Meningkatkan Kemampuan Siswa Materi Aritmatika Sosial Dengan Menggunakan Simulasi Transaksi Jual Beli Bagi Siswa Kelas II

EIKHKL@AT@AK @IEAEZYAK SHS\A EATIRH ARHTEATH@A SNSHAG DIKLAK EIKLLYKA@AK SHEYGASH TRAKSA@SH MYAG BIGH BALH SHS\A @IGAS HH SDK SAEBHRNTN :4 SIEARAKL TAFYK 2::4 – 2::9

S`rhzsh Dhamy`ak dagae Rakl`a Zikxigisahak Stydh Strata 1 ykty` Eiezirngif Ligar Sarmaka Zikdhdh`ak

Ngif = Kaea

= Farx Zaklisth

KHE

= 41: 28: 3: ?2

Zrnlrae Stydh = Zikdhdh`ak Eatieath`a Myrysak

= Eatieath`a

OA@YGTAS EATIEATH@A DAK HGEY ZIKLITAFYAK AGAE YKH_IRSHTAS KILIRH SIEARAKL 2::9

ABSTRA@

Farx Zaklisth' 2::9' ‗ Eikhkl`at`ak `ieaezyak shs|a eatirh arhteath`a snshag diklak eikllyka`ak sheygash traksa`sh myag bigh balh shs|a `igas HH SDK Saebhrntn @icaeatak Tiebagakl Siearakl tafyk zigamarak 2::4 – 2::9 ― Dagae `ilhatak bigamar eiklamar `fysyskxa zigamarak eatieath`a sinrakl lyry dhtyktyt ykty` eikliebakl`ak `ica`azak sicara zrnoishnkag dagae eiklignga `igas Sagaf saty `ica`azak zrnoishnkag xakl zirgy dh`iebakl`ak adagaf `ica`azak dagae eikllyka`ak eitndi ziebigamarak xakl tizat dak ioi`tho Tyktytak balh lyry dagae eikllyka`ak agat zirala saklat dhzirgy`ak zada zrnsis bigamar eiklamar' `fysyskxa zigamarak eatieath`a Zikighthak hkh eiklyzaxa`ak zikhkl`atak `ieaezyak' `ia`thoak' `itraezhgak shs|a dagae eikxigisah`ak snag arhteath`a snshag dak `hkirma lyry dagae `ilhatak bigamar eiklamar diklak eikllyka`ak traksa`sh myag bigh zada shs|a `igas HH SDK Saebhrntn :4 @icaeatak Tiebagakl Siearakl Ykty` eikcazah tymyak tirsibyt dhga`y`ak zikighthak thkda`ak `igas xakl dhga`saka`ak dagae 2 sh`gys xakl eighzyth zirikcakaak' ziga`sakaak' ziklaeatak' dak riogi`sh diklak eikxamh`ak zn`n` bafasak yakl eigagyh sheygash traksa`sh myag bigh' eiebirh`ak tis fashg bigamar dak eiklaeath zrnsis bigamar eiklamar xakl dhga`y`ak lyry diklak eighbat`ak nbsirvir xahty tieak sima|at Eitndi ziklyezygak data xakl dhlyka`ak adagaf tis dak nbsirvash Tis dhlyka`ak ykty` eiklitafyh fashg bigamar shs|a' sidakl`ak nbsirvash ykty`  eiklaeath `ia`thoak shs|a' `itraezhgak shs|a dagae eiklfhtykl' fashg bigamar shs|a dak `hkirma lyry dagae `ilhatak bigamar eiklamar Sybmi` zikighthak birmyegaf 32 shs|a xakl tirdhrh darh 1< ga`h – ga`h dak 19 ziriezyak Eitndi ziebigamarak sheygash traksa`sh myag bigh eiryza`ak sagaf saty eitndi ziebigamarak' dheaka dagae eitndi hkh shs|a eieirala`ak sisyaty dagae bikty` thryak xakl ehrhz diklak `iadaak sisykllyfkxa Fashg zikighthak hkh dh`ata`ak birfashg azabhga `ia`thoak shs|a eikcazah ≩ <9) dagae eiklfhtykl <9)' khgah rata – rata fashg bigamar shs|a ≩ <': dak fashg `hkirma lyry dagae `ilhatak bigamar eiklamar ≩ <': Fashg zikighthak hkh adagaf sibalah birh`yt = Zieakoaatak sheygash myag bigh eaezy eikhkl`at`ak fashg bigamar dagae eikxigisah`ak snag arhteath`a snshag' eikhkl`at`ak `ia`thoak' `itraezhgak shs|a dagae eiklfhtykl dak `hkirma lyry dagae `ilhatak bigamar eiklamar Fag tirsibyt dhhdikthoh`ash`ak darh zikcazahak tarlit xa`kh `ia`thoak shs|a 63'4)' `itraezhgak dagae eiklfhtykl <3' 4) dak khgah rata % rata fashg bigamar arhteath`a snshag 6'6 dak khgah rata – rata `hkirma lyry dagae `ilhatak bigamar eiklamar <'<9 Zirsitymyak xakl dazat dhxa`hkh sibalah sarak = a( Zikllykaaak sheygash traksa`sh myag bigh dagae ziebigamarak eatieath`a zirgy dhthkda` gakmyth sibalah stratilh ziebigamarak agtirkathoi balh lyry si`ngaf dasar' b( Ykty` tnzh` atay eatirh tirtikty lyry dazat eikllyka`ak agat zirala dagae ziebigamarak eitieath`a alar shs|a gibhf eieafaeh eatirh zigamarak' c( Lyry farys `riatho 

dagae ziebyatak agat zirala xakl a`ak dhsamh`ak' yzaxa`ak bafak xakl dhza`ah sidirfaka dak rigathoi eyraf farlakxa

ZIKLISAFAK

S`rhzsh Eikhkl`at`ak @ieaezyak Shs|a Arhteath`a Snshag Diklak Eikllyka`ak Sheygash Traksa`sh Myag Bigh Balh Shs|a @igas HH SDK Saebhrntn :4 @icaeatak Tiebagakl Siearakl+

Tigaf dhzirtafak`ak dh fadazak shdakl Zakhtha Ymhak S`rhzsh Oa`ygtas Eatieath`a dak Hgey Ziklitafyak Ziklitafyak Agae Ykhvirshtas Kilirh Siearakl zada=

Farh

= Sigasa

Takllag

= 2 Alystys 2::9

Zakhtha Ymhak @itya'

Si`ritarhs'

Drs @aseadh Heae S' E S Khz 13:<61:11

Drs Syzrhxnkn' E Sh Khz 13:619349

Ziebhebhkl Ytaea'

@itya Ziklymh'

Dra Rafaxy B_' E Sh Khz 131<6862<

Dra Sykareh' E Sh Khz 131
Ziebhebhkl Zikdaezhkl'

Akllnta Ziklymh'

Drs \ardnkn' E Sh Khz 1319?68:9

Drs \ardnkn' E Sh Khz 1319?68:9

Akllnta Ziklymh'

Dra Rafaxy B_' E Sh Khz 131<6862<

ENTTN DAK ZIRSIEBAFAK

ENTTN =

%

Ga`y`akgaf sisyaty xakl birbida' saat sisyaty xakl akda ga`y`ak thda`  zirkaf birybaf

%

Bakxa` nrakl – nrakl eikcazah e ikcazah sy`sis bir`at bakxa`kxa `isyghtak dak `isy`arak xakl eisth eiri`a fadazh

ZIRSIEBAFAK =

@arxa hkh `yzirsiebaf`ak `izada = Nrakl tya`y tirchkta Syaeh`y tirsaxakl xakl sigagy eiebirh sieaklat dak dnrnklak' sirta `idya aka``y tirsaxakl

