Maths are easy 5

.Ks;h myiqfjka - 5
ixLHdkh
.Ks; fomd¾;fïka;=j
úµd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
Y%S ,xldj

.Ks;h myiqfjka - 5
ixLHdkh
úµd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
Y%S ,xldj
i

10-11 fY%aKs i|yd
.Ks;h myiqfjka
ixLHdkh
© cd;sl wOHdmk wdh;kh
m<uqjk uqo%Kh 2014
cd;sl wOHdmk wdh;kh
uyr.u
Y%S ,xldj
uqøKh ( uqøKd,h
cd;sl wOHdmk wdh;kh
uyr.u
ii

fmrjok
mdi,aj, l%shd;aul jk úIhud,dj ;=< .Ks; úIhg iqúfYaIs ia:dkhla ysñ fõ' tfia jkafka
.Ks;h úIh wksjd¾h úIhhla ùu fuka u wmf.a Ôú;fha fndfyda wjia:dj, § w;HjYH
ixl,amj,ska iu;aú; jQ úIhhla ksid h'
.Ks;h iïnkaO j isiqkaf.a idOk uÜgï ms<sn| t;rï i;=gqodhl ;;a;ajhla fkdue;s nj
miq.sh j¾I .Kkdjl u w'fmd'i' ^id'fm<& úNd.fha m%;sM, úYaf,aIKj,ska ukdj meyeÈ,s
fõ' ishhg mkylg wdikak isiq m%;sY;hla wiu;a ù we;s nj Wla; úYaf,aIK fmkajd fohs'
miq.sh fojir ;=< hï uÜgulska isiq idOk uÜgï by< .sh o th o t;rï m%udKj;a
fkdfõ'
fuu úIhfhys isiq idOk uÜgï wju ùu i|yd úúO idOl n,md we;' fuys§ úIh
flfrys we;s wkHjYH ìh" m%udKj;a .Ks; .=re msßila fkdue;slu" iuyr .=rejrekaf.a
úIh oekqu m%udKj;a fkdùu iy WÑ; bf.kqï b.ekaùï l%uj, we;s wvqmdvq hk idOl
m%Odk fldg oelaúh yels h'
by; i|yka ndOl ;;a;aj wju lr isiqkaf.a .Ks; ixl,am ms<sn| j we;s oekqu iy
yelshd jeä ÈhqKq lr .Ks; wOHdmkfha .=Kd;aul ixj¾Okhla Wfoid hk wruqK
fmroeß j —.Ks;h myiqfjka˜ fmd;a fm< rpkd lr we;'
1' .Ks;h myiqfjka - 1 ixLHd
2' .Ks;h myiqfjka - 2 ñkqï
3' .Ks;h myiqfjka - 3 ùc .Ks;h
4' .Ks;h myiqfjka - 4 cHdñ;sh
5' .Ks;h myiqfjka - 5 ixLHdkh
6' .Ks;h myiqfjka - 6 l=,l yd iïNdú;dj
2010 j¾Ifha § Y%S ,xld úNd. fomd¾;fïka;=j úiska m%ldYhg m;a lrk ,o w'fmd'i'
^id'fm<& .Ks; úIhfha m%;sM, úYaf,aIKhg wkqj" ld¾h idOk o¾Ylh wju l,dmj,ska
uq`M Èjhsk u wdjrKh jk f,i mdi,a f;dard f.k tu mdi,aj, .=rejreka i|yd fkajdisl
mqyqKqjla ,nd § Tjqka mdi,aj,g f.dia kej; b.ekaùu lrk wdldrh iy isiqkaf.a mjq,a
mßir ms<sn| j Rcq w;aoelSï ,ndf.k tu w;aoelSï o by; fmd;a rpkd lsÍfï § m%fhdackhg
.kakd ,§'
wvq idOk uÜgula fmkajk isiqka úiska fuu fmd;a Ndú; lsÍfuka Tjqkaf.a m%dma;s uÜgu
by<g kxjd .; yelsfõ' ir, nfõ isg ixlS¾K nj olajd l%shdldrlï iy wNHdi ilia
lr we;s neúka isiqkaf.a wjOdkh iy fm<öu we;s jk wdldrhg o fmd;a ilia lr ;sîu
úfYaI;ajhls'
fuu fmd;a Ndú; lsÍfuka Tn ,nk m%dfhda.sl w;aoelSï wdY%fhka" ixj¾Okd;au; fhdackd
wm fj; okajd tjkak' tu.ska bÈßfha § fujeks ld¾hhka ;j ;j;a by< m%;sM, f.k fok
mßÈ ie,iqï lsÍfï yelshdj ,efí'
fla' rxð;a m;auisß
wOHlaI
cd;sl wOHdmk wdh;kh
iii

wOHlaI ckrd,a;=udf.a mKsúvh
wm rfÜ .Ks; wOHdmkh ;ju;a wfmalaIs; b,lal lrd <`.dùug fkdyels ù we;s nj
wOHhk fmdoq iy;sl m;% ^idudkH fm<& yd ^Wiia fm<& úNd. m%;sM, úYaf,aIK
u`.ska ms<sìUq fõ' fuu ;;a;ajh rfÜ wkd.; ixj¾Okh flfrys wys;lr f,i
n,mdk idOlhls' fuu h:d¾:h y÷kdf.k Bg úiÿï fiùfï tla ls%hdud¾.hla f,i
cd;sl wOHdmk wdh;kfha .Ks; fomd¾;fïka;=j úiska ".Ks;h myiqfjka " kñka
rÑ; fuu fmd;a fm< yÿkajd Èh yels h'
lksIaG oaú;Shsl wjêfha § isiqkaf.a .Ks; l=i,;d by< kexùu i|yd úêu;a ls%hdj,shla
w;HjYH jqj o" wvq ld¾h idOk uÜgï m%o¾Ykh lrk mdi,aj, isiqka b,lal
lrf.k ,shjqKq uq,dY% fnfyúka úr, fõ'
wvqu ld¾h idOk o¾Yl iys; mdi,aj, .=rejreka mqyqKq lr" Tjqka fiajh lrk
mdi,aj, mka;sldur ms<sn| j cd;sl wOHdmk wdh;kfha .Ks; fomd¾;fïka;=fõ
ks,OdÍka úiska lrk ,o ksÍlaIKj, w;aoelSï o mokï lr f.k tu mdi,aj,
orejka fjkqfjka ilid we;s fuu fmd;a fm< mdi,aj, 6-11 fY%aKs m%;sldÍ jevigyka
i|yd fnfyúka bjy,a fjkq we;' fuu fmd;a fm< ir, uÜgfuka" isiqkag ms%hckl
wdldrhg bÈßm;a lr ;sîu úfYaI ,laIKhls' ls%hdldrlï" ;r." ir, wNHdi jeks
oE iys; .Ks;h myiqfjka fmd;a fm< isiqkaf.a bf.kqï ls%hdj,sh yd .=rejrekaf.a
b.ekaùï ls%hdj,sh ixj¾Okh lsÍug iu;a jk nj ksiel h'
fuu fmd;a fm< mrsYS,kfhka .Ks; úIhfha bf.kqï - b.ekaùï - we.hSï ls%hdj,sh
id¾:l lr .kakd fuka .=rejrekaf.ka o" isiqkaf.ka o b,a,d isáñ'
".Ks;h myiqfjka " fmd;a fm< Tn w;g m;a lsÍu ioyd wkq.%yh oelajq GIZ jHdmD;shg
yd ADB jHdmD;shg;a fuu ld¾hh id¾:l lr .ekSug Ydia;S%h odhl;ajh iemhQ
.Ks; fomd¾;fïka;=fõ ld¾h uKav,hg yd ndysr úoaj;=ka ish¨ fokdg uf.a m%Kduh
ysñ fõ'
uydpd¾h ví,sõ' tï' wfír;ak nKavdr
wOHlaI ckrd,a
cd;sl wOHdmk wdh;kh
iv

mQ¾úldj
wOHhk fmdÿ iy;sl m;% îdudkH fm<& úNd.fha .Ks; úIhfha m%;sM, mokï
lrf.k Y%S ,xld úNd. fomd¾;fïka;=j úiska ilia lr we;s mdi,a ld¾h idOk
o¾Yl wkqj Èjhsfka m<d;a kjfhys u wvq u ld¾h idOk o¾Yl iys; mdi,a f;dard
f.k tu mdi,aj, YsIH idOk uÜgï ms<snò j cd;sl wOHdmk wdh;kfha .Ks;
fomd¾;fïka;=j úiska fidhd n,k ,§' fï iòyd .Ks;fha f;aud yh wkqj ilia lrk
,o m%Yak m;% yhla YsIH ksheÈhlg ,nd fok ,§' tajd mÍlaId lr ,nd.;a f;dr;=re
úYaf,aIKfhka isiqkaf.a ÿ¾j,;d yd idOk uÜgï o" nyq, j isÿ lrk jerÈ yd
ÿ¾j,;d fmkakqï flfrk úIh lafIa;% o y`ÿkd .ekqKs' tu mdi,aj, .=rejreka fuu
lreKq ms<snò j ±kqj;a lr tu mdi,aj, ;;a;ajh ÈhqKq lr,Su .Ks; fomd¾;fïka;=fõ
wfmalaIdj úh'
fuu jevigyk ms<snò j Èjhsfka mdi,aj, .=rejreka 152 fofkl= mqyqKq lrk ,o
w;r" mqyqKqfõ § .=rejreka w;am;a lr.;a foa isiqkag ,nd §u myiq lsÍu iòyd
zz.Ks;h myiqfjkaZZ isiq jev fmd;a fm< ks¾udKh lrk ,§' .=re uy;au uy;aókaf.a
mdif,a ld¾hNdrh jvd;a myiq lr m%;sldÍ jev myiqfjka l%shd;aul lsÍu wruqKq
lrf.k fuu fmd;a ie,iqï lrk ,§'
zz.Ks;h myiqfjkaZZ isiq jev fmd;a fm< .Ks;fha f;aud yh wkqj uqøKh lr we;'
1' .Ks;h myiqfjka - 1 ixLHd
2' .Ks;h myiqfjka - 2 ñkqï
3' .Ks;h myiqfjka - 3 ùc .Ks;h
4' .Ks;h myiqfjka - 4 cHdñ;sh
5' .Ks;h myiqfjka - 5 ixLHdkh
6' .Ks;h myiqfjka - 6 l=,l yd iïNdú;dj
zz.Ks;h myiqfjkaZZ isiq jev fmd;a fm< mka;s ldurfha Ndú; l< yels wu;r uQ,dY%
fõ' fïjd fm< fmd;g wu;r j fhdod .; yels jákd .%ka: fõ' fuu fmd;a fm<
m%Odk jYfhka" u|la fifuka .Ks;h bf.k .kakd isiqka b,lal lr f.k ilia jQ
tajd fõ' y`ÿkd.;a ÿ¾j,;d yd úIh lreKq ish,a, u fïjdfha ix.Dys; fyhska isiqkag
úIh lreKq .%yKh lr .ekSu myiq fõ' fuu .%ka:j, wka;¾.;h my; oelafjk
wdldrhg f.dkqlr we;'
1' fmr mÍlaIK
2' úfkdaockl l%shdldrlï
3' hq., l%shdldrlï
4' ir, m%Yak ^f;aÍï" wE`ÿï" nyqjrK" ysia;eka msrùï&
5' flá m%Yak
6' jHQy.; m%Yak
7' m%fya,sld jeks fjk;a WmlrK
.Ks;h wudre hehs is;d isák isiqkaf.a udkisl ;;a;ajh fjkia lr jvd;a m%shckl
úIhhla f,i .Ks;h y`ÿkajd §ug wjYH l%shdldrlï iuQyhla fuu fmd;aj,
wka;¾.; lr we;' fndfyda m%Yak ir, f,i bÈßm;a lr we;af;a iEu YsIHfhl=g u
úi`§u myiq jk wldrhg h'
v

