V‚U;hVfmUd;gVfkUdjVys;s Ug - eduLanka Online … ·  · 2011-09-2818'lg2=x olg3=y...

2
18' o o úg ljr f,i m%ldY l, yelso@ lg2=x lg3=y lg 12 ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ' ' ' ' ' 19' tla;rd >kldN yev;s fmÜáhl Odß;dj 231 fõ' fuu fmÜáfha È." m<," Wi 1 ne.ska jeä l< fyd;a Odß;dkh jeä ùu fldmuKo@ ' 78 ' 153 ' 231 ' 384 ' 400 20' È. 20 jQ lïì lene,a,la folg lmd iup;=ri% folla iod .kakd ,È' fuu iup;=ri% fofla j¾.M,h 25 kï" lemQ lïì len,s fofla È. fidhkak' ' 18" 10 ' 8"20 ' 12" 16 ' 9" 25 ' 13" 15 21' k.r fol w;r ÿr fõ' k.rfhka iuka mdmeÈhl msg;aj k.rhg meñfka' k.rfhka iuka msg;ajkjd;a iu.u k.rfhka lu,a h;=re meÈhl ke.S iuka yuq jQ jydu kej; fj; meñk wdmiq yeÍ kej; iuka yuq ùug hhs' Tyq yuq jQ jydu kej; wmiq yeÍ fj; meñfka' fuu l%shdj wlkavj lu,a isÿ lf,a kï iuka fj; meñfkk úg lu,a .uka lr we;s ÿr jkqfha " mdmeÈfha fõ.h 20 jk w;r h;=re meÈfha fõ.h fõ' ' 40 ' 70 ' 80 ' 100 ' 140 22' tla;rd iúÈ nyq wi%hl wNHka;r fldaKhl w.h 150 fõ' ty mdo .Kk lSho@ '3 '6 '9 ' 12 ' 15 23' uu ,Õ we;s uqo,g jvd u,a,S ,Õ we;s uqo, fo.=khlg jvd re' 7 la jeäh' wm fofokd ,Õ we;s uqof,a fo.=kh 314 la fõ kï uu yd u,a,S ,Õ we;s uqo,a ms<sfj,ska re" ' 50" 107 ' 107" 50 ' 214" 100 ' 100" 214 ' 114" 200 24' iu mdo ;%sfldaKhl mdohl È. fi( ñ( 10 ls' ;s%fldaKfha j¾.:,h j¾. fi( ñ( j,ska lSAho@' ' 30 ' 25 ' 25 3 ' 60 ' 100 25' my; ±fjk tAjdhska l=,lhla jkqfha" ' Tn mka;sfha ,iaik YsIHdjka ' .fï uy; ñksiaiq ' mka;sfha fi(ó( 120 g jvd Wi <uhs ' mka;sfha oCI isiqka ' fyd| <uhs 2xy 2y+x 2x+y x +y xy m m m 2 2 3 3 m m A, B 40 km A B A B B B B km km h 70 km h 2 -1 -1 Ö VUVUVUVU .;h fmd;g fkdj ys;g .;h fmd;g fkdj ys;g .;h fmd;g fkdj ys;g .;h wñysß fkdj" .;h iqkaorh" olskakg tA iqkaor;ajh" tA iqkaor;ajh ;=,ska Ôú;h Èkkakg mq¿jk'''" ksjerÈ uÕ fmkaùu" W;aiyh yd Wkkaÿj ;=,ska'''' .;fha ixl,am" .;fha udj; - ±k .kak" ±l .kak W;aiyjka; Tn tkak''''' iqkaor jQ .;fha wiajekak ,efnkq ksh;h'''' .;h wñysß fkdj" .;h iqkaorh" olskakg tA iqkaor;ajh" tA iqkaor;ajh ;=,ska Ôú;h Èkkakg mq¿jk'''" ksjerÈ uÕ fmkaùu" W;aiyh yd Wkkaÿj ;=,ska'''' .;fha ixl,am" .;fha udj; - ±k .kak" ±l .kak W;aiyjka; Tn tkak''''' iqkaor jQ .;fha wiajekak ,efnkq ksh;h'''' .;h wñysß fkdj" .;h iqkaorh" olskakg tA iqkaor;ajh" tA iqkaor;ajh ;=,ska Ôú;h Èkkakg mq¿jk'''" ksjerÈ uÕ fmkaùu" W;aiyh yd Wkkaÿj ;=,ska'''' .;fha ixl,am" .;fha udj; - ±k .kak" ±l .kak W;aiyjka; Tn tkak''''' iqkaor jQ .;fha wiajekak ,efnkq ksh;h'''' BSc. (Physical - Kelaniya) BSc. (Physical - Kelaniya) (Pure Mathematics / Statistics & Computer Science / Chemistry) (Pure Mathematics / Statistics & Computer Science / Chemistry) TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected] TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected] BSc. (Physical - Kelaniya) (Pure Mathematics / Statistics & Computer Science / Chemistry) TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected]

