cce up maths

7/31/2019 Cce Up Maths

1/96

VI VIII


2/96

STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING, CHENNAI-62012

aFe,khy fa Muh g Wtd,

brid 600006

iz aFe (l),khy fa Muh g Wtd,

brid 600006

iz aFe (thf),khy fa Muhg Wtd,

brid

600006

cjnguha,khy fa Muh g Wtd,

brid 600006

,KJiy iuahs,khtl Maf kW g Wtd,

bgzh, Utzhkiykhtl.

iuahs,khtl Maf kW g Wtd,UZz,UZz khtl.

iuahs,khtl Maf kW g Wtd,

U,Utq khtl.

iuahs,khtl Maf kW g Wtd,cjknrhHu,nry khtl.

gljh Ma (fj),muR nkiy g,

igaej, jUk khtl.


3/96

aFe,khy fa Muh g Wtd,

brid - 600006

jukhd f neha jHf mu y K Kaahf KgUt f Kiwbjhl kW KGik kL tU fahL Kj (2012-2013) jHf midJgfY xW Kj vlh tFtiu eilKiwgLjgl csJ.

ah KjKiwahf KgUtKiw fia jehL mu gf JiwmKfgLJwJ. j bgUjJl KgUt fKiwfhd tfhL beKiwf,bjhl kW KGik kLKiwfhd tfhL ifnaL, midJ ghl MaifnaLf Madtiw khy fa Muh g Wtd totikJsJ.

tha ifnao, khztfis kL br ghl braghLfsfgLtnjhL, khztflKs wfis KGikahf jumsL brtJ vthbwdMaUF tfhLwJ. j_y khztfS bghJs xU w kLkyhJgKfwfS btbfhzugL. nkY, khztf jwfismilahsfL gUtnjhW ML KGtJ bjhlJ KGikahf kL braMaUF cWJizahf fwJ.

a kL Kiwdh, khzt f braghLf, f izbraghLfshd clf, nahffiy, edy, tha wf, kdghikf kWkf vd midJ TWfS mslgLwd. thW msLtj _ykhztf MSik tsia KGikahf maKowJ. nkY, khWwdhffw a kW ntfF Vg kLtjfhd bejikfS sfgLwd.

fhynjhW fwKiwf bragL tU khwfisaLJ jnghJ kLKiwY a khw mKfgLjgLsJ. a kLKiw MafisCFFgnjhL khztfis nj ga kd mGjUJ LJnkgLJ ; kH br!

Maf, ifnaoYs fUJfis KGikahf cthbfhL tFgiwbragLJj ntL. mnghJjh sjiyKiwdiu MSikftfshfjdif cilatfshf tUfhyij totikgtfshf cUthf aY. ah Kndw ehF RtfSFns cUthwJ vgjid fUbfhL

Maf jfSF mfgl flikid mfiwlD bghWzlDbragLjntLbkd iHnw.


4/96

1. mKf 1

2. tsu kL (m) 33. tsu kL (M) 4

4. bjhFj kL 5

5. braghLf tiff 5

6. kL TWf 6

7. Fiw fj 7

8. fhy ms 8

9. vghfgL fw yFf 910. ghl l bgWs tsu braghLf (Mwh tF) 12

11. Mwh tFfhd braghLf 14

12. Mwh tFfhd kh dhjh 28

13. Mwh tF Ka ghlfUJf - id bfhf 31

14. ghl l bgWs tsu braghLf ( VHhtF) 34

15. VHh tFfhd braghLf 36

16. VHh tFfhd kh dhjh 44

17. VHh tF Ka ghlfUJf - id bfhf 48

18. ghl l bgWs tsu braghLf ( vlh tF) 54

19. vlh tFfhd braghLf 56

20. vlh tFfhd kh dhjh 66

21. vlh tF Ka ghlfUJf - id bfhf 70

22. tsu kL (M) kh dhjh

81

23. w FHijfSFfhd dhf 87

24. gJiufgL bralf 89

25. fj rh izajs Kftf 90


5/96

1

f vgJ FHij clrh kW mrh wdh xUizj

MSikwid bgw, wj Fokfdhf sf bra cjtJ MF.

nkY, Ma kW khztf cwKiw, #dehaf khnghL mikj

ntL. khztf jhf fwij btgilahf, Rjukhf

kwtfnshL gJ bfhs thgfgl ntL.

kL Kiwia bghWjko, Ma vthW fjh vgJ

kL, khztf vthW fwd, fj Kiw, fwYF vthW

JizjJ, khztf fw mil bgwduh vgijbayh mj

KakhdjhF.

khztf jf iyia kL ma, nkY, nkgL

bfhS tif braghLf mikj ntL. khztf fj

fUJfis kdghl brahk fUJfis bghU czJ fF tif

tFgiw braghLf mikj ntL.

xbthU khztU J bfhS wDnfw tif braghLfis

Ma mikJ bfhsyh. nkY, fodkhd fUJfis WW

gFfshf J khztfSF tHfgl ntL.

KGikahd kW bjhl kL Kiwia tFgiw eilKiwgLJ

nghJ Ma ftf ntoait : ifnao bfhLfgLs braf midJ tfhlYF kLnk.

bfhLfgl braghLfis tFgiw gaghonfg Maf

mgonah myJ khaiknjh gagLjyh jHf murh btlgLs KgUt ghl Kj gUtFa

fj braghLf ifnao l bgWsd. UD J nghw

myJ ntW brafis Maf jf khztfSF / cq

njitnfg totikJ eilKiwgLjyh. ifnao FlgLs brafisnah myJ jhf jahj

brafisnah koF gagL bfhsyh. Ma tfho

ifnao bfhLfgLs brafis KiygL, brafis


6/96

2

cUth bfhs totikJ bfhtjF KG cik jugLsJ.

Mdh tsu ko nehf ijglhk UgJ mta. ifnao gtif fw kL cf, braf nghwit

koid nkbfhs tHfgLsJ. ghl bghU jik,

vghF fw is, fhy ms, khztf vif, ilF

tsf Matiw bghWJ, FlgLs brafis nkbfhsyh. tsu koid, Ma kL br bghGJ khztf Rikahf

idfhjthW nkbfhs w ftd vLJbfhSj ntL. tsu koid, gUtYs midJ ghljiyf UJ

nkbfhs ntL. tsu ko Ka nehf , fw khztf lghL bfhS

gFfis mJ, Fiwfis fistjF njitahd eltoiffis

vLJ fwiy nkgLJj MF. nkY, fw fj Ma,

khztf iyid cztjF, fwiy nkgLJtjF ifnaL

cj.

Formative Assessment (FA)

tsu kL vgJ, khztf fwiygNHY tFgiwY gntW fw NHY

Ma bjhlJ kL brtjhF. klhdJ,

fw eilbgWbghGJ bragLtJ. MaUF khztfSF ilna cs ilbtia FiwwJ.

khztf gntW fw iyfis (ghJ, nfL, brJ fw)Mauh cWneh kLwJ.

khztf fwiy LtnjhL Maiu CFwJ. khztf njitia milahs fhgjF, Kndw mila

brtjF cjwJ. tFgiw, fw braghLf kL kW fUJ gkhwF

ttFwJ. jDl gY khztfSF fw cjt t brwJ. fw Fiwghofhd fhuzij MuhJ, mjF fhwJ. be jikilaJ.


7/96

3

vgJ UTWfis cslaJ.

tsu kL (m) - braghLf thyhf

tsu kL (M)- W nj thyhf

Formative Assessment - FA(a)

tsu kL (m) vgJ, fngh gntW tifahd fw braghLf

MtJl gnfgij kLjyhF. ghlbghUis fFbghGnj

fnghiu kL KiwahF. bghUjkhd lf FGfis kl

lkwJ. j klhdJ MaUila cWnehf/fngh gnf/

btghL/ gilw btghL Kja cKiwfis gagL

kLjyhF.

jid jhnd nrhJ ma khztfSfhd xU msnfh. Fiwa kW Fiwfis nghf eltoif vLf MafSfhd

tfho. FGbragho _y tha wfshd KobtLj, uridfis

fisj, ewit nkgLJj, Tjid kW rahd jft bjhlnghwtiw nkgLj cjtJ.

khztf fw ntfnfg braghLf mikfgl ntL. tF cs xbthU khztU Fiwjgr 4 braghLfis xbthUgUtY nkbfhL mt wj 2 braghLfis MakoF vLJ bfhs ntL.

(2 braghLf X 10 kbgf = 20 kbgf)

[FA (a)]

1. bra l ( Project) 9 brJ fw ( Learning bydoing)

2. uridia j( Problem Solving) 10 xgilf ( Assignments )

3. tufis nrfj( Data Collection 11 isahLf ( Games)

4. fUJ tiugl( Concept mapping) 12fh gLJj( Visualisation)


8/96

4

5. bghU sf jUj( Interpretation) 13kLj kW njhuhafhz ( Estimation andApproximation)

6. ( Puzzle) 14

ca jidia Ldhf

( Higher order thinkingQuestions)

7. cW nehFj ( Observation) 15

khztfis fj bkhgkhwF tnfhYj( MathematicalCommunication)

8. flhuhj ( Investigation)

Formative Assessment - FA (b)

klhdJ, fFbghGnj Mauh eljbgW W vGJ njthF. gtifgl dhfis cslaJ. (v.fh. f, Lfijf Kjad.)

j bragho _y xbthU khztUila fw mil cWbragLwJ.

khztf jf fw milit jidjhnd nrhJ ma cjmsnfhyhF.

Fiwa kW Fiw eltoiffis vLf MafSF xU tfhoahf mikwJ.

tF cs xbthU khztU Fiwjgr 4 braghLfis xbthUgUtY nkbfhL mt wj 2 braghLfis Ma

koF vLJbfhs ntL.

(2 braghLf X 10 kbgf = 20 kbgf)

[FA (b)]

dhtiff dhtiff

1. gy bj( Multiple Choice ) 6 tirgLJj ( Sequencing)

2. nfhol lfis uj( Fill in the blanks)

7ca jidia Ldhf ( Higher order Thinkingquestion)


9/96

5

3. bghUJj ( Matching) 8 W dhf ( Short AnswerQuestion)

4. dho dh ( Quiz) 9 FW dhf( Very short Answer Question)

5. fj fUJfis id TWj ( RecallingMathematical Concepts)

10 tiufiy mikf( GraphicOrganisers)

bjhFj kL vgJ, khzt frh fwyilit

thyhf gUt W kL brtjhF. kL,

fw nehffis btbfhzUkhW

Matmogil mik.

bjhFj klhdJ,

dhjh l totikgo gUt W eljbgW vGJ njthF.

mj, j, gagLj, gFjhj, kLj, gilghw mogil

mik.

khzt fw milF rhwF tif mik. fhytiuaiwF cgljhF.

klhdJ,

xbthU gUt W 60 kbgfSF kL bragL.

jfhd dh totik kW tF thahd kh dhjhf

ifnao izfgLsJ.

