Level 2 mathematics

1
Level 2 Mathematics
tcef; (1)
10000 txd udef;rsm;10000 txd udef;rsm;10000 txd udef;rsm;10000 txd udef;rsm;10000 txd udef;rsm;
1 .11 .11 .11 .11 .1 wpfaomif;txdudef;rsm;wpfaomif;txdudef;rsm;wpfaomif;txdudef;rsm;wpfaomif;txdudef;rsm;wpfaomif;txdudef;rsm;
wpfaxmif 2 Budrf = 2 axmif = 2000
avhusifhcef;(1)avhusifhcef;(1)avhusifhcef;(1)avhusifhcef;(1)avhusifhcef;(1)
a&wGufí uGufvyfjznfhyg/
1/ ------- axmif = ---------
2/ ------- axmif = ---------
3/ ------- axmif = ---------
4/ ------- axmif = ---------
( 1 aomif;)
1.21.21.21.21.2 10000 txdudef;rsm;a&wGufjcif;ESifh udef;zwf ? udef;a&;jcif;10000 txdudef;rsm;a&wGufjcif;ESifh udef;zwf ? udef;a&;jcif;10000 txdudef;rsm;a&wGufjcif;ESifh udef;zwf ? udef;a&;jcif;10000 txdudef;rsm;a&wGufjcif;ESifh udef;zwf ? udef;a&;jcif;10000 txdudef;rsm;a&wGufjcif;ESifh udef;zwf ? udef;a&;jcif;
1000 + 200 + 30 + 5 1235
wpfaxmifESpf&m oHk;q,fhig;[kzwf&rnf/
a&wGufí udef;a&;yg/
1/
axmif &m q,f ck
1 2 3 5
axmif &m q,f ck
1 3 2 5

2
Level 2 Mathematics
axmif &m q,f ck
axmif &m q,f ck
axmif &m q,f ck
axmif &m q,f ck
axmif &m q,f ck
axmif &m q,f ck
2/
3/
4/
5/
6/
7/
1.31.31.31.31.3 axmif? &m? q,f? ck Z,m;rokH;bJa&;jcif;axmif? &m? q,f? ck Z,m;rokH;bJa&;jcif;axmif? &m? q,f? ck Z,m;rokH;bJa&;jcif;axmif? &m? q,f? ck Z,m;rokH;bJa&;jcif;axmif? &m? q,f? ck Z,m;rokH;bJa&;jcif;
axmif
&m
q,f
ck
1 3 2 4 1324
a&wGufí udef;a&;yg/
1/

3
Level 2 Mathematics
2/
3/
4/
5/
1.41.41.41.41.4 udef;ukdpmjzifhazmfjyjcif;udef;ukdpmjzifhazmfjyjcif;udef;ukdpmjzifhazmfjyjcif;udef;ukdpmjzifhazmfjyjcif;udef;ukdpmjzifhazmfjyjcif;
2354
2 3 5 4
ESpfaxmif okH;&m ig;q,f av;
ESpfaxmifoHk;&mig;q,fhav;
atmufygudef;rsm;ukd pmjzifha&;yg/
(u) 1562 (c) 1604 (*) 3550 (C) 9035
1.51.51.51.51.5 pmjzifhazmfjycsufukd udef;jzifhazmfjyjcif;pmjzifhazmfjycsufukd udef;jzifhazmfjyjcif;pmjzifhazmfjycsufukd udef;jzifhazmfjyjcif;pmjzifhazmfjycsufukd udef;jzifhazmfjyjcif;pmjzifhazmfjycsufukd udef;jzifhazmfjyjcif;
wpfaxmif okH;&m ESpfq,f ajcmuf
1 3 2 6

