recKo€ rrJraH[poBaHrre
Te*ra
Ko.n-no
qacoB
YpanneHyfl u HepaBenerna (Ll qacon)
flp eo6pasoBaHLr e rplrroHoMerplrqecKr4x
nrrpaxenufi.
2
P e ure nu e upo crefi rulrx rp kr ro HoM erpLr qe cKLr x
yp aBHeHr4 i4. n HepaseHcrB.
3-4 P erueruEe rpLt roHoMerirnue crcrax ypaBH enuir
I
p a3JrLtrIHbrMLr
5
6
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I
2
crroco 6aturu.
Ot6op ropnefi , rpr,rHaAnexarqnx rpoMexyrKy.
Peruenue sata:rrnirEf3.
ZppaquoH€urbHbre ypaBHeHr4s. MeroA
1
I
paBHocLrJrBHocTpr.
7
I4ppaquoH€lJrbHbre HepaBeHcrsa. AmoplrrM
perxeHLr.n HepaBeHcTB MeToAoM r4HTepB€lJroB.
I
8
floragareJrbHhre ypaBHeHrl.f, . MeroAsl perueHlrt
I
Cporcu
TIOKA3ATEJIbHbIX YPABHEHI4
14.
9
florcasareJrbHbre HepaBeHcrBa, [pLrMepbr
1
10
peruenzfi sa4atruiT. Ef 3.
JlorapuQMzrrecKue ypaBHeHVr. Mero4
I
PABHOCLIJIbHOCTI,I.
11
Jlorapv6Mr4rrecKrfre HepaBeHcrBa.
BupaxeHrfl rr nx npeo6pa3oBaHrrr (10
I
qacon)
r2I3
ouro ru eHut Me)KAy rplrroHoMerplrqecKuMLl
QyHrqnxMlr oAHoro rr roro xe apryMeHra.
@opruyru KparHhrx apryMeHToB.
Cnoficrsa crerreHu c ueJIbrM rroKa3areJreM.
PasroxeHkle MHoforIJIeHa Ha MHox(ureJru.
Corpaqenue Apo6z.
Cyrrarraa u pa3Hocru 4po6efi. flpozaneAeHr{e r{
rracrHoe 4po6efi.
2
t7
llp e o6paroBaHr4
I
18
nupaxeHrafr.
Csofi crna crerreHu c parllroH€rrrbHbrM
l4
15
t6
Co
e Lrpp arlLr o H€LrrbHbrx
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I
IIOKUBATENEM.
t9
20-
2l
22
LJ
24
25
Jlorapn0rr,r. Csofi crBa norapndN{os
flp e o 6p ar oBaHUs, n orap z Q rvruq e cKLr x
Bbrpax{eHzfi . PemeHlre 3a,uaHzfi Ef3.
I{ccreAoBaHrre QyHrcqnfi MeroAaMn
MareMarrrrrecKoro aHaJrrr3a (5 .racon)
flpousnoAnafl, SynrqnrE, ee reoMerpzuecrczfi u
dusn.recrcufi cusrcr.
I4ccne4on anue $yHrcqrafi Ha eKcrpeMyMbr.
IrlccneAosaHne Syurcqnfi Ha Bo3pac^raHue u
v6HsaHrae.
IrlccreAon aHr4e QyHrcqnfi sa :crau6 oJrbrrree Lr
I
2
I
I
I
I
HAKIMEHbIIICE 3HAqEHI,IC.
26
I,lccre4oaanvre QyHrqzfi c noMorrlbro rpa0zra
e€ upoussoAnofi . PeureHze salLanuir Ef 3.
Crepeoprerprrfl (8 qacon)
27
llaparnerbHocrb
rrp.f,
Mbrx r{ rrnocKocrefi . Yron
I
1
Mex(Ay rrprMbrMLt.
28
29
30
31
flepnen4r4Kynf,pHocrb rrprMbrx u nlocnocrefi
,IlsyrpaHHufi yrol.
Vror Me)K.IIy upsvrofi Lr rrJrocKocrbro.
llpusNda. llnoulaAr rroBepxHocrz. O6rel,r.
llnpauuAa. lhoulaAb noBepxHocrlr. O6r€u.
.
1
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1
1
32
33
34
UunnnAp. flnoqaab noBepxHocrlr. O6r€u.
Konyc. llnoua.ur noBepxHocrn. O6r€rra.
Cdepa. flnoulaAr rroBepxHocru. O6rdrr,r.
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I{croqnnnu nnQopMarlrr
roA peAaKqnefi @.O. Jlncenro, C.IO. Kyla6yxona; Pocron-ua-.{ony,
Jlerzon-M,2021 r.
2.http:llsdamgia.ru - CAAM fI4A: perry BIIP, Of3, EfO .
3. www.fipi.ru - cafir AIilT/rI (4erraonepcus Ef3-2022, HopMarr.rBHbre
1
. Yqe6no-MeroAlrrrecrufi KoMrrJreKc
4OItyrr,renru)
4.
trup://school-collection.edu.ru
o6pa.roeareJrbHbrx
-
e4nHas. KoJrJreKrIHr quQponux