fuu fmdf;a wka;¾.; jkafka ixLHdkh f;audjg wod< úIh lreKq fõ' fuu f;audj hgf;a
6 fY%aKsfha isg 11 fY%aKsh wjidkh olajd u bf.k .kakd uQ,sl úIh lreKq ish,a,la u
wka;¾.; jk fia fmd; iïmdokh lr we;' ixLHdkh fldgi ud;Dld 6 lska yd l%shdldrlï
04 lska o wNHdi 06 lska o iukaú;h' tla tla ud;Dldj hgf;a jQ fmr mÍlaIKh" isiqkaf.a
uÜgu wkdjrKh lr .ekSu i`oyd ilia lr we;s w;r tla tla ud;Dldj wjidkfha isiqka
<`.d ù we;s uÜgu wkdjrKh lr .ekSug fuu fmr mÍlaIKhu fhdod .ekSfuka Tng
yelshdj ,efí' fuu fmd; mßYS,kfhka isiqkaf.a olaI;d by< kef.kq we; hkak wmf.a
úYajdih jk w;r" fuu fmd; Y%S ,xldfõ .Ks; wOHdmkhg uy`.= w;aje,la fõjd hkak
wmf.a m%d¾:kh hs'
6-11 fY%aKs .Ks; jHdmD;s lKavdhu
cd;sl wOHdmk wdh;kh'
vi

WmfoaYkh ( uydpd¾h ví,sõ¡ tï¡ wfír;ak nKavdr
wOHlaI ckrd,a
cd;sl wOHdmk wdh;kh
tï¡ t*a¡ tia¡ mS¡ chj¾Ok uhd
ksfhdacH wOHlaI ckrd,a
úoHd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
wëlaIKh ( fla¡ rxð;a m;auisß uhd
wOHlaI
cd;sl wOHdmk wdh;kh
ie,iqu yd iïnkaëlrKh ( Ô¡ t,a¡ lreKdr;ak uhd" fÊHIaG wOHdmk{
10-11 fY%aKs .Ks;h m%;sld¾h b.ekaùfï jHdmD;s lKavdhï
kdhl
úIh iïnkaëlrKh - ixLHdkh ( Ô' mS' tÉ' c.;a l=udr uhd
fÊHIaG lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
úIhud,d lñgqj (
fla¡ rxð;a m;auisß uhd wOHlaI" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
Ô¡ mS¡ tÉ¡ c.;a l=udr uhd fÊHIaG lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
Ô¡ t,a¡ lreKdr;ak uhd fÊHIaG wOHdmk{" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
tï¡ ks,añKs mS¡ mSßia ñh lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
ví,sõ¡ whs¡ Ô¡ r;akdhl ñh lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
tia¡ rdfÊkaøka uhd lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
tÉ¡ fla¡ ã¡ hQ¡ .=Kj¾Ok ñh lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
hQ¡ Ô¡ mS¡ wfír;ak ñh lÓldpd¾h" .Ks; fomd¾;fïka;=j
cd;sl wOHdmk wdh;kh
vii

viii
ndysr iïm;a odhl;ajh (
tï' ta' tia rfn,a ñh úY%dñl .=re WmfoaYsld
î' tï' ìfidaueKsfla ñh .=re WmfoaYsld
fldÜGdi wOHdmk ld¾hd,h" jdßhfmd<
tka' Ô' fifkúr;ak .=re WmfoaYl
l,dm wOHdmk ld¾hd,h" foys´úg
wd¾' mS' ã' chisxy .=re WmfoaYl
l,dm wOHdmk ld¾hd,h" foys´úg
uqøK ;dlaIK ( ví,sõ' tï' hQ' úfÊiQßh uhd
l<ukdlrKh iyldr wOHlaI ^uqøK&
cd;sl wOHdmk wdh;kh
mß.Kl joka ieliqu ( fla' fk,sld fiakdks ñh
cd;sl wOHdmk wdh;kh
NdIdj ixialrKh ( tÉ¡ mS¡ iqis,a issßfiak uhd
lÓldpd¾h
ydmsá.ï cd;sl wOHdmk úoHdmSGh
msg ljr ks¾udKh ( B¡ t,a¡ ta¡ fla¡ ,shkf.a uhd
uqøKd,h
cd;sl wOHdmk wdh;kh

mgqk
1'0 o;a; /ia lsÍu 1
2'0 o;a; ksrEmKh 6
3'0 o;a; w¾:l;kh 13
4'0 úúla; o;a; yd ika;;sl o;a; 20
5'0 wiuqys; yd iuQys; o;a; w¾:l;kh 24
6'0 iuQys; o;a; ksrEmKh yd w¾:l;kh 32
7'0 W;a;r 40
ix
msgq wxl

1.Ks;h myiqfjka - 5 ixLHdkh
1.0 o;a; /ia lsÍu
fmr mrSlaIKh (
m%Yak ish,a,g u ms<s;=re imhkak'
1' o;a; /ialsÍfï § tla o;a;hla jdr' 13 la ,enqKs kï o;a; /ia lsÍu
wjidkfha tu o;a;hg wod< jdr .Kk m%.Kk ,l=Kq u.ska olajd ;sìh
hq;= jkafka
(i) f,i h' (iii) /// f,i h'
(ii) //// //// /// f,i h' (iv) //// /// f,i h'
2' //// / m%.Kk ,l=Kq u.ska olajd we;s ixLHdj jkafka"
(i) 5 (ii) 6 (iii) 7 (iv) 1
3' m%.Kk ,l=Kg wod< ixLHd;h iqÿiq mßÈ hd lrkak'
m%.Kk ,l=Kq ixLHd;h
(i) //// 4
(ii) //// /// 5
(iii) //// 8
o;a; /ia lsÍfï § tu m%;sM, igyka lsÍug m%.Kk ,l=Kq fhdod .kshs'
tfia m%.Kk ,l=Kq fhdod ,shk ,o ixLHd lSmhla my; j.=fõ oelafõ'
ixLHdj 1 2 3 4 5 6 8 10 12
m%.Kk
,l=Kq

by; j.=j wOHhkh lr Tfí hy`Mjd iu`. my; i|yka l%shdldrlïj, fhfokak' m%;sM,
igyka lsÍug m%.Kk ,l=Kq fhdod.kak'
l%shdldrlu 1'1 ( m%.Kk ,l=K Ndú; lruq
l%shdldrlu (a)
• ldishla Wv ouñka ,efnk m%;sM, igyka lrkak'
• fofokd u udrefjka udrejg l%shdldrlfuys fhfokak'
• fufia úisjdrhla l%shdldrlfuys fhfokak'
l%shdldrlu (b)
• fgdksla mshkla Wv ouñka ,efnk m%;sM, igyka lrkak'
• tla wfhl= l%shdldrlfuys fhfok úg wfkla wh m%;sM, m%.Kk ,l=Kqj,ska igyka
lrkak' fï l%shdldrlfuys o 20 jdrhla ksr; jkak'
• by; l%shdldrlï foflys § tla tla wjia:d i|yd ,enqKq ixLHd; iudk w.hka
.;af;a o@
• wfkla lKavdhï i|yd o Tng ,enqKq ixLHd; u ,enqfKa o@ hkak ms<sn| j
idlÉPd lrkak'
ixLHd;hm%.Kk ,l=K
Wvql=re
hál=re
ixLHd;hm%.Kk ,l=K

l%shdldrlu 1'2 ( f;dr;=re úuiuq ¦ leálr olajuq'
Tfí mka;sfha hy`Mjkaf.a f;dr;=re úuiñka my; oelafjk j.= iïmQ¾K lrkak'
j.=j I
m%.Kk ,l=K ixLHdkhWmka udih
ckjdß
fmnrjdß
ud¾;=
wfm%a,a
uehs
cQks
cq,s
wf.daia;=
iema;eïn¾
Tlaf;dan¾
fkdjeïn¾
foieïn¾
j.=j II
m%.Kk ,l=K ixLHdkh;udg isák ifydaor
ifydaoßhka .Kk
0
1
2
3
4
5 fyda 5 g jeä
ixLHd;h
ixLHd;h
;udg isák ifydaor
ifydaoßhka .Kk
m%.Kk ,l=K
Wmka udih m%.Kk ,l=K

wNHdih 1'1
1' m%.Kk ,l=Kg wod< ixLHd;h iqÿiq mßos hd lrkak'
m%.Kk ,l=K ixLHd;h
(I)
(II)
(III)
(IV)
11
8
9
10
7
2' rúu,a ;udf.a ksji bosßmi uyd ud¾.fha .uka lrk fudag¾ r:j, j¾Kh i|yka
lsÍfï l%shdldrlul ksr; úh' Tyq úiska iïmQ¾K l< j.=fõ we;eï fldgia
uelSf.dia we;' tu fldgia iïmQ¾K lrkak'
fudag¾ r:j, j¾Kh m%.Kk ,l=K ixLHd;h
ks,a 07
r;=
iqÿ 14
fld,
ly
tl;=j 95
..............
..............
..............
..............
.............. 16
3' my; oelafjk isÕs;s .Sh (Nursery rhyme) wkqj oS we;s j.=j iïmQ¾K lrkak'
Three blind mice,
See how they run !
They all run after the farmer's wife
who cut off their tails,
with the carving knife
Did you ever see such a thing in your life,
As three blind mice
fjk;a j¾K ''''''''''''' ''''''''''''
tl;=j 67
fudag¾ r:j, j¾Kh m%.Kk ,l=K ixLHd;h

jpkhlg we;s
wl=re .Kk
m%.Kk ,l=K ixLHd;h
1
2
3
4
5
6
7
j.=j weiqßka ms<s;=re imhkak'
(i) by; .Sfha" jeämqr ,eî we;af;a wl=re lSfha jpk o @'
(ii) wl=re 4 g jeäfhka we;s jpk .Kk lSho ' @
jpkhlg we;s
wl=re .Kk
m%.Kk
,l=K
ixLHd;h

