1

qqkrw

lVI nM

jmwq ikirAw dw nwm 1 7th ਦੈਨਨਕ ਜੀਵਨ ਦੀਆਂ ਉਦਾਸਯਨਾਂ ਤੋਂ ਰਤੀਸ਼ਤ ਨਿੱਖਣਾ। 2 6th lMbweI, Bwr Aqy Awieqn dIAW iekweIAW dw pirvrqn Aqy auhnw dw ivvhwirk vrqo[

3 6th romn sMiKAw AMkW sbMDI jwxkwrI pRwpq krnw

4 6th l.s.v ( L.C.M ) dw ArQ Aqy ies dI vrqo [

5 8th rojwnw jIvn dIAW hwlqW ivc̀ m.s.v dI vrqoN krnw[

6 8th bhuq vf̀IAW sMiKAwvW nUM Gwq AMkW dI vrqoN krky imAwrI rUp ivc̀ drswauxw 7 8th vrg Aqy vrgmUl bwry jwxkwrI dyxw[ 8 6th fdZs/ j'J/ f;ZfenK d/ e[Zb w[Zb s'A f;ZfenK dh frDsh gsk eoBk.

9 6th buJwrq - 4 iltr du~D mwpxw [

10 6th ;zfynk o/yk y/v ftXh okjhA ;zg{oB ;zfynkvW dk i'V$ xNkT[ gsk ernw. 11 6th ishq kwrf [

12 8th Anupwq iviBMn hlwqW ivc̀ rwSIAW dI qulnw mdW dI vrqoN rwhIN[ 13 6th nkT[ bkG ns/ jkBh pko/ ikDhJ/.

14 8th dYink jIvn iv~c id~qy ਖੇਤਯਪਰ leI twielW dI igxqI pqw krnw [

ਰੋੜੀਦਂੀ ਭਿੱਗਯੀ-ਚਾਯਟ ,ਗਿੱਤਾ ,ਯੰਗਦਾਯ ਕੈਿੱਚ ,ੈਨਨਰ ,ਯਫੜ ,ਕੋਠੀ ਦਾ ਨਕਸ਼ਾ ਾਯਕਰ ਸ਼ੀਟ।

15 6th ਯੋਜਾਨਾ ਜੀਵਨ ਨਵਿੱਚ ਆਉਣ ਵਾਰੀਆਂ ਕਟੌਤੀ ਅਤੇ ਵੇਚ dIAW Awm smìsAwvW ਨ ੰ ਸਿੱਰ krnw ਨਿੱਖਣਾ। ਰੋੜੀਦਂੀ ਭਿੱਗਯੀ

16 6th nkT[ piko ubhJ/ dPwbt ;zfynktK dk i'V, xNkT[. 17 6th dYink jIvn ivc̀ pYtrol pMp rwhIN iekweI ivDI bwry jwxkwrI pRwpq krnw[

18 7th ;kXkoB ftnki ns/ fw;os ftnki ftZu nzso pko/ ikDekoh b?Dk.

19 8th y/v ftXh okjhA nkfeqshnK dh gfjukD eoBh. 20 8th w/b/ ftZu jZE Bkb uZbD tkb/ c'bfvzr gZy/ dh ;jkfJsk Bkb e'DK dk torheoD eoBk.

21 8th pwieQwgors isDWq dI pVqwl krnw[

22 8th y/v' ns/ f;Zy'.

23 8th :fefonK okjhA nkfJs d/ y/socb ns/ gfowkg pko/ o'ue ikDekoh.

24 8th rojwnw jIvn ivc̀ pirmwp dk ;zebg smJxw[

25 8th do vylxwkwr fìbAW dy KyqrPlW dI qulnw krnw[

26 8th o'vo'bo dIAW ivmwvW Aqy lgwey gey ck̀rW dI igxqI qoN sVk dw KyqrPl pqw krnw[

27 8th mwics dh vZph nwl pDkJ/ rJ/ ;'c/ s/ bZrD tkb/ ekri dk y/socb gsk eo'. 28 8th d' idq̀y gey ivc̀oN fe; vZp/ B{z pDkT[D bJh xZN ;wZroh br/rh <

29 8th t/bD ns/ xD d y nkfJsB dk coe gsk eoBk. 30 8th do vylxwkwr fìbAW dy AwieqnW dI qulnw krnw[

31 8th uZeo dk x/ok, ;{so C = 2𝜋𝑟 dh o'IkBk ihtB ftZu tos'. 32 8th gszr dh ouBk 33 8th fefonk okjhA x[zwdh ;wfwsh B{z ;wMDk 34 7th dohrw CVH grwP ( Double Bar Graph ) 35 6th mwfl Tos GxW dI igxqI kr skxw Aqy sUqr sQwipq kr skxw[

36 6th ibMdU AMikq kwgz (Isometric dot paper) aùqyy brwbr dUrI dy icq̀rW nUM AMikq krnw[

37 6th iksy bhuBuj dy ivkrnW dI rcnw krnw[ 38 6th d?fBe ihtB ftZu ;wfwsh dh tos'. 39 6th pypr kitMg Aqy icpkwaux dI ivDI rwhIN pVqwl krnw ik iksy vI bhuBuj dy bwhrI koxW dw joV hmySw 360 huMdw

2

jmwq-s`qvIN AiDAwie –rwSIAW dI qulnw sPw nMbr-178

ਨਕਨਯਆ:-ਦੈਨਨਕ ਜੀਵਨ ਦੀਆਂ ਉਦਾਸਯਨਾਂ ਤੋਂ ਰਤੀਸ਼ਤ ਨਿੱਖਣਾ।

ਰੋੜੀਦਂੀ ਭਿੱਗਯੀ:-ਰਾਰ ,ਕਾਰੇ ,ੀਰੇ ਅਤੇ ਨੀਰੇ ਭੋਤੀ,ਯੰਗਦਾਯ ਚਾrt,ਕੈਿੱਚ ,

ੈਨਨਰ ,ਯਫੜ ,ਰੈਭੀਨੇਸ਼ਨ ਕਵਯ ਆਨਦ। ਨਵਧੀ:- 1. ividAwrQI AwpxI stwl qy v`K-2 rMgW dy moqI Aqy Dwgy lYky bYTygw[ 2. stwl qy Awaux vwly ividAwrQI qoN puìCAw jwvygw ik auh iks qrHW dI mwlw bxvwauxw cwhMudw hY[ audwhrx dy qOr qy ਨਵਤਾ 40 ਭੋਤੀਆਂ ਵਾਰੀ ਭਾਰਾ ਫਨਾਉਣਾ ਚਾਸ ੰਦੀ ਸY[ਆਣੀ ਭਾਰਾ ਨਵਿੱਚ ਵਿੱਖ – ਵਿੱਖ ਯੰਗਾ dy ਭੋਤੀਆਂ ਦਾ ਰਮੋਗ ਕਯਦੀ ਸੈ ਨਜਵੇ:-auh cwr rMgW dy moqIAW dI mwlw ies qrW bxwauxw cwhuMdI hY ik hr rMg dy moqIAW dI igxqI brwbr hovy[

Learning Outcome:-ਨਵਨਦਆਯਥੀ ਦੈਨਨਕ ਜੀਵਨ

ਨਵਿੱਚ ਰਤੀਸ਼ਤ ਦਾ ਰਮੋਗ ਕਯਨਾ ਅਤੇ ਰਤੀਸ਼ਤ ਦੀਆਂ ਭਿੱਨਆਵਾ ਂਦ ੇਸਿੱਰ ਨ ੰ ਭਝਣ ਨਵਿੱਚ ਮੋਗ ਸੋ ਜਾਵੇਗਾ। *jykr ieko rMg dy moqIANw dI mwlw bxwauxI hovy qW moqIAW dI sMiKAW muqwibk moqIAW dI pRqISq ………hovygI [ *ividAwrQI myly ivc̀ Awauxvwly ivijtr dI mMg Anuswr v`K-2 moqIAW dI vK̀-2 igxqI Anuswr mwlw iqAwr krky pRqISq sMklp vI smJw skdy hn[ Suggestive Activities:- pMnW nM 171,172 qy idq̀IAw koiSs kro Aqy pRSn 2 dI AYktIvItI krvweI jW skdI hY[

ਯੰਗ ਭੋਤੀਆਂਦੀੰਨਖਆ ਂ ਨਬੰਨ ਰਤੀਸ਼ਤ lwl 10 10

40 25%

nIlw 10 10

40

25%

pIlw 10 1040

25%

kwlw 10 1040

25%

ਯੰਗ

ਭੋਤੀਆਂਦੀੰਨਖਆ ਂ ਨਬੰਨ ਰਤੀਸ਼ਤ

lwl 20 2040

50%

nIlw 20 2040

50%

pIlw 0 0

0%

Kwlw 0 0 0%

ਉਦਾਸਯਨ -1

audwhrx-2

3. mMn lau stwl qy Awaux vwlw ivid. cwhuMdw hY ik 40 moqIAW dI mwlw ivc̀ 2 rMg dy moqI hI pwauyxy hn Aqy moqIAW dI igxqI vI brwbr hI rK̀xI hY[

4. ies qrHW dy hor nmUny dIAW mwlw bxwaux leI vI ikhw jwvy[

3

jmwq-CyvIN AiDAwie:AwpxIAW sMiKAwvW nUM jwnxw pMnHw nM-11

ikirAw : lMbweI, Bwr Aqy Awieqn dIAW iekweIAW dw pirvrqn Aqy auhnw dw ivvhwirk vrqo[ loVINdI sm`grI : cwrt pypr , gq̀w ,skY~c pY~n, jumYtrI bwks , gUMd Awid [ ivDI:iekweIAW dI lVI nMU inmn vwk rwhI Xwd riKAw jw skdw hY [

„kwky hlvweI dI imTweI fI. sI. mMgvweI [‟ Kake Halwai Di Mithai D C Mangwai

Kilo Hecto Deca Metre Deci Centi Milli

lMbweI, Bwr Aqy Awieqn dIAW v~K-v~K iekweIAW dy sbMD nUM mwfl rwhIN smJwieAW jwvygw [ lMbweI dIAW iekweIAW (Units of length ) ieQ̀y , 1km =10 hm = 101 hm = 100 dam = 102 dam = 1000 m = 103 m =10000 dm = 104 dm = 100000 cm = 105cm =1000000 mm = 106mm iesy qrHW Bwr Aqy Awieqn dIAW iekweIAW dy pirvrqn dy leI mwfl dI vrqo kIqI jw skdI hY[

vf̀I qoN CotI iekweI dy leI hyTW vl̀ hryk hyTlI iekweI leI 10 nwl guxw Aqy CotI qoN v`fI dy leI aupr vl̀ hryk auprlI iekweI leI 10 nwl Bwg krdy hoey dUsrI iekweI pRwpq huMdI hY [ Learning Outcome: mwpx dIAW v`K-v`K iekweIAW dy pivrqn dI kuSlqw nUM hwisl krky Awm jIvn iv`c vrq skxw,ijvNy ik 1. 50 ik:gRw: nMU gRwm iv`c bdlo[ 4) Awpxy Gr dI bwltI Brn dI smrQw (lgBg) =_________ 2. 7000 sm nMU mI: iv`c bdlo[ 5) A~KW,kMn iv~c pwaux vwly dvweI dI SIsI dI smr~Qw=_____ 3. 25 lItr nMU im:lI: ivc̀ bdlo[ 6) id~lI qo muMbeI dI dUrI (lgBg)=________

KILO

METRE

÷ 10 GRAM LITRE

HECTO

METRE

÷ 10 GRAM LITRE

DECA

METRE

÷ 10 GRAM LITRE

UNIT

METRE

1 GRAM LITRE

DECI

METRE

× 10 GRAM LITRE

CENTI METRE

× 10 GRAM LITRE

MILLI METRE

× 10 GRAM LITRE

4

jmwq :CyvIN AiDAwie:sMiKAwvW nwl Kyfxw pMnw nM:29

ikirAw:- romn sMiKAw AMkW sbMDI jwxkwrI pRwpq krnw

sm̀grI:- pYnisl, Put̀w, gq̀w, kYNcI, cwt pypr, PYvIkol Awid[ ivDI:- Awau nMbr plytW dy AwKrI do AMkW nUM romn AMkW iv`c ilKx sbMDI jwxkwrI pRwpq krdy hW[ sB̀ qoN pihlW AsIN romn sMiKAw AMkW sbMDI jwxkwrI pRwpq krdy hW

I V X L C D M

1 5 10 50 100 500 1000 ies pRxwlI dy kùJ inXm ies pRkwr hn:- (i). koeI vI sMkyqk lgwqwr iqMn qoN ijAwdw vwr nhIN AwauNdw hY[ (ii). V, L Aqy D kdy vI dubwrw nhIN AwauNdy[ (iii). jykr Coty mùl vwly sMkyq vf̀y mul vwly sMkyq dy sj̀y pwsy hox qW aus vf̀y

mùl ivc̀ Coty mùl nUM joV idq̀w jWdw hY[ XI= X+I= 10+1=11

VII=V+I+I= 5+1+1=7

(iv). jykr Coty mùl vwlw koeI sMkyq vf̀y mùl vwly sMkyq dy K̀by pwsy hox qW vf̀y mùl ivc̀oN Cotw mul̀ Gtw idq̀w jWdw hY IX= X-I= 10-1=9 IV= V-I= 5-1=4

(v). V, L, D dy mulW nUM kdy vI GtwieAw nhIN jWdw[ (vi). V, L, D kdy vI sMiKAw dy K̀by pwsy nhIN AwaNdy[ (vii). I dI vrqoN kyvl V Aqy X dy Kb̀y pwsy huMdI hY[ X dI vrqoN L Aqy C dy K̀by pwsy ho skdI hY[C dI vrqoN D Aqy M dy K̀by pwsy ho skdI hY[

AwE hux ividAwrQI nwl romn AMkW vwly Kyf Kyfdy hW 1) sB̀ qoN pihlw ividAwrQIAW nUM aus dy Gr dI iksy gf̀I dw nMbr pùiCAw

jwvgw mMn lE nM: PB XX DE XX19 2) aus nMbr dy AwKrI do AMk ley jwxgy Bwv ieh AMk 19 hovygw[ 3) AiDAwpk 19 AMk nUM pihlI kqwr iv`c lgweygw[ 4) hux ividAwrQI aus dy swhmxy vwlI kqwr ivc̀ aus nUM romn sMiKAw

AMkW iv`c lgwaux leI khygw[ 5) AiDAwpk ieh ikirAw v`K v`K ividAwrQI nwl duhrweygw[

Learning Outcome:- ies ikirAw nwl ividAwrQI nUM romn sMiKAw AMk pRxwlI dI Anyk sQwnwN qy vrqo bwry jwxkwrI pRwpq hovygI ijs dI vrqoN GVIAw iv~c smW pVn,skUl dy twiem tybl iv~c jmwqw ilKx leI vI kr skdw hY[ieh pRxwlI bhuq pRwcIn pRxwlI hY[ sbMDq pRSn:- hyT ilKy AMkW nuM romn sMiKAw ivc̀ drswE: 98 ________ 73 _______ 40 _________ 92______