Transcript of V‚U;hVfmUd;gVfkUdjVys;s Ug - eduLanka Online … ·  · 2011-09-2818'lg2=x olg3=y...

Page 1: V‚U;hVfmUd;gVfkUdjVys;s Ug - eduLanka Online … ·  · 2011-09-2818'lg2=x olg3=y oúglg12ljrf,im%ldYl,yelso@ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹

18' o o úg ljr f,i m%ldY l, yelso@lg 2 = x lg 3 = y lg 12

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸ ¸¸

¸¸¸ ¸¹

¹

' ' ' ' '

19' tla;rd >kldN yev;s fmÜáhl Odß;dj 231 fõ' fuu fmÜáfha È." m<," Wi 1

ne.ska jeä l< fyd;a Odß;dkh jeä ùu fldmuKo@

' 78 ' 153 ' 231 ' 384 ' 400

20' È. 20 jQ lïì lene,a,la folg lmd iup;=ri% folla iod .kakd ,È' fuu iup;=ri%

fofla j¾.M,h 25 kï" lemQ lïì len,s fofla È. fidhkak'

' 18" 10 ' 8"20 ' 12" 16 ' 9" 25 ' 13" 15

21' k.r fol w;r ÿr fõ' k.rfhka iuka mdmeÈhl msg;aj k.rhg

meñfka' k.rfhka iuka msg;ajkjd;a iu.u k.rfhka lu,a h;=re meÈhl ke.S

iuka yuq jQ jydu kej; fj; meñk wdmiq yeÍ kej; iuka yuq ùug hhs' Tyq yuq jQ

jydu kej; wmiq yeÍ fj; meñfka' fuu l%shdj wlkavj lu,a isÿ lf,a kï iuka

fj; meñfkk úg lu,a .uka lr we;s ÿr jkqfha "

mdmeÈfha fõ.h 20 jk w;r h;=re meÈfha fõ.h fõ'

' 40 ' 70 ' 80 ' 100 ' 140

22' tla;rd iúÈ nyq wi%hl wNHka;r fldaKhl w.h 150 fõ' ty mdo .Kk lSho@

' 3 ' 6 ' 9 ' 12 ' 15

23' uu ,Õ we;s uqo,g jvd u,a,S ,Õ we;s uqo, fo.=khlg jvd re' 7 la jeäh' wm

fofokd ,Õ we;s uqof,a fo.=kh 314 la fõ kï uu yd u,a,S ,Õ we;s uqo,a ms<sfj,ska re"

' 50" 107 ' 107" 50 ' 214" 100 ' 100" 214 ' 114" 200

24' iu mdo ;%sfldaKhl mdohl È. fi( ñ( 10 ls' ;s%fldaKfha j¾.:,h j¾. fi( ñ( j,ska

lSAho@'

' 30 ' 25 ' 25 3 ' 60 ' 100

25' my; ±fjk tAjdhska l=,lhla jkqfha"