2'0 o;a; ksrEmKh
fmr mrSlaIKh (
1' fjf<|i,l" Èkl§ wf,ú l< ri leú,s j¾.hl melÜ .Kk oelafjk
Ñ;% m%ia;drhl fldgila my; oelafõ'
tla la leú,s melÜ 4 kï" tÈk wf,ú lr we;s ri leú,s melÜ .Kk
lSh o@
2' ld¾hd,hl i;sfha Èk 5l § fiajhg fkdmeñKs fiajlhska .Kk my;
;Sr m%ia;drfhka oelafõ'
8
6
4
2
(i) jeä u fiajlhska ixLHdjla fkdmeñKs oji l=ula o@
(ii) nododg jeäfhka n%yiam;skaod fiajlhska lS fofkl= ksjdvq f.k
;sfí o @
fiajlhska
ixLHdj
>
i÷od
w`.yrejdod
nodod
isl=rdod
n%yiam;skaod
oji

3' uq`M ,l=Kq 50ka ,l=Kq ,nd ÿka mÍlaIKhl § isiqka lKavdhula ,nd.;a
,l=Kq my; jDka; m;% igyfka oelafõ'
(i) ,l=Kq 25g jeäfhka ,nd.;a isiqka .Kk lSh o@
(ii) fuu ,l=Kqj, ud;h lSh o@
4' isiqka lKavdhul tla tla isiqjd jvd;a u leu;s j¾Kh ms<sn| j ,nd .;a
f;dr;=re my; jg m%ia;drfha olajd we;'
(i) x u`.ska oelafjk fldaKfha w.h lSho@
(ii) r;= j¾Khg leu;s isiqka ixLHdj 4 kï ly j¾Khg leu;s isiqka
ixLHdj lSho@
r;=
ly
;eô,s
fld<
300
1200x0
0 4 7 8
1 0 3 5 6
2 1 4 4 4 7 9
3 0 2 2 5 6 9
jDka; m;%

l%shdldrlu 2'1 ( ieuod mdie,a meñfKuq
22 -
20 -
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
ksu,a
meñKSu
idudðlhdf.a ku
• ckjdß udih ;=< ksu,a osk 20la o m%Nd;a osk 18la o mdi,g meñK we;' th
by; ;Sr m%ia;drh u.ska olajd we;'
• Tn leu;s hy`Mjka y;r fofkl= iuÕ lKavdhula idod.kak'
• Tfí mka;sfha kduf,aLkh .kak' miq.sh udifha Tn lKavdhfï idudðlhkaf.a
meñKSu igyka lr.kak'
idudðlhdf.a ku udih ;=< meñKs osk .Kk
1.
2.
3.
4.
5.
• fldgqrE,a lvodishla f.k by; wdldrhg Tn lKavdhfï tla tla YsIHhd
''''''''''''''''''''''''''''''' udih ;=< oS meñKs Èk .Kk weiqßka ;Sr m%ia;drhla w|skak'
• tu udih ;=< jeä u Èk .Kkla mdi,g meñK we;af;a l=uk idudðlhd o@
m%Nd;a
meñKSu
idudðlhdf.a ku
idudðlhdf.a ku udih ;=< meñKs Èk .Kk

• kej; kduf,aLkh /f.k" Bg fmr udifha idudðlhkaf.a meñKSu o igyka lr.kak'
• tu f;dr;=re o by; j.=jg we;=<;a jk fia tu j.=jg ;j;a ;Srhla tl;= lr.kak'
• l,ska w¢k ,o ;Sr m%ia;drfha u by; f;dr;=re;a we;=<;a lrkak'
• udi foflys meñKSu fjka jYfhka oelaaùu i|yd my; i|yka h;=r Ndú; lrkak'
................ udifha meñKSu
................ udifha meñKSu
• by; wdldrfha f;dr;=re lSmhla tljr fmkajk ;Sr m%ia;dr y÷kajk úfYaI ku l=ula
o@ hkak lKavdhu ;=< idlÉPd lrkak'
wNHdih 2'1
1' tla;rd i;shla ;=< 10 fY%aKsfha isiqkaf.a meñKSu my; oelafjk Ñ;% m%ia;drfhka
oelafõ'
oji meñKSu
isl=rdod
n%yiam;skaod
nodod
wÕyrejdod
i÷od
i. i÷od mdi,a meñKs isiqka ixLHdj 36la kï" lska isiqka lShla ksrEmKh
flf¾ o @
ii. isiqka jeä u ixLHdjla mdi,a meñKsfha ljod o @ ta fldmuK o @
iii. n%yiam;skaodg jvd nodod meñKs isiqka .Kk lSh o @
iv. i;sh ;=< meñKs isiqka uq`M .Kk fidhkak '

f;dr;=re jDka; m;%igykl oelaùu
uq`M ,l=Kq 50 la jQ .Ks; m%Yak m;%hlg tla;rd mka;shl isiqka 30 la ,nd .;a
,l=Kq my; oelafõ'
8 8 9 10 13 15 17 18 22 22
22 27 28 29 30 31 32 33 38 39
39 40 41 41 41 43 43 46 48 50
tu ,l=Kq jDka; m;% igykl we;=,;a lruq'
0
1
2
3
4
5
8 8 8
0 5 3 7 8
2 2 2 7 8 9
0 1 2 3 8 9 9
0 1 1 1 3 3 6 8
0
jDka; m;%
2' ñksiqka 20 fofkl=f.ka hq;= lKavdhul tla tla mqoa.,hdf.a ialkaOh kg j,ska
my; oelafõ'
34 40 35 51 54 53 47 36 42 35
62 53 53 65 71 64 53 46 70 71
fuu f;dr;=re weiqßka my; oS we;s jDka; m;% igyk iïmQ¾K lrkak'
3
4
5
6
7
4 5 5 6
0 2 .. .. ..
1 3 .. .. .. 4
.. .. ..
.. ..
m;%jDka;h
jDka;h m;%
9
3 5
7
--''

by; jDka; m;% igyk wkqj lKavdhfï isák"
i' wvq u ialkaOh we;s ñksidf.a ialkaOh fldmuK o @
ii' jeä u ialkaOh we;s ñksidf.a ialkaOh fldmuK o @
iii' ñksiqkaf.a ialkaOj, mrdih lSh o@
iv' ñksiqkaf.a ialkaOj, ud;h lSh o@
v' ñksfil=f.a uOHia: ialkaOh fidhkak'
3' tla;rd mka;shl isiqkaf.ka r;=" ks,a" fld< hk j¾Kj,ska jvd;a u leu;s j¾Kh
úuid ,nd.;a f;dr;=re we;=<;a j.=jla iy tu f;dr;=re f;dr;=re jg m%ia;drhlska
oelaùu i|yd we¢ jD;a;hla my; oelafõ'
(a) fuu f;dr;=re weiqßka wid we;s m%Yak i|yd ms<s;=re imhkak' ^ oS we;s ms<s;=re
w;=ßka ksjeros ms<s;=r f;darkak'&
i' fuu mka;sfha isák uq`M isiqka .Kk lSh o@
(i) 38 (ii) 36 (iii) 34 (iv) 40
ii' ,laIHhla jgd we;s fldaK ish,af,ys tl;=j lSh o@
(i) 900
(ii) 1800
(iii) 2700
(iv) 3600
iii' by; f;dr;=re jg m%ia;drhlska oelaùfï §" tl <ufhl= ksrEmKh lsÍug fjka
l< hq;= flakaøsl LKavfha fldaKh .Kkh l< yelafla"
(i)
0
360
38
(ii)
0
360
36
(iii)
0
360
34
(iv)
0
360
40
iv' tla <ufhl= ksrEmKh jk flakaøsl LKavfha fldaKh jkafka"
(i) 60
(ii) 100
(iii) 200
(iv) 90
v' ks,a j¾Khg leu;s isiqka .Kk ksrEmKh lsÍu i|yd fjka l< hq;= fldaKh
jkafka"
(i) 900
(ii) 1400
(iii) 1000
(iv) 1200
vi' r;= j¾Khg leu;s isiqka .Kk ksrEmKh lsÍu i|yd we¢h hq;= fldaKh jkafka"
(i) 1000
(ii) 900
(iii) 1800
(iv) 1400
vii' fld< j¾Khg leu;s isiqka .Kk oelaùu i|yd we¢h hq;= fldaKh jkafka"
(i) 1400
(ii) 1000
(iii) 1200
(iv) 900
ks,a r;= fld<
14 10 12
.

