1

ku () _________________________ úNd. wxlh () __________________

ishÆ m%Yak j,g fuu m%Yak m;%fhau ms<s;=re imhkak'

A fldgfia wxl 1 isg 10 tla tla m%Yakhg ,l=Kq 1 ne.skao" wxl 11 isg 30 f;la m%Yak j,g ,l=Kq 2 ne.skao B

fldgfia tla tla m%Yakhg ,l=Kq 10 ne.skao ysñfõ'

A fldgi

1. a2 + 10a + 25 mQ¾K j¾.hla f,i ,shkak'

2. 0.75 m%;sY;hla f,i olajkak'

3. log381ys w.h fidhkak'

4. iDcqfldaKdi%hl m<, x cm fõ. tys È. m<, fuka fo.=Khls. mßñ;sh ioyd x weiqßka m%ldYkhla

f.dvk.kak'

10 fYa%Ksh ld,h( meh 2 hs

fojk jdr úNd.h - 2016

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.Ks;h - I

கணிதம் - I

Mathematics - I

10 M I

2

5. re'150 la jákd fmd;la úl ණීfï§ 8 ] l jÜgula fok ,§' fmd; úl=KQ ñ, lSho@

6. § we;s f;dr;=re j,g wkqj ACB fidhkak'

7. √729 idOdrK l%ufhka ,nd.kak'

8. ( x + 5 ) ( x – 7 ) m%idrKh lrkak'

9. 2x, 5x2, 2(x - 3) ys l=vdu fmdÿ .=Kdldrh ,shkak'

10. log212 + log220 - log215 w.h fidhkak'

11. PQR ;%sfldaKhl QR > PQ > PR fõ kï" úYd,u fldaKh kï lrkak'

3

12. rEm igyfka § we;s f;dr;=re j,g wkqj AOP ;%sfldaKh yd AOQ

;%sfldaKh wx.iu jk wjia:dj ,shkak'

13. lg 2 = 0.3010 o" lg 3 = 0.4771 o Ndú;d lr lg 6 ys w.h fidhkak'

14. jD;a;hla iudk fldgia 8 lg fnod we;s whqre rEm igyfka oelafõ tu jD;a;fha

j¾.M,h 1000cm2 kï" wÿre l< fldgfia j¾.M,h fidhkak'

15. l%Svd lKavdhul idudðlhkaf.a ialkaO fuu cd, f¾Lfhka

ksrEmKh fõ nr bis,Sfï l%Svdj ioyd fuu lKavdhfï isák 55kg g jvd jeä ialkaOhla we;s idudðlfhda iyNd.S fj;s tu l%Svdjg

iyNd.S úh yels jeäu idudðlhska ixLHdj lSho @

16. 3x – y = 8

x + 5y = 12 fuu iu.dó iólrK fkdúi|d (x + y) ys w.h fidhkak'

4

17. § we;s fjkarEmfha w÷re lr olajkak'

18. ;dmamhla ne£ug ñksiqka 8 fokl=g Èk 12 la .;úh' tu ld¾hh Èk 6 lska ksu lsÍug ñksiqka lS

fokl= fhoúh hq;=o@

19. 14] iq¿ fmd,shg re' 3000 la Khg .;a ñksfila re' 4260 la f.jd Kfhka ksoyia jkafka fldmuK

ld,hlg miqjo@

20. iq¿ lrkak'

21. PQRS iudka;rdi%fha QR=QT jkfia QT we| we;' SPQ

= 750 fõ'

(i) PS = QT nj fmkajkak'

(ii) TQR w.h .Kkh lrkak'

5

22. fjkarEmfha § we;s f;dr;=re wkqj" l=,lh wjhj

iys;j ,shd olajkak'

23. frdïnihl we;s úfYaI ,laIK folla ,shkak'

24. § we;s rEmfha x yd y fidhkak'

25. ABCD iudka;rdi%fha AB mdoh E f;la È.a lr we;' ADC =

1000 kï a yd b w.hka fidhkak'

26. x2 – 9 yd ( x + 1 )( x – 3 ) ys l=vdu fmdÿ .=Kdldrh fidhkak'

6

27. iq¿ lrkak'

28. mshqñldf.aa mshd wehg fufia lshhs' "oeka uf.a jhi Tfí jhi fuka y;r .=Khls' jir 8lg

fmr" uu Tn fuka fodf,dia .=Khla jhia ùñ'" iu.dó iólrK weiqfrka mshqñldf.aa yd mshdf.a

jhi fjk fjku fidhkak'

29. rEmfha § we;s f;dr;=re wkqj"

(i) RQ È.