@ATA ZIKLAKTAR

Zymh sxy`yr zikyghs ycaz`ak `izada Tyfak Xakl Eafa Isa' `arika `ashf dak akylraf%Kxa' a`fhrkxa ziebyatak s`rhzsh hkh dazat tirsigisah`ak Mydyg zikighthak hkh adagaf ‗ Eikhkl`at`ak @ieaezyak Shs|a Eatirh arhteath`a Snshag Diklak Eikllyka`ak Sheygash Traksa`sh Myag Bigh Balh Shs|a @igas HH SDK Saebhrntn :4 @icaeatak Tiebagakl Siearakl Tafyk Zigamarak 2::4 – 2::9 ‗' dhfaraz`ak dazat bireakoaat sibalah bafak easy`ak' dazat eikhkl`at`ak zrnsis ziebigamarak eatieath`a sifhklla dazat eiebirh`ak `nktrhbysh dagae yzaxa eikhkl`at`ak `nezitiksh dak `yaghtas syebir daxa dh bhdakl zikdhdh`ak Dagae eikxysyk s`rhzsh sydaf barakl tikty thda` gizas darh `isyghtak dak birbalah faebatak' kaeyk bir`at bhebhklak' arafak dak baktyak darh birbalah zhfa`' s`rhzsh hkh dazat tirsigisah`ak Zada `isiezatak hkh' zikyghs eikxaezah`ak rasa fnreat dak birtirhea `ashf `izada = 1 Drs F AT Snilhtn' SF' EE Ri`tnr Ykhvirshtas Kilirh Siearakl 2 Drs @aseadh Heae S' E S Di`ak OEHZA Ykhvirshtas Kilirh Siearakl 3 Drs Syzrhxnkn' E Sh @itya Myrysak Eatieath`a xakl tigaf eiebirh`ak h}hk dak myla eiebirh`ak bhebhklak' arafak' sirta enthvash zikyghs dagae eikxigisah`ak s`rhzsh 4 Dra Rafaxy' B_ E Sh Dnsik Ziebhebhkl H xakl tigaf eiebirh`ak dnrnklak' bhebhklak' dak zitykmy` dagae zikyghsak s`rhzsh 9 Drs \ardnkn E Sh Dnsik \agh xakl tigaf eiebirh`ak arafak dak bhebhklak

? Kar`n' A Ea @izaga Si`ngaf Dasar Kilirh Saebhrntn :4 @icaeatak Tiebagakl Siearakl xakl tigaf eiebirh`ak h}hk ykty` eiga`y`ak zikighthak Zikyghs eikxadarh baf|a dagae ziebyatak s`rhzsh eashf mayf darh siezyrka \agayzyk dieh`hak thda` eikytyz `ieykl`hkak `rhth` dak sarak darh sieya zhfa` xakl shoatkxa eiebaklyk ykty` `isiezyrkaak s`rhzsh hkh A`fhr `ata diklak silaga `irikdafak fath' zikyghs birfaraz sienla s`rhzsh hkh dazat bireakoaat balh sieya zhfa`

Siearakl'

Mygh 2::9

Zikyghs

& Farx Zaklisth (

DAOTAR HSH

FAGAEAK MYDYG

  

h

GNLN YKKIS

  

hh

ABSTRA@

  

hhh

ZIKLISAFAK

  

hv

ENTTN DAK ZIRSIEBAFAK   

v

@ATA ZIKLAKTAR

  

vh

DAOTAR HSH

  

vhhh

DAOTAR GAEZHRAK

  



BAB H

BAB HH

= ZIKDAFYGYAK A Gatar Biga`akl   

1

B Zireasagafak   

2

C Cara Zieicafak Easagaf  

2

D Tymyak Zikighthak   

3

I Eakoaat Zikighthak   

4

O Zikilasak Hsthgaf   

9

L Shstieath`a Zikyghsak S`rhzsh  

?

= GAKDASAK TINRH DAK FHZNTISHS ZIKIGHTHAK A Gakdasak Tinrh   

6

1 Ziklirthak Bigamar   

6

2 Tinrh Bigamar   

8

3 Ziklirthak Eatieath`a  

12

BAB HHH

BAB H_

BAB _

4 Tinrh Zir`iebaklak  

13

9 Oa`tnr – oa`tnr xakl eieziklaryfh bigamar 

14

? Eitndi Sheygash   

19

< Zireahkak   

1<

6 Arhtaeath`a Snshag @igas HH tiktakl Yakl 

1<

B @irakl`a Biroh`hr   

21

C Fhzntishs Zikighthak   

22

= EITNDI ZIKIGHTHAK A Sybmi` Zikighthak   

23

B _arhabig Zikighthak   

23

C Zrnsidyr @irma   

23

D Data dak Ziklyezygakkxa  

2?

I Hkdh`atnr @hkirma   

2<

= FASHG ZIKIGHTHAK DAK ZIEBAFASAK A Fashg Zikighthak   

26

B Ziebafasak   

33

= SHEZYGAK DAK SARAK A Shezygak   

39

B Sarak   

3?

DAOTAR ZYSTA@A    

3<

GAEZHRAK

36

   

DAOTAR GAEZHRAK

1 Giebar Akl`it Shs|a   

36

2 Giebar Ziklaeatak Shs|a Eigagyh Akl`it  

38

3 Rikcaka Ziebigamarak Sh`gys H Zirtieyak 1  

4:

4 G@S Sh`gys Zirtieyak 1   

44

9 Rikcaka Ziebigamarak Sh`gys H Zirtieyak 2  

4?

? G@S Sh`gys H Zirtieyak 2   

91

< @hsh – `hsh Sh`gys H    

93

6 Tis A`fhr Sh`gys H    

99

8 Akaghshs Khgah Sh`gys H   

96

1: Zidneak Nbsirvash Shs|a   

?:

11 Giebar Ziklaeatak Lyry   

?2

12 Rikcaka Ziebigamarak Sh`gys HH   

??

13 G@S Sh`gys HH Zirtieyak `i%1   

?8

14 @hsh – `hsh Tis Sh`gys HH   

<1

19 Tis A`fhr Sh`gys HH    

<3

1? Zidneak Nbsirvash Shs|a   

<9

1< Giebar Ziklaeatak Lyry   

<<

16 Akaghsa Tis A`fhr Sh`gys HH   

61

BAB H ZIKDAFYGYAK

A+ Gatar Biga`akl

Eatieath`a eiryza`ak ziklitafyak xakl zikthkl Sieya aszi`  `ifhdyzak thda` dazat gizas darh eatieath`a' `arika sieya nrakl eikllyka`ak eatieath`a dh silaga bhdakl `i fhdyzak Eatieath`a eiryza`ak eata zigamarak xakl saklat sy`ar dak eika`yt`ak' hkh akllazak shs|a `fysyskxa balh shs|a xakl eirasa `yrakl eaezy atay gieaf dagae eata zigamarak eatieath`a Ykty` eiklfhkdarh fag% fag tirsibyt' sinrakl lyry farys dazat eikxh`azh xahty diklak cara eikchzta`ak syasaka a`rab dak eikxikakl`ak dagae bigamar eatieath`a Zigamarak eatieath`a zirgy dh`aht`ak diklak `ifhdyzak kxata sifarh% farh' sifhklla dazat eiezirgyas dak eiezirdagae `nksiktrash shs|a sirta eiezireydaf shs|a eiebyat tarlit zristash sisyah diklak `ieamyak shs|a Eiklamar eatieath`a farys eikllyka`ak syaty ti`kh`' eitndi dak endig ziebigamarak Diklak dieh`hak shs|a eydaf eieafaeh eatirh xakl dhtirhea dak fashg ziebigamarak dazat eiklagaeh syaty zikhkl`atak Dagae ziebigamarak eatieath`a zn`n` bafasak yakl balh `igas HH SDK Saebhrntn :4 Siearakl tafyk amarak 2::3%2::4 sydaf dhsaezah`ak diklak bikar Kaeyk zikyghs eiklhklhk`ak dagae zn`n` bafasak yakl' `ieaezyak shs|a eatirh arhteath`a snshag gibhf dhioi`tho`ak galh diklak eikllyka`ak stratilh sheygash traksa`sh myag bigh

@ieaezyak shs|a `igas HH SDK Saebhrntn :4 dhbhdakl eatieath`a zada yeyekxa dak zn`n` bafasak yakl tirytaea `ia`thoak' `itraezhgak eiklfhtykl' `hkirma lyry dagae `ilhatak bigamar eiklamar zada `fysyskxa zirgy dhthkl`at`ak galh' `arika khgah rata – rata shs|a fakxa ?'9 B+ Zireasagafak

Birdasar`ak gatar biga`akl xakl tigaf dhyrah`ak dh atas ea`a easagaf xakl dhakl`at dagae zikighthak hkh adagaf ‗Aza`af diklak eikllyka`ak stratilh sheygash traksa`sh myag bigh' `ieaezyak' `ia`thoak' dak `itraezhgak shs|a `igas HH SDK Saebhrntn :4 dagae eatirh arhteath`a snshag sirta `hkirma lyry dagae `ilhatak bigamar eiklamar dazat dhthkl`at`ak >― C+ Cara Zieicafak Easagaf

Ykty` eikhkl`at`ak `ia`thoak' `itraezhgak eiklfhtykl' fashg bigamar shs|a `igas HH dagae eatirh arhteath`a snshag dak `hkirma lyry dagae `ilhatak bigamar eiklamar SDK Saebhrntn :4 sagaf satykxa eigagyh ziebigamarak diklak `ilhatak traksa`sh myag bigh Adazyk xakl dhea`syd diklak traksa`sh myag bigh adagaf shs|a eieirak`ak cirhta sibalah zikmyag dak ziebigh xakl eiryza`ak zirhsth|a dagae `ifhdyzak sifarh%farh

