math - krou.moeys.gov.kh

11>> eellaakk eeddvviitt hhUUvv OPCV/SKM

22>> Dr. Pat Hiddleston RTI

muxviC¢aKNitviTüa fñak;TI 1

lT§plsikSa

cMnYn ³ eRbIviFIepSg² rYmTaMgmuFaKNna edIm,IedaHRsaycMeNaTgay² tamviFI edaybUkBIrcMnYnKt;

EdlmanplbUkminelIsBI 20.

kic©karvaytMél

1> kic©karenHRtUv)andak;[sisSeFVIenAcugqñaM bnÞab;BIsisS)aneronBIviFIepSg² dUcCakarbUkcMnYnKt;

karrab;vtßú kareRbIbnÞat;elx nig eFVIviFIbUktamCYrQr nigtamCYredk.

2> RKUdak;cMeNaT[sisSeFVIrYcKat;GancMeNaT. NavImanXøIcMnYn 9 RKab;. mþayrbs;nag [XøInag

6 RKab; EfmeTot TukCargVan;. etINavImanXøITaMgGs;b:un�an?

3> [sisS 2 b¤ 3 nak; GancMeNaTeT,Igvij edIm,I[sisSTaMgGs;KñacaMcMeNaTenaH.

4> bnÞab;mk Bnül;sisSfa kic©karEdlsisSRtUveFVI KWedaHRsaycMeNaTCa 5 rebobxus²Kña.

5> dMbUg RtUveRbIRmaméd edIm,IedaHRsaycMeNaT. [sisSrab;Rmamédrbs;eKrhUtdl; 9 rYcmk

rab;RmamédcMnYn 6 EfmeTot ehIysresrcMelIyEdleKrab;eXIj.

6> TI2 sisSbgðajcMelIy edayKUrRKab;XøI ehIyrab;. niyayeTAkan;sisSfa : RKUcg;[b¥Ún²KUr

rUbXøIcMnYn 9 ehIynwgcMnYn 6 EfmeTotenAkñúgesovePA. rYc rab;XøITaMgGs;enaH. qUtXøIEdl

b¥Ún²)anrab;rYc ehIysresrcMnYnsrub : . RKURtUvTukeBlevla[sisSeFVIkic©karenH.

7> TI3 sisSbgðajcMelIyedayeRbIbnÞat;elx. KUrbnÞat;elxmYyEdlmanelxcab;BI0 dl; 20

dak; enAelIkþarexon ehIy[sisScMlgcUlesovePAlMhat;rbs;eK.

niyayeTAkan;sisSfa : RKUcg;[b¥ÚneRbIbnÞat;elx Edlb¥ÚneTIbnwgcMlgdak;kñúgesovePArbs;

b¥Ún rab;BI1dl; 9 bnÞab;mk rab; 6 EfmeTot. KUsrgVg;elIelxEdlb¥Únrab;eXIjenaH. :

1

8> TI4 KW RtUvsresrelx9 bUknwg 6 CaviFIbUktamCYredk. niyayR)ab;sisSfa {\T,ÚvenH

RKUcg;[b¥ÚnsresrcMeNaTdUcteTAenH} sresrcMeNaTmYyeTot EdlmanlkçN³RsedogenHKW

4 + 6 = 10. RKUR)ab;sisSfa {cUrb¥ÚnsresrcMeNaT XøI 9 RKab; bUknwgXøI 6 RKab;

dUclMnaMKMrUenHEdr} .

9> TI5 KW RtUvsresrelx 9 bUknwg 6 CaviFIbUktamCYrQr. RKU[]TahrN_ epSgeTotdak; elIkþar

exon edaysresrCaviFIbUkelxtamCYrQr. RKUR)ab;sisSfa :\T,ÚvenH cUrb¥ÚnsresrcMeNaT

XøI 9 RKab; bUknwgXøI 6 RKab; dUcKMrUenHEdr : .

KMrUkic©kar xageRkamenH KWCa]TahrN_sMeNrrbs;sisS eqøIytmeTAnwgkic©karEdlRKÚdak;[eFVIcMnYnBIr

nak; ³

sisS k sisS xrgVaytMél

xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisSnigkardak;BinÞúsisSmñak;².

lkçN³vinicä½y Gtib

rma

sis

SS k

sis

SS x

karyl;BIviFIepSg² 5 5 3

cMelIyRtwmRtUv nigPaBs¥at 5 5 0

srub 10 10 3

2

mUlvicarN_ sisS kk sMerc)andl;kMritlT§plsikSa eday)anbgðajkaryl;dwgc,as;las;GMBIviFIedaHRsaynImYy²

ehIy)anpþl;cMelIy)anRtwmRtUvpgEdr.

sisS xx BuMsMerc)ankMritlT§plsikSaeT,Iy. sisSenHeFVI[mankMhusmYy enAeBlrab;Rmaméd ¬sisS

enHR)akdCaKitfa RtUvEtbgðajRmaméd6 enAeBlbUk6 nwg 9 eKKitfa cMnYnsrub KW16¦. nagKUrXøI

BuMRtwmRtUvnwgcMnYneT,Iy. karBit sisSenHKUrrUbXøIxVHehIysisSenH BuMmanTMnukcitþkñúgkarrab;Edr. sisS

enHGacrab;cMnYnenAelIbnÞat;elx)an EteKBuMyl;GMBIrebobeRbIbnÞat;elxedIm,IbUkBIrcMnYneT. cMeBaH

karbUkelxvij sisSenHRKan;EtcMlgelxBIRKU Edlsresrdak;enAelIkþarexonEtb:ueNÑaH. RKURtUv

elIkTwkcitþdl;sisSenH ehIyerobcM[eKeFVIkarCamYysisSepSgeTot b¤ CamYynwgRKU edIm,Ihat;rab;BI

elx1 dl;20 edayeRbIvtßútMNagtamry³KMnUr BI1 dl; 20. rYcmk sisSenHGaceronviFIrab;epSg²

eTot)an.

3

1 2 3

muxviC¢aKNitviTüa fñak;TI 2

lT§plsikSa

lMnaMKMrU-BICKNit ³ bMeBjlMnaMKMrU tamBN’ tamrag TMhM nig cMnYn .

kic©karvaytMél

1> kic©karenHRtUv)andak;[sisSbMeBj bnÞab;BIsisS)aneroncb;emeron CaeRcInTak;TgeTAnwglMnaM

KMrU nigbnÞab;BIhat;eFVIlMnaMKMrUepSg² CaeRcInelIkrYcmk.

2> RKUcMlglMnaMKMrUxageRkam dak;elIkþarexon. Bnül;sisSfa kñúgkic©karenH sisSRtUvbMeBjlMnaM

KMrUnImYy² bnþ enAkñúgcenøaHEdl[ tamrUb b¤KMrU b¤ cMnYn EdlsisSKitfa RtwmRtUv.

3> sisSRtUveFVIkarCabuKÁl.

