គីមីវិទ្យាថ្នាក់ទី៨ summary of chemistry grade 12 by ReahouLibrary

(a - b) 2

= =

a Âˇ+

2a1~

a ' - 2ab

b2 b '

01S99bi.HilU.HHTnn~h u

!!:!;!

m ru r; ru 9 9 5 cHn

~ ru rq_,'i.Hi.

aim't:HulrtndJs

ISBN 9-789-995-001

II>

Sl.ll ~

:U1.H~

!.,

...

"' H~~YJ!;f~ LSQ.lflJ~~8t,gLY

~ s LHYH~~tl'!;B~:U.a

~LYr§8Sl

~~H~f!

~1Yuuj -

....

" ""

let

I.J1.j

SlfiW

•

~~'-"'~~.., &SHLY!l~

a~s

!.,

1.9

unru lP : 0

lillnB uru :~arn 0

'¥tl~ll~wq!JU~J

1.9~

.p.

u.n.ru c

¥un~ lP : ~n~ru

E:lSH~WfiEU!I

"""

~ ~ s~IJ:l'

~ ~s Ql s UJ.ru ~J !:fa

ttawu '¥Yrn "" BWSlRru

c--.

~-, Pl!flrul.llUJ~~tf~!;fB

LP :

!-,

"" I' q tiS ern u:J 3¥ unY ![!.

~-, ~ma~

1'1

~-,

¥11lru

q..

t;<>

e qrnlS L'l S ELYEY:UU~

rnrnut~NCH§w:J:l~fJE.!JUHfi!lll:;~W!l:!RfiP Lrna~s

~~~unru 0 • c

sQlEBlflJB~Sl ufiii

tlR:l : ~Wfi~f,l~LY

aw1:~ qum~ BR1B s lRr§ ~:~ ~ C.ru 3¥nQ3 s UJ.qQ,nQl q..

gt_yR,y: U1.l ~ gSj t{UU

11'

:1 :1

lY:! t{Y !-, !;{tiS ern u:Jl¥ llf!,Y ![!.tlY2l~B~3 let~ l..tl.1~13!llH~m !Jll

s l..tl.f1jrn :!S:l ~:! ~ ~ :J s mamf.ru

r§~R~:J tf~:J¥P..VH3 UJ.g SHJB t~!JU~ ~3 ~ ~l

U~ShlS9lS

....................................................................................................... 01

"' hliDI='iM .............................................................................. 13 & 1

2 :

S~fill='i$ID .................................................................................. 27 4 :

~tn rdatn& &

5 :

ntSJl'tยงrlOI='i

6 :

ntSJl'tยง

.......................................................................................................... 43 ~ ............................................................................................... 51

9l s .................................................................................................. 75

1Mfยงmsf:lti.f199'tll

f;l@ 8:

IDH~~ ................................................................... 103

to :

M~ "

11 :

tymu ........................................................................................................;....... 141

.................................................................................................................... 123

12 :

maLu]u

tfflM .................................................................................. l47

13 :

U~tfflM

.......................................................................................................... 169

a9 14

tfflM .......................................................................................... l87

15 : ~~ti ..................................................................................................................... l97 &

tai~~Uitmnn

................................................ 205

a9t7: mm ll

...................................................................... 215

18 : 1:lljj1!flS ............................................................................................................ 231

tmlMil 1:\ i

C::.

0 nrul6'iS !15't:HHiitH~IJ 2 tu291 2

o o

tty]m~JulH:uuu

mtiu~2tus1112

d~·mffi n.n1niltms (tin i:ln ?Jn.n fun) &lj IJ IJ I

" f&Srn~~e~~

d5t?Jtj nti~u~ 2?1~ r:HlH:l n-@2 &''1-3 sttl13~ s ?J~L?Jtim !JfnifltM: 7-4

= 3 tit's 4 7 = -3 l In

•

••

!JfnifltM: 6+3 = 2 m2 3+6 =I In 6

21 = s

!4£nU7tM:

Cl)ll::;tl

tiSStuS91S&tjbl5ffiSfll?ltti~HtuSl::l IJ

•

!JfnifliM : lO

= 0.2

-3

10, 100 ... Hltiffll::lt

= -0.03

usu s tus 91 s ftj ruffi sm ?J run sl::lm ?J&'ul::l •

!JfnifliM :

3 = 0.3

: 2 = 2! 3

3 '

-13 =

t2 gu~ 2 n5S&ll2ffitn:fl2 91JB

-2 3 '

u28 -3

1.!

0.5

' 8 ' 5

6 '

0.5 '1

1 : nbutnm'1§u22 "'l

2.3

05 ·

2 '

= 8= = 2= 6

tf:ifUHfUS lO

&ll22ltit'lffl'i§ l...i

1.!

-7

3.5 '

-14

-3.5 '

. I

-7

2 = -14 = -3.5 0

3 ""~

: nMfi' x tw'!§J~u~2n52&ll2 : tr:iH15 7! =

15 tSlg 45 X

_!2 2

15x = 2 x45 X =

2X 3

6 'i

-2

t'lffl'i§thlfil- ' l...i

"""' X

5- '

-0.2 '1

i~~j~i

nur]tntsJuu : ussn5s&lls -5 5udlbus2n5S&lls -I mbn:tH15 -5 <-I &'imgG@S 1.1

1.!

srJS -5 tsitrlh5Sl~Gas

ff12-l t

-5

-4

-3

-2

1.!

0 1

4 g}<3'1

uss~sms-5>-3t'img-s_(--3) =-5+~=-20+21 =..!_>0 '1 7

!.1

t..:i

r;~n-nod.)'iH1h:ni.Hsu~s~smsm't§:

• :!.<~ b

rugumffi

ab_

Mfitsi::nt~t~h "'

fJfTtf.flifJ/792 : ti~8~8918

~ tsi~: d

u:><12 ?

6 X 12 ;,_ 7 X 11

-7 ,

u;~ ~

-l

6 < 7 'l

8 , 028 •

I ~5 " I

n't§tSJ't§ tao~ a~ s 918 91 tl n

n. -6 ... -3

-2

-5

tl.

tH mgr; ~ s Z'l i'HLfil13

ill. 0.45 ... 100 '1

n. -6 < -3 _,

-5

2. 7- > tl.

~ = 7 + 5 = 12

!;tlQl s 28

0.45

sl~ ~ < l~

!;i:tHl5 36 > 28 54

t tn ru 45 < 54 S1°:£:"11 0.45 < 54 '1

100

n. ~ , o.3 4

25 5 -0. 25 = -100 ' 4

3 0.3 = 10

120 ~ - 160 3

03 = 3 .

25 30 5 -0. 25 = -100 = -120 ' 4

5 4 -0.25 < 0.3 < 4 < 3 '1 1

3 ' 3 '

-9

4 ' -l ' 7

l! = ~ 2 = 16 5 - ~ ' -1 = 12 ' -9 3 3 ' 3 ' 4 12 t s g - 9 < -1 < ~ < ~ < z '1 4

2. l

tl.

30 120

2.3.

rngn.n:

~ < t~:m ad< be ad< be t ~:ru

crsu::nuS912lnb u -

-6

n. -13 ' 13

-25

5 ' 7

j;l.

J"'

HHuH

-15 ' 20 "'

Gcf!w: ""

-~ 3 = ~~

g 6 x 13

= 78 9UH!iti~t§Jtifi -

2. -25 = (-5) X 5 = ~ g'it§~ti'ii:lt§~jjfi ~ -35 (-5)x7 7 Li Liu u 7 5 = ~ ''img 36 X 20 = j;1 -l 5) X . 36 -48 Li

= 720

1vflvff : tirm fim j;111 &scrsu s n1s 9ls:nh tHilt§t Nm uH3 MH n csl:.

s..;

- 16 -8 n. -30 ' 15

f/!!><1101

ie~~sauu~n

3.1.

uunn.nlfiijli

-15 ·

21 '

n. ~+ ~ 5 5

2. 3.5 +

n. ~ + ~ = 9 + 7 = ~ "' 5

2 3 5 + 79 .

rJmni:

- 3 + -5 n.

= 35 + 79 lO

~+~

7 7

= 35

+ 79 =

= a+c "'

2 -3 + 5

. 8

til -3 + 4 'I

.. - 3 -5 n.

2. <:;::

3-5

7+7 =

-3

+ -8

-3

-2

-5

- 3- 5

-8

-l

z+-7 = 7-7 = 2 = 0

~·· 8

= -3 + -4 = -21-20

lli. -3 + 4

-41 '1

?i. 437.56 + 127.95 '1

. fi (-3~)

"' (-1) d. 4

+(3!1 = -18 + 19

+ ?+z = 6

1!1. 437.56 + 127.95

fi.

-72 +95

- 3 + 10 + 28 = 35

565.51 '1

(-21) +(-~}

c S ""~ e " "" tl!i'i:.fiS ab' d f thti~Srs.HHflS '1

tjnmn ~+~+~ thusatus9la b

2. ~ + ~ 3.

~ + ~ ( ruQ nn :1Ji9Jli)

(~+~+]= ~+(~+J) (ruQnn:~)

4. ~ + 0 = 0+ ~ 5. 6 ~ 'b 7.

e _ c

-(-~)

-d =

e 'iiflg '1

~ = ~

23 20

...

(!Jfm IU!ij

: fHIJl 21 Jj

G+D +~

n"(~+!I+~= ~+(2+~) 63)3 6 33

(runnn:a) s 1"1 1

= ~ +(7 +5\ = ~ +4 = 5+24 6

3 -)

~ (~+!1+(-l~) = (~+!1+(-12) = 7

"63)

133-72

!!i (~ +~1 +(17 +2)

. 7

63)

-7

5+14_12

19_ 2 6

61 "l

42 = (~ +-5\ +(~ + 17) = 0+20 7 i) 8 8 8

tLf'il'tHf:::IHll 'Llirug nn:~ 1

(~+D +C4~

2·

:unmuuf: !!in.nmdru!:ln n. ~0 - 9 7 n. l 0 - lO

9-7

7 10

2•

= l0 =

2 ~-Z = 1o-1 = ~

. 4

!!i - ~- (-!1 = -5 + 2 = -5 +14 "6 3) 3

tJmni :~-~ b b

~ b

wvnt+tij61 : !!irlJlaljj -

3 7 5-10

n 9

-3

tJtiw: ""

... 3 7 6 7 6-7 -1 n. 5 - 10 = l 0 - I 0 = - 10 9

2 " 12-3 =

i2- 12

9-8 =

~ "l

5 7

4-8

!!i.

-~-(-D

~nttHlHsrhuruth~H;~na '1 d'huml:unh~n~nat

sna ?

...

: ~tlffltelfilhn1~m li Ln 5, 1 5

!+~+

1tlffltelfil1-!Hnan

15 - 15 + 5 - 3 - 20 + 5 - 4

lhfHl.fl t M 1

3 1--

_..

5+8+2

5 8 2 20 + +

m m tel fil h H n tHU n~ li <a II 1.1 li

~h~n1 ~

= 20

4 X 5+ 5 X 4 + W X 2 = .\<!

4-3

: telMsnt:Hu~nn ~x3.8 ~ 38 8X â&#x20AC;¢

38 8 X 10

3 X 38 = ~ = H4 + 2 = 57 '1 8X W 80 + 40

: telMsnjjru~nn (-~)

(-~)(-2) 3 15

= (-2)(-7) = 14 '1 3 X IS

n. o.25 x 48

2. 245.4 x 5.3

tel. (-3.2)(7.4)(-0.l )(-0.5)

m. (-4)(-~)(~(D

. n. 0.25 X 48 = 2. 245.4 X 5.3

2 ; X 48 = 10 2454

~X 48 =

X~~ =

tel. (-3.2)(7.4)(-0.1)(-0.5)

130062

12 =

1300.62

= [(-3.2)(-0.5)]

l)]

= (1.6)(-0.74) = -1.184

w. (-4>(-~)(~)(D

[<-4)(DJ[(-~)(VJ

(-2)(-D

l 'i

MmflJ:

1~5

0.75 x

dru~nn ~·~

t'i. (

-D(~)<o.5)(0.2)

= ac

2. ~.~ = ~.~ (runnn b d

d b

(~·~·]= ~·(~·]) (ruQnJl:~)

~·1

I · ~ = am , ( 1 = m

:;<:

s. 'it1thi2 s NS912 ~b m sn2u a Ns 91 s a£ G u

~. (~ + j)

~ . ~+~ .

" " t'iMSld flJ'UTJfif.'i!:

n Z.~+Z.!!

. 5 4

5 4

4 9 7 4 . -·---·5 4 8 5

nn:2'HH t'i.

;G.~~)

tJcfJw: IN

wRuu :t'inn mo - 9 3 n.

9 11

5. 4-5 "4

(/' ?H1JlSlltHlHtin " a91tn1M:

-n. 4S+ lO 1

3 3 . --+25 10 '1

11 ~ + 1 = ~ x 10 = 40 = 8

. 5

-~ +

3 + ( 2 + 130) =

2130 =

,... 24 6 n. -25 +

28 -4 2. 27 +

. -

n. -25 +

.., 28 + -4 = 28

4X3

51 = 7 X 17 =

119

"'Â· 27

f:l. -18 + -6

-18 X 25 = 3 X 5 = 15 '1

-10

fi. 154.63 + 4.7 'l

n. snnsgu'h:n1r;tsmHnHU1 "" u l

tSl:: '1

2. d~hdh'i:Hi5tStiribfilrultntHMSh 3.26cm ~

r:1.

l.l

...

t1h~hiiiru&gJr; '1 l

f:lMsnt~trl[ltSti~tmnnfnh '1 xcm

3.26cm p = 16.38+2 = 8.l9cm '1

~. ~n'G5t~h~h~ru I

m~ x dlTI5t~~ttl~'\fiD&&lJ 1

x+ 3.26 = p X+ 3.26 = 8.19

al~

x = 8.19-3.26 = 4.93cm

~crtsg ~~'\1IDt9Jntf:lcr~tff1Mtni:!1:f!SLli

4.93cm '1

1 '>

?1. ?JMS"J~~tn!{JHSu~tmM

ffl~ Sdl~~(.!11{JltSu~&Alrultn~ tmgt?JLil2

S = 3.26x4.93 = l6.0718cm

[:jutS& tsn&AlMtn~ffiS:t~'in!m 16.071 II 1 .:; 1..:: iJ'

-5 ?

-5

(?.xl0)+4+(2xOJ)+

?1. (8x1000)+(2x

-5 '1

xO.Ol)

(4x

+ 4 + (2 X 0.01) +

lli. (7x

xO.OOl)

0.000!)

+4+(2x0.1)+

i:!. 5(100) + 4( 10) + s + 6C/o) + 9C~o) + 3Coloo) '1 3.

MHM~cr~s~i:ittffl't§dlLliin?'i

28.45

?1. l 19

9. 1.378

i:!. 0.347 '1

lli.

4. lli. 5.

~. 652

UnlQ)Q~ 0 r~ru < ~ > 2Jms~'t§1]'i~ n. ~

m. 6.

7 2 ·5

-3-

D~ 7

-21

-3

o.54

0.5398

-1 9 '1

6 '

' 9 '

~ ffl'i§

xO.Ol)

.,o

l 3 4 i:HiHl..Jll t ~ tl=i ? 5 ' 2 ' 7 ' 9 1.1 5 3 3 2 'iHiHl.JTJ t!:Hl.H'iu ti ctl ti t l=i ? 6 ' 5 ' 10 ' 9 1.1

t n tHHHl.HHJl S

.,o "" tntiS!HuS9lS 1.1

1.1

m1n Sl

Jo NL1:j ru 1.1

n. (-~) + (2~)

G-D +~

G;)

2. (-3~) -(-2~)

l=i.

+ (-2~)

ti . (!+!)+(~-!) 2 3 8 4

3~- 25 5 8 ti. -7 4 -+512 9

3 25 + 2~ 8 8 + 2 '1

2~-(-~

10. l=in.fl Sl

n. -~5 . (!.! . 1~ 17 1 lli.

11.21+17.~1

16 22

um mm 13 + 13 IJl ......,

13. 14.

tictl~rh ""

tl (- !.! + 1~ . 26

ti. - 11 + 21 - 17

. .

(-!.!).~+(-3)·(-!.!) 21 7 7 21

13 x 13 '1

tU ~<:: b

2• - (11 13' 16 . 26 51

tSlll ~ b

mnti~ti~tsllti~Q)

~ d

e '1

trultiton'fsu.nfiLumt2

~nLtiffltlt!:!rumh2JUnfiMsj

tnUllilil !;'>

Rrul~fiHTTlrulSbSliH3EliDhl

~ru~rul 5 2

•

10 000 = 10 X lOX 10 X lO

(~r HlS~132lb

52 Hlsm 5 fiJru?Jnn 2 us nm 4

"'-

"' t?lnHltHuHfdH~

axaxax ... xa

!S1:£fi(}]S

~-~

nnm "

n. 4 X 4 X 4 X 4 X 4 X 4

axaXaX

•.. X

a 'l

20101iffl

.. li. 4x4x4x4x4x4 = 4

6 :iJ. a X a X a X

•.. X a =

010

2010 '1

nJun n'*i9 2:

.. 8 27

2 X 2 X 2 X 2 X 2 = 32

li.

f!'i.

(-3)

3nm

(-3)

(-3) X (-3)

= -27

31iffl

61iffl

) = 11

[

-1

2. y . y . y . y ..... y '1

li. x·x·x·x·x·x

20131iffl

nn ~~ &Lffll§trr~ 2.

(-~6

fJ ETt'ln 1M"' : li. 2

MHMHH SJl '!§ :11 b

2 = (2

2 X 2)(2

tll

2 X 2 X 2) = 2 X 2 X 2 X 2 X 2 X 2 X 2= 2

3nm

4nffi

...

x3x3x3x

x3x3x3x3x3x

s;;m ...

7nm

= 3X 3X3X3X3X 3X 3X 3X3X3X 3X 3

= 3

5 7 +

= 3

(5+7)n~

111

lli. a ·an

(a· a· a· ... ·

·a· a· ... ·

mnffi

nnffi

(m+n)l'l~

a·a·a· ... ·a=

t?.itf~lnJl ~ ntm ru~csi !:l t!:l ru iJ

·a =

8 2 8 2. (-5y 2 )(7y) = (-5. 7)(y . y )

?.'i. ( -5xy-2 )

n. x 9 ·x4

(3 x y

3 8)

-2 (3 x 3y 8)

?.'i. ( -5xy )

(-5y )(7y )

-35. y 2 + 8

= - ( 5 x S (x · x 3 · y -2 · y 8 )

-35y lO

-3 · x l + 3 · y

?.'i.

2+8

= -3x4y 6 '1

---::---::-"':::---::--- = 2 X 2 X 2 '-----y---'

= 27

= 23

= 8

3Mfl

-..,---::-----,-"-:---:--- =

7 5

3X3 = 3 -

'---y---'

= 32

2li ff1

5 li ff1

l=i.

---2

-5xy .

. n.

3 8

4x Y

-6

106 -

(-2)

~- -

100

= (-2)

6-5

= (-2)

= -2

( -2)5

29l'UlH'Wll=IM21 a

a·a·a·a a·a·a·a t'Ul~HS8 l

a0 = 1

m,y- = -2

ttlru

a a::f.:O '1 2 .

t'Ul6HS2 a

1 'ij .,..

-2 a

.. l=inflal

runt

(D2 (D4

-11

a· a = ..!._ 'i5 ::_ = a. a. a. a a2 .,.. a 4

l=i. 9 y

ill. ( 3yx: ) 4 -15y X

-4

= a--2

.1.

MtlHHUl iSM tlHi C

= (23)·(23)·(23)·(23) = 23+:;~+3 =

(23)4

= 212

41Hfl

" " t:lrulSl nJ'i.JTifitii: IJ

2 3 (10 )

000 000 -2 k

k 5

2. (a ) ·(a) = a

LuRug: n.

--2 'k

- 2k + Sk

t:lMSl

3 -2

2. a·

(a )

4.2. n1ttHHUl is~rufiI C I

5 = 2 X 2 X 2 X 5 X 5 X 5 = (2

5)(2

(2 X 5/

3nliil

7 = 2X2X5X5X7X7 '-y--'

2nliil n

'-y--'

2nliil

= (2 X 5 X

= (2x5x7) 2nliil

'.,

ill'lffilit1J :

2 3

(3xy )

. '

2 3

(3xy)

3 ·

3 6

27x y

+6k

. a-6

2. a·

2x2x2

a· a· ... a

: &{j

a , b dl13Sj;HuS!l1S:Hutl MS'iS~ i.i

&?HilS(~)"

1.1

= -

SJl~ 3 3

_, J (ib c -

runtSJl~

-2)4 n. ( 3

(a_4·bzJ2 c 3

1 = - = 0.1

to'

10 = 1 ...,_. 0

liJSJ l

0.01 z'-2~

10 = I 00 ...,_.

= - = 0.001

l 03

liJSJ 2

'-y-;"'

3~l:l

10 = l 000

= 0.0001

ill

liJSJ 3

10 = 10000

= 0.00001

liJSJ 4

10 = 1 00000

0.000001

6~ti

10 = l 000000

'--y---'

liJSJ 6

10 = 10000000

10" = 10 ... 000 000

= -

1IJJ

~n11&2 tO ftt:U '1

fi. 3.75

10 = 2

~~~X

2. 128.5 + 10 = l

10 OOO = 37 500

2 5

0.00 ... 01

ffiHiM ntt;fiG~U:Hi' Min "'-

n~l:l

liJSJ n

100 = I

285

l~O

l.285 '1

h ~unlยง

62.013 x

2. 0.57 +

62.013 x

2. 0.57 + 1

= 0. 00000 57

2-;ti

--v-',

3:Jti

52ir"' 22i1

t~h

lOcm

9Mfili:1

1:)

O.lm

25cm 136cm

.. U5t~h

9Mfili:1

l?filj:)

IOcm

25cm

O.lm

0.25m

136cm

1.36m

.. 1. i:1n.run

762.0213 x

2. 34.57 +

905fill':l

!':1

gn't§ l

lOg

O.Olkg

325g

l365g

ntl maMnn g~'t§~ 05~ m&s f15 "'l

\.:t'

i..j

rul Ax 10

't:flSfil~~S:i&H'iGS

''hfngu u· 1

t~~tJGL~tl 9uhfl~'t§

~6l~'t§tti~i:;lb15't:flS

...

i1 "tS 2111'i.J1UU7"' : &illJJS

!.!

MStl 299 800 000 m/s ....

'i 05H 05~

!':1 2.998 x 10 m/s <J 0

Q'I.,::::P

filmhlffi6l't§t05Stl 0.000 000 000 003 mm MH u .... 3.0 x 10- 12 mm 'i

rn1::;

490

ooo ooo

490 000 000 = 49

0. 000 000 732

0.000 000 = 4.9 X 0 X 0 000 000

= 4.9 X 100.000 000 ~.

0.000 000 732

<10

732 l 000 000 000

= 7.32 X

1:l13tS2 490 000 000 = 4.9

4.9 X

= 7.32 X l

7.32 X 100 I 000 000 000

t:lmsg o.ooo ooo IJ

732 = 7.32 x 1

Wuntfil.fJ9 2: Htiid~nt2iirlltl 11 n & n

fU'i~~ 1.438 X e.! ru'i~StiHtlcionls&astj '1 e..! n a

'1 ~HlJHntH15tts'lulsHtlcion&s.nnm

1.21 x

Ill

cion&srastj Ill 1.438 X 10

1.438 X

""l.l3xl0= 11.3

1.27 X

ruifr;if: MHnUOSS~b

1..1

37 ooo ooo

)2 =

9L'e{1

1.1

ooo

tt1

2. 0.000 000 000 075 '1

" +4 'i flHHS

) = 16 '1 16

2. (-4) =(-4)(-4)= 16 '1 16

2mt~t~m ~

dru

'"'"'

.:1

ru (-4l=

16 '1

"" ru -4 ttn

&!':'im +4

= 16

i=l6 t2li:x=+Jl6 2

fi.

-4 )

= 16

'1 tl1.1 G G2 g X = +4 = -9 bSl 8 X

u "'-

-9 '1

=+4 X

= -4 '1

UMx==

'tJ

"'-

-4

'Lmg

(+4)

= 16

tha~r:in19n9tHflGSS~t:l'i:flS '1 IJ 1 'W. IJ li!-

ru'i:flst~1Ji![l

wuntit1j62: m

121

turJw: ~~·uthdtlm&~ IJ Li fiJIJ

ffi~ x>O dl~~hl~~filt~ &tnru S dlt~1Ji

lilt~

'1 tf:IUIS

121

s = x ttllru s = 121 i = 121. ii2J X =

&Slll&~ms

tlmsg 1dt1 m&~'i:fls~m II Li IJ

II '1

Hdm '1

[Jtifug: n. ~n X tU x 2

= 196 '1

2.25m

'1 ~MSl~~hl~tlfiltHSlg '1 l

fUTitntftfl"'1 :

~MS"!

n. (+2)3 =(+2)(+2)(+2)= +8 3

2. (-2) =(-2)(-2)(-2)= -8 "' !Jfntniftfl2:

m.., (+2)3 = +8

dlyMf:i11 titS -8 '1 t~flilllflMHM~

x = 27

n. ttllru i 2. ttllru Q

Mfi!W:

i 0

" &Slg +2 dltHdf:i'iHS +8 "'

3J8

IIC$

d'i:fl!:lttllruu Iii-

tr1

oasf:ln:~gngu'i:flatiMf:ititn'i§ru~n: IJ I 'IJ. "' II 1.1

tiM~titsuss~d'i:flsmfis "' u IJ IiiiJ

Mm1 ;;g

ii2J x = = 3 '1 tlm::a x 3 '1 -27 ii2J x = 3J=27 = -3 '1 ~msg x = -3

= 21 =

ru 3,/::s = -2 '1

= +2

= -27

(-2)3 =-8 &21:5 -2

US2H~d'i:flsmtiss iJ IiiiJ

d'i:fl!:l '1 Iii-

: ?I n.n l:ll

ru&'tlm'HlS'Hl~ 125cm

MlJtl la

:mtlx>O = 125

~?IQIS

5cm '1

HS~fi (

~fi'

St'l

li'i

agt?lruntm:&5 ~ 25x5 = 125 '1 run 125 tln 125 5 dlt

625 ' 2312 '1 225' 529Sb 153.76 U:ll

ru:

Jill t?lon 225 I

Nrrn .[ g:g

MITn= m

""' tmrunnNrrn = g:g

E5j

25 '1

JJ53.76

t'i5 15 '1

J625 mnn 625

t?lnn 153.76 1.1mnnN 1

108 '1

225 115 -----1 x2 = 2 125 25 X 5 = 125 125 0

fiudlb uthll25? "'

2 QIS2 '1 u

---------

'f:f/!11= 125cm

?1. V(-128)

N '1

/"" /

. ?IM Sl n .

' ,.J-~w~~-----

tlma

5cm

xxxxx=x

t:::rH'Hl2

th5o ~

? 0

rumui n.m1.1 n. 6 X 6 X 6 X 6 X 6 X 6 X 6

lli.

(-8)

(-8) X

n nfil

n. (4 3 )(2 2 ) 4

l:'i. (-3 )(-6

lli.

)

iJHt5HhJ~ntSJ1~~h

n. (4 3 )( -3 2 ) 2

l:'i. (-2 )(3 )(-5

)

tHHnHl..fltnh~ru'i:flS'i.H I U

2 2

2. (5m n - 6)(m l:'i. -2a 3b4 c 2

Â° mmg

-1 'l l:'iM

a = -2

= -1

c = -1 'l

MTI3 runtSJ1~~tl IJ

n. (4 5 )(4 )(4

)

(~r(~r (~r 6

R. 7.

MU3 runtsJ1~~tJ tun~ IJ

~n.

(25x y

2 3)

4 3

(-3x y )(-x y

(~a 2 b3) (2a -J b4 ) R. 6a

i l=i

18 MHM~GSS21bt'ifil'i:H:.hhlli5~=irulls 8 : 2 1.1 w ./1 l 0

Q'l

93 ooo ooo mi

1.1

frH-'!Ej

an'95iJ'

'1:11

MHMHJ2SS'i:§'li5121bt'ifil'i:Hh 1.1

5 6 )

rul

~. ~b~a5ih~'imti~nrl?hNsb o.ooo 021 m n .;, w u· -i 130 000 000 000 em '1

~mfi5 ./1

LUilll=i

10m!

330ml

1365ml

lOOml

3800ml

7500ml

(2.5x10 )(3xl

~- 4.5

3X 0

(3.3

10 )(6 X 10 ) '1 8 8 ( 1.1 X 10 )(3 X 10 ) X

9Nil1i.l

i"HUHi9UH1Hu'i:ll'HlLri~

n:n:luunumrun9&t~ru!lln9tlstl

<C:::i:>

o n:n g1JUl rum run 9 t t~ ru !11 n Q

" " ~us~~~~~ei

1.1.

~Jmrummu'ltruu 2fTitnuuf:

tf:lt'~th:imhtt~nhill~ot~15Hu lJ

IS-

"'1

&r:l99 !.!

'"'

~tHnnb:JlhtLill~

100

150

250

50 10

100

150

200

t l=i Hl u'i.Hi u~.n uH1 Sl R9 ~ = 0.2 X

U y = 0.2x "'-

~ 100 ~

rnUilillB~sru <t u

R shthru y = oox

~un g

1: rn~ 8 800km th <t

fi.

fti'i:fl81:'"tH']M!i5'i:fl'i:flUia:,tO <t

~mls y

Y2 = a -

YJ = a

tltH88 u

YJ = Y2 'i5 XI

?:1M l

"'1:1

'Yt

soh x 2 Yt XI

d5x 1 Sbx 2 dl

n. mtH~tHunruh~w L n u

B '1

2. Lli~~b9'9b'fs~u

fi ri

w : d n.m::3J uLli ~ Hm ~

tfiQlS

~f:ng

=::8

ru 8

= 2~><8 = 12 l2cm '1

c : ttllrum c li..J'tn'i:flHiSbW A l.j

t1r;mgm IJ tfiQlS

!2 y

tf:ng y =

15 = 10

t~b lOcm '1 1200 i '1

d5 y 1 =

Sb Y2

ax 1

"""' y 1 +y 2 r;ruwms -- =

+xz

= ax 2

fti rn a : f: . 0

ax 1 +ax 2 xl +xz

= a tf:n&

nun : IJ

= xi

~ XI

+xz

Yz Xz

= a

Y1 + Yz '1 XI +Xz

WnM:ff"" 2 · €J

rnxl+xz::f::-0 '1

"" SS211Hl 1 !.! &f:ng ~ x1

=~ Xz

~ = Y1 + Yz + x3

xl+xz+x3

~=~ tf:ng YI XJ

SJft\&15 x 1 +xz+X3::f::.0

Yl XI

-Yz- -Yl -xl +xz Xz

Y3 -Yz --Xz

: Alntil91Jltfl'1:3tns~r~h~~~

320kg

2JU5mdsti'li1nn~HHU1H~tnru9n lJ

hll~S'1:3ti5'J'i::fl2 M'i::fltln 4 Slfl 5 S1R sb 7 Slfl 'i i:f:1~b1Jl'1:3Sl Mi'l:llR')99bli lJ \:to; 1.1

O<J

r; tn rum n.n nLf:l nn ~ lJ

"" 6ti5btn 2 a-

b 5

c 7

ti5 a + b + c

= - = -

= 320

m'1:3ru~n.n:N'i::fl'i::fl1_!i

Hllbtn S ~ = ~ = :_ = a+ b + c 4

320

= 20

4+5+

ni5b9lmtns: ......, ~ = 20 t S1 g a = 4 X 20 = 80 'i 4

c 7

= 20

20 bS1 g b = 5 X 20 = 100 'i bSl g

ti5'J

""f:'i

= 7X

= 140 'i 'i

80kg ' 1

tf:1Hlu'i::flsdt1N

nbmH~n.n6i9'9bsb o; 1

ru'fsufitmn.ntS1nlm.nb l u 4

xy = 1 X 36 = 2 X 18 = 3 X 12 = 4 X 9 = 6 X 6 = 36

nllbffi13tinH0lli5gSlfiSlSh x Sb y &i:llli5g : xy t_; •• 0

&f:lll1Ltif~br/9h

36 'i5 y ""-

36 X

dl9tn

h)'i:flffiLE1Lm h) '1

Sl g &til ru nh aru: tcHliU! Sls ~deo ? os

run'l:§n~ 28 SlR -lJ

tuflw: mh x dlusstd iJCJ &1.1

GSSn'l:§m lJ

132lJ GHG "'

dg&Sl8 4

nlihms: 28x = 35x 16 &Slg x = ~x 16 28

20 '1

t:lmsg n'i:§na 28 SlRM~dg &Slg u vii Gi

runh~ ru:&n ru 20 td "I ct

ruffuii: &f:ltimru'&lni:llRnh

ru&i:llru

l..i

&rlQ:Jffib '1

.!!

Gl ~

eyu

ru '1

"" 70mn &915

fJi

t:::;J

mtf:l&Lti~ms 7 &~UJ~Gn.mru~;nruH u

1::1\jhhJHM~TIJfilf:l lOOO

lJaLtifilf:lWidlmmru

(ti:llru 45

lkm = lOOOm)

x 100% = 4.5% "'

""'f:l4.5% '1

n.n b ~ruwJfitRL&i~ \J

)( 100%

: &si .

75 'i§

fil:lH'i'l§Ul 2 " c, 1

H~ ru 21§ ru tR~h mtt.H~'l§g mmli'l§ ru t'Hi~h~ G"lU "-'ll u G G\1

L~'l§tJi2t2Hil2ruR~oru~~rutu;Jh2Jtrrnfi

"" ~ 2Ql s n t rul fi ruuu n.

rust22 trulntmb G1

ooo$

'i m~fi u

11a~tLmru

s g ~rum so fila ruR~d ru ~ 2Jtrrn fi ru1Ji5S

t ru1 QJ

filj:'j~

2&~ 84 ooo$

fitf;jrutrrnn rus

fi.

sm2:nnl1m~

= 75

nmru1m '

dru~2Jmnntmhru'l§ '1

- 75 000$ = 9

-...$/

'i = 12%

smn..r1

8 12% 'i

I eJ

.r-

2. G~ 2Ltil n t t1 oH ru1 n illLM 2m s tHlm ru l

82u 2101 G r\ &'t1 ill til 22l&H s1 u1 ill fti ill m cim 2illR~G ru2n 84 000$ - 60

= 24

.m 1=1~ rutrn r\ 2l n ~f:i illt ru1 nlfo 2rns 2l n ?1 nu 1

8 4~~~0$$x 100%= 2

28.57%

~m s g 1: s1 t n rtH rul n rnu'ds ms illR~G ru ~ 2Jr: rul n

28.57%

LJM20129mt91G'inli.ilsru 1JfJJifJH: Iii u l "" lJ

t1J"" 2 240 ooo~ 'l

2.a. mrum:n itJ ().

~fi 25 600

mr\

" rnmm g .m ?Ja ruts a l

2. t1J ill r\ n5 t<tfl nu m .VJ GV

tJtfJw: ""

32 000 ~ 25 600 ~

rn m m g 61 "m = 32 ooo ~ - 25 6oo a1

m~~rum~umgnt'H' a1

!:lu m

s g t s1 t n ill~ run

6400

mm m gt1J 30% ts 36 ooo ""

= 6 400 ~ 'l

x 100°/o = 20 °/o ~

fil'l515 tl':\'ti li.i'i611 rn GH?J u u Gu

2. 6lt'tlillRZ1tlt~'tltSM G\1 a1

mr\'tlruRt£3 U GV

x 36ooo i

20%

36 ooo~ =

10800

~ms2nH~J

'~L~~msrufi

200~

: ~tH,n1ms~h]rrHuLHL'8]tl8~s 300 ft:Hl51tl~ULHL'8]tls'\3ru'Jt~ 3 3oo~ 'i m

srnfi~mtsittli:3~15tlS.H151tl!ULH~i:3'ltlcrss 200 ""'

ru~siw

liJ

1o;)

msgmfirunumgG'Jm 15% <>

liJ

6\1

'i m~nffHUru'imnmn.nmmtumG'l 'i

6\1

!ULH~i:3'ltlsi:3ru') tG 3 980~

!.!

dht12lirHumLmfif2h~n~ns'!flrh~sms

15%

""'

tflssrumnrnLmfi

100~

tsiQbLmfi I

sms

lH msttuti~tllnbitnR oo~ 51 ¢:;l.j l

n5n~n~'!flfi~ 320 ooo~ 'i

: 2utflmLmfif2 fif2g: Lmfif2

tsinbitnAt2ttl'l3w'idlll5Hsinb1tnRt2G 'i c:s:li c;lj tfiLmfif2gmn5mG1

= 115 : 100

Lmfif2g

115

.!J:2 x 'if'"'l.!f'n ~_;'-l' n •o

100 115

32000~

368000

dHliLmfi 100 ~ tsiQbLmfif2 l

oo~

tsiQbLmfif2ttl'l3

fif2g: Lmfi Lmfi g Ltnfi ttli:3 fi tl....