69 ______ 100 ________ 205 ______ 67 ______

5

jmwq :CyvIN AiDAwie:sMiKAwvW nwl Kyfxw pMnw nM-79

ikirAw : l.s.v ( L.C.M ) dw ArQ Aqy ies dI vrqo [

loVINdI sm̀grI : cwrt pypr , gq̀w ,skY~c pY~n, jumYtrI bwks ,vK̀-v`K rMgW dy moqI ,gUMd Awid [

ivDI :2,3 Aqy 4 dw l.s.v. pqw krn dy leI [

mwfl iv`c drswey 1 qoN 50 qk̀ dy KwinAw ivc̀ sMiKAW 2 dy leI hry rMg Aqy 3 dy leI lwl Aqy 4 dy leI pIly rMg dy moqIAW dI vrqo kIqI geI hY [

1. sMiKAw 2 dy guxj Kwny 2,4,6,8,10,………… 50 ivc̀ r~Ko[ 2. hux sMiKAw 3 dy guxj Kwny 3,6,9,12,………, 48 ivc̀ r`Ko[ 3. sMiKAw 4 dy guxj Kwny 4,8,12,14,…………, 48 ivc̀ r`Ko[ 4. hux auhnW KwinAW nMU lB̀o ijhnW iv`c iqMno sMiKAwvW dy guxj Awey

hox[ Kwny 12, 24, 36 Aqy 48 ivc̀ ieh iqMno sMiKAwvW dy guxj Awey hn[ ieh 2,3 Aqy 4 dy sWJy guxj hn [ iehnW iv`co sB qoN Cotw sWJw guxj 12 hY[ ies leI 2, 3 Aqy 4 dw l.s.v ( Lowest common multiple ) 12 hovygw [

ividAwrQI nUM rojwnw jIvn ivc̀ l.s.v dI vrqoN hyT ilKI audwhrx rwhIN smJweI jw skdI hY[

“iqMn Al̀g-A~lg cOrwihAW dI tRyYiPk lweIt kRmvwr 20 sYikMf,30 syYikMf Aqy 40 sYikMf bwAd bdldI hY [ jykr auh ie`ko vyly svyry 7 vjy bdlx,qW auh dubwrw iek̀o smyN kdo bdlxgIAW ? ” pihlI lweIt dy blx dy smyN dw kRm = 20,40,60,80,100,120,140,160,180,200,220,240,…… dUsrI lweIt dy blx dy smyN dw kRm = 30 ,60,90,120,150,180,210,240,270,300,…………… qIsrI lweIt dy blx dy smyN dw kRm = 40 ,80,120,160,200,240,280,320,360,400,…………… sB qoN Cotw swJW guxj 120 sYikMf hY [loVINdw smW: 120 60=2 imMt

ies leI iqMno lweItW svyry 7:02 vjy dubwrw ie`ko smyN bdlxgIAW [

Learning Outcome: lGUqm smwpvrqX dw ArQ smJxw Aqy ies dI Awm jIvn iv`c vrqNo kr skxw [

sbMDq pRSn:-svyr dI sYr leI,iqMn ivAkqI ie`k vyly pYr auTw ky clxw

SurU krdy hn[auhnW dy kdmW dIAW lMbweIAW kRmvwr 80 sm,85 sm Aqy

90 sm hn[iehnW ivc̀oN hryk inaUnqm ikMnI dUrI cly ik auh ausnMU pUry-pUry

kdmW ivc̀ qYA krn?

6

jmwq: CyvIN AiDAwie:sMiKAwvW nwl Kyfxw pMnw nM-79

ikirAw :rojwnw jIvn dIAW hwlqW ivc̀ m.s.v dI vrqoN krnw[

ivDI :4 Aqy 6 dy m.s.v qoN pihlW 4 Aqy 6 dy guxnKMf dw ArQ ikirAw rwhIN ds̀y jwxgy [

6 dy guxnKMf

sMiKAw 6 : 1 nwl BwjXog hY, 2 nwl BwjXog hY,3 nwl BwjXog hY Aqy 6 nwl BwjXog hY[

qW 6 dy guxnKMf 1,2,3,Aqy 6 hn[

iesy qrWH 4 dy guxnKMf 1, 2 Aqy 4 hn[

4 Aqy 6 dy sWJy guxnKMf = 1 Aqy 2 hn[

pr iehnW ivc̀o sB qo v`fw sWJw guxnKMf 2 hY [

ies leI,4 Aqy 6 dw m.s.v (HCF)= 2 hovygw [

(Bwv vf̀I qoN vf̀I sMiKAw jo 4 Aqy 6 nMU pUrw-pUrw vMfy ,2 hY[)

Learning Outcome: 1. ividAwrQI nUM dsWgy ik rojwnw jIvn ivc̀ inmn hlwqW ivc̀ swnMU

m.s.v. k`Fx dI loV hY[ sbMDq pRSn: 1. ie`k hwl kmry dy PrS dI lMbweI 42 mI. Aqy cOVweI 30 mI.

hY[ Aijhw sB qoN lMbw &Iqw (Tape) pqw kro jo PrS dIAW donW ivmwvW (Dimensions) nMU pUrw-pUrw mwp lvy [ 42mI Aqy 30mI dw m.s.v.pqw krnw pvygw[ ies qrHW ah loVINdy PIqy dw mwp pRwpq krygw[

2. iqMn tYNkrW ivc̀ kRmvwr 403 iltr, 434 iltr Aqy 465 iltr fIzl hY, aus brqn dI AiDkqm sm̀rQw pqw kro jo iehnW iqMnW tYNkrW dy fIzl nUM pUrw mwp dyvygw[ ieQy brqn dI AiDkqm sm̀rQw leI 403 iltr, 434 iltr Aqy 465 iltr dw m.s.v.pqw krnw hovygw[

7

jmwq :A~TvIN AiDAwie: Gwq AMk Aqy Gwq pMnHw nM :206

ikirAw: bhuq vf̀IAW sMiKAwvW nUM Gwq AMkW dI vrqoN krky imAwrI rUp ivc̀ drswauxw Aqy bhuq vf̀IAW sMiKAwvW Aqy bhuq CotIAW sMiKAwvW dI qulnw

1) sUrj dw ivAws= 14,00,000,000 mI=1.4×109mI

sUrj dw ArD ivAws= ??

ipRQvI dw ivAws=12756000=1.2756×107mI

ipRQvI dw ArDivAws= ??

jy AsIN sUrj dy ivAws Aqy ipRQvI dy ivAws dI qulnw krIey

qW sUrj dw ivAws ipRQvI dy ivAws dw lgBg sO guxw hY[

2) lwl KUn koiSkwvW dw mwp= 0.000007 im.mI. =7×10-6im.mI.

pOidAW dIAW koiSkwvW dw Awkwr=0.00001275im.mI.

=1.275×10-5 im.mI.

qulnw = = = = (lgBg)

3) sUrj qoN ipRQvI dI dUrI= 1.496×1011 mI

ipRQvI Aqy cMdrmw dy iv`c dI dUrI= 3.84× mI

gRihx vyly cMdrmw ipRQvI Aqy sUrj dy ivc̀ Aw jWdw hY[

cMdrmw Aqy sUrj dy ivclI dUrI = 1.496× -3.84×

= 1.496×100 -3.84×

=(1496-3.84) =1492.16×108mI:

pRSn:- jy quhwfI ikqwb dI motweI 24 immI hY Aqy 1 pMnHy dI motweI 0.016 immI hY qW ds̀o ikqwb dy ikMny pMny hoxgy? Learning Outcome:-bhuq vf̀IAW sMiKAwvW nMU Gwq AMkW dI vrqoN krky imAwrI rUp iv`c Aqy imAwrI rUp nUM bhuq vf̀IAW sMiKAw ivc̀ bdl skx dy Xog ho jwvygw[ sbMDq pRSn:-hyT ilKIAW sMiKAwvW nMU imAwrI rUp ivc̀ drswau Aqy Awly duAwly iv~c AijhIAW sMiKAwvW lB̀o (i) 0.0000000000085 =______________ (iii) 602000000000000 =_______________ (ii) 3186000000 =_______________ (iv) 0.00000000837=________________

8

jmwq:AT̀vIN AiDAwie: vrg Aqy vrgmUl pMnw nM: 116 ikirAw : vrg Aqy vrgmUl bwry jwxkwrI dyxw[ loVINdI sm̀grI : bMty, ijau borf Awid[ pRSn:myry kol 30 bMty hn[ mYN ieh bMty ies qrHW rKxy cwhuMdI hW ik kqwrW dI sMiKAwAqy hryk kqwr iv`c bMitAW dI sMiKAw brwbr hovy Bwv bMitAW dI sMiKAW nwl ie`k vrg bx jwvygw[ ies qrHw krn leI ikMnHy bMty myry kol PwlqU hn[

1. jIau borf lE[ 2. 30 bMty lE[ 3. hux ividAwrQI nUM kho ik ikauNik kqwrW dI sMiKAw Aqy hryk kqwr

ivc̀ bMitAw dI sMiKAw brwbr hY ies leI ieh vrg bxygw[ 4. iek̀ kqwr ivc̀ 2 bMty rK̀o,nwl hI do kwlmW ivc̀ bMitAW dI sMiKAW

nMU 2 kro Bwv 2x2 vrg bx jwvygw[ieQ̀y 4 bMty vrqy gey[ 5. iesy pRkwr 3x3 vrg bxwE[ 6. ies qoN bwAd 4x4 vrg bxwE, hux vI 14 bMty bcdy hn[ 7. jdoN 5x5 dw vrg bxw lvygw qW aus kol 5 bMty bc jwxgy prMqU

iehnW nMU iksy vI qrqIb ivc̀ r~Kx qy vrg nhIN bxygw[ 8. aus kol 5 bMty PwlqU hn[ies qrW 30 iek̀ vrg sMiKAw nhIN hY[

ies ikirAw nMU krn auprMq ividAwrQI nMU sMiKAwvW dy vrg Aqy vrgmUl dovW bwry jwxkwrI iml jwvygI[vrg auh sMiKAw huMdIAW hn ijhnW nMU ieko ijhIAw sMiKAwvW dy guxnPl dy rUp ivc̀ drswieAw jw skdw hY[ijvyN joV dI ikirAw dy ault Gtwauxw huMdw hY,iesy qrW guxw dy ault ikirAw Bwg hY[iesy qrHW vrgmUl pRwpq krnw vI vrg dI ault ikirAw hY[ ikirAw: sMiKAwvW dw Gx pqw krnw[ ivDI: AsI jwxdy hW ik “Gx” Sbd dw pRXog ryKw gixq ivc̀ kIqw jwWdw hY ,Gx iek ies qrwH dI Tos icq̀r hY ijs dIAW swrIAW BujwvW brwbr huMdIAw hn[iek iekweI Bujw vwly ikMny Gxw nwl do iekweI Bujw vwlw iek Gx bxygw[ mMn lE swfy kol 8 Gx , 1 iekweI Bujw vwly Gx hn[ ienHW dI inmn Anuswr qrqIb krn qy 1 pUrn Gx iqAwr huMdw hY[ ijs dy iknwry dI lMbweI 2 ieMc pRwpq huMdI hY[ ku~l GxW dI sMiKAW =lMbweI Anuswr GxW dI sMiKAW × cOVweI Anuswr GxW dI sMiKAW × aucweI Anuswr GxW dI sMiKAW Bwv 8 = 2×2 ×2 ies leI , ies nMU AsI 8 = 23 ilK skdy hW[ iesy qrHW, 3 iekweI dy Gx ivc̀ =3×3×3 = 27 Gx, ie`k iekweI vwly pRwpq hoxgy [

Aqy 4 iekweI dy Gx iv`c = 4×4×4 = 64 Gx, ie`k iekweI vwly pRwpq hoxgy [ Aqy 5 iekweI dy Gx ivc̀ = 5×5×5 = 125 Gx, ie`k iekweI vwly pRwpq hoxgy ……………………………………………………………………… Learning Outcome: 1. ividAwrQI smJ skxgy ik hY iek̀ pRwikiqk sMiKAw m nU n2 nwl drSwieAw jWdw hY ieQy n ie`kpRwikiqk sMiKAw hY Aqy m ie`k vrg sMiKAw hY[ 2. ies qrHW ividAwrQI smJ skxgy ik iksy sMiKAW dw Gx sMiKAW nMU ausy sMiKAW nwl iqMn vwr guxw krn qy

pRwpq huMdw hY[ not:- myly ivc̀ ikqwb dw pMnw nM. 102 qy drswey gey vrg sMiKAwvW dy kùJ hor pYtrn vI drsw skdw hY, qW jo ividAwrQI iehnW qoN pirp~k ho jwx[

9

iwks L^ nZmthA nfXnkfJ L fJZe uZb tkb/ o/yh ;wheoD gzBk BzL 30

fefonk L^ fdZs/ j'J/ f;ZfenK d/ e[Zb w[Zb s'A f;ZfenK dh frDsh gsk eoBk.

loVINdI sm̀grI :vK̀-vK̀ mùlW (1ru:, 2ru:, 5ru:, 10ru:) dy isk̀y, gq̀w,rMgIn kwgz Awid[

gqPB L^ pz;h d/ e'b e[M f;Ze/ 2 o[gJ/ tkb/ ns/ e[M 5 o[gJ/ tkb/ jB.

i/eo 2 o[gJ/ tkb/ f;ZfenK / dh ;zfynk 5 o[gJ/ tkb/ f;ZfenK dh ;zfynk dh

fszB r[Dk j? ns/ T[jBK d/ w[ZbK dk e[Zb i'V 77 o[gJ/ j? sK d'B'A soQK d/

f;ZfenK dh ;zfynk gsk eo'.

ftXh L^ 5 o[gJ/ tkb/ ns/ 2 o[gJ/ tkb/ f;ZfenK dh nbZr^nbZr Y/ohnK

pDkT[.wzB bt' fe pz;h d/ e'b 5 o[gJ/ tkb/ f;ZfenK dh ;zfynk x j?.

sK 2 o[gJ/ tkb/ f;ZfenK dI ;zfynk &3x

fJ; bJh 5 tkb/ x f;ZfenK dk w[Zb & 5%x = 5x o[gJ/

2 tkb/ 3x f;ZfenK dk w[Zb & 2% 3x = 6x o[gJ/

j[D e[Zb w[Zb & 77 o[gJ/

5x+6x = 77 o[gJ/

11x = 77 o[gJ/

X=7

5 o[gJ/ tkb/ f;ZfenK dh ;zfynk &x=7

2 o[gJ/ tkb/ f;ZfenK dh ;zfynk &3x=21

gqPB L^ i/eo s[jkv/ e'b e[ZM B'N 10 o[gJ/ tkb/ ns/ e[ZM B'N 50 o[gJ/

tkb/ j'D ns/ 10 o[gJ/ tkb/ B'N gzikj o[gJ/ tkb/ B'NK dh ;zfynk dk

uko r[Dk j'D ns/ T[jBK d/ w[ZbK dk e[Zb i'V 900 o[gJ/ j't/ sK d'B' soQK d/ B'NK dh ;zfynk gsk eo'.

not:-ies nwl sMbMDq audwhrx 11 Aqy pRSn 14,15 ikirAwvW rwhIN myly ivc̀ krvwey jw skdy hn[

learning outcome L^ ftfdnkoEh fdZs/ rJ/ Pkpfde gqPB s'A ryKI ;wheoD pDkT[D d/ :'r j' ikDr/.ns/ T[;B{z jZb eo ;eDr/.bYNkw iv`c isk̀y igxn vwlIAW mSInW AsIN Awm dyK skdy hW