KGikahd kW bjhl ko xbthU khztiu fw cW

bra j eg braghL mtakhwJ. tFgiw khztf vif

Fiwthf UF nghJ braghL Vilajhf mik, braghil


10/96

6

mikF nghJ Ma xbthU khztlY ftd brY, fw

bjh eilbgWwjh? vgij cW bra ntL.

j eg bragho _y eilbgW fwyhdJ, l ehfSF

iyJ F. nkY, fw bghUSilajhf UF.

tFgiw khztf vif fFiwthf UF nghJ

khztfis Ut bfhl FGthf J braghLfis nkbfhSj

ntL. mthnw mFG jiy klyh.

tFgiw khztf vif mfkhf UF nghJ Ma

khztfis W FGfshf J, fw braghil mikf ntL.

W FGfshf fgLtjh xbthU FGdUF fw fj JizfUfis brafis mikgjF Kd tHFtij cW brj

ntL.

bragho nghJ tFgiw xGF eKiw mika Ma

ffhf ntL. FG xbthU khztUila gf l bgWkhW

Ma cW bra ntL.

Ma ghll cs y wfis jeg braghL, izbraghL kW FG braghL _ykhfnth elj ayhj bghGJ tF cs

midJ khztfis xnu FGthf fU brJ fhl, cWnehf (m)

bghU sf _y wid khztfSF fj ntL.

cjhuzkhf, brKiw toa cs tl ehfu tiuj vw

ghlbghUis brJfhl _y fj.

jh bjhlfhw( Initiative )


11/96

7

khzt braghLfis kLbghGJ milw kL,nkFl bghJthd IJ sf Ffis kdbfhL kL brjntL.

tsu kL (m) fhd braghLfis fl tKiw _ykL bra ntL.

10f eW

***

braghoid KGikahf bjthf,xGFlD Koj

braghoid caKiw brj kWgilghw w btgL tif Koj.

braghoid mthjKiw Koj

8-9 eW

** braghoid KGikahf, xGfhf, caj

Kiw kW ftdkhf brJ Koj6-7 Ufu

* braghoid KG


12/96

8

1. va 40 4 442. msitf 10 2 123. toa 6 2 84. brKiw toa 4 2 6

bkhj 60 10 70

1. va 31 4 352. afj 23 2 253. toa 18 2 204. brKiw toa 9 1 105. tufis

ifahSj12 1 13

bkhj 93 10 103

1. va 36 4 402. msitf 20 3 233. toa 11 2 134. brKiw toa 13 1 14

bkhj 80 10 90


13/96

- ca bjhlf iy tFf

9

va

8 yf v tiusvfis J bfhL lkig mj.

a vf, KG vf gmj

10 thghLfis ( bgUf)gagL fhuf,klFfis mj

2, 3, 4, 5, 6, 8, 9, 10, 11MtFgL jikia mj

.bgh.t, . .k flKiwia J bfhSj

df - jFd,jfhd, fy d,jrkd - d TlkW fj

dfis jrk vfshf,jrk vfis dfshfkhWj

gfh vf, gF vf rhgfhvf g J bfhSj

KGf Tl, fj,bgUf kW tFjiymj

Tl kWbgUfiy bghWJmilg, khWg,nrg, gLg,rkgfis flj

d - bgUf, tFj

jikia a brj jKW vfis vnfho

Ff brJ, ehFmogil braghLfisbra fw

jKW vfisjrkvzhf khWj kWthif fzFfbraghLfis gagL fhz

bfhLfgl a vfismLFF vfshf khwmj

jKWgfibgUfbfhS

U j ilgvfis

jKWtha

fhz vfis

mLF

mLFbfh

tf

fhuKiw

KG tvfS


14/96

- ca bjhlf iy tFf

10

mLFF fis JbfhSj

tf fd v

njhuh

msitf

l, Wj kW Kfjmsitf - X myid kwmyFfSF khw bramj

tlntl,gug

_W cs kW

afj

bfhLfgl afjnfhitf kh, kh,

bfGfis flj xj cWf kW ntdcWfis vGj mj

afj T goidvGj mj

toa

, nfhL, nfhLJLkW js - mKf brj

xU nfhLf, iznfhLf,brFJnfhLf, xUnfhLf gfismj

rkjik, Mork jik,RH rkjik, rknfhL/mR nghwtiw JbfhSj

btLnfhLf, mLjLjnfhzf, iznfhLf,FWFbto nghwitfgfis JbfhSj

KnfhTWj

KnfhmogJ bgfifhz


15/96

- ca bjhlf iy tFf

11

rt rkmogSSS,SA

bfhS

brKiwtoa

toa fUbgo -mKf

nfhLJil tiuj,nfhL Jo sijmsj

bfhLfgl totfnfhzf, iznfhLfkW FJnfhLfis idTWj

ehfMa t

tufisifahSj

bjhlahd tufisbjhFf, tifgLjmj

fbt goaiy mikfbrj


16/96

- ca bjhlf iy tFf

12

[FA (a)]

1 va 3 FG FGbraghL VWtir kW

wFtir

2 va

10 j / izxgil FWF v isahL

3va

16j /

iz /FG

xgil gfh vfis fhQbra

4 va 17 FG FG braghL fhuf

5 va 18 FG braghL fhu isahL

6 va

22 FG / j g 2,3 fzF 4 kW 5

tFgL jik

7 va

31 iz /FGrkhd d braghL

8 va

37 iz /FGntd dfis Xddfshf khWj

9 va 48 j jrk vfis vnfho Ff

10va

50 j / FGbral 1 goa jahj (jrkv)

11 va 50 j bral 2 iy goanrfj

12 va 55 FG bral

13 msitf 58 j xgil msitftifgLJj

14 toa 66 j / FG iznfhLf, brFJnfhLffhz

15 toa 67 FG tF FGbraghL - iznfhLf, brFJnfhLffhz

16 toa 68 FG g 5.2 5tJ fzF

17 brKiwtoa 72 jbraghL 1,2,3 Rws fhz


17/96

- ca bjhlf iy tFf

13

[FA (b)]

1 va 3, 4, 5, 9 j g 1.1 - 1.4 tiu cs fzFfistFgiw, L braghL kWWnjF gagLJf

2 va13, 17, 18,

22,23, 27, 28

j g 2.1 - 2.6 tiu csfzFfis tFgiw, LbraghL kW WnjFgagLJf

3 va 22 j braghL

4 va 27 j braghL

5 va 28 j braghL

6 va 34, 36, 40,44,49, 53, 55

j

g 3.1 Kj 3.7 tiu csfzFfis tFgiw, LbraghL kW WnjFgagLJf.

7 va 30 j brJ ghf

8 va 36 j braghL 1, braghL 2

9 va 40 j braghL

10 va 42 j brJ ghf 1, f, thf

11 va 44 j braghL

12 va 52 j braghL 1, 213 va 55 j braghL 1, 2 (id bfhf)

14 msitf 58, 60 j

g 4.1 - 4.2 tiu csfzFfis tFgiw, LbraghL kWWnjF gagLJf

15 msitf 60 j braghL

16 toa 62, 64, 66 j braghL (thf)

17 toa 63, 65 j brJ ghf (braghL)

18 toa 64 ,68 j

g 5.1 - 5.2 tiu csfzFfis tFgiw, LbraghL kWWnjF gagLJf.

19 brKiwtoa 71 jg 6.1 cs fzFfistFgiw, L braghL kWWnjF gagLJf.


18/96

- ca bjhlf iy tFf

14

[FA (a)]

jiy : va

ghlbghU : a vffw nehf : VW tir kW wF tir g mJ

bfhSjgf v : 3

bragLJ Kiw xbthU FGF 6 Kj 8 ng tiu csthWkhztfis J bfhs ntL.

FG thahf, FG cnshf wj njiatUkhW g bra ntL. v.fh 16-6-1997

FGYs khztf taJ mogil VWtirkW wF tir tirgLj brf.

xbthU FGUJ isa kW _j khztfbgaiu wj nj mogil fhz brf.

mnjngh FG cs xnu taJ khztfbgafis goaLf. (ML kW khjij bfhL)

nj nghW midJ FG nkFlij nghWkhztf brwhf vgij Ma cW brantL.

kL TWf f eW : 10 kbgf eW : 8-9 kbgfUfu : 6-7 kbgf

Kanjit : 5 kbgftYLjbraghL

Ma fj ghl fUij nkgLj gntW tYLjbraghLfis tFgiw mikf ll ntL.

tha wbtghL

nkfl bragho khztfsJ jiy cWghL,FG braghL, fhuzfhaJl F w, Raz, jft bjhl wfis Mafklyh.

Fiw fjkW thfbraghLf

5 kbg bgW khztfSF Fiw braghLfisMa totikJ KGw bgWtiu gajntL.

6 Kj 9 kbgf tiu bgW khztfSF mtf

brj iHfis flJ t bra Math mf ntL. KG kbg bgw khztfSF fyhd,

jidia JhL kW rthyhd fzFfistotikJ Ma mj ntL.


19/96

- ca bjhlf iy tFf

15

jiy : va

ghlbghU : a vf

fw nehf : khztfl isahL fzFf JMt Cl brj j braghL

gf v : 10

bragLJ Kiw ghljf gf 10 bfhLfgl FWF visahL iu tFYs midJ khztflcsJ vgij Ma cW brJ bfhf.

Ma FWF v isahL bfhLfglijsf ntL.

v.fh: lUJ tywkhf 620 + 376 = 996 vw iliafl 1 UJ lwkhf bjhl tywkhf _Wfl uf

19

29

36

v.fh: nkUJ Hhf 4311 + 29 = 40 vw ilia fl 43 UJ bjhlneh uL fl uf.