= 95 : 100

95 100 95

X X

'"' nt2 32000 ~

m95 ~

tsinbumfi&28.... '1 ~

= 304000 ~

540 000

• eJ

0 e)

2. munrH2L't.HfH2H5

1rlHnun Fi r2 ,~'t§Ltim r2m rJ mf!m : ""

108% "b2 540 lcJ

000~:

108% ~

000~::

540

583

JQ)

200~

ll!l;

2. un n t2HJ li.H bUl n1_f5ffi srm ~ti bl Ol S 1:l1:9Jh Lmfif2t~'l:3mn5tM nu~m 2ti

108

- lOO 480000

480 000 ~ '1

LuRuH: t9lUUJM2\]11H~Jhti~u~ms tim 851 t'i:3 15% t 24 nHlin t'i:3i~'i:3 fn 846 ooo ~ '1 GVlj ~ I

9lts'in M s t s-, g fil ru ~ r; ~'i:3'tll s 51 t'i:3li s-, s r;{j ru L N

1'-'t

~:~ ?

., fil~Lmfi : mLmfithrnlQJ rnms'l3n~tmfi2Jtl?l~IJhHi5:tnrnmsfirul~fflh I

., HLffl: mfil~Lmfi~Jb\Jru~nliunfi~:~'t§ 1oo~ mh~:ttJru R

., LOlRMfi5 : rtlfil~LOlRSbLOlR&~'i:3~'i:3~

"' ~ru:tnrn: rtlH9Jbmrnf!:lrnms~Lmfitl?l y_2jtl?l~fflhtttlru r

1 ~

tmfltsl?lnfil~LmnLtJml::lm MY.LlimLnm M

o-.,

Llim r;2 Y.Ltim ~:~

H~LMru t clh ru: r; n ru f!:l rnmsuh fila '1 35

: blll '1 ~HlSlSifmLmriQt!Hu:tblru

1~ ~

2oooooo~

x /;

O<:V

3m t:'i 3oooo ~ Cl

3oooo ~

3 = 9oooo ~

~:iJbaJutJm 1

ooo ooo~ '1

ri 15 ooo ooo~ ~@b~st9Jn

@bdsmsutlm

~nHLffiffl

2~tLmru~nm~g~rums

Rtt:irum~g~rums~uhm~Lmfi~@bMs '1

= 15 000 000 ~ , R = 6 T =5 ffl R l = PRT = 15000000 X 6 X 5 =

5000000 ~ + 4500000~ n'

Lm fit~~ m

aru:tnru S

4500000~

19500000 ~

= 18 000 000 i P = 15 ooo ooo ~ I = 18 ooo ooo ~ - 15 ooo ooo ~ =3 ooo ooo ~ 0

T= 2m Cl

&Sig

I= PRT

00!

G'l

R =

100 X 3000000 ~

r;sg@bds~t!UJ~msg~

m~LtnR

~a 10%

ru~

: Gntjmstshffl2LOlR 24 ooo ru:~:nru4

ooo~~GSirn

ruti::tlru'i:fHlHLmm~Ltnri

Gntjmsu~m2Ltnri~uS"JmHnr;iJhmli~

16%

n. d~m~unfi~tHliUl~

2tHl2ti 2 ? 0

u ~

2. t rl t:HHWCil n nH'lH 1:j lJ l.J 1

Ocy

9 1 : P = 8 000 000 ~ ,

R = 15 , T = 1 ~

I = 8000000 ~ X 15 = 12 00000 ~ Ocy

"' m 9 2 : P ~

= 8 000 000 ~ + l 200 000 ~ = 9 200 000 ~ , R = 15 , T = I m ~

I = 9200000 ~ >< 15 =

380000 ~ "I

m~lf.ll n n.J~ti hlL'tflliH15: t rHli 2 ~ '

Qhm~~ri:nhn'lhsg

= 1 200 ooo ~ + 1 380 ooo j = 2 580 ooo ~

1 2oo ooo~ ~t:j

rn2Jm~t

~umciiJl9 Lri~ms lJ

ti~~'t:Hvl~:rnLtnf'it~1:3 8 ooo ooo~ n.JL'tflli~rim~Ltnf'itsi~nm

msGTI2Ltnf'i

9 200 ooo

rutvl

m~Ltnf'in.Jiti 2 58o ooo~ t'i.fflmm~LtnRhl'tflm

si nhG Sl ffi~url~til Stinti ~2'i:3Sh fi'l~'itfl Rru'tfl u "' l.j

'i5 2G'l 'i5 Sl ti '1 .,;

fn1[j(flffMf:17M:

n rn~ umcim G~'i5~2'i:3t ~ "

Ltnrir:~'i:3~ tmruiJltLmrur:~~rim~Lmrir:

1QJ

fU'i:fW: w

OQ!

.hrl9'i:3ti5: ~

3000000~

= 3000000~ X

, R 20

20 , T

= J ffi ~

600000~

3000000 3 + 600000 ~ = 3600000 ~ '1

m9rh : p "'

= 36ooooo ~ ,

= 20 , r

3600000 ~

= 720000i

n' OQ)

lfl 9li

: P

= 4320000 ~ , 4320000 ~

3600000 ~ + 720000 ~ = 4320000 ~ o

= 20 , l

20 X

= 1 lfl

864000 ~

n ro'tn ro fi 60oooo ~ +

"" l:a'tnn591;3li5 P =

=7 500 000~,

7500000~ X~~~ X~

noooo ~ + 864000 ~

= 2184ooo ~ 'i

1 R = 16 , T = 6 "t2 = 2 =

600000

~ 'i

l:a'l:fl n5 """" ~HH : P = 7 500000 ~ + 600000 ~ = 8100000 ~

R = 6

" = -1 =61:2 2

[ = 8100000~ X

648000

= 600 000 ~ + 648 000 ~ =

248 000 ~ 'i

R2 700 ooo ~ fil

.. t3tmg ruR : 9 ooo ooo ~ nl: tlmn 14% '

u ~tiriuciun RnR 2 ooo ooo ~ ~ nHluru n~ r1J9 H s Hfl s

'ejlb t9J flJ;!n@s mi:im

u 0

~r1J9HSg 1:9 'i u

i:itfltll~ntlruti~:rung 'i "' W I M

ffi a

~m9iBb'itl~~tiH'i't3~9tls~n l !J l,j & .... cOU u

01;

~rtrn 2~n:lltimun 14% ~:t:nrumHl5bLtnRLum 9smm'tl~thsgt'UTJmilsmm~9mun.mR '1 "'""'

IJ "'""'

"'""'

fil~unR2lbtm~ 7oooooo~ x 14 x 2 0

e./

ti ~ 8LffHHi51U n:l rnui ~

196oooo~

7 000 000 ~ + 1 960 000 fr = 8 960 000 ~

~ms gLm R tub~ '\1 MDJrrl t'2

8960000

ru1

= 373333.33

Wf.J17fftri9J: iru\J8Gtni'H21Hl~'tlti16'if:l4b~G IJ G;_j IJ

Ltnnnn 15%

000~

tunnu 2

"'""'

% ~b\1

HLmmsLmndmn 1

1 350

fil~tuhLm

o.,

~rntu1umt2 IJ

l.j

'1 man: u

n. LLil R tubi

'\1 tuLur:n

2. &o9mun.mRmbHnHsirn\hamrH21Hl~ '1 GV G'l l -....:>

'\;:1

f:l. filf:lati1tSLLi1rH1:lrntusJrns Ltn R 1 35o ooo ~ {Jl'tl"J '1

t:Jtim: LfilRnR

/~0 x 135ooo~

8~sLrnrhsituru

J35oooofr

2. t~9QJUn.JJlRilbH

147500 ~X

24t2

147500~+244800~

1392300~ 24

mf:l~

"':!

1 475oo~ 32 X 3

58095.8~""58096~

242800~

l392300i

'"l

LLilRnR + 8~sLtnRUt~l:§

= =

1594800~-1350000~

202500~

2o25oo~

~rntu IJ n. LfllRtub~h1JMLur:ilt2

202500 ~ + 1392300 ~

1594800 ~ 'i

= 244800~ I

rutsLm nb1:l rnmg:;Hltitu

242800 X l OO 'X = 18 2 1350000 °

'"'

6ib'"i:Hi1"' ""-!> m

b13}~

fil

{hmrunfi n

iii.

1 080 000 ~

2 700 000 ~

LfllfiMtl~

nnn

"'gmurunn' ""-!>

'\;)

tHHH2 &S fil~ MbHli1.1 M 1.1

50 000 ~

120 000 ~

000~

225 000 ~

450

n. 2.

4:7

=x: 5

n. t ~ 2J

2. X; 8 = 99; 5

=5 :

a : b

9.t~2Jx:y =3:5 Sbx+y 3.

ttl a

Stl

, b , c

;.. a+b

a 2. ~

c+d

ttl a=t=b Sh

..,

mb c

c-d =

21cm

720g

b =; c=t=d I:Sl8

2. ~.

t~2J a :b :c = 4:6:9 '1

a+b+c

n6i "t1:1 "ts

~tfflhlHM~ 2 nJHli

""'

MHM~S1:1 ll

..,

. " s6imi::lum svu em 'i

lli.

a-b c-

~ c

~ ~u2ltltLm1:1

c+d c-

t?i2J a : b : c =7: 3: 20 sh a+ b + c = 520i '1 t?i2J :y :z =6:8: 15Sb z-y = 98g '1 \j~an

c=t=d I:Slg a+b a-

n6it~tSx '1

= 200

d dlGSSlC:l'i::llS '1 'Uinm 1.1 tSVl ""-!>

n. ad= be '!.-.!.

!'fl. lkm :32m = 250g: xg '1

x , y

-a

sh z 34m '1

m 2.

t'n

IOkg

dHn

3kg

"Gd 45 ooo ~ '1 ""

? 8.

n'en~ 25 ::nRd~m~ 26 ...; &

&sinhtnbuUn'i:Hti lJ 01 l

n-enat!t'cH15r;~g1n~&Gm . .; u &

hsb~ud

::ns ...;

ma m~

l300f:l '1 u

450f:l? IJ

runt'lHi5:tnrn 8

m~m

mum

n~m1s 16 ::m~Ui~ m

16 td "'

~tlt'tlrnr;~gfih~ru: rl 01

? 3 750 ~

112 soof '1

" "" " 210~ t'l1J1~Lf1Stlt9Jt'lt~

dhsi~:nrn~9J~&~g

11.

~hhll~Ul~tunUllR~~

SlR A

sb C'i:flS~

n A gglJ

nnruTibmut'M

m '1 01

1osooo~ '1 tlrulSlu~aLmR

sb z

12.

mr;ngm~t'ufl'i(f1R'i:3!55G~H~~hn~m u w· u u u uu

13.

HnGfll ~'i:ll R'l:!l scrm ~1:3lJ !55 nt'l m!;~ St'lGfil~ flH9161 'J nbu6l&fil nn 01

?ilrlUSlR X

ufru

hJ'i:ll'i:lllJ1&Ub~sb 12 49

n. ~~Lnijlhl~u~scrm~

~ 2Uluff167~

2. ~nLuf~h'(Elbt~crm~9 1nbmt~ '1 (I

'1 =

f=lnn::nt~Lnijltsam~s~ruo:~

1oo~)

fi.

14.

mb1Qlruts8m~9

2'i:ll

t'~bt~sb 3 tlblJ

n. 1Hl£rrliruc24Qhhllrrn

ru 'i:llst

~t9t'l '1

~nl'l:!l1Jii1hn

tag '1

~s 2s%r:tHn5J~t.ffi1J&rul'i:Hruln

thl]~tifltsihlrulltsdh~

thlJ~tiflLtHrul'tHruln 'i

~tm@s

NYU:HlHJHHD1SSB!:J~ ·~

!:JW1.H1SfiW6H!::H:Q~lS

"' "'

mes"

h Yl.!:::!

f)'

t!{NU.!JS:JRHHH ·y 0

h %0! w1t-H:Q~:I!:JffiSUJ I

~Y1 !d.Wf;::q.SH1.H~HJUJ1ru:JY I

lt:i'

(';) J

[...S:J!d.UJ1rn m:~ %OZ Y

"' h e::J 8v rut.n:rnE!{Y¥

h ~ 000 OOL Z

w1Hrn~:JNl.fl,N¥

6Sl!Jl.YU

~ :1

'-'

~ooo ooo oz ssf!-~'r§¥u:l1~wqnsUJs

WLP

YUJbruH~SH1 I a;, tf'J

1;:::;,

"' I :1 1'1 h £ t'Q! 6U:IBUJUf;l[...SH1tNYltHSSBYE 0 0 I 0

sUJ %s;I

!{NSL6Sfi !:JW}:l

~ ·sr

~~IJ!{U:JlPn~:J¥

:JnSJnsUJ %!!

~:!

£ f?>l.fl,1N

~ooo oos z ·e;

~~u!{QllPfi~j¥

"' :JfiSJfiSUJ %01

u:l j !1:1

000 008 1 ·y

W!:J~

.L!

"'" h gLSBl.YLSB!{Y~:l~ps I

"' fi!{Y"' ~ h U:~rn

~ gnrn

ooo ooz

PSP!;lf}fY

pgLSHl.Y LSBS~¥ 11

l.YLSB!;{Y~:JS

w1Yt ~-, ~:JYU

"' WlJU:J

h sUJruaBL¥

"' %£I [lljUfrn 0

ww1Hm ~-, rn

"' 11 "' Lt:~rnfi!;{Y

L.Yru!=lJfi~:J¥

EYUJ1t

S}:l~fi

·91

nt~lf.Q:J~~~,¥~86

!{SY1l.fl,l.fl,Nru j:D!:JlJU:JBQ,l}:l!:JB:Jt:> S UJ~Y1ruN ~l!:J« ~

(f;;l

~oto

YUJ1s:~ %9! YUJ1!{~1n~1YH ~

rn Ln:J

$OOO

m.D!{WYUU:l

G"-

os;z s UJ w tJU :J

rn llJUfl-~~N ~lW IJU:lfl-

1, WlJUWY 0 )

%0Z

UJ1Y t ~s

$000 00 I 1 !{ ~ $000 006 '

"'-

fJ1:l

008

w !l:I!{Ysa LS :1

C"'..M.

$:)

Hrnurun 0 I

£:::)

WS}:l!;{Yl.S:Jl.Y 0

~lf.Q:J~~~j ~~1YUU:J!;{~ SB:JYUU:l I

1'1

H:l S BS !:Jj rn t ~ U:J (!!)

~-, rnruurun!{YfYH!{~SLHtJJ:J~

;..

!:Jlfl.jj ·:;y

:~ s e..:~ N H q l6 E:J !J ( 0 ~

¢.,

n I

L.SlJU~m ~-,

~ o:;zz Rl!JS l.fl,rn l}fl %s; y UU:lfiUU:m1t.YH [fy:Js

Sl.fl,rnl.fJ:J %ILYUU:IEUU:J

h rn~urum{!J~:lfiJH!{~SLH

~cN:ISS~!d.t

h !:JUUjfllfl.jj

.M 1'1 "' ruuYrnE!;{Y

~oos;L

r; 1'1 u 1.$ :1 00 ~L..N:lSS~s~m~QBflbjPJSUJrnruurun

l IJil

.M n "' ruuMrnfi!;{Y

·e;

1'1 1'1 :1 tQ NH5Sf!-!{~Lrnfi~6Y'H1~SLH

~c&'Jj!;{l1JS~1:J rutf!J086 Sl.fl,YUU:JfiUUm1tJJH[N

tndru!il G'

o lH1.flSl~~Lnfti1Si:l'i:fl:aftH15'l::ll 0 tHl.flSl'ifHuWJtisb~~Ln 0

1:1MSltb\5~S'i:3uJ'i:3

';:!

sbilln.Hu]tisb'l::ll:a

cy,q;

[lfitS~l:Jlhl(Yt~bt!:lrntl:lSID'l:3tL'i51:1 mm , em , dm ,

ni:lQ ~fil tlHtJtsl fd'i:fH: "1

, dam , hm , km '1

t!:l bli'i:flS~'i:fl'ififiG'J E:luth L:iu

'i:32Alflf21H.Rbni:J~gnbf!:lru'l::lls 1 u w ~~·

'!:32Alflhlfd[fdf!:ln 1

n.ni:lfd~f!:lrn'i:fls

titsnbmsl:lMSl[d'in 1 n« •.d..J

S'1tlfit a

lmm , 2mm , ... '1

citlfit~sb 6mm , 8mm , lOmm ... a ~

nbnHUltS8 tl:lffiGfdHfd~

" I

lmm

0.001

lcm

= O.Oim = O.lm

H~fl~fit~sb '1 (rr

2mm '1

m '1

l:lMSl~~!Slfti1~2mcin~fim

= 3.14)

ruf!m: td'in9fl'l:32mci "" ,.:(.)~·I S =

11: X

U::ll liJ d = 2mm = 2 X

2mm

= 4x l 43

= 3.14x4x 1

= 3.14x

= 314>< l

s ~6ldl {d m

1tÂ·

mm bfitH~

tll

tlln.w:m tllfU tl'i9 'l

tll

'J"i9 50g

rnss

Qb I

thm2tMJ~

'~b

mgLnutMJ~

LntllfUrnSiilfU

Wtmfifi!fJ 1 :

ru'i:fl S !rJ 6i 2l0mm X 297 mm "'

Lnth

sbih tuwJusb t~LnW sog

tJtiw: t~Lnl{Jlfi6idl sm'f~Lnl{Jl m

= Sxd

S = 2l0mm x 297mm

= 210 X

297

= 62370 X

d = 80g m = 62 370 X 1 =

80 X

49 896 X

ihtuLnth

500 X 49 896 X

= 49 896 X

m::::2.5kg

tHHsg u

sih tu m"" 2.5kg

1nthM~

l.J

(!JiJ1thM~6iJ:itÂ£:Jru'i:fl

Wtmtftrt92 :

Lnthtuh~~Gi 210mmx297mm

h~t?1L6i~ttYH~Lnth tu~~ s

tJtiw: l~lJHlflLnth S = 210mm =

210

297mm x297 x

= 62370 X

"t~ "CS1f th 500 X 62370 X J = "

31185

t~ttlruLg;~:ng; 4% u

3ll85x

4 x - = 1247>< 100

21_,ni:il M~ 3 185 X

+ 1247 X

32432 X

in 70x

X 32432 X

= 2270240 X

""2.3kg !;f;'JUl~fll

i:Jlt\5

z2.3kg <J

nnU'\:3 rums ""g m1 n ttl ro21 nti0"ttl rui:fl II IJ ....._, l j ~

~n 210mmx297mm tsitnrum~tf:lU1121nHM II

ttl ftj 9 5 340

mg ~ nftHtitHi "'

"'1

-ttln

7.874g

- hllsl G1

8.94g

-'i:flftj

19.3g

-t,mfi I0.49g Mi:fl;a

nlim

kg 1

st,lif~\:5 12m 2

= 3.

f:1M81ihtut2ttln'DH.n9

10m

= l Omm = lO x l

100 ><

m 10 = 3.14 X _IO_O_x.,-l_

7874

= 7.4l73kg

M 7.4kg '1

d m

= 12mm =

= l44x

3.14 X -14-Â·4_x_l_

10.680kg

7874

m 12 "" 10.7kg

sin M

I0.7kg '1

d= 14mm = 14x

m 14

196

196 X --.,--X

3.14 X

14.537kg

12 X 7874

'1 0

Qtl

c:ll

IDf.fflfi!!iJ92 : l':HlJlSltfl:i!t!:lrHH'ir:h

n 12

12m '1 TC = 3.14

s mt~Ln!{Jl'i:j3fflfi l

ctlTI5f'Hl MtM

V = Sx

V"" 1355 X 1

n 10rnoss 20 tfjt:iftlrunb'i:H15 u u ~

12m '1

siยงn lJ lJ

40km 1

s rusi'l

80km

St15St'U1U 800km i'l

nu:nhtrn~n

s '1 ~ufst 1 i'l

nhtdnm~ q lJ ~

b ffit

mls ~m!':i "'-.:>1!

tf:l

soo ~ f:l n.n 21Util rH'tl run M~ 9--..:> mttl n lJ

rul!:Hi5S'i:Hi1H~tns l08km OIIJ

nl::uru:tnru .:;;

2h 15mn '1

~ n& ru~ S'i:H~J13 'fs t9lu'0 ru-12 ru ~ t Sl g '1 2h 15mn =

(2+~)

UTI5 mtJ s

ru13 n t9

m(!j

~nu~ru~ntl9Lni:l A

B t

ru~i:l

ru~s

BtnS 343m/s '1

x = vt x = 343m/s x lmn 343m/sx60s

= 20580m X""

2.06km B "" '1:1 x = 2.06km '1

t61~

IC);

nf!G1t1 hl'tllJ t~H2~ijlg

ttnW2J'l.h:llStru~s 2i:l1:ll s t{)J tl

6mls '1

n. 2.

~s~;;~ rnci t\5~~ t'1:1 rnm s H~n ciaa n~ndl 1 1

l=H1.fl SH"~ iJ1

1.5mm

6mm

fi. d = 8mm

= 12m

14m

ti. d

10m

tl. d = 7mm

~. d

= 24mm s~ l =

16mm

~- d

~. 0.004mm 'i

lli. 0.03mm

ci~61(d) 2~13

nt!:lrnms

tin.rJSl'!:fl~HS

ti. 0.2mm

2.5mm

Zl~ttrn~

2~ l

l6mm

= 12m

lli. d = 24mm

12m

= 12mm

12m

9m '1

3. 1

200 000 i

t1:ln 16 ru1m '1 " rnms wo9~~ ttllrums[J61148mmx210mm '1 tr:~tli5Ln!:hw

t~LnW 70g/m

"dlS'Ifl

"'1

twJ~

l50glm

Mcin~ '1

s 10 000

tfid rnnt

rutn!:h w't!ls'ih wwJus~ t~

tWitf'lL61~ II

d5n~rn~d

"'1

"" 2. mLntnw

4 soo ~ ~nurnhtl~c~lst

tft~~1.1 ru ~"dl 1

lOOm

rn'1 WtS t~Jt~~&S g tf:ll rutJ~

"dl

wth t'!:lrnltLMtlt2J&~~ rnmsthn~riiJ1~rn

sru:tnrn 4lmn

52s '1

~nt

S~l:SJ~ 5kml h

tWi~ 61 SlL6'll II

7h OOmn '1

t~rhffi~ 7 : oo

MZlm n

~:tn rum struJ11s~ts'i~

g~dtft~tumnt261mci~ul:mnfimmt'!:lru't!lsu't!lrut'H 29Ikm G1 c:w: ......., rsv <SV

.........,

60kmlh

ttll ru~nn i:l g'lยงnwmfiw m~nt261Ulci~u~ ttl ru'i:ll s

S~tH~ 40kmlh '1 tWiHnVJ~fij eJ ct

""'

mtsit'lfl~USlS ? et 1-h

Hithtnil G' I

o finmin.Hmruli:lnm2tl

~nm

1.1.

A1iJJ1

nrnm l

iHtm .,.

2 En 'i.n UlJJ : f:i'U'i:Hll'i:fl u IJ 11!

"" m~f:if:irul Sl "t~t,nf{Jl

li5<]tf:i(ll2

11!

n&2Jll3'2)3ru12lbtru'i:fls

ttflim i:lnm

2En'i.n!M:

i:lnm&GJht9Jn~udl 1iy ,

(x :t: 0)

J 'i

Sfif'ifBfJJ : i:l nm ~dl nt 2Jll3f!d f:i n.Jl nftHli'i:fl2 fnt,ti'i:fl f~ru21Ht5i2dlBBBf:i~1d'i:fl2 tift52i 'i 'd.... IJ ts""- u !.J

'i:flS~HG~ a , b , x

1 :

mu ll

2 : t~ fi &Sj1'1ยง tid ?i nJl

nm?

2 24, x y , 3x + 2 , 25 - a be-

5x yz

723

, Sa be 2

: nt

:m ll 1

5x yz

, ..,..._.

Nt1Ntlnm

123

2x yz

1 2 3 x yz 2

fflnilth ~

2xy , -2x y , ay , 3ax , 2xy

, xy '1

: tlnm 3x 'i:flS'ti

tlnm aiy 'i:flstiq_!14 ~tmgs9NJ~tSHbG~ : '5wttntlnm

' X

'y t~S~ 1+2+1 =4 '1

"" "" " 0 f:ldltHI51JnS9NJ~t2H1:G~9lbH

3 2

, x y

2 3

, -3az y

Gtr!w: ""

bnm 2 b3 xy

3 2 -a be

x, y, b

2+ +3

a ' b ' c

2+1+1=4

x, y

3 2

Lf-1Huf1 : mRnn~~ u

H'i~'l.rlannm

I n. -xyz

:&. 8x yz

-b. 2lab 4 c

2 3 4 u. 3xyz

UHfl M1fi tJ fi iUHHl fi

"'""' 1 !JgJUUM9

1+2+3=6 tun~

?i.

ti axyz '1

tiG <I

: '~Ulijl &au~un n.mnh 2

t.1

b ' 2b

3 +2 = 5

a, z ' y

2 3

-3az y

~ttn

3b '1

1+2+3=6

/fig dnfi5ntrHnfimtauntmnn&'nt!m9 u .:G1J' 1 u b+2b+3b = (1 +2+

tidst! ...,

= 6b (tint~?inn u

&~?inn i

ttfi

rnl:lnbnm 5x- 2x

5x - 2x = 3x

: l=HUlSl

2xy+ 5xy

2 3

?1. 8x y z- 3x y z-

+ x y- 5x y '1

lli.

. n.

+ 5xy = (2 + 5)xy

= (3 2 3

7xy

+7+ l

2 3

- 3 - 7 )x y z = -2x y z 2

+ x y - 5x y = (l 0 + 1 - 5 )x y

lli.

11 2 3

2 3

f.i. 8x y z - 3x y z 2

6x y '1

: f.iMSl

+ (-4ac 2b3 ) + 7ac 2b3

lli.

+ (-3/ c b ) + 8/ c b

5x-y-3xy 2 2

f.i.

+3ax y

+ (-3x 2y)

lfi

2 3

+ ( - 1ac 23) b + 7 ac 23 b '1

li 1

ru'i:flSUUl{p

tlnm

b sx tlnmshg'9hLYt~b

tf.iU1St~jJ'il{JlLNg9mslldlti

n.n~

(5x)(2x) = '1 2

2 : f.iMSl (4x yc )(3x/c) 2

(4x yc )(3xy c) =

2 3

3 4 5

12 xyc

(18a)(l2a) = (1

(l8)(12)(a)(a)

t sinh m~'itJfltJfl ~ w ~ tfiffi tsfi nn En t t:n ru~w I

A = (l8a)(l2a) = 216a

L_j

l8a

i:lmsg td'in9ntH:lJi-@~!ig'tfls A II 4W i.J"N II lj

(5xy )(x y) 2 2

fi. Gab 3)(3a b h. ( ./5x

1.6.

ill.

)

)Gi7)

lfiitHHHim

'tf!St~liiftll'~sh 16x/

fiMEnm

tS8ttl9'9h'tflS'[Yt~ht~Sh

mrl{Pru

= t~Lnftll

ggh

tfiOlStltrl{PWUog ""9nt 16xy

(16)(x)(y)(y) (4)(y)

"'""' 2 : 2tnf.nfM9

"' fiMEnf:lrumn

l8xyi 9. - - 2 9yz

(Sx/) + (xy)

. n.

(Sx/) + (xy) =

2. 18xy2z = 2xz 9yz 2 3

f:i. l a b + 2ab =

2ab '1 : i:i1:UHn1lruffin

ill. xyz

211

---r yz

.1. 3xy

bu'hnlJilslJhmn.n ~m1lru~n~biibu i

~mag

u1m1JitS'l!itmn.n

ABC t~sb 3y+ 2x + 8 m1lru\JnUtlnmgs~'G~tuli

tlnm

cgm ./)

3x+ l 3abc

2x -:- 3y

4x + 3xy

"" lJitrl

si -2x+ 7 i + 2ab 2 + b 3a + 2b

Ow'i.!sw : m.nmm~ruun'ts II

u"'- t~ustmm.Ysl::ltHn lj II OS

mTlm &9m "

ern nHlmmfl::lru'tflaihuunm

!.1

" b2

nmm I

tHHH'itl'Ultn I !.1 !.1 <101

3x-8

2 1!1

l 2 -x -3a +4 2

x,a

3 1!1

-2x3y-3y+5

x,y

3 i!'i

3x 2~ 8

, 3a s~ 4

<101

, 3y s~ 5

Lvffuff : uH~nnfiHtt:Us~dssnlanmm n 11 !.1 !.1 n 3

n. 6x + 2xy- 4

2.2.

2 l 1!1. -3x y+-y-2 '1 2

+3x+3

BiLfi isntJlm fJ!l7tnuuf9 1 : n&SJ1'8 2x + 1 'tfl s ~

'lJ'i ~

5} - 2x + 1 'tfl S~ t1J1 ~ -i

l '1

2iy-l 'tfls~ttn~ "'.Q}

fJ !17 tn HUUJ 2 :

2i-4x+3 mnmm~ i

" x '1 rul&S

II + 5x - 3x , y + 4y x + 7 + y , 2k -4 +

- k '1

11- 3x +

2 3

4y x+y x+y+ 7

7+y+yx+

+x-3

f-1.

+ 2ab+

3 -x+ 3

tHH1 m A= 2i+3a-4 Stl B

-7a+6 '1

f.1rulS1A+B 2

tf.10lSA+B=

+3a-4)+(5a -7a+

mtf.1Hi~dn c; Glll II

A+ B =

+(3a-7a)+(-4+6)

+ (-4a) + (2) (tintlnm!:lmn) U

-4a+ 2 '1 mE=

tf-101!:!

E-F =

-2x+

+ 4x + 5)

-x )+(-2x-

- 6x+ 3 '1

mA=

f.1rulS1 A+B

- 2x + 7

A-B '1

Stl

F =

+ 4x + 5 '1 f-1 rul S1 E- F

-5) (!:lntlnm!:ltHn) II 01

tJCflW :

t:HUl S1 A+ B

si- 2x

!:HUlSlA-B

+ 7x + 4

+7x+4

-6

LfJHuff: n. M

= 2i + 3x +

2. M

ti. M =

tiMSl M+N

N = - i + 2x + 4

I2i+2ab+54 l

M-N tf;Jrn

9i-4ab-25

xy + 2xy- 3

N = -xy -

-16

lfimummm I

t~Ln~u'itmnntnb

<:!>

ti xx 3x

t~Ln~u'itmnn&nb

<:$;

tixxl =x X

t~Ln~u'itm nnfnb drntiM I

x(3x+ l)

tfitJ ttl nlffi S~tJ

StJ 3x + 1 ~

r--r-1 x(3x+ l)

3x +x 'i

tnt! tf;JnlffiSlffilJi 3x+2 ttims t~Ln~~udn I

x+ l

ttiUlS (3x+2)(x+ l)

~ndlt'iยงtJi 'i ru x

ggtJ

3x +3x+2x+2

3i+Sx+2 'i

L_L_1

+3x (xy)-3x (5y) +2+31+3 X y- 1522 X y

=I = 12x

? ? + 3x4y-15x_y_

nmm I

rul

1 +x

3x s~ 2x-3 '1

: ta~jl=lnn!rl

3x+ 1

2x-3 -3x+

+ 9x-3

)(x -3x+ 1)

S?'i~ 7368 dl

3 : fi5H

+3X

: 7368 = 7000 + 300 + 60 + 8 = 7 X 1

: n nn !r!th15?'irul I

n. 2x2(2x 2+ 3x-l) 5

-25)(a +

lli.

1.1

+2ab+

1 M = ;tY 3xy

2(2

21 = 3x7

3) S~

3 '1

0 5x 4 - 30x6 ) + 5x 2 '1 4

(15x -

?'!.

&!rl8

2 : firul!rl

+6xl0+8 '1

"" mqms

wu~~ rugd ru cfJ

SS 21

'G.

+2ab)(a-b) 2

-12xy-16)(x y-7 + y) '1

&?'iffi'Gn5Hn5~

21 +7 =

21 7

= 3 '1

x-1

------

-X

-1)

-x+4

-x+l 3

----------+

rJmni : d5Mnn

cfitab MS'i .... iJ u

d5MnnnHs~1H'or;-@::ufitsbMS'i .... iJ u

tj:im

mdsb

mdabnUJm9 I

2 'l

5 61

+ 4y-- 7) + (2y + 3) 2

: ti='lQiS

+4y -7 3

2y+3

-(8y + !2y )

4y -

0- 8y- -7

....

'"' 1 nHl..fHli9

....

hllliHli9 2

....

MruHli9 3

-(-8y -12y) O+l2y-7

-(12y + 18) 0 3

(8y +4y -7)+(2y+3) =

2 :

25 'i 2y+ 3

- 2) + (x- 1)

x-1

X X

x-1 -1

1=1. ( 6x

2 3 2

+ 5x-

2. (5x y + 2x y

(ab +2ab)+ (2x- l)

ill.

+6a-55)+

l2x y ) + (x y )

-5) '1

,.,

..,

.A.

~dl t~t,nltll fil t~ ti:l rnffi 2~~ fJ'[EJh ~ ~2h 1

trH fi91l m nJtl t hlS hd ffiUfi ttl~fi91l fiG 'J .:G uÂ· "' u .:G i.J'u 2

b -<

(a+b) =a +ab+ab+b2 dl9t94 (a+b) lJ

+ ab + ab + b

(a+b) =

(1) 2

+b) =a + 2ab + '-y---J (+)

+ 3)2 '1 (x + 3)

= =

i+3x+3x+3

+ 6x+ 9 '1

riuruit:fJ@2: r1~r~

ornw : ..,

+ + 2ab+

ffl'i:3n5'i:32 u n 2

t?Hn 2 (2m+ 3n) =

+ 2 X 2m X 3n + + !2mn +

(2m+ 3n) = 0

Grnw .., :

tt:ll

wun fi !!iJ9 3 (J

+ 12mn + 9n

: ?Hl.ll 21 101 - '1

tf.'lHlGfiJa fij~ 1o1

ffl'i:3n5'i:32 (a+b/ u n

ooo + 1)

+2ab+

+2x IOOx l + 1

10000 + 200 + I 10201

~tHS8 101

= 10201 <J

: t1S"JfifHSJl'H2lb 2. (5x + 2y)

ff!i. (6x + 4)

" ff!iM~UHn!ilfltdn~n 0:: W iJ' Oil II

ill. (a+5)

(m'Hm2lb II

tff!i'l:flS a Sb b 1d'l:f!Stl::lru a> b (.'}

a-b 2

1::.

-ab

-b) =

-ab+ b

-ab-ab+

-I )(x-l) L...LJ 2

= x -x-x+ 1

-2x+ l <J 2 : nS"Jn Gm-nr

: ffi'HHms tl In ) 1 a ( 2m-n

i- 2ab +

-mn+ 64

= (I2m) -2x 1

><n+

"""' 1::.

a-bl bi

-mn+

I ~ ,_.

ffl1HU'i:H~ (a-b) = II G'l 2

-2ab+b

tr:iQl S ( 100- 1/ = =

-2 X 100 x I + 1 10000 - 200 +

= 9801 2

99 = 9801 "1

n. (x-2y) 2 e

ri!lfi

-y)

r:i.