10

ikirAw : buJwrq - 4 iltr du~D mwpxw [ ivDI :h̀l kro qW mMnIey ! “ie`k idn Gr ivc̀ jykr quhwfy kol 5 iltr Aqy 3 iltr dy mwp dy hI j~g hox Aqy koeI hor mwp vwlw brqn nW hovy [ rojwnw dI qrHW Aj̀ vI quhwfw guAWFI 4 iltr dùD lYx AwieAw hY[qusIN aus nMU 4 iltr du~D mwp ky dyxw hY[ iks qrWH ieh mwpogy ?” iek̀ hl̀ : 1.pihlw 3 iltr vwly jg̀ nUM pUrw Bro Aqy ies nUM 5 iltr vwly jg̀ iv`c pwE [

2. 3 iltr vwly j~g nMU du~D nwl Bro Aqy pihly qoN 3 iltr Bry 5 iltr jg̀ nMU Brn dI koiSs kro [

3. 5 iltr vwlw jg̀ pUrw Br jwvy gw Aqy 3 iltr vwly j~g ivc̀ 1 iltr dùD bwkI rih jwvygw[ 4. hux Bry hoey 5 iltr vwly j~g nUM KwlI kr dyvo Aqy 3 iltr vwly jg̀ ivc̀ mojUd 1 iltr nMU , 5 iltr vwly jg̀ iv`c Bro [

4. hux iPr 3 iltr vwly jg̀ nUM d`uD nwl Bro Aqy ies nMU 5 iltr vwly jg̀ iv`c Bro [ijs iv`c pihlW qoN hI 1 iltr d̀uD hY [ ies qrwH 5 iltr jg̀ iv`c 1iltr + 3 iltr = 4 iltr du~D ho jwvygw [

iesy qrwH hor keI qrIky hn , lB̀o....... Learnig Outcome :ividAwrQIAW dI mwnisk Xogqw dw ivkws Kyf-Kyf ivDI rwhIN kr skxw [

11

P/qDh ^ 6thA nfXnkfJ^;zg{oB ;zfynktK ;ck BzL136 fefonk L^ ;zfynk o/yk y/v ftXh okjhA ;zg{oB ;zfynkvW dk i'V$ xNkT[ gsk ernw. ;wZroh L^ukoN g/go, ;e?ug?B, ozrhB N/g, eN'ok, Bzpo gouhnK. ftXh L^ fJ; fefonk okjhA n;hA pZfunK B{z ;zfynK o/yk okjhA ;zg{oB ;zfynktK

d/ i'V ;pzXh dZ; ;ed/ jK.fJe eN'o/ ftZu XBkswe ns/ foDkswe ;zfynktK

dh pouhnK gktkr/A.pZuk fJ; ftZu'A e'Jh d' gouhnK eZY/rk ns/ T[;B{z iwk eo

;edk j?.wzB bT[ pZu/ B/ d' youhnK O 3 ns/ ^4 eZYdk j? ns/ fJ;B{z i'VBk

j? gfjb/ n;h 0 s'A ;Zi/ gks/ 3 ;N?g nZr/ iktkr/A.fco ^4 bJh 4 ;N?g yZp/

gk;/ iktkr/A j[D fJ; soQK T[j ^1 d/ o[e/rk.fJ; soQK pZuk T[Zso gqkgs eo/rk

wzB bT[ pZuk ^2 ns/ ^3 dh gouh eZYdk j?.j[D fco T[j yZp/ gk;/ tZb 3

;N?g ub/rk.fJ; soQK T[j ^5 d/ o[e/rk.i' fe T[Zso j?.fJ; fefonK okjhA ftfdnkoEh ;zg{oB ;zfynktK dh s[bBk th

eo ;edk j?. fJ; bJh n;hA dZ; ;ed/ jK d' ;zfynktK B{z ;zfynk o/yk s/ d/y e/ fijVh ;zfynk s[jkv/ ;Zi/ gk;/ j?

T[j tZvh j't/rh rh fit/A ^2 ns/ ^1 ftZu ^1 ;Zi/ gk;/ j? fJ; bJh T[j tZvh j?. fJ;/ soQK 5

ns/ 7 ftZu 7 ;Zi/ gk;/ j?.T[j tZvh j?.

hyT ilKy pRSn h̀l kro:-

(1) (^3)O (2) & ……… (2) 2 O (^5) =……

(3) (^7) O 4 =………… (4) (^3)O (^4) =…… pRSn: somvwr nUM SRI ngr dw qwpmwn -5 ⁰C sI Aqy mMglvwr nUM 2 ⁰C G~t igAw [ mMglvwr nUM SRIngr dw qwpmwn ikMnw sI? bu~Dvwr nUM qwpmwn 4 ⁰C v~D igAw, bùDvwr nUM SRIngr dw qwpmwn ikMnw sI? ividAwrQI ies mwfl rwhIN d~s skdw hY[

fefonkL(T[go ns/ j/mK ikDk) j/mK fdZs/ gqPB dk T[Zso d/t' ns/ T[Zso B{z ;zg{oB ;zfynktK d/ o{g ftZu fby'<

1) iwhB s'A 6 g'VhnK T[Zgo uZb'. 2) iwhB s'A 3 g'VhnK j/mK uZb'. 3) iwhB s'A 4 g'VhnK T[go ns/ fco T[E' 3 g'VhnK j'o

T[go uZb'. 4) iwhB s'A 3 g'VhnK T[go c/o T[ZE' 6 g'VhnK j/mK uZb'. Learning Outcome: L^ ;zg{oB ;zfynktK Bkb ;pzXs i'V ns/ xNkT[ d/ ;tkb B{z jZb eoB :'r j' ikt/rk.

12

jmwq : CyvIN AiDAwie-Anupwq Aqy smwn-Anupwq pMnw nM :303 ikirAw : ishq kwrf [ ikirAw : rojwnW jIvn ivc̀ gixq dy mwpW dI ishq kwrf ivc̀ vrqoN[ ivDI : ividAwrQI stwl ivc̀ Awey ivAkqI bwry inmn drswey kwrf Anuswr AMkVy ie`kTy krygw: 1.ividAwrQI jnm imqI pu~Cygw Aqy aus dI vrqmwn aumr nUM swl ,mhIny Aqy idnW ivc̀ kwrf ivc̀ drj krygw [

2.ividAwrQI AYktIivtI cwrt (iksy vI imqI dw idn pqw krnw) rwhIN jnm imqI dw idn l~B ky kwrf ivc̀ drj krygw audwhrx :jnm imqI : 08.10.1975 dy idn dy leI

102 ‹ 7 = 14 × 7 + 4 bwkI 4 DAY CODE sUcI iv`c “ bu~Dvwr” hY [ 1. ividAwrQI k~d Aqy Bwr nMU mwpdy hoey ivAkqI dw irkwrf kwrf ivc̀ drz krygw [ 2. ividAwrQI 1 Pùt lMbweI leI ivAkqI dI ( ig`T dI lMbweI + auNglW dI sMiKAw ) dw mwpk bxw ky

ds̀ygw qW ik aus duAwrw BivK̀ iv`c̀ srIrk pYmwny dw pRXog CotIAW lMbweIAW dw AMdwjn mwp krn ivc̀ ho sky [

3. ividAwrQI Awey ivAkqI dy pYr dw mwp krky aus dy pYr dw mwp sYmI ivc̀ ,UK ,US,EU Aqy ieMcW „c drj krygw[

Learning Outcome: ividAwrQI Bwr Aqy lMbweI dIAW iekweIAW, mwpx dy qrIky Aqy kYlMfr ivDI rwhIN past jW future ivc̀ idq̀I hoeI iksy vI imqI dy idn dw pqw lgw skdy hn[

idn mhInw kof

sdI dw kof

swl dy AwKrI do AMk

swl dy AwKrI do AMk „c lIp swlw dI igxqI

kul joV

08 + 1 + 0 + 75 + 18 =

102

13

jmwq: CyvIN AiDAwie- Anupwq Aqy smwn Anupwq pMnw nM: 290

ikirAw :- Anupwq iviBMn hlwqW ivc̀ rwSIAW dI qulnw mdW dI vrqoN rwhIN[

sm̀grI- cwrt pypr, skYc pYn, rMgIn typ[ ivDI:-ies ikirAw rwhIN AsIN b`icAW nUM Anupwq Aqy smwn Anupwq bwry jwxkwrI dy skdy hW[ ies ikirAw rwhIN AsIN bìcAW nUM PlW dI dukwn qy KrIddwrI krn dw ivvhwirk igAwn vI dy skdy hW[ ies ikirAW rwhIN bc̀w ieh jwnx iv`c smrQ ho jweygw ik jykr 12 kyly dw mul̀ 50 rupey hY qW v`K vK̀ kyilAW dI igxqI dw mul̀ kI hoeygw? audwhrx dy rUp iv`c iek̀ ividAwrQI stwl qy AwauNdw hY Aqy ausnUM 12 kyilAW dw mùl dìsAw jWdw hY Aqy aus qoN pùiCAw jWdw hY ik ausny ikMnHy kyly KrIdxy hn, jy auh kihMdw hY ik aus ny 36 kyly KrIdxy hn qW ausnUM pt̀I(slide) nUM a`upr Q̀ly kr ky Kb̀y Kwny ivc̀ 36 qy ilAwaux leI ikhw jWdw hY Aqy jo sMiKAw sj̀y Kwny ivc̀ AwauNdI hY auh not krn leI ikhw jWdw hY jo ik 36 kyilAW dw mùl hovygw[ividAwrQI dyKdy hn ik kyilAW dI igxqI vD̀x nwl ,dukwndwr nMU ijAwdw kImq pYNdI hY[ieh ie`k isD̀y Anupwq dI audwhrx hY[ 1) ie`k hor ividAwrQI AwauNdw hY Aqy auh kihMdw hY ik ausny 30 kyly KrIdny hn[ ausnUM vI pt̀I auq̀y-Ql̀y kr ky Kb̀y Kwny iv`c 30 ilAwaux leI ikhw jWdw hY[ jo sMiKAw s`jy Kwxy iv`c hovygI auh 30 kyilAW dw mul̀ hovygw[ 2) ausy qrHW stwl qy Awaux vwly ivid. nUM puiCAw jw skdw hY ik iksy Kws

rwSI nwl KrIdy jwx vwly kyilAW dI igxqI ds̀o[

Learning Outcome:-ies nwl ividAwrQI nUM v`K-vK̀ vsqUAW Aqy kImqW dy Anupwq sbMDI jwxkwrI pRwpq kr lYxgy Aqy auhnW nwl sbMDq smwnupwq vI h̀l krx Xog ho jwxgy[ sbMDq pRSn: a) 12 kyilAW dw mul̀ 50 rupey hY qW 24 kyilAW dw mul̀= _________ , 20 kyilAW dw mùl= __________

A) ie`k kmry dy PrS dI lMbweI 30 mItr Aqy coVweI 20 mItr hY[ kmry dI lMbweI Aqy cOVweI nwl Anupwq pqw kro[kI qusIN kwgz dw ie`k Aijhw Awieqwkwr tukVw k`t skdy ho joik ies kmry dy PrS dy smwn AnupwqI hovy[

Suggestive Activities:-pMnw nM 175 aupr idqy pRSn muqwibk PUrt tokrI bxwky vistor nMU dy skdw ho jykr tokrI ivc 50% syb Aqy 30% sMqry hox qW ikMny % AMb lYx qW jo 100% pRqISq bx jwvy jW PrUt tokrI iksy vI Anupwq iv~c ijvy ik v~K v~K Pl AMb ,syb ,kyly 3:2:1 Anupwq ivc lYxy hn Aqy jykr kul 30 PrUt lYxy hn qW ikMny ikMny AMb ,syb ,kyly hoxgy ? ies qrHW dIAW hor ikirAwvW vI myly ivc̀ krvweIAW jw skdIAW hn[

14

ebk; nZmthA nfXnkfJ ^ rwSIAW dI qulnw ;ck BzL 132

fefonk L^ nkT[ bkG ns/ jkBh pko/ ikDhJ/. ;wZroh L^ ukoN, rZsk, g?B, iKfOxw eko nkfd. ftXh L^ 1H skUl dy mYQ myly iv`c mYN iek̀ KuSiksmq ifp ( kUpx) dw stwl lgwaux jw rhI hW [ ie`k KuSiksmq ifp leI mYN 10 ru: vsUl krWgI pr mYN dyx leI ies qrHW dIAW vsquAW KrIdWgI ijnHW dI kImq 5 ru: hY[ ies qrHW mYN100% lwB kmw rhI hW[( hY nw kmwl dI gl̀! ) 2. mMn lau mYN 12 ;e?u g?BK d y yohd w[Zb nUM 7 ;e?u g?BK d/ t/uw[Zb d/ pokpo rK̀xw cwhuMdI hW qW mYnUM iknMw bkG # iK jkBh # hovygI.(stwl 1)

12 ;e?u g?BK dk yohd w[Zb& 7 ;e?u g?BK dk t/uw[Zb & 12 o[gJ/ fJ; bJh fJe ;e?u g?B dk t/uw[Zb & o[gJ/

bkG & 5 ;e?u g?BK dk t/uw[Zb & 5% & o[gJ/

bkG# & bkG$yohd w[Zb %100 & ( % 100)# & # & 71 #

3. stwl -2 leI mYN 40 ru: drzn cUVIAW KrIdIAW Aqy 1 drzn cUVIAW dI kImq 50 ru:rK̀ ky vycIAW[ jykr qusIN 5 drjn cUVIAW KrIdIAW hn qW mYN 15% Cot idAWgI[mYnUM iknMw bkG # iK jkBh # hovygI.( stwl-2) 4H ;shS fJZe g[okBh yokp eko 73500 o[gJ/ dh yohddk j?.T[; dh w[ozws s/ 10300 o[gJ/ ns/ T[;dh fJB;'o?A; 2600 o[gJ/ brkT[Adk j?.fco T[; B{z 84240 o[gJ/ ftZu t/u fdzdk j?.T[; dw bkG # iK jkBh # gsk eo'.

yokp eko dk yqhdw[Zb w[ozws dk you fJzB;'o?AP dk you

w[ozws dw Krcw, ieMnsorYNs vrgy Krcy nUM auprly Krcy vI AwKdy hn e[Zb yohd w[Zb & 73500O10300O2600& 86400 o[gJ/ mhe eko dk t/uw[Zb & 84240 o[gJ/,i/eo yohd w[Zb t/uw[Zb sK jkBh j't/rh ies qrHW SqIS nUM 86400^84240 & 2160 o[gJ/ dI hwnI ho rhI hY[

jkBh # & %100 & # & 2 #

5. myly ivc̀ AijhIAW hor vsquAW rK̀ ky stwl qy Awaux vwly ividArQIAW leI Aijhy hor pRSn vI iqAwr kIqy jw skdy hn[