(ii) QRS ys úYd,;ajh

(iii) PQR ys úYd,;ajh fidhkak'

30. iq¿ lrkak'

7

B fldgi

ishÆ m%Yak j,g fuu m%Yak m;%fhau ms<s;=re imhkak'

tla m%Yakhlg ,l=Kq 10 ne.ska ysñfõ'

1. NdKav ksIamdolfhla miq.sh udifha ;u ksIamdokj,ska 3 / 5 la fj<ofmd<g heùh b;sßfhka 1 / 2 la

ksjfia§u úl=Kd.ekSug Tyqg yelsjQ w;r NdKav 50la muKla tu udifha ksjfia b;sß úh

(i) fj<ofmd<g heùfuka miq b;sßjQfha ksIamdÈ; NdKavj,ska ljr Nd.hlao@

(ii) uq¿ ksIamdokfhka ljr fldgila ksjfia§u úl=Kd.ekSug yels jQfha o@

(iii) tu udifha uq¿ ksIamdokh fldmuKo@

2. rEmfha oelafjkafka iDcqfldaKdi%dldr yeve;s f.ñÿ,l's tys È. me;a;g udhsï jk fia wrh 9m jk 350

flakao%sl LKav 2l u,a jjd we;' b;sß fldgfia ;Kfld< jjd we;'

(i) f.ñÿf,a È. fidhkak'

(ii) f.ñÿf,a m<, 10m kï tys j¾.M,h fidhkak'

(iii) u,a jjd we;s fldgfia j¾.M,h fidhkak'

8

(iv) ;Kfld< jeùug 1m2 lg re'95 la úhoï jqKs kï ta ioyd jeh jQ uqo, fidhkak'

3. 10 fYa%Ksh bf.kqu ,nk isiqka 48 fofkl=f.ka ;ud leu;s l%Svdj ms<snoj úuiSfï§ ,nd.;a f;dr;=re

ksrEmKh lrk ,o wiïmQ¾K fjka rEmhla my; oelafõ

A = {l%slÜ l%Svdjg leu;s isiqka}

B = {fjd,sfnda,a l%Svdjg leu;s isiqka)}

(i) l%Svd 2ka tllg j;a leu;s ke;s isiqka .Kk lSho@

(ii) fjd,sfnda,a l%Svdjg leu;s isiqka .Kk 12la kï l%slÜ yd fjd,sfnda,a j,g leu;s isiqka .Kk lSho@

(iii) wyUq f,i f;dard.;a isiqfjla hg;a msßifhka tla l%Svdjlgj;a leu;s wfhl= ùfï iïNdú;djh

fidhkak'

(iv) m%foaYh by; fjka rEmfha wÿre lr olajkak'

(v) l%Svd 2lg u wlue;s isiqka oelafjk m%foaYh l=,l wxlkfhka ,shkak'

4. ksjil jd¾Isl jákdlu re' 80000 la f,i ;lafiare lr we;' k.r iNdj jßmkï whlrkq

,nkafka jd¾Isl jákdlñka 6] ne.sks'

(i) wjqreoaolg f.úh hq;= jßmkï uqo, fidhkak'

(ii) ld¾;=jlg f.úh hq;= uqo, fidhkak'

9

(iii) jd¾Isl jßmkï uqo, tu jif¾ ckjdß 31 Èkg fmr f.jkafka kï 10] l jÜgula ,efí' túg

f.úh hq;= uqo, lSho@

(iv) fuu ksji l=,shg §fuka ,o jd¾Isl uqo,ska 20] la ksjfia w¨;ajeähd lghq;= i|ydo úhoï lrhs'

úhoï lr jßmkï nÿo ckjdß 31 g miq f.ùfuka ksfjiaysñhdg re' 43200 la b;sß úh'

(v) w¿;ajeähdjg úhoï l, miq ksjfia jd¾Isl l=,sfhka fldmuK uqo,la b;sßfõo@

(vi) ksji l=,shg §fuka j¾Ihlg Tyqg ,efnk wdodhu fldmuKo@

(vii) ksjfia udisl l=,sh fldmuKo@

5. 10 fYaK%sfha isiqka 120 foklf=.ka wOHdmk pdßldjla hdug leu;s ia:dk ms<sn|j úuid ,nd .;a

f;dr;=re my; ±lafõ'

(i) fuu f;dr;=re jg m%ia:drhlska ±laùu i|yd flakaøSl LKavfha fldaKh .Kkh lrkak'

10

(ii) tuÕska jg m%ia:drh w¢kak'

(iii) fï iu. we;s jg m%ia;drfhka isiqka 36 la isák mka;shl Tjqka mdi,g

meñfKk wdldrh ±lafõ' ld¾ j,ska meñfKk isiqka olajk fldaKh

2000 kï tu isiqka .Kk fidhkak'