KMrUkic©kar

xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn 2

nak; ³

sisS {k}

sisS {x}

4

rgVaytMélxageRkamenH KWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².


rma

sis

SS k

sis

SS x

rUbTI1 2 2 0

rUbTI2 2 2 1

cMnYn 2 2 1

srub 6 6 2

mUlvicarN_ sisS k sMerc)andl;kMritlT§plsikSa. sisSenHyl;c,as;GMBIlMnaMKMrU eBleRbIrUb nigcMnYn.

sisS x BuMsMerc)andl;kMritlT§plsikSaeT. RKUKYrEtsesIrsisS eRBaHsisSenHmanbMNinrab;elx

)anl¥ EtRKURtUvcMNayeBlCamYysisS xx nigsisSdéTeTotEdlmanlT§pldUcsisS xx enHpg Edr.

RKUGacrkvtßúgay²mYycMnYn ¬dUcCa XøI RKYstUc² nigeQI¦ dak;TaMgbItMerobtamlMdab; ¬]> XøI RKYs

eQI¦ ehIyniyayfa : ebIeyIgerobvtßúenHeT,Igvij b¤ eFVICaKMrUmYyeTot tamlMnaMenH etIeyIgKYrEt

dak;GVIbnÞab;? bnÞab;BIsisS)anGnuvtþ rYcRKUGacniyayfa :cUrRkeT,kemIllMnaMKMrUTI 2. etImanrUbGVImun

eK? dUecñH etIeyIgKYrdak;rUbGVIenAkEnøgcenøaHTI1 ebIsinCaeyIgerobrUbTaMg3enHeT,Igvij? bnÞab;mk

segátemIllMnaMKMrUTI 3 etIeyIgKYrdak;elxGVII enAkEnøgcenøaHTI1ebIsinCaeyIgerobelxTaMg 3 enH eT,Ig

vij? RKUGacpþl;»kasdl;sisSeFVIkic©karenHeT,Igvij.

5

muxviC¢aKNitviTüa fñak;TI 3 {k :

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ cMnYn³ eRbIrUbiyvtßúú kñúgkarTijj lk;; nigGab;; edayeRbIRkdasR)ak;Rtwmm 10 000 erol..

kic©karvaytMél

1> kic©karenHRtUv)andak;[sisSeFVI bnÞab;BIsisS)aneronemeronGMBIrUbIyvtßú nigkareRbIR)as;RbmaNviFI

bUk nigdk Tak;TgeTAnwgrUbIyvtßú. kic©karenH sMrab;vaytMéleTAelIkic©karrbs;sisSCaRkum ¬kñúg1

RkummanbInak;¦. RKURtUvBinitüemIl rgVaytMéleTAelIlT§plsMerc)anrbs;smaCikRkumnImYy²

EdlRKUdak;[sisSeFVI bnÞab;BIkargarCaRkum etI)anRtwmRtUvEdrb¤eT?

2> sisSeFVIkarCaRkum EdlmancMnYn 3nak; kñúgmYyRkum.

3> sresrcMeNaTdak;elIkþarexon³

BUsuk)an[rgVan;CaTwkR)ak;cMnYn 8 000eroldl;k� ÜyRbus/RsIcMnYn3nak;. k� ÜyRbus/RsIcMnYn 3nak;

enaH)ansMercnaMKñaeTApSar edIm,ITijvtßú. BYkeKsMercfa RtUvTijvtßú1muxmñak;.

¬k¦ sresreQ�aHrbs;xøÜn rayeQ �aHvtßúEdlxøÜn)anTij nigtMél.

¬x¦ etIenAsl;R)ak;Gab;b:un �an?

4> Bnül;dl;sisSmYyRkum Edlman3nak; eday[eKedIrtYCabgb¥ÚnRbus b¤ bgb¥ÚnRsI.

5> sisSRtUvsMEdgqakenH CamYyRkummYyepSgeTot EdlmanbInak;dUcKña edayBYkeKsMEdgCaBUsuk

nigGñklk;enApSar.

6> muneBlsMEdg sisSRtUvbMeBjkic©karenAkñúgtaragKMrUxageRkay.

7> enAcugbBa©b;énkarsMEdg RkumsisSnImYy²RtUvpþl;cMelIytbeTAnwgkic©kar ¬k¦ nig ¬x¦xagelI

edaysegçb [sisSdéTeTotenAkñúgfñak;sþab;.

6

KMrUkic©kar xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKÚdak;[eFVIcMnYn 3

nak; ³

sisSRkum {k} namm

nigeKatþnam

muxTMnij tMél

nIta b‘íc 2 2000erol

cinþa sMeBot 1 3 000erol

sn esovePA 1 1 500erol

srubR)ak;cMNay 6 500 erol

8 000- 6 500 = 1 500 erol

dUecñHR)ak;EdlenAsl; 1 500 erol

sisSRkum {x} eyIg[suCata nigEsn 3 000 erolmñak; nigsuvNÑ 2 000 erol.

suvNÑTijesovePAGs; 1 500 erol dUecñH suvNÑsl;luyGab; 500 erol.

EsnTijkatabGs; 3 000 erol dUecñH EsnBuMsl;luyGab;eT,Iy.

suCataTijb‘icBIredIm Gs; 2 000 erol dUecñH nagsl;luyGab;1 000erol.

dUecñH luyGab;EdlenAsl; srub³ 500 + 0 + 1000= 1500 erol

sisSRkum {K} eyIg[ lI 2 000erol. lITijeckGs; 1 500erol enAsl; 500erol.

[sn 3 000erol. snTijnMGs; 3 000erol dUecñHsnK�anR)ak;enAsl;;eT.

[m:a 3 000erol. ma:TijePsC¢³Gs; 2 000erol enAsl; 100erol.

dUecñH R)ak;enAsl;TaMgGs; 500 + 0 + 100 = 600erol.

7

rgVaytMélxageRkamenH KWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisS

mñak;².


rma

sis

SS k

sis

SS x

sis

SS K

vicarc,as;las; 5 5 5 5

KNna)anRtwmRtUv 5 5 5 2

srub 10 10 10 7

mUlvicarN_ sisSRkum kk yl;c,as;GMBIcMeNaT eFVI)anelIsBIkMritsþg;dakm�viFIsikSa edayeFVIvicar)anc,as;las; nig

KNna)anRtwmRtUv.

siisSRkum xx )aneRbIviFIepSgBIsisSRkum kk b:uEnþ BYkeK)anQandl;kMritsþg;dakm�viFIsikSaEdr eday

eFVIvicar)anc,as;las; nig KNna)anRtwmRtUv.

sisSRkum KK eRbIviFIdUcKña eTAnwgRkum xx . kareFVIvicarrbs;eK)anc,as;las; EteFVI[mankMhusmYy kñúg

karKNna. BYkeK)anQandl;kMritsþg;dakm�viFIsikSa EtRKURtUvrMlwkBYkeK[eFVIkarRbugRby½tñ enA

eBleFVIkic©kar nig[]TahrN_bEnßmmYycMnYn Tak;TgeTAnwgkardkcMnYnKt;xÞg;Ban; ecjBIxÞg;Ban;.