4
Level 2 Mathematics
1/ atmufygwkdYukd udef;jzifha&;yg/
(u) ig;axmifwpf&mav;q,fhESpf -----------------------
(c) av;axmifwpf&mESpfq,hfukd; -----------------------
(*) ESpfaxmifajcmuf&mhckepfq,f -----------------------
(C) okH;axmifav;&mhig; -----------------------
(i) wpfaxmifig;q,hfckepf -----------------------
1.61.61.61.61.6 ae&mvkdufwefzkd;ae&mvkdufwefzkd;ae&mvkdufwefzkd;ae&mvkdufwefzkd;ae&mvkdufwefzkd;
axmif*Pef; 2
&m*Pef; 3
q,f*Pef; 4
ck*Pef; 6
1/ uGufvyfjznfhyg/
(u) 5236 (c) 1572
&m*Pef; ------------- ck*Pef; -------------
axmif*Pef; ------------- &m*Pef; -------------
ck*Pef; ------------- axmif*Pef; -------------
q,f*Pef; ------------- q,f*Pef; -------------
2/ tajzrSefukda&G;yg/
(u) axmif*Pef; 4 jzpfaomudef; 5426? 5147? 476? 4715
(c) &m*Pef; 1 jzpfaomudef; 5310? 2156? 1784? 1054
(*) ck*Pef; 6 jzpfaomudef; 6532? 2968? 4136? 1624
(C) q,f*Pef; 0 jzpfaomudef; 6740? 3705? 2067? 150
3/ atmufygudef;wkdYwGif 4 *Pef; ae&mvkdufwefzkd;rsm;ukda&;yg/
(u) 2345 (c) 3534 (*) 7452 (C) 4856
(u) 2345 wGif 4 *Pef; ae&mvkdufwefzkd; 4 q,f 40
(c) 3534 wGif 4 *Pef; ae&mvkdufwefzkd; --------
(*) 7452 wGif 4 *Pef; ae&mvkdufwefzkd; --------
(C) 4865 wGif 4 *Pef; ae&mvkdufwefzkd; --------
axmif &m q,f ck
2 3 4 6

5
Level 2 Mathematics
4/ 2645 wGif 2? 6? 4? 5 *Pef;toD;oD; ae&mvkdufwefzkd;ukda&;yg/
(u) 5 *Pef; ae&mvkdufwefzkd; 5 ck 5
(c) 6 *Pef; ae&mvkdufwefzkd; --------
(*) 4 *Pef; ae&mvkdufwefzkd; --------
(C) 2 *Pef; ae&mvkdufwefzkd; --------
5/ uGufvyfjznfhyg/
(u) 1625 wGif 6 ae&mvkdufwefzkd; ---------- ----------
(c) 8453 wGif 8 ae&mvkdufwefzkd; ---------- ----------
(*) 2507 wGif 2 ae&mvkdufwefzkd; ---------- ----------
(C) 2510 wGif 6 ae&mvkdufwefzkd; ---------- ----------
1.71.71.71.71.7 ae&mvkdufwefzkd;t& tus,fjzefYjcif;ae&mvkdufwefzkd;t& tus,fjzefYjcif;ae&mvkdufwefzkd;t& tus,fjzefYjcif;ae&mvkdufwefzkd;t& tus,fjzefYjcif;ae&mvkdufwefzkd;t& tus,fjzefYjcif;
7315 = 7000 + 300 + 10 + 5
4706 = 4000 + 700 + 6
1/ atmufygwkdYukd ae&mvkdufwefzkd;t& tus,fjzefYyg/
(u) 39 (c) 326 (*) 1682
(C) 4703 (i) 3110 (p) 5072
2/ atmufygwkdYukd pHykHpHjyifa&;yg/
(u) 5000 + 200 + 90 + 4
(c) 6000 + 400 + 30 + 5
1.81.81.81.81.8 udef;rsm;ukdEIdif;,SOfjcif;udef;rsm;ukdEIdif;,SOfjcif;udef;rsm;ukdEIdif;,SOfjcif;udef;rsm;ukdEIdif;,SOfjcif;udef;rsm;ukdEIdif;,SOfjcif;
b,fbub,fbub,fbub,fbub,fbufrS pí EIdif;,SOfyg/frS pí EIdif;,SOfyg/frS pí EIdif;,SOfyg/frS pí EIdif;,SOfyg/frS pí EIdif;,SOfyg/
Oyrm (1) 4523 ESifh 3657 wkdYwGif rnfonfhudef;uykdBuD;oenf;/
4523 ESifh 3657
4523 > 3657
ae&mvdkufwefzdk;tBuD;qHk; axmif*Pef;u
pí EIdif;,SOfMunhfyg/
4 axmifonf 3 axmifxufBuD;onf/