D+ Tymyak dak Eakoaat Zikighthak

1 Tymyak Yeye

a Hklhk eiklitafyh `itizatak eitndi ziebigamarak diklak `ilhatak sheygash traksa`sh myag bigh ykty` eikhkl`at`ak `ieaezyak shs|a dagae eatirh arhteath`a snshag b Eiklybaf heali shs|a baf|a eitieath`a adagaf zigamarak xakl syght' eiebnsak`ak dak eika`yt`ak eikmadh zigamarak xakl eydaf' eikxikakl`ak' dak eikaktakl' sifhklla shs|a eikmadh liear eatieath`a 2 Tymyak @fysys a Eiklitafyh aza`af diklak eikllyka`ak stratilh sheygash traksa`sh  myag bigh' `ieaezyak shs|a `igas HH SDK Saebhrntn :4 dagae eatirh arhteath`a snshag dazat dhthkl`at`ak > b Eikhkl`at`ak

`ia`thoak

shs|a

dagae

`ilhatak

ziebigamarak

eatieath`a zada eatirh arhteath`a snshag c Eikhkl`at`ak `itraezhgak shs|a dagae dagae eiklfhtykl zada eatirh arhteath`a snshag d Eikhkl`at`ak `hkirma lyry dagae `ilhatak bigamar eiklamar zada eatirh arhteath`a snshag

I+ Eakoaat Zikighthak

Zikighthak hkh a`ak eiebirh`ak eakoaat balh = 1 Shs|a a Shs|a dazat eikhkl`at`ak rasa zircaxa dhrh

b Shs|a

dazat

eiebaklyk

`itraezhgak'

ziklitafyak

dak

ziklagaeak dagae zra`ti` `ifhdyzak sifarh%farh c Shs|a dazat eieyzy` zirsafabatak aktar shs|a' zirsatyak dak `irmasaea d Shs|a eiezirngif ziklitafyak xakl gibhf birea`ka 2 Lyry a Eikhkl`at`ak `ieaezyak lyry dagae eiklamar`ak eatieath`a `izada shs|a `igas HH tirytaea eatirh arhteath`a snshag b Eikhkl`at`ak `ieaezyak lyry dagae eikikty`ak eitndi xakl tizat ykty` eikxamh`ak syaty zn`n` bafasak dagae eatieath`a 3 Si`ngaf a Eiebirh`ak dnrnklak `izada easxara`at ykty` gibhf eikdy`ykl ysafa zikhkl`atak zristash si`ngaf b Eikhkl`at`ak chtra xakl gibhf znshtho balh si`ngaf dh `agaklak easxara`at' zada saat bakxa` si`ngaf tirytaea si`ngaf dasar kilirh dhtytyz `arika zada |a`ty zikdaotarak eyrhd bary thda`  eikdazat eyrhd bary atay eyrhd bary `yrakl darh 1: aka`

O+ Zikilasak Hsthgaf

Syaty hsthgaf dazat dhtaoshr`ak diklak ea`ka xakl birbida Ykty`  eiklfhkdarh zikaoshrakxakl birbida eiklikah mydyg s`rhzsh hkh' ea`a dhzirgy`ak batasak sibalah birh`yt =

1 Eikhkl`at`ak xakl dhea`syd dagae zikighthak hkh adagaf tirbatas eiklikah zirybafak rata – rata khgah zigamarak eatieath`a shs|a zada zn`n` bafasak yakl 2 @ieaezyak xakl dhea`syd adagaf tirbatas zada fashg bigamar shs|a dagae eikxigisah`ak snag arhteath`a snshag  3 Eatirh xakl dhea`syd adagaf eata yakl 29 ryzhaf saezah diklak 1::: ryzhaf 4 Arhteath`a snshag adagaf sagaf saty zn`n` bafasak eatieath`a `igas HH xakl birfybyklak diklak myag bigh 9 Sheygash traksa`sh myag bigh adagaf tirbatas zada `itraezhgak shs|a dagae eieirala`ak sibalah zikmyag dak ziebigh diklak eikllyka`ak agat zirala yakl 29 ryzhaf saezah diklak 1::: ryzhaf ? Shs|a `igas HH SDK Saebhrntn :4 adagaf aka` – aka` ysha si`ngaf & birysha aktara < tafyk saezah 8 tafyk ( xakl tirdhrh darh 19 aka`  ziriezyak dak 1< aka` ga`h – ga`h xakl zada tafyk zigamarak 2::4 – 2::9 dydy` dh `igas HH SDK Saebhrntn Sa ebhrntn :4 @icaeatak Tiebagakl Siearakl

L+ Shstieath`a S`rhzsh

Ykty` eieydaf`ak zikyghsak dak zieafaeak hsh s`rhzsh ea`a dhsysysk shstieath`a sibalah birh`yt = 1 Balhak Zikdafygyak Tirdhrh darh Fagaeak Mydyg' Giebar Ziklisafak' Enttn dak Zirsiebafak' @ata Ziklaktar' Abstra`' Daotar Hsh' Daotar Tabig' Daotar Gaezhrak

2 Balhak Hsh S`rhzsh Bab H =

Zidafygyak Birhsh

tiktakl

Zikighthak'

Gatar

Biga`akl'

Zireasagafak'

Tymyak

Eakoaat Zikighthak' Zikilasak Hsthgaf dak

Shstieath`a Bab HH =

Gakdasak Tinrh Birhsh

Ziklirthak

Bigamar'

Tinrh

Bigamar'

Ziklirthak

Eatieath`a' Tinrh Zir`iebaklak' Oa`tnr – oa`tnr xakl eieziklaryfh

bigamar'

Eitndi

Sheygash'

Zireahkak'

Arhteath`a Snshag `igas HH tiktakl yakl' @irakl`a Birzh`hr' Fhzntishs Zikighthak Bab HHH =

Eitndi Zikighthak Birhsh

tiktakl

Zikighthak'

Zikiktyak

Zrnsidyr

@irma'

Sybmi` Data

Zikighthak' dak

_arhabgi

Ziklyezygakkxa'

Hkdh`atnr @irma

Bab H_ =

Fashg zikighthak dak ziebafasak Birhsh tiktakl Fashg Zikighthak dak Ziebafasak Fashg Zikighthak

Bab _ =

Shezygak dak Sarak Birhsh tiktakl Shezygak dak Sarak – sarak

3 Balhak a`fhr s`rhzsh Tirdhrh darh Daotar zysta`a dak Gaezhrak

BAB HH GAKDASAK TINRH DAK FHZNTISHS ZIKIGHTHAK

A+ Gakdasak Tinrh

Tnzh` zikighthak hkh' sibalaheaka tirshrat dagae mydyg ‗ Eikhkl`at`ak `ieaezyak shs|a eatirh arhteath`a snshag diklak eikllyka`ak sheygash traksa`sh myag bigh balh shs|a `igas HH SDK Saebhrntn :4 Siearakl tafyk zigamarak 2::4 – 2::9 ‗' adagaf tiktakl ziebigamarak eatieath`a' dak yzaxa eikhkl`at`ak `yaghtas ziebigamarak eitieath`a Tnzh` tirsibyt thda` bhsa gizas darh fag – fag sibalah birh`yt' xakl a`ak dhbafas dagae bab hkh 1 Ziklirthak Bigamar Bigamar adagaf syaty zrnsis xakl dhtakdah diklak adakxa zirybafak zada dhrh sisinrakl Zirybafak sibalah fashg darh zrnsis bigamar dazat dhtykmy``ak dagae birbalah bikty` sizirth birybaf ziklitafyak' zieafaeak' sh`az dak thkl`af ga`y' `itraezhgak' `ica`azak' `ibhasaak' sirta zirybafak aszi` –aszi` gahk xakl ada zada hkdhvhdy xakl bigamar % Eikyryt Enygx &2::3(' dagae by`y CBSA Zrnsis Bigamar Eiklamar' zada fa`h`atkxa bigamar adagaf zrnsis zirybafak thkl`af ga`y sisinrakl bir`at adakxa ziklagaeak % Eikyryt Larrx dak @hklsgix &2::3( eikxata`ak bigamar adagaf zrnsis zirybafak thkl`af ga`y xakl nrhshkhg eigagyh ziklagaeak dak gathfak% gathfak Tinrh Bigamar

Diklak dieh`hak bigamar zada dasarkxa adagaf zrnsis zirybafak thkl`af ga`y bir`at adakxa ziklagaeak Zirybafak thkl`af ga`y eikyryt \htfirhkltnk

eighzyth

zirybafak

`itraezhgak'