(a-b)(a+

!UJ1tnlnn : r:irulS"H~lJiW

nTIHd8

m~au9

't~lJiWf~n~

8t~fH~

- b

IHGgtf!iQlS (a-b)(a+ II

~GCS8 l<a-b)(a+b) nlumfn1u 1 : n!ln

= a

-b

-2)(x+2)

tr:i'i:nS (x-2)(x+2) =

+2x-2x-2x2 =

nlunlinlu 2 : rl!ln

- 3n)Gm + 3n)

ocflw : "" tr:iQlS

m~m~a II

ocflw: ""

~tHS8

Gmr

&r:iffitHuHN~ 101 x99

ooo+ l)(Wo- n lOI

-(3n/ =

~m 2 -

: r:innSl 101 x 99 "~ = (IOO+

nooo-o

-b2

+ tr:ims

-4 "1

G'l

Gm-3n)Gm+3n)

nlunnnlu 3

=(a-

99 = 9999 "1

- 1 = 10000 - 1 = 9999

( l + l )( - l) = 0

(2 +

1) = 3

(3+2)(3-2) = 5

(10 +

-3) = ...

10-

...

=(a+

U:l"H15 (a+b)

+2ab+

~Slllt?iOlS (a+

+b) (a+ 2

+2ab+b )(a+

+3x+ l '1

+ 2y)

?i.

-- 2ab +

ill. ( 1a + b 5

tr:l'i::n S (x- 1)

n. •

(3x-2y)

r:l~H'l

= x -

+ 3x

(5)

?.1. (2x-y)

(a-b)(a-+ab+

1:?-'lffitHdHnH (a-b)(i+ab+b

) =

a3 +

" fit:i! '" : 1:1 Sl 61 (xf/Jf.ffl II tN 2

tfi'i::DS (x-l)(x +x+ 1) =

-1 'i

l:'fJtifJU : rl~rinbSJl~;nt~ n.

(a-l)(i+a+1)

+3x+

2. (x- 3

fi. (2x-1)(4i+2x+ l)

•

1:1~&1

(a+b)(a -ab+

(;?.'lffitHuHhl~

(a+

-ab +

=a -

" '" f/Jf.fflfit:i!: 1:121&1 (x+ II .., tfi'i::n S (x + l)(x

x + 1) = x + l 'l

+ 1) (a 2 -a + 1)

fi. (2x+ 1)(4i

2. (x + 3

3x+ 9)

2x+ l)

i-2ab+

+ab+

-ab+

1 I

1 1

+l) =x+l· 2

1 2 1

+) =x +2x+l 3

+ 4i + 6x + 4x + l

+ 1) = + l) =

1 3 3 1 14 6 4 1 1 5 10 1 5 1

+ 3x + l 2

+ wi + 5x+ 1

.. ~tHSll

l'HSJl'i§

t2Jl'i§ 3x+3y+3z 'l

3x+3y+3z

HltHuHNHtl

3x+3y+3z

3(x+y+z) '1

3(x + y + - 3) + y(2b-

-3) = (2b-3)(x+y) '1

t~QlS

W'lf1Ui f!ij

: ttl n rH SJI 'iยง

Grim : n&SJI'iยง

(3x

+l)

+ l)

+l)

+1)=

+ 2y- y)

+I +I)

2 t'ltiams (a+b) l.i 11 n

~ U?'lf11

-b)

+1) =

n.n"' : ttl n.n t SJI 'iยง :11 t:aun 'iยง

dru~n.nn 2

2. ~-4x+ 16 '1

ttl fin&SJI'Eยงtild rn~ n.n n

4a + 12a + 9

4a + !2a + 9a = (2a) + 2 X 2 x a X 3 + 3

(x\2 2)

, 4x

+ 3) '1

2. ~-4x+ 16 tttlW

+2ab+ 2

12a=2x2ax3 atl9=3

(2af

2x~x4

-2ab+

n. i+ 10x+25

= x +2xxx5+5 2

+5) =

tlID tH S 8 2

~. X -

+ lOx + 25 =

20x + 100

i - 20x + 100

+5)(x+5)

= X - 2 X X X lO

+ 5) "' +(

-1

I:HHS8 x 1.1

20x + 100

-1 "'

+ 16/

(2x) -2 x 2x x 4y +

= (2x-

+ Jimn +

(Jim) 2 + 2 X Jim

- 8x+ 12

(n\

n + 2)

J2m+~2

= (

(Jim+ ~2

- 12n + 32

2. 27y -64 '1

t~'i:flS

si + /

tt!Hi.HTI5ih51.3ffHl t~Hl'Uih5Hih5~

t~'i:flS

(2x/ + (/)

8x + y

27y -64

=(a+

(2x) +

-ab+ = (2x+

t~Hl'Uih5Hih5~ 27/ 64

+ab+ 3

+ 12y+ 16) '1

= (3y) -

: t:n r'i m SJll:3 21 iH Lffll:3 r:ll d blH] nn nff1

. 2.

8a + 1 =

2xy+

(3y) b =(a-

(2a+

2a + 1) '1

lli. a + 16y+64 '1

tSjl'i:3dldrn~n.nn

" smJmdJh<JQtimHn I

:t~2Jnt

fJfn'i111M9J

A=i-2x-8

2 truhMtbnn.limm i-2x :ifll3hlHM~ x -2x+I-l n ..._,

- l) - l

-1) -1-8

+ A

= i- 2x- 8

- l

3 )(x- 1 + 3) =

+2) '1

-28l + 16

E =

ntSjl'i:3 9/+ 16 l:~:ifll3NHN~

-24l+

ntSJ1Y21titbU:ifll3fUHhl~ E =

-28i+ 16

"" &t:llll.HTIJ MY ffHl a 2 -

E = 9t -28t + 16 =

bt:r1 liJ

-4X

(3t -4) -

4)(3l

(3i-2t

c~ms

2t+

+ 1) - 7 (x + 1) =

2 2

morn~n.nnm l

4x + 8 2

B = 4x +y -b C = (a-4)(y+2)D = x\r + 1) + / (x + I) "'

+ 1)-

+3x-7x-7 =

Wtmfifi$ : t:llnn&SJIY21b

A =x

-28t

+ 1)(3x-7) '1

(3t

= 3x - 7X

run (x+ 1) dlnm G'l

-4) -

n!:SJl'i:321btru:ifll3hlHhl~ F

-4-2t)(3l =

+24t =

+2)

G'l

+ )

. 2

-2x )+

- 2)(x- 2)(x + 2)

2 +y-

= (4x 2 -

2 +y)-

= (2x =

(2x- y-

-y+

+2)-

"' +2-

= -2y(aD

x 3 (x + l) + y 3(x + ) = (x + l == (x +

x+2y

-2)

-xy

3 .

+ 2)]

+2)-

1997 , 2674 ' 20011 ,82470 , 872036 ' 973248, 881722"'

tel. (x +2y)(x+

tel.

X "!

t'Hl.fl m tHU\lfi 21 ~ CLf'i1U 2 2

2 2

fi. 3x y + 2x y

2. (5a 3b2 -3ab)+(2a 3b 2 -

f:l. (4x 4 -3y3 +z)+(3x3 + 3

'W.(5t + t- 3b) + (4t -21 +

- 5) "I

tf:l~nts,_pu a(x-h)-

"lf:lM

~sunu

tp tS thljl~UCU '1 0

c:1

fiHl.iJ ~ I':W:HU ~ tHUtm In 6

fi. y(x+ a- y) -a(x

+i) + 3)

2. (t-l)(t-2)-(t+ l

f:l. (b-~(b+~ -(b8.

+ 3)-

LM wu n;J.l ri Num 2

fi. (l +x)(l-x)O +x) = 12

2. sb + 3(h + 9.

n<h- n =

+3 '1

s,.

tflil f:l nn mctn wct!J Num n 39x4U , 54x66 , l9x2l

' 39

w. n~nnuwu21~cLmua~ 2

(x-I) 3 -(x+2) 3

fi. 9(2x + 1)- 16(2x + 1) 2

?1. (a-3b) -9(a-3b)

8(x-l) -27(x+2)

2. 4(3a - 4a + 2) + 25(a +a+ 1)

tnrin&~U21~ttfflUidl~

tsunurutn1Hsn

fi. 9(x - 2x + l) - 16(9x + 6x + ) E!i. (a-3b) +9(a -

-12xy

-h+5) '1

film Ill

2. (3a

l2a)- 5(a-

ill. x(4x-8y)

(2a-2h+

-2y)

-b+5)

~ &l.HHlil n ffi l

(2x-3)(5x- )-(2x-3 2

+ 1)

+ 2)

-1) -(7a-

~. (2x + 3/- (2x+ 3)(5x-7) lli. (3x+ l)(2x

3)+

+2)(3x+ l)-(3x+ l

i:l. (y- 8)(4y- ) + / - Sy G. Sax-bx+Say;l;i,

ax + ay - 2bx -

"' ~ ru~Mnffi S1

n. ... 'W.

-25

25x -16y 2 2

ru5. 25x b

si -SOx

"""'

2 2

b2 c2

-4

;l;i,

-ax

lli.

2 2

-4y

tl. 49b 2 -25

15. 9a 2 -(a+2) 2

+ 1)2 -4

!:l.

n. si 24x + 32x 3 2

+4x y

lli. 5.

tn~n&SJ1~2lhtgn~m~ru~MntP 2

n. i+3x+2

2. 3x + 14x + 8

;l;i,

+ l8a-20 ?

+3a +2

ru5. 6x--x+ 1 6.

h. ic-2acx+ci

2xy

+ 32x+ 8

"""'

-4x-2

lli. 2/+ 15x+ 7

24/ -7lx- 35

!:l. 3i+

-X

tl. 6/+5x+ l

15.

x +/ -2x-l '1

t~~r!Ujffi A= b +8b+ 15 2

n. t~H'i~WnUSSMl~n'litS~t Liu

1.1

+ Sb ttl~j~OISdlfi'HH~m ?

~ru~Mnffi1j ! S1

2. ttnrut'iurug~ru~stn~ A Li

+ 4x + 3

1 '1 C = 4/ - 8x + 3 '1

r;L

LRru~~g:Jt.Y!;l-~

h x

kkJSLRru~1~~~

J6w1Pi!;l-t.ttn[n:~rup!H: Un~n?

h · /'"-- f!::;J !;;!~1LRtn!;l-SJ6w1pj!;ft.tmrn:~rupgsw~ ~ ~ c.. ~

l.;!!;fWHJUU:!l~BSHHLRW!;l-S q::p c., tt

x)z

l;::tt

LS:ISS~H~SF1L.ll:lrupgs:JB~h

l +u

tfx

~fl,LS

l.;!!;fWHJUU:!:J~BJ6W1Pl q::, e..

't;

1'1

;;s s B gLS :1 ~!;;! 0

s s11 B

·w

"" : f!JfjJ!J h If 1;!-S

uu U:!S~BSl bHLR~J!.!;l-~ J6Y1Pi 1;!-t.tm[mru P

lflru ~1

·e;

~~!;;!SSBWSH1rll:Jrup ·w e._ ~ I

Sl.B

BLfs l YLPEU:!1:~

UBt~

C:,:,

Y ~Jnm mHw n

fl : ttJ!J unm "

WmUtPSBJ~ tJ" gw1s 6jSL6~ruBLfSSWL;jSEJ~ ~ BLfSjY: fUWfJ h 0 =t 8

.rnt.nlW

!;!-~

ru~J ~ ~B1BSLRBLfS:IW SLB~ruBLfSlY: J.fJJ~f.!J h

n l.PB~W

s LB ~ru Etfs :IY lfJ

WI;!-~ Y.rn!;;! UJS

lflru ~J S l.6

I- X _,_' _q_

X+I

" v.

l ' r;

£ z- ' zLPB~

.+!

L'l

S SB~ S SP..uYPJ 1;!-S !;fnlj «::I 0

1;::J

h o::;:.q

q 1;!-S v ru}:l:J ~ ~fllBSlfl § '

q+v db

.~I 1'1 mm:mauB~~!;;!SBLP «:: «::I ljt:lll 0

S L!J!;!-mlru j:;!j S l.BSPJ S SB b 0 ~

~~~~er~u~

·1

BLfSH~~j~~UUlflnl~J D M

sLB~ruRLfs:~wruE1ru o SLBSruBtfSH.ll;jBWUWmLf\HWn D 0

" tW1HHH 0

..sgJiun

IllS 3x

sgmmg x = -t

=o ,x =2

~ x wi~tHHSJ1'iHt1S91Stf:lru2J : 1

" tstm2 x

= -1 ,

mm2 x

-1-2

rns ~ =~ =

2 , Inti

mmg x

ufiurns 3<- 1)

= - 3 = 1 '1

= 0 flltitlHH~Btl 0 si~n&SJ1~&~stl 0

x-2 = 0

snt

"' n. mssru ~

n. m

= 0 si

2a + 6

a = -

= -3

o a-5

81_,ffitnmt'irunt

~a= 5 '1 4

mg X = -1 , X = l

n. tiMSl

~~~ ~

{

t'onmfirunstlmti

~En f.n Ul/7

2x- 6 1 : Ml,3:Hl5 -::--.......,.-:: w

} 2 5

!Hu~pn.gx-J:;eo ~x:;e3 'l

nt2J11H·fluMTIHums gun

,a~jm

Frutg1jl'trHl.n~G

tru~mii~nn

m~ML~runt w

LUfill=lffi s sruf'n~t~&

ttn~rs g rl=l-@smmrlu

~Enmuzn2 : ML~ru

i"iiH1 rug~n.grS"Ju9

l2ib

12ib

Jib. 4b 2 2

15a b

3a b · 5a 4b

{

nm!=lruns

}

t'i

= - 'l

~Enmuuf3 : ML~ru 3/

+ 4x - 16

3i+4x

9/-16

s~ml=l t'u~m cs

run { ttn""i"iml=l rumnnffl 1:h

x(3x+4) (3x-4)(3x+4)

G1 IJ.!

=-X-

3x-4

nmw IJ.!

}

G"l

1-x +x-2 x / +x-2 I

(x-I)(x+ 2) { -(x -1) (x- l )(x+ 2)

1-x s~ x-1 fi~tl5Ql 1 l -x = -l) ""

1-x

<:!;

{ fun.fflfitlJnfHun

= - - 'l

x+2

m~rf7f: ta~jM~runt w

•

ttin.ffll=lruns~mfi

tU 1_B

nffl~~~hlrlMSi 'l G1 IJ.! 1 II U

ctlntsn~MS91StS"lg AK li"

B '

K:;eO 'l

} x-1 }

1J bli n !: SJ11:Hi5 B9l 8

1: M

-'-----'-0-----'---'-::----'-'------"

1.1

_ (x-3)(3x-l)-2(x-3)(x+ 1)

..:..____.:_..:..__..;__'----...:....;_--'- -

-(x -I)

(x-3)(x-1) -(x- 1 )(x + 1)

x-3 '1 x+ 2 : ~l:Hl'i:mHri1nntlmt~fi::lru1r:li::lms~m J.l

lJ 1

.. 1

tf6stl ""'

~ntlt~Lnl{Jlts~~t1si::lmt~ "J

: ~tlt1'i:flsmtf62tl x""'

t~Lnl{Jl~~t1~ n(~

t~i_!il{Jlfilt~~ i

: hl1Jblint8jl't§MB91s~btLfil't§ 1.1

n. a-b ~-

~x~

~;; 5

{

fnnm~runsbm~ttibshn}fl~'t§}

=-3-= 3 '1 2x5 n" 7b ou - X

5a-

lOa

x8b

7b·5i- 35ib - 80ab

Sab · 7 a ( tunm~runsbm~ttihsbn

= 7a 16

x '1

5x 5x 4x- 12

-6x

--X--::---

lox-(x- 3 ) (tunfil~Hi5nShfil?ittlh ShfHflftj) l2(x 3) nu

•

WUTifi!!i11 : ?i M Sl ~ (;15?1 rul u l 2

., a-- 2a + 1 11.

a +a

X-,--

a -1

a--2a

GtiJw: .., _ a 2 -2a + l n.

a -1

a 2 +a

x-2--

a -2a 2

a(a 1) (a+l) a(a-l)(a+ l)(a-2) _ a -1 '1

a-2 ?

"'m-+6m+9 ¢. (a+2b)2

7a+14b m+

X----::--

(a+ ?

7(m+3f(a+2b)

+ 2b/(m + 3) '1

ruHuH: tn

{.j

?i'Mm~rn?i'M I

_ 9i-6a+ 1

5 -a

5(a-2)-a(a

x -'---=-2 -"-----'--.-:. a -4a +4

2. (3x +

x+4 +5x+4

: HHHU ~tHi n ~:

l:lJl 'lยง

l:Tl s :n taLill 'lยง

4x 3x 4x 10/ n. - + - = - x -

,.,.

15y

i0y2

_ 8xy -9'1

-9 a+3

. _,_2a+ 6

4x + 8x

6x + l2x

b+2

+--:----

i-9

-2x-3 4x(x+2) x<x-3)(x+ 1) (x- 3)(x + 3) 6x 2 (x + 2) _ 4x(x + 2)(x- 3 )(x + 1) -

: r:Hl..rHndrutonm n.

4x + 8 + (x

+ 2)

6x (x+2)(x2(x + 1) '1 3x(x + 3)

Nsl:Tls:niHLfil'lยง ~.

x-y .

""22 ~ -::--....::.....---;:: X -y 3 2

4a b lli. ---..,,----

+3)

~ + 2= 5 + 7 = 12 a a a a

~. 3y- 2 + 8y + 7 = -"--__..,;:;.__y-5 y-5

3x-6

1:1.

(x-l)(x-2)

•

flJfm fi f!ii : ?Hl.fl Sl II

_2_+_1_ x-3 3 -x

a-3 '1 2a+ 3

tJtfJw : ""

n. _2_+_7_ x-3

2 x-

3-x

2-7

x-3

=-=

.s .s LfJnfJfl :

1:1 M Sl

+ 4t +

tS13j2J1ff1JnStHlnffiuiY(n~

5x _ 5y '1 x-y y-x

rna tl:11JiH~2J'tflaml:1 1.1

l:jfiffi '1 1.1

sl::Ji:j n&s ntSJl'e fdS 111 s

n. L + ...::._ 2x

y · 3y + x · 2x 2x · 3y

~+2x 6xy 6xy

+ l) )

2.---

n n+l

tuL'l:H1Hli

2oru tti ffi 13 '"'

if! ~H1H.Ul3 €ltS'i.H~ liHi } IJ u 1 "

{

-5)(t+5)

+ t

5t + t- 5 + 8t

+ 2

t + 4t- 5

(t+ 5 )(t-l)

t( t + 5 )( t- 5)

•1

S= ·;;-n+

(r:il~iflf'H:l.H'itildrul!lM)

l 1 +--+--+ 2x3 3x4

"'"

ffliHti'iHl

., n(n

+ 1)

1 - -= lx2

- --

o:nru~ n = 1,2,3,4

1-Y J

2~3= f-Y

y_y

_1_= 3x4

S=l-!=~ 5

LfJfffJH: ?IMSI n 2m +-1_2_ ?I

2. _1_ + _.!._ - ---,:--1x- 1 3x _ 1)

m2 -25

. m-5 2

a -1 _a+2 . i-2a-15 a+3

x-2 '1

-4

6. ~

~ fJ7 'f.f1 Ulfl : NUHl5

n' SJl '!:§

1 +! b

-,.--a

1..1

t?Jffiu hll_¥ rnn&SJlYhlS 9l s mY~U2lb &LfliY 1..1

b+a

!+! a

aiJ

b a 2a- 2b

t~1ti'l:ll rut~fiutmgm?irunabm?Jtlib MS ~w

2ab

a+ b - x -2ab --ab

- (b-a) '1 A B C D

A B

-=-X

ruB ,C ,D:tO '1

x+S "

t:lff.fTI ri

!fi! 1 : hll_¥ rn n' 0

1..1

i- -4x-5 --X x-

WtmtftfJ 2

: tfltl~Gltltl~gng 1 H'IGU~

ni:ll~

2 u~

ni:llRH'l~tittlrutntlhtrtrgttii~

: fU'[~Hl5ni:SJl13~h 114

1 1-3

n+l

n-1

ru:tnru

?..

ruunri

" W5 2 "&S fi t ?Hl.Jl 21 6H't§

S;JltltLfil't§

x-3(x+ 1) x-3

fi.

-i+4

y-3

utmg a = -2 c

til

y - 5y+ 4 3x+4y c

mm& y

x -xy 3

b -b

tl.

(l+ab) -(a+b) 2.

" " ~fint~ts~tG~ x ~

7x n. 6x+ 7

= 1 stl y =

a =-56

stJ b

125 '1

"' !15 IUS"' 91 Si:fl S B

3 "'§Jn& tw't§J

l=i.

x+l

lli. x + 12x + 32 '1

-16

(x-3 a

fi. a a-

t~'t§j~n&SJl't§ 2.

" mssru

91S;IJtl

""'

l=i.

-1

2x-3

2:X"

" mmg

~fint~ts~tG~

stl

, a=

o 'y

X=-

"" y = -] = -1 Stl 4

mm& x

-2--

2i -a -1

l=i.

1 stJ x 2

mmg x = -1

ill.

(x-.3) '.2

2x ,+ 1

MU3 run&SJl't§ MS 91 s;ntl u

I4x

-2

7x y

u. l-25x

-8a b\ (-2abx)

l=i. x(a-b) b)3

5x-l an-mn

m. .....:> 2

.., a - ab- ae +be w. - ? : - - - - - a-+ ab-ae- be

ru ~

a •

+4a-l2

a + 2a-8

--i +a +a-2

1.5. ax-

+ 8x+4 +lOx+ 5

3x + 5xy+ y 2 ? 4x +7xy-2y-

2. 4 5

72x y 54xy

-4xy

2 3

-!5x y 3 3

2c d

-64a b 28ib

2 2

40a b 90b

f : ' i . - x - -2 4c2d 3ab

'155.

b b(b+4)

(3x- 4 )(2x + 3) X (2x + 3 )(2x- 3) u. ..;._-.,.:-:-,-----.o.

b 3

(b+3)(b-3) b+4

(3x+5)(3x-5)

..,.. -:2:-----"'---=2

x + 2xy+ y

+3y

--X

(a+ 7)

(2x+5)(2x-l)

x+y

r:l.

ru5.

+--

_.......::...-----=-- +

xu- yu- xv + yv

(7 _

2b-8

tl.

-4b+3

-m-15 2m-3

;;).

2m +3m 1-

~n'Gru\jn y_drutlnn&SJ11:Hua9ls;;nb&Lfil1:1 12a + 2a 7

n. '155

b. 6x + 6y

y + 2y . b+6 b+6 ?

x+y

~. __:[__ + -b-

a-b

3x-y +2x n. -2-

3c _ a

c-a a-b ~. b c +--+ c a a

m. "'-" '15.

r:l.

x+y

r:l.

'155.

r:i'. ~+

2. l__ 14

2x + _ x 4a

5y 6

+-3a+3

ru5

xy yz a-b

x-3

x+2

x+4

-4

(a+b)

a+ I a+2 Â· 2a-8 -12-3a

-4a +Sa a-2 a+2 -:---- + - + 4a + 4 a-2

20x

23x

-i

-3n-4

bl.fl.

+ 8x+ 16 + l2a + 35

(a-b)

tl.~+~+~

a-- 25

a-b

8n+l6 61.

r:i'. 2.+i

ru.

2x+ 1 +--l i-1

ru5.

c a + b + (a - b ) ( b - c) -:-::----:--:-:----:- -:-----:--:----:-:-

+ _,_____.;....:.::....,..__:..

x-l xa+b a+b x- -3-x

n +7n+l0 2

n +5n+6

42x

5x- 2

30i -17x -35

30x -l5x- 3

56/+ 5y

24y -2y-l5

49y + l4y

6 8

12/+37y+2l

tun~ run &SJ113 MSm S

!+! 6 3 -+-5 5 2x +2 3 5x

5+~

[~-~ +~+~-2)]+(1 +~

iJN

b ] ab +

MS'i '1 U U

tiblmrfH'it'i3tS A 2 +

) _

(a-a--b a) a-b

+ 2b '1 -,---1 . 1-2b

1- 2b .

'd.

thGSSMS&ilS~

y z ttl A = - +Ql

+ d -ABC @Sffi'ihl l.j

thBSStuS&il22MnMS'i u 1 uu

2. a, b, c

+(-aa+b

.......,

lit

-+-7

ti.

a-b a--1 +ab tl. - - - l+a(a-b) 1 +ab

3 -

a + ab _ [a(2a + ab- b + ab + b 2 a 3 - b3

10. n. x,y, z

?1.

13.

5 6

3----

a+b

~·

5 24

d. (a- 4ab +b)

8 7

x,y,z '1

tiblm§'i l.fl~u

m ~

ttl abc= 1

(a+~Y +(b+~Y +(c+~Y = 4+(a+B(b+B(c+~) 1.

12.

~n61~1;! x t~13j2JntSJ113

fl Sl'l:fl s t tu'lu~ tfii.m hfl t2f s~m hfl~-H~ I:?~~ tuil~H M-8su s 45 nn ru ~~ ~ ~ ~·

~ 'ts~:tuJ~tfiimhflfa~stJ ~ 'tsttuJ~tfiimhfl ttn ru~tlmcr~'l:fls t tuJ ~

d 2 'tos~'l:flficglndhmrun~ ~

~ I

s nJ1 ru ?

~t:l~ '1

n. ttit?~~hn'i;1miltJtiSlfi~:sg u~ ~ c< ~ 2. HSdnSw,tru2Gtmg 1Gi

uln'i3tn.nn

tn.nmn.n nil~H

Lm n.ngc ru1 nthm hfl &a~~ ~

Mtht

d1 =

fil~~gm~m ~.~ .. ~

tueo-

"""

SlStr.H9mfiFnH~lHSlgttf1ru? --1"' a

15 ~"" tu Cl

:5 ~

!'l'W

= 12

lx2=l-2 l

_ l

l-3

_ I

3x4_3_4

51 fi.

b '1

15.

11-2 = 3

1 -22 = 33

1111 11 - 222 =

X-

y = 33333333

n. MHMdHt3n9 1..!

tsint~rus-1 C$

csg

157

rut tl d"U'i' x 2 - y 2 "'

157 '1

HiUMil G' i

Rruui sru~ sUHu-iยง nu 'i!l

l'i:fl

o tttHt,MIDfi5'ihna'i!lq_,n9 1 m~~atdJ~'1msiJi~U1~ ll 0

t r:n 81_,M rum rung

fi1

~iiffl~~G~ii 1

1.1. t\HJ;j'Hl.n ruii mt

2fTiif!UuJ91

rums~mU1t

OfflH

~n1_,Ut~~gg~Ufi1HSH ttlt?lf:l~ d5t~Hil~ x mt,u&~~gg~

ID'i:flS1_?

tsm

3528m

td~ 14m '1

6x + 14

dl m run ru '1 tl m s g t 1!1 m~Hu'tยง ffH1 "

x+6x+l4=3528

7x+ 14

3 528

'------v------'

H~Ul

7x+ 14

"" b'iJ

3 528

502

bSl 8 t 1!1 Ql S 7 X 502 + 14 = 3 528

3 514 + 14 = 3 528 '1

~msg t..ut'~~g9~nm~ Gtffig

X =

502 t'iSflttJ

ffl~ t mo~~H1:lruU1~~n '1 0

t~QlS 2t-l5 = 75

turlth

rum 89

m"" t = 45 tl!iOlS 2t-15 = 2x45-15 = 75

mmg

t = 45

+ 5)

:J;I!i'i::flS ~l!iOlS

+3)(x+5)= 2

":;:: Sl~

+3)(x+5) = x +8x+ 15

x + 8x + 15 - x - 6x - 3 = 0 !:imsg 2x+ 12 = o u

Om=

~~h'i::flht l'l 9

= 3

1. ' t~gLhflti5

AI~

6x+ 5

= 45

6x+ 15

6x + 15 - !5 = 45 - 15 6x

= 30

+ 6x + 3

5 "!

t9Jnt~ruums&n~~MbJJ! IJ

2m+ 6 = 12 ?

1 :

tu-@nutltin'9 1'i::flS1:HiHHTIH1 '1 ~ w ~

"''

+ 8x + 15

2x + 12 = 0

: tsinbtuf:1mal!iHlm

M'tlfii~

= 45

t(}btpcf:

6x + 15

6(5)+ 15

J 45

30 + 15

=45 ?

45 ~msg

x =

fin

" 5 mynHs

.,..., 2U?U7UlJ7f:l2 :

nu ""

5 3 1 -x- -x + 3 5 5

!x-7 5 1

~x+3

~x+ 3-3

-7

~(~x)

5x-7

~(-10)

2 5

= -25

~x+3

!x 5

~(-25) + 3

~(-25) -7

-15+3

-12

= -10

3 Sx+3

= -7

td7bthcf:

tt:tH1_,hlHiHu1:Hil~

~x+3

5-7

-12

fin

n~ fil~TIJ~'li~ t?JffitH'i M2ltfl s t til ru2 ttll runlinn ,

S'l

nf1:!ruffisHrmnt94H~9 2 &tnruuHurmnt2lg 'i ll

....

t?Jtfl2

€:\!

~X- ~X =

~X = -10 5

-10+~

= -J 0 X ~

= -25

€:gil

ill'tflS~Hmn~nH~ 9 1 €:\!

: ttn

4x -20 = 10

4x-20 = 20 4x- 20 + 20

20 + 20

4x-20

10 '1

nii

10 = 10

rufi5i§nu 3(x+l)

: ttn

3(x+ 1)-5

3x-2

3x+ 3

3x-2

3x- 3x

2 2

3x-2

""tH'iUiti~H~ "' x

Ox = 0

f.HHJ '1

115fi5'i5ill~

3(x- )

6x -·

6x-

= 6x - 6x -

-6 = -1 u

i§snn

ttnru -6 = -1 @slflu'i:flS f:imsg

6x2-l

) =

3(x-1)

fi5i§illHilStifi5 '1 ~~

th~U/1 : t~YjU:h

fflf~tl_!i9 1 'i:ll~~I15H'Jrri

115

- t?lffimrunnnu-h'i:llh n.s ~e

nu:llrumturrnnt~Â·u '1

u-h'i:llh 1'19

ll ?lrul Uf'UnHhmhn~St'IG~~ I "'1'1 !.!

- t?lffi'UUll II

n.s

ffl~ 2x+:: = 26 '1 5

GtfJw : 2x 611 5

+::

ffl?ltUh~Y~ 20

= 26

zoe;+~)

zo(25~

2 zo( {) +2o(~)

2o(25~

?lnn I

mt~

r~N~ffl~sh

8x+ 5x = 104

Bx X

2x 5

104

= 8 '1

+::

2(8)+~:Z26

16 + ~ J 26 5 4 5 64+40 J !04

20 20

104 _ W4

20~msg

"" NYffl~'i:ll~YN

nluntit!t9 2 1J

8 '1

: snud~s 1.1

t?l01Sx+(x+2)+ +

=-12

3x+ 6 = -12 3x + 6- 6 = - 2 - 6 3x X

x+2 =

-6+2

= -18

= -6

-4

X+ 4 = - 6 + 4 = -2 '1

f:lmsg II

dssmhutSl I!

-6 -4

ah -2

7 93

3 : O~&fnM

tmgtfh~=i!lhm

tl5tnSWt1h&~at~fhlh9'9h

r~t~

: &{'ยง b

tl=iO'l

SU'li:lll_,rit~Sh 148cm '1 Hi'l51tnjJ1tSO~tfnM

r~t:~m

7cm '1

tmg

tl5 a= 3b+ 17

P = 2b + 2a = 148 i:lO&S8 2b + 2(3b + I!

= 148

2b + 6b + 34 = 148 3b+ 17

8b + 34 = 148 8b = 148-34 8b = 114

b=~ 8

a = 3b + 17 =

4 3(1! ) + 17

= 478 = 59.75cm

14.25cm

n. 8- 2(x + 1)

= -3x +

114

-3(2n- 5) =

~..

3x _ (x- 5) = ::

l4.25cm 59.75cm '1

1 lli.

St:iUHlin IDY'l 111

1 (-12n +

l=i. u.

b =

3y+

-y)=4(1-2y)

1' .

= 2a(a-

(a+

-2a(a-

HlOHu&N~

2 ~n~t:\9 1 &f:hrum Nrm

1'1

+ 12 -2a) 2-

nhn~ ~

&I:U&l=i01St5t~h~t:i9 l tBN~Fn~ctl 1'1 ~

!lru~Mnffltl''~n9 1 n w 1 '1 94

U!H:OS a-4 = 0

tl.....

a= 4

12-a=O

a= 12 "!

&9jbrJ7fi:

(a+ 12)(a-

= 2a(a-

tf:iQlS

(4+ 12)(4-

o=o rh1"1 run a

dSNni:l

\1.1

(a+ l2)(a-

2a(a-

tf:iQlS (12+ 12)(12-

= 2x 12(12-

192 = 192

tilJtag u

Miยงnwicflamiยงrufh~ w

fl n "!

Si:!

a = 4

a = 12 "!

ffilJNHN~

tSM~ffUdltS

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

tf:i{ll S

X+

X-

&9jbrJ7ti :

run x

0 S"J"

Mii

-3 "!

= -3

tf:iQlS (-3)-9 = 0

o = o fin"! run x

= 3

t9idaNnh II

tf:iQlS (3/-9 = 0 9-9 = 0

o = o fin"'

-mmgLf=itllJ~Sa a

~ru a U

ah b m ab

&~ShflJSJ

ts-Jg

a= 0

b = 0 UG~anm

1 : U:ll

: (2x-l) 2 2

+ 3)2

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

(2x-1 +x+ 3)(2x-l-x-

= 0

(3x+

= 0

3x + 2

S1 <dJ x

2Jx=4'1

x-4=0 : (2x-l) 2

ttHl'H~

[(2 X

j) - 1

+3) 2 IDnx =

j+ (~~2 = (D2

(2x-l)

= -3 -~3 ~SN II

"" ttl'i:ll a N"iHiU (2x- 1)2 = (x + 3) 2

rqu

2x-l=x+3 2x-l-x+3 = 0

x-4

S1"

IDx=4 '1

agmuf:ll glJUI ru' ag{h~~YiJi~ I!

: 'f:l1

+2)-

+ 1)(2x+ l) = 0 '1

tJtiJtJJJ : w

(x + l)(x +

r~:uns

(x+ 1

+ l)(2x + l) = 0 fiHi +2)-(2x+ 01 =

(x + l

+ 2- 2x-

+no ~tHS8 x+ l = 0 l

-X

t~b~ri: Wli

~ x = -1 ~

= 0 X=

(x+l

i'Hfi~'M n 1.1

+ 1)

l "1

X =

-1

+2)-

&9id~MM~fi'U

+1)=0

tii!1Q1S

o = o niniiilnuu

li. (a+ 3 ) 2

11!1. b (3b

4(3b +

= (x + l)

2. (3x+

25 = 0

ill. 8(x + l) = 27(2x -I)

fi tS'tยงjUtl81.,MWGUlffi9M~ffU~'Ui9 l 'tnS'13WH

intll!ljJi~ iii

l. t@Nt'JNH~

mbij

NHN~N~ffU~ Ulit,MWUf!UtSGtnffi9

U:$Ht,MWN~fi'U ~~

~ c~b~ri:,n~ruli

"U ~ :?V'Dtntnn9 1 L

rultUiiU:llWHiiJ~

uiii

~in

~ri ~

aruuliudssnrinnuNah 3oo, alidssnritSlg, II 1.1 "' 1.1 ~

c@Nt'JNH~in <$

n a+2

2. NHN~NiJnU

ct:n rutlilma ruuli lauds1.1 s nrin mc iii 0$

a+ (a+ l) +

300

cnms

+ 2) = 300 "1

a + a + l + a + 2 = 300

3a + 3

300

i;:l

3a + 3 - 3 = 300- 3 3a

a 0

297

= 297 =

99 "!

C$;

13~S911Hi

a+ 1

99+ I = lOO

a+ 2 = 99 + 2 = 101 "!

+ l) +

+ 2)

99 + (99 + l) +

t~msg i5tiss II II

300

+ 2)

300

300 Llfi

ru'iMHi ~99 100 ~t1101 "' l.j II

chn~:hnst

:lim

run ta~t nih tl:ll W&rh 'Ob lit! 0 <:;

s 15kmlh

4km/h"'

Hnilt!naam~w.ii~ntUntltnruth1Hnffi <:; <:; iJ <:; -..!)