8

muxviC¢aKNitviTüa fñak;TI 3 :x :

lT§plsikSa

FrNImaRtt ³ sg;RtIekaNedayeRbIbnÞat; EdkQan nig Ekg.

kic©karvaytMél

1> eKalbMNgd¾cMbgénkic©karenH KWpþl;skm �PaBrIkraymYy eday[RKUCaGñksegát faetIsisS

sÁal;rUbRtIekaNenAkñúgesovePAsisSEdrb¤eT? etIsisSGacKUrrUbRtIekaNedayxøÜnÉg)anEdr

b¤eT?

2> Cakarl¥Nas; ebIsinCasisSmñak;²manbnÞat; nigex �Aéd. ebIsinCasisSBuMmanbnÞat;RKb;KñaeT

BYkeKGaceRbIR)as;vtßúepSg² EdlRtg;dUcCabnÞat; edaykMNt;ykRtwmRbEvg 5 sm ¬]>ex�Aéd

EKmesovePA¦.

3> Bnül;sisSfa dMbUg sisSRtUvKUrkaerFMmYyenAkñúgesovePAlMhat; ¬TMhM 10sm�10sm¦.

RKURtUvTukeBlevla[sisSeFVIkic©karenH.

4> Bnül;sisSfa kic©kardMbUg RtUvKUrrUbRtIekaNmYy EdlmanRCugBIrRbEvg 5sm erogKña nigRCugTI3

ykRtwmRbEvgNamYy. sisSminRtUveFVIkic©karenHeT,Iy Tal;EtRKUR)ab;[eFVI. RKUGaceFVIbgðajGMBI

rebobdUcxageRkamdak;elIkþarexon³

� KUrbnÞat;mYyEdlmanRbEvg 5sm dak;Rtg;kEnøgNamYy

� KUrbnÞat; 5sm mYyeTot pÁúMCamYybnÞat;xagelI

enAcugbnÞat; begáIt)anCamuM

� KUsbnÞat;mYyeTotpÁúMCamYybnÞat;TaMgbI begáIt)anCaRtIekaN

5> Bnül;fa sisSRtUvKUrrUbRtIekaNenHdak;xagkñúgrUbkaer EdlBYkeKeTIb)anKUrdak;kñúgesovePAenaH.

9

6> bnÞab;mk Bnül;sisSfa kic©karTI2 RtUvKUrrUbRtIekaNCaeRcIn EdlmanRbEvgRCugb:un�ank¾)an dak;

enAkñúgrUbkaerEdleTIbnwg)anKUrkñúgesovePArYc Et rUbRtIekaNTaMgenaH eFVIy:agNakuM[KUrCab;Kña b¤

kat; ExVgKña. sisSRtUveRbIbnÞat; b¤vtßúepSg²CMnYsbnÞat; edIm,IKUrRtIekaNTaMgenH.

7> CacugeRkay RtUvR)ab;sisSfa enAsl;eBl1naTIeTot edIm,IbBa©b;kic©kar KWRtUvBinitüemIl nrNa

KUrRtIekaN)aneRcInCageK ¬bUkrYmTaMgRtIekaNEdlmanRbEvg 5sm pgEdr¦ enAkñúgrUbkaer

enaH. Bnül;sisSfa sisSnwg)an 4BinÞú ebIsinCaKUrRtIekaN EdlmanRCugRbEvg 5sm )an

RtwmRtUv 3BinÞú eTot ebIKUrRtIekaN)anRtwmRtUv nig 3BinÞúeTot ebIsinCakic©kareFVI)ans¥atl¥ ehIy

BuMmanRtIekaNNab:HKñaeT,Iy.

8> RKURtUvrMlwkeBlEdlenAsl; kñúgnaTIcugeRkay dUcCasl;30vinaTI eTot sl;15vinaTI eTotbnÞab;mk

R)ab;[sisSQb;. sisSTaMgGs;RtUvdak;bí‘ccuH ¬Qb;sresr¦ ehIyyk kic©kareTAdak;[RKU.


nak;³

sisS {k} sisS {x}

10


mñak;².


rma

sis

SS k

sis

SS x

sg;RtIekaNEdlmanRCug2 RbEvg

5sm )anRtwmRtUv4 4 4

cMnYnRtIekaNbEnßm 3 3 2

kic©kars¥at 3 3 1

srub 10 10 7

mUlvicarN_ sisSS k sMerc)anlT§plelIsBIkMritlT§plsikSa. sisSenHGacKUrrUbRtIekaN)anRtwmRtUv kic©kar

s¥at ehIyeFVI)anelOn.

sisS xx k¾GacQandl;kMritlT§plsikSaEdr. EteTaHbICa sisSenH)anKUrrUbRtIekaN)aneRcInCag

sisS kk k¾eday k¾rUbxøHminEmnCaRtIekaNeT eRBaHKUselOneBk eTIbeFVI[rUbRtIekaNxøHb:HKña

b¤kat;ExVgKña. eTaHCay:agNak¾ eyIgenAEtGacbBa¢ak;[eXIjfa sisSenHGacKUrrUbRtIekaN)anEdr.

11

muxviC¢aKNitviTüa fñak;TI 4 ________________________________________________________________

lT§plsikSa

rgVas;rgVal; ³ eRbI]bkrN_xñatÉkta nigeRCIserIsxñatsmRsbedIm,IkMNt; ³ RbEvgBI KILÚEm:t eTA

mIlIEm:t.

________________________________________________________________

kic©karvaytMél

1> Bnül;sisSfa eKalbMNgénkic©karenH KWeFVIkar)a:n;s�ancMgay[)ankan;EtCak;c,as; cMgay

BIpÞHeTAsala.

2> [sisSeRbIbnÞat; edIm,IKNnacMgayénCMhanmFüm KitCasg;TIEm:t Camunsin ¬sUmemIlKMrUskm�PaBeron nigbeRgon¦. sisSRtUvsresrcMgay KitCasg;TIEm:t ¬bgÁt;[eTACacMnYnKt;¦ enAkñúg

esovePAlMhat;.

3> [sisSrab;cMnYnCMhan EdleKedIrBIpÞHeTAsalaeron enAéf¶bnÞab;. [sisSsresrcMnYnenHenAkñúg

esovePAlMhat;.

4> RKUBnül;sisSfa kic©karenH sisSRtUvKNnarkcMgayBIpÞHeTAsalaeron edayeRbIcMnYnTaMgBIr

EdlrkeXIjxagelI KitCaKIT,ÚEm:t b¤CaEm:t.

KMrUkic©kar

xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKÚdak;[eFVIcMnYn 2

nak;³

sisS k

mYyCMhanrbs;´ RbEvg 50 sm. ´edIr)an 1300 CMhan.

dUcenH cMgayBIpÞHeTAsalaeron KW 503001 � sm = 65 000 sm.