`ibhasaak'

sh`az'

ziklitafyak' dak azrishash Xakl dhea`syd diklak ziklagaeak dagae zrnsis bigamar thda` gahk hagaf hktira`sh aktara hkdhvhdy diklak ghkl`yklakkxa  Ngif sibab hty' bigamar adagaf zrnsis a`tho Bigamar adagaf zrnsis eiria`sh tirfadaz sieya shtyash xakl ada dh si`htar hkdhvhdy Bigamar adagaf syaty zrnsis xakl dharaf`ak `izada syaty tymyak' zrnsis birbyat eigagyh birbalah ziklagaeak Bigamar adagaf zrnsis eighfat' eiklaeath' eieafaeh sisyaty xakl dhzigamarh & DRFKaka Sydmaka'CBSA Dagae Zrnsis Bigamar Eiklamar ( 2 Tinrh Bigamar = Bibiraza zikdazat darh zara afgh zsh`ngnlh tiktakl tnirh bigamar dhaktarakxa = a S`hkkir birzakdaklak baf|a bigamar adagaf syaty zirhga`y Zada saat nrakl bigamar' ea`a risznkkxa eikmadh gibhf bah` Sibagh`kxa' ha thda`  bigamar ea`a risznkkxa eikyryk Dagae bigamar dhtiey`ak adakxa fag birh`yt = &h(

@isiezatak tirmadhkxa zirhsth|a xakl eikhebyg`ak risznk

bigamar & hh ( Risznk shzibigamar' dak

&hhh(

@nksi`yiksh xakl birshoat eiklyat`ak risznk tirsibyt Zieir`yat tirmadh zada stheygys xakl eiklyat`ak `nksi`yiksh tirsibyt Sibalah hgystrash' zirhga`y risznk shzibigamar xakl bah`  dhbirh fadhaf Sibagh`kxa zirhga`y risznk xakl thda` bah` dhbirh tilyrak dak fy`yeak & Bigamar eikyryt S`hkkir dagae by`y Bigamar dak Ziebigamarak' Dr Dhexath dak Drs Eyd Mnkn (

b Rnlir eikliey`a`ak zikthklkxa lyry eiezirfath`ak zrhkshz zikdhdh`ak Zrhkshz zikdhdh`ak dak ziebigamarak tirsibyt sibalah birh`yt= 1 Eikmadh eakysha birarth eiehgh`h `i`yatak |amar ykty` bigamar Shs|a thda` farys bigamar tiktakl fag – fag xakl thda` ada arthkxa 2 Shs|a a`ak eiezigamarh fag – fag xakl birea`ka balh dhrhkxa 3 Ziklnrlakhsashak baf`ak ziklamarak birarth eiklnrlakhsash`ak bafak dak hdi bary Sibalah balhak xakl birea`ka balh shs|a 4 Bigamar xakl birea`ka dagae easxara`at endirk birarth bigamar tiktakl zrnsis – zrnsis bigamar' `itirby`aak bigamar eiklagaeh sisyaty' bi`irmasaea diklak eiga`y`ak ziklybafak dhrh tirys eikirys 9 Bigamar xakl nztheag a`ak tirmadh' bhga shs|a birzarthshzash sicara birtakllykl ma|ab dagae zrnsis bigamar ? Bigamar eiklagaeh & Izirhiktag Giarkhkl ( dazat tirmadh' bhga shs|a eiklivagyash dhrhkxa sikdhrh Bigamar eiklagaeh dazat

eiebirh zigyakl ykty` bigamar `riatho' sigo ivagyathnk dak `rhth`  dhrh Fag hkh birarth bafak ivagysh darh hkstry`tyr birshoat si`ykdir < Bigamar eiklagaeh eikyktyt `itirghbatak shs|a sicara zikyf dak sykllyf – sykllyf Gakl`af – gakl`af ziebigamarak xakl zirgy ngif lyry Sarak ziebigamarak hty eighzyth fag sibalah birh`yt = 1 Lyry eiebirh `izircaxaak `izada `igas alar `igas eiehghf bigamar sicara tirstry`tyr 2 Lyry dak shs|a eiebyat `nktra` bigamar 3 Lyry eikllyka`ak eitndi hk`yhrh' atay bigamar eikiey`ak &Dhscnvirx Giarkhkl ( 4 Lyry eikllyka`ak eitndi sheygash 9 Lyry eiklada`ak gathfak `izi`aak alar shs|a eaezy eiklfaxath zirasaak dak birzarthshzash diklak `ignezn` gahk ? Lyry birthkda` sibalah oashghtatnr bigamar < Sibagh`kxa lyry eikllyka`ak ziklamarak birzrnlrae' alar tirchzta zigyakl balh shs|a ykty` thebygkxa `riathvi c Eikyryt Aysybig &18<1(' bafak zigamarak xakl dhzigamarh farysgaf ―birea`ka―& eiakhkloygg( arthkxa bafak zigamarak hty cncn` diklak `ieaezyak shs|a dak farys rigivak diklak stry`tyr `nlkhtho xakl dhehgh`h shs|a Zigamarak bary farysgaf dh`aht`ak diklak `nksiz% `nksiz xakl sydaf ada sidieh`hak fhklla `nksiz%`nksiz bary bikar%

bikar tirsiraz Diklak dieh`hak hktigi`tyag % ienshnkag shs|a tirghbat dhdagae `ilhatak bigamar eiklamar d Eikyryt ryeysak L A @hebgi' bigamar adagaf zirybafak xakl rigathvi eikitaz dagae zntiksh thkl`af ga`y xakl tirmadh sibalah a`hbat darh gathfak diklak ziklyatak dak thda` tireasy` zirybafak – zirybafak `arika `ieataklak' `igigafak atay `irysa`ak zada sysykak sxarao' atay diklak `ata gahk baf|a eiklitafyh dak eieafaeh sisyaty sifhklla tirmadh zirybafak dagae dhrh sisinrakl xakl bigamar 3 Ziklirthak Eatieath`a Hsthgaf eatfieathcs &Hkllrhs('  Eatfieath`  &Mireak('  Eatfieathqyi &Zirakchs('  Eatieathcn & Htagh('  Eatieathcis`h &Rysha( atay  Eatfieathc` .  |hs`ykdi &Bigakda( birasag darh zir`ataak gathk eatfieathca' xakl

eygakxa dhaebhg darh darh zir`ataak Xykakh'  Eatfieath`i xakl birarth ‗  Rigashkl tn giarkhkl ‗ Zir`ataak hty eiezykxah a`ar `ata eatfiea xakl

birarth ziklitafyak atay hgey & `kn|gidli' schikci ( Zir`ataak eatfieath`i birfybyklak saklat irat diklak sibyaf `ata gahkkxa xakl

siryza' xahty eatfakihk xakl eiklakdykl arth bigamar & birzh`hr ( %

Maeis dak Maeis & 18
%

Mnfksnk dak Rhshkl dagae by`ykxa eiklata`ak baf|a eatieath`a adagaf znga birzh`hr' znga eiklnrlakhsash`ak' zieby`thak xakl gnlh`' eatieath`a hty adagaf bafasa xakl eikllyka`ak hsthgaf xakl dhhdikthoh`ash`ak diklak cireat' migas' dak a`yrat' rizrisiktashkxa diklak shebng dak zadat' gibhf biryza bafasa shebng eiklikah hdi darh zada eiklikah bykxh

%

Aktnk E Eaghnkn & 188: = 9?? ( dagae by`y fakd nyt nyt Dasar – dasar dak Zrnsis Ziebigamarak Eatieath`a H' eatieath`a dharth`ak sibalah hgey tiktakl bhgaklak – bhgaklak' fybyklak aktara bhgaklak' dak zrnsidyr nzirashnkag xakl dhlyka`ak dagae zikxigisahak easagaf eiklikah bhgaklak