H9innnruus.,

tim ithn~

»nilt! n~tlu l=ntntiu ttll .; iJ .; A

nnnn

'l?

M»ITnfi

mb x

mm:n

"" 2. M~tM~M~fil~

Hn:tnrurufirun 9 2x - 10 (h) t~runfstltluffi~ iJ

~ru:tnruamta~t 0 o

tl:llru~ru:tnru»n!Tlb <:;

S 10

<:;

<II

2x-10

c.w o

Usi;:ltMHMm Uitns &! ...;,.;

gfimmmsa'i:flru 2x-IO "' "' 2x

15 x 10 = 4(2x8x = 150 + 40 8x = 190

190

x= X

= 23.75

4. tdl~m~mfhu

tl::ilru

= 2.5

ttliru 2x-l0 15

2x23.7-10

= 2.5

mfiruc~:a tdl~m~

<:J .:

!:ltm::~g cr'Hlrunjjg&ghtn&uHils1i x II

nJuntrtYie 1

lcm

23.75km

crtHfi1Mtiih'l§tu'HlS99h 2cm 2htHnffii'.U 9cm "! 1 u n

sh'i.Hrt.gli'.U x em

tt1Q1S

ntill(!p:n&~Liift!lt~

tSHtt:i

S = 2x9 = 18

d.ht1m3s99h !em 2hm n

em tlrUtjjifi~i!ntH'Hfi1Mtiih~1i .: l.,j OW·

"'"

(9+x)(2+ l) = 18x2 18 + 9 + 2x + x

3x+ 27

36-27

3x = 9 X=

&(ji:J!'tt: 3

3 'l

3 + 27 = 36 36 = 36

~mas tyt~tlt~rulf~Hi x

fin"! =

3em

2 : 36

: mt!

dlG~SnNm '1 U:llttinMnU:flS&ot!rh

urudaatm~hfi'fat! 36-m '1 nnrutn1'tflsttlt!uM M

4(36-

= lOO

S 2m+

2m + 144 - 4m = lOO -2m = 100- 144

= 44

(i:HlJl I

m=2

= 22 '1

naat m 36 M

22 = 14 '1

: 22 + 14 = 36 2x22+4(36-22) = 100

100 = 100 22

rl fi

mfi~t~d~atm

rwru '1

nt!ttlR'i3Wtti99 qI

~at\5

amfinrunru'tflsdaa ~ II

sMMJ9it!HM~bMMJiยงams

~ndsa Mftn9it!H rdtainb

ad~a ~

100

11"1

i;t

"'I

â&#x20AC;¢

rut.mn n.

2x+3 = 12

~- 2x-3 = ll

n.u. 2.

5x+ 18

G. 8b+ 16 = 120

3x + 5 = 2x - 3 [g.

2n + 5 = 25

= 12

3(x+

=25+3y

t:!.

a +40 = 6a

'W. Sa- 12

= 35

ti. 5m-2=7-4m 3x- 2

-17 'I

=5x

5(x-3) = 5(3-

= -18n

-3)=2(t+

= 2(z + 3)

n.u.

'W.4(a + 6) = 24a

ti. 3z + lO

3:3. 4(x-2) = 3(x+ l) t i:fl g1...M

2(x- 3) = x(l3

liHuihru

n. ~x-4

3 2

I 2

I = 8 3

2. -b+-

'W. 32a = 9

9x + 29 = 78

"" t t:!l g1...M nHu1Hi'U n. 3(x-3)

2 3 3x

~- 2x+- = -

= 15

:: =

12(x-27)

&i:fl g1...M llHu'i:HiU

x(x-3) = 0

= 0

tl.

-x)(x + l) = 0

-9 = 0

+ 64

n.u.

tl.

'W. (x-3)(2x-8)=0

3:3.

3x(x-

[g.(x-3) -4 = 0

= l6x

= 0

+ 1 =2m

+ )=

+Sa= 0

+1)

2. (2x-3) = (2x-3)(x+ 1) ru.x(x- 3)(5x+ 3) = 7(5x+

nn. 5.

(x-7) = (5x-6)

t s1 t tHli f f:HlH ru1 lil_!i i:fl fi lJ

t~~tu1'fnu 6m -15 = lOm

' 0 "" i:fl nHtl !lliH1HiH~ ru~nnnm 3(2m- 5) = 1'1 n n

&GnH~Hil~n~s~ 2m-s ~"~

a 3<2 m-

(2n -5)

5 %1J05) (

-5)

101

H1ti~ IHH'l91tlLfrHS1& '1

nu s HHi.hn ~

nHl.Hlm t\51 run 'HHUfl em f6.... tl 1

sHlru 21 m '1

tru~sYUJ1:3 450m/h

300mlh '1

mtsit~bl!ltihtl .....,

Yntl nfstl ""

ttfirum~

l8h45mn

'1tsi

nnruJi '1 "

10.

Ulltl

SL~tl l 00 S1 r\ &9 '1

C!:!.

Gss~n'i:3trutltin1HS'i:3Stltrutl 1.1

l.)

1.1

limf§1:3 ! &snssin1:3trutl~1:3iltl~nn'hjlnrrhnr\ •• 1.1 l.) 1.1 iJ . .....,"' 4 ~MSIN'i:fli:lnQtl1j1Ym m1 '1 6'1

tndMil "' I

Rrul fl nHT1Hl.fl 1 M~ fi1 ~ ~ !;!J

CJ &'iU run9 rul :1 M'i:U'iH1 n~ fi1H til l,j <II I

CJ &tngt,nnruthn.m91M~fi1

i~iSMi~~~fl 1

1.1.

ruW~nnlruamt 3fTIUbtM9 1 : M:Jl'i:flS9'1H~ I .,

)> .

48kg y_ X . >

fi1 rul ABC

tRfl~ffid ru\jni_EJ~ 'fi~ tst,ihfi1

'RfflS CA + CB>AB

y_ AC+ AB>BC y_ BA + BC>AC 12

2x 2x + x > 12

2x + 12 > x

12 + x > 2x <t

12 0

27 <t

m~ m dlG~EHl:lrut,6'1Hn iJ

tRtflS 2m+ 12<27

dl1

~Gdl3t+72':0 ; 5(2m-

~m+3 S~

+l)<t

ttl rn &Lff1 ru nu~'t!~a !.!

ax+b>O

'i:flS

Y. ax+b<O 1

U5HUH a:t~=O

3 7 /"+m;s>4- m- '1

m~~t'in9 c. 1 'i:fla't!ruHrmntrl !.! ~

lif!:ZtHHSJ11Hf:lg~&9im

15-15m+5m+25>120_18m 42 30 30 30 f:infl 30 '2tlHl:311il:3nHf:iQ1S '3(1{15-15m) +'3Q,(5m+25) ~j£0 _'3Q(l8m-42) I

"3:Q

"3{!

15- 15m+ 5m + 25 > 120 -18m+ 42

(~amrl~~

"3{!

Mfiff1H~HLmg 30 mfi~a

'!J

8m-122 > 0

: tf:i'i:flS1Mfiff1~ 3x 5>4

daMnt~x=4 nb u

"'I

9x-15>12 (ii)

ff1~3x-5>4

tf:i(i1 21 M'~fi'H'l

3 X 4-5 > 4 7 >4 ~~Ui~ '1 '!J

tf:iffi x = 4 tn'UM'HH151Mfiff1~ 3x-5>4 '1

M~ff1~

9x-15 > 12

9x4-·15> 12 21 > 12

Y. 7>4

~~Ui~ '1 '!J

fi1~

3x- 5 > 4

tlu tH S 8 1 Mij fi1 ~ rl ~ 'i:fHHij M~~ i i Mtl tHfl u ~

1Mijnu9~ru rh:llyMta1

nu9

ftl~

tun Gl 1 ru~ru1§n1(l)l,!lUY I

ffUHWgnn:1M'i:1tnn

(11

ttitnfr;yyrufiaa u1§ru !.! !.! "'- 14

mcnnnn»~ffl~ I

1'1

mcgi&nh~~9i~n~la1Mijfi1~ tnms1Mijfi1,Yru 1'1 14

"" """S~'i§tl5G" S S M1§fi1~

l.l

a tnm

fi1~'i§ l.l

ru MY'!§u

1Mijfi1H~Y 'l ®

tti tn ni n.n »~A 9-l~ ~ ls1 QHl~ Mij fi1 ~y ru M'i§Y !.!

""" " fi1SS~'i§tl5GSS lJ

a tmrum

l.l

Iii IJ

""' MYfi1

Mijfi1H~'i§ 'l

"" fi1 ~ a + 1 > 2a - l MY

2 1

-+l>2Xl-l 2

5i~~ffl?ittl~»~9 l II

&?iGl a = l t:llyMm

dSMntY a= I n~~ !.! "" ~

fi1~2>a-2

2>1-2

- - l < -4x M'!§'!§IJ rum 'l ~ 6

105

0 0

ru~

: nn t ?iffi S x

X-

fil~ x

15 > 18 '1

15 > 18

15 + 15 > 18 + 15 (tin~tliit~ri~fH~ 15) u 1'1

t?iUlS

x>33 33 '1

ru~

: nn

fil~ y + 3 > 65 Â·1 y+ 3-3 > 65

y>62 '1

m"" y

: y + 3 > 65

65 + 3 > 65 68 > 65

rl?i y '\?I

<l'o

af11tnUU?93 : tl::llgtnnru~ t?ii:fHl 8y + 3 >

8y + 3- 8y >

fill

ruuthtl

62 '1

+3>9y-14 '1

- 14 - 14-

(tl

3 > y- 14 3+14>y-!4+14 t?iUlS

7>y 17'1

a>b tSlg

+c>b+c

a-c > b c '1

a<b tSlg a+c<b+c

a-c < b- c '1

t't:auil~~M{§nw;9im~MYfflrJ~G'l" '1

~;(jyjnn

fru

ffl r1 tt:i UHflB'iti'l§ rtJ'i?iUG'i Vlb ~ &'JYn 1:il rh s4 ~bA gyll ru W U U ll 0

fljfJT1 t1

t/:!1

tlJ fl 1 ()

: t 1:il guul

tf:iffimTI5m~ru~:1

ru~b9nHMMS'i '1 A Yl ll I.J

+ 4 > 87

ffl~

GtiJtiJ: tt:i'i:flS m+4>87

'"'

m+4-4>87-4 (tin~b9lb U A

-4)

m >83 ~msg

tim M

';l

83 '1

rum{§ru~ N{§m~ mYusnlliaa a

-2

f:'<-1 m .w

~MYffiHSZ'i:flSY

-1

ffl~ 5m-4~4m+

GtiJw: tf:i'i:flS 5m-4~4m+

'"'

2 Yn~b9 1 A

trunnttlrt.JdlU~rrTH'i m m !.1

""'

~:t:nrumM u

Sb~ M{§mu(jy 5m- 4m ~ 1+4 m~

timsg ~M{§ffla&Sg'i:flsy u

'liliLMrum!rumyu~ x'

-4

-3

-2

-1

n. 3(x- 2) ~ 2x + 5 2. 2x < 2(x + 1) 'i

tt:ili!S N{§ffl~~...,

&t!

15 '1

til: "'-

a 2

tt:i'i:fla3+~<19 3+::-3<19-3 (tlnHb

sb3)

:: < 16 4

4x~<l9x4 (~

x < 76 '1

m ~'i:fl ay aH

O!~

ft~ ru~othb 76 '1

1- m + m + 5

-2-

3m- 7

> 4 --5-

tt:iffl S 15(1- m) + 5(m + 5) > 4 X 30 _ 6(3m 7) 2 X 15 6X5 30 5X6 15- 15m+ 5m + 25 > 120 _18m- 42 30 + 3Q(5m + 25) > .3-Q_x 120 _ 30.(18m- 42),

t:iMHb9ibfhab 30 &fiff!S I

15- 15m+ 5m + 25 > 120- 18m+ 42 (~am fl.mnla'1 ~

tfiff!S

fflWHims 30thuaa1oma)

â&#x201A;¬3)

15-15m+5m+25-120+18m-42>0 8m-122>0 ffl~

122

~t:iff!S

8m-122+122>0+122

8m> 122 122 61 m>g- Y.m>

~mag ~

61 4

108

musgmsyMtt:i'cint~ x

-1

rudmb

61 4

a t!79tfli : unh~s!J 2 a ' b st5 c 11 1. ttl c mthls1d'i:fls (3-

a>b tS'U ac >be '1

ttl c ctlnss1d'i:f1S 1.1

a <b

(3-

2. ttl c ctlGSSH~d'i:flS (31.1

m c muss 1.1 ""

d'i:flS (3-

~;::ng

ac <be '1

a> b t:=ng ac<bc '1

a< b '::ng ac>bc '1

lll~tltLn9 I 'i:flS\1ttlHIJJHW.11J1~ .....

l.)

1.1

n~'e~.fillHtJt5H:Hiuti~6lmffiu '1 C)

illti .fil R~15 b!J~ 'i3 I

btfl ttl 9 n g1'15 t tii1 n5{§ lll ~ I

M!:11lG'itS18) '1 ~

t'un»bmbn~abt-eRn.n (2MnMs'i) ls»r:m61 A l 1 U i.J ~

m9 Mttii~ MYlll~ ttltill2&'i3RMctlGS s 1 1.1 \11

If} 1

f/JfJT] tf f!i

: ttiH uul

tR'i:fl S 3x- ~ +::: > 1 3 2 18x- 2x+ 3x 6

>;s

19x> 6

6 x>19

~msg ~1'15YlllHS2'i:flSYMtrtint~ X r~rucrmt5 169

tin'~L:iM rum{§ru~ rJ{§lllun't§tJ::n5da a .., & 1.1 6 19

lll~

S(x-3)-9?:

-3)+7x '1

"" : 5(x- 3)- 9?: 4(x- 3) + 7x t1!'ffl1J

15-9?:4x-12+7x (11Sl6l»bmhnn ""

Sx-24?:: llx-12 5x

l x>24

-2 ""

11J't§' ill~

: bi::Jl

- + X-3 + -59 < .X - X6- + -21 '1

X 5 X 1 •• t?J'8lS X-+-+-<x--+-

2 3 9 6 2 9x+ 6x+ 10 18x- 3x + 9 --:-::-- < ----:-::--

9x+6x+ 10< 18x-3x+9 9x+6x- 8x+3x<9-10

ill~

+ l)+ 15m<2(m+3)+6m + 10 '1

(2m-

- 5)(3m + 1) + 15m< 2

6m +2m-l5m-5+ 5m<2m+6+ 2

6m + 2m- 5 < +2m-

+ 10

+ 3) +

+10

+2m+ 16

-2m< 16 + 5 Om <21

~Mi§illHSg~;clltlt:tHh?Jtint'e x '11Mi§ill~'8lsmi§rut'iosnti<@sHn5 '1 ~~l.J

aa um

m~f!ln

\1.1

n.2(3

3)+x-4?::5(x+J)

3. 4(2

:::;; 3x + 8 -7x

3. m~~t'f_!19 t '~Ln~

ctj13jtf:hgln.nruthnm

ttl13j2J~:~~nm sm~rulsthnmg '1

t@ nH1 hlHQJ16l

""' 2. hlHhl{~hl~m~ 3.

nUulruuntHsutnm9ctt~ru1hl'em

r;f;hgln.nru1M~fll:i ~H1L~tl6lt~tSH

afTltnuz.n: "'

bm 21 "r:sts~s~:mg

~nts~s~ii'Hth 0

61 '1

3tJctlb 7 'i

I. r;'in Mt1 MH ITn 6l ~

l_j

mb X mu~stt!ruLn~H'i

2. MHM~1M~nH

tthrutlbm ~ tsu~sr;mgtd13 3crmb 7 r;~ms ~+3>7 '"~ 3. r;f:hgLn.nru1hl~nu

t~'i:ilS ~ + 3 > 7 :::+3-3>7-3 2

x>8

-4

--2

J1Ht.flt2~stlm~n~ ...; Li n

tl:h:nsiis 82Stl &

89 '1 t~hfl~i:3 'in~nut1strn'e2~dl~w.lln~9n W

s t~'ej2jm

e.J'

IS-

ii~ftlrutqtn

iltl

fi~gn tl'

otUm:mbmdlrJSf:i & A'

ttnru

fP 'til S1:3 UJ'e iil f:i 82 + 89 + m ;::::

82 + 89 +

;: : 270

171 + m;:::: 270

171-171+

;::::270

m~sb C-171))

171

tlmsg Mi1:3'iM m~rlsr:inJln~ U I W & U

t3 ~ s 8 900

ru [IS

tihb~t; 99

rut9Jn

~sl!iqtJ

t~'ej2jm

~------~~~-------=------~~--~

nJI ru 9 200 nJI ru s b 9 ooo tr:ilJl~ill~

rls

?" l.

ruunri n::IH Utfl ru~ N-@ m ~ n.

-3x+ 5 ;:?;:x-1

2. 1Ox+ 7 < 2x

j:'J,

5x- 6 < 5x - 1

lli. 7 + 6x < 6x

tl. x + 5 s;x + 7

UUl ru~ N-@ m & Jr;u

1: ~ g

7a>-21

2. - 3x- 6 < 0

j:'J,

5 lli. 6- x

12::5

~. 8 + 6m:::;

U<fl ru~ N-@ m ~

2x + 7 > 3x- 2

j:'J,

G. -

6 < 2x + 2 "l

2: < 1 + 3'

2. 3x

m-1

'2 + m '3 +2m >3

lli. -4- - 3 < -'--:c---"

tl 5(x+ 1) __ 1 < 9x+ 1_ 8x+ 1

3 G. 2 + _;"---=-_...;.

~. 3x-l _ 13 -x < 7x __1....:...,::---'-

d 2x _ .2_

25 <

. 25

< 7x + 12

-26

d. 3x

+ 12

t~g

tl. 3x- 20 < 7 x + 4

2(x+3)<2x+

d. 4.4- 1.3 < 5.05 "l

2.3m + 0.75 2::4.2

t ~ gLn.n ru~ N-@ m ~ R. x-3:::; 7 3

lli. ~.

X+

4> 4

X+

"" SlnG s s rum'e"" rut rnu .: 1.1 "" '

tl.

5<5

>~ -7

2x- 5 + 3x > - 5x + 15

fl15.

13 + 5x _ x

1.5 2:: 0.5

f-1. 2 + 3x < 2x + I

j:'J, X+

30 >50

d.y+3

m. "" 15.

:::; 3 +I)s;l2+y

x-100 2::200

5 +6m2 5m + 2

rul. 3a-5+2a-7:S:8a+a-!2+2 "l 0

m~nGSS lJ

1.1

u;l:31J1 !'H!Hi513HW~rum s sl t{j] ~till ~Hi5J Sl tm,mn.n:tHh~~nt'is l.l

.t:::J;1

&run '1 &run91:3ru

1.1

Sln '1 &n1Jll:3UJSWfduHUHSl8

Ln~Sl IJ

t{j] ~ t:t fduHJl nlin9ti~ff1 s Sl rh:tJ n &~1:3j 2Jm sl:3uJ1:3ts nu il t{j] 1liilh ~um sri~ s !40 s-1A: 7.

lijl1msg~run~ 82% 91% sh 84% QhnU~9Jht=1nJi 1

ru:t~ rums

Slh

so% sb 89%

t29iJst~l:3j2JmJ~9Jh

A:2soooo~:Dru '1 &um~ml:3rutd .............. 1.1

sooootDru

ts-Jg

'in~ m~Sl ....... ml:3nus stis-1 s &~1:3iยง1m 2101 A: l.l 1.1 1.1 l...; e.! lJ l.l IJ

~m.5~n soo ooo taJ ru ?

ru1 ~ '

tHLf1h~

...

g~~ruffis

tS~tlhtHrl.!Jlli5 '1

9Jltlt2~~b

~n~~mfd !

strunffi Sl:31:3Jl:3.mmmm~g

tndnnil "'I

•

0 rHlil ntH~ nHH L:Jl tS u <V

o hli1Lfntilsu~~m sL~1:3Ln~

&J:l'i:f1SnSZliSl~ Ox rt~rn'i:f12 u dl'iUr~btlnffi <V <I l.)

trnnsmSl~ ""

ox m s rihbnn ~·

&Slg&J:lffiutti4uMu A ms I

u B

tl'q

•

fJfnifUM91 : tsinbU~ P "'

G\1

HflJ x'Ox sb y'Oy

fnb~Lni1 0

&J:lJ:lhl u

"' "" ""rH~bWi HnJ&tln x'Ox 'i:f1S9hl& l.

whUli m iinu-mhfhu 'i n U 1

Hf1JbliH y'Oy 'i:f1 s 9hlttrl~

------------~------------~ x' -5 -fl -;l -2 -1 0 1 2 3 4 5 X .

-.L

-2..

t9itrnttflim iinJHHL:JJts

-3 ..

UMu'ilihlbl o dlJ:l I l.) & mb~~ '1

y -4

13 B(3) '1

tsitnh~nJ x'Ox

lftlGnJlti A

ciuuusbHr1J

= 4

nlib

. --2

-1-• --

.-3. ; -- -,---.-

tiP'"!

t~m unnu P i:flSn~Ht:rHs (4 , 3) '1 l IJ

tl'!i&UHM~

. '.- '---

-2 -1 0 "I 2 3 4 --- -- -- .-L;-- _;_-. ~--;--

-4 -3

tiSlci "'

x'Ox '1

l..,j

·'·

: : : 3. ....,- --:-- -.--- ·- -

'-.-- . - -l-; x'

~MtiSlciHimsb

: - - .: - - - -2 - ; - - .:. - - ~

tsitrnHnJ u

m HnJhflth6M '1

4 P (4 • 3 ) { 3

m HnJiiHI':ll tS

,l) 6

C(2, 2)

, 5)

sr-~~~-,~--~--.

E(6 , 3)

' 2)

tl'!i(fiS

C, E, F

tsitrn&l:itl

A ,B ,D

tsitrutd

'1 '1

~s9riasit

ui:fl s rum , ttl u 1 :

nJ x'Ox A 3 , 4)

f1J y'Oy m

ti':Jlrurun

lcm

mun9ff1b

'"~

"1'"

x;,,~

-3 .................... ~ B(3, -3)

Ntlnmtsi

C(O, 7)

y'Oy t i:t!G ru11J ftHlii:fl s fi~ H 1':ll t 2 l u

B ( -2 , 5)

tiru11J A(-2, I

: t si nb ~ t\1nunti s1-1 s9'1I.J5 rut sit rnH n'il j 01 l..,j x'Ox

B(-2, 5) ~-------·s-

C ( 0 , 7) '1

1 j

1 :

: ffl'15tl fltl~b t rn n.tib (fl Satii::lG~b tul u u G'l

: x'

-6

-s

-4

-3

A (3, 4)

4 ................

-2

-1

-1 -2

·3

tOo

c::;

....,

ruun tif!iU/2 : Hi n HH !:!l t ~H SHH nHl.fl II \l L:i ABC ( ffl'iWli~iH1Jl) '1 u

t !:!l ru

Â£1

mritntw::flb

<iJ

~ri 1JSLOlliLmli91Jir:nwmmg '1

tufJw: ""

tHUlti A l:llSnHH!:!ltS (2, 4) '1 l u

-4

-3

-2

X -2

tirl.Jlti Cl:llSnHH!:!ltS (0 ,2) '1 l u ABC ctllJitfilMtnblJi~ A '1

tfilrultnh ABCD (ffl'i:3H5~ u y t

u~~1j'dtHlhHnJfnbm '1

tf"\OlS A(-1 ,4) B(4,1) X'

C( 2, -2)

-4,

. ------- ..

D ( -3 , 1 ) '1

ctl

y''

ttno B

:X= -2 'y

= 4

D:x=O,y=5

:X= 5 'y

: c:

rdtlnmt

A:x=5,y=3

niJ:wm

- -:---'---:--- .-3-;-- -:---:--- .:

LfJHvg: t!:!lrurun ~ HnJil~ri~ x'Ox s~ y'Oy

_:_-- -2 ;

10h

12h

-3

c :X

= -4

F:x=3

l4h

y = -2

, y=O

18h

nJHH!:!ltS x'Ox S~ y'Oy

"' n.H """ x'Ox UliHnJ

t15

0.5cm

f'jg)filj:J tmtru~~nJ

'"~

O.ey

rn1Ht15:tt1ru 'i:llSVlbHhlLUlm &rubm s

rum'tllfltiHlG'i:llst~Jbti~tm

: &m

HdJb'Jt9JS1~Gm &'2Jtmbmb

r2J m ci\j t15 f'i:j ru~3tifil &1

~q~ul=lHlLHTIJ~~Mmb

6'J\JS'l~ti19Jl(Hmru finnn tir~

~Mini a2HR1b9't3S n'tlnJ&nb MS'lrulfilC'lHnd~ ... ) 'i L<l ')j "' 111 ... l Ill ""

ruH"JmhlmS'lI ... ) 1 :

m nb;nl::H'inl'tlts gm rugr§ ru~r::s nUH&bS'ln n5n~nJNni'i'i:llRnb l.j a:; n n u"" "" 1

"' hlni I

172

••••••••••..••••.••••••

170

• • • • • • . . • • . • • • • • • • • • • • • • • • • • • •••

168

Scm

166 158 148 138

: t

mrufi1nJ1Ll=lms~ ll

rummru ~

:;;b ruggru 1.1

134 130

;w:mw (t)

lOh

llh

l2h

l3h

14h

15h

16h

fi W:i[JlfC'i:fU1J( em)

216

112

110

200

Lti ~ il B1H'i:fH15 'f:Hli tLti Lt.H15

lin 'tl Hl5 : ' nru '1

7h tsinliHnJ~·m5

mil

ML'i:flti lh)

tlnm

mhLtit~hLM&'i:flrutsirrnHr1J

tlnm

HHtiH2 ( lcm

40cm ) '1 80

~nl ln.nm r1m M»ndfJ'i:fl rhsi nil'tls~ t r1 gmru fl 01 .,01 ct 4 tlu

nh~ru:tnru lOtd ~mtHHo9'tlru!::lrrHo9tlti '1 Gt (Yl.,l tv (Y

lrJ

IJtinnmn I In

37°4

38°2

39°7

39°8

39°5

39°

38°

37°

37°1

tm~n.n~nsa&otsitrnHn'i u et u x'x

ru~nn.nmmsit ! Ui

dhr:H~rul~ 37°C m

usa 1J

tsinhl:'1tfn m w~:si 01

9S~fi9 ah~nh:hnriHl=lffiB

36°8

Gtm2~n1

CH'iGSdlb w

nJl..llnttil

3. 1

'i5n'iMtDttiltD'i52l~!::ludl G 4 Ill

afl7mtnn@ 1

rumsb~ru:mru '1

tg:utlb~"H~

d5mb y dlu'i:fltum sh X "'

~qb~:ru~a

4kmlh '1

8 7

m~ru:wru~:Slgl:j:]QlSM-HnH

y = 4x '1

e--•e-8 12

3 2

nb y

4x t?H'UTh:tJ

X -1

y' 9

fiU y = 2x S~ y = -2x "l

Lffi'RHS N't:HfU y = -2x fi (I'H X

"f X

= -2x

a< 0 )

I0 ,-1 0 -2 : N~LffltltSN1ยงff!~ y = -2x+ l "l

djt:1jN~LffltltSN1ยงff!Hfl~&

SJflt!

~GfiMSl

~mts y "l

-2x+ I

-:---;-- -:--4---;-- -:---:---''

Y ffi~y=x+3

y=x+3

" "" "" fi'IHHI:!HS tSlgfi~Gt'i:1WS'i:1 'ij

"l intlGMG91~H G 1 ffi~y=x+3

120

ffl~tt:llru ':I

&SlUfitnSUffitlta

x1 -1 0

-1

___yx~~~--~~-----e-----;-----~ 1

-3

-5

tb'lHH'i'l~H!:iltS U 0

-1

tS18tlHH'13 II t

"" 0

tH1.nu~ru '~ fil'i5uMu91tl~ IJ

hl~ fi'U

IS-

y = - 2x + 1 '1

nluntint93 : mNti~mtitsN{§nu W II

y=-x+4 'I 5

fil~y=-x+4

x' ~

tru~n'i~H!:hts U

on.no~ru '~ fil'i5uMu91tl~ I

M~ fi1 ~

.QP

cS"JgtJ~m~rus~

IS-

1.1

-1

= -x + 4

~MMM~---

····!··--:--·:

o -1

mht

y' ";..

[S"Jg&tJQ1S'ifiltHa W

y = - x + 4 '! m~~btLm~ fi.

y-x

= 5

2. y-x = H

tl. 2x + y = 8

ill. 3x +

b.x-3y=-3

G.-3x+l5y=9'1

= 10

121

t.iHiH'l l em ct1

A:x=3 ,y=5

B: x = -3 , y = 4

D:x=O,y=6

-5 'y = 2

2 'y = -3

X=-

l=1ft5tHHnHUHntl ABCD tÂ£::ibli'i:fl8n!:Hli A(-3 , 8) ; !J l u

5) ;

4. A:

0 , y = 5)

,y=4)

=6 ,y=6)

=3 ,y=O)'l BC , AC , BD ~tl AD 'i t~~nMttliHIDm "'

"'-"

y-3x

R. 2x+ y

=5 =

tl. x-3 = -3y

122

2. y

ill. 3x + y = 2

= -4

'y = 6 '1

2) ~i5 C( -6, 3) '1

"" 0 l=HuHH ffHwl ABC "'61:H1H:fl8 i'HHli A u ~ u "'

= -1 'y

-4 'y = -3

-3x = 9- l

10 ' 6) ; C(5 ' -5)

2J..

!=!'W

iflthtn~ 1;\

o r:Dti119ssrur:nRntHn c< c< l

'UnLhllru9~2rumurm

~n'i:Jm'i:J u

1§n sbmi;jns'ts9ssru-@sd u u· .,. " fiR .,.

e•

2fl7'lf7WJ?:

filJ'itutl13ssnsnb •

L:i

"' l

11mm'i:J 24 'i?H'lllHf:'llfl s9 s ru!:l1321b lJ1.1

2 0 2

2 4 3

3 4 3 3 2 2

3 2 5 3 2 2 4 4

g2 8ru2lh (;ruts :d5n r;ghfu ~ "'

ti&nnbfm;q~n~

11ssnstl;jrnH'lhll~S'i:Jru<J 'l::flsmhtr:nru x IJ !J lJ 1.1 IJ

s'\3ru'Jt'lflim

q~n~ffibtr:nru

r '1 23

'tty 0

•

ossns x u u

lttH1~ f

Hf!titiSStli's u

Ill

JHt II II

Jl-ft I

II II

tLUn~

t'ilfl _<: fru~ ts fun tLun~ ~dl m~ t{jur39

as rum Rnb m nts m~ ru 1:t1ti cs g; c~sts "'I

m~G 2 2 u

C:Jts u t mg

tll'J tt:lhi.HRn'i:fl2t~t's

ru~~oru~ruug;ft:Jru u 11

usc

dth~ J I

Ni'i:flR'J u~t~Qsmflfl vcs

stsnti K U

msm~rutlu~tstum~ I! <Ill

EERFJEEC F E J C F J E C K J E F K E J E C J C E F E E F J C F E K E

•

m ~~&tlhl E Gil

m "' R l

~hl

Jl-ft Jl-ft

I Ill

tLUn~ f 14

7 1

ellis J

usc

Jl-ft I

nt~ K I!

Ill

tLUn~ 124

~QltiuSStlb

&9 h1

2. ffi-tHnnbufn.nbttHHLtin~

mnb 7 SH~

H~I

nubnllQJ MMJ&{]SfflM~~&~nH:fiS

14SH'i

unA- t::lus 7 SlR fis 6 SlR 2bnll&h SlR 'i I

6 2 7 6 3 3 0

4 3 0 5 2 2 0

4 4 2 0

4 0 2

6 3 2 5

7 5 0

2 2 4 0 6 3 2 0

2 3

{Chapter 1·4) Nome:

afTif17UuJ:

21b &Liii~:H SHtl fi ~ffl M I

~kn \!it:kuJ([,

Cla,:_M;L Mork:___il6

Answer the following qu.rnions

l. How did the bobY gof stung?

"[4,

7'15

I ,l

'""f'~ <rowls ·N-!.. .,. ~ £, ?"J''J} {,,. ,J ;.,, {, 1:) 1o;jJ ,;,J ·~,J I.

0~t_;~{f~a::G~ t~t;"&:e~~Y after 1he boby got stung?

fn.nb fun&Ltin~ 1:lu21btrut?11f~ qfim II II

d5nub t{JtitHi s st:H15'J .:::

~I! ru f1:1 ru1:n so~ tf:l ntLcrs run n1 1J

nbnHWi&sg 01

~uticr9sarum~nhtJtHsnswdmmA'"~ .:::u n <~

uuJm{lucrm~H~

ma{]ticrm A-'fs 9s ~ ru1:11 ~nb mnhtHn.nh q

"' i

rhntl 9 ~

45- 50 ' 50- 55 , 55-60 ' 60- 65 , 65- 70 , 70- 75 ' 75- 80 '

80- 85 s tl 85 - 90 'i 45

50 mmR9 1 fl::lrn45 n.rrlmtmrn&Hn'i:3tsmRstl5o t'ifllmtmrutnHsmR 'i L

c:t;

""'

so- 55 mmR9 2fl::lru5o t'ifllm~:mru~:Hn'i:3tsmRstl55 r:'ifllmr;mrunli'fsmR 'i cs G ct ct

d]cilltl tS 2'i:fl s rum t~L{H~ti1tl'i:39 s ru~tl brum 9 m R tJ Q;l

0 eJ

Liw

ttli tlj'i:fl s f.l5fHUl :m tl5 s

blintl filHtHn fltltitMtl Wnl:'itifi~ 'i "'l

en llltlUtMtl ~mth3ss1:1tl 1.1

tH!:fHffiR

45 -50

50 -55

Ill

55 - 60

J.Ht I

60 - 65

/Ill

65 - 70

J.Ht Ill!

70 - 75

J.Ht If I

75 - 80

Ill

80 - 85

If//

85 - 90

'"' "'

ltti

n5m l

s~R~tHnnt218 fil~~m~'i:fl s ru~M :@sEJli!EbtLdl ru 'i I

!26

q35nti f

iliunffit: II

s gmifl MLfi so G'tHum smti

9ssruZ"Ji:'l

ntlLMg rhn'aLfi'e ru "'I

~:m ruih M~&ldl ~9JLFn'i1 (kg) 'i u

0.62

0.83

0.78

0.77

0.88

0.79

0.84

1.07

0.81

0.88

1.10

l.Ol

1.03

0.87

!.13

0.94

0.68

0.97

0.71

0.80

0.73

0.86

0.92

0.65

0.89

0.97

0.92

0.85

1.08

1.14

1.00

1.05

0.95

1.01

0.91

0.75

0.68

1.19

0.73

0.85

0.66

0.87

0.81

0.77

0.83

1.05

l.Ol

0.80

Ltlf~i:lm~·H 0.1 '1 2.

dh~fr:Hli'HISihM~tidli:'l l.i

kg 't:flSGSSUSlS? ll ,...,

~tidli:'l2kg't:flSGSSUSlS? 1.1 1..;

n. r:Dtl89 s~ ru fil'a ill ttlti t ttl rud~ mm rt ttl rt ni:'l fll n i:'lu ~ ~ 1

i:'l fun '~tlnl:1 G

0.62 2bnssutict61~ Ll9 'i

61t1§61m5ct61ts9s2 GV U

mrt ..

HfltlGSStlb u

nl:1

0.60 - 0.70

JHt

0.70 - 0.80

J+H /!I

0.80 - 0.90

Jill

0.90 - 1.00

1.00 - 1.10

////

1.10 - 1.20

5 ttyntiMfu

hl~11dlh 1

""" 2. 110 ~ S1f U:Hli'i:fl

t::»

11~21f'i:fl2'i:flhls:l11thh lkg ri

~mhH

= 36

nq~ntits~~mhHn5

'i dsstsgmd 1.1

ffi'ij

S11~S50'1

MUlm~J s t si ~h hll

: nUH&hftffi n

= 5+8+ 15+8

hl~11thb 2kg

f11 n t'[35n ti ii h H

nci'ts 4ttl~~'i5h '1 UJ

dld

rugg1.1 ru01 s9sa ru1:l11:nh 'Lm'l:3 "' u

dJtid9~srum'l:3

nnru~m9~~£n~~hmn l

fnnht11ntLtinti

2. ~~iritit'it:\~S'i:flSffiru~udlh 50m'i:flSUSSUS1SS1~ ? lJ

l.j

·"'

: tinLhll ru9 ~ 2ru &so~ s

, ....