Learning Outcome:1.ividAwrQI dYink jIvn dIAW prsiQqIAW ivc̀ lwB jW hwnI hox bwry Anumwn lgw

skdy hn[

2. ividAwrQI lwB% jW hwnI % pqw krn dy Xog ho jwxgy[

& 73500 & 10300 &2600

stwl-1

stwl-2

15

jmwq-CyvIN AiDAwie – pirmwp Aqy KyqrPl sPw nM- 258 ਨਕਨਯਆ:- dYink jIvn iv~c id~qy ਖੇਤਯਪਰ leI twielW dI igxqI pqw krnw jykr twielW dw Akwr pqw hovy[ ਰੋੜੀਦਂੀ ਭਿੱਗਯੀ-ਚਾਯਟ ,ਗਿੱਤਾ ,ਯੰਗਦਾਯ ਕੈਿੱਚ ,ੈਨਨਰ ,ਯਫੜ ,ਕੋਠੀ ਦਾ ਨਕਸ਼ਾ ਾਯਕਰ ਸ਼ੀਟ। ਵਿਧੀ -:ਇੱਕ ਕਠੀ ਦਾ ਨਕਸ਼ਾ ਲਿ ,ਵਿਸਦ ਕਭਰ ਦ ਪਰਸ਼ਾ ਦੀਆ ਂਬੁਿਾਿਾਂ pqw hox[ ਵ ੱਤਰ ਅਨੁਸਾਰ ਵਿਿੇਂ ਇੱਕ ਲਾੱਫੀ ਦ ਪਰਸ਼ ਿ ਵਕ ਆਇਤਾਕਾਰ ਹ ਵਿਸ ਦੀਆ ਂਬੁਿਾਿਾਂ 30Put ×20 Put ਹਨ (lMbweI 30 Put̀ Aqy cOVweI Pùt ਇਸ ਪਰਸ਼ ਤ 10Put ×5 Put‟ਅਕਾਰ ਦੀਆ ਂਟਾਈਲਾਂ ਲਗਾਉਣੀਆ ਂਹਨ ਿ ਵਕ ਆਇਤਾਕਾਰ ਅਕਾਰ ਦੀਆਂ ਹਨ।ਇੱਥ ਪਰਸ਼ ਤ ਲੱਗਣ ਿਾਲੀਆਂ ਟਾਈਲਾਂ ਦੀ ਵਗਣਤੀ ਤਾ ਕਰਨ ਲਈ ਵਿਵਦਆਰਥੀ ਹਠ ਵਲਖ ਪਾਰਭੂਲ ਦੀ ਿਰਤੋਂ ਕਰਗਾ:-

ਟਾਈਰਾ ਂਦੀ ਨਗਣਤੀ= = = = 12

ਇ ਰਈ ਪਯਸ਼ ਤ ੇਰਿੱਗਣ ਵਾਰੀਆਂ ਟਾਈਰਾ ਂਦੀ ਨਗਣਤੀ 12 ਸੈ।

ਨਚਿੱਤਯ ਅਨ ਾਯ ਇ ੇਤਯਾ ਅੀ ਡਯਾਇੰਗ ਯ ਭ ਨਵਿੱਚ ਨੀਰੀਆਂ ਟਾਈਰਾਂ (7’ x 6’ Aਕਾਯ)ਫੈਡਯ ਭ-1 ਨਵਿੱਚ 8’ x 6’ ਅਕਾਯ ਅਤ ੇਫੈਡਯ ਭ- 2 ਨਵਿੱਚ 7’ x 2’ ਅਕਾਯ ਦੀਆਂ ਸਯੀਆਂ ਟਾਈਰਾ ਂਦੀ ਨਗਣਤੀ ਤਾ ਕਯ ਰਵਾਂਗੇ। ies qrW myly ivc̀ idq̀y gey vK̀-2 KyqrPlW leI twielW lgvwaux leI loVINdI twielW dI igxqI ds̀Wgy ijvyN hI twiel dw Akwr bdlygw qW idq̀y KyqrPl ivc̀ twielW dI igxqI vD̀ Gt̀ skdI hY[ sbMDq pRSn: 1)p'ph 3 whNo u"VkJh ns/ 4 whNo bzpkJh tkb/ fJZe ewo/ ftZu torkeko NkJhbK brkT[Dk ukj[zdk j?.i/eo jo/e torkeko NkfJb dh G[ik 0H5 whNo j't/ sK ewo/ d/ coP B{z YZeD bJh fezBhnK NkJhbK dh b'V gt/rh< (jmwq 6vIN pyz 258 audwhrn-16) 2)coP pBkT[D d/ bJh T[g:'r ehsh ikD tkbh fJZe NkJhb dk neko ;wKso usoG[I dk j? fi;dk nXko 24 ;w ns/ fJ; dh ;zrs T[ukJh 10 ;w j?.1080 tor whNo y/socb d/ fJZe coP B{z YZeD d/ bJh fezBhnK NkJhbK dh io{os j?< (coP dhnK B[ZeoK B{z YZeD d/ bJh s[;h NkJhbK B{z b'V nB[;ko fe;/ th o{g ftZu s'V ;ed/ j') (jmwq 8vIN pyz 179 pRSn 4) Learning Outcome:-ਇ ਨਕਨਯਆ ਯਾਸੀ ਨਵਨਦਆਯਥੀ ਕੋਠੀ ਦੇ ਨਕਸ਼ੇ ਨ ੰ ੜਨਾ ,ਟਾਈਰਾ ਂਦੀ ਨਗਣਤੀ ਅਤੇ ਉਸਨਾ ਂਤੇ ਸੋਣ ਵਾਰੇ ਖਯਚ ੇਫਾਯ ੇ,ਨਿੱਖਣ ਦੇ ਮੋਗ ਸੋ ਜਾਣਗੇ।

16

jmwq-AT̀vIN AiDAwie – rwSIAW dI qulnw sPw nMbr -129

ਨਕਨਯਆ:-ਨਕਨਯਆ ਯਾਸੀ ਯੋਜਾਨਾ ਜੀਵਨ ਨਵਿੱਚ ਆਉਣ ਵਾਰੀਆਂ ਕਟੌਤੀ ਅਤੇ ਵੇਚ mul̀ dIAW Awm sm̀isAwvW ਨ ੰ ਸਿੱਰ ਕਯਨ ਫਾਯ ੇਨਿੱਖਣਾ। ਰੋੜੀਦਂੀ ਭਿੱਗਯੀ:-ਗਿੱਤਾ ,ਯੰਗਦਾਯ ਚਾਯਟ ,ਯੰਗਦਾਯ ਕੈਚ ,ੈਨਨਰ ,ਯਫੜ ਨਵਧੀ:- ktOqI: AMikq mùl jW sUcI mul̀ qy Cot dyky jdoN mwl vyicAw jWdw hY qW idq̀I Cot nUM ktOqI kihMdy hn[ 1. ਇਿੱਕ ਭੈਗਾ ਭਾਯਟ ਨਵਿੱਚ ਇਿੱਕ ਫ ਟੀਕ ਦੀ ਦ ਕਾਨ ਸੈ ,ਇ ਨਵਿੱਚ ਕ ਰ ਦੀਆਂ ਕ ੜੀਆਂ ਜਾਂਦੀਆਂ ਸਨ ਅਤ ੇਉਿੱਥ ੇ ੰਦਯ - ੰਦਯ ਪਯਾਕਾ ਂਨ ੰ ਵੇਖਦੀਆਂ ਸਨ। ਪਯਾਕਾਂ ਦੇ ਵਿੱਖਯ–ੇਵਿੱਖਯ ੇਯੇਟ ਅਤੇ ਕਟੌਤੀ % ਨ ੰ ਦੇਖਕੇ ਵਧੀਆ ਅਤ ੇਤੀ ਪਯਾਕ ਰੈਣ ਫਾਯ ੇਇਿੱਕ ਦ ਜੀ ਨਾਰ ਰਾਸ ਕਯਦੀਆਂ

ਸਨ।

2. iehnW PrwkW iv`coN ie`k Prwk dw AMikq mul̀ 450 ru: hY ijs aup̀r ktOqI 30% hY , dUjI Prwk dw AMikq mùl 300 ru: hY ijs aup̀r ktOqI 20% hY Aqy qIjI Prwk dw AMikq mul̀ 200 ru: hY ijs aup̀r ktOqI 15 % hY[iehnW ivc̀oN iek̀ kuVI nUM lgdw hY ik 30% ktOqI vwlI Prwk sB qoN ssqI hovygI pr iPr dUsrI kuVI smJwauNdI hY ik ktOqI hmySw AMikq mul̀ 'qy hMdI hY iesleI Awau AsIN hryk Prwk dw vyc m`̀ul pqw krIey: 3. ਸ ਣ ਕ ੜੀਆ ਂਨਸਰੀ ਪਯਾਕ ਨਜਦਾ ਅੰਨਕਤ ਭ ਿੱਰ 450ਯ ਅਤੇ ਕਟੌਤੀ30% ਸ ੈਦਾ ਵੇਚ ਭ ਿੱਰ ਤਾ ਕਯਦੀਆ ਂਸਨ।

ਨਜਵੇਂ:ਕਟੌਤੀ=ਅੰਨਕਤ ਭ ਿੱਰ ਦਾ ਕਟੌਤੀ%

= 450 X

= 135 ਯ ਏ ies leI vyc mùl= AMikq mùl- ktOqI= 450-135=315 4. ਇ ੇਤਯਹਾ ਉਸ ਦ ਜੀ ਅਤ ੇਤੀਜੀ ਪਯਾਕ ਦਾ ਵੇਚ ਭ ਿੱਰ ਵੀ ਰਿੱਬਦੀਆਂ ਸਨ ਅਤ ੇpqw lgwauNdIAW hn ik ikhVI Prwk sB qoN vD̀ ssqI ssqI pvygI[ Learning Outcome:-1. ਨਵਨਦਆਯਥੀ ਕਟੌਤੀ ,ਅੰਨਕਤ ਭ ਿੱਰ ਅਤ ੇਵੇਚ ਭ ਿੱਰ ਫਾਯੇ ਚੰਗੀ ਤਯਹਾ ਜਾਣ ਸ ੋਜਾਵੇਗਾ ਅਤ ੇਫਜਾਯ ਨਵਿੱਚ ਨਭਰਣ ਵਾਰੀਆਂ ਵਤ ਆਂ ਤ ੇਨਭਰਣ ਵਾਰੀ ਕਟੌਤੀ ਨਾਰ ਵੇਚ ਭ ਿੱਰ ਤਾ ਕਯ ਕੇਗਾ। 1) fJZe coke dk ;{uh w[Zb 220 j?.;/b ftZu 20# eN"sh dh x'PDk ehsh iKdh j?.fJ; coke s/ eN"sh dh okPh eh j? ns/ fJ;dk t/u w[Zb eh j?

17

iwks S/thA AiDAwie – dPwbt pMnw nM :164 fefonk L^ nkT[ piko ubhJ / dPwbt ;zfynktK dk i'V, xNkT[. gqPB 1) i/eo ewb pkIko ftZuoN ie`k coke 75H08 ru ns/ d{;oh coke 68H5 ru dh yohddI hY sk dZ;' ewb B/ e[Zb fezB/ o[gJ/ dh Pkfgzr ehsh.i/eo ewb B/ d[ekBdko B{z 500 o[gJ/ fdZs/ sK d[ekBdko ny ewb B{z fezB/ g?;/ tkfg; fdZs/ < B'N L^ dPwbt ;zfynktK B{z jZb eoB bJh fJjBK ;zfynktK B{z ;wkB dPwbt ;zfynktK fatZu fby' fit/A 12H5 ns/ 24H78 B{z 12H50 ns/ 24H78 ) jZb: fJZe coke dk w[Zb & 75H08 ru d{;oh coke dk w[Zb = 68H5 & 68H50 ru e[Zb youh rkm & 75H08 O 68H50

& 75H08 O 68H50 &143H58 ru

j[D d[ekBdko B/ fezBh oew tkfg; ehsh. ewb B/ d[ekBdwr B{z ijMny o[gJ/ fdZs/ & 500H00 ru d[ekBdko B{z d/D :'r oew &143H58 d[ekBdko vloN vwps kIqI oew & 500.00-143.58= 356H42 ru gqPB 2) o/Pwk B/ pIko ftZu'A fJZe ;?Avb dk i'Vk 578H28 ru dk fbnk ns/ fJZe coke KrIdI ijsdw mù̀l 398H97 ru j?.fco T[;B/ fJZe g?ZB yohfdnk i' fe 15H5 ru dk ;h. i/eo o/Pwk dh wzwh B/ T[;B{z bzwr jwx s'A gfjbK 1000 ru fdZs/ sK dZ;' o/Pwk B/ nkgD/ wzwh B{z fezB/ g?;/ tkfg; fdZs/ < jZb L^ ;?Avb dk w[Zb & 578H28 ru coke dk w[Zb & 398H97 ru g?B dk w[Zb & 15H50 ru rySmw vloN Krc kIqI geI kul rwSI= 578.25+398.97+15.50= 982H75 ru o/Pwk B/ d[ekBdko B{z fdZs/ & 1000H00 ru d[ekBdko vloN vwps kIqI oew &1000H00 - 982H75 ru =17H25 ru Learning Outcome: ftfdnkoEh dPwbt ;zfynktK dw joV Aqy xNkT[ eoB d/ ;wZoE j't/rk. gqPB H i/eo gqGi's B/ fJZe coke fi;dk w[Zb 515H08 ru j? ns/ fJZe ;?Avb fi;dk w[Zb 333H80 ru j?, piko ftZu'A yohd/ sK dZ;' T[;B/ e[Zb fezBh oew dh Pkfgzr ehsh ns/ i/eo gqGi's dh wzwh B/ T[;B{z 1000 ru fdZs/ sK dZ;' T[;B/ e[Zb fezBh okPh nkgDh wzwh B{z tkfg; fdZsh <

Suggestive Activities:- pMnW nM 129,131 qy idq̀IAw koiSs kro dI AYktIvItI krvweI jW skdI hY[

not- hryk ividAwrQI nUM myly ivc̀ kwpI pYn r~Kxw XkInI bxwieAw jwvy qW jo shI Calculation kIqI jw sky[

18

jmwq: CyvIN AiDAwie-12 pMnw nM :303

ikirAW: dYink jIvn ivc̀ pYtrol pMp rwhIN iekweI ivDI bwry jwxkwrI pRwpq krnw[

loVINdI sm̀grI: g̀qy dw fb̀w, cwrt pypr, kYNcI, PYvI kol Awid[

ivDI: hr ie`k ivAkqI dYink jIvn ivc̀ pYtrol pMp qy pYtrol jW fIjl pvwaux Awp jW Awpxy mW-ipa nwl jWdy rihMdw hY[pYtrol Brvwaux vyly pYtrol pMn mSIn vl̀ vI vyKdy hW ijs ivc̀ pYtrol dI kImq Anuswr ikMny rupieAW dw pYtrol jW fIjl lYxw hY ieh Br idq̀w jWdw hY Aqy Aqy kImq Anuswr pYtrol/fIzl dI kul mwqrw Aqy kImq Aw jWdI hY[ies ikirAw nUM myly ivc̀ lgw ky dSmlvW dw joV, Gtwau, guxw Aqy Bwg bwry isKWgy[pr sB qo pihlW ies ikirAw rwhIN AsIN iekweI ivDI dI vrqoN nwl pYtrol pMp auqy rupey Aqy pYtrol dI mwqrw bwry jwxkwrI lYNdy hW[

Aj̀ dw pYtrol dw ryt:- 1 lItr=72.83 rupey 2 lItr=72.83 rupey x 2= 145.66rupey 3 lItr=72.83 rupeyx 3=218.49rupey ------------------------------- … 6 lItr=72.83 rupeyx 6= 436.98rupey --------------- n lItr=72.83 rupeyx n = 72.83 x n rupey pRMqU jykr ivAkqI ny 100 rupey, 200 rupey, 300 rupey, 500 rupey dw pYtrol lYxw hY[ qW auh pYtrol dI mwqrw AsIN iekweI ivDI rwhIN pqw krWgy[ 72.83rupeydwpYtrol pRwpq huMdw hY=1lItr=1000imlIlItr

1 rupey dw pYtrol pRwpq huMdw hY= lItr

= imlIlItr

100 rupey dw pYtrol pRwpq huMdw hY= imlIlItr

=1373 imlIlItr = 1.373 lItr

200 rupey dw pYtrol pRwpq huMdw hY= imlIlItr

= 2.746 lItr ………………………………………………………………………..

