8th maths samacheer complete tamil medium part 1

8/6/2019 8th Maths samacheer complete tamil medium PART 1

http://slidepdf.com/reader/full/8th-maths-samacheer-complete-tamil-medium-part-1 1/64

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Kf¥òiu

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Kidt®. ». Ïuéghlüš MÁça® FG¤ jiyt®

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t. v©. m¤Âaha« g¡f«

1. bkŒ v©fë‹ bjhF¥ò 1

2. Ïa‰fâj« 59

3. thœéaš fâj« 100

4. msitfŸ 150

5. toéaš 173

6. brŒKiw toéaš 207

7. tiugl§fŸ 252

8. étu§fis¡ ifahSjš 269

éilfŸ 303

bghUsl¡f«

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1

bkŒ v©fë‹ bjhF¥ò

1.1 m¿Kf«

m¿éaè‹ muÁ fâj«

fâj¤Â‹ muÁ v© Kiwæd«

Ït® òfœ bg‰w,K¡»akhdA§nfça¡fâj tšYe®Mth®. v®lh° ü‰W¡ fz¡fhdtšYe®fSl‹nr®ªJv©âaèšk‰w vªj fâjtšYe®fisÍ«

äŠR« t©z«MŒntLfisbtëæ£LŸsh®.

ÏtUila fâjM®t« ÏtUila_‹W taÂnynabjçªjJ. ÏtuhšxU kåj‹ thœªjéehofis¡ Tlfz¡»l KoªjJ. ÏtuJ thœ¡ifMdJ Ït® thœ ehënyna “N

v‹w v©. ghšv®lhi[¡ F¿¤jxU Á¤Âu«’’ v‹wbgaçš Mtz¥glkh¡f¥g£lJ.

v©fŸmHfhdit. mitmHf‰wit våš,k‰w vit mHF?’’

vd v®lh°T¿dh®.

ghš v®lh°26 kh®¢, 1913 -

20 r l g , 1996)

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1.2 ÛŸ gh®it - é»jKW v©fis v©nfh£oš F¿¤jš

é»jKW v©fŸ

cjhuz«:

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1.3 é»jKW v©fë‹ eh‹F g©òfŸ

1.3.1 (m) T£lš

(i) milÎ¥ g©ò

b

a k‰W« c v‹gd VnjD« ÏU é»ÂKW v©fŸ våšb

a c+

v‹gJ« xU é»jKW v© MF«.

cjhuz«:

(ii) gçkh‰W¥ g©ò

b

a k Wd

c v gd VnjD ÏU é»jKW v©fŸ

åšb

c

b

a+ = +

cjhuz«:

x›bthU Ïaš v©Q«

xU é»jKW v© MF«.

Ïj‹ kWjiy c©ikah?

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(iii) nr®¥ò¥ g©ò

cjhuz«:

(iv) T£lš rkå

b

a

v gJ xU é»jKW v© våš b

a

b

a+ +

.T£lš rkå

cjhuz«:

(v) T£lš vÂ®kiw

T£lš vÂ®kiw

b‹gJ xU é»jKW v© våš j- v‹w é»jKW v©iz 0

b

a+ =j-

v‹wthW fhzyh«.

cjhuz«:

ó¢Áa« xU Áw¥ò

é»jKW v©zhF«.

Ïjid 0 =q

0

q 0

vd vGjyh .

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v©fŸT£lš

milÎ¥g©ò

gçkh‰W¥g©ò

nr®¥ò¥ g©ò

Ïaš v©fŸ

G v©fŸ M«

KG¡fŸ

é»jKW v©fŸ M«

1.3.1 (M) fê¤jš

(i) milÎ¥ g©ò

b

a

k‰W«c

v‹gd VnjD« ÏU é»jKW v©fŸ, våš, b d

c

-‹gJ« xU é»jKW v© MF«.

cjhuz«:


bk W

d c v gd VnjD ÏU é»jKW v©fŸ våš

bc c

ba- - .

cjhuz«:


b,d

c k‰W« f

v‹gd _‹W é»jKW v©fŸ våš

ba

f e

- -`d c e

- jba

d c

-`! MF«.

ÏU é»jKWv©fŸ rk« våš,mit gçkh‰W¥g©ig ãiwÎbrŒÍ«.