434

0

nkflij nghy lUJ tykhf nkUJHhf khztfis ug brf

tFYs midJ khztfS bragho


20/96

- ca bjhlf iy tFf

16

jiy : va

ghlbghU : fhuf

fw nehf : fhufis flj

gf v : 18

jiy : va

ghlbghU : tFf, fhuf

fw nehf :


21/96

- ca bjhlf iy tFf

17

jiy : tFf, fhufghlbghU : gfh vffw nehf : gfh vfis ma brjnjitahd bghUf : A4 jh, Sketch Pen myJ tz vGJnfh

fhu flj vf vj


22/96

- ca bjhlf iy tFf

18

jiy : df

ghlbghU : rkhd d braghL

fw nehf : rkhd dfis mj

gf v : 31

7I gir w tlLf. 7- klFfmidij f w FWFnfhL (x) l.

gir w tll vfS, FWFnfhL (x) lhj vf midJ gfh vfns. nkY midJ gfh vfS (2, 3-I ju) 6-

klF K myJ bjhlahf mikUF.

bragLJ Kiw xnu khahd brtf tot milfis bfhL 1-klF, 2 klF, 3 klF, 4 klF.....MaklFfSfhd JizfUfis njitnfg cUthtF itJbfhf.

cjhuz.

: 1 2 3 4 5 6 7 8 9 10

: 2 4 6 8 10 12 14 16 18 20

v.fh : 32

fhd rkhd dfis cUthFj

klF milfis bfhL flthW mLFf.

: 2 4 6 8 10 12 14 16 18 20

: 3 6 9 12 15 18 21 24 27 30 nkfl mltizUJ,

32

=64

=96

=128

=1510

=1812

Mfnt,

6

4,

9

6,

12

8,

15

10,

18

12Mait

3

2 rkhd

dfshF.


23/96

- ca bjhlf iy tFf

19

jiy : va

ghlbghU : df

fw nehf : ntd dfis XddfshfkhWj

gf v : 37

njitahd bghUf : 1 Kj 10 tiu cs klF mltiz

nj nghW Ma xbthU FGF njitahdd vfis, brtf tot v milfisbfhLJ rkhd dfis FGbragho fltijcW brf.

bragLJ Kiw21

,53

vw ntd dfis Xd dfshf khw

bfhLfgl xbthU viz klFmltizia gagL rkhd vzhf khw ntL.v.fh

1 2 3 4 5 6 7 8 9 102 4 6 8 10 12 14 16 18 20

2

1 rkhd df =

21

=42

=63

=84

=105

=126

= . . . =2010

njngh,3 6 9 12 15 18 21 24 27 305 10 15 20 25 30 35 40 45 50

53

rkhd df =53

=106

=159

=2012

uL df rkhd df gF vFrkkhwJ vd ghf ntL.

21

Xdd =10

5

53

Xdd =106

nkTaij ngh gntWntddfis bfhLJ Xdd vfshfkhw brayh.


24/96

- ca bjhlf iy tFf

20

jiy : jrk vf

ghlbghU : jrk v totfw nehf : mwhl th o cs gntW bghUfis

msJ jrk v mj

gf v : 50

jiy : bk msitfghlbghU : l, Wj, Kfj msitfis

tifgLJjfw nehf : bk msitfis tifgLJj

gf v : 58

njitahd bghUf : filfUJ bgwgl gWLf

bragLJ Kiw khztf tFgiw cs bghUfis cWneh

mt s, mfyfis msJ mYs

jrk vfis mltizgLj ntL.

v.fh: jf nkw ( s kW mfy ), fUgyif mnjngh khztfSF o cs vj

bghUfSF jrk v to s, mfy msf

Ko vd flJ mtiw mltizgLj

ntL vW brhy ntL

bjhiyfh bgo, toa fU bgo..............


25/96

- ca bjhlf iy tFf

21

jiy : toa

ghlbghU : iz nfhLf, brFJnfhLf

fw nehf : My vGJf iznfhLf brFJnfhLf mJ bfhs. khztfSF iznfhLf,brFJnfhLf g bjthd

jidia VgLJj.

gf v : 65, 66

bragLJ Kiw Ma braghoF Kd filf thFbghUf gWLfis khztfisnrfJ tu brj.

khztflUJ bgwgl gWLf UJ bgwgl bghUfis bfhL

mltiz gLJf.

t.v

bghUfmsitf

l Wj Kfj

1 m

2 f. vbz3 g 4 J. gU

5 gh

67

xbthU bghUS vthW mslyh vd

nfgj _y bghUjkhd l ( ) FpL_y tifgLj ntL.


26/96

- ca bjhlf iy tFf

22

[FA (a)]

jiy vf mik

ghlbghU d

fw nehf d tiuaiw kW tifghLfis mJbfhSj

bragLJ Kiw tiuaiw goJ gyj. cUtf tiuJfhl. fhj ko _y dfis mj. thanyhL dij bjhlgLJj

i)d tiuaiwia J bfhSj

jbraghL Ma j kW My vGJf iznfhLf brFJnfhLfis flJv.fh xiw T J iznfhLfsh myJbrFJnfhLfsh vd dh vGkhztfl il fhf.

xbthU khztlK brFJnfhLf, iznfhLf cs vGJfis flabrf.

nkY brFJ kW iznfhLf izJtU vGJfis goaLf.

FG braghL Ma tF cs khztfisvifF Vg FGthf f itf ntL.

Ma brFJnfhLf, iznfhLf vWTal khztf mjnfwthW iuthfiff _y brFJnfhLf, iznfhLffhfbrayh

Ma brFJ nfhLf vwl khztfjf FG brFJnfhLfis jfisbfhnl mikJ fhf ntL. njngh iznfhLfis brJ ghf.


27/96


28/96

- ca bjhlf iy tFf

24

cW neha , khztfis d tifghoid tUkhWmltizgLjyh.

jF d jfh d fy d

iii

: rkhddij g J bfhSj.

xU d bjhF kW gFia xU vzh bgUdhnyh myJtFjhnyh md milgL gF gugs rk vgij ma brj.

1.

53

106

=53 x

22

2.

12

9

43

=129

33

vLJfhil cWneha flit rkhd dfsh? gl tiuJsfkf

1) 28

= -----

2) 168

=64

3) 97

=63

4) 73

kW219


29/96

- ca bjhlf iy tFf

25

_W efuf kf bjhif tUkhW

efu bga kf bjhifbrid 80,03,608ffjh 1,62,24,534Kig 1,10,14,641

mltizia cWneh ilaf.1) _W efufY thG kf bjhif vts?2) Kigia ffjhnthL xLif vts ng TLjyhf

ffjh thwd?3) ffjh cs kf vif ngh brid

cnshf vjid klF (njhuhakhf)?

i :khztfis mwhl th gagLJ bghUf, mj

iy goaiy nrfJ tu brj.

ii)

tU bghUf iygoaiy cWnehFf.

t.v bghUf ms iy %1 nrh 1 22.252 cSj gU 1 68.503 jfh 1 1 8.754 btfha 1 1 6.255 ebybz 1 80.75

jiy : vf mikghlbghU : KG vf jhd braghL

fw nehf:

KG vfis bfhL Tl, fj kWklif tYgLJjbragLJ Kiw : mltizia cWneh mogil braghil

khztfis bra brj.

jiy : vfghlbghU : jrk vfis mKfgLjfw nehf : jrk vfis ifahSj

bragLJ Kiw :


30/96

- ca bjhlf iy tFf

26

( m) nkny bfhLfgl goaUJ KGgF kW jrk gFia vLbjGJf.

t.v iy % KG gF jrk gF

(M) iygoUJ tU mltizia iw brf.

t.v iy%

gJf xWf gxWf

EhxWf

() cdF oj uL bghUf iyfis To vGJf.

(


31/96

27

(Summative Assessment)

1 2 3 5 1 2 3 5 1 2 3 5 1 2 3

1 va 6(6)4

(2) - -4

(4)16(8)

12(4) - - - - - - -

2 bkmsitf3

(3)2

(1) - -3

(2) - - - -2

(1)6

(2) - -

3 toa 2(2) 4(2) - - 2(5) - - - - - 6(2) - -

4 brKiwtoa - - - - - - - - - - - - - -

21 37 14

25% 44% 17% 14

1 kbg dhf 20 x 1 = 20

2 kbg dhf 10 x 2 = 203 kbg dhf 5 x 3 = 155 kbg dhf 1 x 5 = 5dh totik ( ) mil Fs vf dhf vifia FF.


32/96

28

I 10 x 1 = 10

1. 1000 vw v K .......................MF.m. 999 M. 1001 . 599


33/96

29

II 5 x 1 = 5

11. jsij mikf Fiwjgr ......................f njit.

12. vnghJ xiw xW btobfhsh nfhLf......................vdgL

13. xU tahf......................nfhLf tiuaKo.14. 14br = ........................

15. 9.4 4 lk......................MF.

III5 x 1 = 5

16. 1000 - U vf bgUfgy

17. 100

6- gfh v

18. 23 - 5 M tFglhJ19. .bg.t x ..k - 1 20. 237 - 1

- 0.06- gF v

IV. 10 x 2= 20

21. 204351 vw viz a v Kiw vGJf.22. va Kiw ilfhf: 25 x 62 x 4

23. 1 Kj 20 tiu cs vf gfh vfis vGJf24. 24I gfh fhugLJf25. tU nrhof vit rhgfh vf (13,17), (7,21), (19,23), (11,22)26. brFJ nfhLf vwh vd?27. f vwh vd?28. 10 bl liu luhf khWf

29. 40 + 7 +10

3I jrk vzhf khWf

30. TLf124

5+

12443

+12433

31. xU U ehfh vil 5. 300uh v 7 U ehfhfvil vd?

32. ff 9.67 - 1.2133. 6, 8 .bg.t. fhf.

34. 372

I jfh dkhf khWf.

35. AB kWCD nenfhLf O rFgo gl tiuf


34/96

30

A B

O S

A

A

B

B

OS

V. 3 x 5 = 15

36. 12350 vw v 2, 3, 5M tFgLkh vgij rghf

37. 12, 45, 75 vw vf .bg.t kW .,k fhf

38. ilfh 43 + 52 + 84

39. RUFf ( 9

8-

9

1 ) -

9

2

40. xU FHijF 200 . . gh j 40 FHijf bfhl tF vyh

FHijfSF gh juntL vwh vjid l gh thf

ntL?

41. gl UJ xU nfhlikfis vGJf

42. uL ghuf cs j ms 1 4 750 . . kW21 250 . . bkhj ms vts?

43. gl iznfhLf kW brFJ nfhLfis vLJ vGJf

VI. 1 x 5 = 5

44. msnfh cjnahL AB = 5.9 br mss nfhLJL tiuJgoiyfis vGJf

( myJ )msnfh kW ftuhaij gagL PQ = 7.8 br. msFnfhLJL tiuJ goiyfis vGJf.