500 rupey dw pYtrol pRwpq huMdw hY= imlIlItr

= 6.865 lItr Learning outcome: ikirAw krn auprMq ividAwrQI iekweI ivDI, dSmlv sMiKAwvW dI guxw Aqy Bwg bwry jwx jwvygw [ Suggestive Activities:- myly ivc pMnW nM 304 qy idq̀I koiSs- 2 vI krvweI jw skdI hY[

19

jmwq :A~TvIN nfXnkfJ^rwSIAW dI qulnw g/i BzL 136

fefonk L^ ;kXkoB ftnki ns/ fw;os ftnki ftZu nzso pko/ ikDekoh b?Dk. b'Vhdh ;wZroh L^ rZsk, ukoN, c?the'b, g?Bf;b, opV, ;e?u g?ZB nkfd. ftXh L^ (i) o'fjs B/ ;[fozdo s'A 3 ;kb bJh 5000 o[gJ/ T[Xko bJ/ jB.ies rwsI nUM 5# ;kbkBk do s/ ;kXkoB ftnki s/ w'VBk s?n j'fJnk j?. (ii) d{;o/ gk;/ o'fjs B/ SBI p?Ae s'A 5000 o[gJ/ 5# ;kbkBk do s/ 3 ;kb bJh p?Ze dh fw;os ftnki ftXh okjhA w'VBk j?.gsk eoBk j? fe o'fjs B{z fe; ftXh okjhA o[gJ/ w'VB ftZu ckfJdk j'fJnk j?.

fefonk eoB T[gozs gsk uZbdk j? fe roihq nUM p?Ae B{z fw;os ftnki okjhA bJh okPh ftZu finkdk ftnki tkg; eoBk fgnk j?.

Learning outcome : ftfdnkoEh ;kXkoB ftnki ns/ fw;os ftnki ftZu nzso gsk krn Xog ho jwvygw[

;kXkoB ftnki ftZu jo ;kb w{bXzB fJZe ;wkB ofjzdk j?.

fw;os ftnki ftZu phs/ ;kb dk fw;os XzB nrb/ ;kb dk w{bXzB pDdk j?.

;kXkoB ftnki fw;os ftnki

gfjbK ;kb S.I1 = = 250 S.I = = 250

gfjb/ ;kb A1 = 5000 + =5000

(1+ )

d{i/ ;kb P= 5000 , r = 5%, ;wK & 1 ;kb SI2 = = 250

d{i/ ;kb P = 5000 (1+ ) , r = 5% , ;wK & 1 ;kb fw;os XzB &5000 (1+ ) (1+ )

shi/ ;kb &P = 5000 o[gJ/, r= 5%, ;wK & 1 ;kb SI3 = = 250

fszB ;kb pknd w'VB:'r e[Zb okPh e[Zb XB &P+SI1 +SI2 +SI3 = 5000+250+250+250 = 5750 o[gJ/ fw;os ftnk; & e[bXB ^ w{bXz & 5750^ 5000 & 750 o[gJ/

shi/ ;kb P = 5000 (1+ ) (1+ ) , do & 5# , ;wK & 1 ;kb fw;os XB &5000 (1+ ) (1+ ) (1+ )

fw;os XB & 5000 (1+ )3

= 5000% (1+ )3

= 5000% ( )3

= 5000 % % %

& 5788H125 o[gJ/ fw;os XB &p%(1+ ) (1+ ) (1+ )

= p(1+ )n

fw;os ftnki & fw;os XB ^ w{bXB & 5788H125 ^ 5000 & 788H125 o[gJ/

20

iwksL S/thA nfXnkfJ^nkozfGe nkekoK B{z ;wMDk ;ck BzL 104

fefonk L^ y/v ftXh okjhA nkfeqshnK dh gfjukD eoBh.

;wZroh L^ rZsk, g/go, r{zd, e?Auh nkfd. ftXh L^ fJ; y/v okjhA n;h ftfdnkoEhnK B{z tZy^tZy gqeko dhnK nkfeqshnK dh gfjukD ;pzXh ikDekoh d/tKr/.

1) ;G s'A gfjbk tZy^tZy nkfeqshnK fit/A tor, nkfJs, uZeo nkfd B{z rZs/ s'A eZN fbnk ikt/rk. 2) T[; s/ tZy ozrK d/ g/go bk bJ/ ikDr/.

3) fuZso nB[;ko ie`k ukoN g/go fsnko ehsk ikt/rk. 4) ;kohnK nkfeqshnK B{z fJZe eN'o/ ftZu gk btKr/. 5) ftfdnkoEhnK B{z eN'o/ ftZu fJZe nkfeqsh eZYD bJh ejKr/.s/

T[j T[; nkfeqsh B{z ukoN d/ T[go Bkw d/ ;kjwD/ brkt/rk. 6) ftfdnkoEh ieh pRikRAw tkoh^tkoh duhrweygw[ 7) i/eo ftfdnkoEh ;kohnK nkfeqshnK ;jh^;jh brk d/t/rk sK

T[j y/v fiZs ikt/rk. 8) T[; B{z T[sPkfjs eoB bJh pDdk fJBkw fdZsk ikt/rk.

iesy qrHW ividAwrQI nUM iqMn pswrI AwikRqIAW dI pihcwn krvwE[

;pzXs gqPB L^ j/m fdZshnK rJhnK nkfeqshnK dh gfjukD eo' ns/ fwbkB krvwE[

21

iwksL 6thA nfXnkfJ^nkozfGe AwkwrW B{z ;wMDk ;ck BzL 117

fefonkL w/b/ ftZu jZE Bkb uZbD tkb/ c'bfvzr gZy/ dh ;jkfJsk Bkb e'DK dk torheoD eoBk.

;wZrohL ozrdko ekrI, ukoN, c?the'b, e?Auh nkfd. ftXhL s[;hA w/b/ ftZu jZE Bkb uZbD tkbk c'bfvzr gZyk d/fynk j't/rk (d/y' fuZso) fJ; Bkb n;hA e'DK d/ gqeko f;Zy ;ed/ jK. 1H ukoN ftZu'A fJZe bzph nkfJskeko gZNh eZN'. 2H T[;B{z fJ; soQK Bkb c'bv eo' fe T[j fJZe d{i/ B{z YZe b?D. 3H j[D fJZe ozrdko ekri ftZu' fJZe nkfJskeko bzph gZNh, fi;dh u"VkJh ukoN ftZu'A eZNh nkfJskeko gZNh Bkb'A brGr fszB r[Dk j't/, eZN'.

4H

ozrdko ekri ftZu'A eZNh nkfJskeko gZNh 1 ;w fJZe gk;/ ns/ 1 ;w d{i/ gk;/ c'bv eo'. fJj c'bv T[d'A sZe eo' id'A sZe gZNh ysw Bk j' ikt/.

5H c'bv ehsh gZNh B{z fJZe gk;/ ;N?gb eo fdU sK i' d{;o/ f;o/ s'A gZNh B{z y'bD s/ uZeo pD ;e/. 6H c'bv ehsh gZNh d/ ;N?gb ehs/ feBko/ B{z c'bv ehsh ukoN tkbh gZNh B{z y'b e/ e'D/ ftZu c?the'b Bkb fugek fdU. nkU fJ; Bkb e'DK dI v~K v~K iksmW ;wMweIey . Learning Outcome: tksktoB ftZu e'DK dhnK T[dkjoBK fit/A dotki/ dk y[ZbDk, g?Bf;b pke; B{z y'bDk nkfd B{z y/v y/v ftZu ;wM ;e/rk. e'fPP eo'L T) T[j e'D fi;dk wkg 105 j't/, HHHHHHHHHH ejkT[Adk j?. n) T[j e'D fi;dk wkg 15 j't/, HHHHHHHHH ejkT[Adk j?. J) T[j e'D fi;dk wkg 270 j't/, HHHHHHHHHHejkT[Adk j?.

22

klws-sq̀vIN AiDAwie: iqRBuj Aqy iesdy gux pMnw nM.139

ikirAw:-pwieQwgors isDWq dI pVqwl krnw[

loNVIdI sm̀grI:-cwrt pypr,kYNcI,PYvIkol,skyl Awid[

ivDI:-sB qoN pihlw ieh jwxnw jrUrI hYN ik iksy iqRBuj ivc̀ smkox dy swhmxy vwlI Bujw nUM krx AwKdy hW Aqy ieh iqRBuj dI sB qoN v`fI Bujw huMdI hY[

1.hux iek smkox iqRBuj lE ijs iv`c krx 10 sm Aqy bwkI do BujwvW 6 sm Aqy 8 sm hox[

2. hux iesdy A`T pRqIrUp bxwau[iek kwgj aùqy smwn mwp vwly do vrg A Aqy B bxwE, ijsdI Bujw dw mwp 14sm (8+6) hovy[

3. hux bxwey gey A`T pRqIrUpW ivc̀oN cwrW nUM vrg A Aqy bwkI cwrW nMU vrg B qy r`Ko

ijvyN ik icq̀r iv`c idKwieAw igAw hY[

4. AsIN jwxdy hW ik donNo vrg Aqy AT̀oN iqRBuj iek smwn hn[

ies leI vrg A dw ibnW F̀ikAw KyqrPl = vrg B dw ibnW FìkAw KyqrPl

102=62+82

100=36+64

100=100

5. ividAwrQI ies ikirAw nUM vK̀-2 mwp dy smkox iqRBujW qy kr ky idKwvygw[

6. ividAwrQI ies dw ivAwpIkrx krdy hoey stwl qy Awaux vwly ivid. nUM ds̀ygw ik iksy vI smkox iqRBuj

ijsdIAW do BujwvW dI lMbweI a Aqy b iekweIAW hovy Aqy iesdw krx c iekweIAW hovy, leI

c2 = a2+b2 hovygw[

krx2= AwDwr 2 + lMb 2

Learning Outcome: 1. smkox iqRBuj bwry jwxkwrI imlygI[

1. pwieQwgors isDWq dy sUqr bwry jwxkwrI imlygI[ Suggestive Activity: hor pwieQwgors iqRgut bxw ky pVqwl kro

vrgA

vrgB

23

fefonk L^ y/v' ns/ f;Zy'.

;wZroh L^ rZsk, ukoN, e?Auh c?the'b, ;e?u, p'sb d/ YZeD pbpK dh bVh nkfd.

ftXh L^ nkU BzpoK Bkb fJZe Kyf y/vhJ/ fi;dk BK n;hA y'v' ns/ f;Zy' r/w oZfynk j?.fuZso ftZu s[;hA fJh d/y oj/ j'.fiZE/^fiZE/ ftZu d' o/yktK eZNdhnK jB T[ZE/ fJZe S'Nk pZbp bZfrnk j? i' fe ekNt/A fpzd{ B{z do;KT[Adk j?.fJ; ftZu fJj' fij/ 10 ekNt/A fpzd{ jB.fJjBK ftZu'Aa 9 ekNt/A fpzd{nK B{z 9 gkJhg d/ N[efVnK iK p'sb d/ YZeDK Bkb eto eoBk j? go fJ; soQK eto eoBk j? fe fJZe ekNtK fpzd{ SZv ;ed/ jK.j[D ekNt/A fpzd{nK B{z eto fet/A eoBk j?< nkU f;ZyhJ/ ! fJZe' o/ykyzv T[Zgo fszB brksko fpzd{ frDe/ sh;o/ fpzd{ s/ gkJhg dk N[ZeVk oZyDk j?.

1) fJ; soQK eod/ j'J/ 9 ekNt/A fpzd{ eto eoB/ jB. fi; fpzd{ s/ gkJhg dk N[ZeVk oZfynk frnk, T[; fpzd{

s'A frBDk P[o{ BjhA eoBk. eh 9 ekNt/A fpzd{ kvr j' rJ/< BjhA j'J/ < feT[Afe fJ;d/ fgZS/ fJZe soe j?,

nkU d/yhJ/ !

soe (logic) :- id'A gfjb/ fszB brksko ekNt/A fpzd{ fJZe o/ykyzv T[Zgo frD/ ns/ sh;o/ ekNt/A fpzd{ T[Zgo

p'sb dk YZeD oZfynk.nrb/ fszB brksko ekNt/A fpzd{ fJ; soQK frBD/ jB fe sh;ok ekNtK fpzd{ T[ZE/

nkJ/ fiZE/ gfjb/ tkbk ekNtK fpzd{ frBDk P[o{ ehsk ;h.

Learning Outcome L^ ftfdnkoEh o/yk rfDfse ftukoK fit/A o/ykyzv, ekNthnK o/yktK, ekNtK fpzd{, ;wo/yh

fpzd{nK nkfd pko/ y/v^y/v ftZu ikDekoh jkf;b eo/rk.

gqPB L^ 1) fJ; r/w ftZu fezB/ ekNt/A fpzd U jB<

2) e[Zb o/ykyzv dh frDsh gsk eo'.

3) tZy^tZy fszB fpzd{nK d/ ;w{j i' ;wo/yh j'D.

24

klws-sq̀vIN AiDAwie: KyqrimqI pMnW nM: 206

ikirAw:fefonK okjhA nkfJs d/ y/socb ns/ gfowkg pko/ o'ue ikDekoh.

b'VhAdh ;wZroh L^ ozrhB ukoN g/go, e?Auh, c?the'b, ;e/b nkfd.

fefonkL^ ;G s'A gfjbK n;hA nkfJs Aqy vrg d/ y/socb ns/ gfowkg d/ ;{so pko/ gsk j'Dk ukjhdk j? L^

nkfJs dk y/socb& (l%b)

tor dk y/socb & G[ik % G[ik

nkfJs dk gfowkg & 2(l+b)

tor dk gfowkg & 4 % G[ik

fuZso ^1 nkT[ fJe fefonk okjhA nkfJs d/ y/socb ns/

gfowkg d/ ;pzX B{z ikDhJ/.

;G s'A gfjbK 10 ;w % 5 ;w dk fJe nkfJs bT[/.

j[D nkfJs dk y/socb & 10 % 5 ;w & 50 ;w2

nkfJs dk gfowkg & 2(10O5);w & 2 % 15 ;w & 30 ;w

fuZso^2 nkT[ fJe 2 % 2 ;w dk fJe tor fJ; nkfJs ftZu'A

eZNhJ/ fit/A e/ fuZso ftZu do;kfJnk frnk j?.fJZE/ fJj t/yD

:'r j/ fe ies qrWH Bkb pD/ fuZso dk gfowkg tZX ikt/rk ns/

j[D nkfJs dk y/socb & 50;w2 ^ 4;w2& 46;w2

nkfJs dk gfowkg & 30O(2O2);w & (30O4) ;w & 34 ;w

fuZso^3 ftZu fJZe j'o tor 4%4 ;w2 fdykJ/ nB[;ko eZN' sK

nkfJs dk y/socb & (46^4);w2& 42 ;w2

ns/ nkfJs dk gfowkg & 36 ;w O (2O2) ;w

& 36O4 &40 ;w

fJ; fefonk s'A gsk uZbdk j? fe fit/A^fit/A n;hA fJZe nkfJs ftZu'A tor eZNd/ iktKr/ , T[;/ w[skfpe nkfJs dk

gfowkg tZX/rk ns/ y/socb xZNdk ikt/rk.

i/eo fe;/ th nkfeqsh ftZu'A e'Jh Gkr eZfNnk ikt/ sK T[;dk y/socb xZNdk ns/ gfowkg tZXdk j?.