6
Level 2 Mathematics
Oyrm (2) 7251 ESifh 7253 wkdYwGif rnfonfhudef;u ykdBuD;oenf;/
7 2 5 1 ESifh 7 2 5 3 - axmif*Pef;rsm;upí EIdif;,SOfMunfhyg/
7 ESifh 7 wlonf/
- &m*Pef;rsm;ukdMunfhyg/
2 ESifh 2 wlonf/
- q,f*Pef;rsm;ukdMunfhyg/
5 ESifh 5 wlonf/
- ck*Pef;rsm;ukdMunfhyg/
3 onf 1 xufykdBuD;onf/
xkdYaMumifh 7253 > 7251
1/ rnfonfhudef;uykdBuD;oenf;/ oauFw ( > ) vu©PmokH;íajzyg/
(u) 3867 ESifh 3992 (c) 5362 ESifh 2784
(*) 6378 ESifh 6375 (C) 9116 ESifh 9106
2/ rnfonfhudef;uykdi,foenf;/ oauFw ( < ) vu©PmokH;íajzyg/
(u) 5652 ESifh 5734 (c) 8100 ESifh 7999
(*) 3610 ESifh 3671 (C) 2711 ESifh 2714
3/ > okdYr[kwf < udkokH;í ( )wGifjznfhyg/
(u) 684 ( ) 678 (c) 1687 ( ) 1787
(*) 8234 ( ) 6234 (C) 2049 ( ) 2046
1.91.91.91.91.9 udef;pOfjcif;udef;pOfjcif;udef;pOfjcif;udef;pOfjcif;udef;pOfjcif;
4253? 4736 ESifh 4517 wkdYukd i,fpOfBuD;vkdufpOfyg/
axmif &m q,f ck
- axmif*Pef;rsm;rSpí i,fpOfBuD;vkdufpOfyg/ 4 2
- wlaevQif &m*Pef;rsm;ukd qufípOfyg 4 5
2 < 5 ? 5 < 7 4 7

7
Level 2 Mathematics
- i,fpOfBuD;vkdufpOfí&oGm;vQif 4 2 5 3
usefq,f? ck*Pef;rsm;ukd qkdif&mwGifjznfhyg/ 4 5 1 7
4 7 3 6
1/ atmufygudef;wkdYukd i,fpOfBuD;vkdufpOfyg/
(u) 5000? 7000? 6000 (c) 3700? 3500? 3600 (*) 6780? 6800? 6790
2/ atmufygwkdYukd BuD;pOfi,fvkdufpOfyg/
(u) 4998? 4997? 4999
(c) 7624? 7316? 7532
1.101.101.101.101.10 10000 txd taygif;? tEkwf10000 txd taygif;? tEkwf10000 txd taygif;? tEkwf10000 txd taygif;? tEkwf10000 txd taygif;? tEkwf
Oyrm(1) 2416 + 3751
2 4 1 6
+ 3 7 5 1
6 1 6 7
tajz = 6167
Oyrm (2) NrdKUe,fwpfckwGif trsdK;om; 3564 a,muf? trsdK;orD; 5237 a,mufaexkdifMuonf/
pkpkaygif; rnfrQaexkdifMuoenf;/
3564 + 5237
3 5 6 4
+ 5 2 3 7
8 8 0 1
tajz/ pkpkaygif;OD;a& = 8801 a,muf
ck tcsif;csif;aygif;yg/
6 + 1 = 7
q,ftcsif;csif;aygif;yg/
1 + 5 = 6
&mtcsif;csif;aygif;yg/
4 + 7 = 1 1
axmiftcsif;csif;aygif;yg/
1 + 2 + 3 = 6
cktcsif;csif;aygif;yg/
4 + 7 = 1 1
1 + 6 + 3 = 1 0
&mtcsif;csif;aygif;yg/
1 + 5 +2 = 8
axmiftcsif;csif;aygif;yg/
3 + 5 = 8
1
11