E F D

P T Q

E D

F C

P T

Q R


35/96

31

1 a vf, KGvf 4 a vf N = {1, 2, 3,}

2 a vf, KGvf 4 KG vf W = {0, 1, 2, 3,}

3 tFf, fhuf 14 tFf X viz tFF vfmidJ tFf

4 tFf, fhuf 15 gF vf uoF nkgl tFf bfhlvf

5 tFf, fhuf 15 gfh vf 1 kW mnj vzh kL tFgLjik bfhl vf

6 tFf, fhuf 19 2M tFgL jik 0, 2, 4, 6, 8 Ko vf7 tFf, fhuf 19 5 M tFgL jik 0, 5 Ko vf

8 tFf, fhuf 19 10 M tFgLjik 0 Ko vf

9 tFf, fhuf 20 4 M tFgL jik fil 2 yff akhfnth(m)4 klfhf Uj

10 tFf, fhuf 20 8 M tFgL jik fil 3 yff akhfnth(m)8 klfhf Uj

11 tFf, fhuf 20 9 M tFgL jik yff TLj9 klfhf Uj

12tFf, fhuf

213 M tFgL jik yff TLj

3 klfhf Uj

13tFf, fhuf

2111 M tFgLjik

Xiw l yff TLjYF uil l yff TLjYFcs ntWghL


36/96

32

14 tFf, fhuf 24 ..k bghJ klFf fa klF

15 tFf, fhuf 25 .bgh.t bghJ tFf fbga tF

16 tFf, fhuf 26 rhgfh vf mLjLJs U vf .bgh.t1 v mj vf17 df, jrk

df30 d KGgFia ghffshf

FbghGJ ilgJ18 df, jrk

df38 d Tl dTlYF U dfis

Xd dkhf khw ntL19 df, jrk

df41 jF d gFia l bjhF ajhf

Ujh

20 df,jrk df 41 jfh dgFia l bjhF bgajhf Ujh

21 df,

jrk df

42 fy d KG vQ jF dK nrjJ

22 df,jrk df

45 jrk df 10 mLFfis gFfshfbfhl df

23 df,jrk df

47 jrk df vyh KG vfS jrk vfshF

24 ,nfhL,nfhLJL, js

62 vgJ xU Fl iyidFF

25 ,nfhL,nfhLJL, js

62 nfhL f beUfkhf xU Fl netir mik f bjhF

26 ,nfhL,nfhLJL, js

63 f xU UJ tiuagL nfhL

27 ,nfhL,nfhLJL, js

63 nfhLJL nenfho xU gF. jF xUbjhlf, Ko cL

28 ,nfhL,nfhLJL, js

65 js js vgJ midJ irfYKoyhj viyfis bfhlJ


37/96

33

29 ,nfhL,nfhLJL, js

65 izyhnfhLf

izaw ne nfhLf xU bto bfhS

30 ,nfhL,

nfhLJL, js

64 iz nfhLf xiwbahW bto bfhshj

nfhLf31 ,nfhL,nfhLJL, js

67 xU tbrYnfhLf

_W myJ mjF nkglnenfhLf xU tbrwhm nfhLf xU tbrYnfhLfshF.


38/96

34

[FA (a)]

1. bkbafbjhF 3 FG / jKGf Tl, fjbraghL

2. bkbafbjhF 4 FG / jKGf bgUf mltiz

3. bkbafbjhF 5 FGv mik KiwbgUf

4. bkbafbjhF 12 FG / jKGfmogilbraghil

tYgLJj5. bkbafbjhF 15,16 FG

dfis KG vfshbgUFj

6. bkbafbjhF 22 FG / jjKW vfis vnfhoFfbrj

7. bkbafbjhF 43FG /

izdbgUfiy glthyhf sFj

8. afj 47 FGtifgLJj( nfhitUJ cW, bfGkW khfis mikfyh

9. afj 49 FG tifgLJj xj cW,

khWgl cW

10. afj 57 FG nfhitf Tl, fj

11. toa 62, 63 j rk nfhL fhz

12. toa 66 FG / j g 3.1 4tJ fzFmltizgLJj

13. toa 67 FG RHnfhz flj

14. toa 76 FG thf

15. toa 77 FG Fbj nfhzf

16. brKiw toa 85 j, nfhL, nfhz, iznfhL, brFJnfhLfis dfhz

17. tufisifahSj 93 FG / jilj tufis nenfhLFf _y, fbtgoa jah br.


39/96

35

[FA (b)]

1. bkbafbjhF

5, 7, 17,19, 20,

25, 27, 31,35, 37,40, 43

j g 1.1 - 1.12 tiu csfzFfis tFgiw, LbraghL kW WnjFgagLJf

2. bkbafbjhF

6, 8, 9, 10,11, 12, 15,18, 20, 21,

27, 30,33, 34,36, 41

j KaWgh - tFgiw kWWnjF gagLbfhf

3. afj46, 47,49, 51,55, 56

j KaWgh - tFgiw kWWnjF gagLbfhf

4. afj 48,51,57 j

g 2.1 - 2.3 tiu csfzFfis tFgiw,LbraghL kW WnjFgagLJf

5. toa 64, 65,70, 81 j

g 3.1 - 3.3 tiu csfzFfis tFgiw,LbraghL kW WnjFgagLJf

6. toa 69 j RH rk tiria flj

7. toa 73,74,75 j KaWgh - tFgiw kW

WnjF gagLbfhf

8. brKiwtoa85, 87,

88, 90, 91 j KaWgh - tFgiw kW

WnjF gagLbfhf

9. brKiwtoa 91 j

g 4.1 tFgiw braghL,LbraghL kW WnjFgagLbfhf

10. tufisifahSj 93 j KaW gh

11. tufisifahSj 98 j

g 5.1 W njF kWtFgiw fF gagLbfhf.


40/96

36

[FA (a)]

jiy : bkbaf bjhF

ghlbghU : KGf Tl, fjfw nehf : KGf Tl, fj vthW brj

vgij J bfhSj.gf v : 3

bragLJ Kiw+ -2 -1 0 1 2

-2 -4 -3 -2 -1 0-1 -3 -2 -1 0 10 -2 -1 0 1 2

1 -1 0 1 2 32 0 1 2 3 4 khztfis FGfshf J d xbthU

FGit nkfl mltiz csJngh btntWvfSF mltizia cUthf brj.

nkY Ma btntW vf bfhl mltizy flfis ughk FGF mJ bra brj.

tYLjbraghL

Ma fj ghl fUij nkgLj gntW tYLjbraghLfis tFgiw mikf ll ntL.

kL TWf f eW : 10 kbgf eW : 8-9 kbgfUfu : 6-7 kbgfKanjit : 5 kbgf

tha wbtghL


Fiw fjkW thfbraghLf

5 kbg bgW khztfSF Fiw braghLfisMa totikJ KGw bgWtiu gajntL.

6 Kj 9 kbgf tiu bgW khztfSF mtfbrj iHfis flJ t bra Ma thmf ntL.

KG kbg bgw khztfSF fyhd,jidia JhL kW rthyhd fzFfistotikJ Ma mj ntL.


41/96

37

jiy : bkbaf bjhF

ghlbghU : KGf bgUf

fw nehf : xU Fiw KGit kbwhU Fiw KGthbgUFjiy v mik _y JbfhSj

gf v : 5

bragLJ Kiw xU Fiw KGit kbwhU FiwKGthbgUFtjF K Ma, Fiw KG x if KG =FiwKG vw ia v mik KiwflthW %f ntL.

( +2 ) x ( +10 ) = +20( +1 ) x ( +10 ) = +10( 0 ) x ( +10 ) = 0( -1 ) x ( +10 ) =( -2 ) x ( +10 ) =

thnw fl mltizia brJ FiwKG x Fiw KG = ifKG vwia bgWf.

( -2 ) x (+ 3 ) =( -2 ) x (+ 2 ) =( -2 ) x 0 =( -2 ) x ( -1 ) =( -2 ) x ( -2 ) =

khzt, khzfis vifnfgFGfshf J, xbthU FGF mtfnsnkflthW vfis njbjLJ MabrjJ ngh v mik Kiw fLoJma brf.


42/96

38

jiy : bkbaf bjhF

ghlbghU : KGf bgUf.

fw nehf : KGf bgUf mj.

gf v : 4

jiy : bkbaf bjhF - df bgUf

ghlbghU : U jF df bgUfgy

fw nehf : jF df bgUfgyid fwnjitahd bghUf: brtf toyhd A4 jhf, brtf

toyhd xF jhf ( Transparent sheets )

gf v : 43

bragLJ Kiw ghl totikfgl mltizia nghykhztf vifnfg njitgLvif milfis khztfisbfhnl Ma jah bra ntL.

xbthU FGF xU milia tHmltizia ug bra ntL.

bragLJKiw

khztfis VnjD U jF dfis Tw brhy

cjhuzkhf,43 x

85

kig fhj ko _y fhz.

go 1: brtf tot fhjij s th 4 rkghffshf kof


43/96

39

go 2: m 4 3 ghfij HLf

go 3: Hl mnj jhis mfy th 8 rk ghffshf kof

go 4 : 8 5 ghffis ntW ir HL

F U irfY Hlgl gF 3215

mjhtJ43 x

85

=3215

F uL xF jhfis vLJ m U jF dfis xnu

msyhd brtf btbtW tzf tiuJ bfhf.

mtiw x nk xiw bghU ghJ U irfY Hl gFahdJ, vLJ bfhl jF df bgUfgy vgij khztfis bfhnl cW brf.


44/96

40

jiy : afj

ghlbghU : cW, kh, kh kW bfG

fw nehf : nfhitUJ cW, kh bfG kWkhfis milahs fhz.

gf v : 47

jiy : afj

ghlbghU : xj cWfS khWgl cWfS

fw nehf : xj cWfis khWgl cWfismJ bfhSj

gf v : 49

njitahd bghUf: milbgo x,y,z vGa milf3 br, ( 1 Kj 9 ) tiu vGa mil3 br kW +, -,, FpLf vGa3 br milf

bragLJ Kiw khztf vifnfg gy FGfshf J milf gy tifahd afj nfhitfisjah bra ntL.

FG cs khztfis xbthUtU xU miliavLf brJ kh bfGf, kh kWcWfis ma brj ntL.

bragLJ Kiw xU mil bgo a, b, c, . . . . z tiu vGjgl 3br milf, 0 Kj 9 tiu vGjgl 3 br milfkW +, -,, FpLf vGa 3 br milfistiugl jh vG nghl ntL. xbthUkhztfis jjahf miHJ tU

braghLfis bfhLfyh.1. khia vLf brj.2. khia vLf brj.3. FpLfis bfhL xj cWfis vLf

brj.4. FpLfis bfhL ntd cWfis vLf

brj.