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cjhuz«:

v©fŸfê¤jš

milÎ¥g©ò

gçkh‰W¥g©ò

nr®¥ò¥g©ò

Ïaš v©fŸ Ïšiy

KG v©fŸG fŸ

é»jKW v©fŸ Ïšiy

1.3.1 (Ï) bgU¡fš

(i) milÎ¥ g©ò

ba k W c v gJ VnjD ÏU é»jKW v©fŸ våš

b d c

bd ac# =

‹gJ« é»jKW v© MF«.

cjhuz«:


bk W

d

c v gd VnjD ÏU é»jKW v©fŸ våšb b

a# # MF .

cjhuz«:

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b

a , c k‰W« f e v‹gd VnjD« _‹W é»jKW v©fŸ

våšb

e# ##

a#`= MF«.

cjhuz«:

(iv) bgU¡fš rkå

b

a v‹gJ VnjD« xU é»jKW v© våšb

a

b# # MF«.

cjhuz«:

(v) ó¢Áa¤Â‹ bgU¡fš gy‹

cjhuz«:

KG¡fS¡F 1v‹gJ bgU¡fšrkå MFkh?

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(vi) bgU¡fš vÂ®kiw mšyJ jiyÑê

bv‹gJ é»jKW v© våš,

a

b v‹gJ bgU¡fš vÂ®kiw

mšyJ jiyÑê MF .

cjhuz«:

v©fŸbgU¡fš

milÎ¥g©ò

gçkh‰W¥g©ò

nr®¥ò¥g©ò

Ïaš v©fŸ

KG v©fŸ M«

KG¡fŸ Mé»jKW v©fŸ

1.3.1 (<) tF¤jš

(i) milÎ¥ g©ò

bk W

d

c v gd ÏU é»jKW v©fŸ, k Wd

c0 , våš

b

a

d

c

v‹gJ xU é»jKW v© MF«.

cjhuz«:


i) 0 é‰F jiyÑê »ilahJ.ii) 1 k‰W« – 1 v‹w é»jKW v©fS¡F

m›bt©fns jiyÑêfshF«.

0.3 v‹gJ 33

1 Ï‹

jiyÑêah?

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b

a k Wd

c v gd ÏU é»jKW v©fŸ, våšb

a

d d b'' MF«.

cjhuz«:


b , d

c

k‰W« f e

v‹gd _‹W é»jKW v©fŸ

åšba

f e

' ''a

'` MF«.

cjhuz«:

v©fŸ

F¤jš

milÎ¥g©ò

gçkh‰W¥g©ò

nr®¥ò¥g©ò

Ïaš v©fŸ Ïšiy

KG v©fŸ

G¡fŸ

é»jKW v©fŸ Ïšiy

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1.3.1 (c) g§Ñ£L¥ g©ò

(i) T£lè‹ ÛJ bgU¡fè‹ g§Ñ£L¥ g©ò

,b

c k‰W« e v‹gd VnjD« _‹W é»jKW v©fŸ våš

ba c

ba e

# # #+ MF«.

cjhuz«:

(ii) fê¤jè‹ ÛJ bgU¡fè‹ g§Ñ£L¥ g©ò

,b

a

d

c k W f

v gd VnjD _ W é»jKW v©fŸ våš

ba c

ba e

# # #- MF«.

cjhuz«:

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gæ‰Á 1.1

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1.3.2 ÏU é»jKW v©fS¡»ilna cŸs é»jKW v©fis¡ f©l¿jš

ÏayhJ.

ÏaY«.

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ÏaY«.

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ÏU é»jKW v©fS¡F Ïilæyhd é»jKW v©fis¡ f©l¿jš

1. N¤Âu Kiw

2. kh‰W Kiw

vL¤J¡fh£L 1.1

ÏU v©fë‹ ruhrç v¥bghGJ« mªj v©fS¡F Ïilna mikªÂU¡F«.

bt›ntW Kiwfis¥ ga‹gL¤Âdhš bt›ntW é»jKW

v©fis a ¡F« ¡F« Ïilna fhzyh«.

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Ô®Î

N¤Âu Kiw:

kh‰W Kiw:

vL¤J¡fh£L 1.2

Ô®Î

F¿¥ò: Ïªj é»jKW v©fis eh«5

3 1

20

1

2

1< < <

- - - vd vGjyh«.