~ 2 ~hLr; hll~

rum 2 rlfflnJl t si :nh &~'1:3~11

!.!

f'nnh f11nq~nci 21hLnl'l:3 t s g thLnlti '1

(fl 0

11S2li2 u II

tLtinci

................... .

7 6

3 2

dtmg9ss "'

sdmm~triffiG~Uci'imtim'l:3~ nl

t si iibtib iiHH m &s a;GVIJ I

l.j

1:lG21~hll u

t r; t [:Jj ft t'I§S'I§ ru ") &s gs rut GVI.l a;

nliHniHa£h tsm Mci M N~ li

run t'I:3S'I:3 li5 "] ts gS S ""

!.!

t ruH n1 ffith\5I NSb t'itinci U W

0li! S'l t2Q1n sb t'i'i5nbctln'1:3 M lj S1

mfi ..

ms-Hmfi ..

&Lun~!

45-50

50-55

55-60

60-65

8 7 6

65-70

70-75

75-80

80-85

85-90

t~mtmnuUlru9~arum~ttlYtllLfnu~r;m~ •

tsin~U~nHHi:t'HS c::;GVU

t~HttlntYtSUtS"HGl 6\IQii

liN

" HnJHH~HS '1

• w~LfnU"Hi.umti~'JttHliY1SQlndlLuf1~m~g fis~ SYtil'J '1 u

'~fntltt:!ruw~ G

snrrlm

HM'~ffl"U ~, I

niffntiit: u 9ssru21~H'~fi1Ytsgmlru:tn .. G -@smstm~~ru

mgfn~-@sms

ttfiru$ru:&n

~~ru~nm

21.0

34.7

13.2

3.6

14.7

31.0

17.1

22.1

16.4

21.2

15.2

11.3

6.8

2.7

31.2

9.0

6.8

23.7

16.3

30.0

28.6

19.0

29.0

4.4

44.3

18.5

5.3

5.5

10.0

n. dJun9 s s ru mY nht1tidmm fin~ m G1 I

t~~ms-u lOh t~rumtitoYn 6V

mHfitn D

1.2

tlnUUlt159~sru&sg

o "" H I

or;

t'Jmq~n~cs~fi

(ili

"mn

~djt»!{juLfiBu 30 IJ

tt:!rumfisYru'J Y1 .. u

'1 '1

129

m~ ell

q_ynci f

0-10

10-20

··------ -·----·--

20-30

30-40

40-50

rug asru r: s g dHHuHil'£3 'i "'

ell

: mnb

l.)

tLfil'Su~Q_J~~~i_Y9Jb~'i:fltut~nl=HUi61~9Jlttl,1.H~tuJ9~rums 'i 1

"'ns

"' " "GSS u

n5J

20-30

30-40

40-50

50-60

60-70

70-80

80-90

r:fi eli n5imb~H'15'i:fl s-Gsu sti £n s Sl R ? ij-

l...,

• 0

2. nrwlGi"USS l-1

ruggrums~s~m:llb 70 'i l-1

"'l

::L liR'ifil n tl dl'i:flS fil1 li

rnm nnb filH~ ru ell

srnHm~~LfnRmJ1GiJ~S1i~runLRli Q\

.-.

Q.'l

b'Uin'S'UlStSlg'i:flS'URbliilt'it3S 'i titS l.) l 1fl li l " 1

RHl"U

tliJ n5ru nLOl RmJ 1nJ nn1~ ru ftl ru

nb nHm ts g d5t:~Gif~tHn

"'1 "' d~LmrhuJ~nJruTIML'Hlli~runbunrimJ~nJ~13m

~run? LtnrimJ~nJ~:sg

13~13'1

"' dh~RM ~runts1Ln~LmrimJ~nJrun t~13jtGn1{~runm nu-m&tHli'tfls 50% l

li~rur;g~rumsLmfimJ~nJ~I'15sb

t'U"Ti d"H13 t:lJl8

50%

&9JnmsLmrimJ~nJEnU?

Ltnri

~nJ~:sg

"' r;~ll~runG~rnmsLmrimJ~nJ1Jti5runttÂ¥smbt~? LtnfimJ~nJ

~msgQbma~MSl13GJ13 mtiJlSSh~n ~G~r;~rns~2nQhf11HLo I

SM13U15U1Jti5!:~13jtgm~ runh ~Lm fimJ ~nJ~21{~

6 000

5 000

4 000

8 000

5 000

ilh~-HJ

6 000

8 000

dh~u~~bo'H~Lm fi8 run rurun MLrnliLmri8run

,.,...J

Q)C:o.

t:h~f~t: b'i59~8ti5ffi:::l x 1 ,

t2'H13~13nMfitl:llti5

_ X =

, ... ,

8htLUnbMfi5

x 1 +x 2 +x 3 + ... +x n n 'i

us SnS u

(x)

cr~sUinna (f)

!.1

M SlGS 8n2dl138~13nb~~ M~ u u "' lJ lJ

'(J(~fij ;

138J13 X =

!.1

G88nSEnbHM 0

G~s~nn~mhHM IJ

I l

•

ti~s~s x

qynlj U~~tj_~n~N~U

0 X 6 + 1 X 14 + 2 X 18 + 3 X 9 + 4 X 10 + 5 X 3 132 = 2.2

x 5 = 4 , [ 5 = 10 , x 6 = 5 ,

'i§Uj'i§ x =

_;,_;-,:;:-;:;...-=-::.....::----.,..;-'-::_;_;:--_;:,_;;

HJ~Ug: tj:iQ1Sljifii12

2.2

1.1

ruu;~msnfiLffl

m ntis1.1 f':H~lJiti ~fjj ""

-,:;

f~Lnti lOO&nM

1.1

agu

1.1

ti~St~Lnti~fjj (x)

4 2 2 9 1+2x3+3x2+4+9+10

tiSStnM 1.1 in'i§GJ'i§tSt~lj1ti

fjjQti~fjj&nN

1.1

m~ j:i nn Sl 1§ GJ'i§ x-

= -.....,.---=--=---:----,----:--

dhj:it{]uLmfiu

rut9iffl'i§

----1~

4 4

£10

ru ·tHo t ~n ~w.ti m Gl'i::ll2 'iHHi5'i\:!' 6 Sl R'i:ll2 Hll li

"'-.!>

Cl..fHli u

40 ooo i

ttii W'i::lls~ a I

n.sHl521'1 115m~ 40 ooo ~ 'i

fn 2 mfiihnm &ttHli'i:llS'iOl I M lj

n~m

0\1

tliJ Nt1 NWnLmfit3ru;J rnnm

• 0

~nffi~LOlnGru;)

t9ti13Hhl~t:h~ 'i 3 nsnmt~

108

134 I 140 'f

120

'-----or-----'

tru~ Nt~ntllimm9 s011 swftl rnm a t{Jum~ n "'-.!>

tllt.hs g'i:fls

6 maasf-1 1.1 u

&f-ltillmmn't~nn.mrntf-1 'i:llsrh~ 134Sb 140 tmgt~tlns'in~nt'HS"'mmg 134ab 140 ......:; w n tr L:J

~msgmt!Jl2 Me= 134+ 140 thfltfli: d59ssw~ru'i::lls u 011 ~.~

fiN

137 'i

~tmgt~tlns u· w

'i:flSgfflbUnts1n9 n + l 'i 1.1

""' 0 - ttint:hGSS 1.1

GSSnS (x) 1.1 Ill

a~ l~nm

158

246

268

100

150

tLtin~ N1u

300

GSSnaMm u 1 1.1

1050 133

HH'i:H:1J1SStl'1:3tsJ'I:3t£tlfn.ntl

t£8 '1

odJw: ti;JJtiJU££HiM~i!tlH w 1.! J..j

m~tin~fDHJ 300 "'-Li I

1.1

t:$

':I

t'1:3tlns~dl'l§ts1'1:311££n£tsm'i~M~nnmru iJ' i.J 1.1 IJ Liw "

tltH£8 IJ

££~ 1.! IJ '1

9mtlt'l§tlJ1st5ncsi~9 300 + 1 = 150.5 c:iJ

Q'j

C))

n~L~M~n~rur;Slg~ UiM~9 w w

150 st\151 '1

n5 n5m nhm m rt11:S rutin fl ~usIJ s ~tit! t~liu s1.1 s ~tiIJ tl csi ntl t'~tin~ nIJ ~ n.m ~ -....:> IJ IJ "" I_; l

stl 11 +79+82

11 +79 = 90

d]tl'J~ '1 tS8tib[1Rrtlutmgfl~L~M~~m

= 112

t.l

y UJY

_ X

r;ssnsfl1tlH = _,..,.....::l.l:........::ll:...___---:,----

U~SUiM~srltlHM IJ

1050

3.5

fufiufin : 9s ru21h t'ifilY t s gm1rn Rttl ru~M'i:fl R rn su nm ru;timtd nh'l§ru fDrnui lJ Li t_; G~c:; u

l.J

Gic::G

5"1

mEhU 6

II ~~

nM619fflhtYtljl£Sh~MSl6Y

81:218 '1

3.3.

Z'lh tifilYtS gmg £ runs SnS &94 ff'IYU£ s Li

!.1

r;ssns x IJ lJ

qyn~ Y

M ~ ttl t~~ nYUiY GSu S S n S nhi~ M~ 8'1:3 tiJ') i.J

134

!.1

"' 1

LiIJ

!.1

2.5

QbHHUlt 2 g t?11j1~ r1 61J u

'tfl!HLlin~ih:nbt?'l

ttfl~~sg t?'lrun 2 miirunb~&l~srur;'i.fflmin m0

flluntfr.1t: ~s&nM?'!Mn~9Jlmf11 II .: li1

2 '1

MJ 12m R9 ~ rnm s ~ts2lh r:un'B

?'! ru1 m in 'BOJ'B SbmtlJlS '1

&cf!w : ~lib ~:um:i rl!:Hil'B mi::lltHs n t'B ""

.:1

truhMt~n~:illmm

" " ..

'Hli:HLtin~trrtsh 3dl&Ltin~umbr:?'l r:utoJm9isb~~

~~ "" ruM'i?'l u

= 63 '1

(50 X 2) +(52 X 2) +56+ (63 X 3) + 67 + 69 + 70 + 77 2+2+1+3+1+1+1+1 732 12

61 63 + 63

mrl~nCUJlbl5?1639lbm '1 ~utSH'BE:!JlS?'l Me=

""'

'B~H292Stl5r1Sm u 01; .:

t9 61 '1 E:lutsg u 'BO'i'B

.,.

63 '1

'" (x) LU1nt2

100

120

dss'U?'lrnn (f) IJ

l"'

4 ; Me = 3 Sb Mo = 2

'Bw'i'B'tfl s n ~Yudlb nfil Rt'iG s tJ ~9 r;g'l5r; s4 nb 9s s ruts 815 iJ GV 1J l_j 'J 01; ot

rn'Bn nn t'Bntsb t G\IIJ1

sb 10 'tflS?'lrulnff12lbnm '1 ot<V

~tlmt:~ni:HrtlntrnfHilbnrunrnmrung i.J" li1 li1 1 M

OJ=:t.

Ot::>J

rl?'ln~H1 I

ntsbtmgr;g '1 Btlliln~n~mn5n::lirunfnnrunttlrn'tflstmn~ndlbt?'l '1 lJ 1 u -....:; IJ l_j

x= 6

; Me= 6

ig)'tll s M~ M~JHiQh ffU

~th:ยง'jt~hH'i9dJl~

N tkrfl ~ 9 o mri

: nu fhm <I

nl~""

100

ru'tll a

15$ 't11 s t'l'Ufi~~H'Jtllti ttl '1 muus g ntJlgj l~~~ N'~'tlltl'tll n5 fiHJ..m ffH lJ

m rlmHl.m

l'l

: ~fiJ~ x == taJu9~sn.Hn~ 2

iigJ Mo tl

<11

9 '1

7 + 12 + 6 + 12 + 2 + 9 = 48

12 '1

: l~csgtfirufit'tuJntotims 10~ttlru't11s 2

!:tltits

t~tlJlS Me= ?+ 9

I!Hl.flSl~tiJ~ t~ 136

Shin '1

~G2lhtLm~ w!

t?l'Ul~t1.9~ tf:l~j~nffih~g~sli.HSll '1 tl

~f:l~'"hq eJ u

ttiOl ~H'J~L~m~}Hsi hll

nUtnROfi!HtHdhl .!1 6

tl5'J'1

2 3

n. tDuo9~arut:ilflQ~H'iU1t~ufn.nhfonqyn~

t~'i:llS'if:iut'iti~sos c. w 1.i

SlSBlRtf::lrumsd~runtlm~ ... "" q

r:i.

~no~st'l:lltltf::lrumson.mruq_?sthtlttl '1

tr:i012l!l&itlB6'ii~

&sg

100 tfi

nGiUn ~o!ntl tLfil'i:l cntm'i:1Mru ~

OSStfiM 1.i

tr:ifimsl!i6'ins61J'~tm'i:1wotnMt9Jri&t!rum~::un1drunungM B ttfiruu~sr~ lJ

Mrum snGi'i~H:lO!nh tUfil'i:l ~ wu I

focm'i:1Mru .., ~

OSStliM 1.i 0

e)U

Q10

fi. 3nOS1.1 StO"' &011:1 Mrut'lO SlidI 61tH mg fil ~ ii W

lliOSStdtQl'i:JM 1.1 "" ii

rd~m~l s tsi !Jtl hll

9ssru!nhtUfil'i:1tS8til!l nffi ""

HMtHmHfUSltiillS'i:ltu') u 1.1 OJ'I

1.1

30 53

59 42

50 43

56 42

36 45

50 40

49 45

46 '1

n. cuuu9 sa ruts g m1:1 ru mudmm rhh Rntl ff1 ""

'l:flsLuf~t~m~gc~st~

6'1 I

s "~

q I

fn.nbfuntLtin~ftl ru~

2. t~[51tH0isftJru'i:fl~Hflttifl13ctlb 50

HM1m-ecljy"hnb9ssrutsg 1nli e.! ~

1!1.

m'i:flSUSStlSlSSlR? ~ U I~

9~ 2tti!nbtLmYtS gijt,p!] rlLfflRGrun rutrnt MfH~b

MSLtim ~~Hti~HflGd 2

(~~m~st~ru)

Rurunru (~st~ru)

10-15

G~SHflGdS (~~ctlEHi.fla)

!5-20

20-25

25-30

30-35

35-40

45-50

Htu'im-ernb9ssrutsg 1 01li ~

fl.

~MSnh'ettit2H~rihbfi13 300 OOOl?

2. t~'i:fl SHflGd S~ [1 SUl ftJU ttl rurtuun

1.1

ru1tJm tumul'tsffiQ ~ mruRta ~ u

mnb !nh tLm-et sgtJ!;p Â£!J riun Au

LfflnG

"' I

151

ru Llim Mff' m"'

usSffiQ~n~ruAf::l~ lJ u

80-85

85-90

90-95

95-100

l00-105

105-1!0

ll0-1 5

63 'l

100 snAtsinbnn~ "'

li'

n. uHiJtit39sstlHil13 ththr:tHTidm 7lhR Rntann u .; n .; .; 1

mth\]'erl 40 n

"' "" "" 2. tinUMI'i59SSru!:sgm~HdUAlU '1 "'

?1.

~fiMMJttlrums~~

bqjs'Lri'e60~~YlSG~2~ยง1221R?

nOJHi 'etiJ'e mtlJlS n.

~u~~c)

Sb\jn!:S9~Sru~bi:'Lfil'e

102

104

102

?1. X

2 l

lli. X

'eu'i'ehltiSGSS 4 u l.J l.J

13m'etS'idl'eruGsstM'8b 41 U L.i l.J l.J ...;

stl

thHib 6 '1 :innt13"" X ....

t?JnnnH58ss~ 32 , 31 stl42 '1 ut3ssttlrut A U 1.1

s'eru<J~Nsb a '1 l.J ....

~ndilltintS'iQl13rutssst2lg u Li 1.1 1.1

""blS x

tLtin~ f

lrl~~n'eOJ'e ~'etijlS

ntsil~~:sg '1 1

11.

mnb ~b tUAl13tihl mrilifnn b ftsnt:'iUn~ ยฃst3s1.1 s m~ M~ t M~21 MHn9 n~~g t th ru Li 10'1 lJl

.,._,

GSSnUlM x IJ

G~SMMJf

139

12.

A ,

s sb c, Qb~f:H3JI

ruNml:lln'isb

2 โ ข

3 sb s 'Ub~

""... 30cm 'l CN ~- d5tt1td'iH~1:3dl D 'eli5t~'l:3t9'"~mm8n1:3nhยงti'i'l:3t2t~'1:3dlilbust~'t3th5sh33cm '1 n 1.1 ;j n it! n 1.1 ..., m~nn1:3nHst~1:3dl D '1 u n ~

13.

N't3fiJ't3 ls 'EihLU N 20 Sl Rsh b I

14SlRtMsb ... 14.

t1Mm

15lcm '1

'tJ

ty~U'iJrul:llsu

tru~ 5 N~ntr:l

4 sb 5

tt'irnsmurun

'1-l

100 r:lb

ttf1rumnb~bnm'l:3ummnrugdruurMh G

Ul""-'

nttyn~ '1

n. ummm x+y 111

""' "tSU" 2. tU1:3tiJ1:3

!40

sb y

2.9 '1

umm 111

t'i.

lli.

tH1J1Rtmti~~sbt1:3r:ljlStsu

ruil

~m'"~msg'i~~mstnnncrHult91b lJu

stptru~ 1 , 2 , 3 ,

rurnsnfi~rrHru2mfdtucrtilRtirut9inh'iU~ti~m '1 lJ II.! U <t lJ "

tlM1:3tl5NSnn1UWU Ml.l lJ

N1:3tiJ't3tSttibLUN 20SlR '1 I

bttin&sg

2x+3y= 112 '1

""'

I!I:::Pib

k<l:l H m[;fU:~llJgl!JBl!::!!;fb!L,OrnU\Hb!fiBLH

~~ !;f~PJjill}:lj ~

I ~

h % o~ gf~w~fil BWUHl!;fY I ""

% o~ rngk<!UJLPn

1'1

~·o k<IUJNa~~pLP

'il

= d ~NBN\21JU~k<l:J

1'1

BLH ~

•

gf!:JHrnu:lH~IJUbJk<l:J '

l..lfl.l

nru1utnYa~n L,OI..lfl.liJU~Y

El!::!~lHLPrum "=" ~ ~ (')

n ~ ~ m!;fLZ~l!JgllJjl,Ol!Jtk<!lm

,.,

~ lRL,t lP " lJj ~!,j ~

l.ll ~

1'1

rnRIJU~l!::!~I.H~l p "CHICO' (\

f:lJnN1!JlHb!~sp!:ft.tmCttlrup

BLH IJU tb!~ ~B!;f~ H ~U!;flZ ~ llJ g ""

l.ll

k<jj

arnuu~b!s:sp

L,OIJJ1l!JUgy l

~lRt.t

1.3~ k<l:J~lR~b!Hll.Hill}:lliJUgl!::!~I.HLP.L

l,OWffil~

()~

"wmruf:lJillPtlill "'

l'b

P.H

~cs;:,

"" !;flZSLOgl!JW!.Hk<l:J h 1 !;fi.ZP.H

!;f!=J I gLS:J!:Jl!::!gl!J:Jk<!lm

""' .L gfyHrn u:ll !:flY eru l ~u;~~ H

+! n '"' Ub!Hrnu:l:J~t.Ym~u;yrn~SNk<ll n

h eru:J~lR~t..,Bl~LR.~~

LA. ill }:l :1 rn Eb! l!::! gLOW U\l Hl k<ll : J{JU1J ll.fJ/..8 ~ (OJ

a:;l

I::;,

::;!.:>

~~~€J~St'S~~ <::1 t;;;;

"':

t!:~=J ~~1mU\l :~ ~ n.Y ~ b!ES UJru !=lJ1flHW~ 0sl nUJn1\21JU~ o ~f:l

I ;::,sttU\lH:Jruf:ll(;:. ~

gw~u1s:~nUJn1~1JUY b~

c:..

" ~IJUP!H

sgfiun ""

~:fiu:nntldl'i:fls

10o% QtlmHmHnfitti13Jt11S HY. r tLmg1]i~maruiftlnnmg 1

., Lt11ni:l&nfi'i:flS

HY.

~SnHWtt:lrutm Q

"" """' "' "' rtrnruLn~fflHWlU6'Un'i:flS

Hy_ r o:m P = 22 =

1 '1

sms HY. T&9Jru 'Lmgm~ C»

ntlmMt82tiSSnH1JlLMut '1 IJ

Ot~:m

0 '1

ti 0

{

"" ""' 10 tiSSmMHlmM .... IJ

2, 3, 4, 5, 6, 7, 8, 9,

"" ~Si'UMLhl'U

"" ti~SmMUt5'U

{1, 3, 5, 7, 9}

!iJ

5 '1

&~ 4 'l

l:fit11SlJt11'UttlrumtimsHnJ~~tilJru2b iJ

2 Qbthrun'8 3Yhl~13 66% '1 1

~:mm

ms~:ru2musIJ

142

0 0

2. nob Alm8.0 rnr.tHu'iH15 .. IJ 1

sb'intn1:! (!::lm152lbnn) '1 c. u u .,

u ~ rn t S'llJi ci tuliHm:; b

tJtiJw: ""

t:»

ti~BnHU1Lfl5'i5

{2, 3, 5} ti~SnHWlLM'Ut~ 3 '1 t?i01S1Jtll'i5 u

p =

tiSSnHUl'iM'i5 lJ

= - = - = 0 5 = 50 % '1

nssnHUhfw IJ

} tiSS lJ 1 'i 0

p =

tiSSnHUlLM'U 0

tiSSnHlilHlti

= 4 = 0.25 = 25

% '1

i:flSStl5ffH?ii:f1SM~1:! 1 Qbmrun13 4'Y "

25% '1

niunfft.5j9 4 : Ll=ilflS!:;IH~ 6 Mru;p~ A, B, C,

E sb F

tfl1:!j2J~MJtl5n

dJs

~M'ii:flflt{Jsm sf~ 4 MMfth ;;.. IJ l

d'hmnm c. "' 2

g '1

tS'HHltii:flSM~1:!~~Sfilmtl5 tfl'l§j2JA1HuQ_'J

M~nbntrun'l§ 6 1.1 ..

M~ '1 1.1

~1Ji~il-hfi~

tfi

tJt'!w : 2'i5i:f1rh ~MJtEn 2 t{J s f51 M "'

""""

Ul~fil~MHlti

Cll

~ A, B, c, D

ttfi ru

F dl MO{j~ c~Hu~ ff:l

tiSSnHl.flHltitM 15SbtiSSn~M'iM'i5 {AB,AC, lJ ~ 1.1 lJ 0

t~ 6 '1 t?i01S1J0115WQ_'J 2M u 0

u~SnaMLM'U 0

tiSSn~MHlti

a:p

~1Ji1ShMO{JH!::lb15 u

= 1.5 = 5 =

CD} tiSSna IJ

0.4

MJlflS

= 40 %

i:f1SStl5dl

hlMJ&Slgi:f1SM~'l§t~ 2 QbGtrun13 5~ M~'l§ 40% I

Slfish'qHu2Slfi'l mt~hnru~ GSlgfntlยงmf:l u ~~

n&Slgtl3nm:m.hmnnt'!N ~ ~ u 2

Ei1fit[j'tยงjt[j~fihll~ 'l H1LUQl'li

ruSlfiSh'liH\mruSlfi 1 IJ

dhf:l ~ t hlltHQl gill fifn'tยงIJ ru t!h mfim:fHa9jh~

tSl g

ffl~f:lrulSll_YQl'litSUJ~ill~

nSh

u 0

'\;)

G!HH:lh&smhlltHltludl &Qlgff1n'tยงIJ IJ u

tlh tQl2'1filU9'1n u 'W I

Rul.H:J ru

~-, rs~.!ll.mu:n.mfl~kP U~S

£1

I'!

1'1 11

SS.!lUtl!J~

U L

SS~~cell

:ilH~E I'!

~J nLONU:Jt.ru .t<~

ss~RmY1

h 9

':1

·s

~uru u ~ ~j fl~ 1:1 s LRLJ:J t

b 1 ~UJnennsLOgLO:J ·m 0

~ ~~{lu:Jh!.!lJeruHJLOgLO:~ ·.t<~

£ ~UJneru:~sLOgLO:J ·e 0 ~~l~ru:~sLOgLO:J ·y 1'1

~Le!JU~LY~U1sH1LOfi1h!~ c. ~

'bid::;)

·z

b .ffiflh!illJYD3nt.!-.H8LO:J!<!:J t

~-, RY1~rurusLRs~ ·.t<~ 11

l'l

YIJU~~ru~SLR

·e

RY1:~rurusLR " . I!

·y 11

':1

11 11

h UtlY~~~ru~Jfil.OfiJ. U:JlfU.t<~

~-, J.s~m.mu::u~

"' ru ~ s uhwH 8 El,HHu ,. ~ s

':1

1'1

':1

~J.Hl:Hfl,UH

1'1

u UBY~g~

.1!1111

l'l

SlR2U:Jl~Y

Yt.ruJ~ru~SLRftj~~j~~ 11.!1 u Y~ ~~

fl,ll:11vz

I'! :J ., S !.fl,.ffi flfJ,Mfi1~Y

'[ 0

~un!l-1

M :J 11 h f!U:l.ffiR~fiJ.SY.!l~~lf.U ·~ 11

.!lf:Jtl!JliSLRf!U:l~~!,BSh! ·m I

n~LB~Nsh! I

I'!

':1

.ffifl~fi1Sh!~SW~1Sh!

£J1s~.m I?

SLR~~

':1

n lfU.\<1 h h!U:lfiSh!!::l.ffi~IJU I

"' "'""' n

~.!l~S ~Q.J.SYfiU:lfi ~1Sh!~fij::l ~

·!<!

11 n "n !.fl,.\<!.ffiflRL!\l.\<1: ::0

·e ·y

ZBMJJ.!IJJ,J, OCt t:l' (.,

eru:JS lOft

!::lr6fl,ll:118LOlllR~:J

Htlll.m lj:J j .m a!::! LTh!::! I

WU ~R~~ S lR!<!l~:J

n lJ:i1 glO Ell!\l j(j !<I j I

~:;::)>

1JmuH

Ot::J

t;;ll

LJ:i£),~

~~ Z

9v1

QS HH1 g!:{LZ S l!J k!; U:! nl:J.H.J1H ll::l ~ u1 S c.H1l!J n1LS U1H! ·e tb p

1, rnEeru:~

'l;:;;>d::)!

B!R lf1Hk!S S£l.LS UU !Z ·y 0 11

Qb!fiSS£J.rnEk!U:I8l!Jl!Zl

·g

9 erulSl!Jk!Uek!r6fil!:!lgl!Jj!:{SfigQu;

s l!Jk! w g l!Jl ;:uu t LY ~ u1sl nUJnl.LS uu !Z ~

'1::1~

·e

1'1

Bl.Hlfl.Hk!SSBLSUU!Z ·y ""

1-:

uhi.u1Qr6l8l!J:JrnEk!UeYilJnLY1Qsrnfiyw (b

I;:)'

6 QSNln QL~H:Hll!:lltlk!Uek!rBnLY1s:~ru:Je c::::PC o ifi'::1 o ' <;.<0

1\.ruprubJ:Jruu:~tEmUJnlYE ·e ("

S tl~~H~Q~);dUak!r6p..LY1SHJ5lf>EYnru

b!Jrull:l!Elnl!JnJ.yg ·y I

filY1Wk!Uak!ilJnUJ1gl!Jj!ZHUb!lrullnS:J co

I, i,

lYB~t>rulWBlfi!;lltlk! 0

·9

YPiwLY1ru

ruUl!El

1, I,

ill3YrBnUJ1gUJ:J!Zlrumruuns:~

t.Y

Sfik!~SIJ:!fi1ru <::o.

UH fi lYfJI..PS I"

UU!Z .B II ~

U:H fi lY fJ I..PY lP S U:lfibru b! l fil!Jfi~LS utJ !Z "tl "'

~swn1rub!:JnUJruLSuu!Z ·!Z

"' II run1frut;J lP);d~S wruru b!Jfil!JNLS UU!Z ·e I

~swn1rub!ml!JNLSUU!Z ·y

£J1frut;J I

1, II

s UJ ~ ~1¥ t.Rfru t;J

¥LS oI

t:tYfru

!.};! j ¥

ufs

:J.P.

SU:l 10

~jPJ

! ~

tlS'b YlS vi N HN N S LA.ru b!Wl.PtlY !El!.};! gQS'l::lt lYU I

(t:il

~ #

t;l

1-.

~[t>l1J1lll"fi mE:JPUfUll ·tf .1'1:

1111

U6k!NutJI:JSEH3E ·m ""' "' "' Ua ll S EJ S @- "!Z

~cel.~J1H3 l"

·e

ffifij PHJU [j ·y

·s:

tttdnnil " l

ul:Hl5tiblm'i~tmn.ntis m2tlmnH1~m ~S'i~tm Musm ~ Ill '-'!_j I ~ IL:i ~ l.j 1 ~ u

o tLtirnQ n.n: nJ rui~ s ~ &slfltm ru1 ~:~~jti:h gLM rude rung ubrntimm9SlR9stl~ntlH:lbsb~ntl'i~tm n.n ~Ill'-' l.j I~L:i

0 HS~n'igfti~M~J1H1'i~tfnllil 1 G1 L:i G1 L:i 'Lti~tu~mn&tlrnmRgtJstJlflcmn.n~~ ,~~jti:h

t:>l

t\iiiUi~~ee~

1.1.

srutrsruistihm

c A

A'B'C' ~

ttfirumfitltu£!)

ttl&t'll'.lln1f\tmllil

CIJQ)QI

i:hR

M n

~LnnmrnLntmn.n A'B'C' t

ABC

QJffiLntmn.n

c:»

91-tlmLnnhi~

':I

l:llssrumm

C»

l'.ll<JtSLntmn.n

1.1 0

ABC

1.1

Lnn~~m~Ul~ ~ tsL~tm n.n ABC

tt1mlfltm n.n

1.1

sblfltmn.n A'B'C'

dlL~tmn.n~s~

<J .

t?iRMfituHMa

~Ln~m 1 ~ u

flABC=.!J.A'B'C'

1}l

B'(B)

C(C)

~m ~

LA= LA'

A'B'

LB'

A'C'

LC'

BLC

: d5t,~tffH1.flrJ~dlt,~tnHlil~S[l t~~nffitHu~~sms~tm~u? ~~~ cf

~ 9lUl Hl.fHl SHl5U&"tH1H'tHuH n

B' '1

~m~m'l:3ruf:ldlm'llism"' <'l l) 1.1 U l I <'l

LA =LA' , LB = LB' , LC = LC' , , AC

AB =A

, BC =

""' tUl'i~OlS

: ~H1SJ

n~~tlhfi<@stism"' n

1. "

: N~~tfllM ABC Stl~tfllM A'B'C' LB

LB'

40°

stl AB

= A'B' = 6cm

ru LA =LA'= 60° ,

3tl&l,tlJ'iHU'JUt,~tfllM9itlnHsg '1

N~~tfllM ABC trut,ntnM~ a~fi l .,;

- tsit C»U

r:J

f:lu 0

- 'l?nugst,ntiunflu A stl -

'i:3ru&1:iru AB 1.1

6cm

B ~

~tl "tS'l4" A

tmru~t~:.~ruu;~mstu~"' II

U&ffilll,'l&fllM A'B'C' 0

•

Ntiffi'l:3~

C'(C)

'Lu]moJutfitmM ABC sbtfitmM A'B'C run t,.ABC tgi~fi!J1~ritru llA'B'C'

t~ru~~b AB IJ1~

trutl~Dt~~nih:gm ~tl Ac L~~~ I

~Hru

'Lmg

LA =LA'= 60°

b BC 'i~~NFIU l.j IO'l

g LB = LB' =

t~rumm~~mtism IWu "'

A'B'C

ctl'ifitmrultlSffi l.j 1

trubffiuiUS~2Q1

ffi't3St15'1:1St15

'ifitmM ABC sb l.j

O'lct

umtirh:nstm'lmo'lu§HfitmMnn5smm't3run2M Y. d. '1:1 u~mmrumYsruY 4 wJ U uw s ~ 1

tmflu9lmtnsm~'i~1mtlt9 ......, 1l,j a

~tismt'UTlm ~ cr;

1 n '1

IUS~S O'lQ

IU't3flnY ~

~mn

LA =LA' AB

= A'B'

llABC:

= LB'

(mYrun2 s

nJrmfif.11: t~§'iHb~ u

Y. d. Y)

= A'C'

= LC'

NtlffiH'i~Grulu E ""' w 1

B'C'

ru EA

= EB

AD LN'i5SbH~~ CB '1

n. ttyJutaJutfitmrul AED Sb BEC 2. 9lmurmrim tt

ED = EC '1

n. nob

llBEC'tflS

"'.!>

"'I

MED

LAED EA

n~ru)

LBEC

( MYfln't3) "l> --1

MQbttmg

LEAD= LEBC

ADIIBC)

tlmsg u

llAED:IlBEC

2. 9l mmm rim tt "'.!>

tlmsg u

EC '1

(ffiYrunrul2M Y. d. s ~

C "-----___;;B

: !.1HHf:Hl5<.i11::lti~i.Htflt28 tJ !.1 "'

:;::

'HlS

LABC

£)]Gl

LAED

Sb AB

!J.ABC=.!J.AED

W~Sl~~f'i:H

= AE "'

Sb AB

AE "'

Wl9tln~~Sl&Ub~

U. d)

: ruti~tffHUl LA

LA'

60° , AB

ABC A'B'

A'B'C'

ftlrn

Sb AC

4cm

A'C'

6cm JtitlJ]tituJUL~hnHl..fl

rutitWitfflrul ABC tsitrntni:il - ttti'U~~0n~N1Jh

'Hl

4cm

- t19'hli9HS1§j~

LBAx

60°

- tttitJ~~LRnu:Hfin.IJti c ~:sit - tl=lUISLWitmnn

ABC ttlrnLn~ !.1

ruti fill§~

lL..l..---!------1

A "-'-------"B

ti:ilru2J~ LA [ji61~~2h LA'

i:ilR[jintlt

MBC

ntibrut~n

£!Jffi1Jtl

Lnn

B' (B)

4cm

run

C'(C)

n ~trutdb A'C' ttmg AC

till1Jh

A'B'

'Lmg

A'B'

4cm

ttf1ru1Jh

A'C' = 6cm "'

150

ru &ABC sb

&A'B'C' 'HlSmn'in~ffitl~H1lffll§SI151§Sti5'iWitfflMmbnHSgtis ll.Ju "'

1 "'

l.J

AB = A'B' LA =LA'

!lABC:

AC = A'C'

LB'

LC'

U21~ oxsh OY&l=Hmun.nu Ash B &Uhmftlru OA I

tmUnf1G M1ifti5 '1

3G9l[!Jl

t1}5]mtsJu@tfilrul OMA

Gtjl!J: ttU]UttsJUt~tffirul OMA ntl !lOMA ~

OMB

OB '1

n'i X

OMB

Sb !lOMB 'i:1l S

OB ( M~~n~) ..; -..,)

LAOM

LBOM

" "" OM~h3~&S1JHA1rul

'"'m

MB , LOAM

LOBM

~M !lAOB ~ru [Jfififilf: Gl IJ 1.! h

LOMA

LOMB '1

'1 A' dlUMul1g ~sA co'1ush 0 1

"" I

WJUS~ 0 '1 Lh1lti5U!}Gl !lOAB:!lOA'B' '1

t'i.