45/96

41

jiy : toa

ghlbghU : rk jik, rk nfhLf

fw nehf : rk jik, rk nfhLf vjcUthwJ vgij mj

gf v : 66

jiy : toa

ghlbghU : RH nfhz

fw nehf : gntW js cUtf RH nfhz mj

gf v : 67

ghlbghU : Fbj nfhzf

fw nehf : Fbj nfhzf rk vd flj

gf v : 77

bragLJ Kiw khztfisIJ FGfshf J bfhf. rkgf Knfhz, rJu, brtf, Urkgf

Knfhz, rhrJu Ma totfis jhfjJ bfhs.

xbthU FG jfSF mfgl totfrk jiknfg koJ mj fisnfholgl ntL.

nfhol f vifia (rknfhL)gf 65 cs mltizia xbthU FG brj ntL.

bragLJ Kiw Ma gf 66 cs braghLfgoRHkh jahJ bfhL Knfhz 120 0 2400, 3600 RH nfhzij brf

Ma khztf vifF VgFGfshf J bfhf

xbthU FGit RH kh jahJ tu brantL. jahJ tj RHkhfis bfhLxbthU FGF rJu, brtf, mWnfhz,

izfu Matiw tH RH nfhzfisfla brayh.


46/96

42

jiy : tufis ifahSj

ghlbghU : fgoa

fw nehf : gfilia bfhL tufis nenfhLFf bfhL fgoa jahj

bragLJ Kiw gf 77 gl cs l , m vw U nfhLf Pvw btLkhW tiuJ L1, L2, L3, L4, vdnfhzfis Ff ntL.

xF jh bfhL mglij tiuJ mjnkbghUJkhW brJ 1 80 0 F RHWkhW bra.

L1, L2, kWL3, L4 j iyfis khbfhtijma bra ntL.

UJ uL nfhLf btobfhS nghJclhF Fbj nfhzf rk vgijfla brantL.

bragLJ Kiw Ma khzt/ khzf vifF VgFGfshf J xbthU FGF xbthUgfil bfhLf ntL .

xbthU FG bfhLfgl gfilid 25 KiwcUo mj tuij nrfJ bfhs ntL

xbthU FG nH bfhLfgLsmltiz ilj tuij bfhL ugntL.

vj v mf Kiw tJsJ vgij fhf.

12

3456


47/96

43

(Summative Assessment)

Blue Print

1 2 3 5 1 2 3 5 1 2 3 5 1 2 3

1 va - - - - 3(3)8

(4)3

(1) -3

(3)2

(1)6

(2) - -

2 afj 2(2) - - -4

(4)8

(4)6

(2) - - - - - 0 -

3 toa 4(4)2

(1) - -1

(1)4

(2) - - -2

(1)6

(2) - -

4 brKiw

toa- - - - - - - - - - 3

(1)- -

5 tufisifahSj1

(1)2

(1) - -1

(1)2

(1) - -1

(1) - - - - -

7 4 - - 9 22 9 - 4 4 15 - - - - 11 40 23

13% 48% 27% 12

1 kbg dhf 20 x 1 = 202 kbg dhf 10 x 2 = 203 kbg dhf 5 x 3 = 15

5 kbg dhf 1 x 5 = 5

dh totik ( ) mil Fs vf dhf vifia FF.


48/96

44

I 10 x 1 = 10

1. -70 x 1025 x 0 k................................ MF.

m. 1 M. 71750 . -71750


49/96

45

9. Kj 20 KG vf R.................m. 20 M. 21 . 19


50/96

46

25. 5m 2 - 9UJ -3 m 2 + 63 + 9 ff.

26. x = 2vd bfhLfglh7x 2 - 2 x 2

( 3x - 1 ) (2x + 1) k vd?

27. fl TF afj nfhit vGJfy kW 6- TLj UJ x - 4 klif ff.

28. ikaij bghWJ 90 o myJ 180 oF RHW bghGJilF cUtfis tiuf.

29.

gl AOB kWAOD + DOC fhf

30. gl UJ iz kW izyh nfhLfis goaLf

31. 5, 4. 6, 8, 2 Ma tufSF R fhf

32. ab, a 2 b,a 2b 2 , 7a 2b Mat xj cWfis khWgl

cWfis FLf

33. fl totf vjid rk nfhLf csd?

34. R vwh vd?

35. 27 , 52 vJ bgaJ?


51/96

47

V 5 x 3 = 15

36. RUFf - 35

4+ 2

8

3

37. xU ngUJ 5 k neu 200 . bjhiyit flwJ.1 kneu flF bjhiy vd?

38. xU Knfhz 3 gff ( 3a + 4b -2 ) , ( a - 7 ) kW

( 2a - 4b +3 ) v, mj Rws vd?

(4-a) 2+(12-b)39. a = 5, b = -3 v kig fhf.

7 b 40. gl nfhzmsf x ,y,z kig fhf.

A 65 0 x E

y z

41. bfhLJs glUJ x 0 kig fhf.

42.xU bjhiyfh bgo iy %.5200 v, 25 bjhiyfh

bgof iy vd ?

43. 1000 mss nfhzfis tiuJ mj U rkbtoia tiuf.

VI 1 x 5 =544. 20 egf vil () nH bfhLfgLsJ. 42, 52, 45, 51, 55, 49, 62, 41,

52, 48, 64, 42, 49, 50, 47, 53, 59, 60, 46, 59 f goaiy bfhLJs ilbtfis itJ mikf. 40-45, 45-50, 50-55, 55-60kW 60-65

( myJ )

AB = 8 br. mss nfhLJoF ikaFJnfhL tiuf.


52/96


53/96

49

7 1 5 KGftFj

8 1 6 ajhtFj

vj xU viz {ajh tFj vgJtiuaWfglhjJ. nkY {aij ajh tFj

0/0 vgJ bghUswJ.9 1 8 Tl rk 0 KGf Tl rk.

10 1 10 ajhbgUf akyhj VnjD xU viz ajh bgUfilgJ akhF.

11 1 10 bgUf rk 1 vgJ KGf bgUf rk.

12 1 12 d d vgJ xU KGgF xU gF MF.

13 1 12 fyd a v + jF d

14 1 18 xU d

jiy

akw U vf bgUfgy 1 Mf Ujhy mj

vf xWbfhW jiy vd miHfgLwJ.

15 1 18xU KG vizxU djhtFjh

xU KG viz xU djh tFf mj KG vizmj d jiyah bgUf ntL.


54/96

50

16 1 19

xU dijkbwhUdjh

tFjh

xU dij kbwhU djh tFf Kj dij ulhtJ d jiyah bgUf ntL.

17 1 20 jKW vf q 0, p kWq KGf v p / q xU jKW v

vdgL.

18 1 43 mLFFf

19 2 44 kh btbtW v kfis bgwToa x cW kh

vdgL.20 2 44 kh iyahd v k bfhl X cW xU khvdgL.

21 2 44 vnfhit v fj braghLf _ykhf nrJ vGjglvf v nfhitf vdgL.


55/96

51

22 2 44 afjnfhitkhfis vfis fj braghLf _ykhfnrJ vGJtJ afj nfhitahF.

23 2

45 cW

xU khahfnth myJ xU khahfnth myJ kh

kW khf bgUf nrifnah X cW vdgL

24 2 45 bfG X cW cs kh (m) fhu bfG vg W kbwhU fhu MF.

25 2 48 xj cWf xj mLFfis bfhl xjkh myJ khfbgUf xj cWf vdgL.

26 2 48 khWglcWfbtntW mLFfis bfhl btntW khfmyJkhf bgUf khWgl cWf vdgL.

27 2 49 nfhit go

Xnu xU khia bfhl nfhit mj kh f

caj mLF mj nfhitgo vdgL.XWF nkgl khfis bfhl nfhitia xbthUcWfYs khf mLFf TLj cscaj k mj nfhitgo vdgL.

28 2 49 xU afjnfhit kxbthU kh xU kigbgWnghJ nfhit xUkig bgWwJ.

29 2 51 nfhitfTl, fj xj cWfis kLnk eh Tl kW ff Ko

30 2 53 nfhitffjxU cWig fF bra vgJ mj nekiw TLbraYF rkkhdJ MF.

31 3 60 rk jikxU bghU U miughff xnwhblhW cUtkW ms rahf bghUdh mJ rkjikvdgL.


56/96

52

32 3 61 rk nfhL

xU nfhL bfhLJs gl mikig UrkgFfshf wJ. l gh tygg ghnahrahf bghUJkh mtot rkuhf csJ vdyh.

mnfhL rknfhL myJ rkmR vdgL.33 3 67 RH rktir

xU tot mj ikaij itJ vjid Kiwf xUKGR mnj totij ngh csnjh mjvif RH rk tir vdgL.

34 3 70 FWnfhz xU nfhz ms 0 o l mfkhf 90 olFiwthf csJ v FWnfhz MF.35 3 71 brnfhz nfhz ms 90 o v mJ brnfhz.

36 3 71 nfhz xU nfhz ms 90o l mkhf 180 olFiwthf Ujh mJ nfhz.

37 3 71 nenfhzxU nfhz ff vffshf cUthF nghJnenfhL clhwJ. thW clhF nfhz

nenfhz vdgL.38 3 71 tisnfhz

nfhz ms 180o l mfkhf 360o lFiwthf cs nfhz tisnfhz vdgL.

39 3 71 KGnfhz xU KG tl 360o VgLJ nfhzijKGnfhz vdgL.

40 3 71 unfhzf2 nfhzf TLj 90o v mj uLnfhzfS u nfhzf MF. xbthU nfhzKkbwhU nfhz unfhz MF.

41 33 72 if unfhzf

uL nfhzf TLj 180o v mj uLnfhzfS if u nfhz MF. xbthUnfhzK kbwhU nfhz if u nfhz MF.

42 3 73 btLnfhzf U nfhLf xU btobfhS nghJnfhzf clhwd.

43 3 73 mLJsnfhzf2 nfhzf bghJ cia xU bghJfiubfhoUjh mit mLJs nfhzf vdgL.


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53

44 3 75 Fbjnfhzf2 nfhLf btobfhS nghJ VgL Fbjnfhzf rk.

45 4 85ikaFJnfhL

xU nfhLJo ikaFJnfhL vgJ

mnfhLJo ika tiuagLbrFJnfhL MF.

46 4 88 nfhz U rkbto

bfhLfgl xU nfhz nfhz Urkbto vgJmnfhzij U rkghffshf F rknfhLMF.