(iv) jEka j,ska meñfKk isiqka .Kk 8 kï tu isiqka olajk flakaøSl LKavfha fldaKh wxYl lSho@

11

ie,lsh hq;=h () m<uq m%Yakh yd ;j;a m%Yak y;rlg ms<s;=re imhkak' ms<s;=re fjku lvodishl imhkak'

1.

ku () _________________________ úNd. wxlh () __________________

A flgiska m%Yak 5 l=; a B fldgiska m%Yak 5 l=;a we;=¿j m%Yak 10 muKla ms<s;=re imhkak'

tla m%Yakhlg ,l=Kq 10 ne.ska ysñfõ'

A fldgi

1. tla;rd úÿ,s WmlrKhl wdkhk ñ, re' 40000 ls' fuh wdkhkh lsÍfï§ f¾.=j 25] l ;Sre noaola

whlrkq ,efí' fuu úÿ,s WmlrKh úlsKSfï§ 40] l ,dNhla ,efnk mßÈ ñ, ,l=Kq lrkq ,efí'

w;amsg uqo,g úlsKSfï§ 5] l jÜgula fokq ,efí'

(i) ;Sre nÿ iys;j úÿ,s WmlrKfha ñ, lSho@

(ii) fuu WmlrKfha ,l=Kq l, ñ, lSho@

(iii) w;amsg uqo,g fuu WmlrKh .ekSfï§ mdßfNda.slhdg ,efnk jÜgu lSho@

(iv) túg WmlrKh úl=Kk ñ, lSho@

(v) fjf<ka|dg túg ,efnk ,dNh lSho@

(vi) fjf<ka|dg ,efnk ,dN m%;sY;h lSho@

2.

(i)

a) úi|kak' 18 – 5 (x + 1) = 3 (x – 1)

b) úi|kak'

(ii) r: .d,l ;%sfrdao r: yd fudag¾ nhsisl,a 35 la kj;d we;' fuu foj¾.fhau we;s uq¿ frdao .Kk

90 ls'

a) ;%sfrdao r: .Kk x o" fudag¾ nhsisl,a .Kk y o f,i f.k iu.dó iólrK hq.,la

f.dvkÕkak'

b) th úi£fuka r: .df,a we;s ;%sfrdao r: .Kk yd fudag¾ ihsl,a .Kk fjk fjku

fidhkak'

3.

10 fYa%Ksh ld,h( meh 2 ½ hs

fojk jdr úNd.h - 2016

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.Ks;h - II

கணிதம் - II

Mathematics - II

10 M II

12

(i) io,s yÈis uqo,a wjYH;djhla ksid re' 20000 l uqo,la ,nd.;af;a 10] l jd¾Isl iq¿ fmd,shla

iu. jir wjidkfha uq¿ uqo,u f.jk fmdfrdkaÿj wkqjh' tfy;a jir wjidkfha tu uqo, f.jd

.ekSug fkdyelsjQ neúka Tyq Kh uqo,ska nd.hlao kshñ; fmd,sho f.jd ouk ,§' Tyq b;sß uqo,"

fmd,sho iu. fojk wjqreoao wjidkfha re' 11200 f.jd Kfhka ksoyia úh'

a) m<uq wjqroao wjidkfha Tyq f.jQ fmd<sh lSho@

b) m<uq wjqreoao wjidkfha Tyq f.úh hq;= uqo, lSho@

c) fojk wjqreoao wjidkfha Tyq f.jk ,o fmd,sh lSho@

d) fojk wjqreoao wjidkfha b;sßjQ Kh uqo, i|yd wh l, fmd,S wkqmd;h 12] nj fmkajkak'

(ii) mqoa.,fhl=f.a jd¾Isl wdodhu 1 200 000 ls' m<uq re' 400 000 wdodhï noafoa ksoyia jk w;r

B,Õ re' 400 000 i|yd 4] lao B<Õ 400 000 i|yd 8] l noaola rch wh lrhs' Tyqf.a

wdodhï noao .Kkh lrkak'

4.

rEmfha olajd we;af;a iDcqfldaKsl ;%sfldaKdldr yrialvla iys; msi%auhls'

(i) § we;s o;a; wkqj m%siaufha uq¿ mDIaG j¾.M,h i|yd ùÔh ml%Ykhla f.dvkÕkak'

(ii) x = 12 cm , y = 5 cm kï" m j, w.h .Kkh lrkak'

(iii) m%siaufha uq¿ j¾.M,h 540cm2 kï" m%siaufha È. ^ l & .Kkh lrkak'

(iv) m%siaufha mßudj x , y , l weiqßka ,shkak'

(v) ta wkqj m%siaufha mßudj .Kkh lrkak'

5.