65 000sm = 650m.

sisS x

mYyCMhanrbs;´ RbEvg 47 sm. ´edIr)an 987 CMhan.

dUcenH cMgayBIpÞHeTAsalaeron KW 47987� sm = 46 489 sm.

46 489 sm = 46 m.

12

rgVaytMél xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúeGaysisSmñak;².

lkçN³vinicä½y

GRt

aBinÞúú

sis

SS kk

sis

SS xx

kareRbI]bkrN_sMrab;vas; 2 2 2

viFIKNna 2 2 2

bMNinkñúgkarKNna)anRtwmRtUv 2 2 1

karbþÚrxñatBIsg;TIEm:t eTAEm:t 2 2 0

srub 88 88 55

mUlvicarN_ sisS kk sMerc)ankMritlT§plsikSa edaysisSenH)aneRbIbnÞat;)anRtwmRtUv edIm,IKNnaCMhan ehIy

)anbgðajBIkareFVIvicarc,as;las; karKNna nigkarbþÚrxñat)anRtwmRtUv.

sisS xx mankMhuskñúgkarKuNcMnYnénCMhan RbEvgmFüm. sisSenHeFVsRbEhs kñúgkarbþÚrxñatBIsg;TI

Em:teTAEm:t. eTaHCay:agNak¾eday kareFVIvicarrbs;sisSenH)anl¥Nas;. RKURtUvbegáIt]TahrN_mYy

sMrab;[sisSenHeFVIeT,Igvij ehIyrMlwk[sisSenHykcitþTukdak; minRtUv[mankMhusdEdleT. krNI

ebIsisS x eFVIkarKNna)anRtwmRtUv enaHsisSenH GacQandl;kMritlT§plsikSaehIy.

13

muxviC¢aKNitviTüa fñak;TI 5 ________________________________________________________________

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦sßiti³ sg;; nigbkRsayTinñn½yEdlbgðajenAkñúgtaragg RkabExSS Rkabssrr nigRkabpøitgay².

________________________________________________________________

kic©karvaytMél

1> kic©karenHvaytMéleTAelIsmtßPaBrbs;sisSkñúgkarsg;Rkabsrsrgay² tamTinñn½yEdl[.

kic©karenH RtUv)anvaytMéleTAelIRkabsrsrenAkñúgsþg;dakm�viFIsikSaEtmYycMNucb:ueNÑaH .

2> kic©karenHRtUv)andak;[sisSeFVI bnÞab;BIsisS)aneroncb;emeronTak;TgeTAnwgxøwmsarénRkab

srsr nigrebobsg;.

3> [sisSbMeBjkic©karxageRkam³

tamlT§plénEtsKNitviTüaf� I²enH sisSTTYl)anlT§pldUcxageRkam³

� sisS 20 nak; )anBinÞú 8/10






sg;RkabsrsrtamTinñn½yEdl[enH. sg;Rkab edayykG½kS x tagBinÞúrbs;sisS nig G½kS y

tagcMnYnsisS.

14


nak; ³

sisS k

sisS x

rgVaytMél xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúeGaysisSmñak;².

15

lkçN³vinicä½y

GRt

aBinÞúú

sis

SS kk

sis

SS xx

karbkRsayTinñn½yenAkñúgtarag 5 5 3

karerobcMTinñn½yenAkñúgtarag)anRtwmRtUv 5 5 2

srub 10 10 5

mUlvicarN_ sisS kk )anbegáItRkab)anl¥ nigbkRsayTinñn½y)anRtwmRtUv. sisS xx BuM)aneFVItamkarENnaM

edaysg;Rkab dak;bRBa©asG½kS x nig G½kS y.

RKURtUvrMlwksisS xx GMBIsar³sMxan; énkarGankarENnaM[)anm:t;ct; nigBinitüeT,IgvijeTAelIkargar

Edl)aneFVI faetIRtwmRtUv tamkarENnaMb¤eT. eTaHCay:agenHk¾eday sisS kk nigsisS xx sMerc)an

kMritsþg;dakm �viFIsikSaEdr.

16

muxviC¢aKNitviTüa fñak;TI 6 ¬k¦ ___________________________________________________________________________

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦cMnYn ³³ KNnatMélmFümm R)ak;cMeNjj xatt ehIysresrr nigepÞógpÞat;vikáybRt)anRtwmRtUv.. ___________________________________________________________________________

kic©karvaytMél

1> kic©karvaytMélenHRtUv)andak;[sisSbMeBj bnÞab;BIsisS)aneronGMBIGtßn½yénBakü {tMél}

{R)ak;cMeNj} nig {xat} nigbnÞab;BIsisS)anGnuvtþkñúgkarKNnatMél R)ak;cMeNj nigxat

rYcmk.

2> kic©karenHvaytMéleTAelIcMeNHdwgrbs;sisS GMBIBakü {tMél R)ak;cMeNj nigxat} nigeTAelI

smtßPaBénkarKNna)anRtwmRtUv. kic©karenHBuMvaytMéleTAelIsmtß PaBrbs;sisSkñúgkar

sresr nigkarepÞogpÞat;vikáyb½RteT,Iy.

3> RKUdak;cMeNaT[sisSeFVIdUcxageRkam³

suPaBeTIbEt)anTijtUbf�ImYyenApSar edIm,Ilk;mYk.

nagRtUvcMNayGs; 2 000erolkñúgmYyéf¶ sMrab;bg;PasIu.

enAedImExmInanag)anTijmYk 100 mkBIeragcRk EdlmantMél 700erol kñúgmYkmYy.

ebInaglk;mYkmYykñúgtMélmFüm 1 500erol etInagcMeNj b¤xatenAeBlnaglk;mYkGs;;enA

cugExmIna?

17

KMrUkic©kar xageRkamenHKWCa]TarN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karRdlRKÚdak;[eFVIcMnYn 2

nak;³

sisS k

dMbUg ´KNnatMélCamunsin ³

ExmIna man31 éf¶ dUecñH tMélPasIu KW 000231� erol = 62 000erol

ebImYkmYytMél 700 erol enaHmYk100 tMél 70 000erol

dUecñH tMélsrub 62 000erol + 70 000erol = 132 000erol

\T,ÚvenH ´KNnarkéfølk;mYkTaMgGs;³

kñúgmYkmYy1 lk;)an 1 500 erol enaHmYk 100lk;)an 150 000 erol

R)ak;cMeNj b¤xat = éfølk; – éføedIm

dUecñH R)ak;cMeNj b¤xat = 150 000 erol –132 000 erol = 18 000 erol

dUecñH R)ak;cMeNjsMrab;ExmIna KW 18 000 erol .

sisS x

R)ak;cMeNj KWCaR)ak;Edl´lk;)an dkCamYynwgR)ak;Edl´cMNay.

dUcenH R)ak;cMeNj 1500 – 700

R)ak;cMeNjsrub 900.

rgVaytMél xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúeGaysisS

mñak;².