47 5 91 tu njitahd jftfis jUw vrh to mikjvj xU jft bjhF tu vdgL.

48 5 91 bjhFfgltuftufis FGf myJ tFfgLjgoUjh mit bjhFfgl tuf MF.

49 5 92 kh aiy bghWjtiu msl ToaJ kh vdgL

50 5 92 fbt

xU Fl k L L vjid jlitf

tUwnjh mj vif mj k fbtMF.

51 5 92 R xU Fl tu fbga kF fakF ilnas ntWghL R vdgL.

52 5 93 ilbtmfy

xU ilbt nk viyF viyF ilnas ntWghL milbt ms mfyvdgL.


58/96


59/96

55

[FA (b)]

1. bkbafbjhF 3, 4, 8, 9 j f

2. bkbafbjhF6, 9,15,31 j

f, muh?

3. bkbafbjhF 21 j Ka br

4. bkbafbjhF

12, 17,19, 26,31, 40,47, 52,

57

j g fzFf 1.1 Kj 1.9 tiucs fzFfis tFgiw,LbraghL kW WnjFgagLJf .

5. bkbafbjhF55, 57,

58 j brJ gh, f

6. msitf 65, 70,68,81 j brJ gh, f, Ka br

7. msitf 65, 79 j g fzFf 2.1 Kj 2.2 tiucs fzFfis tFgiw,L braghL kWWnjF gagLJf.

8. toa 84, 91,102 FG

Uj kW g 3.1. Kj 3.2tiu cs fzFfis tFgiw,L braghL kWWnjF gagLJf.

9. brKiwtoa115, 125,

132 FG

brJ gh - g fzFf 4.1Kj 4.3 tiu cs fzFfistFgiw, L braghL kWWnjF gagLJf.


60/96


61/96

57

jiy : bkbaf bjhF

ghlbghU : vf njhuha k

fw nehf : vf njhuha kig fhz brj

gf v : 52

njitahd bghUf: rJu tot v milf ( 0 Kj 9 tiu )

jiy : toa

ghlbghU : _oa gf msit bfhL - nfhzfTLj fhz

tha wbtghL


Fiw fj

kW thfbraghLf

5 kbg bgW khztfSF Fiw

braghLfis Ma totikJ KGwbgWtiu gaj ntL. 6 Kj 9 kbgf tiu bgW khztfSF

mtf brj iHfis flJ t braMa th mf ntL.

KG kbg bgw khztfSF fyhd,jidia JhL kW rthyhd fzFfistotikJ Ma mj ntL.

bragLJ Kiw khztfl 0 Kj 9 tius vfisbfhLJ VnjD xU Iyf viz cUthfbrf.

vLJfhL4, 5, 3, 9, 4 UJ X Iyf v 45394.

45394 vw v xwh, gjh, wh, Mukh lnjhua Kiwna 45394, 45390, 45300, 45000 MF. nj nghW xbthU khztU rJu tot v

milfis bfhL njhuha viz khztfmJ bfhtij cW brf .


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58

fw nehf : nfhzfis Jakhf msj, gfmsF, nfhzfSF ilnasbjhlid mj, gf vifF Vgnfhzf TLj VgL khwijbjhlgL mj.

gf v : 86,90

jiy : toa

ghlbghU : Knfhz rkikg

fw nehf : xU Knfhz VnjD Ugf msfTLj _whtJ gf msitl mf vdmj.

gf v : 89

njitahd bghUf: btisjh, Knfhz, cR FHf,Ff (cq njitnfg)

bragLJKiw

1 gfmsfvif

2 tifghL3 nfhzfTLj

Ma khztfis jjna nkflthWmltizia tiuJ bfhs brj.

Ma cjl mltizia brf. cjhuz Knfhz gf vif = 3

ehfu gf vif = 4Infhz gf vif = 5

g bragl gufis xl brf. mltiz cs gufis bjhFf brJ

totf gf vifnfg nfhzfTLj VgL khwij bjhlgL mj.


63/96

59

jiy : toaghlbghU : rtrkjik

fw nehf : rtrk totfis milahsfhz brj.

gf v : 92

njitahd bghUf : rk toyhdmriyf, fLf,tz milf, nehLjff.....

bragLJ Kiw 3 br., 4 br. kW 5 br. msf bfhl cR

FHhfis vLJbfhf. 3 cR FHhfis bfhL xU Knfhzij

mikf.

F VjhtJ Ugf msf TLj tUkhWmikayh.

3 + 4> 5 br 4 + 5> 3 br 5 + 3> 4 br MF.

njnghW cR FHfis bfhLkhztfshfnt _W gf mss Knfhzijmikf.

khztf cUtha gff Knfhzkhfmikkh myJ mikahjh vgij Ma cWbrf.

Wahf xU Knfhz VjhtJ Ugfmsf TLj _whtJ gf msitlmfkhf UF vgij ma brf.

khztfis btisjh nehLjfgff kW nfhzf mogilY 6tifahd Knfhzfis tiua brf.

tiuj Knfhz sfis msJ vGj brf. gf 88 cs mltizia tiuj

Knfhz gf msfis bfhL brabrf.

mltizUJ Knfhzrkik gig khztf _y bgWf.

3br. 4br.

5 br.


64/96

60

jiy : toaghlbghU : rtrk Knfhz ( mogil bfhif )fw nehf : g - g -g , g-nfh-g, nfh-g-nfh, br-f-g

Knfhz tif mogil bfhifia mabrj.

njitahd bghUf: Knfhz milfgf v: 97

bragLJ Kiw Ma 2 mr iyfis ( xnu khahd )jjahf itf.

mr iy I, mr iy Jitf it uL x nk bghUJtjhrtrkkhF.

nj nghW khztfis fLf, tzmilfis bfhL rtrkij ma brf.

bragLJ Kiw Ma tFgiwia W FGfshf J xbthUFGF rk toyhd Knfhz milfisbfhLf.

vLJfhL

Knfhz ABC I, Knfhz PQR J itf cA MdJ c P J njngh B MdJ Q J C MdJ R J bghUJkhW brf.

UJ Knfhz ABC MdJ Knfhz PQR -J bghUJtjh, U KnfhzfSrtrkkhF.

F AB = PQ

BC = QR

CA = RP vW csjh AB / PQ = BC / QR = CA / RP Knfhz ABC Knfhz PQR MF.

nj nghW g-nfh-g, nfh-g-nfh, br-f-g mogilbfhif bfhl rtrk Knfhzfis njitahdKnfhz milf _y ma brf.

A B


65/96

61

[FA (a)]

jiy : bkbaf bjhF

ghlbghU : mLFFffw nehf : nfhfSF, F ilnas JhuijflJ mLFFf to vGJjiymj.

njitahd bghUf: 1. Na FLg Na FLg gl.

2. A4 jh kW vGJnfh

bragLJ Kiw Ma khzt/ khza vifnfgFGfshf J bfhs ntL.

Ma xbthU FGF NaFLg glkW nfhfSilnaahd u kW nfhf iw tHfgl ntL.

xbthU FG jjahf itUF glkW tufis bfhL fl dhfSFilia fhz bra ntL.

1. NaFLg bkhj vjid nfhfcsd?

2. NaFLg ikakhf cs nfh vJ?3. xbthU nfhfS Naid RtU ghij vj

tot csJ? xbthU FGF xbthU nfhfis bfhLJ

mj nfhfSFa iwia vLJ vGj brf. xbthU FG bfhLfgLs nfh kW

F cs Jhuij mLFF to vGjbra ntL.

xbthU FG nrffgl tufisfl mltiz Ff bra.

t.v nfhfbga UJ Jhu

JhumLFFto

iw


66/96

62

jiy : toa

nehf : totfis cUthFjY, gugs kW Rwsit fhz.

bragLJ Kiw:go 1 : Ma khztfis 5 ng csla FGthf J bfhsntL.

go 2 : xbthU FGlK xU A4 jhis tH mjid _iylkoJ U Knfhz JLfshf btl bra.

go 3 : bto bgwgl Knfhzf vtif Knfhz vgij makhztfis xiw kbwh J bghU ghf brayh.

go 4 : ilj U Knfhzf, xU Knfhz gfij kbwhUKnfhz gfnjhL izJ (gff KGikahfbghUJj ntL) gntW xGfhd totfis cUthfbrf.

go 5 : khztfl fl dhfis Ma nff.1. J nghw vjid totfis cfsh cUthf Ko?2. cUtha totfis goal brayh.3. cUtha totf Rws, gugsit fhz brayh.4. Rws kW gugsF cs ntWghil xbthU

totij bfhL Ma ma brayh.

jiy : toa

nehf : totf kW gfis milahsfhz brj

fhy ms : 30 lf

bragLJ Kiw :go 1 : Ma fhj fjfgl gntW totfis jah brJ

bfhs. wF FGthf f.go 2: fjfgl midJ totfis Ma xU FGl mfntL. Ma gfis Tw mFG gF Vw totfismilahsfL fgl ntL. kw FGd mFGbraghil cWnehf ntL.

go 3: Ma Ta gfSF VwthW mFG Wahf milahsfltot rahdjh, iyah vgij kw FGdUl thfyh.


67/96

63

go 4: totfSF cfj gig milahsfhgnjhL kL, kwgnghL khztf xLwhfsh vgij Ma cWnehfglntL.

jiy : braKiw toaghlbghU : ehfufw nehf : 1) ehfu kW mj gfis bjJ

bfhSj.2) ehfu 4 nfhzf TLj 360 0.

i

1.tUtdtW ehfuf vit vgij TWf.

1. 2. 3.

4. 5.

6. 7. C

2. c o kW tFgiw fhQ ehfu tot bghUfis goaLf.

P

Q

OG H

A B

CE

FD

W

VU

X

T

RS

MN

K L

IJ

DA B


68/96

64

ii

(1) khztfis Ug ngh xU ehfuij tiua brJ mtnfhzfis ghifkh bfhL msJ mt TLj fhz brj.

(2)mil xU ehfuij bto bfhs ( gl ) mj ehF _iyfisgl csthW bto vLJ, xU nenfhil bghWJ (gl 2 csthW )mikjh xU tl mikig fhzyh.

gl 1 gl 2

UJ ehfu ehF nfhzf TLj 360 0 MF.