8
Level 2 Mathematics
avYusifYcef;(10)avYusifYcef;(10)avYusifYcef;(10)avYusifYcef;(10)avYusifYcef;(10)
1/ wGufyg/
(u) 4106 (c) 1056 (*) 2536
+ 3523 +2563 + 5175
(C) 5624 (i ) 1086 (p ) 6739
+ 1752 +2552 + 2154
(q) 5921 +246 (Z) 3086 + 1830 (ps) 397 + 2868
2/ uREkfyffonfaiGpkbPfwGif yxrtBudrf 4524 usyf?'kwd,tBudrf 1578 usyfoGif;aomf
bPfü pkpkaygif;aiGrnfrQoGif;xm;oenf;/
3/ rD;&xm;ukefwGJwpfwGJwGif c&rf;csOfoD; 1754 ydóm?a*:zDxkyf 266 ydómygaomf xdkwGJ½dS
ukefypönf;rsm; pkpkaygif;tav;csdefudk½Smyg/
4/ trsdK;om;jywdkufodkY azazmf0g&DvwGifvma&mufavYvmol 1576 a,muf?rwfvwGif
vma&mufavYvmol 2654 a,mufjzpfonf/xdkESpfvwGif pkpkaygif;vma&mufavYvmol
rnfrQenf;/
1 .111 .111 .111 .111 .11 udef;rsm;aygif;jcif;udef;rsm;aygif;jcif;udef;rsm;aygif;jcif;udef;rsm;aygif;jcif;udef;rsm;aygif;jcif;
Oyrm - qdkif½SifwpfOD;onf yxraeYwGif 250 usyf? 'kwd,aeYwGif 335 usyf?wwd,aeYwGif
421 usyf a&mif;&aomf pkpkaygif;a&mif;&aiGudk½Smyg/
2 5 8
3 3 5
+ 4 2 1
1 0 1 4
tajz/ pkpkaygif;a&mif;&aiG = 1014 usyf
1 1 cktcsif;csif;aygif;yg/
8 + 5 + 1 = 1 4
1 + 5 + 3 + 2 = 1 1
&mtcsif;csif;aygif;yg
1 + 2 + 3 + 4 = 10