4 Tinrh Zir`iebaklak Eikyryt Miak Zhalit ' ada iezat tafaz zir`iebaklak `nlkhtho darh sithaz hkdhvhdy xakl bir`iebakl bir`iebakl sicara `rnkngnlhs & eikyryt ysha `agikdir ( xahty = a Tafaz Siksnrh Entnr' darh gafhr saezah diklak yeyr si`htar 2 tafyk' ziklagaeak dhzirngif dhzirngif eigagyh zirbyatak ohsh` ohsh` & lira`ak akllnta akllnta tybyf ( dak siksnrh & `nnrdhkash hkdra (  b Tafaz Nzirash' si`htar yeyr 2 tafyk saezah diklak < tafyk' zieh`hrak gibhf gibhf bakxa` birdasar`ak birdasar`ak zada ziklagaeak `nkl`rht darh zada zieh`hrak gnlhs' sifhklla mh`a ha eighfat nbmi`%nbmi` xakl `ighfatakkxa birbida' ea`a ha eiklata`akkxa birbida zyga

c Tafaz Nzirash @nk`rht' si`htar yeyr < tafyk saezah diklak si`htar yeyr 11 tafyk' dagae eieafaeh nzirash gnlhs dikla baktyak bikda – bikda `nk`rht @ieaezyak @ieaezyak hkh tir|ymyd dagae eieafaeh eieafaeh `nksiz `nksiz `i`i`agak' `ieaezyak ykty` eikl`gashoh`ash dak sirash' eaezy eieakdakl syaty nbmi` darh sydyt zakdakl xakl birbida sicara nbmi`tho dak eaezy biroh`hr rivirshbig d Tafaz nzirash onreag' si`htar yeyr 11 tafyk dak gibhf' eiga`y`ak zikagarak diklak eikllyka`ak fag – fag xakl abstra` & F Ireak Syfireak Ar' Drs' E Zd' 2::3' Stratilh Ziebigamarak Eatieath`a ( 9 Oa`tnr – oa`tnr xakl eieziklaryfh bigamar Bigamar adagaf syaty zrnsis xakl eikhebyg`ak tirmadhkxa syaty zirybafak atay ziebafaryak dagae thkl`af ga`y dak atay `ica`azak Zirybafak dh dagae bigamar' birfashg bah` atay thda`kxa tirlaktykl `izada bireacae – eacae oa`tnr xahty = 1 Oa`tnr hkdhvhdyag' adagaf oa`tnr xakl ada zada dhrh nrlakhsei hty sikdhrh ' aktara gahk = a @ieataklak atay zirtyebyfak b @icirdasak atay hktigiliksh c Gathfak dak ygaklak d Enthvash i Shoat – shoat zrhbadh sisinrakl 2 Oa`tnr snshag' adagaf oa`tnr xakl ada dh gyar hkdhvhdy' aktara gahk =

a @iadaak `igyarla b Lyry dak cara eiklamar c Agat – agat zigamarak d Enthvash snshag i Ghkl`yklak dak `isiezatak & Drs E Klaghe Zyr|aktn' EZ' EZ ' 1882' Zsh`ngnlh zikdhdh`ak ( ? Eitndi Sheygash & Bireahk zirak ( Sheygash eikyryt Zysat Ziebhkaak dak Zikliebaklak Bafasa' @aeys Bisar Bafasa Hkdnkisha Dizdh`byd adagaf eitndi zigathfak xakl eieirala`ak sisyaty dagae bikty` thryak thryak & hea`ak ( xakl ehrhz ehrhz diklak `iadaak sisykllyfkxa sisykllyfkxa Eikyryt by`y CBSA Dagae Zrnsis Bigamar Eiklamar ngif DR F Kaka Sydmaka' & 1868 ( Sheygash birasag darh `ata sheygati xakl arthkxa birzyra – zyra atay birbyat singaf – ngaf @ata sheygathnk arthkxa thryak atay zirbyatak xakl birzyra – zyra Darh `ata hty migas baf|a sheygash adagaf thryak atay zirbyatak xakl fakxa zyra – zyra sama Sheygash dazat dhlyka`ak ykty` eiga`y`ak zrnsis thkl`af ga`y sicara hehtash atayzyk bireahk zirakak eiklikah syaty thkl`af ga`y xakl dhga`y`ak singaf – ngaf dagae `iadaak sibikarkxa

Tymyak sheygash hagaf =

a Eigathf `itraezhgak tirtikty' bah` birshoat zrnoishnkag eayzyk balh `ifhdyzak sifarh – farh b Eiezirngif zieafaeak tiktakl syaty `nksiz atay zrhkshz c Eigathf eieicaf`ak easagaf d Eikhkl`at`ak `ilhatak bigamar diklak eighbat`ak shs|a dagae eiezigamarh shtyash xakl faezhr siryza diklak `imadhak xakl sibikarkxa i Eiebirh`ak enthvash bigamar `izada shs|a o

Eigathf shs|a ykty` eiklada`ak `irmasaea dagae shtyash `ignezn` 

l Eikyebyf`ak daxa `riatho shs|a f Eigathf shs|a ykty` eikliebakl`ak sh`az tngiraksh Bikty` – bikty` sheygash = a Ziir tiacfhkl xa`kh gathfak eiklamar xakl dhga`y`ak ngif shs|a `izada tieak – tieak cagnk lyry b Rngi zgaxhkl' xa`kh zireahkak zirakak ykty` eikl`riash `iebagh zirhsth|a – zirhsth|a xakl tigaf tirmadh atay a`ak tirmadh c Snshndraea'

xa`kh

zireahkak

zirakak

xakl

dhtymy`ak

ykty` 

eikikty`ak agtirkathvi zieicafak easagaf snshag Tymyak snshndraea adagaf alar eyrhd dazat eiklfarlah dak eiklfaxath zirasaak nrakl gahk' eieyzy` rasa takllykl ma|ab zada dhrh aka` d Zsh`ndraea' xa`kh zireahkak zirakak xakl dhtymy`ak alar shs|a eiezirngif & zieafaeak ( xakl gibhf bah` tiktakl dhrhkxa' dazat

eikiey`ak `nksiz sikdhrh' dak dazat eikxata`ak ria`shkxa tirfadaz ti`akak – ti`akak xakl eikheza dhrhkxa i Sheygathnk laei' xa`kh zireahkak zirakak Zara shs|a bir`nezithsh ykty` eikcazah tymyak tirtikty eigagyh zireahkak diklak eieikyfh ziratyrak – ziratyrak xakl dhtitaz`ak < Zireahkak Eikyryt by`y Stratilh Ziebigamarak Eatieath`a `nktieznrir & 2::3 (' zireahkak adagaf zireahkak eikxidha`ak ghkl`yklak bigamar zirgy diklak eahkak dheaka zara shs|a eiklh`yth atyrak – atyrak xakl tigaf dhlarhs`ak `arika eiri`a tirtarh` ykty` eikdazat`ak taktaklak Zireahkak hkh eiryza`ak ti`kh` xakl dazat eienthvash zara shs|a' `fysyskxa ykty` eatirh xakl birygakl – ygakl eiebnsak`ak 6 Arhteath`a snshag `igas HH tiktakl yakl Arhteith`a Cabakl darh eatieath`a Arhteith`a dhsibyt myla hgey fhtykl Dagae hgey fhtykl dhbhcara`ak tiktakl shoat – shoat bhgaklak' dasar – dasar ziklirmaak sizirth eikmyegaf' eiklyrakl' eiiebalh dak eiklagh`ak' eikarh` a`ar dak sibalahkxa & ST Kilarn B Farafaz' 1886' Iksh`gnzidha Eatieath`a Lfagha Hkdnkisha Akllnta H@AZH ( a Eata yakl 29 ryzhaf saezah diklak 1::: ryzhaf

Dya zygyf ghea ryzhaf

Ghea zygyf ryzhaf

Siratys ryzhaf

Dya ratys ryzhaf

Ghea ratys ryzhaf

Sirhby ryzhaf

b Khgah Si`ignezn` Yakl Khgahkxa

5 9: + 9: +

1:: 5 1:: + 1:: 5 2:: ryzhaf

Khgahkxa

5 9:: + 1:: +

9: 5 ?:: + 9:

5 ?9: ryzhaf Khgahkxa

5 2:: + 9:: 5 <:: ryzhaf

c Ty`ar Eiky`ar Yakl Dazat dhty`ar diklak

1 `izhkl yakl 1:: ryzhaf

2

`izhkl

yakl

9:

ryzhaf Khgahkxa 1:: ryzhaf

Khgahkxa 1:: ryzhaf

Birarth 0 1 `izhkl yakl 1:: ryzhaf khgahkxa saea diklak 2 `izhkl yakl 9: ryzhaf 1:: 5 9: + 9:

Dazat dhty`ar diklak

1 giebar yakl 9:: ryzhaf

9 giebar yakl 1:: ryzhaf

Khgahkxa 9:: ryzhaf

Khgahkxa 9:: ryzhaf

Birarth = 1 giebar yakl 9:: ryzhaf khgahkxa saea diklak 9 giebar yakl 1:: ryzhaf

9:: 5 1:: + 1:: + 1:: + 1:: + 1::

d Bireahk ‗ bigakma ‗ diklak myegaf yakl saezah diklak 1::: ryzhaf Zirca`azak zikmyag dak ziebigh Ziebigh = ‗ Biraza farla `yi hkh za` > ‗ Zikmyag = ‗ Farlakxa ghea zygyf ryzhaf ‗ Ziebigh = ‗ Saxa Sa xa eiebigh siratys ryzhaf' Za` ‗ Zikmyag = ‗ Hkh eikdazat 2 `yi ‗ Snag Cirhta Zirfath`ak snag cirhta dhba|af hkh ! Hby Kaka eiebigh sibykl`ys cabah eiraf diklak farla 99: ryzhaf Biraza ryzhaf`af yakl `iebagh > Zikxigisahak = Eiklfhtykl dafygy myegaf yaklkxa `ieydhak dh`yraklh farla ziebighak Cara eiklirma`ak eikllyka`ak `agheat eatieath`a Ma|ab = & 9:: ryzhaf + 9:: ryzhaf ( – 99: ryzhaf 5 k 1::: ryzhaf – 99: ryzhaf