(i) lg 2 = a iy lg 7 = b kï" nj fmkajkak'

(ii) w.h fidhkak'

log 10 25 – log 10 4 + log 10 8 – log 10 5 + 2

(iii) ,>q.Kl j.= Ndú;fha w.h fidhkak'

13

6.

(i) my; oelafjk jg m%ia;drfhka" ue;sjrKhl § mlaI y;rla

,nd .;a Pkao m%udK oelafõ' jeäu Pkao m%udKhla ,nd .;a

mlaIhg ,enqKq uq¿ Pkao m%udKh 9300 ls'

a) mlaI 4u ,nd .;a Pkao ixLHdj fldmuK o@

b) f;jk ;ek ,nd .;a mlaIh ,nd .;a uq¿ Pkao ixLHdj

fldmuK o@

c) y;rjk ;ek ,enQ mlaIh ,nd .;a Pkao m%udKh uq¿ Pkao

m%udKfhka Nd.hla f,i olajkak'

d) jg m%ia;drfha § we;s o;a; weiqfrka" fojk ;ek ÈkQ mlaIh

,nd .;a Pkao ixLHdj uq¿ Pkao ixLHdfõ m%;sY;hla f,i olajkak'

(ii) pkaøhd u; fuka yh .=Khl .=re;ajdl¾IK n,hla mDÓúh u; mj;S' tA ksid" pkaøhd u; §

jia;=jl nr yd mDÓúh u; § tu jia;=fõ nr w;r wkqmd;h 1 : 6 fõ' mDÓúh u; § 54

kgla jQ ..k.dñfhl=f.a nr" pkaøhd u; § fldmuK fõ o@

B fldgi

7.

a) idOl fidhkak'

(i) x2 + 2x _ 15

(ii) 2x2 + x - 3

(iii) 9x2 - 25

b) iSkq ;=kla tljr kdoù bkamiq tlla ms<sfj,ska ñks;a;= 12" ñks;a;= 18 yd ñks;a;= 24 lg jrla

kdofõ' fuu iSkq ;=k kej; tljr kdo jkafka meh lShlg miqjo@

c) iq¿ lrkak'

8. ljlgqj cm/mm mßudKh iys; ir, odrhla muKla Ndú; lrñka" fuu ks¾udKh meyeÈ,s f,i

ks¾udKh lr olajkak'

14

(i) AB = 10 cm , BAC = 300 , ABC = 600 jk ABC ;sf% ldaKh ks¾udKh lrkak'

(ii) ABCD iudka;rdi%hla jk fia o" D ,CIh AC f¾Ldfõ B msysá me;a;g úreoaO me;af;a msysgk mßÈ

ABCD iudka;rdi%h iïmQ¾K lrkak'

(iii) A yd B ,laIH j,g iuÿßka msysgk ,laIHhkaf.a m:h ks¾udKh lrkak'

(iv) tu m:h AB f¾Ldj fþokh jk ,laIH O f,i f.k O flakaøho OA wrho jk jD;a;h ks¾udKh

lrkak'

(v) ABC = ADC jkafkao fya;= olajkak'

9.

a)

(i) my; fjkarEm igyka w÷re lr we;s fmfoi l=,l wxlkfhka ,shkak'

(ii) hk l,= lh my; fjka rEm igyfka w÷re lr olajkak'

b) wjqreÿ l%Svdjlg iyNd.s jQ orejka 35 fofkl= w;ßka 19la msßñ <uhska jQ w;r" 17 fofkla wjqreÿ

15g jeä h' wjqreÿ 15g wvq .eyekq <uhska .Kk 6 ls'

(i) by; f;dr;=re iqÿiq fjkarEm igykl olajkak'

(ii) wjqreÿ 15g jeä msßñ <uhska .Kk lSh o@

15

10. ABC ;%sfldaKfha AB = AC fõ' yd fldaKj, iuÉfþol O ys§ yuq fõ'

Èlal, AO g D ys § BC yuq fõ'

(i) BOC iuoaúmdo ;%sfldaKhla nj

(ii) nj

(iii) AD, BC g ,ïn nj idOkh lrkak'

11.

a) rEmfha oelafjk ABCD yd CDEF hkq iudka;rdi% 2ls

(i) ADE = BCF nj idOkh lrkak

(ii) ADE Δ yd BCF Δ wx.iu jk nj idOkh lrkak

(iii) ABFE p;=ri%h iudka;rdi%hla nj idOkh lrkak

b) frdïnihl yd iup;=ri%hl we;s wiudklï folla ,shkak'

12.

-End of Paper-

“ f,dalh fjkia lsÍug Ndú;d l< yels n,j;a u wdhqOh wOHdmkhhs ”

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