Learning Outcome:

1. nkfJs d/ y/socb Aqy pirmwp bwry jwxkwrI imlygI[

2. vrg d/ y/socb Aqy pirmwp bwry jwxkwrI imlygI[

25

P/Dh L^ S/thA nfXnkfJ^ y/sofwsh ;ck BzL 242 fefonk :rojwnw jIvn ivc̀ pirmwp dk ;zebg smJxw[

;wZroh L^ rZsk, g?B;b, ukoN, Xkrk, nkfd.

ftXh L^ fJ; fefonk ftZu n;hN tZy tZy gqeko dhnK sb dhnK nkfeqshnK ns/ t;s{nK dk x/o/ dk wkg gsk eoB ;pzXh ikDekoh gqkgs eoKr/.

1) ;G s'A gfjbK ftfdnkoEh B{z Xkr/ dh wZdd Bkb p'ov s/ brkJ/ tor dI sImw dI lMbweI gsk eoB bJh eoKr/.

2) ftfdnkoEh Xkr/ B{z tor d/ uko/ gk;/ x[wkJ/rk. 3) fiBQK Xkrk tor d/ uko/ gkf;nK B{z bZrdk j? T[;

B{z j/mK brkJ/ rJ/ c[ZN/ T[Zs/ wkg/rk. 4) fizBh Xkr/ dh bzpkJh j't/rh T[BQK jh tor dk

gfowkg j't/rk. 5) fJ; gqeko n;hA tZy^tZy sb dhnK nkfeqshnK dk gfowkg gsk eoB bJh eoKr/. 6) j[D nfXnkge nkgDk w'pkfJb Pon N/pb s/ rKygw Aqy ividAwrQI nUM fJ; dk

gfowkg gsk eoB bJh ej'/rk. 7) ftfdnkoEh Xkr/ ns/ c[N/ dh wZdd Bkb w'pkfJb Pon dk gfowkg gsk eo b?Dr/. fJ; fefonk B{z ebk; dhnK tZy^tZy t;s{nK fit/A pb?e p'ov, p?Au dI ;sQk nkfd dk gfowkg gsk eoB bJh d[jokfJnk ik ;edk j?.

Learning Outcome; hyT ilKy pRSnW duAwrw rojwnw jIvn ivc̀ pirmwp dI vrqoN bwry jwxkwrI idq̀I jw skdI hY ;pzXs gqPB L^ 1) fJZe fe;kB d/ nkfJskeko y/s dh bzpkJh ns/ u"VkJh eqwtko 240 whL ns/ 180 whL j?. T[; y/s d/ uko'A gk;/ oZ;/ okjhA 3 g{o/ uZeo dh tkV brkT[Dk ukj[zdk j?. T[; d[nkok tos/ ikD tkb/ oZ;/ dh e[Zb bzpkJh gsk eo'.

2) myly ivc̀ ividAwrQI lys, gotw Aqy klr typ rK̀ygw Aqy Awaux vwly nUM ds̀ygw ik rumwl, dupt̀w, tybl kloQ Awid nUM lys jW iknwrI lgwaux leI ikMnI lys, gotw jW klr typ dI loV hovygI?

26

jmwq:AT̀vIN AiDAwie-KyqrimqI pMnw nM :200

ikirAw: do vylxwkwr fìbAW dy KyqrPlW dI qulnw krnw[

pRSn: ie`k t/bDkeko vZp/ A dk ftnk; 7 ;w ns/ T[ukJh 14 ;w j? Aqy dUsry t/bDkeko vZp/ B dk ftnk; 14 ;w ns/ T[ukJh 7 ;w j?.fejVk vZpk pDkT[Dk ;;sk gJ/rk? loVINdI sm̀grI : cwrt ,gq̀w, kYNcI, ijaUmYtrI bwks [ ivDI L^1H vylxwkwr vZbw A bnwaux leI 22 sm × 14 sm dw ie`k nkfJskeko cwrt dw N[eVk bT[ Aqy ArDivAws 3.5 sm vwly do ck̀r k`to [ Awieqwkwr tukVy nMUM lMbweI vwly pwsy moV ky ie`k byln bxwau [

vylxwkwr vZp/ A dh pwsvIN ;sQk dk y/socb &nkfJskeko cwrt dy N[eV/ dk y/socb = 22 × 14= 308;w2

vylxwkwr vZp/ A dh kul ;sQk dk y/socb &nkfJskeko cwrt dy N[eV/ dk

y/socb+ d' uZeoW dk y/socb = 308+ O2%227%7

2%7

2& 308O77

& 385 ;w2

2. vylxwkwr vZbw B bnwaux leI 44 sm× 7 sm dw ie`k nkfJskeko cwrt dw N[eVk bT[ Aqy ArDivAws 7 sm vwly do ck̀r k`to [ Awieqwkwr tukVy nMUM lMbweI vwly pwsy moV ky ie`k byln bxwau [

vylxwkwr vZp/ B dh pwsvIN ;sQk dk y/socb &nkfJskeko cwrt dy N[eV/ dk y/socb = 44 × 7= 308 ;w2

vylxwkwr vZp/ B dh kul ;sQk dk y/socb & nkfJskeko cwrt dy N[eV/ dk

y/socb+ d' uZeoW dk y/socb = 308+2%227%7%7& 308O308 & 616 ;w2

3. BwvyN dovyN vylxwkwr f̀ibAW dI pwsvIN sqHw dw KyqrPl brwbr hY pr vylx B dw ivAws vD̀ hox kwrx iesdI kul sqHw dw KyqrPl vylx A nwloN ijAwdw hY[ iesleI f̀bw A bnwaux leI Gt̀ sm̀grI lgygI Aqy ieh bnwayxw ssqw pvygw[

Learning outcome:ies ikirAw rwhIN ividAwrQIAW nUM vylx dI vkr sqwH Aqy kul̀ sqwH bwry jwxkwrI pwRpq hovy gI Aqy auh Apxy rojwnw jIvn dy iv`c vylxwkwr vsqUAW dI vkr sqwH Aqy kùl sqwH pqw krx dy Xog ho jwxgy [

Suggestive Activities :-AiBAws 11.4 dy v`K-2 svwlW dI AYiktIvI duAwrW h̀l krvwey jW skdy hn[ijvy:

quhwnMU iek̀ vylxwkwr tYNk idq̀w igAw hY hyTW ilKy iv`coN iks siQqI ivc̀ qusIN ausdI sqHw dw KyqrPl pqw krogy Aqy iks siQqI ivc̀ Awieqn:

1.ieh pqw krn dy leI ies ivc̀ ikMnw pwxI rìKAw jw skdw hY[

2.iesdw pls̀qr krn dy leI loVINdI sImYNt borIAW dI sMiKAw[

3.ies ivcly pwxI nwl Bry jwx vwly Coty tYNkW dI sMiKAw[

27

jmwq: A`TvIN AiDAwie: KyqrimqI pMnw nM:195

ikirAw: o'vo'bo dIAW ivmwvW Aqy lgwey gey c`krW dI igxqI qoN sVk dw KyqrPl pqw krnw[

lOVINdI sm̀grI : cwrt ,gq̀w, kYNcI, ijaUmYtrI bwks ,iKfOxw tRYktr Awid[ pRSn:fe;/ ;Ve B{z gZXok eoB bJh fJZe o'vo'bo B{z ;Ve d/ T[Zgo fJZe tko x[zwD bJh 750 uZeo brkT[D g?Ad/ jB.i/ o'vo'bo dk ftnk; 84 ;w ns/ 1 whNo bzpkJh j't/ sK ;Ve dk y/socb gsk eo'. lOVIdI smg̀rI : cwrt ,gq̀w, kYNcI, ijaUmYtrI bwks ,iKfOxw [ ftXhL jZb o'vo'bo dk ftnk; & 84 ;w o'vo'bo dk noX ftnk; &42 ;w o'vo'bo dh bzpkJh & 1 whH ikayuNik rofrolr bylnwkwr hY iesleI

o'vo'bo dk y/socb & 2 rh = 2% %42%100 ;w2

&26400 ;w2 o'vo'bo dk y/socb & 2H64 wh2 1 uZeo ftZu sfj ehsk y/socb & 2H64 wh2 750 uZeoK ftZu sfj ehsk y/socb & 750%2H64 =1980 wh2 ;Ve dk y/socb & 750 uZeoK ftZu o'vo'bo d[nkok sfj ehsk y/socb &1980 wh2

not: ies dw aultw vI pqw kIqw jw skdw hY[jykr sVk dw KyqrPl pqw hovy Aqy rofrolr dIAW ivmwvW pqw hox qW AsIN rofrolr duAwrw sVk nUM pD̀rw krn leI lgwey kul ck̀rW dI igxqI vI pqw kr skdy hW[

fefonk L^ c'N' co/w d/ jo/e fjZ;/ dk y/socb gsk eoBk. ;wZroh L^ c'N' co/w, ;e/b, ijaUmYtrI pke; Awid. ftfdnkoEh fdZs/ j'J/ c'N' co/w dh bzpkJh, u"VkJh ;e/b dh ;jkfJsk Bkb gsk eo ygw. c'N' co/w dk pkjoh wkg &24 ;w % 28 ;w c'N' co/w dk nzdo{Bh wkg & 16 ;w % 20 ;w c'N' co/w dk y/socb & 24%28 &672 ;w2 c'N' co/w d/ nzdo{Bh Gkr dk y/socb & 16%20 &320 ;w2 c'N' co/w dh pkjoh gZNh dk y/socb & c'N' co/w dk y/socb ^ nzdo{Bh Gkr dk y/socb & 672^320 &352 ;w2 ftfdnkoEh bJh L^ fdZs/ co/w dh pkjoh gZNh dk gfowkg gsk eo' ns/ nkgD/ xo ftZu j'o c'N' co/wK d/ y/socb gsk eoB dh e'fPP eo'.

Learning Outcome: 1.ividAwrQI Awpxy Awly duAwly ivc̀ auplbD vsquAW dw pirmwp Aqy KyqrPl pqw kr skxgy[

2. ividAwrQIAW nUM auhnW dy Gr iv`c pey iksy Poto Prym, iKVkI Awid dw KyqrPl pqw krn leI vI ikhw jw skdw hY[

28

jmwq: A~TvIN AiDAwie: KyqrimqI pMnw nM : 194 fefonk L^ mwics dh vZph i' fe fJZe xDkt (l×b×h) neko dh j?.d[nkok pDkJ/ rJ/ ;'c/ s/ bZrD tkb/ ekri dk y/socb gsk eo'. ;wZroh L^ mwicsk dhnK vZphnK, ekri , kYNcI,PYvIkol Awid ftXhL^ 1) fuZso ftZu do;kJ/ nB[;ko uko vZphnk B{z i'Ve/ fJZe PhN tkbk ;'ck fsnko ehsk ikt/. 2) ;'c/ d/ j/mb/ Gkr dk y/socb gsk eoBk fJ; Gkr dh bzpkJh &h+l+h = (l+2h) fJekJhnK fJ; Gkr dh u'VkJh &b+h fJekJhnk fJ; Gkr dk y/socb & (l+2h) (b+h) tor fJekJhnk (A) 3) ;'c/ d/ pkjoh Gkr dk y/socb gsk eoBk fJ; Gkr dh bzpkJh = h+l+h = (l+2h) fJekJhnK fJ; Gkr dh u"VkJh &b fJekJhnk fJ; Gkr dk y/socb & (l+2h) b tor fJekJhnK (B) 4) pkjoh ;Zi/ ns/ yZp/ gk;/ dk y/socb gsk eoBk . fJ; Gkr dh bzpkJh &l fJekJh fJ; Gkr dh u"VkJh &b fJekJh fJe Gkr dk y/socb &l × b tor fJekJhnK d't/ GkrK dk y/socb & 2(l × b) tor fJekJhnK (C) 5) p?mD tkbh ;hN dk y/socb gsk eoBk fJ; Gkr dk y/socb & (l ×b) tor fJekJhnK (D) 6) nzdo{Bh ;Zi/ ns/ yZp/ Gkr dk y/socb gsk eoBk fJ; Gkr dh bzpkJh &(l- h) fJekJh fJ; Gkr dh u"VkJh & (b - h) fJekJh fJ; Gkr dk y/socb & 2 (l - h) (b - h) tor fJekJh (E) 7) Y'j dk y/socb gsk eoBk L fJ; Gkr dh bzpkJh & l fJekJh fJ; Gkr dh u"VkJh & (b-h) fJekJh fJ; Gkr dk y/socb &l(b-h) ftfdnkoEh (F) 8) ;'c/ d/ ;kjwD/ tkb/ Gkr dk y/socb gsk eoBk. fJ; Gkr dk y/socb &swhmxy idKx vwly iqMnW PlkW dk y/socb &bxh+lxh+hxb = bh + lh + hb = (2bh+lh) tor fJekJh (G) 9) ;'c/ d/ T[gob/ Gkr dk y/socb gsk eoBk fJ; Gkr dk y/socb & 3(l x h) vrg fJekJh (H) 10) ;'c/ s/ bZrD tkb/ ekri dk y/0& (A+B+C+D+E+F+G+H) t.ie. Learning Outcome L^ 1HfJs fefonk d[nkok ftfdnkoEhnK B{z d' ns/ fszB g;koh nkfeqshnW ;pzXh ikDekoh gqkgs jvygI'. 2H tZy^tZy nkfeqshnW B{z i'VB T[gozs gqkgs j'Jh nkfeqsh dhnK bzpkJhnK ns/ u"VkJhnW gsk eoky iesdI sqHw dw KyqrPl pqw krn dy Xog ho jwxgy ;pzXs gqPB L^ 1) wzB bT[ fJZe vZph dh bzpkJh 2 whNo, u"VkJh 1 whNo ns/ T[ukJh 50 ;?Hwh j?.fJ; B{z bZrD tkb/ eZgV/ dk y/socb gsk eo'. i/eo 1 tor whNo eZgV/ dk w[Zb 300 o[gJ/ j'J/ sK bZrD tkb/ e[Zb egV/ dk w[Zb gsk eo'.

29

jmwq: A~TvIN AiDAwie: KyqrimqI pMnw nM : 194 ikirAw: d' vZp/ jB fit/A fe fuZso ftZu fdykfJnk frnk j?.fe; vZp/ B{z pDkT[D bJh xZN ;wZroh br/rh <

sm̀grI:- ie`k Gx Aqy ie`k Gxwv dw mwfl[ pRSn: ie`k Gxwkwr f̀bw hY ijsdy iknwry dI lMbweI 20 sm hY Aqy iek̀ 30;w % 20;w %10 ;w dw Gxwvkwr f̀bw hY [ fe; vZp/ B{z pDkT[D bJh xZN ;wZroh br/rh <

fXnkB fdT[ L^ d'BK d/ feBko/nK dhnK bzpkJhnK dw joV brGr fJe' ijhw bZr irhw hY[ xDkeko vZp/ d/ feBko/ dhnK bzpkJhnK 20 ;w % 20;w % 20;w

xDkeko vZp/ dhnK bzpkJh, u"VkJh ns/ T[ukJh eqwtko 30;w % 20 ;w %10 ;w xDkeko vZp/ d/ feBko/ dh bzpkJh & 20 ;w

fJj vZpk 6 toreko cbeK B{z fwbk e/ pfDnk j?. vZp/ dh e[Zb ;sQk dk y/socb &I tor dk y/socb + II tor dk y/socb + III tor dk y/socb + IV tor dk y/socb + V tor dk y/socb + VI tor dk y/socb

& 20%20 O 20%20 O 20%20 O 20%20 O 20%20 O 20%20 = 400 + 400+ 400 + 400 + 400 + 400 = 2400 ;w2 xDkteko vZp/ dh bzpkJh L 30 ;w, u"VkJh & 20;w, T[ukJh & 10 ;w fJj vZpk 6

nkfJskeko cbeK B{z fwbk e/ pfDnk j?. vZp/ dh e[Zb ;sQk dk y/socb &I nkfJs dk y/socb + II nkfJs dk y/socb + III nkfJs dk y/socb + IV nkfJs dk y/socb + V nkfJs dk y/socb + VI nkfJs dk y/socb & 30%20 O 20%10 O 10%30 O 30%10 O 20%10 O 10%30 = 600 + 200+ 300 + 600 + 200 + 300 = 2200 ;w2 xDkteko vZp/ B{z pDkT[D bJh xZN ;wZroh b'VhAdh j?.fJ; bJh T[j ;;sk gt/rk.