5k 5 49: ryzhaf

Madh yakl `iebaghakkxa 49: ryzhaf

i Eikyghs`ak khgah eata yakl ryzhaf Rz

<9:'

::

Ryzhaf

Khgah yakl

Khgah sik

Madh' tymyf ratys ghea zygyf ryzhaf dhtyghs Rz <9:'::

B+ @irakl`a Birzh`hr Dagae ziebigamarak eigagyh `ilhatak sheygash traksa`sh myag bigh' shs|a gibhf a`tho sicara ohsh` eayzyk zsh`hs Sigahk shs|a a`tho sicara ohsh` eayzyk zsh`hs' shs|a dazat eiklfhtykl myegaf khgah yakl sirta dazat eiklfhtykl zikliebaghak dagae birtraksa`sh

Ziebigamarak diklak `ilhatak sheygash traksa`sh myag bigh shs|a a`ak gibhf eydaf eiklhklat' `arika sisyaty xakl dhga`y`ak a`ak gibhf bir`isak dak syght ykty` dhgyza`ak' sisyah diklak zrhkshz bigamar saebhg birbyat Cnghk Rnsi dak Eagcnge M Khcfngg &18<<=12:( eikxata`ak ‗  H fiar akl H onrlit' H  sii akd H ykdirstakd' H dn akd H rieiebir― &saxa eikdiklar dak saxa gyza'

saxa eighfat dak saxa zafae' saxa eiga`y`ak dak saxa hklat( Ziebigamarak diklak sheygash traksa`sh myag bigh eiryza`ak varhash ziebigamarak `arika bhasakxa marakl dhlyka`ak' ea`a shs|a a`ak gibhf sikakl Ziebigamarak xakl eikxikakl`ak a`ak eiebirh`ak enthvash balh shs|a dak enthvash saklatgaf zikthkl `arika takza enthvash ziebigamarak `yrakl birea`ka

C+ Fhzntishs Zikighthak Birdasar`ak `irakl`a birzh`hr dh atas dazat dhsysyk fhzntishs sibalah birh`yt Diklak `ilhatak sheygash traksa`sh  myag bigh shs|a a`tho dagae zrnsis ziebigamarak' `itraezhgak dagae birtraksa`sh' fashg bigamar shs|a `igas HH dak `hkirma lyry dagae `ilhatak bigamar eiklamar SDK Saebhrntn :4 dazat eikhkl`at

BAB HHH EITNDI ZIKIGHTHAK

Sitthkl Zikighthak A+ Sybxi` Zikighthak

Zikighthak thkda`ak `igas hkh dhga`saka`ak dh Si`ngaf Dasar Kilirh Saebhrntn :4 Sybxi` zikighthak adagaf `igas HH &dya(' xakl tirdhrh darh 19 shs|a ziriezyak dak 1< shs|a ga`h%ga`h' myegaf sigyryfkxa 32 shs|a Khgah rata%rata zigamarak Eatieath`a eiri`a zada sieistir 1 adagaf ?'9 Ziehghfak tiezat zikighthak hkh dh`arika`ak zikighth sibalah sagaf saty tikala ziklamar dh si`ngaf tirsibyt Adazyk ziga`sakaak zikighthak dhga`saka`ak zada sieistir 2 xahty ehklly `i%2 bygak Earit 2::9 Eigagyh sheygash traksa`sh   myag bigh' fashg bigamar shs|a `igas HH dh SDK Saebhrntn :4 Siearakl zada eatirh arhteath`a snshag zn`n` bafasak Yakl dazat dhthkl`at`ak B+ _arhabig Zikighthak

Xakl eikmadh varhabig zikighthak hkh adagaf = 1 @ia`thoak shs|a sigaea ziebigamarak 2 @itraezhgak shs|a dagae birtraksa`sh myag bigh 3 Fashg bigamar shs|a zada zn`n` bafasak yakl 4 @hkirma lyry dagae `ilhatak bigamar eiklamar

C+ Zrnsidyr @irma dagae Zikighthak Thkda`ak xakl Dhtiezyf

Zrnsidyr `irma dagae zikighthak thkda`ak `igas biryza rikcaka thkda`ak xakl a`ak dhtiezyf sicara birtafaz Tafaz zikighthak thkda`ak `igas hkh eighzyth tafaz zirikcakaak' ziga`sakaak' ziklaeatak dak riogi`sh Tafazak tirsibyt dhsysyk dagae syaty sh`gys xakl tirdhrh darh 2 sh`gys' xahty =

1 Sh`gys H a Zirikcakaak 

Eiebyat endig eata yakl xakl biralae khgahkxa



Eiebyat rikcaka ziebigamarak tiktakl eatirh eiklikag eata yakl' khgah si`ignezn` eata yakl dak ty`ar eiky`ar yakl



Eiebyat agat ivagyash

b Ziga`sakaak 

Eiebirh`ak zirsizsh



Eiga`saka`ak ziebigamarak tiktakl eatirh eiklikag eata yakl' khgah si`ignezn` eata yakl dak ty`ar eiky`ar yakl



Eiebalh shs|a eikmadh ikae `ignezn` birdasar`ak zieirataak thkl`at `ieaezyak birzh`hr shs|a



Shs|a eiklirma`ak giebar `irma sicara `ignezn`



Eiebafas giebar `irma diklak zikxigisahakkxa



Eiebirh snag ivagyash zada a`fhr sh`gys H

c Ziklaeatak 

Eiklaeath magakkxa ziebigamarak



Eiklaeath magakkxa `ilhatak eiky`ar yakl



Eiklaeath shs|a dagae eikxigisah`ak snag

d Riogi`sh Diklak eiklnbsirvash tafazak hezgieiktash dak eiklada`ak ivagyash zada tafazak ivagyash ea`a fashgkxa dazat dhakaghsa ykty` eikikty`ak aza`af sh`gys birh`ytkxa zirgy dhga`y`ak

2 Sh`gys HH a Zirikcakaak



Eiebyat rikcaka ziebigamarak tiktakl eatirh traksa`sh myag bigh dak ty`ar eiky`ar yakl



Eiebyat agat ivagyash



Eiebyat zidneak nbsirvash

b Hezgieiktash 

Eiebirh`ak zirsizsh



Eiga`saka`ak ziebigamarak eigagyh sheygash traksa`sh myag bigh



Sicara birlakthak sithaz `ignezn` eiga`y`ak traksa`sh myag bigh' `ignezn` gahk eikmadh ziklaeat



Sieya `ignezn` eiklirma`ak snag cirhta xakl tigaf dhzirak`ak



Eiebhebhkl dagae eikxigisah`ak snag cirhta



Birsaea shs|a eiebafas snag cirhta diklak zikxigisahakkxa



Eiebirh snag ivagyash zada a`fhr sh`gys HH

c Ziklaeatak 

Eiklaeath magakkxa ziebigamarak



Eiklaeath magakkxa `ilhatak traksa`sh myag bigh



Eiklaeath shs|a dagae eikxigisah`ak snag cirhta

d Riogi`sh Zikighth birsaea ziklaeat eikdhs`ysh`ak fashg bigamar dak eikikty`ak aza`af dhzirgy`ak sh`gys sigakmytkxa atay thda` Mh`a fashg bigamar sydaf sisyah diklak hkdh`atnr `hkirma ea`a sh`gys dhakllaz sigisah

D+ Data dak Ziklyezygakkxa

1 Syebir Data dak Mikhs Data a Syebir Data Syebir data zikighthak hkh adagaf shs|a b Mikhs Data Mikhs data adagaf data `yakthtatho xakl dhaebhg darh khgah eatieath`a sibigye zikighthak eayzyk tis zada a`fhr sh`gys dak data `yaghtatho  dhaebhg darh fashg ziklaeatak sigaea zrnsis ziebigamarak 2 Cara Ziklaebhgak Data a Data

tiktakl

`ia`thoak

zrnsis

ziebigamarak

dhaebhg

eigagyh

ziklaeatak b Data tiktakl `itraezhgak birtraksa`sh dhaebhg eigagyh ziklaeatak c Data fashg bigamar dhaebhg darh fashg tis t is zada sithaz a`fhr sh`gys d Data fashg `hkirma lyry dhaebhg eigagyh ziklaeatak