' Tn mka;sfha ,iaik YsIHdjka ' .fï uy; ñksiaiq

' mka;sfha fi(ó( 120 g jvd Wi <uhs ' mka;sfha oCI isiqka

' fyd| <uhs

2 x y 2y + x 2x + y x + y x y

m m

m

2 2

3

3

m

m

A, B 40 km A B

A B

B

B B

km

km h 70 km h

2

-1 -1

0

Ö

VUVUVUVU.‚;h fmd;g fkdj ys;g.‚;h fmd;g fkdj ys;g.‚;h fmd;g fkdj ys;g

.‚;h wñysßfkdj".‚;h iqkaorh"olskakg tA iqkaor;ajh"tA iqkaor;ajh ;=,skaÔú;h Èkkakgmq¿jk'''"

ksjerÈ uÕ fmkaùu"W;aiyh yd Wkkaÿj;=,ska''''

.‚;fha ixl,am"

.‚;fha udj; -±k .kak" ±l .kakW;aiyjka;Tn tkak'''''

iqkaor jQ .‚;fhawiajekak ,efnkqksh;h''''

.‚;h wñysßfkdj".‚;h iqkaorh"olskakg tA iqkaor;ajh"tA iqkaor;ajh ;=,skaÔú;h Èkkakgmq¿jk'''"

ksjerÈ uÕ fmkaùu"W;aiyh yd Wkkaÿj;=,ska''''

.‚;fha ixl,am"

.‚;fha udj; -±k .kak" ±l .kakW;aiyjka;Tn tkak'''''

iqkaor jQ .‚;fhawiajekak ,efnkqksh;h''''

.‚;h wñysßfkdj".‚;h iqkaorh"olskakg tA iqkaor;ajh"tA iqkaor;ajh ;=,skaÔú;h Èkkakgmq¿jk'''"

ksjerÈ uÕ fmkaùu"W;aiyh yd Wkkaÿj;=,ska''''

.‚;fha ixl,am"

.‚;fha udj; -±k .kak" ±l .kakW;aiyjka;Tn tkak'''''

iqkaor jQ .‚;fhawiajekak ,efnkqksh;h''''

BSc. (Physical - Kelaniya)BSc. (Physical - Kelaniya)(Pure Mathematics / Statistics & Computer Science / Chemistry)(Pure Mathematics / Statistics & Computer Science / Chemistry)

TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected]: 071-6341436 / 078-6050650 / E-Mail: [email protected]

BSc. (Physical - Kelaniya)(Pure Mathematics / Statistics & Computer Science / Chemistry)

TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected]

Page 2: V‚U;hVfmUd;gVfkUdjVys;s Ug - eduLanka Online … ·  · 2011-09-2818'lg2=x olg3=y oúglg12ljrf,im%ldYl,yelso@ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹ ¹ ¸ ¸¸ ¸¸¸ ¸¹

08'olajd we;s iup;=ri%fha me;a;l È. 7 kï

jD;a;fha w÷re lr we;s fldgfia j¾.M,h lSho@

09' tla;rd Rcq fldaKS ;%sfldaKhl fldaKfha w.h } 5$12 fõ' fuys

ys w.h jkqfha"

10' j¾. iólrKfha uQ, jkqfha"

cm

x + 4x = 0

cm

tan

2

¸' 12 ¸¸' 28 ¸¸¸' 49 ¸¹' 75

¹' 77

¸ 12$5 ¸¸ 12$13 ¸¸¸ 13$12 ¸¹ 13$5 ¹ 5$13

¸ -4 fyda 4 ¸¸ 4 fyda 0 ¸¸¸ -4 fyda 0 ¸¹ 4 fyda 4 ¹ 4 mu‚

¸ 0 ¸¸ 1 ¸¸¸ 2 ¸¹ 3 ¹ 4

¸ 17'5 ¸¸ 35 ¸¸¸ 70

¸¹ 105 ¹ lsj fkdyel

¸ 2 ¸¸ 3 ¸¸¸ 5 ¸¹ 6 ¹ 12

¸ 3 ¸¸ 5 ¸¸¸ 8 ¸¹ 13 ¹ 20

¸ 3$2" 0 ¸¸ 2$3" 0 ¸¸¸ 3 2" 1 ¸¹ 3$2 ¹ 0" 2$3

¸ 9 ¸¸ 10 ¸¸¸ 15 ¸¹ ¹ 40

¸ f.a Wml=,lhls ¸¸ f.a Wml=,lhls

¸¸¸ f.a wjhjhls ¸¹ f.a wjhjhls ¹ lsis;a fkdfõ'

q tan tan

A B = , n(A) = 8, n(B) = 5 n(A B)