B) fefonk L^ t/bD ns/ xD dh gk;thA ;sQk dk coe gsk eoBk. gqPB L^ fJZe t/bD fi; dk ftnk; 7 ;w T[ukJh 7 ;w j? ns/ fJZe xD fi;dh G[ik 7 ;w j? fe; vZp/ dk gk;th ;sQk dk y/socb finkdk j?< ;wZroh L^ fJZe t/bD ns/ xD ftXh L^ t/bD dk ftnk; & 7 ;w noX ftnk; & 7$2 ;w

t/bD dh gk;th ;sQk dk y/socb & 2 rh =2% % %7& 154 ;w2

xD dk G[ik & 7 ;w xD dh gk;th ;sQk dk y/socb & 4a2 = 4%(7)2& 4%7%7 & 196 ;w2 xD dh gk;th ;sQk dk y/socb finkdk j't/rk. Learning outcome:1.ies ikirAw rwhIN ividAwrQIAW nUM vylx Aqy Gx dI vkr sqwH bwry jwxkwrI pwRpq hovygI [ 2. auh Apxy rojwnw jIvn dy ivc̀ vylxwkwr Aqy Gxwkwr vsqUAW dI vkr sqwH ivc AMqr pqw krn dy Xog ho jwxgy [

30

jmwq: A~TvIN AiDAwie: KyqrimqI pMnw nM : 194

A)fefonk L^ t/bD ns/ xD dk nkfJsB dk coe gsk eoBk.

;wZroh L^ fJZe t/bD, xD ns/ o/s. gqPB L^ fJZe t/bD fi; dk ftnk; 7 ;w, T[ukJh 7 ;w j? ns/ fJZe xD fi;dh G[ik 7 ;w j?.fe; vZp/ dk nkfJsB finkdk j't/rk. ftXh L^ t/bD ftZu o/s Go'.j[D fJZe o/s B{z xD ftZu gkT[.s[;hA d/ yKogy/ ie xD ns/ t/bD d/ wkgK B{z d/y e/ bZrdk j/ fe d'BK dk nkfJsB ;wkB j't/rk.go o/s xD B{z g{ok BjhA GoZdh.fJ; s'A gsk bZrdk j? fe xD dk nkfJsB finkdk j? nkT[ j[D ;{so okjhA nkfJsB gsk eoKr/.

t/bD dk nkfJsB & r2h= % % %7

= & 269H5 ;w3

xD dk nkfJsB &a3 = 7%7%7 = 343 cm3

ies dw pqw lgd̀w hY ik xD dk nkfJsB finkdk j't/rk. B)ikirAw: do fb̀y hn ijvy icq̀r ivc̀ idKwey gey hn iks fb̀y ivc̀ cIj vD̀ AwvygI? sm̀grI:- iek̀ Gx Aqy ie`k Gxwv dw mwfl[

ivDI:-Gxwkwr f̀by dy iknwry dI lMbweI= 20 sm

Gxwvwkwr f̀by dI lMbweI, coVweI Aqy aucweI=30 sm, 20 sm Aqy 10sm kRmvwr

Gxwkwr f̀by ivc̀ ijnI cIj AwvygI = aus vsqU dw Awieqn = (iknwry)3

= (20 × 20) × 20)

= 20×20×20 = 8000 sm3

Gxwv Akwr f̀by ivc̀ ijMnI cIj AwvygI= aus vsqU dw Awieqn

= AwDwr dw KyqrPl × aucweI

= (30×20)×10

=600×10= 6000sm3

Gxwkwr f̀by ivc̀ cIj v`D AwvygI

Learning outcome:

1.:ies ikirAw rwhIN ividAwrQIAWnUM Gxwv, Gx aqy bylx dy Awieqn bwry jwxkwrI pwRpq hovygI [

2. auh Apxy rojwnw jIvn dy ivc̀ Gxwvkwr Aqy Gxwkwr vsqUAW dy Aieqn iv`c Prk pqw krx dy Xog ho jwxgy [ 3. auh Apxy rojwnw jIvn dy ivc̀ vylxwkwr Aqy Gxwkwr vsqUAW dy Awieqn ivc̀ Prk pqw krx dy Xog ho jwxgy

31

C)ikirAw:- vylx A dw ivAws 7 sm Aqy aucweI 14 sm hY[ vylx B dw ivAws 14 sm Aqy aucweI 7 sm hY[ gxnw kIqy ibnHW kI qusI ds̀ skdy ho ik iehnW donW ivc̀ iksdw Aieqn ijAwdw hY? donW vylxw dw Aieqn pqw krdy hoey iesdI pVqwl kro[ ;wZroh L^ t/bD ns/ o/s. ftXh L 1.idq̀IAW hoeIAW ivmwvW vwly do byln bxwa[ 2. pihlW vylx A ivc ryq Bro hux iesy ryq nMU vylx B ivc̀ pwau[ jykr mwpW dw iDAwn kIqw jwvy qW ieMJ lgdw hY ik donoN vylxW dw Awieqn ie`k swr hovygw Aqy vylx A dI pUrI ryq vylx B nMU pUrw-pUrw Br dyvygI[pr jdoN ryq pUrI vylx B ivc pweI geI qW vylx vI pUrI qrW nhI BirAw[qW ies qoN pqw lgdw hY ik vylx B dw Awieqn vD̀ hY[Awau hux vylx dy Awieqn dy sUqr rwhIN pqw krky dyKIey[ vylx A dw ivAws= 7sm

ArD ivAws= = r

aucweI= 14 =h

vylx A dw Awieqn=

= =539 sm3

vylx B dw ivAws= 14sm

ArD ivAws= = 7sm=r

aucweI= 7sm =h

vylx B dw Awieqn = = =1078sm3

vylx B dw Awieqn vD̀ hY[ vylx A dI sqHw dw KyqrPl =

= )

=44x21 =924 sm2 vylx B dI sqHw dw KyqrPl=

= )

=88×21 =1848 sm2 auprokq idq̀y ijAwdw Awieqn vwly vylx dI sqHw dw KyqrPl vI vD̀ hovygw[ Learning outcome:

1. ies ikirAw rwhIN ividAwrQIAW nUM vylx dy Awieqn bwry jwxkwrI pwRpq hovygI Aqy auh Apxy rojwnw jIvn dy ivc̀ vylxwkwr vsqUAW dy Aieqn ivc̀ Prk pqw krx dy Xog ho jwxgy[

32

jwks L^ nZmthA AiDAwie: KyqrimqI ;ck BzL 179 fefonk L^ uZeo dk x/ok, ;{so C = 2 dh o'IkBk ihtB ftZu tos'. ;wZroh L^ ukoN g/go, c?the'b, ;e?u g?B, Xkrk, ;e/b, ozrhB ekri nkfd. ftXh L^ (1) ;G s'A gfjbK nfXnkge, ftfdnkoEh B{z N/pb Nkg d/ feBkfonW dh e[Zb bzpkJh Xkr/ Bkb wkgD B{z efjzdk j? ns/ dZ;dk j? fe fe;/ pzd nkfeqsh dh e[Zb bzpkJh T[; dk gfowkg nytkT[aAdh j?. (2) fco nfXnkge Xkr/ dh ;jkfJsk Bkb uZeo ns/ noX uZeo dk gfowkg Xkr/ Bkb wkgD B{z efjzdk j?. nfXnkge ftfdnkoEh B{z Xkr/ dh ;jkfJsk Bkb fJZe eIVh d[nkok G'iB gdkoE d/ N[eV/ bJh s?n ehsh bzph d{oh j/mK fby/ ftXh okjhA fwfDnk ik ;edk j?. nfXnkge Xkr/ ns/ ;e/b dh ;jkfJsk Bkb noX uZeo dk x/ok mwpygw ivAws&2H8 ;w noX uZeo dk x/ok& &

& %

& sm ehVh d[nkok s?n ehsh d{oh & = 2.8+4.4 = 7.2 cm

ehVh d[nkok s?n ehsh d{oh &cwp AB + + + = 4.4+1.5+2.8+1.5 = 10.2 cm

ehVh d[nkok s?n ehsh d{oh & 4H4 O 2+2 & 8H2 ;w

ivid. nbZr^2 nkekoK dh bzpkJh mwpdk j? As/ rDBk eodk j?. T[es ehsh fefonk nB[;ko ehVh B{z tZy^tZy nkekoK d/ G'iB gdkoEW d/ uko' gk;/ x[zwD bJh fuZso ‘B’ ftZu ;G s'A bzph d{oh s?n eoBh pt/rh. Learning outcome :- ftfdnkoEhnK B{z gfowkg (x/ok) dy ;zebg pko/ frnkB fwbdk j?.ftfdnkoEh tZy^tZy nkekoW d/ gfowkg mwp ;edk j?.

ic`qr-B

A B

C D

ic`qr-A ic`qr-C

33

jwks L^ nZmthA AiDAwie: cqurBujwvW nUM smJxw gzBk BzL 50

fefonk ^ gszr dh ouBk ;wZroh L^ fJZe w'Nk ekrI, ;e?u, ;e/b, e?Auh, ;?ZN^;[e/no ftXh L^ pqMg iek Kws qrHW dw cqrBuj huMdw hY[ies ivc Alg Alg lwgvIAW BujwvW dy jOVy huMdy hn,ijnHW dI lMbweI brwbr huMdIAW hn[ 1H fJZe w'N/ ekrI dh PhN bt'. fJ; B{z d'jok eo'. 2H d' nbZr^nbZr bzpkJh tkb/ o/yk yzv fyZu'.fi; soQK fuZso

ftZu do;kfJnk frnk j?.j[D fJjBK o/ykyzvK B{z fdPk nB[;ko eZN bt' ns/ y'b' ;kB{z fJZe gszr dk fuZso gqkgs j[zdk j?.

3H eh gszr dh e'Jh ;wfwsh o/yk j?< 4H gszr B{z d'B'A fteoBK’ s/ w'V'. ;?ZN ;[e/no d/ T[g:'r Bkb gVskb eo' fe T[j fJZe d{;o/ B{z ;we'D’ s/ eZNd/ jB.eh fteoB pokpo bzpkJh d/ jB< BjhA, fteoB pokpo bzpkJh d/ BjhA jB. 5H j[D n;hA g/go B{z w'V e/ iK wkg e/ d/yKr/ fe fteoB fJZe d{i/ B{z ;wd'Gkfis

eod/ jB. 6H gszr d/ fJZe e'D B{z fJZe fteoB dh fdPk nB[;ko w'VB s/ pokpo wkg tkb/ e'DK

B{z bZG'. 7HfteoB’ s/ gJh sfj d/ fBohyD eoB s/ n;hA d/yd/ jK fe fteoB e'D dy

;wd'Gkie jB. 8. pqMg qo smcqrBuj bxwaux qy iPr icq̀r ivc̀ idKwey ilPwPy bxwaux leI iks qrHW dy cqrBuj dy Awkwr dw kwgj cwhIdw hY, pqw lgwa[ Learning Outcome L^ivid. nUM hyT iliKAW dI jwxkwrI ho jwvygI: 1H d' lwgvIAW G[iktK d/ i'V/ pokpo j[zd/ jB. 2H fteoB fJZe d{;o/ ‘s/ bzp j[zd/ jB. 3H fJZe fteoB d{;o/ fteoB B{z ;wd'Gkfis eodk j?. 4H fJZe ;Bw[Zy e'DK dk i'Vk pokpo j?.

34

jmwq:sq̀vIN AiDAwie: smimqI pMnw nM:288

fefonk L^ fefonk okjhA x[zwdh ;wfwsh B{z ;wMDk.

;wZroh L^ gkodoPh PhN, ukoN g/go, c?the'b s/ e?Auh.

ivDI: fJj fefonk ;wMD s'A gfjbk nkT[ n;h ;wKso us[oG[I dh gfoGkPk ;wMhJ/[ pirBwSw: ijs us[oG[i dhnK ;Bw[Zy G[iktK ;wKso ns/ pokpo j'D ;wKso us[oG[I nytkT[Adk j?. fJZe' jh soQK d/ ;wKso us[oG[I (fJZe ;wKso us[oG[I ABCD fJe ukoN dh PhN T[go ns/ d{ik A'B'C'D' gkodoPh ekri T[go pDkU[.fJjBK d/ fteoBK d/ ekNt/A fpzd{ B{z eqwtko O ns/ O' Bkb nzfes eo'.

;wKso us[oG[iK B{z fJ; soQK oZy' fe A' f;yo A s/ oj/, B' f;yo B T[go oj/.

fJjBK nekoK ftZu fpzd{ O T[go fJZe fgzB brkT[.j[D gkodoPh ekri B{z ;Zi/ r/V s/ xVh dh ;{Jh w[skfpe xwkT[.fJZe g{o/ uZeo ftZu gkodPh ekrI T[go pfDnk fuZso ekrIK s/ pD/ fuZso Bkb d' tko ;zgksh j[zdk feT[aAfe 1800 T[Zs/ x[zwD d/ pknd nkozfGe ;fEsh ftZu nkT[Adk j?.

iesy qrHW icq̀r iv`c idKwey Anuswr tor dh x[zwD ;wfwsh dw kRm 4 j?.feT[Afe fJ;dw x[zwD e'D 900 j? ns/ nkfJs dh x[zwD ;wfwsh dw kRm 2 j?, feT[aAfe fJ;dk x[zwD e'D 1800 j?.Awieq sbMDI ikirAw vrg vWg kIqI jw skdI hYN[

Learning Outcome:

1. x[zwD ;wfwsh bwry spSt jwxkwrI[

2. x[zwD e'D bwry pqw kg̀ygw[

3. smWqr cqurBuj bwry jwxkwrI imlygI[

ivMf iml (WIND MILL) iqAwr krxw:- ies smimqI dy gux dI vrqoN krdy hoey ivMf iml iqAwr krdy hW, icq̀r ivc̀ idKwey Anuswr ie`k vrgwkwr kwgj dw tuk`Vw lau, iesdy ivkrn bxwau[ icq̀r ivc̀ idKwey Anuswr ivkrnW nUM QoVw k`t ky moV ky ipMn lgwau,ie`k stRwA lY ky ies dy ipCy ipMn iv`c lgw idau,ivMf iml iqAwr hY[jykr vrgwkwr kwgj dI QW Awieqwkwr kwgj lY ky ivMf iml bxwieey qW ieh nhIN bxygI[ies ivMf iml dI x[zwD ;wfwsh dw kRm pqw kro[

35

jmwq sqvIN AMkiVAW dw pRbMDn pMnw nM.79 ikirAw : dohrw CVH grwP ( Double Bar Graph ) audyS :swrnIb~D AMkiVAW dy qulnwqmk AiDAYn leI CVH grwP dI vrqoN kr skxw [ ivDI :- ividAwrQI swrnIbD̀ AMkiVAW dI pySkwrI dy leI AwpxI kwrgujwrI dy AMkiVAW dI pySkwrI dy AiBAws leI inmn swrnI Anuswr dohrw CVH grwP bxwaux dI AYktIivtI krygw [ “ ie`k ividAwrQI dy pihly Aqy dUjy smYstr dI kwrguzwrI idq̀I hoeI hY[ FùkvyN skyl dI vrqoN krky dohrw CVH grwP iKc̀xw[ ivSw AMgryjI ihMdI gixq ivigAwn smwijk

isìKAw pihlw smYstr (v~D qoN v~D 100 AMk)

67 72 88 81 73

duUjw smYstr (v~D qoN v~D 100 AMk)

70 65 95 85 75

AMkiVAW nMU drswaux dy leI icq̀r ivc̀ drswey Anuswr kuJ sitRp kt̀ygw qW jo drswey AMkiVAW Anuswr CV dI lMbweI nUM sQwipq kr sky [ CV grwP bxwaux auprMq inmn pRSn pùC skdw hY [

1. iks ivSy ivc̀ ividAwrQI ny AwpxI kwrgujwrI ivc̀ sB qoN vD̀ suDwr kIqw hY? 2. iks ivSy ivc̀ suDwr sB qoN Gt̀ hY? 3. kI iksy ivSy ivc̀ kwrgujwrI hyTW ifg̀I hY? 4. pihly smYstr ivc̀ ikMny pRqISq AMk pRwpq kIqy? 5. dUjyy smYstr ivc̀ ikMny pRqISq AMk pRwpq kIqy?