I+ Hkdh`atnr @hkirma

Ziga`sakaak thkda`ak `igas dhakllaz birfashg mh`a = 1 @ia`thoak shs|a eikcazah ; <9 ) 2 @itraezhgak shs|a dagae eiklfhtykl ; <9 ) 3 Khgah rata – rata fashg bigamar shs|a ≩ <': 4 @hkirma lyry dagae `ilhatak bigamar eiklamar ≩ <':

BAB H_ FASHG ZIKIGHTHAK DAK ZIEBAFASAK

A+ Fashg Zikighthak

H Sh`gys H Zada sh`gys hkh lyry eiga`y`ak zikighthak tiktakl zrnsis bigamar diklak zn`n` bafasak yakl 1 Fashg ziklaeatak tirfadaz a`thvhtas shs|a sigaea ziebigamarak' sitigaf dhaeath dak dhcatat eiklikah thkl`at zarthshzash dak `ia`thoak sithaz shs|a dagae zrnsis ziebigamarak' ea`a dh zirngif data sibalah birh`yt = a Shs|a shaz dydy` dh `yrsh zada |a`ty zigamarak arhteath`a 32 aka`  atay 1:: ) b Shs|a shaz diklak by`y atay agat zigamarak 32 aka` atay 1:: ) c Shs|a tikakl dak tirtarh` diklak zikmigasak lyry 32 aka` atay 1::) d Shs|a eikcatat eatirh xakl dhmigas`ak lyry 32 aka` atay 1::) i Shs|a a`tho birtakxa 19 aka` atay 4?' 6 ) o

Shs|a eikma|ab & eirisznk ( sithaz zirtakxaak lyry 16 aka` atay 9?' 2 )

l Shs|a tirtarh` & sikakl ( eikllyka`ak eidha dagae zrnsis ziebigamarak 32 aka` atay 1:: ) f Shs|a sikakl eiga`saka`ak `irma `ignezn` 32 aka` atay 1::) h

Sigyryf shs|a a`tho dagae eiga`saka`ak `irma `ignezn` 16 aka`  atay 9?' 2 )

 m

Shs|a dazat bi`irma saea atay birfybyklak diklak shs|a gahk 16 aka` atay 9?' 2 )

Darh fashg ziklaeatak dh atas ea`a dazat dh aebhg rata – rata `ia`thoak shs|a xahty 61' 9 ) diklak `atilnrh bah` si`agh 2 Fashg ziklaeatak tirfadaz a`thvhtas shs|a sigaea ziebigamarak sitigaf dhaeath dak dhcatat eiklikah thkl`at `itraezhgak eiklfhtykl shs|a dagae zrnsis ziebigamarak' ea`a dhzirngif data sibalah birh`yt= a Ada ysafa atay enthvash ykty` dazat eikla`fhrh sheygash traksa`sh  myag bigh diklak bikar 22 aka` atay ?6' < ) b Shs|a tiraezhg dagae eikllyka`ak agat zirala yakl 16 aka` atay 9?'2 ) c Shs|a tiraezhg dagae birtraksa`sh myag bigh 1? aka` at ay 9: ) d Shs|a tiraezhg dagae eiklignga `irma saea dagae `ignezn` 16 aka` atay 9?' 2 ) Darh fashg ziklaeatak dh atas ea`a dazat dh aebhg rata – rata `itraezhgak eiklfhtykl shs|a xahty 9<' < ) diklak `atilnrh sidakl 3 fashg gaznrak ziklaeatak lyry sigaea zrnsis ziebigamarak Sitigaf eiklaeath zrnsis ziebigamarak xakl tigaf birgaklsykl' ea`a ziklaeat eiebirh gaznrak baf|a zada dasarkxa zikighth dagae eiklignga `ilhatak bigamar eiklamar sydaf gibhf darh cy`yz' kaeyk balh lyry hty by`ak birarth gibhf darh cy`yz zyga balh shs|a `arika = a Dagae eiebakty shs|a eikxadarh `i`yatak dak `igieafak dhrh eashf `yrakl b Dagae bir`neykh`ash diklak shs|a xakl eikllyka`ak i`szrish ghsak atay tirtyghs eashf `yrakl migas

c @yrakl eiki`ak`ak shs|a eiklikah ea`syd dak zikthklkxa tnzh` d Dagae eiga`saka`ak thkda` gakmyt eashf `yrakl i @izi`aak tirfadaz `isagafak birbafasa shs|a myla eashf `yrakl 4 Fashg tis sh`gys H Dha`fhr sh`gys' shs|a – shs|a eiklirma`ak snag t is fashg bigamar tiktakl eata yakl 29 ryzhaf saezah diklak 1::: ryzhaf' khgah si`ignezn`  eata yakl xakl biralae mikhskxa' khgah ty`ar eata yakl ryzhaf' fashgkxa sibalah birh`yt = a Khgah tirthkllh

5 1:

b Khgah tirikdaf

52

c Khgah rata – rata

5 <'4

HH Sh`gys HH Zada sh`gys hkh lyry eiga`y`ak zikighthak tiktakl zrnsis bigamar diklak syb zn`n` bafasak bireahk bigakma diklak myegaf khgah yakl saezah diklak 1::: ryzhaf dak eikyghs`ak khgah eata yakl 1 Fashg ziklaeatak tirfadaz a`thvhtas shs|a sigaea ziebigamarak' sitigaf dhaeath dak dhcatat eiklikah thkl`at zarthshzash dak `ia`thoak sithaz shs|a dagae zrnsis ziebigamarak' ea`a dhzirngif data sibalah birh`yt = a Shs|a shaz dydy` dh `yrsh zada |a`ty zigamarak arhteath`a 32 aka`  atay 1:: ) b Shs|a shaz diklak by`y atay agat zigamarak 32 aka` atay 1:: )

c Shs|a tikakl dak tirtarh` diklak zikmigasak lyry 32 aka` atay 1::) d Shs|a eikcatat eatirh xakl dhmigas`ak lyry 32 aka` atay 1::) i Shs|a a`tho birtakxa 16 aka` atay 9?'2 ) o

Shs|a eikma|ab & eirisznk ( sithaz zirtakxaak lyry 2: aka` atay ?2'9 )

l Shs|a tirtarh` & sikakl ( eikllyka`ak eidha dagae zrnsis ziebigamarak 32 aka` atay 1:: ) f Shs|a sikakl eiga`saka`ak `irma `ignezn` 31 aka` atay 8?'6 ) h

Sigyryf shs|a a`tho dagae eiga`saka`ak `irma `ignezn` 26 aka`  atay 6<'9 )

 m

Shs|a dazat bi`irma saea atay birfybyklak diklak shs|a gahk 16 aka` atay 9?' 2 )

Darh fashg ziklaeatak dh atas ea`a dazat dhaebhg rata – rata `ia`thoak shs|a xahty 63'4 ) diklak `atilnrh bah` si`agh 2 Fashg ziklaeatak tirfadaz a`thvhtas shs|a sigaea ziebigamarak sitigaf dhaeath dak dhcatat eiklikah thkl`at `itraezhgak eiklfhtykl sithaz shs|a dagae zrnsis ziebigamarak' ea`a dhzirngif data sibalah birh`yt = a Ada ysafa atay enthvash ykty` dazat eikla`fhrh sheygash traksa`sh  myag bigh diklak bikar 2? aka` atay 61'2 ) b Shs|a tiraezhg dagae eikllyka`ak agat zirala yakl 29 aka` atay <6'1 ) c Shs|a tiraezhg dagae birtraksa`sh myag bigh 29 aka` at ay <6'1 ) d

Shs|a tiraezhg dagae eiklignga `irma saea dagae `ignezn` 16 aka` atay 9?' 2 )

Darh fashg ziklaeatak dh atas ea`a dazat dh aebhg rata – rata `itraezhgak eiklfhtykl shs|a xahty <3'4 ) diklak `atilnrh bah` 3 fashg gaznrak ziklaeatak lyry sigaea zrnsis ziebigamarak Sitigaf eiklaeath zrnsis ziebigamarak xakl tigaf birgaklsykl' ea`a fashg ziklaeat xakl dazat dhgaznr`ak = a Dagae eiebakty shs|a eikxadarh `i`yatak dak `igieafak dhrh sydaf eikhkl`at b Dagae bir`neykh`ash diklak shs|a xakl eikllyka`ak i`szrish ghsak atay tirtyghs migas c Sydaf eiki`ak`ak shs|a eiklikah ea`syd dak zikthklkxa tnzh` d Dagae eiga`saka`ak thkda` gakmyt eashf `yrakl i @izi`aak tirfadaz `isagafak birbafasa shs|a bah` 4 Fashg tis sh`gys HH Dha`fhr sh`gys HH' shs|a – shs|a eiklirma`ak snag tis fashg bigamar tiktakl bireahk bigakma diklak myegaf khgah yakl saezah diklak 1::: ryzhaf dak eikyghs`ak khgah eata yakl Khgah ty`ar eata yakl ryzhaf' fashgkxa sibalah birh`yt = a Khgah tirthkllh