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gæ‰Á 1.2

1.4 _til¥ò¡ bfh©l v©nfhitfë‹ RU¡f«

- mil¥ò, O - Ï , D - tF jš, M - bgU fš, A - T lš, S - fê jš

F¿¥ò:m t bg T f

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jhF¥òF¿pLfŸ

ga®

--- nk‰nfh£L mil¥ò (é‹Fy«)

( ) mil¥ò F¿pL

{ } fz mil¥ò

[ ] rJu mil¥ò

‘ Ï‹’ mšyJ ‘ Ïš’ mšyJ ‘kl§F’ (of) v‹w braè

vL¤J¡fh£L 1.3

Ô®Î

vL¤J¡fh£L 1.4

Ô®Î

vL¤J¡fh£L 1.5

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1.5 mL¡FfŸ : v©fis mL¡F¡ F¿ toéš KG¡fë‹ goahf

vGJjš

tiuaiw

‘ ’ v‹gJ äif KGthf ÏU¥Ã‹ x v‹gJ x.x.x.....x MF«..

mjhtJ, xn = x × x × x × ..... × x ( Ï§F n 1 )

F¿¥ò : x1 = x.

n jlitfŸ

fhuâfŸ

v¥go thÁ¥gJ?

Ïij nkY« éçthf és¡f Ñœ¡fhQ« m£ltizia neh¡Ff :

t.v©.

v©â‹ bjhl®bgU¡f‰ gy‹

mL¡F¡F¿mik¥ò

momL¡bf©mšyJ go

mšyJ mL¡F

1 2 2 4

2

2 44- 3h4- 4- 3

3

3

2

`3

# #

`3# # #

6

j 3

2

4 ...a aa jlitfŸ m a

vL¤J¡fh£L 1.7

Ô®Î:

mL¡FmšyJ

go

mo

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1.6. mL¡F¡F¿ éÂfŸ

(i) bgU¡fš éÂ

éÂ 1a a a

m n m n

= , Ï§F ‘ v‹gJ bkŒba© k‰W« , n v‹gd äif

G v©fŸ.

cjhuz«

(ii) tF¤jš éÂ

éÂ 2 n

m

m n , Ï§F a 0 k‰W« , n MdJ äif KG v©fŸ,

Ï§F m > MF«.

cjhuz«

(iii) mL¡F éÂ

éÂ 3a

n m n

am , Ï§F m k‰W« v‹gd äif KG

©fŸ MF«.

cjhuz«

(iv) ó¢Áa¤ij mL¡fhf¡ bfh©l v©

,m o våš k‰bwhU Kiw :

m m m3 3 3 3

= ( 2« éÂ¥go); m mm m

m m3 3

3

3

#m

#m= = = 1

1a( ) ( ) x y

#a =d ãWÎf

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éÂ 4a v‹gJ ó¢Áa« jéu ntW vªj é»jKW v©zhf

ÏU¥Ã‹, a 1= MF«.

cjhuz«

(v) jiyÑœ éÂ

cjhuz«

éÂ 5

‘ v‹gJ X® bkŒ v©zhfÎ«, ‘m MdJ KG v©

MfÎ« ÏU¥Ã‹ a1m

m=

- MF«.

(vi) xnu mL¡F v©fis¡ bfh©l v©fë‹ bgU¡fš

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bghJthf, a, b v git VnjD ÏU KG v©fŸ våš

2 a b b2 2^ ^ h

Ïj‹ _y« ek¡F¡ »il¥gJ mL¡Ffë‹ bgU¡fš éÂ MF«.

( ....a aa # m Kiw)# ( .....b b m# Kiw )= ( ......b ab m# #a # Kiw) = mhab

mjhtJ, a m = mhb

éÂa

m = m^ hb , Ï§F , b v‹gd bkŒba©fŸ k‰W« m v‹gJ

KG v© MF«.

cjhuz«

(vii) mL¡Ffë‹ <Î éÂ

éÂm` j =

b

am

m

, Ï§F 0! , k W , v gd bk ba©fŸ, m

KG v© MF«.

cjhuz«

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vL¤J¡fh£L 1.8

Ô®Î

vL¤J¡fh£L 1.9

Ô®Î

gfh¡fhuâ¥ gL¤jš

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vL¤J¡fh£L 1.10

Ô®Î

vL¤J¡fh£L 1.11

Ô®Î

vL¤J¡fh£L 1.12

Ô®Î

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vL¤J¡fh£L 1.13

Ô®Î

gæ‰Á 1.4

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1.7 t®¡f§fŸ, t®¡f _y§fŸ, fd§fŸ k‰W« fd _y§fŸ

1.7.1 t®¡f§fŸ

X® v©iz mnj v©zhš bgU¡F«nghJ »il¡F« v© m›bt©â‹

t®¡f« vd¥gL«. Ïjid m›bt©â‹ mL¡if mšyJ goia ‘2’ Mf ca®¤Â

Gjyh .