(b) Tn ,nd.;a f;dr;=re wkqj § we;s jD;a;h u; jg m%ia;drh w|skak'
4' jvd;a u leu;s l%Svdj ms<sn| isiqka 24 fofkl=f.ka ,nd.;a f;dr;=re my; jg
m%ia;drfhka oelafõ'
l%slÜ
w;amkaÿ
1200
r.¾
600
i' l%slÜ l%Svdjg leu;s isiqka ksrEmKh lrk flakaøsl LKavfha fldaKfha w.h
lSh o @
ii' tla YsIHfhl= ksrEmKh lsÍug fjka lr we;s fldaKfha w.h lSh o @
iii' tla tla l%Svdjg leu;s isiqka .Kk fjk fjk u ,shkak'
5' mqoa.,fhl= ;u udisl wdodhfuka 20] la f.j,a l=,S i|yd o" 60]la wdydr i|yd o"
10] la wOHdmk lghq;= i|yd o úhoï lrhs' b;sßh Tyq nexl=jl ;ekam;a lrhs
fuu f;dr;=re jg m%ia;drhl oelaùu i|yd my; oelafjk j.=j iïmQ¾K lrkak'
úhoï lrk wdldrh m%;sY;h wod< fldaK
20%
.............
............
............
.............................
.............................
.............................
20
360 72
100
 
450
0 0
úhoï lrk wdldrh m%;sY;h wod, fldaKh
f.j,a l=,S
wdydr
wOHdmkh
b;srslsrSï

3'0 o;a; w¾: l:kh ^wuqo;a;&
fmr mrSlaIKh (
1' 3" 7" 8" 5" 9" 10" 8 ixLHd jHdma;sfha ud;h jkafka"
(i) 3 (ii) 10 (iii) 8 (iv) 5
2' tla;rd wdmk Yd,djl i;shla ;=< Èkm;d wf,ú jQ f;a fldamam .Kk my; oelafõ'
25" 32" 40" 28" 32" 40" 27
fjf<|if,a Èkl § wf,ú jQ f;a fldamam .Kfka uOHkHh ,nd.; yels jkafka"
i' ( 25 + 32 + 40 + 28 + 32 + 40 + 27 ) x 7 u.sks
ii' 25 + 32 + 40 + 28 + 32 + 40 + 27 u.sks'
iii' ( 25 + 32 + 40 + 28 + 32 + 40 + 27 ) 7 u.sks '
iv. 27403228403225  u.sks '
3' isiqjl= jdr mÍlaIKhl § úIhhka 8 la i|yd ,nd .;a ,l=Kqj, uOHkHh 65 ls' Tyq
,nd .;a uq`M ,l=Kq .Kk ,nd.; yels jkafka"
i' 65 8 u.sks'
ii 65 x 8 u.sks'
iii' 65 8 u.sks'
iv'
65
8
u.sks'
4' 4" 5" 6" 7" 7" 8" 10" 12" 13" 14" 15 ixLHd iuQyfha uOHia:h jkafka"
(i) 4 (ii) 15 (iii) 7 (iv) 8
5' 3" 5" 4" 3" 6" 5" 8" 4" 7" 5 ixLHd iuQyfha mrdih jkafka"
(i) 3 (ii) 4 (iii) 7 (iv) 5

wNHdih 3'1
1' my; oelafjk ixLHd;aul f;dr;=rej, ud;h fidhkak'
^Tnf.a ms<s;=r jgd rjqula w|skak'&
i. 1, 2, 3, 4, 5
(a) 3 (b) ish,a, u (c) ke; (d) 2
ii. 57, 82, 84, 82, 57, 82
(a) 57 (b) 82 (c) 84 (d) ke;
iii. 127, 134, 143, 134, 127
(a) 127 (b) 124 (c) 127 iy 134 (d) ke;
iv. 3, 5, 7, 6, 9, 5
(a) 7 (b) ish,a, u (c) ke; (d) 5
v. 21, 32, 26 , 42, 55, 32
(a) 21 (b) 32 (c) ke; (d) 55
vi. 116, 121, 116, 165, 121
(a) 127 (b) 165 (c) 116 iy 121 (d) ke;
2' uer;ka ;r.hla wjika l< ;r.lrejka mia fofkl= ta i|yd .; l< ld,h my;
oelafõ'
meh 2'7 meh 3'5 meh 3'5 meh 5'1 meh 4'9
tu o;a;j, ud;h jkafka"
(i) meh 8'3 h (ii) meh 2'7 h (c) meh 3'5 h (d) ud;hla fkdue;'
o;a; iuQyhl jeä u jdr .Kkla
fhoS we;s ixLHdj tys ud;h fõ
ksoiqk ( 1 1 2 2 2 ixLHd iuQyfha
ud;h } 2 fõ'

ksoiqk (
1 7 9 12 13 16 ixLHd i,luq
tys uOHia:h } 12 fõ
2 6 2 8 4 ixLHd i,luq
m<uqj fuu ixLHd wdfrdayK ms<sfj,g ilikak
túg 2 4 6 8 fõ
túg uOHia:h fõ
. .
.
. .
.
.
.

  
4 6 10
5
2 2
3' my; oelafjk ixLHd;aul f;dr;=rej, uOHia:h fidhkak' ms<s;=re w;ßka oS we;s
uOHia: w.h jgd rjqula w|skak'
(i) 3" 4" 7" 2" 5
(a) 5 (b) 4 (c) 3 (d) 2
(ii) 1" 5" 9" 11
(a) 4 (b) 7 (c) 5 (d) 8
(iii) 6" 5" 8" 4" 7
(a) 5 (b) 8 (c) 6 (d) 4
(iv) 3" 9 " 7 " 12
(a) 3 (b) 8 (c) 4 (d) 5
(v) 5" 10" 9 " 7" 11" 8" 13
(a) 5 (b) 13 (c) 7 (d) 9
(vi) 80" 87" 93" 102" 108" 131" 147" 153
(a) 80 (b) 153 (c) 102 (d) 105
wjfrdayK fyda wdfrdayK
ms,sfj<g ilia l< o;a;
iuQyhl yß ueo mj;sk w.h
tys uOHia:h fõ'
wjfrdayK fyda wdfrdayK
ms<sfj<g ilia l< o;a;
iuQyhl yß ueo mj;sk w.h tys
uOHia:h fõ'
ms<sfj<gm<uq j

oS we;s tla tla o;a; iuQyfha uOHkHh w.h fidhkak' ta wkqj § we;s ms<s;=re w;=ßka
ksjerÈ ms<s;=r jgd rjqula w|skak'
o;a; iuQyhl we;s o;a; j, tl;=j
tys we;s o;a; ixLHdfjka fn¥ úg
tu o;a; iuQyfha uOHkHh ,efí
ksoiqk ( 1 2 3 4 5 ys uOHkHh fidhuq
wh .Kkaj, tl;=j
wh .Kka ixLHdj
uOHkHh
     1 2 3 4 5 15
5
 
15
3
5
4'
(i) 5" 8" 7" 6 9
(a) 6 (b) 5 (c) 8 (d) 7
(ii) 16" 19" 22" 25" 28
(a) 20 (b) 22 (c) 24 (d) 21
(iii) 20" 20" 20" 20
(a) 4 (b) 5 (c) 10 (d) 20
(iv) 100" 200" 250" 150" 300
(a) 200 (b) 225 (c) 250 (d) 275
(v) 2" 6" 9" 9" 9
(a) 8 (b) 6 (c) 9 (d) 7
o;a; j, tl;=j
uOHkH
o;a; ixLHdj


my; i|yka ksoiqk wOHhkh lrkak'
ksoiqk ( 5, 5, x, 20 ys uOHkHh 10 kï xys w.h lSh o@
l%uh 1 (
5 5 20
10
4
4
x  

30
4
x
 10 4
30 40
30 30 40 30
10
x
x
x
 
 
   

l%uh 2 ( uOHkHh 10 ksid ixLHd 4 ys tl;=j 10 4 40  
oS we;s ixLHd 3 ys tl;=j 5 5 20 30   
b;sß ixLHdj (x) 40 30
10
 

5' (a) my; i|yka tla tla wjia:d i|yd x ys w.h fidhkak' oS we;s ms<s;=re w;rska
ksjeros ms<s;=r f;dard th jgd rjqula w|skak'
(i) , 4, 6, 8, 10x ys uOHkHh 6 kï" x ys w.h jkafka"
(a) 6 (b) 28 (c) 7 (d) 2
(ii) 3, , 6x ys uOHkHh 4 kï x ys w.h jkafka "
(a) 3 (b) 6 (c) 9 (d) 12
(iii) 100, 110, 115, 120, x ys uOHkHh 114 kï" x ys w.h jkafka"
(a) 125 (b) 100 (c) 445 (d) 130
(iv) 101, 121, 131, , 151x ys uOHkHh 129 kï" x ys w.h jkafka"
(a) 131 (b) 141 (c) 120 (d) 150
(b) my; i|yka .eg¨ úi|d ms<s;=re ysia fldgqj ;=< ,shkak'
(i.) 45, 62, 72, , 59, 62x ys uOHkHh 61 kï" x ys w.h }
(ii.) 3, , , 8, 5x x ys uOHkHh 10 kï" x ys w.h }
(iii.) 2, 3, , 2, 1x x  ys uOHkHh 4 kï" x ys w.h }
(iv) 6, 3, , 4, 3, 5,x y ys uOHkHh 5 kï" x y ys w.h }
(v) ixLHd 15 l uOHkHh 12 ls' thg ;j;a ixLHdjla
tl;= l< úg uOHkHh 13 la úh' tl;= l< ixLHdj"
12" 25" 13 iy 28 w;=ßka l=ula úh yels o @ }

6' isiqka 5 fofkl= mÍlaIK 4 l § ,nd.;a ,l=Kq m%;sY; my; oelafõ'
tla tla YsIHhd ,nd.;a ,l=Kqj, uOHkHh yd tla tla mrSlaIKfha oS YsIHhd ,nd .;a
,l=Kqj, uOHkHh fidhd j.=fõ ysia;eka iïmQ¾K lrkak'
(i) Wmßu uOHkHh w.h ,nd f.k we;af;a l=uk mÍlaIKh i|yd o @
(ii) wju uOHkHh w.h ,nd f.k we;af;a l=uk mÍlaIKh i|yd o @
(iii) iudk uOHkH w.hka ,nd f.k we;af;a l=uk mÍlaIK i|yd o @
(iv) iq.;a mÍlaIK ish,a, u i|yd ,nd .;a idudkH w.h lSh o @
(v) mÍlaIK ish,a, i|yd 80] l idudkH w.hla ,nd f.k we;af;a ljqo@
7' oS we;s rel=,a mo wkqj my; oelafjk m%fya,sldj iïmQ¾K lrkak'
my<g
(a) 20" 35" 48" 50" 56" 58" 62" 68 hk ixLHd
iuQyfha uOHia:h
(b) hk
m%.Kk ,l=Kqj,ska i|yka ixLHdj
(d) ixLHd 20 l ftlHh 360 fõ' tu ixLHd
iuQyfha uOHkHh
yryg
(a) 2" 5" 7" 3" 5" 8" 3" 5 hk ixLHd iuQyfha
ud;h
(c) 5" 8" 9" 12" 12" 15" 25" 32 hk ixLHd iuQyfha
mrdih
(e) iy,a f.daks 20 l uOHkH nr 24kg ls' tu
iy,a f;d.fha uq`M nr kg j,ska'
iq.;a
wkqr
foajl
fcdaka
ud,ka
idudkHh
^uOHkHh&
75]
50]
90]
80]
60]
80]
55]
90]
70]
50]
70]
45]
90]
80]
70]
75]
60]
90]
90]
90]
YsIHhdf.a
ku
mÍCIK
1 2 3 4
mÍCIK mÍCIK mÍCIK idudkH
^uOHkHh&
a b
c
d
e
YsIHhdf.a
ku
mrslaIKh
1
mrslaIKh
2
mrslaIKh
3
mrslaIKh
4
idudkH
^ uOHkHh &