5 1:

b Khgah tirikdaf

5 4'?

c Khgah rata – rata

5 6'6

B+ Ziebafasak

1 Sh`gys H Darh fashg zikighthak tirghfat baf|a rata – rata `ia`thoak shs|a 61' 9 )' rata – rata `itraezhgak eiklfhtykl shs|a 9<' < ) dak rata – rata fashg bigamar <'4 sifhklla zikighthak dazat dh`ata`ak bigye birfashg `arika rata – rata `itraezhgak eiklfhtykl shs|a eashf dh ba|af hkdh`atnr xakl dhtitaz`ak Fag hkh dhsibab`ak ngif = a Oa`tnr shs|a •

Shs|a eashf tirlaktykl zada tieakkxa xakl zakdah dagae eikxigisah`ak snag arhteath`a snshag tiktakl yakl

•

Shs|a dazat eikxigisah`ak snag arhteath`a snshag thda` eay eikllyka`ak agat zirala

b Oa`tnr lyry •

Lyry `yrakl ea`sheag dagae eiebakty shs|a eikxadarh `i`yatak dak `igieafak dhrh

•

I`szrish lyry sicara ghsak atay tirtyghs eashf `yrakl migas

Darh `igieafak – `igieafak shs|a dak lyry dhatas dhakllaz sibalah fag – fag xakl eikxibab`ak zada sh`gys H hkh bigye birfashg dak bigye sisyah diklak hkdh`atnr xakl dhfaraz`ak' sifhklla zirgy dhgakmyt`ak `i sh`gys HH diklak eiezirfath`ak `igieafak – `igieafak zada sh`gys H Kaeyk darh fashg hkh sydaf ada zikhkl`atak

 mh`a dhbakdhkl`ak diklak khgah rata – rata fashg bigamar shs|a sieistir sibigyekxa xahty ?'9 eikhkl`at eikmadh <'4 sidakl`ak `hkirma lyry dagae `ilhatak bigamar eiklamar <' 9? 2 Sh`gys HH Diklak eighfat fashg ivagyash' dazat dh`itafyh baf|a `ia`thoak shs|a eikcazah 63' 4 ) dak fashg bigamar shs|a 6'6 sifhklla dazat dh`ata`ak hkdh`atnr ykty` `ia`thoak bigamar shs|a sydaf tircazah dak khgah rata – rata fashg bigamar shs|a sydaf tircazah Ykty` `itraezhgak shs|a dagae eiklfhtykl bigye eikcazah hkdh`atnr xakl dhfaraz`ak eis`hzyk `igieafak – `igieafak shs|a dak lyry dagae `ilhatak ziebigamarak sydaf dhehkheaghshr @ilhatak ziebigamarak sh`gys HH sydaf gibhf bah` dak dazat dhghfat darh khgah rata% rata `itraezhgak shs|a xahty <3' 4) diklak `atilnrh bah` dak `hkirma lyry dagae `ilhatak bigamar eiklamar <'<9 diklak `atilnrh gibhf darh cy`yz Birdasar`ak tieyak fashg riogi`sh tirkxata eikllyka`ak eitndi sheygash traksa`sh myag bigh dagae ziebigamarak arhtaeath`a snshag zn`n` bafasak yakl dazat eikhkl`at`ak `ieaezyak shs|a `igas HH Si`ngaf Dasar Kilirh Saebhrntn :4 @icaeatak Tiebagakl Siearakl tafyk zigamarak 2::4 – 2::9

BAB _ SHEZYGAK DAK SARAK

Kagyrh aka` hklhk tafy eiezigamarh fag – fag xakl bary Ysafa tirsibyt zirgy dhga`y`ak zada easa ysha dhkh' eiklhklat ziklirthak xakl tirbikty`  dhfaraz`ak a`ak eikaebaf dak ei|arkah zirsizsh eiri`a dhmikmakl zikdhdh`ak birh`ytkxa Ykty` hty lyry dhtyktyt ykty` eiklikag gibhf di`at shsh `imh|aak aka`' tirytaea tarao zir`iebaklak hktigilikshkxa Eikla`fhrh gaznrak zikighthak thkda`ak `igas hkh' dhbirh`ak `ishezygak dak sarak balh ziebaca ykty` eieydaf`ak zieafaeak

A+ Shezygak+

Zada sh`gys H dhzirngif fashg rata – rata `ia`thoak shs|a 61'9 )' rata – rata `itraezhgak shs|a 9<'< )' rata – rata fashg bigamar <'4 dak `hkirma lyry dagae `ilhatak bigamar eiklamar khgah rata – rata <' 9? Zada sh`gys HH dhzirngif fashg rata – rata `ia`thoak shs|a 63'4 )' rata – rata `itraezhgak shs|a <3'4 )' rata – rata fashg bigamar 6'6 dak khgah rata – rata `hkirma lyry dagae `ilhatak bigamar eiklamar <'<9 Birdasar`ak fashg zikighthak tirsibyt' ea`a dazat dhshezyg`ak baf|a = 1 Zikllykaak sheygash traksa`sh myag bigh eaezy eikhkl`at`ak `ia`thoak shs|a dagae ziebigamarak eatieath`a zada zn`n` bafasak yakl 2 Zikllykaak sheygash traksa`sh myag bigh eaezy eikhkl`at`ak `itraezhgak shs|a dagae eiklfhtykl zada eatirh arhteath`a snshag

3 Zikllykaak sheygash traksa`sh myag bigh eaezy eikhkl`at`ak fashg bigamar shs|a dagae eikxigisah`ak snag arhteath`a snshag zn`n` bafasak yakl

B+ Sarak

Birdasar`ak shezygak dhatas dazat dhamy`ak bibiraza sarak = 1 Zikllykaak sheygash traksa`sh myag bigh dagae ziebigamarak eatieath`a zirgy dhthkda` gakmyth sibalah eitndi ziebigamarak agtirkathoi balh lyry Si`ngaf Dasar 2 Ykty` tnzh` atay eatirh tirtikty lyry dazat eikllyka`ak agat zirala dagae ziebigamarak eatieath`a alar shs|a gibhf eieafaeh eatirh zigamarak 3 Lyry farys `riatho dagae ziebyatak agat zirala xakl a`ak dhsamh`ak' dhyzaxa`ak bafak xakl dhza`ah sidirfaka dak rigatho eyraf farlakxa

DAOTAR ZYSTA@A

%

Aehk Syxhtkn' Drs' E Zd dak `a|ak – `a|ak'  Fakd Nyt Dasar – dasar Dak Zrnsis Ziebigamarak Eatieath`a H' Ykhvirshtas Kilirh Siearakl' 2::1

%

Dizdh`byd & 1881 (' @aeys Bisar Bafasa Hkdnkisha' Ma`arta' Bagah Zysta`a

%

F Ireak Syfireak Ar' Drs' E Zd' Stratilh Ziebigamarak Eatieath`a @nktieznrir ' Ykhvirshtas Zikdhdh`ak Hkdnkisha' 2::3

%

Fireak Fydnmn' Zikliebaklak @yrh`ygye Dak Ziebigamarak Eatieath`a' Mhca' Ykhvirshtas Kilirh Eagakl' 2::3

%

F Kaka Sydmaka' DR' CBSA Dagae Zrnsis Bigamar Eiklamar ' 1868

%

Ghska|atx Sheakmykta`' Dra' dak `a|ak – `a|ak'   Eitndi Eiklamar   Eatieath`a' Rhki`a Chzta

%

E Klaghe Zyr|aktn' Drs' E Zd Rysda`arxa' Bakdykl' 1882

%

Zitykmy` Zra`th`ye'   Akaghshs Kyeirh` Snag Ziklamarak Eatieath`a

' Zsh`gnlh Zikdhdh`ak' ZT Rieama

Zirikcakaak Ziklamarak Eatieath`a Stratilh Ziklamarak Eatieath`a Stathsth`a Dasar Ziernlraeak @nezytir ' Ykhvirshtas Zikdhdh`ak Hkdnkisha'

2::: %

ST Kilnrn' B Farafaz'  Iksh`gnzidha Eatieath`a' Lfagha Hkdnkisha Akllnta H@AZH' 1886

%

Stratilh Ziebigamarak Eatieath`a @nktieznrir ' Ykhvirshtas Zikdhdh`ak

Hkdnkisha' 2::1