~~~HnbU~fH~t1 ~ I

d) ~

IQ\

2UJU?!M: Mht~Hffirul ABC Sb A'B'C'

Sb BC =

AC = A'C' =Scm

B'C'

A'B'

6cm ,

mJu@tmn.nmbrJHSg

3cm

- M~~h AB tsitruu~~ l ftlru AB = 6cm 1

- run - run - mtl

dl~n~Mmsb-l:l~ru'i:fiSnltMSb Scm ..

l.!

B dl~n~Mm ..

-..,)

ru'i:Jls

"' IJ

'::>

tMSb -..,)

3cm

Cl:1

c dlun.numMtHS09lbm l_j I

~ !J

C'(C)

ril1J~&::urun AABc

ulintglr:tHhru AA'B'c'' ru2J1Et'l AB LiH1fi1~trnu~t'l A'B' I

tiD(QGlR~ru c

UHHru[J~msit~~htSUlh A'C' tUlWTIJt~hlEhtnhti

at'l

1.1

finnG'ims9mt'lladhmnnr~~

SSWt:tlLritfilrul ABC sh A'B'C' L~~fi1~ 'Lmg IJ

m9lhut1m

s;;1fitmnn9lhnas sm '1 ~

LA= LA'

AB = AC

LB = LB'

AABC:

AB = B'C'

HK , FJ

Uhlmt:tl AEFG:AHKJ vn ...._,

FJ= GK FG

FJ+JG

JG+GK

AEFG

sh AHKJ i::fl S

FG = JK

} ttm FG

(LMW2lh

LC' H

~HLti]mwJu

1.a.

VW , TZ = SW !J.RZT

sh L1VWS

TV "'

nui~Hmnim:un 9 IS

c ,., nh "'

ZfTI'i.fliM:

!J.ABC Sb L1A'B'C 'tflS

LA = LA' = 90° BC = B'C' {

L.C = L.C'

tiblmm U1

MBC:=L1A'B'C

QbL~tfilMtnb ABC

S L.B+ L.C =

QhL~hAlMtnh A'B'C' 't'iQlS L.B'+LC' = 90° ~a-18 LB'

-LC

tt!lru L.C = L.C' (M'l:§fln'l:§) &alg LB = LB' ...; ...;

QhL~tfil M ABC Sh A' B'C' ~l:fls l

L.B = L.B' = 90° BC = B'C' {

&alg L1ABC:=

L.C = LC'

(!)ttl

rufw: ~tfilMtnb

MA = MB '1

X OMA

'fil ru1

OMA 'i:flS OM dl~Ut~Sf\5~'1:§ 1

L.MOA = L.MOB

tS L.AOB ) tltHSg !J.OMA:=!J.OMA (ffi'l:§ffin2rul ~. u 19 g

itnn:

153

"""" 1J'}!fi9 :

lij ifi ~{5 61 t sit fihrtfllij 'rhdb ilb nat£~l t S1 g '1 lj ~ l.j

HitlG lliltH si nlin £ g'tj S1 rim lJ i

Hn !U'!§n~ '-'l.J mHiUG llilu fe:~ illffi £ uffi lij t lJ ~ C'

:ABC

wt9is bidlJ b o..1J

n ~ t£~'1§ lij'ifi ~1561' sit runsGV g BU! l.j U

dl~tAlllil!U'!§Qlfi[J1tiR~rn A '1 n~

i:l AC Si:l AB 161!1 D Sb E tflbm lJ 'J c:t '1

tiblmm VI..,_,

BD = CE

am ( q

!Utuf.!JOR~rn B sb c Alri Sb BE= CD '1

: Qb~tAlllil ABC ShL~tAlllil I

LA =LA'=

A'B'C'

ffi£ AB {

= A'B'

BC = B'C'

AB = A' B' t rub HltiL619Jtl

trn ru !:!1 ~

i:l A'C' [J16ltru1Eh AC ttirndllEbtf:l 1

IJ.ABC '1

t !:llru LA

tillbtlbm

LBAB' = LBAC+ LCAB'

LA' = 90°

c BB'

Yru !,!

(C')

'1 IJ.BCB'

ffi£ CB •

t Aln.n !U'!§Ql fi!J1b n ~ rn

CB' tSH IJ.BCB' dlL~

'1 B

tf.11TJ £!J Ql £ LB =

QhL~GAllliltnb BAC Sb B'ACffi£: 1

CB = CB' ~tlt61S!UUSffl(!U'!§ I U I I c:t ...; LB = LB'

tiutSll IJ.ABC:IJ.A'B'C'(ff!Yilln~llil . a }u '1

us ff1 '1 1

mwuff-1i: FiSg'i5ffi~mts !1 GV I &

LB S~ LC Fi~1~hfilM ABC co l.j 1

'1 ffl'i:3

ftHlfflH'ici 4 co l.j

~hl'i5~~tfi~t94S~U:l~ AB , BC 2~ AC 1Jlci D , E 2~ F

tf:i

n. ummm w Ul

=IE=

Fi. Q~L~h ill rul tfi~ BE! s~ BDI ffi s 1

BI ct1HUtns 1 u L.IBE = LIBD

1mn : ID

= IE

( 1)

Q~L~tfflrultfi~ CEI2~ CFiffiS: 1

CI ct1HUtnShlS'i:3 1

!.1

LICE= LICF (IC dlFi88'i58l~fl8 tS LBCA) 'IN & 1

1mn :IE =

}

~1."HS8llCEI:=llCFI ( ffl'i:3rnn2 nns 9

1:3)

( 2)

ffl'i:3( 1 )S~( 2)tf:19lmtns ID =IE= IF

2. Q~L~tfflrultn~ IDA

IFAffiS:

ct1HU&61Shl~'i:3 1 I

}

1.1

ID =IF (hlfliD2l~Gru)

1mn: L..IAD MRIW:

tl'!."HS8MDA :MFA (ffl'i:3n5Fi2M ~- tl) u

LJAF 'i5 LIAB = LIAC

"'"

ffl'i:3hlfliD2l~t

lD = IE= IF

Gffi&thtrp:s I Un

t~ts'jff1IDrJLd~ 1

: ABC thtilitnH11l~tl5Sb M

n1J1n5tSl_;lb

ffi~ M

BC '1

roti~ci

t!Tishl_;lh AB sb AC U1h

tUb [1

mm ttl MD "

= ME

fi~

LC '1

4'$

Ci115

" tHHlffi th tHlil 1 "'

tSm LB

~tl5tntlStlH~ci

ci BC

BC '1

USlciA ~

U1h I ?imt~!:lJ19itS

Hb~ BC '1 n

Of! u M 'iJ tl5

t si t

ruu ~ ci A t~ !:lJ1 g$

tSHb~ BC '1 n

!,1btili t ffl nfl fntl

MIB

Stl MIC 1f1 S

LMIB IB

f:lmsg u

LMIC

90°

u mdnnun I

~ sc)

ruts

AMIB:AMIC (m~run2nfl d.~. d)

: MB

MC , LIMB

= LIMC Stl

LIBM

LICM

tt:'immr.nsrunnn:tlu2ltlt'Hn~: ....., 9 u c,

" UJtid Of! uti ra sit

1:lJ1 9~ ts »~ ci~ rut~~ 15 ~ t t ~u\fl ru nqtl ii tl ri ~ ls »~ ~ t ~n g IJ

156

~RUG nn11j f!:l ru\5~ t sit Nu'tfl fjj nutl i1 b nts Hb ci~ fjj l.j -1 "' I n 11.1

d nnuil tl t s g~TI~ &si' ru I

m·~:HuLl:flru:nhtru MB 1:3'nl:H9QG1 LIMB iJ'

&Slg MI ctlnS8'iJSl~i:UtS LM w C: I

L.IMC

G1R~rn M

Mc &Slg llBMc mLficmnn

smmguH~ BC 0

tSlg MI ctl

IB = IC

1:2 !lBMC

MI J_BC

LE1~11lli)tin

f.l5

&Slg MI

ctln~MStlctl&'i:3t!Jl9~1JI;mg~tl BC l

QhLfit m nn M'i:3fll G11:fl s l

•

t:::l

1:3Uln9lhmm'i:3'i5Sm l l l 01

tAlrul ABC

b AB 2h BC

n. 'Ubimm l/l

OA = OB

Nrlffi'i61~ 0 '1 "01

= OC

AC 'iJ-I:rlmm ON j_AC Ul'-'

cuffw: ..,

n. t1:31:lJlg~ tS~tl AB Sb BC Al~ AB Sb BC l

Ln~ L sb M dJb~ '1 n:nru 0 ctlL'iJN~

t1:31:lJlGl~ tS~b AB

tSlgt~9lQJU12

~. l:~l:flS OA

OA = OB = OC '1

ti52ltltru)

OC (

&Slg !lAOC ctl~tAlrulM'i:3UlG1R~f.l5 0 0

N dltilli)tint1{fl f.l5tS~b AC tSlll ON

t1:31:ljl

tl ACtS llAOC

&ll'i:3f.l5~rul:~tAlrulN'i:3UlG1t~UlS'iJ~~ 0Nctlt'i:3

Gl~tS~b AC '1 l

C!J

MfilflJ: t1:31:lJl S9HS~tl9ltlmS1JHAl rul ABC [YN~ ~lJibtilli)ti 0 '1 l

ttllru oA = OB = oc tSlg o 1:fl8111:flrutfift9"i'si.:!Finu ~

MBC

: t'i:HlJl g~1_,tH~Wl ~ f.fh~ t,?i ~ Al M I

f•.Hl4osW ffl'i~~on.nrsr~~rutl:l ruu~tsit~""il t U

.A "" ""' 0 Q~UHAlM ABC ~~ AC bill~s~ 9

L.B ~~ AB bill~S~ L.C

ru AC>AB

t5irlmrh

L.B>L.C

tsitrn'lt:l~ AC tf:liUMts D ~tl5 lJ I 'W

ru AD= AB

ttlQi 2

AB = AD ts-Jg MBD

A~ru A il~ LB 2 ~t~

dl1_,?itm M

fd~Qi~

L.D2

dl~t1_,nltS MCD ttlQiS

L.D 2

L.B 1 + L.C Gfl~ L.D 2 > L.C

thtu L.B 2

L.D 2 &s-Jg L.B 2 >L.C

&9J~ L.B

(1)

L.B 1 + L.B 2 tSH L.B > L.B 2 (2)

} Gll~

L.B>L.C

&r:J9l mm s1g ~unw21~ tim~ '1 ~ Li n u l.j

: Q~t,?itm

d51d~ rh@su1 2 ffl ~ttl rubill~a~'id~ iJ~ fiHS d~@su~Hfl ttH ttfi tu~tl:l blibill'l§~~ lJ q I l.j I q I I

~~Gdl~ ct19Gctl~ 1 ®

'iuHu~n1 m tu~ri~@sus ffl'id~tl:l rum5~s~~il~rius gfhn sus ffl t'tu ttfiru'id~ Li ~ 1 1ql) 1 jq Li 1

Cll

ttl blibill'l§S~9Gt:il~ctl~~Gctl~ '1 I

n~ MBC'b'lS LA= 6x+4° , L.B q 1

dJu~~ ~s MBC ffl~ 1

thtH1~

= 7x+12°

~~ LC

= 6x-7°

rufJw: nb MBC t!'im s

LA+L.B+L.C = 180째 (drutin~nbls MBC) If l<'l 1

L.C = 6x-7째 = 6(9째)-r = 47째

~t.H!H lJbffl~rntnti

~:t:llru

LB>LA>LC &Sl8&!'ili1Sl AC>BC>AB

W1~ti~ AC>BC>AB

1Vifufl: nbm21bMtS8tt:i2~ tn .. If G'l tJ

l..i

AB = AC =AD

L.ABC<LBAC

2U1'i.fi1M: ABC thl!it1'1HWl~ru '1 t!'iti~ru

L~b sc 2Jms eM &'L:Jru CM AB

= CA '1

~HLti]mtsJti

BC+AC <J

nb MAMtf!i(flS L.BAM

= L.BAC+L.CAM

sl2J L.BAM> L.CAM ""

MCMYlS CM = CA tSl8 MCM dlHHnH1JlM~li151n~ru C '1 tf!i91ffi(flS L.CAM = L.CMA ....., t'Ul~&ag

L.BAM> L.CMA 'Y_ L.BAM> L.BMA

Qb MAMYlS L.BAM>L.BMA sl2J BM>AB I

t~::llru

BM = BC+CM = BC+AC (&Lmg AC = CM)

~ti&S3 If

AC+BC>AB <J

159

Wifmff:ft: 'itl'tmhn sยงHrillti s firuntit94 tu~ ttl-e1m8 n'ifitm nn-eru tu~'i::llth~m II l.Jc>~; U 1.1 I eJ n lj 1.1 lJ &

l:H15-efig tuStn'eli5ntStl 1 "' 1.1 n 1.1

t~tl ~sfiruntitntl'i::ll S 2m, 4.5m, 5.8m

1:fl SlJ ss

r:g n.

Sib

10.2m '1

ftHlH1j~ ffim@ tut1 tu& ru5{5 fi run ti ttl-ejm~ nLfit mnn

tl ~-en~ f!JS~

2m, 4.5m

~~nm@ tut1 tutisJ~ti~tltLm-e

5.8m

stl 10.2m tl. 2m' 5.8m sb 10.2m lli. 4.5m ' 5.8m sb 10.2m 2. 2m' 4.5m

t tl-ejfi ru1 tim 'i5 sJ s~ li5') tS'i5 sJ

9l blJ s ffi tiqy ML'i::llU~ til slJi t mrul~ li5 ttllj1 ~ u

hl1 n

sJ 9'1-l::lH tliot m n.

f~ b ~s~b 9'1-l::lti~:~b ~ti1 tu-em nlJit mnn

sb 5.8m

2m ' 4.5m

4.5 + 5.8 > 2

"'nntit9? ("'nn ) "'-

~ 5.8m

fi run tit ru59lbti ts gffimLli

2 + 4.5 > 5.8 "' b1

2. 2m ' 4.5m

10.2m

2 +4.5 > 10.2 rinm9? (-@srin) 'l "'10.2m

tl.

2m' 5.8m

sb 10.2m

2+5.8> 10.2

"'t151Y.t9? 10.2m

fi run tit ru59lt!ti ~: s g@s ffititLti ttl-ejm~51Lfitmn.n~rumst9 '1 160

ill. 4.5m, 5.8m ~b l0.2m

4.5+5.8>10.2 rinB_t9? (rln)

10.2m

4.5+ 10.2>5.8 ilnm9? (rln) "'-

5.8+ 10.2>4.5 nny_t9? (nn) '1

Luifuu: Firu~fim ~:~~~n5!Eh i

n. 12, 11 , 17

G~~j~GfSj~

1. u~ ri f fii.1Sil u~ ri <!)

f!i. 4.7 ' 9' 4.1 'i

' 2' 3

fl A

l:HiJ{hd~ ~H S"J t 1.1

fS A

AHl.!J. 'i Hh~ AH n

&'if!i

!J.

4.2. iLu]uitaJuu~ri

L~tfilM AHB rtlL~tfilMtnh1Jl~ H tf!'lms LH> LA

sl~ AB > BH

LH>LB

sl~ AB>AH

!:lmsg nh'i~bfilM u

"' l

l.i

f1H9Jnmlish~fnh

Hthr~sMt~hm 1

" : tHlllts B "' !'lb C 1

A 6i BC '1

) '1

tt?]mtijti AB Sh AC A

c nh ~AHB 'BlS LABC dl~tifflts LABH "'

l.j

t?i'QlS LABC = 90°+LHAB

i::lts~:sg nh MBC 1J

dl~tmru I

LABC> LACE sl§1 AC>AB

"'I

B Sh C tsl!Uh:&lh H (mg 2)tt:!ithlilu C' 'tHiHsl&rntiS'l~ ~ 1J 1 !.! .:: HC' = HC '1 t?i'QlS AC = AC>AB

162

tt!ru

~tl~~~fiqgnfl~ ~~riqJn1:llS~rulnthn~~riqJnU

~n~~~fiqgnfl~ ~~fiqgnudl~~riqgnt'c:~rn1:lls~Mnfi '1

dfunl'ff!tr t?12J ABC dl~tfilrul~rutl::lru AB<AC

tsiQ~~tfilrultsg

n~n5 AH S~i:'i:ll::lJlS AO '1 t1_Y]mtsJ'u AH, OA S~ AC '1 ~~fi AH dl

tJtgw: ""

rifn~

,U)ru AO dl~~riqgn t?l'Q'1SAO>AH

ttnru

(1)

AB<AC (N'i:l~n'i:l) ...; ...;

ttfl ru13 rLJlti H ij n t

g B S~

t?19lQ)U1S HO<HC s12J AO<AC

ffl'i:l ( 1 )S~ (2}(?1tf1S:

B L----i..:,J,----l...,....----..,:,Y.

(2)

AH<AO<AC '1 !!ABC '1

'i5-lrlmm AB+BC+AC>AD+BE+CF 1.11

"""

163

MBC =. !::JJEF BC = (2x + 30)cm EF = (5x-90)cm

?'HlJl Sl B C '1 p

tLfilYtsgtf:i2J

LPST

LPTS

MQSStl MRT '1

hf:i2J

MA = MO '1

MT = MB

mdl !:MTO=.!:MBA '1

T A

i:fi2J

AB = BC

tclJu

MED

AD = CD '1

Stl

!:Â£ED '1

A AB

II CD Stl

TR = TS '1

um mm U1

MBT=. !::JJCT '1

fi2J

LEAD = LCAD

stl AD j_ BC

mm MBD=.MCD sb AB = Ac

DiD

t?i~ P rtH~MG'tHi515ntsitrnnsgu2lrimls LA I 1J "' .,;; I

"" mMLnl:fllrulM'l:Hfln ABC '1 0<:$

Uult15U{]Gl PB

PC '1

ABC ctlLntfflrulhl'tHilnn~ru A ~~ ""

M sb

N ctlcrMGnrun rutSLJ=ih AB sb AC tUb ffi 1

G'1

ttfiru P mcrrt.nGLUMblts BN 1

sh cM

ummm MBC dlL~tfilrulhl'IHiln '1 l/1 -..:>

c 9.

t?i

§UAB

CD Sb AC = BD tl1Jm2lb fiJ1 '1 IJ IJ G'1

tLu]umJuL~tfil rul ABC

sh BDC

A BA

MWm~Ablru B -..:> IJ

10. ABC ctlL~tffl M'l:§ru '1 fi'l:§ IJ S'l

c ffl rilll b bill'\:§ Ln~

D shE

m"" BD

ffi'i umm l/1 -..:>

CE &SUL.ABC = LACE '1 B

ll.

t?i~ HOJ..OB, DB.lOB OP = BE, HO = DB '1

fi. I::J!OE := t;.DBP

12.

nbm2lbw1r;sg r;r:;§1 "'I

AC = BD

it.l

G'1

LC = LD

Uirlmm BC =AD l/1 -..:>

90° '1

BCIIAB '1

3. mm

tfflMSl:l u

21~ 'Lffll:l M~ t M~~ ffll:l

mtH1ih91r~u ij

Scm 3cm

mgL~tffl n.ns~

14.

4cm

21~ 'Lffll:l M~ &Ml~~ ffll:l

mti~f~~t912...,

15. PQR dl~tfflM~

PQ '1

ru QR> QP ~~

mm LP>LQ '1

A 16. ABC dliJHfflMMl:lQ'Hin~ru A '1 ""

U.1ti~tl5~~ BC ~018 CD= AC '1 1

tiblmm LACD>LCAD '1 U'l

17. ABCdlL~tfflM~

~AMdlt1:11:lJ1S

ru LAMB< LAMC '1 tiblmm LB>LC '1 U'l"'-"

8. ABC dl1JHfflMM1:101~n~ru A '1

tiSlfif!lMtUm~O IJ

fflfitiSlfif!ltummn &

A 1Mti~~id~ BC L:i

c 'ini:l D L:i

'OinmffiAD+AB>CD 'i tn " '

L:i 1

t~um21~nn '1 ij

'' '

LB fflflLdtl AC H'~~ D '1 H mthn.mrufntl l

'S D

.., ' till15S"H'i .:;

BC '1

'' \

15trlmctl AD< CD '1 lll .....,

' ,/'

\ / ' , AW-----~''~--------~

Oeb

Q)'-::1

UMID15tictldru15nn't:HtHntmts LlABC u n ~

~mtl

L15 t' Hm~'i:fl H1 ~15 ni tl '1

B 1:..---.,!-:J------___;::,.c

21. ABC dl~tfflM~tlJtf;jru AB

3 Stl AC

4 '1 ttli1ti.ri::UllrJUhfflM 15~£!)

l <BC<7 '1

GM13 M '1 l n. tt15]mt{J15 MBM stl WCM

~- LMIDtl~Gl AC;AB <AM<AC;AB '1

c ~-

tn13M13 D, C, E I

~n1ntldH1ltlt9? LJ Ill "' "'-

(15ITTlR : t'!M 21 LDCE) c.s0

24. ntl~~tffl M ABC fi@g152lfArlll tS LB Stl L.C c; L.:; ~ 1

t'l.HH111n~ I '1 ffl'i:§" I l.J ,Oc;rj;

¢V

~IDLfl.mstm~fl BC ~UliDfflfl15~fl AB Hi~ D stl AC Hi~ E

Oeii

LMID15.0Gl DE= BD + CE '1 25.

ntlt~tfflM ABC nS:Sli2lfltllltS LA 'ilit\Hl BC 'in~r3n.nts D '1 152lfil3rutt:Jrut'lli5 , "".:; l l.i .I LJ l <Ill u

ttsmn ....,

ttniD1Jii515Stl152lfi AD fflfi152lfi BA 'inti E '1 15trlmm AE "'

lll-..:1

AC '1

----~~------------~~--------------d' B C

LABM

LMBC '1 21 ~ d , d' ,;

27.

6?Jtltl LBCE

LBAC = 90° , LABC =

90° '1

60°

A B '1 D

ri LBDA = LDAB Sb

LCAE =LACE '1

?l!lf!Sl LBCA , LACE , LCAE , LDBA

LEAD '1

28. ABC rtl'i~lltfil!lfl'i:Hi5 '1 fiSgti2l~r12tS LB l.j

!.!

IUWQ)rl A

168

DE= AB+AC '1

uuu~bti~~ BC 'if~ D Sb E dJtl[!

n. MEC Stl !'i.ABD rtlt~tfil !lfl IU'i:Hf!Gi ~.

1.,t1fltm5~m

nrulf!UH.RtHSu~tfilrul

o u~ Â£!) ruQ nn: sb@ ~159 tstytr~59JLfil~ 1J

o um mrun9 nn: sb'i'9 f'6u 9 tSufl1 r; m nn t m nn lin lfl"'-'

cr~tmnndlrl'Ujtfilnn

'i u~&mnn

rul:flsi_Eib4 I

S~ t15']'i:fl Si_Eib 4 sb~ 4 &Ul ti5'i:fl Su~& fil rul &dJb WJfiBl S I

run rul :u tS"e~ t Olb Sg L:lu2lb 9

iJDti~

ABCD 0

m"" ABCD 'i:flS

dluf!tmnnmru I 01

tytrubiltm~ dlu~tmnnt'1:lrul:flsi_Eibm5~ 1J

uuu~ "" m'] '1

"" ABCD m

tn59JLfil~ 1J

I:RUl S [AB] e

II [CD] sb

II [BC]

a~tmnnfnt! mtyr;ru9JLfil~

rul:fls~tnt!

~ru '1

ttl ABCD dltU&ru9JLfil13 sb

n~----------~c

&Sm ABCD

dltif!&filrul I

~~S~ '1

ttl ABCD dltmru

AB = BC &S'HABCD

dlun&filrul!;hl 'i 1

""'

169

nH~

ctlDJ ~ruSJLfflt3 &'i::Hlil:fl s~~ riHtl'ci~~ s ~ s~ u

l:flS~fn~~ru

ABCD

90° S~ AB

ctlDJ&ru9JLfflt3 ttfiru

BC tSH ABCD ctlfilt~ 'i

- - - - - - /t._tJUiflfj'{fn1!

Lm ru 9J 1J11 '1:3 m11 ~ t mru1 rt~ rul:fl s Ltl ~ ru5'1:3 u

~Cl~'J 'i

ttl ABCD ctlLmru9JLfflt3

t~ms n~--------------~

II [CD] s~

l}fgfir~g 1 : »~rl1J~S~ti5'J ttinDJ&rulULfflt3ctll!itmMria~s~ u

ABCD

mm !J.ADC =. !J.ABC

ctlDJ&b159JLfflt3tt!ru

-...:>

L~, m ru1 A De

sh !lAse l:f1 s

AC LA 4

LC 2 (t3~Hun~) 'i IGV ell 1

t!msg u

!J.ADC=.LlABC

(nHUl

'1:3-d-

&~LilS llADB:!lDBC &~Lil

2 : AD

(nHL.fi '6-d-

= DC

BC , AB

LA = LC , LD = LB

1mn : 151iHlli'6sh~rn5'6'&s trn9JLfil'6~s ~ 1

ABCD

dlL'iHill9JLfil'6ttlrn "

LB dl~n~ '1

ummm U'l

LA+ LB =

1soo

ML"l:f7 W'iJ

n;p !'# :

t~'Hls [AD]

II [BCJ msht:tH.l5~~ "'

l}tgug@ 3 : ~~~1Jh tsLmru9JLnl'6LunJ~~Ln~linf1unn!Jl rnt{Jh~ o tUTl u

mon~g '1 .!!

""1

ABCD

dlDHill9JLfil'6ftlru'!:flsÂ»~~1Jh [AC] sh u

Uhlmm U'l

0 GliTMUnrunrut~Qb'&s 1

ML"l:f7 W'iJ

LUnJ~~Ln~ 0 "'

n;p !'# :

Lfitmrul AoB sh

lloDc 'tfls

LOAB = LOCD

('thnfdnb) 1GV "' 1

AB =DC

(Ldhrn5'6Lutru9JUD'6) u

LOBA = LODC

(~ffihlnb) 1GV

~msg

AAOB:AODC

tf-1012

OA = OC <I

OB = OD '1

~fitS g0 u

(nHJl '6-d-'6)

o mnMunrun ruts o moMunrunruts 0

dliTMUnMrl rnt{Jh tS 1

[AC]

O~tfilllil ABCD 'inS AB = CD ShAD= BC '1 U~QJGl ABCD

dltytrt59JLfil'6 '1 u

fiiJhAC u

L~tmn.n ADC AB

sb ABC 'i::flS ~n'i:3) ....

Ac Loha'i:3 1

!:Jm:::lg AADC:t!.ABC (~laM d-d-d) '1 u

lcnn: LA 1

LC3 m9mh~mn5nhtf.lms i<v ..

(1) '1

LA 4 = LC 2 m9mb~mMnbtf.ltnS jG\1 c;

II [BC] (2)

r11m~ s ~ il ~ 'J n:n gu~t m M ts 8ctli,YtilllilJLffli:3 '1 u

m'ibfflrul ABCD 'i::flS LA l

= LC

Sb LB

f!Jrfl

LD '1

ABCD ctli,Ytill9JLffli:3 '1 u

' '

tf.l'i::flS LA+LB+LC+LD

'1 (

ornun u

r;m M) LA

LC Sb LB

tf.ltnS 2LA+2LB LA+LB

= 1800

LD ( tu'i:3~n'i:3) .... ....

360°

sh LA+LD

= 1800

(rlilltin'i:3nbm2lh) u jc; !.1 0

II ~msg u~tffln.n ABCD

W'ILtitill9JLffli:3 '1 u

GSHAlM ABCD 'i::flS l

sb AB =

DC '1 ti1;fl£!JG1 ABCD ctlLtitill9JLffli:3 '1 u

M['i:n l!J'iJ f[{l If

M~H~fl1Jh AC u

1_,fitnHl.!l f].ADC Bh !].ABC 't:llB AB =DC LACD = LBAC

AADC=:f].ABC (d-~-d)

tSlg

~tfln : LDAC

LBCA !\5msi9mh~m

sb [ABJ n[Dc]

tH'itnH1.fl ABCD 't:llS l

tltH!H tHHffHlJl ABCD II l

7 : dhHHnH1.fl~ttl't:ll2Hhfl19bi'tinH1 ffiH'i~G n u n Li Li Li lJ9MfJ99 1

Unrunru n

<lot

tSlg

U~tnH1.fHSgdl1JHru9JLnl~ '1 1J

~1JhU~tA'lMn

0 dlGn.f1UnruJHUG2

rudJb

ABCD dl1_,titru9JLA'l~ '1 1J

M['i:n l!J'iJ f[{l If

: A

1_,fitA'lM AOB Sh LWDC 't:llS OA = OC 0

â&#x20AC;¢

L.AOB = LCOD (~9run~

D 0

dlUMUnrunru&S 1 n

OD = OB

~tfln : L.CAB

ttfl ttl

L.ACB = LCAD

'1 tru9J1_,1ll~ '1 1J ~

fiJ'i.fTUif.'it: tl!l't:llSUntnlM ABEF Sh EFDC dl'i'i.H IJ

ABCD dlLmru9J1_,1ll1:1 '1 u

~msg U~&A'lM ABCD I

l>?J

LACD

UntnlM ABCD 't:llS 1

.----------------. E

b{j ABEF dl'U5WHilJl,iil'i:HS'U AB

FE ,

(I)

t{j EFDC dlt,utru9Jl,iil1HSlg FE= DC , II

(2)

fl)'t§ ( ) 2b tf!'lQlS

(2)

II [DC]

AB =DC ,

~msg u~tfil M ABCD

dl'U5tru9Jlfll't§

"' tmru D

0 " dlun.nu~8ts

ru9Jl,iil't§

o.,

ru'i:fls9u1b\jru

II ~

""1

A; - - - - - - - - - - ,B

t tn ru Wl~u~tm nn tnt! nmt,m rul{lt,Al't§ t Sl gl,f!'lti II 0

nn:9lbHtum tu'U5Ul59Jl,iil't§ndl ruQnn :m tuu~tm nn IJ

tSlg

LA = LC , LB = LD

11 D''-'----------:c

llli't§tStytn511Jlfll't§) IJ

t'lflru

LA =

=>LC

A,-,--------,8

LA+L.B = 1 +L.B =

tlmsg IJ

=> L.B

LB = L.C = LD

900 t Sl g L.B = LD = 90o '1

DL----------'c

f)ffl

ML'i:fll111J f[fl ?#

t{j ABCD dltHWilM i

nh !:s.ADC

&lrJg AD

= BC

ru:rl§ hn:s 61 t mnn fnb ) A~----------.,~

ab !!.BDC 'tflS

AD= BC LC = LD = 90o

!!.ADC=.!!.BDC (n~

0-'1§-d) '1

~tnn: AC = BD '1

titH£H AC u

= BD '1

tf!i'HlS ABCD

ML'i:fll111J f[fl

dlLU&ru~Lffl'l§ttiru AC

= BD '1

tl~[gdl ABCD dlu'ttfflM

&u ABCD dll}5tru9JLffl'l§tlrlg II

AD = BC (~hru5'1§tstmru~Lffl'l§) u

AC = BD ( DC

dl~hJ'I§ I

&~012 !!.ADC=.!!.BDC

~Oiii :

tl-d-d) '1

AD = BC '1

LADC = LDCB

nJiru

LADC , LDCB m'l§dltitltS'I§ I

tlrJg LADC+ LDCB

2LDCB = l80o si2JLDCB = 90° '1 l:H'HS!l ABCD u

t:htHHffln.fl l

175

fil~ffiY M 2jma MR

'l5

Rffi MP+MQ

= BH '1

Qb1.f\tfilrul BMPffiS LPBM+LBMP = u

Qb1.f\tfilrul MQC ffiS LQMC+ LQCM

u ~

ttfltu LQCM

lfOlntntfi1lJHuYQ1n ABC

= LMBP

f:jtJtS8 LOMC = LPMB 1J

= LRMB

LQMC

~SU

= LRMB

LPMB

1.f\t fil nil BMP SbtWitfil MBRM ffi S : MR = MP ( fUY~fiY)

'"*

LPMB

'"*

MB (~b~Y)

LRMB

llBMP:!J.BRM

(mnfi r:l-Y-0)

lmn : LPMB = LRMB

= MP

90° , MR

~Qlfi RQ = BH tn RQ = MR+

L.RQH

MP+MQ = BH '1

: tf:i"tf!StJ£11 filrultfih ABCD SbHb~ n

tihl un

LCAD = LBDA '1

nnt m nn t fij

m1m !.J

~'i9h SYtuC) ttJfifj£1 tfil nn' Mdl'i~tfil nn

'"* w 3. idhrumsb~ntiYtS11ntfilnnti6usm wl l l '"* l "" 4. Hh~'i9btS1Jntfiln.flt n w 1 !.J1J

1.1

dlnnt fil n.n fnb ttfi rul!l m u

, He

= MP

LQRB

900 dltJntfilrultfih '1 I

tf!l'i:!lS ABCD ct"J1!.Hru~un~ttlru AB =AD '1 tl~(gGl AB = BC =CD= DA '1 iJ

ML'f:fl UJfj rrJ7 fi

t{j ABCD thijl&ru~un~

l.l

tSH AB

CD Sb AD = BC (!Jlbru5~tS

tlmag u

AB = BC = CD = DA '1

ML1f'l UJfj rrJ7 fi

: B

dj ABCD thtHHffHlfl& I !:.ABO Sb !:.ADO 'i:fl a AB =AD OD = OB

AO (!Jlb~~) 1

si~

t:.ABO:=t:.ADO (Fi~

~Qln : LAOD

tmru

d-d-tl)

LAOB '1

LAOD , LAOB th~dlUtltS~ I

2LAOB

1800 , LAOB

900 '1

tf!1'i:!l2 ABCD dlijltru9JLfil~ttl II

177

!iABO Sb !iADO 'tllS : OD

LAOD

LAOB

D AO (~b~'i§) I

!iABO: MDO nHW(d-'i§- d) '1

l(fln :

AB = AD '1

ABCD th1YU15~Lfll'i§ttlru'tlls AB =AD ffi'i§Stl5'i§SttHI!'i(flS u

ABCD thtHHfi1fl1HM '1 I ~

.. B

!iABO Sb AADO 'tll S OD

LAOD

LAOB

AO (~b~'i§)

il2J AABO:!iADO l(fln : LBAO

(d-'i§-d) '1

LDAO '1

ri 1J b '1 II

mm AOBJ th13WHfi1rult

-...:J

m11 fl.fJ ti'\3 ru f tl ru

d5 AOBJ mnHru9JLn1l:H~Ol2

OB , IB

ABCD

tiltHHffiMtntl 1

t~OlS

AO =DO= OB = OC

t~OlS

AO =AI

~msg AOBJ mnHru~Lmattlru'tf!S ll

;ot~mti Ao =AI lJ I

mmHmMtM--& "~ 1

'i'i.J~fi~: ~MiSfUUl trl <II

LDAB

l..i

tHHffiMthl ABCD

LBDC

Stl

c 2

rugn.n:mu mt~ tilti~tmn.nr~t'!:lru'tlls~&ntl'\1ru "~ rr:nrucr~&mn.n&~mnnru~Lma&su ll

mw~mLmru9JLma

tilLmru~tJLma u

m&H:hu~tmMtnht!:lruffisiJlhmtir~~

rr:nruu~tmM

tSl8n1UntilTIHru9JLma "!

~msgffic~ffis

tMshmHmMtnh --& I

3. '~Ohru.mmttutHnshrMm lJ c:;l.j c; ~q1

" »ru~g

tatijl9itS1Jlh I

5. Hh~'i9htlSffi n lJ 1 "~

ffi'ini.1dn.ncrn lj

<'I

mi:!Jl9atsiJlhru.mmiinJ~g

7. »h~HilhtilnSllUSl~m'ts~n.tla&Uirumiin;~g '1 n

,:;

tiw

l}igfffJYJ : Qh~tffi M»~~tti ru.lJIUU 1

ttflrutMshmRnrunru;ot~gti '1 »h~rsgctfTlm ""'

tmru;prutSLdh rhLn~uutiShiJlhgu

l,'; I

,13

13 E nrunrn [ACJ '1 G1

uinmm lt1

DE= l

u~ru

~ms DE= EF

•

.. ..

M ~ [1U1~13

13n

t blililJ1J1l'ij

rn E

.........