8' tla;rd udihl oS mka;shl fkdmeñKs isiqka ixLHdj my; oelafõ'
4, 2, 5, 2, 1, 4, 2, 5, 2, 3, 4, 5, 2, 3, 5, 2, 2, 3, 5, 4, 2, 6, 2
i' fuu ixLHd wdfrdayK ms<sfj<g ilia lrkak'
ii' uOHia:fha msysàu fidhkak'
iii' uOHia:h fidhkak'
iv' ud;h fidhkak'
9' (a) 56" 58" 59" 60" 61 (b) 56" 58" 58" 59" 60" 60" 61" 62
by; a yd b ixLHd jHdma;s fol weiqßka ,shd we;s my; m%ldY yß kï  ,l=K o"
jeros kï ,l=K o fhdokak'
i' a jHdma;sfha mrdih 6 fõ' ^ &
ii' b jHdma;sfha ud; 58 yd 60 fõ' ^ &
iii' a jHdma;sfha ud;h 58 fõ' ^ &
iv' b nyqud; jHdma;shls' ^ &
v' a jHdma;shg ud;hla ke;' ^ &
vi' b ys uOHia: 58 yd 59 fõ' ^ &
vii' a ys uOHia:h 59 fõ' ^ &
viii' a ys uOHkHh 58'8 fõ' ^ &
ix' b ys uOHkHh 60 fõ' ^ &
10' f.j;a;l ;snQ ;lald,s .ilska Èk follg jrla wiajekak fk<d .kakd ,§' tfia
,nd .;a ;lald,s f.ä .Kk 5" 5" 8" 6" 4" 8" 10" 5" 12 fõ' fï wkqj my;
i|yka m%YAakj,g ms<s;=re imhkak'
(i) Èk lShla wiajkq fk<d ;sfí o @
(ii) fuu ld,h ;=< ;lald,s .fika Èkl § lvd.;aa wvq u ;lald,s f.ä .Kk lSh o @
(iii) fuu f;dr;=j, mrdih lSho @
(iv) fuu .fika lvd.;a ;lald,s f.ä .Kfka ud;h lSh o @
(v) fuu .fika Èkl § lvd .;a ;lald,s f.ä .Kfka uOHkHh w.h fidhkak'
(vi) fujeks .ia 15 la md;a;sfha ;snqfKa kï" tajdhska Èkl § lvd .; yels hehs wfmalaIs;
uOHkH f.ä .Kk fldmuK o@
(vii) by; .ia 15 ka wjia:d 10 l § .; yels hehs wfmalaIs; uq`M f.ä .Kk fidhkak'

4'0 úúla; o;a; yd ika;;sl o;a;
fmr mrSlaIKh (
1' A - ;lald,s .ilska lvd .kakd ,o f.ä .Kk 12 ls'
B - ;lald,s f.ä 10 la weiqrE nE.hl ialkaOh 200g ls'
A yd B m%ldY w;=ßka ika;;sl o;a;h we;=<;a m%ldYh l=ula o@
2' (a) <uhskaf.a jhi
(b) i;shla ;=< ffoksl j¾Idm;kh
(c) i;shla ;=< Èkm;d lvk ,o fmd,a f.ä ixLHdj
(d) Èùfï ;r.hla i|yd iyNd.s jQ l%Svlhska ;r.h ksudj i|yd .; l< ld,h
(e) .ul mjq,ays idudðlhska .Kk
by; oelafjk úp,H w;=ßka úúla; o;a; we;=<;a jkafka"
i' (a) yd (b) ;=< h'
ii' (c) yd (e) ;=< h'
iii' (d) yd (e) ;=< h'
iv' (c) yd (d) ;=< h'
3' my; oelafjk úp,H" l=uk o;a; j¾.hg wh;a oehs fidhd iqÿiq mßÈ hd lrkak'
i' k.rhl ffoksl WIaK;ajh
ii' mdi,l tla tla mka;s ldurfha we;s mqgq .Kk
iii' lmd bj;a l< lïì len,sj, Èk úúla;
o;a;
ika;;sl
o;a;

mjq,l isák idudðlhska .Kk ms<sn| f;dr;=re oelaùfï oS idudðlhska
.Kk 5" 6" 7 wdoS jYfhka ksYaÑ; j oelaúh yels h' tu f;dr;=rej, wdikak
o;a; folla w;r fjk;a w.hla fkdmj;S'
fujeks wdikak o;a; w;r fjk;a w.hla fkdmj;sk mka;shl isák isiqka
ixLHdj" flfi,a wejßhl f.ä ixLHdj jeks o;a; úúla; o;a; f,i ye|skafõ'
<ufhl=f.a Wi ms<sn| oelaùfï oS 161cm, 162cm, 163cm wdoS jYfhka
olajk úg wdikak w.hka jk 161cm, 162cm w;r 161cm jvd jeä 162cm jvd
wvq w.hka mej;sh yels h'
fujeks wkq.dó o;a; w;r ;j;a w.hka mej;sh yels" ÿr" Wi" ld,h"
ialkaOh jeks rdYsj,ska ,nd.kakd f;dr;=re ika;;sl o;a; f,i ye|skafõ'
l%shdldrlu 4'1 o;a;" ika;;sl yd úúla; f,i j¾. lruq
my; oelafjk m%ldY ;=< wvx.= o;a; ika;;sl o;a; yd úúla; o;a; f,i fjka fldg
,ehsia;= .; lrkak' ta i|yd my; oS we;s wdldrfha j.=jla fhdod .kak'
1' <ufhl=f.a jhi wjqreÿ 10 hs'
2' oskl mx;sfha isák YsIH ixLHdj 20 hs'
3' fmd,a f.ähl nr 725g ls'
4' fmd,a f.dvl f.ä 25 la ;sfí'
5' oskl j¾Idm;kh 20mm ls'
6' iukaf.a mjqf,a idudðlhka .Kk 6 ls'
7' ldishl isri jegqKq jdr .Kk 12 ls'
8' óg¾ 100 osùug .; jQ ld,h ;;amr 45 ls'
9' jpkhl wl=re .Kk 5 ls'
10' ñßia me<Eáhl Wi 6cm ls'
ika;;sl o;a; úúla; o;a;
jhi YsIH ixLHdj

wNHdih ( 4'1
1' my; i|yka m%Yak i|yd ksjeros ms<s;=r f;darkak'
i' ika;;sl o;a;h wvx.= jkafka mQid iïnkaO l=uk m%ldYfha o @
A W!g weia folla ;sfí
B W!g megõ mia fofkla isáhs'
C Wf.a nr 4 kg
D W!g mdo y;rla ;sfí'
ii' úúla; o;a;h wvx.= jkafka n,a,d iïnkaO my; oelafjk m%ldY w;=ßka l=uk
m%ldYfha o @
A W!f.a os. 128.6cm ls'
B W!f.a Wi 88.8cm ls'
C W!f.a nr 15.9 kg ls'
D W!g o;a 30 la ;sfí'
iii' úúla; o;a;h wvx.= jkafka iEï iïnkaO my; oelafjk m%ldY w;=ßka l=uk
m%ldYfha o @
A iEïf.a Wi 160cm ls'
B iEïf.a nr 60kg ls'
C iEï ;;amr 10'2 oS 100m ÿjhs'
D iEïg ifydaorhka fofofkla yd ifydaoßhla
isáhs'
2' my; i|yka o;a;" ika;;sl fyda úúla; f,i fjkalr my; oelafjk j.=fjys olajkak'
1' mka;shl isák isiqka ixLHdj
2' tla;rd úNd.hl .Ks;h m%Yak m;% i|yd isiqka ,nd.;a ,l=Kq
3' lvodis melÜ lSmhl tla tla melÜ tflys we;s lvodis .Kk

4' ud`M l+Íka lSm fofkl=f.a ialkaO
5' .ul ck.ykh
6' fros len,s lsysmhl os.
7' úÿ,s nqnq,l Ôj wdhqld,h
8' fld<U k.rfha tla udihl WIaK;ajh
9' rdlalhl we;s fmd;a .Kk
10' .ul mjq,l isák orejka .Kk
3' .e<fmk mrsos hd lrkak'
(i) i;shlg we;s osk .Kk
(ii) mka;shl isák tla tla isiqjdf.a ialkaO
(iii) flfi,a wejßhl we;s f.ä .Kk
(iv) <uhska lKavdhul tla tla <uhdf.a Wi
(v) ÿrl:k ixjdohla i|yd .;jk ld,h
(vi) ñksil=f.a udisl jegqm
ika;;sl o;a;úúla; o;a;
ika;;sl
o;a;
úúla;
o;a;

5.0 wiuqys; yd iuQys; o;a; w¾:l:kh
fmr mrSlaIKh (
tla;rd fjf<| wdh;khlg i;shla ;=< meñKs mdßfNda.slhska ixLHdj we;=<;a
lsÍu i|yd ilia l< mka;s m%dka;rj, fldgila my; oelafõ'
fuu mka;s m%dka;r weiqßka m%Yak wxl ^1& iy ^2& i|yd ms<s;=re imhkak'
1' 56 - 60 mka;s m%dka;rhg wod< mka;s udhsï ,nd.; yels jkafka"
i'
(55 56)
2

yd
(60 65)
2
 u.sks'
ii'
(51 56)
2

yd
(60 61)
2

u.sks'
iii' (55 56)
2
 yd
(60 61)
2

u.sks'
iv' (55 60)
2
 yd
(60 65)
2

u.sks'
2' 61 - 65 mka;s m%dka;rhg wod< uOH w.h ,nd.; yels jkafka"
i' 61" 65 ka .=Klr 2 ka fn§fuks'
ii' 65 ka 61 la wvqlr 2 ka fn§fuks'
iii' 65" 61 ka fn§fuks'
iv' 61 iy 65 tl;= lr 2 ka fnoSfuks'
mka;s m%dka;r
51 - 55
56 - 60
61 - 65

tla;rd oskl nexl=jl uqo,a .kqfokq i|yd meñKs mdßfNda.slhska msßila ;u ld¾hh bgqlr
.ekSu i|yd fmda,sfuys /¢ isá ld,h ^ñks;a;=& we;=<;a ixLHd; jHdma;shla my; oelafõ'
^fuys 4-10 hkq 4 fyda 4 g jeä yd 10 g wvq jYfhks&
ld,h mdßfNda.slhska
^ñks;a;=& ixLHdj
4-10 15
10-16 12
16-22 8
22-28 3
28-34 2
fuu ixLHd; jHdma;sh weiqßka m%Yak wxl ^3& isg ^5& olajd m%Yakj,g ms<s;=re
imhkak'
3' jeä u msßila fmda,sfï /£ isá ld, m%dka;rh jkafka"
i' 28 - 34
ii' 4 - 10
iii' 16 - 22
iv' 22 - 28
4' ixLHd; jHdma;sfhys uOHia:h wvx.= mka;sh jkafka"
i' 10 - 16
ii' 16 - 22
iii' 22 - 28
iv' 28 - 34
40