lkçN³vinicä½y

Gtib

rmaa

sis

Skk

sis

Sxx

vicar nigviFIedaHRsaycMeNaT 5 5 2

karKNna)anRtwmRtUv 5 5 1

srub 10 10 3

18

mUlvicarN_

sisS kk sMerc)antamkMritsþg;dakm�viFIsikSa eday)anbgðajBIbMNinvicar nigKNna)anRtwmRtUv.

sisS xx BuMsMerc)antamkMritsþg;dakm �viFIsikSaeT. sisSenHyl;BIGtßn½yénBakü EtBuMGaceFVIcMeNaT

)an ehIyeFVIvicaredIm,IedaHRsaycMeNaT)aneT. sisSenHeFVI[mankMhusmYy enAkñúgkarKNna. RKU

RtUvelIkTwkcitþdl;sisSenH eRBaHsisSenH)anyl;c,as;GMBIGtßn½yénBakü. RKURtUvCYyBinitüemIlkar

KNnarbs;sisS. RKURtUvniyayfa :cUreyIgeTABinitüemIlcMeNaTvij :. ebIeyIgcMeNj)an 800erol

kñúgmYkmYy etIeyIgcMeNj)anb:un�an ebIsinCaeyIglk;Gs;mYk100? cUrb¥ÚncMlgdak;kñúgesovePA.

\T,ÚvenH cUrb¥ÚnGancMeNaTeT,Igvij ehIyR)ab;RKU BIGVIxøHEdlb¥Ún)ancMNay. etIcMNayGs;b:un �an?

cUrb¥ÚncMlgdak;kñúgesovePA. etIenAsl;b:un�an ebIsinCaeyIgdkéføedImecjBIR)ak; éfølk;srubenaH? l¥

Nas; b¥ÚneqøIy)anRtwmRtUvehIy !

19

muxviC¢a KNitviTüa fñak;TI 6 ¬x¦

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ rgVas;rgVal;; ³ KNnary³eBll edaydwgel,ÓnmFümm nigcMgaycrr ..

kic©karvaytMél

1> kic©karenHRtUv)andak;[sisSeFVI bnÞab;BIsisS)aneroncb;emeronTak;TgeTAnwgrebobKNnary³

eBlcr edaydwgel,ÓnmFüm nigcMgaycr.

2> [sisSeFVIcMeNaTxageRkam. ENnaMR)ab;sisSfakareFVIcMeNaTenHsisScaM)ac;RtUveFVIkarbk

Rsay.

suxa)aneFVIdMeNIrtamrfynþBIPñMeBjeTAkan;extþesomrab cMgay 306Km edayel,ÓnmFüm

45Km/m:. Kat;ecjdMeNIrBIPñMeBjenAema:g10RBwk . ehIyenAtampøÚvKat;Qb;sMrakBisar)ayéf¶Rtg;

Gs;ry³eBl !ema:g. etIsuxaeTAdl;esomrabenAema:gb:unñan?

KMrUkic©kar

xageRkamKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn2nak;³

sisS {k}

eRbIrUbmnþ ry³eBl= cMgaycr ÷ el,ÓnmFüm 306 ÷ 45 = 6.8

dUcenH ry³eBleFVIdMeNIr KW 6.8em:ag

0>1 m: = 6 naTI

0>8 m: = 8 x 6 = 48 naTI

naM[ 6>8 m: = 6 m: 48 naTI

ry³eBlCiHrfynþ KW 6m: 48 naTI. edayQb;Gs;mYyem:ag edIm,IRss;RsUbGaharéf¶Rtg;

ry³eBleFVIdMeNIrsrubKW ³ 6 em:ag 48 naTI + 1 = 7em:ag 48naTI. dUecñHsuxaeTAdl;esomrab

enAem:ag10RBwk + 7m:48naTI = 17em:ag48naTI RtUvnigem:ag 6nig 48naTIl¶ac.

20

sisS {x} ry³eBl= cMgaycr x el,Onénrfynþ KW 306 x 45

306

x 45

13770

dUecñH ry³eBlsrub KW 13m: 77 naTI

rgVaytMélxageRkamenH KWCalkçN³vinicä½yrgVaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².


rma

sis

SS k

sis

SS x

vicar nigviFIedaHRsay cMeNaT RtwmRtUv 5 5 0

cMelIyRtwmRtUv 5 4 2

srub 10 9 2

mUlvicarN_ eTaHCa sisS kk BuM)anpþl;cMelIycugeRkay)anRtwmRtUvk¾eday k¾sisSenHGacQandl;kMritsþg;dakm �viFIsikSaEdr. kareFVIvicarrbs;sisSmanlkçN³c,as;las; ehIykarKNnak¾RtwmRtUvEdr. sisSenH

eFVI[mankMhusmYy KWbþÚr 24 em:ag eTA 12 em:ag. sisSenHenAEtGacbgðajTaMgcMeNHdwgénkar

KNnary³eBlcr nigbMNinKNnay:agl¥\tex©aH.

sisS xx BuM)ansMercdl;kMritsþg;dakm�viFIsikSaeT. RKURtUvbgðajdl;sisSenHfa kic©karEdlsisSenHeFVI

KW)anl¥Nas;CaBiess kareFVIviFIKuN.

RKURtUvrMlwksisSenH GMBIkareRbIR)as;rUbmnþ edIm,IKNnael,Ón cMgay nigry³eBl. RKURtUv[cMeNaT

gay²mYycMnYnedIm,I[sisSenHeFVIedayeRbIRtIekaN. rYcmk RKURtUvCYysisSenH b¤[sisSNamñak;

CYyrMlwkGMBIrebobbþÚrxñatBInaTIeTAem:ag.

RtIekaNenHeFVI[sisSgayRsYlkñúgkarcgcaMrUbmnþ

cMgaycr

el,ÓnmFüm ry³eBlcr

21

muxviC¢a KNitviTüa fñak;TI 7

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ FrNImaRt ³ edaHRsaycMeNaT KNnamuMM edayeRbIlkçN³muMrbs;RtIekaNN nigRbelT,ÚRkam..

kic©karvaytMél

1> kic©karvaytMélenHRtUv)andak;[sisSbMeBj bnÞab;BIsisS)aneronGMBIlkçN³muMénRtIekaNrYc.

kic©karenHepþatEteTAelIlkçN³muMénRtIekaNb:ueNÑaH minEmneTAelIRbelT,ÚRkameT.

2> Bnül;sisSfa PaKeRcInenAkñúgEts eKtMrUv[edaHRsaycMeNaT b¤ eqøIysMNYr. EtcMeBaHkic©karenH

vij RtUv)an[sisSbegáItcMeNaT nigsYrsMNYr edIm,I[sisSdéTeTot edaHRsay.

3> kic©karenH KWsisSRtUvKiteTAdl;sßanPaBRbcaMéf¶NamYy EdlBak;B½n§eTAnwgmuM RtIekaN nigbegáIt

cMeNaTsMrab;[sisSepSgeTot yklkçN³muMénRtIekaNmkedaHRsay. [sisSelIk]TahrN_

BIsßanPaBRbcaMéf¶NamYy EdlTak;TgeTAnwgclnaénvtßúEdlGacbegáIt)anCaRtIekaN ¬dUcCa

El,g CaBiess )al;Tat; b¤ b‘Íy:a¦.