Learning outcome:-rojwnw jIvn ivc̀ CV gRwP dI vrqoN nwl AMkiVAW dw qulnwqmk AiDAYn krn Xog ho jwxgy[

36

ikirAW : ikMny Gx hn ? pMnw nM.302 ( sq̀vIN )

audyS :mwfl Tos GxW dI igxqI kr skxw Aqy sUqr sQwipq kr skxw[

sm̀grI : lk̀V dy iekweI Gx , cwrt , ijamYtrI bwks Awid [

ivDI : ies stwl ivc̀ ividAwrQI lk̀V ( kwgj ,plwsitk Awid ) dy bxy iekweI dy GxW dy smUHhW vI vK̀-v~K siQqIAW sQwipq krky GxW dI ku~l Anumwinq igxqI pu~Cygw Aqy aùqr dI pVqwl vjo Asl igxqI krvwky vKwvygw [

GxW dI sMiKAw = 18 GxW dI sMiKAw = 8 GxW dI sMiKAw = 9

GxW dI sMiKAw = 4

Short cut Trick

kqwrW dI sMiKAw = 4

ies leI

1 × 4 = 4 2 × 3 = 6 3 × 2 = 6 4 × 1 = 4

kùl joV = 20

ie~Qy 4 kqwrW iv`c GxW dI sQwpnW hoeI hY ies leI ies ivDI iv`c 1 qoN 4 q`k pihlI lVI iv`c ilKo iPr dUsrI lVI iv`c pihlI lVI dI ault qrqIb 4 qoN 1 ilKo [iehnW dI guxW krky joVo quhwnMU GxW dI ku`l sMiKAW pRwpq ho jwvygI [

37

jmwq – sqvIN AiDAwie: Tos AkwrW dw icqrn pyj nM.- 300

ikirAw – ibMdU AMikq kwgz (Isometric dot paper) aùqyy brwbr dUrI dy icq̀rW nUM AMikq krnw[

sm̀grI - ibMdU AMikq kwgz, pYNsl, kYNcI, Pt̀w Awid[

ivD̀I- (1) pswr 3 3 6 vwly ie`k Gxwv dw brwbr

dUrI dw icq̀r iqAwr krx leI idKwey Anuswr lMbweI = 3 iekweIAW Aqy coVweI = 3 iekweIAW lY ky icq̀r bxwau[hux iesdy Ag̀y vwly iqMn iSKrW qoN aucweI = 6 iekweIAW lY ky ryKwKMf iK̀co qy sMgq koinAW nUM auicq ryKwKMfW nwl imlwau[ieh Gxwv dw brwbr dUrI dw icq̀r iqAwr ho igAw hY[kYNcI dI shwieqw nwl iesnUM

k`t lau[

(2) iesy qrHW icq̀r ivc̀ idKwey Anuswr Alg- ALg Akwr lY ky qusIN ibMdU AMikq kwgz qy brwbr dUrI dy icq̀r bxw lau[kYNcI dI shwieqw nwl iesnUM k`t lau[ieh brwbr dUrI dy icq̀rW dy iqrCy icq̀r bx gey hn[

Learning Outcomes – iesdI shwieqw nwl ividAwrQI ibMdU AMikq

kwgz aùqyy brwbr dUrI dy icq̀rW nUM AMikq krnw isK jwxgy[

sbMDq pRsn: ividAwrQIAW nUM hyT idKwey brwbr dUrI vwly AkwrW

ivc̀oN iqrCw icq̀r bnwaux leI idq̀w jw skdw hY[

38

jmwq- ATvIN AiDAwie- cqurBujwvW nMU smJxw pyj nM.- 42 ikirAw- iksy bhuBuj dy ivkrnW dI rcnw krnw[ sm̀grI- cwrt pypr, skYc̀ pYn, Dwgw, Pt̀w, pYNsl[ ivkrn:- iksy bhuBuj dy ivkrn ausdy koeI do isKrW (lwgvyN isKrW nUM C`f ky) nMU joVn nwl pRwpq ryKwKMf huMdw hY[ ivD̀I- icq̀r (1) ivc̀:-icq̀r ivc̀ idKwey Anuswr ie`k Awieq PQRS bxwau[iesdy isKr P nUM iesdy snmuK̀ isKr R nwl Dwgy dI shwieqw nwl joVo[ iesy qrHW isKr Q nUM iesdy snmuK̀ isKr S nwl Dwgy dI shwieqw nwl joVo[iesy qrHW qusIN dyKogyN ik ies Awieq dy do ivkrx bxdy hn[ieh hn- ivkrx PR Aqy ivkrn QS kI ies qo ielwvw hor ivkrx bx skdy hn? (2) icq̀r (2) ivc̀:-ic`qr iv`c idKwey Anuswr iek̀ pMjBuj ABCDE bxwau[ iesdy isKr A nUM iesdy snmuK̀ isKr C Aqy D nwl Dwgy dI shwieqw nwl joVo[iesy qrHW isKr B nUM iesdy snmùK isKr D Aqy E nwl Aqy isKr C nUM iesdy snmùK isKr E Aqy A nwl Dwgy dI shwieqw nwl joVo[iesy qrHW qusIN dyKogyN ik ies pMjBuj dy pMj ivkrx bxdy hn[ ieh hn- ivkrx AC,AD, BD,BE Aqy CE ivkrxW dIAW lMbweIAW mwpo[ kI swry ivkrnw dI lMbweIAW brwbr hn? (3) icq̀r (3) iv`c:-icq̀r ivc̀ idKwey Anuswr ie`k iqRkox LNK bxwau[pqw kro ik iesdy ivkrn iK̀cy jw skdy hn ik nhIN[ ikirAw- bhuBuj dy koxW dw joVPl pqw krnw[ sm̀grI- cwrt pypr, skYc̀ pYn, Dwgw, Pt̀w, pYNsl[ ivD̀I- (1) icq̀r ivc̀ idKwey Anuswr ie`k iqRBuj bxwau[ieQy ivid. nMU pqw hY ik iqRBuj dy koxW dw joVPl 1800

huMdw hY[ (2) icq̀r ivc̀ idKwey Anuswr ie`k cqurBuj bxwau[hux iesnUM Dwgy dI shwieqw nwl do iqRBujW iv`c vMfo[ qW cqurBuj dy koxW dw joVPl = 2 iqRBuj dy koxW dw joVPl = 2 1800 jW (4-2) 1800

ivid. iehnW koxW nMU D dI shwieqw nwl vI mwp ky joV ky vyK skdw hY[ (3) icq̀r iv`c idKwey Anuswr ie`k pMjBuj bxwau[hux iesnUM Dwgy dI shwieqw nwl iqMn iqRBujW ivc̀ vMfo[ qW pMjBuj dy koxW dw joVPl = 3 iqRBuj dy koxW dw joVPl = 3 1800 jW (5-2) 1800

ivid. iesnW koxW nMU D dI shwieqw nwl vI mwp ky joV ky vyK skdw hY[ (4) icq̀r ivc̀ idKwey Anuswr ie`k Cy Buj bxwau[hux iesnUM Dwgy dI shwieqw nwl cwr iqRBujW ivc̀ vMfo[ qW CyBuj dy koxW dw joVPl = 4 iqRBuj dy koxW dw joVPl = 4 1800 jW (6-2) 1800

ivid. iesnW koxW nMU D dI shwieqw nwl vI mwp ky joV ky vyK skdw hY[ies qrHW jykr iksy bhuBuj dIAW BujwvW dI igxqI pqw hovy qW AsIN ausdy koxW dw joVPl pqw kr skdy hW[ ies leI sUqr (n-2) ×1800 hY, ieQy n BujwvW dI igxqI hY[ Learning Outcome: ividAwrQI nUM bhuBuj dy ivkrxW dI igxqI Aqy iesdy AMdrly koxW dy joV pqw kr skxgy[

39

iwks L^ S/thA nfXnkfJ ^ ;wfwsh g/I BzL ^ 320 fefonk L^ d?fBe ihtB ftZu ;wfwsh dh tos'. ;wZroh L^ nkb{, eZNo, ukoN g/go, pb?e wkoeo, ozr nkfd. G[fwek L^ ftfdnkoEh s[;hA nkgD/ d?fBe ihtB ftZu ;wfwsh d/ pj[s T[djkoB t/y/ j'Dr/.fit/A fsZsbh, ski wfjb dh c'N', nzro/Ih d/ nZyo fit/A A, H, O, K, nkfd, e?Auh nkfd. s[;hA kpiVAW,cwdrW, vwl-pyprW nkfd s/ th c[ZbK s/ j'o fvIkfJB t/y/ j'Dr/ i' fe ;wfwsh fdykT[D [ nkgK fJjBQK fvIkfJBK B{z xo ftZu th pDk ;ed/ jK.n;hA fJ;B{z fGzvh, nkb{, krylw, p?ArB nkfd dh ;jkfJsk Bkb pDk ;ed/ jK.nkT[ nZi n;hA fJ; ;wfwsh fvIkfJBW B{z nkb{ dh ;jkfJsk Bkb pDkJhJ/ . ftXh L^ 1) fuZso ftZu ftykJ/ nB[;ko nkb{ b? e/ T[;d/ tZy^tZy fvikfJB eZN bT[ i' fe nZX/ fvIkfJB d/ j'D. 2) fJ; eZN/ j'J/ fvIkfJB vwly AwlU dy ihsy B{z tZy^tZy ozrK ftZu v{p' e/ fuZso ftZu ftykJ/ nB[;ko fvikfJB pDk fbT[. 3) fJj ;wfwsh fvIkfJB pD rJ/ jB. Learning outcome:- fJ; dh ;jkfJsk Bkb ftfdnkoEh ;wfwsh fvIkfJB pDk e/ fJ;B{z ;wM ;eDr/ ns/ fJ; dhnK ;wfwsh o/yktK pDk ;eDr/. jmwq : A~TvIN AiDAwie: vrg Aqy vrgmUl (pMnw nM. 100) ikirAw nM.1: tWk sMiKAwvW dy joV dw sMiKAw dy vrg nwl sbMD sm~grI : klr pypr/cwrt, skyl ,pYnisl ,skYc, kYNcI, grwP pypr, gUMd Awid[ ivDI: 1) mMn lE swfy kol inmn Anuswr lgwqwr tWk sMiKAwvW id~qIAW geIAW hn[ 1,3,5,7,9……………………………………………… 2) hux AsIN ienHw tWk sMiKAwvW dw joV pqw krnw hY Bwv 1+3+5+7+9+……………………………… 3)

1(pihlI ie~k tWk sMiKAw) = 1 = 12

1+3 (pihlIAW do tWk sMiKAwvW dw joV) =1+3 = 4 = 22

1+3+5 (pihlIAW iqMn tWk sMiKAwvW dw joV) =1+3+5= 9 = 32

………………………………………………………………………………………… iesy qrHW is~tw:n tWk pwRikRiqk sMiKAwvW dw joV=n2 Bwv 1+3+5+7+9+…………………….n=n2

40

jmwq: A~TvIN AiDAwie - cqurBujwvW nUM smJxw sPw nM :47 ikirAw: pypr kitMg Aqy icpkwaux dI ivDI rwhIN pVqwl krnw ik iksy vI bhuBuj dy bwhrI koxW dw joV hmySw 360 huMdw hY[ sm̀grI: plyn pypr(4-5), pYNisl, Pùtw, pRkwr, rMgdwr pYNislW, gUMd Awid [ ivDI: 1. icq̀r ivc̀ idKwey Anuswr ie`k iqRBùj iK`co[aus dIAW iqMny BujwvW nUM vDwE[iek̀o ArD ivAws lY ky

pRkwr nwl ies dy iqMny bwhrI kox bxwE Aqy iehnW bwhrI koxW nUM k`t lE[ iehnW iqMny bwhrI koxW nUM nwl

bxwey gey ck̀r qy r`K ky dyKo[qusI vyKogy ik ieh ie`k

pUrn kox bx jwvygw[ ijsdw mwp 360 hY[

2. iesy qrHW iek̀ cqurBuj bxwE Aqy aus dIAW cwroN

BujwvW nUM iek̀o qrqIb vl̀ vDwE[ie`ko ArD ivAws lY ky

pRkwr nwl ies dy cwry bwhrI kox bxwE Aqy iehnW

bwhrI koxW nUM k`t lE[ iehnW cwry bwhrI koxW nUM nwl

bxwey gey ck̀r qy r`K ky dyKo[qusI vyKogy ik ieh ie`k

pUrn kox bx jwvygw[ ijsdw mwp 360 hY[

3. icq̀r ivc̀ idKwey Anuswr ie`k pMcBuj iK̀co[aus

dIAW swrIAW BujwvW nUM vDwE[ie`ko ArD ivAws lY ky

pRkwr nwl ies dy pMj bwhrI kox bxwE Aqy iehnW bwhrI

koxW nUM k`t lE[ iehnW pMj bwhrI koxW nUM nwl bxwey gey

ck̀r qy r`K ky dyKo[qusI vyKogy ik ieh ie`k pUrn kox bx

jwvygw[ ijsdw mwp 360 hY[

4. ividAwrQI nUM hor bhuBujW leI vI ieh ikirAw

duhrwaux leI ikhw jw skdw hY[

Learning Outcome:-

1. ividAwrQI nUM iksy vI bhuBuj dy AMdrly Aqy bwhrI koxW ivc̀ AMqr smJ Aw jwvygw[

2. ieh ikirAw krn auprMq ividAwrQI jwx jwvygw ik iksy vI bhuBuj dy bwhrI koxW dw joV hmySw 3600

hovygw[