5' by; ixLHd; jHdma;sfhys mka;s m%dka;rj,g wod< uOH w.h ms<sfj<ska 7" 13" 19" 25
yd 31 kï" tÈk mdßfNda.slhl= nexl=fõ /£ isá uOHkHh ld,h ,nd .; yels
jkafka"
i' 4031)251913(7  u.sks'
ii' 40)23812(15  u.sks'
iii' 4031)225319813127(15  u.sks'
iv' 4031)251913(7  u.sks'
6' tla;rd m,;=re fjf<|i,l udihla ;=< Èkm;d wf,ú jQ mefmd,a lsf,da .a?ï
.Kk we;=<;a ixLHd; jHdma;shla my; oelafõ'
wf,ú jQ mefmd,a
m%udKh (kg)
4-8 4
8-12 6
12-16 10
16-20 5
20-24 3
24-28 2
i' jeä u Èk .Kkla wf,ú jQ mefmd,a lsf,da .a?ï .Kk we;=<;a m%dka;rh
l=ula o@
ii' 12-16 mx;sfha uOH w.h Wml,ams; uOHkHh f,i f.k Èkl § wf,ú lr we;s
uOHkHh mefmd,a lsf,da .a?ï .Kk fidhkak'
iii' mefmd,a 1 kg l ñ, re' 60'00 kï" Èk 45 l § mefmd,a wf,úfhka ,efí hehs
wfmalaIs; wdodhu fidhkak'
Èk .Kk

wNHdih ( 5'1
1' my; j.=fõ oelafjkqfha j;a;l ;snQ fmd,a .ia 50 lska tla uqrhl § lvd .;a
f.ä .Kka h'
wh.Kk (x) ixLHd;h (x)
.ilska levQ f.ä .Kk .ia .Kk
8 1
9 2 ....................
10 4 ....................
11 14 ....................
12 10 ....................
13 8 ....................
14 6 ....................
15 5 ....................
by; f;dr;=re weiqßka"
(i) .ilska lvd.; yels f.ä .Kfka ud;h fidhkak'
(ii) uOHia:h fidhkak'
(iii) uOHia:hg jvd jeä .Kkla f.ä lvd.; yels jQ .ia .Kk lSh o @
(iv) fx ;Srh iïmQ¾K lrkak'
(v) ixLHd; ;Srfha tl;=j tkï
(vi) fx ;Srfha tl;=j tkï
(vi)
2'0 my; j.=fjys § we;s mka;s m%dka;r w;ßka 32 - 38 mka;s m%dka;rfha"
(i) my< iSudj l=ula o@
(ii) by< iSudj l=ula o@
(iii) my< mka;s udhsu l=ula o@
(iv) by< mka;s udhsu l=ula o@
818 
fx
 f =
 fx =
 fx lSh o@
 f lSh o@


f
fx
hkak Ndú; lr" .ilska lvk ,o uOHkHh fmd,a f.ä .Kk wdikak mQ¾K ixLHdjg
fidhkak'
25 31
32 38
39 45




(v) mka;sfha ;ru lSh o@
(vi) uOH w.h fidhkak'
3'0 <uhska 40 lg ksjfia isg mdi,g taug .;jk ld,h ms<sn| ,nd .;a f;dr;=re my;
ixLHd; jHdma;sfha oelafõ'
^10 - 15 hkq 10 fyda 10 g jeä " 15 g wvq fõ'&
.;jk ld,h ^ñks;a;=j,ska& ixLHd;h
5 - 10 4
10 - 15 9
15 - 20 15
20 - 25 4
25 - 30 5
30 - 40 3
(i) ñks;a;= 10 lg wvq ld,hl § mdi,g meñfKk <uhska .Kk lSho@
(ii) jeä fofkl=g mdi,g meñKSug .;jkqfha l=uk ld, mr;rhla o@
(iii) fuys ud; mka;sh l=ula o@
4'0 ,l=Kq 50 ka fok ,o m%Yak m;%hlg <uhska lKavdhula ,nd .;a ,l=Kq my;
ixLHd; jHdma;sfha oelafõ'
mka;s 0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50
m%dka;rh
ixLHd;h 2 2 3 3 5 10 6 4 2 3

fuu mÍlaIKfha § <ufhl= ,nd .;a uOHkHh ,l=K fiùu i|yd my; oelafjk j.=j fhdod.kak'
mka;s ixLHd;h (f) uOH w.h (x)
m%dka;rh
0-5 2 2'5 5'0
6-10 2
11-15 3
16-20 3
21-25 5
26-30 10
31-35 6
36-40 4
41-45 2
46-50 3
(i) uOH w.h ;Srej iïmQ¾K lrkak
(ii) fx ;Srh iïmQ¾K lrkak'
(iii)
5'0 tla;rd .Ks; .eg¨jla id¾:l j úi£ug isiqka iuQyhla .;a ld,h wdikak ñks;a;=jg
my; j.=fõ oelafõ'
mka;s 1-3 4-6 7-9 10-12 13-15 16-18 19-21 22-24
m%dka;rh
ixLHd;h 0 5 6 8 10 9 7 5
(i) .eg¨j úi£ug .; jQ ld,fha ud; mka;sh fidhkak'
(ii) .eg¨j úi£ug .; jQ ld,fha uOHkHh fiùu i|yd my; oelafjk j.=j iïmQ¾K
lrkak'
fx
 f = xf =
uOHkHh =


f
xf
hkak Ndú; lrñka" isiqjl=g ms<s;=re ,sùug .;
jQ uOHkHh ld,h wdikak ñks;a;=jg fidhkak'

(a)uOH w.h ;Srej iïmQ¾K lrkak'
(b) ñks;a;= 14 Wml,ams; uOHkHh (A) f,i .ksñka ;Srh d iïmQ¾K lrkak'
(c) fd ;Srh iïmQ¾K lrkak'
(d) uOHkHh


f
df
A hkak Ndú; lrñka isiqjl=g" fuu .eg¨jg ms<s;=re ,sùug
.;jQ uOHkHh ld,h wdikak ñks;a;=jg fidhkak'
6'0 my; oelafjk m%ldY .Ks;uh jYfhka i;H kï" ,l=K o wi;H kï"
,l=K o bÈßfha we;s fldgqfõ olajkak'
1' ixLHd jHdma;shl ud;h hkq jeä jdr" .Kkla fhfok ixLHdj hs'
2' uOHia:fha msysàu
1
2
n
hkafkka ,nd .; yels h'
3' ud;h uOHia:h yd uOHkHh w;=rska" uOHkHh jvd;a fyd|
ksrEmH w.hls'
mka;s ^ld,h& ixLHd;h uOH w.h wm.ukh ixLHdkh x wm.ukh
m%dka;rh f x d f x d
1-3 0 2 ''''''''''''''''''''' '''''''''''''''''''''''''
4-6 5 '''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''''''''
7-9 6 8 ''''''''''''''''''''' '''''''''''''''''''''''''
10-12 8 '''''''''''''''''''' ''''''''''''''''''''' ''''''''''''''''''''''''
13-15 10 '''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''''''''
16-18 9 '''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''''''''
19-21 7 20 ''''''''''''''''''''' '''''''''''''''''''''''''
22-24 5 ''''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''''''
 f 50  df
 

wxl 4 - 8 olajd we;s m%Yakj,g ms<s;=re ,sùu i|yd my; oelafjk j.=fõ we;s f;dr;=re fhdod
.kak'
mka;s 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54
m%dka;rh
ixLHd;h 2 6 10 12 11 5 3 1
4' ud;h wvx.= mka;s m%dka;rh 30-34 fõ'
5' uOHia:h wvx.= jkafka 25-29 mka;s m%dka;rfha h'
6' fuys o;a; 50 la ;sfí'
7' fuys iEu mka;s m%dka;rhl u ;ru 5 fõ'
8' 20-24 mka;s m%dka;rfha uOH w.h 22 fõ'

6.0 iuQys; o;a; ksrEmKh yd w¾:l:kh
fmr mrSlaIKh (
1' isiqka lKavdhula .Ks; l%shdldrlula iïmQ¾K lsÍu i|yd jeh l< ld,h we;=<;a
cd, f¾Lhla my; oelafõ'
i' l%shdldrlu i|yd ñks;a;= 35 g jeä ld,hla jeh l< isiqka .Kk lSho@
ii' lKavdhfï isá uq`M isiqka .Kk lSho@
iii' fuu cd, f¾Lh msgm;a lr th u; ixLHd; nyqwi%h w¢kak'
2' 7" 8" 9" 10" 11" 13" 14" 15" 16" 17" 18 ixLHd jHdma;sfha
i' m<uqjk p;=¾:lh lSho@
ii' ;=kajk p;=¾:lh lSho@
iii' tu.ska wka;Ya p;=¾:l mrdih fidhkak'
15 20 25 30 35 40
ld,h ^ñks;a;=&
>45 500
2
4
6
8
10
12
isiqka.Kk
>