4> bnÞab;mk sisSRtUvtak;EtgcMeNaT nigbegáItsMNYrmYycMnYn sMrab;[ sisSdéTedaHRsay.

5> RKUGac[sisSdUrcMeNaTKñaeTAvijeTAmk edIm,IBinitüemIlfaetIBYkeKGacedaHRsaycMeNaTrbs;

sisSepSgeTot)anEdrb¤eT. rgVaytMélelIkic©karenH KWEp¥keTAelIfaetIsisSGacbgðajcMeNH dwg

kñúgkarbegáItcMeNaT nigsMNYr)anl¥RtwmRtUvTak;TgeTAnwglkçN³muMénRtIekaN Edrb¤eT.

KMrUkic©kar


sisS {k}

kILakrbukb‘Íy:amñak;)anbBa¢Ún

kUn)al;BITItaMg A[eTAb:HkUn)al;

BN’ex �AenATItaMg B edIm,I[kUn)al; TItaMg

B remolcUlrn§ enATItaMg C . edaydwg

famMuEdlpÁúMrvagknøHbnÞat; � �AB nig

22

AB

C

� �BC manrgVas;es� I nwg �130 ehIymMu EdlpúMÁrvagknøHbnÞat; � �AB nig � �AC manrgVas;es�I nwg �

21 .

cUrKNnamuMEdlbegáIteT,Igeday � �AC nig � �BC .

ebI cmAB 36� eRbIra:b:T½r nigbnÞat; edIm,Isg;RtIekaN xagelI edayeRbImaRtdæan cmmm 11 � .

cUrvas;tamrUbxagelI edIm,IrkRbEvg AC nig BC.

sisS {x} kILakr mñak;)anTat;bBa¢Ún)al;BITItaMg A

eTA[kILakrmñak;eTotenATItaMg B.

ehIykILakrTItaMg B enaH)anTat;)al;

bBa©úÚlTIRtg; TItaMg C .

eKdwgfamMu �� 80ˆCBA nig �� 75ˆACB

k> cUrKNna CAB ˆ .

x> ebIcMgayEdlkIT,akrenATItaMg A

bBa¢Ún)al;eTAkIT,akrTItaMg B manRbEvg 10 Em:t cUreRbIbnÞat; r:ab:T½r nigmaRtdæan mcm 11 �

edIm,IKUrRtIekaN EdlbegáIteT,Igeday cMNuc A , B nig C .



rma

sis

SS k

sis

SS x

begáItcMeNaT edaymankaryl;dwgc,as;

GMBIlkçN³muMénRtIekaN. 5 5 5

bMrab;nigsMNYr)anRtwmRtUv 5 5 5

srub 10 10 10

23

mUlvicarN_ TaMgsisS kk nigsisS xx )anbegáItcMeNaTl¥RtwmRtUv edaybgðajBIcMeNHdwgTak;TgeTAnwgkareRbIR)as;

lkçN³muMénRtIekaN edIm,IrkmuMEdlBuMsÁal;. sisSTaMgBIrenH)ansMercdl;kMritsþg;dakm�viFIsikSa.

sisSTaMgBIrenHcaM)ac;RtUvbgðajkaryl;dwgmYykMritepSgeTot EdlTak;TgeTAnwglkçN³muMénRbelT,Ú

Rkam edIm,I[GacQandl;kMritsþg;dakm�viFIsikSa)aneBjelj.

24

muxviC¢aKNitviTüa fñak;TI 8 ___________________________________________________________________________

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦sißtii ³ rkmFümm emdüann m:Utt BITinñn½yEdl[[ rYmTaMgtaragbMENgEckeRbkg;; ehIyEjk[[

eXIjBIPaBxusKñaa rvagmFümm emdüann nigm:Ut.. __________________________________________________________________________

kic©karvaytMél

1> kic©karenH RtUv)anerobcMeT,Ig sMrab;dak;[sisSeFVIEtmYyEpñkxagedIménlT§plsikSa xagelI.

2> kic©karenH RtUv)anerobcMeT,IgsMrab;dak;[sisSeFVI bnÞab;BIsisS)aneronGMBIGtßn½yén Bakü mFümm

emdüann m:Ut nigBYkeK)anbMeBjlMnaMskm�PaBxageRkam enHrYc³

k> [sisSeFVIkarCaRkumEdlman 5 nak;

x> sisSeRbIbnÞat; Em:t b¤ rgVas;epSg²EdlminEmn]bkrN_sþþg;da ¬RbEvgéd eQI¦ edIm,IRbmUl

Tinñn½y Tak;TgeTAnwgkMBs;sisSnImYy² enAkñúgRkum.

K> [sisSeFVIkarCaRkum edIm,IKNnamFüm m:Ut emdüan BITinñn½yEdl[.

X> sisSeT,Igbgðajkic©karenAxagmuxfñak; edayBnül;GMBIGtßn½yénBakünImYy² nigGMBIrebob

KNnaedIm,IrkcMelIy.

3> bnÞab;mk dak;cMeNaTxageRkam[sisSedaHRsayerogxøÜn.

mþayrbs;ssuFaa )anlk;RCUkcMnYn5k,almanTMgn;dUcxageRkam ³ 77.5 kg ; 98 kg ; 77 kg ; 86 kg ; 93 kg

Bnül;GMBIGtßn½yénBakü mFüm emdüan nigm:Ut rYcrkmFüm emdüan nigm:Ut BITinñn½yenH.

KMrUkic©kar

xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn 3nak;

sisS {k}

mFüm³ mFümmann½ydUcCamFümPaKEdr. eyIgGacKNnarkmFüm)an edayRKan;EtbUkcMnYn

TaMgGs;ehIyEcknwgcMnYnénvtßú³

25

77>5 + 98 + 77+ 86 +93 = 431>5

mFüm = kg3.865

5.431�

dUcenHTMgn;mFüménRCUkKW kg3.86 .

emdüann ³ emdüan KWCacMNucéntMélkNaþl.

´GacKNnarkemdüan edayRKan;EterobcMnYntamlMdab;BITabeTAx<s; bnÞab;mkqUttMélEdlx<s;Cag

nig tMélEdlTabCagecal rhUtdl;tMélkNaþl³ 77 77.5 86 93 96

dUcenHemdüanKW ³ 86

m:Ut³³ m:UtKWCatMélNaEdldUcKña. enAkñúgenH K�antMélNadUcKñaenaHeT,Iy. dUecñHTinñn½yEdlRbmUl

pþúM)anK �anm:UteT.

sisS {x}

mFüm³ mFümKWmann½ydUcCamFüPaKEdr. eyIgGacbUkcMnYnelxTaMgGs; ehIyEcknwgcMnYnénvtßú³

mFüm= 77>5 + 98 + 77+ 86 +93 = 401>5

mFüm = kg3.805

5.401�

dUcenHTMgn;mFüménRCUkKW 83kg

emdüann ³ emdüan KWCacMnYnelxkNaþl.

eyIgGacrkemdüan edayqUttMélEdlx<s;Cag nigtMélEdlTabCagecal ³

77 77>5 86 93 96

dUcenHemdüanKW 86 .

m:Ut³³ m:UtKWCatMélNaeRcInCageK. 77 manBIrdg. elxepSgBIenHmanEtmYydg.

dUecñH Tinñ½yEdlRbmUl pþúM)anm:Ut 77.

sisS {K} Tinñ½yEdlRbmUlpþúM)anm:Ut 77.