A B B C

A C

"a B"

a, B B , a

a, B B, a

q q

Ç f È

Î

' ' ' ' '

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11' kï ys w.h fidhkak'

' ' ' ' '

12' ys w.h wxYl lSho@

' ' '

' '

13' fofla ;=k kHdihla 2 ka .=K l< úg ,efnk kHdifha wjhj ixLHdj lSho@

' ' ' ' '

14' kï lSho@

' ' ' ' '

15' ir< f¾Ldfõ wkql%ukh yd wka;#Lkavh ms,sfj<ska olajd we;af;a@

' ' ' $ ' 0" '

16' k.rfha isg k.rhg hdug ud¾. 5 la fõ' k.rfha isg k.rhg hdug ud¾. 4

ls' kr.fha isg k.rhg mqoa.,fhl=g wdldr lShlg .uka l< yelso@

' ' ' ' 20 '

17' fuys f;areu l=,l weiqfrka m%ldY l, úg'

' '

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2

log x = 0 x

x

2y = 3x

3

350

8 miq.sh Èkl ksu,af.a jegqm wu;r §ukd iuÕ re' 425 ls' ksu,af.a Èkl jegqm wu;r

§ukd j,g jvd re' 75 lska jeäh'

01' ksu,af.a uQ,sl jegqm lSho@

' re' 75 ' re' 150 ' re' 175 ' re 250 ' re 275

02' ksu,a ,enQ wu;r §ukdj lSho@

¸ ¸¸ ¸¸¸ ¸¹ ¹

¸' re' 75 ¸¸' re' 150 ¸¸¸' re' 175 ¸¹' re 250 ¹' re 275

¸' re' 500 ¸¸' re' 1000 ¸¸¸' re' 2000 ¸¹' re 3000 ¹' re 4000

¸' 5"5 ¸¸' 6"5 ¸¸¸' 12"10 ¸¹' 10"12 ¹' 8"4

¸' 1$3 ¸¸' 3 ¸¸¸' 2$3 ¸¹' 3$2 ¹' 2

¸' 20 ¸¸' 40 ¸¸¸' 60 ¸¹' 80 ¹' 100

¸' 4 ¸¸' 8 ¸¸¸' 10

¸¹' 12 ¹' 20

03' msfhla ;u mq;=ka fofokd w;r re' 6000 la fnod ÿkafka f;jeks mq;dg re' 100 ,efnk

úg fojeks mq;dg re' 200la o" m<uq jekakdg re' 300 la o jk mßÈ fõ' fojekakdg

,enqKq uqo, fldmuko@

04' lvhl lsß melÜ 400g yd 500g melÜ f,i we;' lvfha lsß melÜ 11 l lsß 5 úks

kï 400g yd 500g melÜ .Kk ms<sfj,ska olajd we;af;a"

05' tAldldrj .,k .Õl by,g fndaÜgqjlg ls(ó( 2l ÿrla hdug meh 03la o tu ÿr kej;

my, tAug meh 1 la o jeh fõ' .Õ .,k fõ.h j,ska fidhkak'

06' tlu ÈYdjg .uka lrk ldrhla g%la r:hla Wfoa 8'00 g biair lrhs' ldrfha fõ.h

60 o g%la r:fha fõ.h 40 o kï Wfoa 10'00 jk úg jdyk fol fldmuk

ÿr mr;rhlska msysghso@

07' olajd we;s f;dr;=re wkqj iudka;rdi%fha ±lafjk

ys È. jkqfha "

kg

km h

km h km h

cm

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xx 8cm

10cm

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9" 10" 11".‚;his;kak .Ks;h - 01 ld,h úkdä 50

ieliqu( wfia, ksYaYxlBSc. (Maths-Kelaniya)

.e,fmk ms<s;=r f;darkak'

wñysß jQ .‚;fha iqkaor;ajh" Wkkaÿfjka olskak''''' tkak - .‚;h iqkaorhs 1 .‚;h lKavdhï yd ;ks mka;s i|yd úuiSï 071-63 414 36 $ 078-60 50 650

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