3' t<j¨ wiqrd we;s fmÜá lsysmhl ialkaO we;=<;a ixLHd; jHdma;shla my; oelafõ'
ialkaOh (kg) fmÜá .Kk iuqÉÑ;
^ixLHd;h& ixLHd;h
2 - 4 1 1
4 - 6 2 3
6 - 8 4 7
8 - 10 3 10
10 - 12 x 12
i' § we;s f;dr;=re weiqßka x ys w.h fidhkak'
ii' my; § we;s wlaI moaO;sh msgm;a lrf.k th u; iuqÉÑ; ixLHd; m%ia;drh
w¢kak'
>
iuqÉÑ;ixLHd;h
by, udhsu
0
2
4
6
8
10
12
2 4 6 8 10 12
>
14

wNHdih 6'1
1' f;a o¨ tl;= lrk uOHia:dkhlg" jeú,slrejka f.k wd f;a o¨ m%udK oelafjk
wiïmQ¾K j.=jla iy tu f;dr;=re oelaùug w¢k ,o wiïmQ¾K cd, f¾Lhla my;
oelafõ'
ialkaOh (kg) 5-10 10-15 15-20 20-25 25-30
jeú,slrejka .Kk 2 ''''' '''''' 7 4
^ixLHd;h&
(i) cd, f¾Lfha b;sß ia;ïN fol iïmQ¾K lrkak'
(ii) cd, f¾Lh fyd¢ka ksÍlaIKh lrñka j.=fõ ysia;eka iïmQ¾K lrkak'
(iii) fï wkqj tÈk f;a o¨ f.fkk ,o uq`M jeú,slrejka .Kk lSho@
(vi) 20kg fyda 20kg g jeäfhka f.k tk ,o jeú,slrejka .Kk" (a) 29 (b) 11
(c) 7 (d) 28 hk fïjd w;=ßka lSh o@
(v) by; cd, f¾Lh u; ixLHd; nyqwi%h w¢kak'
5
10
0
20
ixLHd;h
15
5 10 15 20 25 30
nr(kg)

2' 50 ka ,l=Kq fokq ,enQ mÍlaIKhl § isiqka msßila ,nd .;a ,l=Kq weiqßka w¢k ,o
cd, f¾Lhla my; oelafõ'
(i) by; cd, f¾Lfha oelafjk f;dr;=re wkqj my; oelafjk ixLHd; j.=j iïmQ¾K
lrkak'
mka;s ixLHd;h
m%dka;rh ^isiqka .Kk&
0 -10 3
'''''''''''' ''''''''''''''
'''''''''''' ''''''''''''''
'''''''''''' ''''''''''''''
40 - 50 '''''''''''
(ii) by; j.=j weiqßka isiqka ,nd .;a ,l=Kqj, uOHkHh" wdikak mQ¾K ixLHdjg
fidhkak' tu w.h;a " cd,f¾Lh weiqrska jeäu isiqka .Kkla ,nd.;a ,l=Kq
m%dka;rh;a fidhd tajd ii|kak '
(iii) § we;s cd, f¾Lh msgm;a lrf.k ixLHd; nyqwi%h w¢kak'
3' tla;rd mdi,l l%Svd ksjdihl isá isiqkaf.a Wi ms<sn| ,nd .;a f;dr;=re my;
j.=fõ § we;' j.=j fyd¢ka ksÍlaIKh lr m%Yakj,g ms<s;=re imhkak'
mka;s m%dka;rh 110-125 125-130 130-135 135-140 140-145 145-155
Wi (cm)
ixLHd;h 21 10 11 12 8 6
^isiqka .Kk&
>
0
2
4
6
8
10
12
10 20 30 40 50 60
isiqka.Kk
,nd.;a ,l=Kq
>

(i) j.=fõ we;=<;a iEu mka;s m%dka;rhl u ;ru iudk jkafka o@
(ii) 110-125 mka;s m%dka;rfha ;ru 125-130 mka;s m%dka;rfha ;ru fuka lS .=Khla o@
(iii) my; i|yka wlaI msgm;a lrf.k by; j.=j weiqßka cd, f¾Lh w¢kak'
4' isiqka msßila .Ks; we.hSul § ,nd .;a ,l=Kq weiqfrka w¢k ,o cd, f¾Lhla my;
oelafõ'
fuu cd, f¾Lh weiqßka"
(i) ud; mka;sh fidhkak'
(ii) ,l=Kq 30 g jeäfhka ,nd .;a isiqka .Kk fidhkak'
(iii) fuu we.hSug ,lajQ uq`M isiqka .Kk fidhkak'
(iv) fuu cd, f¾Lh u; ixLHd; nyqwi%h w¢kak'
isiqka
.Kk
Wi (cm)
60
>
0
2
4
6
8
10
12
10 20 30 40 50 80 90
>
70
14
,l=Kq
isiqkaixLHdj

p;=¾:l
ksoiqk ( 2" 2" 4" 4" 5" 7" 8" 8" 10" 10" 12"
fuu ixLHd iuQyfha
i. m<uqjk p;=¾:lh - Q1
ii. ;=kajk p;=¾:lh - Q3
iii. wka;Ya p;=¾:l mrdih 3 1(Q Q ) fidhkak'
2" 2" 4" 4" 5" 7" 8" 8" 10" 10" 12"
m<uqjk uOHia:h ;=kajk
p;=¾:lh p;=¾:lh
Q1
Q3
(i) fuu jHdma;sfha f;dr;=re .Kk 11
m<uqjk p;=¾:lfha msysàu = 3
4
12
4
111


m<uq p;=¾:lh 4
(ii) f;jk p;=¾:lfha msysàu
  9
4
312
4
3111





f;jk p;=¾:lh 10
(iii) wka;Ya p;=¾:l mrdih 3 1(Q Q ) 6410 
5'0 my; i|yka ixLHd jHdma;sj,
(a) m<uqjk p;=¾:lh - Q1
(b) ;=kajk p;=¾:lh - Q3
(c) wka;Ya p;=¾:l mrdih 3 1(Q Q ) fidhkak'
(i) 8 ,9 ,10 ,12 ,13 ,15 ,17
(ii) 4, 5, 5, 6, 7, 7, 7, 8, 8, 9, 10, 12, 14, 15, 16
(iii) 15, 24, 20, 18 16, 26, 23,
(iv) 2, 10, 8, 7 , 5, 3, 11, 13, 9
>
>
>

6'0 iq`M mrsudKfha lsrsyrla f.dúm<l ffoksl j ,nd .;a lsß ,Sg¾ .Kk weiqßka
my; oelafjk j.=j f.dvk.d we;'
lsß ,Sg¾ Èk .Kk iuqÉÉ; jl%h i|yd
^mka;s m%dka;rh& ^ixLHd;h& LKavdxl
0- 2 2 2 ( 2 , 2 )
2- 4 6 8 ( 4 , 8 )
4- 6 6 14 ( 6 , 14 )
6- 8 4 ...... ( 8 , .... )
8-10 ....... 20 ( .... , 20 )
(i) by; j.=fõ ysia;eka iïmQ¾K lrkak'
(ii) § we;s iuqÉÑ; ixLHd; jl%h Ndú;fhka by; f;dr;=rej, uOHia:h fidhkak'
(iii) by; ixLHd jHdma;sfha m<uqjk p;=¾:lh Q1
=3.0 fõ' iuqÉÑ; ixLHd;
jl%h Ndú;fhka ;=kajk p;=¾:lh 3(Q ) fidhkak'
ixLHd;h
5.3
1
Q
iuqÉÑ;
ixLHd;h
by< udhsu0 2 4 6 8 1 0
20
15
10
5
by< udhsu

7' ksñ we÷ï lïy,lska bj;a lrk ,o frÈ len,s 100 l È. uksk ,§' tu f;dr;=re
my; j.=fjys oelafõ'
lene,a,l È. len,s .Kk iuqÉÑ; jl%h i|yd
(cm) ixLHd;h (d) LKavdxl
0-10 3 3 ^10" 3&
10-20 6 9 ^20" 9&
20-30 11 20 '''''''''''
30-40 18 ''''''''''' '''''''''''
40-50 23 ''''''''''' '''''''''''
50-60 16 ''''''''''' '''''''''''
60-70 15 ''''''''''' '''''''''''
70-80 8 ''''''''''' '''''''''''
i. by; j.=fjys ysia;eka iïmQ¾K lrkak'
ii. fuu f;dr;=re weiqßka iuqÉÑ; ixLHd; jl%h w¢kak'
iii. w¢k ,o iuqÉÑ; ixLHd; jl%h weiqßka bj;a lrk ,o frÈ lene,a,l uOHia: È.
fidhkak'
iv. fuu f;dr;=rej,g wod< Q1
yd Q3
fidhd wka;Ya p;=¾:l mrdih fidhkak'
8' mefmd,a f.ä f;d.hl ialkaO ms<sn| f;dr;=re my; j.=fjys oelafõ'
mka;s 250-500 500-750 750-1000 1000-1250 1250-1500 1500-1750
m%dka;r
ixLHd;h 2 5 12 10 8 3
^f.ä .Kk&
i. by; f;dr;=re weiqßka iuqÉÑ; ixLHd; jl%h w¢kak'
ii. iuqÉÑ; ixLHd; m%ia;drh Ndú;fhka ms<s;=re imhkak'
(a) mefmd,a f.ähl ialkaOfha uOHia: w.h fidhkak'
(b) fuu f;d.fha jeä u nr we;s mefmd,a f.ä 25% fjka lr .ekSug wjYH j
we;' ta i|yd f;dard .; hq;af;a ialkaOh lShg jeäfhka we;s f.äoehs
fidhkak'

ms<s;=re
1'0 o;a; /ia lsÍu
fmr mrslaIKh
1. ii. 2. ii. 3.
1.
tl;=j 67
i) .Sfha jeämqr ,eî we;af;a wl=re 3 jpk
ii) wl=re 4 g jeä jpk .Kk = 11
2'0 o;a; ksrEmKh
fmr mÍlaIKh
1. 24 2. i) n%yiam;skaod ii) 6
3. i) 8 ii) 24
4. i) 1200
ii) 12
2. fudag¾ r:j, j¾Kh m%.Kk ,l=K ixLHd;h
ks,a 7
r;= 10
iqÿ 14
fld, 8
ly 16
fjk;a j¾K 12
m%.Kk ,l=Kq ixLHd;h
(i) 4
(ii) 5
(iii) 8
3. jpkhlg we;s wl=re .Kk m%.Kk ,l=K ixLHd;h
1 1
2 2
3 13
4 10
5 9
6
7 2
wNHdih 1'1
11
8
9
10
7
2

wNHdih 2'1
1. i) 4 ii) wÕyrejdod - 38 iii) 2 iv) 172
2. jDka;h m;%
3 4 5 5 6
4 0 2 6 7
5 1 3 3 3 3 4
6 2 4 5
7 0 1 1
3. (a) i. (ii) ii. (iv)
iii. (ii) iv. (ii)
v. (ii) vi. (i)
vii. (iii)
(b)
4. i. 1350
ii. 150
iii. w;amkaÿ 8 , fgksia 3 , r.¾ 4 , l%slÜ 9 .
5. úhoï lrk wdldrh m%;sY;h wod, fldaKh
f.j,a l=<S 20% 20 x 3600
= 720
100
wdydr 60% 60 x 3600
= 2160
100
wOHdmkh 10% 10 x 3600
= 360
100
b;srslsrSï 10% 10 x 3600
= 360
100
1400
r;=
ks,a
fld<
1200
1000
b;srslsÍï
100
wOHdmkh 100
2160
wdydr
720
f.j,a l=<S
 