69/96

65

Blue Print

1 2 3 5 1 2 3 5 1 2 3 5 1 2 3

1 bkbafbjhF1

(1) - - -6

(6)10(5)

9(3) - -

4(2) - - -

2 msitf 3(3) -3

(1) -5

(5)6

(3) - - -2

(1)6

(2) - -

3 toa 4(4)

2(1) - - -

6(3)

6(2) - - - - -

4 brKiwtoa 1(1) - - - - - - - - - - - - -

14 48 12 17% 57% 14% 1

1 kbg dhf 20 x 1 = 202 kbg dhf 10 x 2 = 203 kbg dhf 5 x 3 = 155 kbg dhf 1 x 5 = 5

dh totik ( ) mil Fs vf dhf vifia FF.


70/96

66

I 10 x 1 = 10

1. U jKW vf fj................................ MF.

m. jKW v M. uilgil v . xiwgil v


71/96

67

8. xU Knfhz U btnfhzf 130 0, 1400 v _whtJbtnfhz.....................MF.

m. 100 0 M 90 0 . 110 0


72/96

68

22. RUFf ( 74

3+ 6

3

2) 3

5

4

23. 24 vw v tf xwh yfij fhf.

24. xU Ehyf khztf gogjF xUehisF, xU KiwF 16nguhf 5

Kiw mDkfglh mEhyf mW gojtf vifahJ?

25. 725 cl vj viz Todh mJ fd_yij bgW?

26. mltiz iw brf.

tir 1 2 3 4 5 6Mfvif 3 9 27 ? ? ?

27. 529 vw viz 1000M tFFnghJ bgW jrk v vd?28. xU tl l 84 br v fhtl Rwsit fhf.

29. gl Hlgl gF gugsfhf.

30. xGF gynfhzF xU cjhuz jUf.31. xU miutl gugs 44 2 v xU tl gugs ahJ?

32. gl x 0 = 78 v y 0 kig fhf.

33. gl DAB CAB vd Wf.


73/96

69

34. U nfhLf rtrk nfhLfshf Uf gjidf ahJ?

35. Knfhz ABC A= 75 0 , B = 600 kWB + C = 1050 vwh C kahJ?

V 5 x 3 = 1 5

36. RUFf. -3

1x

4

5+

5

3 (

2

1-

4

1 )

37. f 3 ( x 4 ) = 12

38. 2.14829 vw jrk viz 1, 2, 3 kW 4 jrk lUjkhf vGJf.

39. miutltoyhd fh Mu 21 xU lUF %.15 j mjFRWnt mikf MF bryit fhf.

40. tl toyhd xU jhu f Mu 35br J xU rJu totisfgLwJ v mrJu gfij fhf.

41. 14br lKs miutl Rws kW gugsit fhf.

42. Knfhz ABD nfhzfis fhf ?

43. 23 br, 17 br, 8 br vgd Knfhz gffshf mikkh vdrghf.

VI 1 x 5 = 5 AB = 6 br BC = 6br BAC = 500 ACD = 300 kWCAD = 1000 vw

msf bfhl ehfu tiuJ mj gugsit fhf.

PQ II SR , PQ = 6.8cm , QR =7.2 cm PR = 8.4 cm RS = 8 cm msf bfhl rtf tiuJ mj gugsit fhf.


74/96

70

1. 1 3 jKW vf q p

vw to mik vf jKW

vf q 0 nkY, p, q vdgd KGfshF.

2. 1 4jKW vfmil g(Tliy bghWJ)

ba

kWd c

vgd VnjD U jKW

vf vba

+d c

vgJ xU jKW

v.

3. 1 4jKW vgkhW g(Tliy bghWJ)

ba kWd c vgd VnjD U jKW

vf vba

+d c

=d c

+ba

4. 1 5jKW vfnr g(Tliy bghWJ)

ba

,d c

kW f e

vgd VnjD _W jKW

vf vba

+d c

+ f e

=ba

+d c

+ f e

MF.

5. 1 5 jKW vfTl rk

ba

vgJ xU jKW v v

ba

+ 0 = 0 +ba

=ba

, F 0 vgJ vj xU

v Tl rkahF.


75/96

71

6. 1 5 jKW vfTl vkiw ba vgJ

ba Tl

vkiw MF.

7. 1 6

jKW vfmil g(fjiy bghWJ)

ba

kWd c

vgd VnjD U jKW

vf vba

-d c

vgJ xU jKW

v MF.

8. 1 6gkhW g(fjiy bghWJ)

iw brahJ

ba

-d c

d c

-ba

9. 1 6nr g(fjiy bghWJ)

iw brahJ

ba

-d c

- f e

ba

-d c

- f e

10. 1 7 jKW vfmil g(bgUfiy bghWJ)

b

akW

d

cvgJ VnjD U jKW

vf vba

x d c

=bd ac

vgJ jKW

v MF.


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72

11. 1 8jKW vfnr g(bgUfiy bghWJ)

ba

, d c

kW f e

vgd VnjD _W jKWvf v

ba x

d c

x f e

=ba

x d c

x f e

MF.

12. 1 8jKW vbgUf rk(bgUfiy bghWJ)

ba

vgJ VnjD xU jKW v v

ba

x 1 =ba

= 1 x ba

MF.

13. 1 8 a bgUfgy (jKW v) b

avgJ VnjD xU jKW v v

ba

x 0 = 0 = 0 x ba

14. 1 9jKW vbgUf jiy (m)vkiw

ba

vgJ jKW v vab

vgJ

bgUf vkiw (m) jiy MF.

15. 1 9jKW vftFjmil g

ba

kWd c

vgd U jKW vf kW

d c

0 vba

d c

vgJ xU jKW v

MF.

16. 1 9gkhW g iwbrahJ(tFjiy bghWJ) b

akW

d c

vgd U jKW vf v


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73

ba

d c

d c

ba

17. 1 10

jKW vfnr g(tFjiy bghWJ) iw brahJ

18. 1 21 mLF F f

bga m

tF

am

a n

m(a

a 0

jiy


78/96

74

19. 1 22xnu mLF vfisbfhl vfbgUf

a m

m

( ba

20. 1 27 tf

X viz mnj vzh bgUFnghJilF v mbt tfvdgL.

F

21. 1 32 tf _yf

X viz mnj vzh bgUFnghJilF bgUfgy mbt tfvdgL. mj v, mbgUfgy tf_y vdgL.v.fh. 3 tf 9 ( 3 x 3)

9 tf _y 3

X

ga( x (m

22. 1 41 fdX viz mnj vzh KKiw bgUfilf bgUfgy mbt fdvdgL.

23. 1 44 fd _yffd _y vgJ fd fhg jiy Kiw 3

v


79/96

75

24. 1 49 njhuha k

xU v uL vfSF il rkfs Ujh mj vfSl f bgav kng mj v njhuhakghF.

ji_y

25. 1 49 vf KGjhFj

bfhLfgl vf f mUYskfis fU bfhtij vf KGjhFj vdgL.

1.

2.

26. 2 61 gu xU rkjs gF milgL _oa cUtgFia gu vnwh.

27. 61 Rws xU _oa tot Rws vgJmUt viy s MF.

28. 2 61 tl gu

A

Ft36


80/96

76

29. 2 62 miutl gu A

30. 2 62 miutl Rws

P =Fm=

31. 2 62 fh tl gugs A

32. 2 63 fh tl Rws P

33. 2 66 TL cUtf

uL (m) mjF nkgl cUtfis xwgfij kbwh J bghU itjhJ cUt ilwJ. it TL cUtfvdgL.

34. 2 67 gynfhz_W myJ mjFnkgl nenfhL Jlh cUthfgL _oa rkjsguiggynfhz vnwh.

35. 2 67 xGF gynfhzgy nfhz gffS, nfhzfSrkkhf U mJ X xGF gynfhzvdgL.

36. 2 68 xGfw gynfhz xGfw totik cUthF gynfhzf xGfw gynfhz vdgL.


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77

37. 2 68 F gynfhzgy nfhz Fiwjgr xU nfhzkhtJ1800 l mfkhf Ujh F gynfhzvdgL.

38. 3 85 Knfhz

xU js _W nfhL JLfshmilgL cUt Knfhz MF.

jiFF1)

2)

3)

39. 3 89 Knfhzrkik g

xU Knfhz VnjD U gfmsf TLj _whtJ gf msit lmfkhF.

40. 3 93 rtrk Ujs cUtf x J xWrahf bghUdh mit rtrk vdgL. ijF

41. 3 94 rtrk Knfhzf

U Knfhzf VnjD xU

Knfhz _W gffS _WnfhzfS Kiwna kbwh _WgffSF _W nfhzfS rk vmit rtrk Knfhzf vdgL.


82/96

78

42. 3 95 g-g-gmogil bfhif

Fg-xUgKgmr

43. 3 96 g-nfh-g mogilbfhif

xUgnf

KmKmr

44. 3 97 nfh-g-nfh mogilbfhif

xUnf izKnf

izmr


83/96

79

45. 3 98 fzxU brnfhz Knfhz brnfhzvgf fz MF.

46. 3 99 br-f-gmogil bfhif

xUfcxbrfcx

mr

47. 3 100 U rkgf KnfhznjwxU Knfhz rk gffSF vnusnfhzf rk.

48. 4 107 ehfu

xU js ehF gffsh milglcUt ehfu.

F1)

2)

3)


84/96

80

49. 4 116 rtf

xU ehfu xU nrho vgff kL izahf U mj ehfu rtfMF.

Frtfbjhrt

2

1

50. 4 126 izfu vgff izahf cs xU ehfu izfu MF.

F1)

2)

3)

4)

5)


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81

[FA (b)]

I.

1. a v fz yhj vm. 2 M. 0 . 1


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82

[FA (b)]

1. Knfhz 3 nfhzf TLj 180o MF.

2. xU Knfhz xUgfij l ilF btnfhz mj

cbsnfhzF rk.

3. miutl mik nfhz 360 0 MF.

4. gy nfhz N gff Ujh mj cnfhzf TLj.

( N-2) 1800

5. xU Knfhz a nfhzF vnu cs gf bga

nfhzF vnu cs gfij l aJ.

1. xU tl cs fh tlf vif vd?

2. rkgf Knfhz cs xbthU nfhz ms vts?

3. ehF gff rkkhf cs ehfu vJ?

4. 5 br gf sKs rJu gugs?

5. 1 br MuKs tl gugs vd?

1. tl Rws vd?

2. xU rkgf Knfhz gu Nu ahJ?3. xU brnfhz Knfhz gu vd?

4. xU ehfu gu vd?

5. xU rtf gu fhz cj Nu ahJ?


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1. AC = 7 br mss nfhLJoF ikaFJnfhL tiua ntoagoiyfis tirgLJf.

m) C I ikakhf bfhL tiuagL mnj MuKs tlf Kijafis X kWY fis btLkhW tiuf.