' ''

' ,'

B~--------------·=·c

tEm AD= CF ,

sl~ DB= CF

ttntllAD =DB

136HffHl.ll BDFC "ddS DB= CF , 1

tmg DF

F '

= BC ,

I I ruDE= -DF =

"' ' DE= -BC 2

' '

tf:'ifflf;l

13&'Hfi'HWl BDFC "ddS [AB] II [CF] ' [DF] II [BC] 1

~ffln: BD = CF"' DA

= DB (G"

13 D n

136'Hfflru1 DAFC "ddS DA 1

t?l01S H~~lJ~

rn CF ,

lJ 0 " t:Jmsg E dl13ru113nrunrnts [A lJ G1 j

180

) !:Sl8 DA = CF "'

] II bliE"'

t~'Hl2 b.ABC fnhUi~ B BO =

~AC

um Ill

ML'i:!7 UJ'iJ fJJ1 rf :

U~t1Hl:H:iJ12

2Jms

BO == OD '1

t~Ql2tHHfiHl11 ABCD ft~ru'HlSHh6h9hiUnHlffl Li

L'1~Gn.f1unn.JJ1 ru

.o"'

o £hLUHl59JLfil'l§ '1 IJ

TIHru!ilJLfil'l§ ABCD ft~ru'l:fls

dluntfiln.n I

LABC =

1mn : BD o ....'5f

1JtgVfUI4 :

i12J

~AC

BO =

c::;

QhL5itfil

bn~:l~bu;~sbn &Sl::~~:filn.ntm::

t'l§1:ljlS&

m~tfil n.n &nb&1:! ru'l:fl s~bu;~sht'l§i:lJl sm IJ

l S BO = -AC '1 2

ML'i:!7 UJ'iJ fJJ1 rf : U~ti5t'l§i:lj12 [BO] 2Jms BO

tHHfilnfl 1

ABCD

OD '1 t~QlS

ttnru

f1:lru'HlSHbn

&2'H BO + OD

1 BO = 2.AC

C+!Ac = BD 2

BD U

"'-

= BD '1 1_?tru9JLfil'l§ ABCD ft~ru'i:flS

fllJh

= BD dlu~&filrulfnb

~m~a b.ABC fnhLn~ B '1

2.5.

runnn:mnmnn 9

u'1tfilnnmru dluntfilnn 1 c; a ~hLruu~&sgnmmmn Li 1

m '1 "

ru~bfh

'~db '1

ru'l:flS'idh LJ

n~sLruu~

untfilnnmrufr:Hli'Hl l

mruru'I§Qln(m9 "'

tsiruh:nbts~hm

1 Htfi

'i:l'ru t~tUTlm~Ql'1tSuntfilnnmruru'i:l'Qln I

un filnnmru l

&t~ru'l:fls~fnb'i:l'rutUTlmun&filn.nmru&nb I

A.-----,B

2) '1

tl'i

LD st~ Lc

tunm

~m~ '1 l

. II

ru DA

,.---'\~Z~7

ti?:'iQlS EBCD dlttnilllijLf'O'i:j 'i ti?:'i'i:flS DE= CB

CB (1_Elb l

tffH1.1l UltllM'i:jQl~)

~ DA = DE 'i

!lADE dltli&nH1.1l n5'i:jtfl~ '1

1mn

:LA = LE

ttfiru

LE = LB (~L~~

) ~~

~ ABCD ttlru

DA = CB ('idtifi~tffHUlmtllM'i:jQl~) lJ I 01 I

'i:j LD = LC ('i:jQl~fi~tffHUl Q

n AC =DB

182

tH!lmttl AC lll

L~tffHlll ADc st~ !lDBc 'tfls

tllM'i:jQl~)

= DB 'i

t~'i:flS ABCD tHHnHl.ll I

ruftHli'i:flSO'l~

II [AB] &tfi ru

i'Hl{fl &li hq_~ tl ij ~ Htni G1 01 fi'i:HiJU t S

tHi &ffl M

ummm [DCJ 11 Ul --.:1

mru '1 <I

EF = !(AB +DC) '1 2 ML'ln wu fJJI

ffi'lยง C ~MliSln CE ffl ~

Ui~ G L~hfflnn AGE a~ EDC 'i:flS rdn~) "'I

LGAE = LCDE

" ED (E dltiMtHHl.ffi&li 1 51

AE =

rnn~

LAEG = LDEC

lifin :

= DC a~

= EC

Q~l!itfflM CGB 'i:flS I

E mttnru:;nrunrula I 1"1

II l l I EF = -GB = -(GA +AB) =

16Mf!fJ94: n~n~tfflM L;n cs 1 I

ruannnnrunrnts'itltl 1 n lJ i

lJ~ ~msiHliu~rir~~ruftlrnLM'iHms~m~ '"~ II

&~'i:flS

ABCD tHHfflM I

'lJ~ [AD] ' [BC] S~H~rilJ~ II

&li'i:flS E , Fa~ G , H dlGMfinrunru I Gl '1 ti!rlmm E , Fa~ G , H ~~tsiUtlli IJl --.:1

. ~~Uitmn.n ADC ma I

" ruts

" G marup:sn

ts-12 [EG] d1Qln1H:$J~laU~tffirul ADC '1 [DC] II

U1(fl~

a [DC] II ~Jl~teJs;

" s;~a'l~taafitffin.nmu:ns-H tJ I <t

"" "" Lrirl"l&ru

11 [EF]

(3) '1

"' maatlH:tl E ,

.. Fa~ G , H ,e. un

IJ 0

GM1 G E ,

C::.

&rutlSlntn~ru '1 <I

N~ts~~tlยงlrl

a~ H

nfJti19N~tSH~fllยงl~ AC a~ BD

: Uitfnrul OAB N~Q'ln t'iH~JlS

rl LA

= LB)

dltU!:W

n~ l!.ADC , l!.BDC oe

'i:flS

= BD H~rilยงI~Grl t ffi M n 1

!llNUQlri '1

CD AD =

Ul~iaantmn.nmru I <t

&'1'1

~mas

llADC: ABDC '1

ttlQlS LDAC = LDBC LDAB = LABC t?l(fllEl LDAB-LDAC

m~ AHAB mU~tffirul

mu (1) a~ (2) t?l(fl a

LABC-LDBC m~ LCAB

n tSlUUf:.lJlS dltU mt~l:lJl

"ts

u:rhruumrifn~ru, <I

184

O,H

tt'iQlS

" " AB '1 G dlGMGnrunru&a I ~

: ttl'i:flSGrltffiMmruNUQ'lri ABCD i <t 0

G e/

Fa~ G , H

LDBA

"' " [AB] (2) '1 9US

•

nnmn

t,tn'lhrtyHt,~hfilM ABC '1 ttn~ij ?

ttnthru.mtfitfilM i.j .... i.j

!!!.

tfi

&tnnH

11ABO:I1ADO ii(g ? ~

I 6

tS [AC]

&UlW

ffl~ I '1

timmt:n

? D

nnmu1mru I 6l

Qbt,utruf{lt,fil~ ABCD , J l

ttnnH

ADO '1

[EF] t:h~tH%~rufl:lrufilri n

Ul"'-'

!.1

IE = IF '1

U:hW&l_.tlG~&filM EFGH

n. t!!l2J

= IF Sb~ LEHI = LFIG '1

ti~(!JGlG~tfilM EFJH t:h,YUU9~t,fil'tf '1

2. t!!!2J [EH]

II [FI]

, EH = IF

FG = IF

ru~LfilY '1

t'dn~l:lbis~uwt9'ln .... i !.1 \J '1 nnns·umfJ~2'1§WCJ 6 i !.1

4. l.Y'ruf{}Lfil~ '1 II

d5~~ru&snHru9JLm~ms

N"'....' (2x+ 20)

" " x '1 (x-50) '1 !!!MSlnt~ta 6.

N~l,Y' ruf{lt,fil~& f:ll ru £)[1 II

LA = 60° , AB = 6cm , AD = 4cm

2. AD = 4cm , AB = 2.5cm , BD 7.

t!!ltflSUHruf{ll_.fil'tf

3.5cm '1

ABCD

[CD]

tUb~lJl~ A' sb

u ri

11 ~tiH9Jnmriffl'l§ 0

mri

[BC]

Stl

l_.n~ B' sb D' '1 U~(!)Gltl~tfilM A'B'CD' m,ytru~ilJLfil'l§ '1 II

185

..,

t fi'H1Jl ABC 'tf1 S E Si:l D th tHlJH1 fi ClJTH1H S I lil

tl='l'tflStH'jtfi'HlJltnh ABCE shTIHrn9J1§1i:1 BCDE

10.

ifl fD m 15i' nH1Jl A cD mL5' m nn N'i:Hi1 fl '1 Ill ABCD t~rn

tl='l'tflSUfltfilrul I

" r munnunnm I

lil

Sl AB

1='1 rul

l='lrulSlflt~tS

" "

fi.

12.6

Si:l

3 '1

DC= 4x-7 , XY

2x + 1l

AB = 2x+1 '1

1 . tt'i'tflSUfltfilrulmlllN'i:1'Q1fl ABCD t~rn I

sh LA = 67° .,

12.

?'inn

g'i '1

tt'i'tflS ABCD

L.CDE

ill AD= CE

L.CED

ABCD UfltfilrultM '1 l ...

.1 [BC] '1 tll:rl mdl BE = DF '1 Ill .......

L.OCD tn'i:1tl t nm ffi '1 I

186

'-'"'

rHl1lnt~Lni{JlTI5'ru9JLm'iยง

nnnnt~u;I{Jlu~'mfl.fl

IJ 0

t j:'j m~u;:J nJlJ 131:1 n ttfl

m~ fi nn 21 &~ Ln 1{11

hl13ntm nn &nil ttl ru&Mtl ruj:'j nn ~nil am 115 l

'-'o

1361 tm ru1 &nil ti:l rut24 ;;n~

has gtnsm n~m 115 4 tJ nm 2~

ttl'in9nts13ntmrultn~~:sgms~m ,; lJ i.l' l "

8tlnmttl ,;

'I D

"" Lm1:1mnH15

&S"J&fn~j:'jnflS"J

Lni{Jl lswcru9JLm1:19lR9h tlh~an IJ

... run sh ma~ n td'in9n tS13nt mnn &l.J i.l' ~

':)

fn~ 'I

TI5till9JLnl1:1 ABCD uHHl"" IJ l eJ

If'.}

0 Q

13~tm fl.fl tni:l tth ruun 2 &61~ fi ru t~(Jirfn fl.fl (tnHtfl

druj:ifl.fltsHnnhd~mn2hn't1 1 l,j ยฃ'1 I)

n~ I'Jtm ru 9JLfil't1th H ~ fi

ru ~ M m ()] tl fi ~ ru

t9ifnhsh~i:lru.J~ 1

ctfiru~hru.J~tsnmmmmn 'I l

.. dln~~Tiltrul{jLfilY ABCD

[AE] ,

tel rulJl

tf16'i [DC]

dl n~ ~Lm ru

ABCD

llAFD S~ llBEC "!

ABCD

thTI5&

" LADF = LBCE (Y'i6iHil) l

LAFD = LBEC = b =DC= AB

t~Ln~G~tfilrultn~ ABEF

t~~~G~tfilrultn~

t~Gn~G~tfilru1£PID

t~~~Tiltrul{jLfilY

ABEF =

ABCD

t~:mt~~~TI5tru9JLfilY

= t~~ijlfi~tfilrul

ABCD =

ABED+

t~~~~&filrul

ru ABED+ t~~ijl~tfilrul

t~Ln~G~tfilrul

AFD BEC

ABEF = bh

~mag "'t~~~TI5tru9JLfilY ABCD = bh '1 u

: tl:h ruH~E'ilJ~ s~1Ji:ITI5tru9JLfilY m~ nm s~tfil n.n tia~s [1 tmg l~1fijl llJ

" • MnMntl:hru s

llJ

bxh '1

: cutmrueJunY

fJlt~cru

llJ

ntl\'fsi:l ...

NSi:l ...

Scm

l~Lfi~TiltrueJunY u

l~~~L~tfilrul

188

3cm r;mg

s = 3 x 8 = 24cm 2

~(3x

;]·:···················...

= 12cm

A '1

8------~

muntffttj91: ttl'i:flS ABDF th'UHbl59J

JOcm

Lfi1Ytl:1ru'i:flS AB

fi.

lOcm , BD = 7cm

" x '1 t:Hl.fl SHH'H

" "" ~. ~nt~U'i!ffl'[!Hfil

n.n AFG

ocrJw: IN

&tlQlS FDxAE

= DBxAC

(t~Lfi!ff!LtHru~LfilY ABDF)

lOxx = 7x9 X

= 7X9 =

" ""' ~. ~nt~Lfif{JllJHfilM AFG

dht1tltun

t~1Jif{Jlt!hmn.n AGF u~sl:l 3.15cm '1 2

FE= FD-ED

t~LnijliJhmn.n

t~Ln!ff!L~&mn.n

AFG = = =

~titS:! t~1Jif{JlUHfi1M AFG 0

muntittj92 : tlMSlt~Ln~

5xl4+5xl4+5xl4

= 3(5xl4)= 3x70= 21

AFE-

2FExAE-3.l5 2l X 2 X 6.3 - 3.15

= 3.!5cm "

= 10-8 = 2cm

= 3.1

t~Ln~L~tmn.n

AGE

: ABCD

dlTIHru9J1.fll"dtf.Hl5 u

= 9cm, AD= 6cm S~ BK = 8cm '1

'i:ll8 AB ~Hlll

£fl :

ts~tffHl.flt~~dltutrulilJLffl"d

~msg ~~Uiltflts~~:mrult~RruHh~ru

':l>

•

t s g t?inffits?l ru1 m t~tn~trts~ &m ru1 t ~ t~ rut'iY»~ R1J~m hltlm s tr:a '1

'i5

ms =

'i5 ir1 m U'l

xd ' B

~~Lf'iltflu~tfflrult

fflrul

ABCD =

t~Uiltfltfltfflrul

ABD+

sA seD

t~tnltJl

BDC '1

1Ao x BD + 1co x BD

= !BD(AO + OC) 2

1 !:!UtS g S u

xAC =

1 xd'

xd' B

G%1J~1Yt~~ l3cm s~

?irul£fl~~

14cm '1

u "" tSuRtfflrul&f\.HS"Jg

D 'i:ll ::::n~~G%'Hi'~~irl n

l3cm s~ 14cm

firul6'Hi:!lli5 S 90

•

xd"

1 2

=-X

14 = 9lcm

bh '1

~-,

= s rn t.m

1f x (.q + q)T

l.9 ? "' I .11 ':1~'> Ill r/ ~uu¥ Lf ~fl.Ytl~ ,q' q ~Ltlnllfl.!2UHUf:l~rnwuuwHHlU6Y1Pt: BnCJ~~,

l.9

h ~ fl.Y lP !JS!.:l

h ~ s:!.Y LP !JS!.l

h ru gy LP!JJ13

Y Ul lP !JS!.l [.JG] ' [8Vl

!2l!l LP!JS!.:l [.JGl '

J~ v

8 b

l.9

f7a v

,_..

!;fi.Effi W lJU lY l !2BSlPJ EY !;fS Yl!l nrn..1H1lJ : jQUU!lJlli3~ ~I

1"1

Nil

h s erunmnEru f:l ~l.lUru ~ s '

f'\1

"- 'l

C,.

d!;P

W Wlfi+..,E~:J

ru l.Yl l.Pffi W l.lU U:!l!2B!:Jffi

"' h Wt{ltlYUl!;flUffil..A.B :ib 0

SSBffiE~.Q.t!::1!:J~ 0

l.9

l.PffiWl.lUlY:I!2BSHYSl..!::l h YUJLP!JS!.l

I "' LY.Q.PJ 1t U!;f!=l!.S L.A.ru ~3l.lU lY 3!2Bl.Pffi W ""

l"l,.j:!

l.lU U:!l!2B !.Pill !JlHHU!::ICJ S UJ~j

!YseruY1~9<t h

~-,

UI.?O£

ru~~Slfl.tlPtlB112 . " .

unuooz WUIO! =

" ll.lUlYl~B:

HnHn7

U{E!;f~:J!;f61Y!;f~ ggjB}:!

,px OI x ~!

,_..

wwooz

= ,p rr.LS :.:; o

e !;{tHY t{~!;fS

PJll.lUU:!mBS3\;f!=J1PJL.q.tl.Sl.lU~ '

l UeY1PtSL.A.rn I,

,_..

'£

= OOOI Sl!l!::1l

.1'1! 'l

SL.A.~3

S PJJlJUU:!l!2BU6!:J!.fjj

h ,pxp- = S l

rn u:;J m l.lU Y .P tl s P •

Ltl g

!;f~S

,_..

.f1! 'l

L.A.ru ~jPJ j l.lU Wl!2BU6!::1!.fjlc,. : {:l(b

fliP

fiJ.f!,J!J 0

I, i;Hj!;fiH~!;f~~U{tl.Sl.lU~ ll

~tSlfl.~!;f61Y~~m h "' "' !)G

.11 'l

11 ,_..

h UIUIQI

! U6!::11fj:ISL.A.ffiEPJll.lUlYJ!2D: Z!JJtJYLl.Jlf/J c..

et;!l

AB CD

tll tHH mn.n mru f t:Hu mn'tll s Hn n1 l

b'Sbn'i:1 11"1

""'

h'ltiblmG1S=(b+ 111 ....., 2

tfilrul

--------------[~

xh'l

I I I

: ffltlHb~19b n c; Ill-

can

1.1

rutlllJitmMfh~ llADC

Sb llABC

D G

ABC 'l

t~1J1~1H'jtfi1M

ru ABCD

t~Ln~LritmM

~AGxDC+

ADC+

i~Ln~lJitmM

ABC

xAB

+ !h X b' 2

x(b+

r.:H:a ag u

+ b') x h 'l

tm n.n [I ruu; afa 11th rl~l{~ 'S ~r; u t1fil' i:1 'l triu~'S1:1runmmEH1mntllb li "" u

150cm

[!StY'(!ifilt~ ?

120cm

A -B = 16.560m -14.690m = L870m

192

126cm

JOOcm

130cm

!Hi

"' "tS1JnlijrutSUl " fflHSI:l '1 ~H1.11S1t~1_!iltll GtDw: ..,

S = SAsCF+ ScDEF

12m

= (6+12)x4+(Sx

132m

JOcm

6cm

B 2

193

n Â£)) m n tl ;;n t'H Lill 15 rn s Lfi'!5'[f ~ IJ

t~1_!lijl (em )

G'1

fi'i5 hi

rnn

42.9

7.8

S = 834cm

'f~1J1ijl (cm

n'i5G'1 hi

tnnf.l

126

[~tl~tlAC

l '>

2. t~lj1ijl!:Su~!:illrul ABCD

ntlm;;ntl <t lJ

tnl:flS

AB = l7cm ,

BC = 25cm , AP = 8cm , =

5cm , CR = 14cm 3J.<. >'l'W

25cm

194

38cm

mtitnmmntl;;ntl IJ .....,

tnn61cr IJ

2 )

12cm

!Oe~n

14cm

-24cm-

3cm 3cm 3cm 3cm 3cm 3cm -

19cm-

2/cm

~30cm-

13cm

32 4.5 6.7

----------tJ---------

/ /

4.0

' ''' '' ' : ''

7.5cm

~3cm 12cm

9 _,'J._. :6 _______

10 I

' ' sl' '' I

16cm

I I

____ J]____

20 15

llcm

15 9

llcm

2.3km 'l

~HIJlSlt~Lf'if[!Gfilaniilj~ndltntHil

Htln9flti1:Hil'i::f1Sflti'i~l&mn.nftH15'i:f1SOln 5m nui.J' 1.1 li

n~N 3m '1 n

dhf:Hlldln9flti nui.J'

'l tWit~mtHlldln9fltiQ1StlSlSt~~ntHuStifiHS8 ? n u i.J · 1--1 "~ 1.1 iJ · I

o~tmn.n

ru '1

tnntsmm~maTIH1ti 400m

mfill'tflS~t~ti 150m '1 mm~msn~N~

soom

CeJ

t!:llrudltlnmnnHu~rumtimstd "'

tS-

1.!

d~hm5trif!JlE1:ltsmmasg

l 0

t'UliD1:11Jn.Hs

tnt~'in1t'itinmn~·HdtiS1Sr.tl1:3? l.i lJ tSI --1 <I IJ

tnun.nu G" I

0 0

rhtfl ~ hl ITTHlil t S ~ tlII ~ !t!J • o,.. fuHl.H:H~ tl tHfl S t3ilJ' n 1'1 l ..

rul

•

~~e

1.1.

swusw

....

..,

t~Hli'i:flSLtit~tlt~stl r "~

qjstdJtl'1~

tih1j~m

t?Hl!§

firuJlS

'1 &tcH'fl~Utl~~ II \\.1 0

rl5'i:f1S~rulnty

rnt:nsijn 0 ~

OA =

rl5

•

firuln&tlliD C(O, r) '1

ms~~~tLfism.H~s~HJ "i

n ntS~tl~ iit~' Sl g Mn ts1 a 11

197

t15 ~ hHY ~

g~ H5 MLd b l

!:~'11M

ABC '1

Sb C ~l:lru-@Shl6lbsi!:rut5Sl~t61Yli5(UMU9lb "

rhtlcrn.nu A

, B

c L61~ ~6l&sit

.::

1.1

Sb C hl6ltsitru~btlt61Yli5 '1 "' ~ 1.1

tYi:lJlGl~ MN

tl tl

UMU~6lt 1 a

rurun

~mn5m~bi:hsng;6)~fil~ff1YUrulU A ' B sb .a a lJ 1 tl

Sal"lffiUl"lMU12abtlt6ll~li5ti~ti:lrufil~UrulU A , B Sb C '1 tl

2cm)

' 3cm)

ti.

1.1

, Scm)

Sb C(B , 2cm) '1

nsguS15 .., <:

stl

~~ ~rnru xOy stl~~n I I

Oy bt'it[l

f'ttrnYJsRt'HliH1tiGn o ls~tlti '1 ~iltinusg II L.:i ~ I

xoy

c:.

Si:l

U:lh Ox

.....

&Sl:j

B '1

UrulG A Si:l B ttfflm I

xOy '1 2fTI'i.fliM9 2 : t?'i'i:flStsn~ AB <;

DE t

u1hbti IJ

C(O, r) '1

dlt?i?'ihlG'1:3bfi DE tttlfllinttlruG'1:3bmu3rn II "" l:i "" 1.1 1J

~2W'1:3bU DE II

tttlruยง;fin.ncr D 'in~Hrn A U l:i I

d'JG

tsi'rn B tS18U DE Stirs AB 'innfihnt?iffiU AB US L.:i o;

o; iJ

I<;

1.1

mSbU DE ttflfll'i:f12~Gnttlrt5Af15tsilbnHSg n o;

o; iJ

mrnruntl1nnf'6m L.:i !<;

"'"" 3 : 2fTI'U11M9

t?'i'i:flS

ABj_CD '1

tni:l

ttfiruu AC <;

rss'1:3ru') lJ

= CB = BD = DA

th9t91: nb~tlti'1:3ru mhtinalism unatl2ffl El I! lJ "'- I! o; <;

'1:3n~mA1rnrun~onn '-' Ia

tims ,....

mcsgu <;

5n:nru~onn~lism Ia I <;

ttflfll'iffihl (.j

5ilhn:ilism '1 I

dm?

199

: tl1'i:fl'Ui~~b P == 2n:r P == 2x3.l4x lO == 62.832dm

360째 _, 62.832dm

135fH1~

36째 _,

'II

[H:m == 62.832dm x 36째

6.2832dm

360째

~mag 135r~~~~ 6.2832dm '1 'II

Sffl" !Scm

: ~sit ~

== 3 ,

P == 2n:r P=2x3.14xl5 = 94.2cm

9 .2dm x 800 == 20.93333cm ..,,

<:i\

TI5t~~~f:i 20.93333cm '1 IJ

'~'-t<~'ii<f-r-ri:!: &f:iYliU~b~WYllilafi 0 a~finr@Stllilffi AB <I

<Ill

11.1

LCOD '1

nnitn AB t ru uAB ~~

rin AB nnru AB o;

'II

MOM I

AB = MN '1

""" o A UifitrumtrJO c n.n""

D '1

200

u 0

S8 G91~ o; u

LfiiH

AB S~ CD tlSffi '1 1 q

1Jt1fi9 : @

Ht~~a£1mHt~~nft:HliGdl~:um a

1.1

ntl~tl~'l§ru mh~rhusm ct <1 11.! "'- <I I 011

d5nusm &Sl8

'itJlM'i§n~mmrurun l,j -...:>

~nn~usm nt'f:lruroatlt'iffl'i§Hh~nilhnsfiusm co 101oa o:~l) noa 101

ntl Oil

intl 0 Sb truh'i:flS

'muat~nilt~nuSld~us o:1 ct I u

'i}

AB>CD 'l

sb D

C, 0

13-

tl.CDO

~a61 AB ~hHtlfits CD 'l

UllbStlLfU1115U~2Jtill(!Jth

~n<11

Wtmtftt191 : tfi'i:flS OtifW:

<11

ntl~h~'l§ru 'l

OC+OD>CD

tfi

OC+ OD = AB

ffj'i§gSlfi9st~ (i)

trubtnS AB> CD i::ll:HS8 II

AB>CD 'l

M MN = PQ '1

Htflll5'iHlllfirhts MN l_j 13-

otUw:

ANOM

"' u

'i:flST;lh l

OM= ON= OP = OQ ( ffl~h~

sl 2J ~Qln

!\NOM:: APOQ n~

3 (d. d. d)

L.NOM = L.POO sl2iHtl~fi MN =

, r)

uAB> u CD '1

LMU5tir1Jl

U.i'i:flS

HhriG AB >CD n

"' u

fits AB >CD "'u MOB

sb !\COD 'i:fl S OA =

= OB

OD = r

"" " L.COD 'I§StlSm : 1 ct tl!'iQlS L.AOB> L.COD ( uAB>

u CD) '1

i::lmsg Hh~fi AB >CD '1 11 n ct ll

201

c"o

Q;l

297f.flHU191: tl'1'i::flB C(O, r) btlUMU B Sb B' r:h I

Uf:i8~8~sUb~ C(O, r) t8lgt!'1Q1B OB

""I

OB' (fn~b~ IJ

2Jcr

s· ~~L6i~

us . o

tlmsg mttlOlli'lU B U I

msbcr IN l

u B'

w'Ulusbcr

0 '1

c C))

l<ll

1.1

~ AB l. CD

ttllru OA

= OB '1

fUQ1S~h~t6i'i3 l) ll

II:» 0

It)

'il,:;6'16'1Mffl ttJruun.nu A 16i6itruun.nu B l,:; l

ffl'i§O

UA , B

fi5msb1titH'oni1bH lOll lJ ..

&13t!J1

tt'iQ1B OP = OP' = r

m2J PE (0,

~b~'i::flS~6if:ig'i3fjj~ "

""I

C tl'1

si:nh nil '1 G1

P tnJusbti~~ AB

n:nru

297f11Wn93: tt'i'i::flS PE (0' r) '1 ttflfjj P'

u p

~ PP' r) '1

1.1

'ir=JtlHb~~GisrlbH lJ n .!<

~msgmrhfonusm '1 d$ c; ~et

Hh~~ 6i fr::H15 ffl ~ffl'i§O nnun run ru csn'i3 ru n " 1 n <~1.1

202

fnh '2hHbn ~n.; tti ru nn ~nts g ttfi rut'un n ., IJ

c SiHHH~u~ru &Slg'ifi~tunHb~u sbnnn~mfl~ftintlSffl '1

"'u u

"'u

"'n u

tUf!W: tf:'l'i:ll2Hb~ AB l. CD ""

t::::$

ttHf:'lti6'i~tHil~'li~61 AB

';)

bl5dlHnJ~HS l

&f:'llilSurt.flli C 1Ji61Gbl5u

13 D

l.J

sl~

HC = HD

~uc2g

uCB = uDB ~ uCA

uDA

rhnnfl~f[;j rut "'IJ tJtf!W: tiDb'i:llSHb~cr AB Sb CD 'Huti ev n cq; lj

g}ib~nfl~Hu'Omdlcrus m '1

nif.mcftit6 2: m'inn ru'li u

"' u

"'u

f:'lhlHb~Ofi MN tnbsb u n a 0 tf:'llil2urulu I

slยงJ AP = f;j1.Jb28

B ,

~ AB Sb CD

sb Q t{Jb B

BP, CQ =

uAC =

uBD ~gffitu'l'OsbHb~ MNdlu

AB II CD 'itiblmrtl AB = CD '1 tn -...:>

""l

"' II

1. ttci2J~~ci C(O , r)

(!:lru A

= 25° '1

tcinllSl~ AB '1 IJ

2. ttci2J~~ci C(O , r)

ttlru

uAD

u CB

fim~HH~ti AC = BD n ell

tti'tl

&tci

~Uell AB = CD '1

Q(O, r)

W'iHlnRGl 134. &tci§i~~~~G'i 0

u /)

uAC=

(tlru

CD= -4x+4 '1

~~ (G) a

uBD '1

OQ = OR

W AB = 6x+ 14

t~~

AB a~ CD '1

t:lrul

run~~ AB = CD n

uAC '1

uBD=

ABC a~ I, J, K dlGrult.Hirunrutfl~m'fsH~~ AB, BC S~ 1 n U ell n

cA '1 H\.nrummfimonnnil~us n, 1, K, c csinlh~~&n'i:Hllf!:lru'l:flson J '1 · l:i 13I II.! I! II a

tmnn

ABCD 'l:flsu~sh9~ n li

r~~rn~m '1 ell

M, N, R,

s mdnnnnrunruc~D~ls v n

U~~ AB, BC, CD, DA '1 H\.flWUft§Hillmmonn n l_j N U ~ I 8. ttci'i:flSnS&~~ci ,., &

ru'l:flSOn a AB a~

~CD '1 LMruu

~Uell CD i§W '1 11 IJ

E:H\1»~~ AP S~ DS tn~S~ u n

fimn~~ PC= Ds '1

ti=i'i:flS~~~ X(O , r) S~GMG P t I! 1

n~~~~&sg '1 .::; /) 1

rum~ffii§GnllG P 'i:flSHrHJ2dl~i:tci '1 I

H~~ti AB n .::;

GrulOnrunrut~o~~SH~~ AB a~ CD '1 1 1>1 n

n. LM ruu 2.

tci. 204

~ OK'i:flSG'i:flW&Nt9iS~OnllG O,K,P,H '1

fim d

'Lu]muJu HKO a~ PKO tUJU KH a~ KP

'""

tmhl.flil

" !

o 'i5 1;r1 £!] b ttfhli Qru1: ~:-e CUl a &-e L::!Jl 9~ n~ &[j-ejnflgLnnrurhrung

"' ABC dl[J1!:mrul~ti5Sbt'eL::!JlS "' "' 2f17f.fl!M: BB' Sb

CC mnHlffl~n.J:l G 'i tlirlmch t-etlnstL::Irt.HH\Hum l.i

ot t..:i

i.J'

"'-"

"'r1 A mfiffl'e · "' AG G "'tl:lrn GA'= -I AA' Sb 3

mb D mcrru113~g ~a A m'ltisl::l I lJ 6\J

"'-"

2 -AA' 'i 3

ll.ABD 'i:flB

c' dlurulunrun rn&s I 51 G

A AB}

0 " ctl13rul13nrullrl.HB AD I G1

'l5Sl~

CG II BD (!)

.,:;

nb l:iACD ot

'i:flS

G ctltHUjliilb1.1J1n5tB AD} o

mcr ru1 cr n run rn t a A c I

"".,

ffl'e'i9fU'i5913rulun 1

n5tj:jQ1SGB'IICDY.GBIICD (2

li "'

m-e (I )Sb (2) CGIIBD}

m2Jcrfitm rul BDCG dlLtit

GBIICD

!:?19lmQ12Hl::l~i9b BC sb GD m~ffl'ifitiUrulunruTl ""' nt..:i ott..:i 1 n

A' '1

205

1=1jltH9Jn A' thUbU1linrl[lbl5tSH~ci1Jtl BC Stl GD J'UnJTI5tbl59JLfil13 BDCG u

t~r.n S

= !on tJ GD = 2GA' 2 ""-

GA'

"" G tSl& AG t'UlliJ D thtirulli.hl8tS AtEutJSb

tG'i

il2j GA'

ti: Sl:d'i AG

"" 1

AA' = AG+GA' = 2GA'+GA' = 3GA' AG = AA'- GA' = AA'- !AA' =

2GA'

~AA'

: r;-et~n s ilb{Hs,fi t m M-eru;tJ nH1 Fn'ini:1n Mu1:1 ruft:l rnlir;r; sim:ll ru .. ~a 1J'813fJ9 n t.l" Li u L.; """ Li 1 u "' m~ti " 'tst1:1L:lnss1:1ru')~~rau 'i urulmsg&trrl i..l'

ijtl~&filrul

'ltJd91:1~ta 'ifitmn.n r;tilru lj

ABC

t1:1tlJIS~IUbti!!J~~~rn

B Stl C

'!:flSTI5t~tl

!!Jffi9LtJ~9~S G tS~tfilrul ABC ~r;r;sit

n. 2.

II!:»

t1:1tlJlihts»~ci BC 0

9lmurrnnm;r;r;mn.n ABC th'ifitffllliln51:1f.l1finrlrn A ""

cs-

n. ff'ltl A', B' Stl C r:JltOtlt1:1L:lflS~IUWm~~rlill u· u "" u , B Stl C tS AABC '1

ti:tlru G GB =

~BB' Sb

tfi BB'

1'\;)

th9TI5~9~S&S AABC t~f.i1S

= CC

GC =

~CC'

(IU~~n~)sl§H~l.i1S GB ... ... u

= GC

AC 'i

L:lmsg u

I:~Hlu!llmr.nsm AABC ""

mRfJR: IUtiUrulli c ttlbl5tJSlci n l <:

/..j

th'iG'itmn.n IU~lflfinrlrn A Li

sb d' tht1:1L:lns~~'ts eJ"

!JABC 'i d'

206

2. (If

t1H:1J19HStdb

fJfl7ifiUl17:

ABC

LliM~~Lnb

tii;TlQJttl t'i:ltljl9~~s~b

o 'l

QhUHfilllil

m~rn1:1

0 'l

tu o ctlLtiM~~nbt'i:l

g~ d Sb d 1 tS~b AB sb BC 1

t{Jbmnb c; c;

tf:l'QlS

!:.ABC

OA = OB} OB = OC

m2J

OA = OB = OC

ttn%jtSg tf:l91QJU1S

~ntsitrnmtljl9~ d 2 tSLdb AC '1 1

~msg t'i:lf:lJlg~iJbu d, d 1 sb d2 tSLdb AB, BC sb AC QhLfltfilllil ABC '[YN 1

nnru

tt:J

ffl'in-bun.nn o tn'i:lruf:ln c; w 1 u t

oA = oB = oc tSl8 o msr;mru~:fih9lsbRnrnilbuls t:.ABC '1 ... -1> u

ABC '1

A el

<Qt

Ql~

t n'i:l rut tl rn u n t si um rut M~ nn n rn 91 b15 t s 1n t m n.n 1: Sl g '1 u

-1>

fin.nm s Hh~nabbm1ntHrl'ifl& m n.n 1 .;, li w <!