(i)34kg
(ii)71kg
(iii) 34 71 ,37
(iv)53
(v)53


3'0 o;a; w¾: l:kh
fmr mßlaIKh
1. (iii) 2. (iii) 3. (ii) 4. (iv)
5. (iv)
wNHdih 3'1
1. i. (c) ii. (b) iii. (c) iv. (d)
v. (b) vi. (c)
2. (c)
3. i. (b) ii. (b) iii. (c) iv. (b)
v. (d) vi. (d)
4. i. (d) ii. (b) iii. (d) iv. (a)
v. (d)
5. a. i. (d) ii. (a) iii. (a) iv. (b)
b. i. x = 66 ii. x = 17 iii. x = 6
iv. x + y = 14 v. 28
6. 75% 52.5% 90% 80% 67.5%
71% 69% 71% 81%
i mrslaIK wxl 4
ii mrslaIK wxl 2
iii. mrslaIK wxl 1 yd 3
iv. 75%
v. fcdaka
7. 5 4
3 2 7
1
4 8 0
8. i. 1,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6
ii. uOHia:fha msysàu = 23 + 1 = 24 = 12
2 2
iii. uOHia:h = 3
iv. ud;h = 2

9. i.  ii.  iii.  iv.  v. 
vi.  vii  viii.  ix. 
10. i. 9 ii. 4 iii. 8 iv. 5
v. 63/9 = 7 vi. 15 x 7 = 135 vii. 1350
4.0 úúla; o;a; yd ika;;sl o;a;
fmr mrSlaIKh
1. B 2. (ii) 3. i yd ii ika;;sl
ii úúla; o;a;
wNHdih 4'1
1. i. (c) ii. (d) iii. (d)
2. úúla; o;a; - 1 , 2 , 3 , 5 , 9 , 1 0
ika;;sl o;a; - 4 , 6 , 7 , 8
3. úúla; o;a; - (i) , (iii) , (vi)
ika;;sl o;a; - (ii) , (iv) , (v)
5.0 wiuQys; yd iuQys; o;a; w¾: l:kh
fmr mrSlAIKh
1. (iii) 2. (iv) 3. (ii) 4. (i)
5. (iii)
6. i. 12 - 16
ii.
wf,ú jQ mefmd,a uOH w.h wm.ukh osk .Kk f x d
m%udKh (x) (d) (f)
4 - 8 6 -8 4 -32
8 - 12 10 -4 6 -24
12-16 14 0 10 0
16-20 18 4 5 20
20-24 22 8 3 24
24-28 26 12 2 24
  30f   5668fd
12

oskloS wf,újQ uOHkHh mefmd,a ialkaOh
30
12
14 
kg4.14
4.014


iii. lsf,da.%Euhla re 60 kï osk 45 l wdodhu = 45604.14 
= re 00.38880
wNHdih 5'1
1. i. ud;h = 11 ii. uOHia:h = 12 iii. fmd,a.ia .Kk = 19
iv.
.ilska levQ f.ä .Kk .ia .Kk f x
8 1 8 x 1 = 08
9 2 9 x 2 = 18
10 4 10 x 4 = 40
11 14 11 x 14 = 154
12 10 12 x 10 = 120
13 8 13 x 8 = 104
14 6 14 x 6 = 84
15 5 15 x 5 = 75
  50f   603fx
v.   50f
vi.   603fx
vii. uOHkHh fmd,a f.ä .Kk
50
603
 = 12.06
wdikak mQ¾K ixLHdjg = 12
2. i. 32 - 38 mka;sfha my< iSudj = 32
ii. 32 - 38 mka;sfha by< iSudj = 38
iii. my< mka;s udhsu = 31.5
iv. by< mka;s udhsu = 38.5
v. mka;shl ;ru = 38.5 - 31.5
= 7
vi. mka;sfha uOH w.h = 35
2
70
2
3832


oskloS wf,újQ uOHkHh mefmd,a ialkaOh = Wml,ams; uOHkHh +  fd
 f

3. i. 4 ii. 15 - 20 iii. 15 - 20
4.
mka;s ixLHd;h (f) uOH w.h fx
m%dka;rh (x)
0-5 2 2.5 5.0
6-10 2 8 16
11-15 3 13 39
16-20 3 18 54
21-25 5 23 115
26-30 10 28 280
31-35 6 33 198
36-40 4 38 152
41-45 2 43 86
46-50 3 48 144
40 1089
iii. uOHkHh = 225.27
40
1089

5. i. ud; mka;sh = 13 - 15
ii.
mka;s m%dka;rh ixLHd;h uOH w.h wm.ukh ixLHdkh x wm.ukh
^ld,h& f x d f d
1-3 0 2 -12 0
4-6 5 5 -9 -45
7-9 6 8 -6 -36
10-12 8 11 -3 -24
13-15 10 14 0 0
16-18 9 17 3 27
19-21 7 20 6 42
22-24 5 23 9 45
50 114- 105
  09fd
d. uOHkHh =
50
9
14 
= 18.014
= 18.14
ms<s;=re ,sùug .;jQ ld,h = ñks;a;= 14
6. 1.  2.  3.  4.  5. 
6.  7.  8. 

6.0 iduQys; o;a; ksrEmKh yd w¾:l:kh
fmr mrslaIKh
1. i. 2+2 = 4 ii. 25
iii.
isiqka ixLHdj
ld,h ^ñks;a;=&
15 20 25 30 35 40 45 50
10 --
8 --
6 --
4 --
2 --
0 --
ixLHd; nyqwY%h
2. i. m<uq p;=¾:lh = 9
ii. m<uq p;=¾:lh = 16
iii. wka;¾ p;=¾:l mrdih = 16 - 9 = 7
3. i. x = 2
ii.
iuqÉÑ;
ixLHd;h
ialkaOh
12 --
10 --
8 --
6 --
4 --
2 --
0 --






2 4 6 8 10 12 14 16

wNHdih 6'1
1. i.
5 10 15 20 25 30 35
25 --
20 --
15 --
10 --
5 --
0 --
ixLHd;h
nr ^lsf,da.%Eï&
ii.
nr 5 - 10 10 - 15 15 -20 20 - 25 25 - 30
jeú,slrejka .Kk 2 10 18 7 4
iii. jeú,slrejka .Kk = 41
iv. 20 kg fyda Bg jeäfhka f.fkk jeú,slrejka .Kk = 11
2. i.
mka;s m%dka;r ixLHd;h m' m%d' u'w' f fx
0 - 10 3 0 - 10 5 3 15
10 - 20 8 10 - 20 15 8 120
20 - 30 12 20 - 30 25 12 300
30 - 40 5 30 - 40 35 5 175
40 - 50 4 40 - 50 45 4 180
ii.
isiqka .Kk
10 20 30 40 50 60 70
,nd.;a ,l=Kq
12 --
10 --
8 --
6 --
4 --
2 --
--
0
32 790
790
24.68
32

uOHkHh = 25

3. i. mka;s m%dka;r ;ru iudk fkdfõ
ii. ;=ka .=Khls
iii.
4. i. 30 - 40
ii. 16
iii. 30
iv.
10 20 30 40 50 60 70 80
iuqÉÑ;
ixLHd;h
ialkaOh
12 --
10 --
8 --
6 --
4 --
2 --
0 --
105 110 115 120 125 130 135 140 145 150 155 160
isiqka ixLHdj
,l=Kq
16--
14--
12--
10--
8 --
6 --
4 --
2 --
--
0

ii.
5. i. m<uq p;=¾:lh = 9
f;jk p;=¾:lh = 15
wka;Ya p;=¾:l mrdih = 15 - 9 = 6
ii. m<uq p;=¾:lh = 6
f;jk p;=¾:lh = 12
wka;Ya p;=¾:l mrdih = 12 - 6 = 6
iii. 15 , 16 , 18 , 20 , 23 , 24 , 26
m<uq p;=¾:lh = 16
f;jk p;=¾:lh = 24
wka;Ya p;=¾:l mrdih = 24 - 16 = 8
iv. 2 , 3 , 5 , 7 , 8 , 9 , 10 , 11 , 13 ,
m<uq p;=¾:lfha msysàu = 5.2
4
10
4
19


m<uq p;=¾:lh = 4
2
8
2
53


f;jk p;=¾:lfha msysàu = 5.7
4
30
4
310
3
4
19




f;jk p;=¾:lh = 5.10
2
21
2
1110


wka;Ya p;=¾:l mrdih = 10.5 - 4 = 6.5
6. i. mka;s m%dka;r osk .Kk iuqÉÑ; LKavdxl
^lsß ,Sg¾& ixLHd;h ixLHd;h
0 - 2 2 2 (2 , 2)
2-4 6 8 (4 , 8)
4-6 6 14 (6 , 14)
6-8 4 18 (8 , 18)
8-10 2 20 (10 , 20)
iuqÉÑ;
ixLHd;h
by< udhsu
0
5
10
15
20
25
0 2 4 6 8 10 12

7.
mka;s m%dka;r len,s .Kk iuqÉÑ; jl%h i|yd
lene,a,l os. ixLHd;h LKavdxl
0-10 3 3 (10 , 3)
10-20 6 9 (20,9)
20-30 11 20 (30,20)
30-40 18 38 (40,38)
40-50 23 61 (50,61)
50-60 16 77 (60,77)
60-70 15 92 (70,92)
70-80 8 100 (80,100)
ii.
100
90
80
70
60
50
40
30
20
10
iuqÉÑ;
ixLHd;h
by< udhsu
0 10 20 30 40 50 60 70 80 90
ii. 45cm
iii.Q3
-Q1
= 56 - 33
wka;Ya p;=¾:l mrdih = 23

7. i.
ii. uOHia:h = 1050
iii. 1300 kg g jvd jeä ialkaOhlska hq;a f.ä f;dard.; hq;=h
40
30
20
10
0 250 500 750 1000 1250 1500 1750
miq iSudj
iuqÉÑ;
ixLHd;h

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