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KG t®¡f«

t®¡f v©fë‹ g©òfŸ

v© t®¡f«

1 1

1

11 121

19 3 1

v© t®¡f«

2 4

64

12 144

1 324

v© t®¡f«

3 9

49

13 169

17 2 9

v© t®¡f«

4 1

6 36

14 196

1 25

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vL¤J¡fh£L 1.14

Ô®Î

vL¤J¡fh£L 1.15

Ô®Î

vL¤J¡fh£L 1.16

Ô®Î

t®¡f v©fë‹ mH»a totik¥ò

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b

a v‹w é»jKW v©â‹ t®¡f§fis¡ fhQjš

b#

b

a =b

a2

2

=

cjhuz«

gæ‰Á 1.5

bjhFÂæ t® fgFÂæ‹ t®¡f«

(i) 452 = 2025 = (20 + 25)

(ii) 552 = 3025 = (30 + 25)2

∴ 5, 55 v‹gd

'nf¥çfh®' v©fŸMF«.

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1.7.2 t®¡f _y§fŸ

tiuaiw

t®¡f _y«

X® v©â‹ t®¡f _y¤Â‰F v‹w F¿pL ga‹gL¤j¥gL»wJ.

F¿¥ò: x t®¡f _y¤ij x mšyJ x 2 vd vGjyh«.

vdnt, 4 = 2

1

h4 k W 100 2

1

h100 MF .

9 Ï‹ t®¡f _y« 3

3 Ï‹ t®¡f« 9

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X® v©â‹ t®¡f _y¤ij¡ Ñœ¡f©l Ïu©L têKiwfëš fhzyh«

(i) fhuâ Kiw

(ii) ÚŸ tF¤jš Kiw

(i) fhuâ Kiw

vL¤J¡fh£L 1.17

Ô®Î

gfh¡ fhuâ¥gL¤jš

KGt®¡f« t®¡f _y«

1

1

3

81

1

4

9100

225

2025

7396

801

10

15

45

86

9

10,000

14, 41

2,97,025

,98,001

100

121

545

99

10,00,00015,00, 25

7,89,96,544

99,80,001

10001225

8888

999

m£ltiz 1

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vL¤J¡fh£L 1.18

Ô®Î

vL¤J¡fh£L 1.19

Ô®Î

vL¤J¡fh£L 1.20

Ô®Î

vL¤J¡fh£L 1.21

Ô®Î

vL¤J¡fh£L 1.22

Ô®Î






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(ii) ÚŸ tF¤jš Kiw

ÚŸ tF¤jš

vL¤J¡fh£L 1.23

Ô®Î

go 1 :

go 2 :

go 3 :

go 4 :

go 5 :

go 6 :

go 7 :

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vL¤J¡fh£L 1.24

Ô®Î

go 1 :

go 2 :

go 3 :

go 4 :

go 5 :

go 6 :

go 7 :

1.7.2 (m) jrk v©fë‹ t®¡f _y«

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vL¤J¡fh£L 1.25

Ô®Î

vL¤J¡fh£L 1.26

Ô®Î

KGv© gFÂ jrk¥ gFÂjrk¥ òŸë

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vL¤J¡fh£L 1.27

Ô®Î

vL¤J¡fh£L 1.28

Ô®Î

F¿¥ò : t® f _y fhQ v©â KG v© gFÂ ó Áa våš, mj t® f

_y¤Â‹ KG v© gFÂÍ« ó¢Áa« MF«.

vL¤J¡fh£L 1.29

Ô®Î

0.1 2329 0 18 23 29

t©L«. Ï§F KG v© gFÂ Ïšiy.

dnt t®¡f _y¤ÂY« KG v©

gFÂ Ïšiy. vdnt K‹ò brh‹d go

iwfis¡ ifah©L 1 2329 v‹w

©â‹ t®¡f _y« fhz nt©L«.

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vL¤J¡fh£L 1.30

Ô®Î

F¿¥ò : v.fh 1.30 Ïš jrk òŸë¡F K‹ò KG v© gFÂ Ïšiy. vdnt <éY«

jrk òŸë¡F K‹ò xU ó¢Áa« vGj nt©L«. jrk òŸëia mL¤J

clnd Ïu©L ó Áa§fŸ ÏU¥gjhš t® f _y Âš òŸëia mL J

xU ó¢Áa« vGj nt©L«.