IDUT11U1f: AMB

ctlUJGfiln.Jltnbtn-b

'1:1

M '1 0 r::hullijunruJlrntSH~n AB '1

fi'l'i:l

tf:lf:lNtiSl~'i:JrutnbSbtiSl~ AM 'i&'lb N '1 u ~ u ~ w

tiblmttl 'US!~ 1.11

ON dlt'i:Je:Jflg~~SHb~ AM '1 i.J"

tuUw: ntl'ifltfillliltnb AMB ms o mun.nr; w w ~

wmnnnrn M "

207

t?'ililS OM= OA =A:

s12Ju

1Ji t ffHtfl t1i ~ AN0 S~ 1Ji t fiH1Jl

MNO 'iSIS

OA =OM ( r:h~~~~

~:ITls~~~ I

lJtflttltl~tfl'U

ffl~ A', B' S~ C'

tt~~n~hlMtHUmnfinru A, B S1 ll ll

c tD~~h~t,Witmn.n ABC

r:hUrulUn I

~PR

}

emu"

rollffiHiUUrulU'i3"ttl 'l ~ 01 l.j I 1.9

f'1.HS'iG'Hfflrul ABC ?'iroWmll A 'l l.j ll ~

~AHr:h~~f:!Jlg~[SH~~

~utS'iWitfflrul ABC l.j Ill

!l" ffl~~ij1tl A 'l H mtel~

ruts~

tS18tfililS'US1~ BC!IRQ ~

AA' l.BC ij1U A'

} tS18t?'ililS AA'l.QR

BCII

1_,tiUA Q

tf:llru A r:hU

rutS~~ I

u ~

mmf:!Jl9~[su~~ RQ

ruti~f:lUff121~trn t?'is~msu 01 <~~~II

208

~Jlbt9Jnn~hl AA', BB'

CC'

'h:qJil;mnn

ABC fflbt~

g~iJb{'Hs

'lfitmn.n PQR tErHtl'iffi13MS~2tfl2Glli~M AA', BB' Sh CC' t21W\tmn.n ABC l:i "'et G'l l:i •

'~U run ffl'ln{ju n.nu H lJ ""' l:i 1

t 21 g u:a '1

A A

QhiJhmnnru.ijbJ n~h.iihta~ttrssh&~f:lJl9~ &2lg~fi~~~m1mun9ty~ 1

sb~UnNl:HhnnMffl '1 II W 1"1

Wtmfi!!it: nbm;r~h 1.1

•

ABC

"'I

A'BC

tsg

t:hLWitmnn

BC ti13ffl '1 u

'!:)

* I t:h13rul13'1UNtlt2U2ln AC 2hU2161 A'B 1

• ti~rit'nbsbu~ri

Bc mrim~ I

~ri AB 1.r~ J '1 B

209

~tlt~tffHUl BCJ'tllSAC.lBJt~~ A tf:rHH~ci CA til I ~

':)

f:)

tutumr:HHHli C tS !:J.BCJ '1 'USl~ JI l:nbSb'USl~ """

tffl M BCJ '1

<t{pbt9J~ti~ci A'B tnb'U~ci A'C L~~ A' ttfirumcim-e I tSl8t?'imf!_Jmsm A' til ~

n'eN?'itutomnnrHl5 B mmg'idb cJ ts I:!.BCJ '1 I'IU ...._, U lJ I

tlmsg tir;mo u 1

c , A' 2b J $ci'i~~dHi1 lJ IJ

01l

LfiRuH: t?l2Jtmrn9JLffl"e ABCD ~ru '1 u

•

0 tilOMO'i'UtumtlbHtl~i9tlS'UNt'l 1li ~ nli u

HtilHS~N~tSt~tfflM ABC H' tilm~tu~tS~tfflM ACD '1 0

c:b

tnnru'U{jffi

o tilo

"::

tin11.[1rul:sH~~ HH' '1

"" H

tfflM ABC

tffl M ABC '1 n. m-emff;:Jrut?l§m.tlmm u ll -..:> LAB!= LCBI = 34° ~b LBCI = LAC!= 21 o

1 tsithlti1:fH.Ut'J15Sl~ BC .... "' .;

•

tf:HTJmQl2 JR -.....:J AB

Stl BA: JR

IQ, I l:sithl1'31:ntllrl'i5Sl~ ......,) &

Stl AC <t

r;~tlbf:tlt.uti~ci AB Stl AC '1 rl5ntsi2ltlntlt2~fiunn.n r:S"Jgn{hn;si&rnn2g'i5Slcimls LA ntl MBC '1 et lj GV 4 1 C1

tE:ht.u

t1..fHH2g fi2g'i5Slcimi1tlfHs MBC 'itinH1fil1nbUM1'3J <t I "" & I t_; & "' W 1 fU'BJ1H1 IP

= IR J;SlgGn.Jl1'3 P, Q Stl R hlntsitrtJ~tlbfn-et.uft:Hl51:n2~n

stlUtltlm nhfitm n.n mu a1 ~tig trllstlatlb 1:2 g <t~tlb r 2 gr:mi mstltim1nntl1Wftm n.nABC t_;

r@ M'iJ9 : n 2 gu a1 ci r1

1...i rn

"'I

ntl iltJ{J'ts,Wf Mr1&<>~ffl'inbcr n.nu fn-eu t.u ft:l "' w ~: m n.n-eu t.u'iti t_; t_; 1

t sir; hll31:n t.u tlUd tl iltltHs~fi t m n.n r; Sl g '1

'"" "'

cr n.n ms gm ~a n~ tlti m1 nntlifi 1: m n.n " <>~ w 1

297fflUJJ7:

'i5Sl6i &

Ax,

t2 LA , LB Stl LC t~Jtl ~ (s

nil <j Htflt.uti.fim J, n W w

stl L Unl:sitrnn22'i5Slcim ~ ~ ]

Qtlt2 LA, LB Stl LC r:utl~tstfi~:mn.n ABC

•

Mbn22tiSlcirJgfitJ stl~;'inits MBC <t 1 4 l.j &

mtl D' E stl JF mcrt:rulHlifntl GS J r;rn tiSl~ AB, AC

Stl BC

fil <t "'

tE:htll J Untsitmnsg'i5Sl~r1H'ifii'2 LB Stl LC tS "" .; I lj MBC '1 t!='iUlS JD

JF = JE ']J_JD = JE

l:rlJfi2g'i5Slcir18ntlt2 LA ntl MBC w & 1 ~

• 'ififlt.uU.fit:l1'3fil2ltltmt!=19lmms G u es ........, 6\1

sl2J J i5msi

stl

i5ntsi&m

MBC '1

t sit ~13¥1 run~tl iltl{Hst~ t m ru1 ts-H '1 I

on~tltim1nntl~b'inli~tm ru1 '1

()

"' 1

l.j

l,j

muntff-11: ABC dl'i~&fflrulfD'i:HilnRb'Hli A, I dlontS~tltim1nntl'i~tfflruli:SllStl IJ l,j u "' () "' l,j 1

LBic = 12oo '1 Lfinruu~m ABc mt~tmMfD'HtlJ '1 1 mon~tltim1nntl1~tm ru1 ABc "'

"'1

l,j

fSlll I dlGrult3'i'i5fDr!tSfiSgtiSlg:im~ntliJtltihl'i~tfflrul ABC '1 I l,j IJ "" C: 1 I q l,j I

ttHTl S LAB/

LJBC = LBCJ = LJCA = LB = LC

g LB = LC

(~01nl!itfflruli'D~01n ABC) '1

&r::llru ABC m0tfflrulfD'H01nR~ru A il2Jti~g:i t'Hf:iJlg

~~fi BC '1

6?1012 JB

tits LBJC l

JC il2Jt~tfflrul/BC dlt~tfflrul

120° &?101S

LJBC + LBCJ = 60° , (LJBC 2 LJBC

= 60°

iJ2j LJBC = 6~o

6?101 S LB = 30°

2j LB

iJ2j LC =

30°

LBCJ)

30°

= 60° 60°

tfflrulfD'H01n ABC'i:flS~01n LB

= LC = 60°

I:Slg ABC dlL~bfflrulhl'HtlJ '1

ABC dli~&fflMtntl'intiRr~ru A stlJ dlon~tltim1nntltst~tfflrul&sg '1 l,j

2 2

l,j

rumui

1. 'i ~ t mn.n ABc

m~~U1~ 2. ABCD

P "'

siH'i:H:luÂ·n s ?i ru u:s

m'iw~ t mn.n ru'i:Hll ~ fi f:1u ru A n'i:H'th\' rum ..,_, mri A n u ~fi

Lful

dlLtHru~Lfil'i:l,

dlGblJlUFirt{fl ruts

L~~fi

ri B

UrHl{flru "! J

mfi

BC "' 3.

HtfHtiUtlrfl'iHllfi AJ s~ l_j w .:

~ruLmru~Lfil'i:l u ,.., ""'

CI d'tH'ill:sitrnH~ u

UE j;ig

ABCD JU&f:tlG

""l

9~SHSIJ1Cfiln.Jl AEC "'

A 4. H

dlH~~ru~tS~tfilfi.Jl

ABC "'

15 f:1J1 Rttn ti

H~~ru~tSL~tfiln.Jl ABH, CAH S~ BCH 'i 5.

UrH5D5t.Fi9tS~tf'ilfi.Jl ABC fl:iruH~~ru~m nn~tsitrnt'i:3tlJ19~&s

6. ABC

ii ec

mL~tmnnrn~L~~ A 'i ~~~m1n

L~'m nn &sgug t9is~w~~

mn.n &sgL~~

Gn.JlU p' l

0 s~ R (I dlGnmnh~~tsg) 'i -

.:.

..,

Llf115Wt.n9tsu~tmn.n

utf:lQJmn~~~'Lm'i:lt

ru&Luatirtlru~~

~~nil'i S1

A LMBC

'i:3

LBMC

L.CAM

L.AMC

~~mrhLn 8. ABCD ~

ctlLtitn59JLfil13

ctlG

Unrt{flrulsH~~ AB

u 0

'\;)

s~ J ctltHl..flunrunrutsH~~ BC "! 1

ctl'eti5S~152lii DIS~ 1.1 .:

DJ "'

t?irun

C,\

P s~ Q mu

tihl mdl AP = Ul"'

';)

umrurHSH~ lJ

= OC - = AC

213

l:bliltilf'il'i§ ABCD USl~~Clru~nhShtHn~ BC Al~rn'i§ A ~hUSl~~nhShUSl~

Al~ffl'i§ B t?tu~~1J'l~ E '1 Lff1'ULm.n9tSL~tAlnfl CDE '1

10. ABC ctlL~tAlnfltnhu;~ Ash D ctl&Ohn~M

i!ltummfl A u -...:>

'i I

ctlUnflunruTlbli~SHh~ BD sh J 1 n n

UM ru 'i5 .fl"' ttl 'i5 Sl"' g; 0

nfl 11 n ruTl ru t::Hi h g; AD !

AI ShUSl~ CJ ctlUSl~fnhffl '1

"' '* 1. ~i!12J ABCD ctlLmrufULAl'i§'lBru &i!lRnn~ u e

ctlmwJuLUtu~ tsH~g;1Jht?tb159JLAl'i§ u

ctlHa~M~tSL~tAlnfl ABC H~~tu~tSL~i:Alnfl ACD

o ctlunnunnm rutsHhg; HH' n n

I '1

nh'ifHAlnfl ADE nSgusng;mtS'i§ D Sh'i§ E

-...:>

12. 1

<:1: 1

Mrlffl'ifi~ J '1 uirlmdlGMu A, <~osli Ul"'.:> 1

':)

Sh J ~~'ifi~ li D

214

'1.1

tndn.nil

"'I o fi n.mhu mHl.fl9u t 9i l ~Huu ~

o ant~Lni{Jl21~lfi hl fl'h-@fi s~tm n.n o f!1n.nSl'i:ll:alfiM fln.fยงfi

s~tmn.n '1

1. Q~ r:13dJ s 9 15 t1=itn ~HdnJ1 t~ tSfi5ts:mn'i:lltn ttHli'i:ll s1'i:lllJ1 fl ~ ~tH:ll t~Lni{Jl ts I

Gntfilllil~n~ I

filtL.

ttlru'i:llsmrunru

n~ClliiH1HcJ&sihlrltG&1:'itfi~tfidtlS~mmnJi'i:ll'ifi'i:ll <> I! cv 1.1 U U Li I

gg~ 8~n13

B A E

215

'l:iIn N'i:fl ag 2 n~C) 'Il:iMtH'il n.Ji ruu a ffH'i.ni ttl d tl 'I N'iHil rl:HU ffi uRmug) tl Q'HH'i.ni ttl l:i l:i I

<'I

M'1

<'I

~ 2:n tl 9i t1 ~u1.H a l§i N ttl U1 u;u 9J1J11g

t m'i.ni mywLri N t 91 mgt rty1 g&s n'lll t mru1

tn Nlji~dll§i tmMtntl '1

'' ''' ' ''' ''

,.'

,!)

..........

........

./';'

" "" ti ru1rln "UH~1Jlf{Jl~2:nt!UJ

Nthdruunla td'in9n~221 u ..:~u:w·~

216

........... ..

~Hl.Jl sn "'t~Ln !{11 ~ b 'l

2. f:H1fl S1 &~ Lii !{11 f11 b H

r:ujw : Lfi hl1Ji~L~'i:i2ffi sm trl'il.j~ &ffl

rt.fl SbtHH ffl rt.fl fii bUctl 'i§ 2~ b 'l I

&~Lnftll ~b s,= 13 x 20 + 14 x 20 + 15 x 20= 260 + 280 + 300= 840

2. t~Lnftllffll:'lHN

s,= S 1 +2B=

~rt.flSl&~)Jifti191l:'l»

tJt01l1: IN

840+2C 2 ~ 14)= wos bnffit~

ctltHHffHlJl I

2 + (0.5

= 0.32 X 2 + 0.2 X 2 = 0.64 + 0.4 = l

'~Lnijl9ll:'l»hl s,=

'i:f2'irl hl'in~tHi'i:f:Jfflb 6 W W I

bnffi l~ 'l

s1 +2B =

L04+

[pHu~: ~n.nsnt~LnfUl~l:'l sbt~)Ji!{P

x0.5)x2 = 1.04+0.8 = l

ni&sauw

q_.fil'd

n. Lri hliJ1~1Ji'i:i2 2. Lrl hl1Jl~G~'i:j2

'' ' '' '' 8mm ''' ' 6mm 6mm ,_.¢.,,

--------

-----,,,

8.5mm

217

;;

61P..1Yj

'-:J HJill~6

""""

!;1'YJUUL!d:J~1Sl!;{r.J1LSuuYtR~p:

ll?

(,)

';:::7

(Q!

~UUl!dW1U

h wshNH\;1'l6\;1'U:!;1'S61!;1's 0 '1;:::1 I

(:1

'11:;:1

t#<t::l

H\;1'l6!;1'U:~a.gs

shYLOf!.N UU UdlY1UJYrn SYR!Jll

UJYrnSYf!.!Jt:JSlN c;.)

YfiH=lJ!;1'YJ~

h YI.OUUU:!H.fl.t:JSHF1\;{S\;]'YHUI..lY e. G d::;:l ~ o

~#,:0

UJs t.Rru hlH2R!J llUJ~rn s Yn!J u tt:lt (;I

U{b

(:)

UC'Q

e:MJJnlliJLf.!J

Y:!JJ q...

::l

q...

UU U:! j lS!.ll Sl gj_ffij lnlY !13 :J ~n!J U W1m [JSl.:J Y:J h UU Ud :1 Y1lPYn!J ll S:Jc.. N H \;]' l6 \;]' U: ~ n co co Â«:::1 o ~

~~c

nt~:~>

ru llY 0 n

::l "'"

::l

rn f!.OlJtHJ.~YH.Y UN P..1rn lS!.:l LY P..N 1S EN H !;{l6 !;j>U: t{S 61 h YYrnnYlr:> Y1.0 S LR~fl!Jni'O ll o 'b o 1

~ ~

Y1;!

"l.

?Hl.n Sl "~~Lnltll2l~ '1

?Hl.fl Sl t~Lnltll9l~ ~ "

----~ ..........

------,,,

ruilw : ""

\;)

";,

t::ll

'1;1

~~Lnltll2l~ dl d bt51:Jn ~:s ~:~Lnltl'UH nHl1Hu'i:3

tnn'lh:n:n9l~~f15 '1 1

'' '

m~ H mdrnp:m

rntSL£:l~ AB '1

m'Bt¥ ~

U9rJffln~~S~6ln~'i~tfiHl..Jl SAH l

lil"'l

'\D

-------'-',, ',

tl:itfl S AH + SH = SA

'' '' ''

',,_ \, '...:"~

B " ~msg t~Lnltl'2l~ ':1

4x \11

..,

192 tlnffll:~ '1

2x(8x 12)= ~

':1

'\::)

2. &~U11tll9l~~ rumd bt51:Jilti:H~Lnltll2l~S~ t~LnWtnndl nH~

S1= S 1 +B = 192+(12x 12) = 192+ 144

336

tlnmtd <:\

lOcm S~ 8cm '1 A

..,

i:iMSlt~Lnltll9l~~M '1

tJti!w : ""

2. i:iMSlt~Lnltll9l~~

ttfH15AH S~ AG dln'i:3hltS'i:322l~ '1 S1 1

15= AG

219

13= AH

~路(l3xl8)+~路(13x18)+~路(10xl5)+~路(10x

5)+(10xl8)= 564cm '' '

14cm

fH:l

30cm '1

~\, --------- ..0.., __

----------,

nffiti tn'i:3 b d t S'in'i:fl s ~in M~ s t Mm ~: g t'r~ r; si nb 1.1

l._j

"'""

QbmtDs~;sgmnJffitnH111 l

tff1 n.n ttl ru'i:fl s

220

""1

'i:flS

m ~ tll:tlo&D n'J ttfi ru~m n

trt.HUlfll'i:5

111 fit Fi1 n.ny_

x 2nr

111ntsLutru~ULFi1'i:5t

mAn

run~Mctlt:itSLntStfi1M s '1

th~t91: t~lj1ij12lbtFi1Mt!:lrumst:itsLn s sbnl111fi r RM~t '3

":1

"::

t~Lnij19ltl ~ rtHS t Fi1 Mctl d ru\ln ts '~Lnij12lb em M

s,=

rcrs

'::1

'~Lnijl 111 r~tm ru1

nr Â· (s + r) '1 ~

'::1

f"::

"';)

fiJifnfi!!iJ91 : f!iM2lt~lj1ij12lbSbt~lj1ij19lb~ftHS

tfi1M

(nz3.l4) '1 GtjftJ:

t~lj1ij12lb&Fi1rult!:lrumst:itSiJ'i S

6cm

Fi1111fi

r = 2cm 0

nn.Jlntf:illi5

S1 = 1trs = 3.14 X 6 X 2

ST = s,+B= nrs+rcr = 37.68+3.14x

= 37.68m '1

50.24cm

S r= nr + 2nrh + nrs

= 3.14 X 2~ + 2 X 3.14 X 2 X 5 + 3. !4 X 2 X 5 = 106.8

(tlnmtd) .::

221

~Hlfl Sl t~ iJil{ll il~:UH1.Hs f~JbU&l ~u~ti 2ll:HLfil1ยง

'1 bfi

ยงj (1t"" 3.14)

4 ttl1ยงjR nil ~'i:fl2 h~~tim M'i:fl1Jl ttl rn'i:fl s~'i:flLflli r;m'h n fTI n t E:il rub n m

~ti~ts<J ti:l ru

SSirHJ lmm ti lcm ti ldm ti lm '1 1rJN1&l~tt!ill'i:flSU1&lctlufttAlniltn{lttjru & "1.::1.. 'A. lj G 1 "\ZZ,.

2cm , 3cm s{l4cm '1 tfiffitsfltlUSSfitints<JtjU2l{ltUAl1ยง

'i:fl

&l'i:flS 2 X 4 = 8

' "" LN9ltitill'i:flS 2x4 = 8

~ti

us Sfititi':l rud mm8nm1n N1&l~'i:fl suss u

!'le~

S~ g tfiffiufi nil S~'i:fl2Lfl N1J1~ ttl ru'i:fl s 4

222

4cm ~ V

2X3X4

= 24cm 3

nJmuft§J9I : f!Hl.n 21m ~Lrl ML?)i1 ft:j ru'tfl s mndltifl,nH1..nfn~tlmti21~ l u u

GtfJw:

I I I I

,. ,/'·-------------- ... ---~

V = lwh

-----

V = Bh

=20x5xl5

=(20x5)xl5

mtnuf;;t91: f!lM21'tfl~1rlM'i~'i:i~tltinJ iff li l.ilUU 0

21~Nl '1 G'l

Ql6itSUJMdl1ftfilMnMnt!::llru B =

2l X 12.8

= 48 '1

'tfl~LLlhlnMm!::llruv =

b n ffi'tfl ~ '1

'LuHuH : f!lM21'tfl~tsLnM~tifu21~tLm'i:i '1 n.

12m

5mm

7mm

4mm

223

mn~·n~ns~mnL~ fJ~'h~ns~n'i:i

S'l

tt'i&ID(gtfl'i:fl ~ ~h~n~tsth~'i:fl ~L~ fij '1

2J MMJ~lY~3 t s gsb ;JJ1GrHlJl

t~'l:3jtg nU

tqJti'i:fl2tl '1 tt:itiD(Qttl 'i:fl2L~M1J11mstitr!£!)&tllru'i:fl~~·n~nti '1 'IJ Qn

e»

ot:»

QJ'::I

1 3

!:ltHSgtfifllS'i:fl2rlrl'i:ifibfiJ'i:ittl.fflt:'ititS'i:fl~'irlfiJfi V = - B · h ~u

: ~·n~nt!:lru'i:flst~iJi tll ru

. h b n ffi'i:fl ~ '1

" ,,"" '' '' II

: mn&a~·n~nth~tmn.n t fi1 rul B = -1 X 5 X 6 = 15

l: 8

' ' '' ''

"' <t IJ fi fn !0 ~

,0}-.,

/s I I I I

tJtriw : m n &a ~·n~nthti6H m n.n tn~ tfiQl a td ""

tintmn.ntn~ B = 7x5 l ~~~

.t:::l)

35 bnffitd.: '1

'i:fl2rlrl'i:3nnMnti::llru V=

224

·h=~x35x6=70bnffi'i:fl2'1 3

: ............. 6

....... . ', ', ', ' .... , ,

mtH:Jtsm~ht'iffll:5&sg '1 U

gugnbi:n s g Sl n&l sb i':lts ffi n:l rui:fl s run:J n.n !':lts~b tiffll§ li.l' u "'' 19 !all lj 1.

QlsHfflM ShQln

"''

V = -B · h '1

th~C91: tfilMttlru'i:llSnl

v = jnih bnrni:fl::l 0

bnm Sbn~

bnrn&Slg'i:ll:HfflMRMshr:nru

a 0

W'i171titiJ111: ?iMS1'i:ll:2tfflM (run

1t"'

3.14)

i':ltsm~bhli '1 U II n = 0

•

t Sl 8'i:fl2 t m n.n n n.n n &r:n ru

V =

2 !nr h 3

!3 x

3.14 x 3 x 8 = 75.36m

225

., ffl'ij1J"""" ~'li9 n ffl n~ ttlOl s +6

"1':

10 Sl<1J h

"'100-36

ti1H1.fltl:Hli'i::112nl r = 6 S-t:lli'ijN h = 8 tSlgffi~ 11 0.

tffHtnnniHH

=fer

liJV

3 x3.14x6

h =

x8= 301.4

!-.

wnffl'i::11~"'

'i'itnuff: tln.flSl'i::11~tfiln.n(run n:z3.14 )tirsm::nht'ifil'ijtsg"' u ~ u u G

';)

Ql I!J Â¢~

";)

r; n.n Sl t~'[J1~ tu~'li tSTIH r!Hl ttifi ~u::nh 'Lfil'ij '1

= l3cm '

12mm , w = 8mm , h = 13mm

tl.

8dm , w

= lOcm

w = 6cm

= lldm , h =

19dm '1

r; n.n Sl l~lJi~ ::n-t:l ls(ri tuLfi~L~hf2 tti ru'l::11 s ~rs::nhtLfil'ij '1

2. a

226

= 3cm ' b = 5cm

c = 7cm , h = 10cm

= 12mm , b = 7mm

7mm , h

= 15mm

~Rl:flsLfl ft5U1~L~t:J2 ft5i:HiH1 "1 tH Rrul Sl u

" "" 'i n. "~~Lnijl2liH2UHu p

J;l.

3cm

Rrul Sl '~Lnij12lb

stl ~~Lnijl ft5ru tS

tfflMnbm9 1 &sg '1 .. u I

l:fl2ffl 21cm "1 dt2UHStfflMtil:fl2

n5 55 em 2bdtS'inhHm Mnul:flS Hn d w u

Hnft5 10.5cm '1 A

" RMSltO'in9flft5~1H2 c:GiJ"

mb'lbti?il~(run n:""3.14) "1 (ElGm9 2)

riJ

u u

227

?i.

N. 57 em

&'n61 1§u ti5 tHlhH gi~ tH ttH1J fil ti bffHwl t f:HlHfl S ~

49cm

't:f!Sn~

SbnlQlflHjl

SbnlQlfi~~M

98cm

b~flllb&tirn

18cm

18cm '1

tULfflti1&'n61

198

...... ..... _______ ... ..,..,.

v v

tm n!Hnl:Hrn rutHWlfi 1

rndJb&s~b

r , z mu n.nu

AB , Be

tUb~ '1

o mnnlsmnri'h1§fl '1

?iMSl

\;)

";)

t:»~t

?i. td'lnlfn '1 ,,d_:. 9..J. hl~ut!Hlfl'i§nfin'i§~ I 1 I 11.

228

'i::ll2tStnlM'i::llS~bl b

l8n:cm Sbtd'in!.mtnn'i::llS~bl ~ l) ;w· b 3

12.

?Hl.fl2l t~Ln t{JHufi5 ts &Al n.n rfH~Lntfl m 61ffi s~ijl 12cm

13.

(run n""3.142) '1

ffi~tS,filrulffiS~ijllli 420ncm SfH'i~fdffiS~ijllli 15cm '1 t~Lntf121 3

" 216ncm 2 'i ?lrulSl&~Ln ~

14.

?lrul2lffi~fl1'i:3~&L:HlH?l!Jl

11Ul~IJlfi'i.HrlQ) u

d:itHH'i:3tH~g~~61( 9nUG~ li

1t) '1

(fN

ffi s~ffi~61tlunbH5 '1 l_j u

"'1 u

n. ?Jrul2lffi~ts~nhlttintSl8 '1

20m -- --------l

229

1H1.Qh'9nniH~ttP

ru'i::fladtL'i:Jl

som ~h

" Ul6lLMLHS~Ht-Qb'i::flSnb lJ

tffH"l.flttlrn'i::flsd~sLmijl

5m '1

?H1fi Sl 'i::fl2 8 ~Hl.fl51 b '1 ll

20.

ru18ffi~ff1hl'i:3tl5'i::fl8~'i::fl'i6itl8a5 '1 lJ l:i U II

50 I

60%t8rut8ML'i::fltl~nq~h

'1 !!Hl.flSl'i::fl2

~:HtflSl'i::fl2ttlrnt

Nrutsinb

"'1

'19b~mn110dm '1 'i9Sb2lbS'i:3ru")'i::flS li & l:i1 lJ IJ

~m &

230

13d;n '1 j:irtJlf!ll:fl~tslih-@ri ~

I I

I I I

I I I I

tfiUMil G\ g

o o

RMrinHJJHlil~~~~ras9msuJ1

Mn5

....

wg~hlf:i~ hlffi~l:flLfl~sm S1Jl't3Lfl~ u

o mg ttiHUuHllmnm 9l:f1Lm ~ sm SLfl'i:lLfl~ 0

'"I

MmJM9UrT: tsitru~ntllhl'i:3li5 !JJ

.s.

t::p

"")

M~ ntf:i1:3 s ffiu m~ 9'Ul rlflLtn n 1:l tSLlit9 M

't3li5tnStiHf:ii6i~f:ihl~Shl't3li56iudl~ '1 Um ll [.ju UllU u

ttlru~MtsitruLntllhlLfl~2J~

~fl ms

u ey

'Munfh 6'1

m9l~ ml:fl s

':1

td'ir;gn 2 hl?i'Hfll:fl s .:;C,t.J'i OS

&f:itn s ru~d rur:s:; &tll ru~ hlti~'tยง~l:fllJl ~Slj.H9 hl Q~ W

fums~m.mm ti~ ti ros9 '1

"'-

c D'

A '1

d'hm'lnhi~!'J ~tiGfliibnH~'QlS 111 u

26mmntmgm A Si:l u

39mm ntmll~ti B '1

hl' 26mm

t~ms 26

titm 0

tJ ruwJti99i:l3ti'Cifl

t~ms?

ntih

sHIDt!Jffiti ru wJti h ria~~

"'-

t~hlHhl~

~Jlb t9J r; d5ni5h~nd rutnJm tlht;~H.ti

l/1 000 '1

"'""' 2 : 2'fl1'i.JJWJ19 bSlg~:~rnt'tis9tsg'i::Jls'i::llLG1~s

1 10 000

y_ t~MHMa 1110 ooo

: t'ns9ru9M~Mt~8m~t1ti 'i::llS'i::Jl1fli::hs J/50 ooo ti 1120 ooo '1 t'ns9Hm G1 • l.i l.iot "" lj 1¢

tllflfit~rufi'i::JlLfl~s 1120 ooo 232

9ti

muntffitgJ : '2"1~1:1 ll ~ru1:flStllA'BlU1~s

!:li:Hcr~tn.fl~nn'Jru l <l l

1/80 oooshLlit~btsitrufos9

mt'os9d~'iH55t2~t!:lru~nbdru --..:> w !.! U I l.! u

somm 'i

t~~ltS'U1:flS1_Y

u Ql

eJII

!=19H' ? \1 HH1 u . tuffw: thmg1:f1U1~2 l/80 0001:flSSli5ffitYt1b trut~~Llit~b

ooomm

~ 80m

lmm

Llit~bnm24tru&~t!~ 80mx !50=

~6H

t24t tds91:fls1Y 12

ooom

~ 12km

E:!tHS81tit~bd~~ 12km ~I IJ u 6U

Wtmtffitg2 : d~dl~ u ""

tr1mt9illibtHib1:flS1tit~brJn 455km ffl'Hd~

tru2 7 sbtrn2

""'

13 '1 dhs-ltrlHns9ct:Jru1::flS1:fl~n l,.j

tHfw: thmg1:f1Ln~s 11200 ooo1:flssrumLli t24&rutdtl'i't5t~b c; W

200

OOOem

ti 2km ~

mrun ruu nHH n1i'Hli51:fl S'iUtH~ ,;, 1.1 l,j

'itit~bt24t L,

3.5em

w u

~t"-52

s 11200 ooo1::flSu1:flru'ihns 1~

lcm

t24trut'ns91:flsLlif~bnn

fos9~ 455 +2

227.5em

tti

m~run51:flstyf~b 70m 'l t~fos9&s-H

1:fl s 1:fl Hi tlls Â·1hn s l,j ct I ..;

!em 1 OOOem

- Jmm

trut'o s9 Lnfsb

1 ooomm

trutl

1:fl2SIDGl --1 ~.-l OOOem emS

- I em

trufos9 .

t~~sb 1 oooem ~:rut! '1

- ldm

trufos9

U1~sb 1 OOOdm

trutl

rJmfli :~1:f1Lniihijlru~s~m trut'ns9Ln~ nShij G&mgfos9'1:3IDI:tl~1:fl'int1JFi G

t!=l IUH hl~ !II 00

000

~s~11~

!00 ()00

tSmt!=1GltdS91:flS1:fli6itll8 __ l __ G ct l 00 000

'1 233

: 't:llLG'l~Hl 't:llssrum

lem

2 5100 em

trn

s9tnfsb

2 500 em

trutl '11

25m

tltitsg ti't:llru~G'lt u

~:rntl~ 25m

: Ll'=ltMil~fihoJtut~G'l

rut't:isSitsiQh~fit~Js

t'~.n9il.nn5;ns; ~l\5tuJ?lllilm1Yt'~.n~G'ltsitrnt~'S

4. : t'ns9tstm9tun1idl't:lls 1

u~ci~~mb~

fl dm~fithlmtfli9HH261Rfln't:llsmf1b "'"'

27em

l.i

\.151

m~nti't:llru~ntsitm'S '1 u ,

d5't:ll'iG'l li

-=-=~-=- t 21 iW't:ll liJ f1 G'l't:llS 500 000 ~

f~bt

tl b ti.

f~s9 'i

ti't:ll rufl n dm ~fir; nm~:949~~&2 G'JR nn "'

"'"'

\.151

Gn~u~ciLG1~'Hl8 27emx500000 = I3500000em

tlmsg ti't:llru~m:lm~fir;nmt u

~l35km

t2~Rrlnffi~ti~'lfl'ln~ 135km '1 ••

1 : ~nmf~btsitrnfns9ii{hnru~ru tl::llrutlumfns9~mg't:fls'Hl1G'lf::lls l.i

: d5'Hltn~s ~ r~ .n, s-1 ~: rn fn s9'Hl s l 500 = 0.06m

60em

~msg UJf~btsitrnftls9~ 60em '1

234

\.1

li c:t

dj~~tn;5n~ti~tst'os913rutl't:f12n13f15 l8.50cm G\l u 111

~Witi~tst'os9't:fls't:flrr61t:llstisns? w 1A ~

turfw: w

n13f15n~tib 18.50cm = 0:-l ~5m S1 c;:; 6\.1 l

't:flUnt:llStSti~tSlg~ O.l 85 ct 37

~o&sg 'H11.fi~Sts~btSlgfi 2 ~ 0

LVff'lJP: 9Ln~rl~'t:f12ti'i[lli5~n 225km 'i tfiu't:flru~sgm~ยง~itit1tlti2lsts4t fos9 d5t~run ~ uu ~~ I

'HILn~s 'i

1 n. 50 000

~. 80 000

lli. Ill 00 000

1/20 000

~. rhmg't:flLn~ 22l~t

tfi~nt~ fl.HS Mli5Fil;Jli5ruTI ttl13j~~fo s9~~~ ru2J't:fls u

1'Hitn~J13~13J '1

?"'

rumui ros91Jru't:fls't:f1Ul~s l/80 ooo 'i

~n.nSlti'iflrunnt~1,rut~

,u,~nf15u'iflru9Uit~n~ I

trlH'o s9 2.

343mm '1

thm~~tty~1Jli5't:fl!Ultl

tmn.nftHli't:flS~b 6km , 4.5km

st!

3.9km 'i

tJHilt!GAl

tS"Jgcrufos9t'tHli't:fls'HIU'l s 1: 75o 3.

fos91Jru't:fls't:f1Ln~s

~ 00 mf15fim~ti']tmn.ntnbl;Jruttlrn't:fls1't:f1Ln

3.5cm '1 ttit~illRGfflH21'5nb13li5ffi~t13 10 c;:; 'U GV

ooo ooo~

4cm

~n.nSltGGAlHSlg '1 GV

t s1 t ru&o s 9~-@rn rn~ ru't:fls't:fll~ ~ s

litfWJlliJ s.

52mm

; 2 00

't:flsfim~~tunt~u~tm n.n tnt! ft1 rn't:fls

Sh99t! 25rmn '1 ~n'(Yt~h1'HILntlnSht~tn~Gfil~tl%1dltfltil.'il '1

tsitrnt'os9fim~~gJh-@1Jrun u

mrw1

s't:flu;~s

'iHfWJlli5&s4trnfos9't:flsjy&~t! o.7dm st!99h 4.7dm '1

1 "' 200 000

tfil,li

ctir~nfJ

nn'fs1'Hiu;fim~

&Slg't:flSl,tit~~~fflSt~Ui?

235

thU'i:fliJl~S

l/20

OOO'i:fl!:.i9tnhtiff::lrutr:rlOrt.fjti A , B sb C ~~ctlnblJitfilMCnb I

ctirn'i:flSLdh AB

4.5cm

sb AC

5.2cm 'i

n. tiHHuWยง'iQlSi~~;~~Hitl uuuu GGu

f1b BC

trnCJ:i

2. tlrulSlTIJC~bil~ AB , AC

Sb BC tsitrn~~ij

2. 9.

~n'i:flL~~s~sfos9tGnll '1

t1u

ts-1

tffi M ABC

rul:flS'i:flL~~s

ti5

ttiUJhiihtimt151JitfilM'i:flS I

b 5.ldm ' 4.5dm sb 3.6dm

2.5dm

10.

n. ~n'i:ll:&2'lu tsinbusti ~ &

tl'i:f1Sn~hl3.75m '1 n

2. JnHnRff::lrutt11~~9m~f::lfil~ 1..; J ......, c:t u U

ttlifflruHf::l~~nb G c:t u~

2dm

2.9dm

ilh~t'J&sauiih'il~Zlhttffl~ '1

I Q

l . fJ~tlhl1Jbl:tlb~hlS I

t s g til ri nh ff1 n b~ ru I

tfl~u u

1.1

hfi~tS8tiU u

SlJ:irut~}5~S1JhiJ1~ ~ I

&t::i

g ?

D G

236

t=~J