26

mFüm = 77 + 77>5 + 86 + 93 + 98 = 401

emdüan = 7.812

5.163

2

865.77��

� .



rma

sis

SS k

sis

SS x

sis

SS K

yl;GMBIBakü nigbBaØtiþ 3 3 2 1

bMNinkñúgkarKNna 2 2 1 0

cMelIyRtwmRtUv nigkic©kars¥at 3 3 1 0

srub 8 8 4 1

mUlvicarN_ sisS kk yl;c,as;GMBIniymn½yénBakü nigGacGnuvtþcMeNHdwgrbs;xøÜn enAkñúgkaredaHRsaycMeNaT.

sisS kk )ansMercelIskMritsþg;dakm�viFIsikSa.

sisS xx yl;c,as;Biniymn½yénBaküb:uEnþmankMhuskñúgkarKNna nigeRCIserIs RKURtUvCYyBnül;ENnaM

GMBIBaküm:UteT,Igvijfa m:UtKWCatMélEdlekIteT,Igjwkjab;CageK ehIyvamantMéldUcKña BuMEmnman

tMélRbhak;RbEhlKñaenaHeT. RKURtUvCYyelIkTwkcitþ[sisSenH BinitüepÞogpÞat;emIlcMelIyeT,Igvij

ral;elIkEdl)aneFVI. RKURtUvdak;kic©karNaEdlRsedogKña [sisSeFVI ebIsinCasisSenH GaceqøIy

cMelIyenH)anRtwmRtUv enaHbBa¢ak;fa sisSenHsMerclT§plsþg;dakm�viFIsikSaehIy.

sisS KK BuMsMerc)andl;kMritsþg;dakm�viFIsikSaeT,Iy. sisSenHBuMyl;GMBIBakü nigbBaØtiþ nigmankMhus

kñúgkareRbIRbmaNviFITaMgbYn. RKURtUvcMNayeBledIm,ICYyBnül;BIbBaØtiþenHdl;sisS RKUGaceRbIrUbPaB

edIm,IbBa¢ak;BIGtßn½yénBaküTaMgenaH ]TahrN_ KUrrUb)al;tUc²EdlmanTMhMxusKña edaydak;tMerobKña

mYyCYr ehIyBnül;GMBIn½yénBaküm:Ut emdüan nigmeFüm tamrUbPaBenaH. RKUKYrEtCYysisS b¤[

sisSBUEkNamñak;CYYyrMlwkBIkarbUkcMnYntamlMdab;. RbkarenH KWCYy[sisSecHbUktamlMdab;)anRtwm

RtUv.

27

muxviC¢aKNitviTüa fñak;TI 9 ¬k¦

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ BICKNit³ edaHRsayRbB½n§smIkardWeRkTII 1manBIrGBaØat..

kic©karvaytMél

1> kic©karenHRtUv)aneFVIeT,IgbnÞab;BIsisS)aneronsMrYl nigBnøatkenSamBICKNitgay²rYcehIy.

2> sresrcMeNaTdUcxaeRkam³

ebIpløaTijsURtRbEvg 3Em:t nigRkNat;cMnYn 2 kI tMél 44 000 erol.

suPaTijsURt 5 Em:t nig RkNat; 3 kI tMél 72 000.

etIsURtmYyEm:téføb:un �annigRkNat;mYykIéføb:un �an?

3> sYrsisS[eqøIysMNYr edayBnül;tamdMNak;kardUcxageRkam.

KMrUkic©kar


sisS {k}

tag x tMélsURtkñúg 1 Em:t KitCaerol nigtag y CaRkNat;kñúgmYykIKitCaerol eyIg)ansmIkar ³

pløaTijsURt m3 nig RkNat; 2 kI yx 23 � eyIg)an 0004423 �� yx

suPaTijsURt m5 nigRkNat; 3kI yx 35 � eyIg)an 0007235 �� yx

edaHRsay � �iiyx

iyx

0007235

0004423

��

��

KuN �i nig 3 ehIy �ii nig 2

� �ivyx

iiiyx

000144610

00013269

��

��

yk �iv – �iii naM[ 00012�x .

28

CMnYs x kñúg � �i eyIg)an 0044200036 �� y

00036000442 �y

0004�y

epÞogpÞat;kñúg � �ii eyIg)an 00072000120006000043000125 �� RtwmRtUv

cMelIy³ sURttMél 12 000 erol kñúg 1m nigRkNat; 1kI tMél 4 000 erol.

sisS {x}

tag x tMélsURt 1Em:tKitCaerol nigtag y CaRkNat;kñúgmYykIKitCaerol eyIg)ansmIkar ³

pløaTijsURt m3 nig RkNat; 2 kI yx 23 � eyIg)an 0004423 �� yx

suPaTijsURt m5 nigRkNat; 3kI yx 35 � eyIg)an 0007235 �� yx

edaHRsaysmIkar � �� iiyx

iyx

0007235

0004423

��

��

rktMél x kñúgsmIkar � �i eTACMnYskñúgsmIkar � �ii eyIg)an

3

200044 yx �

� � � �iiiyy000723

3

2000445��

KuN � �iii nwg 3 eyIg)an � �ivyy 000216910000220 ��

y�0004

CMnYskñúgsmIkar � �i eyIg)an

000123

00036

3

0004200044��

��x .

epÞogpÞat;kñúg � �ii eyIg)an 00072000120006000043000125 �� RtwmRtUv

cMelIy³ sURttMél 12 000erol kñúg 1m nigRkNat; 1kI tMél 4 000 erol

sisS {K}

sURttageday x KittMélCaerol nigtagkMNat;eday y KittMélCaerol

pløaTijsURt 3m nig kMNat; 2kI yx 23 � eyIg)an 0004423 �� yx

suPaTijsURt 5m nigkMNat; 3kI yx 35 � eyIg)an 0007235 �� yx

29

edaHRsaysmIkar � �iiyx

iyx

0007235

0004423

��

��

cMelIy³ sURttMél 12000erol kñúg 1m nigRkNat; 1kI tMél 4 000 erol


mñak;².