1.7.2 (M) KGika‰w t®¡f v©fë‹ t®¡f _y§fŸ

vL¤J¡fh£L 1.31

Ô®Î

vL¤J¡fh£L 1.32

Ô®Î

eh« Ïu©L jrk Ïl¤ÂU¤jkhféilia¡ fhz nt©oÍŸsjhš,t®¡f _y¤ij _‹W jrk Ïl§fS¡Ff©LÃo¡f nt©L«. Ïj‰fhf eh«6 (_‹W nrho) ó¢Áa§fis¤ jrkòŸë¡F tyJòw« vGÂ¡ bfhŸsnt©L«.

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gæ‰Á 1.6

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vL¤J¡fh£L 1.33

Ô®Î

F¿¥ò : X® Fiw v©â mL F X® Ïu il v© våš mJ xU äif

v©zhF«. mj‹ mL¡F X® x‰iw våš, mJ xU Fiw v©zhfÎ« ÏU¡F«.

mjhtJ,1

1

n=

-- '

m£ltiz 2fd v©fë‹ g©òfŸ

1. X® v©â x wh Ïy f 1 Mf ÏU¥Ã , m bt©â fd Â

x‹wh« Ïy¡fK« 1 Mf ÏU¡F«.

, 1 1 11 13313

= 21 92613

= 31 297913

= .

v©fŸ fd«1

2

3

4

5

8

10

1

8

27

4

125

21

343

512

729

1000

v©fŸ fd«11

12

13

14

15

16

17

18

19

20

1331

1728

2197

2744

3375

4096

4913

5832

859

8000

eh§fS«, v§fŸfd§fS«

Ïu£il v©fŸ

eh§fS«, v§fŸfd§fS« x‰iw

v©fŸ

n xU x‰iw v©

, n xU Ïu£il v©

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2. 1 4 5 9 k W M»a Ïy f§fis 1 M Ïy f Âš bfh©l

v©fë‹ fd v©fS« mnj Ïy¡f§fis 1 « Ïy¡f¤Âš

bfh©oU F .

cjhuzkhf: 14 27443

= ; 15 33753

= ; 16 0963

= ; 20 80003

= .

3.2I

1M« Ïy¡f¤Âš bfh©l v©â‹ fdkhdJ MfÎ«, I

1M« Ïy¡f¤Âš bfh©l v©â‹ fdkhdJ 2I 1M« Ïy¡f¤ÂY«

bfh©oU¡F«..

cjhuzkhf: 17283

=^ h12 ; 58323

=^ h8 .

4. 3I 1M« Ïy¡f¤Âš bfh©l v©fë‹ K¥go (fd«) MdJ IÍ«, 7I

1M« Ïy¡f¤Âš bfh©l v©fë‹ K¥go 3IÍ« 1M« Ïy¡f¤Âš

bg‰¿U¡F«.

cjhuzkhf : 21973

=^ h3 ; 196833

=^ h27 .

5. Ïu£il v©fë‹ fdkhdJ Ïu£il v©zhfÎ«, x‰iw v©fë‹fdkhdJ x iw v©zhfÎ ÏU F .

bjhl® x‰iw v©fë‹ TLjš

Ñœ¡fhQ« x‰iw v©fë‹ TLjš fhQ« mik¥Ãid¡ ftå¡f:

1 = 1 = 13

mL j ÏU x iw v©fŸ, 3 + 5 = = 2

mL¤j _‹W x‰iw v©fŸ, 7 + 9 + 11 = 27 = 33

mL¤j eh‹F x‰iw v©fŸ, 13 + 15 + 17 + 19 = 4 = 4

mL¤j IªJ x‰iw v©fŸ, 21 + 23 + 25 + 27 + 29 = 125 = 5

Ïªj mik¥ò éa¥gë¡»wjh?

vL¤J¡fh£L 1.34

Ô®Î

vL¤J¡fh£L 1.35

Ô®Î


gfh¡ fhuâ¥gL¤jš Ï§F 3 IªJfŸ

cŸsd. Mdhš 2

Ïu©LfŸ cŸsd.

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vL¤J¡fh£L 1.36

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1.9 v©fSl‹ éisahLjš

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ab

ab a b

a b

ba b ab a

abc

abc a b ca

a b c

cab bca

cab c a ba

bca b c ac

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gæ‰Á 1.9

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8th maths samacheer complete tamil medium part 1

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