M) AC =7 br mss nfhLJL tiuf. ) XY I nrf. nfhLJL AC I O btLwJ.


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1. nfho, gJyr, yr,..................................Wtiu br.

2. jhnd 5,6 yf vfis cUth mj K, bjhl fLo.

3. 129+47+2+11+13= vjhd Kiw ilfhf.

4. 126- tF, gfh fhuf fhf.

5. 156,36 vw U vf W bghJklF 468 v .bgh.t ahJ?

6. xW ilahdh IJ dhfis jah brf.

1. X U ehfh vil 7.. 200 v 10 U ehfhf

vil vd?2. uh# vgt fil 65l ebybz UwJ. 25l 250.. ebybzia wwF cs ebyiz ms vts?

1. xU t brY nfhLfis fhf.

2. tU gf msfis bfhl Knfhzfis tifgLj.

m. 7br 7br 7 br M. 7br 7br 5br . 4br 5br 6br

IHGF

A B C D E


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1. msnfhiy kL gagL nfhLJL tiuf.a) AB= 7Cm b) CD= 7.5Cm C) PQ = 8 Cm

2. msnfhiy ftuhaij gagL nfhLJL tiuf.

a) AB= 5Cm b) BC= 7.9Cm C) LM = 9 Cm

1. RUFf. 50 x ( -30 ) x ( -14 )

4 x ( -6 )

2. xU kGJ xU l bgnuh 18. brwJ. kGJ 22

1

bgnuh vts uij flF ?

3. xU rhuz UilF njitahd J ms 221

v 4921

J vjid Uilf ijfyh?

4. 5

3F

7

5F ilgl IJ jKW vfis fhf.

5. vj vQl21

46I Todh

3

10ilF?

6. U jKW vf TLj 1 mt X v20

4v kbwhU

v ahJ?7. U vf bgUfgy 98 mtW X v 35 v kw viz

fhf.

1. x = -2 v fhQ nfhitf k fhf.(1) x + 6 (2) 8 x -2 (3) 18 - 5x 2

2. a = 6,b=-4 v tUtdt k fhf.(1) 4a -3b (2)a 2 + b 2 (3)5a 2 + 4b - 2

3. P= x 2 + 7 kWQ = -x 2 + 3 x -2 v, P Q 8 k fhf.

4. xU Knfhz _W gff 6c c 2 + 3, -3c9 kWc2 + 4c +10 v mj Rws vd?


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87

1. xU tlid tiuJ.

(1) mtl Rws kW gugs fhf?

(2) mtl miutlkhdh Rws, gugs vd?(3) mtl fh tlkhdh Rws, gugs vd?

2. xU brtf mfyth UwK miutl mikjhnghcsJ. mj brtf gF s 24br mfy 14br v mj guahJ?

1. xU Knfhz _W nfhzf jf 1 : 2 : 3 v nfhzmsfis fhf.

2. fhQ msf vJ Knfhzij cUthF?

(1) 2, 5, 6 (2) 1, 2, 3 (3) 12, 13, 24 (4) 1, 4, 6

1. AB = 7.5 br, AD = 6 br, CD = 5 br , nfhz BAC = 450 kWnfhz ABC = 500 msf bfhl ehfu tiuf

2. AB ||CD, AB = 9 br, BC = 5.6 br, AC= 8.5 br kWCD = 7 br msf bfhl rtf mikJ mj gugsit fhf.

3. AB = 8 br, AD = 7.1 br kWBD = 9.2 br msf bfhl ABCDvw izfu mikJ mj gugisit fhf.

(Open Ended Questions)1. xUt xU fz il 3 vW Tdh m fhz fzid mikf.

vzw dhf mikfyh. m Tl, fj, bgUf,tFj, ..k, .bg.t, df, gugs, j nghwghlfUJfis gagLjyh.

2. KUf _W vfis Toa bkhj 20 vW il iljJ.1) mbtf VJ 3 klF iyba,2) mbtf VJ 4 klF iyba, mbtf ahit?

3. nl, rhy l `54 vw xnu a v kL jh 6 klfhf,U vGdh 5 klfhf mikJsJ vwh. Mdh rhymjifa vf nkY gy csd vwh. t ahUila TW r?

4. uL dfis Todh il83

t xbth gF 8 Mf

UUf ntL vgJ rah? iyba vLJfhL xiw jUf.


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5. 120 nfhfis xUt 4 bgof tUkhW glh.Kj kW ulh bgoYs nfhf vifahdJ, _whkW ehfh bgoYs nfhf vifl j rk Ujh mt nfhfis vjid tf glh.bgo vif, ulh bgo vif Ma j MdJ

_wh, ehfh bgo viffSilna Md jJl jrk csJ vwh mt nfhfis vthW glh.6. bgUf gyid l mfkhd TL bjhif cs 3 KGfbsf fhz

mnrh Kawh. f cjt aYkh?7. uL KG vf bgUfgy 96, mt TLj 30 l Fiw v

ayToa U vfis vGJf?

1. 86, 97, 66, 87, . . . vw tir mik mLj v?2. xU brtfij vjid tf ghahfyh (koj _y)?3. 86 ghia l bga 5 klF ahJ?4. 5/8 kig vthW fhgh?

1. eh X Myf viz idnw. mj yff TLj 43.tU TWf uL kLnk bkm) mJ xU tf v.M) mJ xU fd v. ) mbt 500000I l aJ

mj v ahJ?

1. ghjhs rhfil MwF Ff V rJukhf Ugiy? eikRs bghUf, fUf t totikf, mt

gaghLl bjhlsikF vLJfhLf jUf.2. xU jh uL btntW jj rJuf csd. mit uL izjh xU a rJu ilFkh?

1. xW ilahf tUkhW 10 dhfis / TWfis jah brf.2. {a ilahf tUkhW 10 dhfis / TWfis cUthFf.3. 2 iltUkhW 10 dhfis / TWfis cUthFf.4. . . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .. . . . . . . . . . .5. 100 a + 10 b + c

100 b + 10 c + a100 c + 10 a + b TWfis gagL _yf vfis cUthkf.

6. 10 a + b vw Tiw gagL


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90

nkY, mbghUf gugs kW Rwsit fhz brf.

mwhl th f fhQ nfhzf cUthF lf 10 idgoal brf.

mitf vtif nfhzf vgij fhf.

VnjD xU brjh cs xU gia vLJbfhL mYs 2vGJf, 3 vGJf kW 4 vGJfis bj brJ, mjidbfhL fbt goaiy jah brf.

6. nehL milia gagL Ugkhz cUtfis fjJ tubrayh kW mYs nfhzf kW gffvifia goal brayh.

7. FWF mltizia brjhUJ fjf brJ, mbkhj rJufis fLof brhy. m, Hlgl rJufkW Hlglhj rJuf vifia flJmtilnas j, d kW rjj FLf.

1. nrich.maths.org2. http://www.aimsedu.org/index.html 3. Harold Reiters Home Page_files4. 5. http://www.mathcats.com/explore/tessellations/tesspeople.html 6. http://www.mathleague.com/ 7. http://www.shodor.org/interactivate/activities/perm/index.html 8. www.gogeometry.com 9. www.ct4me.net/Ohio Graduation Math Test Prep GeometryStrand.htm10. http:www.scribd.com/Theorems-and-proofs11. http://mathforum.org/ 12. http://www.auntymath.com/ 13. http://www.coolmath.com/ 14. http://www.cut-the-knot.com/content.html 15. http://www.k111.k12.il.us/king/math.htm 16. http://www.olemiss.edu/mathed/contest/contests.htm 17. http://matti.usu.edu/nlvm/nav/ 18. The New Zealand Curriculum Exemplars (Use google.com)19. Teacher Lab20. http://www.worldofnumbers.com/ 21. http://my.hrw.com/math06 07/nsmedia/tools/Algebra Tiles/Algebra

Tiles.html/ Perimeter and Circumference:22. http://www.regentsprep.org/Regents/math/ALGEBRA/AS1/pracper.ht

m 23. www.gomath.com/ 24. http://www.regentsprep.org/ 25. New Zealand Maths Olympiad Committee online


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26. www.cumbavac.org/Math.htm 27. www.AAAmath.com 28. www.figurethis.org 29. www.mathcats.com 30. www.easymaths.org

31. www.bbc.co.uk/education/megamaths/tables.html 32. www.mathleague.com 33. www.fleetkids.com 34. www.funbrain.com/numbers.html 35. www.teachnet-uk.org.uk 36. http://www.tes.co.uk/ 37. www.mathsroom.co.uk/index.htm 38. www.interactivemaths.net 39. www.illuminations.nctm.org 40. www.cimt.plymouth.ac.uk 41. www.mathsmistakes.info

42. Absurd Math: Interactive mathematical problem solving game series.43. A Maths Dictionary for Kids: An animated, interactive dictionary forstudents which explains over 400 common mathematical terms

44. Archimedes Book of Lemmas: Geometry Step by Step from the Land of the Incas, 15 propositions on circles.

45. Archive of math Puzzles:46. AplusMath: math resources47. Ask Dr. Math48. Bamdads Math Comics:49. Centre for Innovation in Mathematics Teaching: Resources, Puzzles,

topics50. Curious and Useful Math: Tricks and rules for quick calculations.51. Figure This: Math challenges for families52. Fun Brain: Interactive math activities, change maker and wacky tales53. FunSchool.com: Educational games and activities54. Free Math Games: Free math games, symmetry activities & examples,

shapes and other activities.55. Mrs. Glossers math Goodies: Interactive, self-checking math lessons,

puzzles, & homework tips.56. Making Mathematics: Student, teacher and mentor resources.57. Martindales The Reference Desk: Calculator on-line Center58. MathEbook.net: Math resources and fillable pdf worksheets that can be

printed.

59. Mathematical Interactivities: on-line math activities for students topractice their math skills.

60. Mathematics Worksheet Factory:61. Math Journals for All Ages: Great information to help student clarify

their thinking in math.62. Math Playground: Online math activities and resources.63. Measure 4 Measure: Collection of sites that estimate, calculate, evaluate

and translate.64. PowerPoint Presentations for Math: by Monica Yuskaitis


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65. Tessellations.org: Observe and create your own tessellations.66. Virtual Library of Mathematics:67. Virtual Manipulatives: Glencoe math manipulatives K-8 grades.68. NCTM Home.69. amtionline.com

70. Proofs without words.71. Open-ended questions in mathematics.72. edHelper.com73. Active worksheets74. www.heymath.com

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