rma

sis

SS k

sis

SS x

sis

SS K

vicarKNitviTüa nigsmIkar)anRtwmRtUv 5 5 5 2

bMNinedaHRsaysmIkar)anRtwmRtUv 5 5 5 0

cMelIyRtwmRtUv nigkic©kars¥at 2 2 2 2

srub 12 12 12 4

mUlvicarN_

eTaHbIsisS kk )aneRbIviFIbUkbM)at; edIm,IedaHRsaysmIkar nig sisS xx )aneRbIviFICMnYsedIm,IedaHRsay

smIkark¾edayBYkeKTaMgBIr)anrkeXIjcMelIyRtwmRtUvdUcKña . enHbBa¢ak;[eXIjfa BYkeKeFVIkic©kar

sMerc)anelIsBIkMritsþg;dakm �viFIsikSa.

sisS KK eFVI)ancMelIyRtwmRtUvk¾b:uEnþ sisSenHBuM)anQandl;kMritsþg;dakm�viFIsikSaeT,Iy. smIkar

sresr)anRtwmRtUv cMelIyk¾)anRtwmRtUvEdr EtkaredaHRsayBuM)aneFVItamsmIkarBIrGBaØat. sisSenH

GaccMlgcMelIyBIeKk¾fa)an . dUecñH RKURtUvrMlwksisSfa kareFVIkic©kar sMxan;KWRtUveFVItamkarENnaM.

RKURtUvdak;kic©karNamYyeTot EdlRsedogenH [sisSeFVI ehIy[sisSbgðajBIkareFVIvicar nigkaredaH

Rsay.

30

muxviC¢aKNitviTüa fñak;TI 9 ¬x¦

lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦³

BICKNit³³ edaHRsaysmIkardWeRkTII 1manmYyGBaØt..

kic©karvaytMél

1> kic©karenHmanlkçN³s� úKs�ajCagkic©karenAfñak;TI 9 Epñk kk. ebIsinCasisSGacbMeBjkic©kar

fñak;TI 9 Epñk kk )ansisSenaH)ansMercdl;kMritsþg;dakm�viFIsikSa niglT§plsikSaehIy. kic©kar

xageRkamenH sMrab;[EtsisSBUEkeFVI ehIyRKURtUvKitrkskm�PaBbEnßm edIm,I[sisSGacTTYl

)annUvGtßRbeyaCn_tamry³skm�PaBTaMgenaH.

2> RKUdak;cMeNaTdUcxageRkam³

m:UtUumYYyeRKOgecjdMeNIrBIPPñMeBjj eTATIrYmextþttaEkvv enAem:ag mnh308 RBwkedayel,Ón

mFüm hkm40 . knøHema:geRkaymanrfynþRkugmYyecjdMeNIrBIPñMeBjeTATIrYmextþtaEkv

edayel,Ón hkm60 .

k> sresrsmIkartagcMgaypøÚvBIPñMeBjeTAkEnøgEdlyanynþTaMgBIrCYbKña.

x> etIrfynþRkugtamTan;m:UtUuenAema:gb:un�an ?

K> cUrrkcMgayBIPñMeBjeTAkEnøgCYbKña.

3> sYrsisS[eqøIysMNYr edayBnül;tamdMNak;kardUcxageRkam.

KMrUkic©kar

xageRkamKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn 2nak;³

sisS {k}

k> sresrmIkartagcMgaypøÚvBIPñMeBjeTAkEnøgEdlyanynþTaMgBIrCYbKña. tag t ¬KitCaema:g ¦

ry³eBlm:UtUeFVI dMeNIr BIPñMeBjeTAkEnøgCYbKña. ehIy ¬t -1/2¦ CaeBlEdlrfynþRkug eFVIdMeNIr

BIPñMeBjeTAdl;kEnøgCYbKña.

31

xageRkamenH KWCataragmYy tagtMélxusKñaénel,On ry³eBl cMgaycrrbs;m:UtUnigrfynþRkug.

yanynþþ el,ÓnmFümm ry³eBll cMgayy

m:UtU 40km/h t(h) 40t km

rfynþRkug 60km/h (t -1/2 )h 60(t-1/2)km

tamtaragxagelIsmIkarcMgaypøÚvBIPñMeBjeTAkEnøgEdlyanynþTaMgBIrCYbKña ³ 40t = 60(t -1/2)

x> ´GaceRbIrUbmnþenH edIm,Irkry³eBlEdlyanynþTaMgBIrCYbKña ³ 40t = 60(t-1/2) 40t = 60t - 30 30 = 60t - 40t 30 = 20t t= 30/20 t = 3/2h = 1h30mn8h30mn + 1h 30mn = 9h60mn =10h

dUcenHyanynþTaMgBIrCYbKñaenAema:g 10 RBwk

K> ´GaceRbItarag edIm,IrkcMgayBIPñMeBjeTAkEnøgCYbKña³ d= vt (v = 40km/h ; t =3/2h )

dUcenH d =40 ×3/2= 60km

dUecñH d = 60km

sisS {x} k> ry³eBlm:UtUeFVIdMeNIrBIPñMeBjeTAkEnøgCYbKña 8h30h + 30m =9h

smIkartagcMgayBIPñMeBjeTAkEnøgCYbKña 40x = 60 x 9x = 540/40 x = 54/4x = 13.5h

x> ry³eBleFVIdMeNIrBIPñMeBjeTAkEnøgyanynþTaMgBIrCYbKña 13.5h + 30min = 15h30m

32

K> rUbmnþcMgay d = vt

dUcenH d = 60 x13.5

dUecñH cMgayBIPñMeBjeTAdl;kEnøgCYbKña KW 810km



rma

sis

SS k

sis

SS x

vicarKNitviTüa nigsmIkar)an RtwmRtUv 6 6 1

bMNinedaHRsaysmIkar 4 4 4

cMelIyRtwmRtUv nigkic©kars¥at 2 2 0

srub 12 12 5

mUlvicarN_ sisS kk )aneRbIrUbmnþ nigGnuvtþ)anRtwmRtUv. sisSenHeFVIkic©karsMerc)andl;kMritsþg;dakm�viFIsikSa.

sisS xx GaceRbIrUbmnþ nigGnuvtþRbmaNviFITaMgbYn EtsisSenHBuMyl;BIrebobedaHRsaycMeNaTtam

rUbmnþeT,Iy. RKURtUvCYydl;sisSenH kñúgkarKUrtagcMeNaT edIm,I[sisSenHyl;BIcMeNaTenH. RKURtUv

R)ab;sisSfa sisSRtUvEterobcMBt’mandak;enAkñúgtaragdUcsisS kk Edr. BIeRBaH sisSenHeFVIkic©karBuM

)anl¥ BuMmann½yfa sisSenHBuMGacsMerc)andl;kMritsþg;dakm�viFIsikSaeT,Iy. eRBaHenHKWCakic©kar

EdlBi)ak s� úKs�ajCag kic©karfñak;TI9 Epñk kk eTAeTot. ebIsinCasisSenHGacbMeBjkic©karfñak;TI9

Epñk kk enaHbBa¢ak;[eXIjfa sisSGacsMerc)andl;kMritsþg;dakm�viFIsikSa)anehIy.

33

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