9
Level 2 Mathematics
avhusifhcef; (11)avhusifhcef; (11)avhusifhcef; (11)avhusifhcef; (11)avhusifhcef; (11)
1/ wGufyg/
(u) 265 (c) 527 (*) 1580
485 812 754
+173 + 134 3062
+ 91
(C) 1437 + 604 + 1718 (i) 4610 + 1311 + 27124
2/ arG;jrLa&;jcHwpfckwGif Muuf 2089 aumif? bJ 3117 aumif? iHk; 1305 aumif
arG;xm;onf/ pkpkaygif;taumifa& rnfrQarG;xm;oenf/
3/ &yfuGufwpfckwGif trsKd;om; 4207 a,muf? trsKd;orD; 4925 a,muf ESifh
uav; 155 a,muf &Sdaomf xdk&yfuGufwGif vlOD;a&aygif; rnfrQaexdkifMuoenf;/
4/ OD;vluav;onf bPfü yxrvwGif 2575 usyfpkonf/ 'kwd,vwGif 3889
usyfpkonf/ wwd,vwGif 395 usyfpkonf/ OD;vluav; bPfwGifpkxm;aom
aiGaygif;rnfrQ&Sdoenf;/
1 . 121 . 121 . 121 . 121 . 12 udef;rsm; Ekwfjcif;udef;rsm; Ekwfjcif;udef;rsm; Ekwfjcif;udef;rsm; Ekwfjcif;udef;rsm; Ekwfjcif;
Oyrm - NrdKUwpfNrdKUwGif trsKd;om;? trsKd;orD;aygif; 5384 OD;&Sd/ trsKd;om; 2471 OD;
&SdaomftrsKd;orD;rnfrQ&Sdoenf;/
ay;csuf - NrdKUwpfNrdKU&Sd trsKdom; + trsKd;orD; OD;a& = 5384 OD;
trsKd;om; OD;a& = 2471 OD;
ar;csuf - trsKd;orD; OD;a& = ?
pOf;pm;&ef - × ÷ + −
ajz&Sif;csuf -
5 3 8 4
− 2 4 7 1
2 9 1 3
tajz/ trsKd;orD;OD;a& = 2913 OD;
1/ wGufyg/
(u) 4327 (c) 9436 (*) 7653
− 2516 − 1274 − 4217
134

10
Level 2 Mathematics
(C) 7756 (i) 9323 (p) 2837
− 5463 − 2106 − 1264
(q) 8695 − 6742 (Z) 9453 − 4371 (ps) 4835 − 1127
Oyrm -
3 7 4 5
− 1 3 5 8
2 3 8 7
1/ wGufyg/
(u) 8363 (c) 6484 (*) 7294
− 715 − 3705 − 1656
(C) 5378 − 4586 (i) 7050 − 4236 (p) 4600 − 1325
2/ ausmif;wpfausmif;wGif ukvm;xdkif 1875 vHk;&Sdonf/ 386 vHk;usKd;aeaomf aumif;aom
ukvm;xdkifrnfrQ &Sdoenf;/
3/ NrdKUwpfNrdKUwGif rdef;uav; 3815 a,mufESifh a,musfm;av; 1908 a,muf &Sdonf/
rdef;uav; OD;a& rnfrQ ydkoenf;/
4/ vdar®mfoD; 527 vHk;xyf0,fí um;ay:wifvdkuf&m um;ay:wGif pkpkaygif; 2306
vHk; jzpfoGm;/ rlvu um;ay:wGif vdar®mfoD; rnfrQ&Sdoenf;/
5/ tdrfwpftdrfwGif {nhfcef;ESifh rD;zdkcef;twGuf jyifqifc 6040 usyf ukefus/ rD;zdkcef;twGuf
1527 usyf ukefusaomf {nfhcef;jyifqifctwGuf rnfrQukefoenf;/
Oyrm - 4752 ESifh 3509 wdkY aygif;v'frS 6154 udk Ekwfyg/
4 7 5 2
+ 3 5 0 9
8 2 6 1
− 6 1 5 4
2 1 0 7
tajz/ 2107
wpfenf;
(4752 + 3509 ) − 6154 (uGif;udkOD;pGmajz&Sif;yg/)
= 8261 − 6154
= 2107
13 156

11
Level 2 Mathematics
1/ wGufyg/
(u) (4706 − 2538 ) − 1346
(c) (2654 − 327) + 4682
(*) 9782 − (1543 + 3850)
2/ udef;oHk;vHk;aygif;v'fonf 8547 jzpfonf/ yxrudef;ESifh 'kwd,udef;wdkYonf 2372 ESifh
1540 toD;oD;jzpfaomf wwd,udef;udk &Smyg/
3/ OD;armifarmifonf bPfwGif pkxm;aom aiG 6475 usyfrS yxrvwGif 285 usyf
xkwfNyD; 'kwd,vwGif 1237 usyf jyefoGif;aomf bPfü olpkaiG rnfrQ&Sdrnfenf;/
1 .131 .131 .131 .131 .13 cefYrSef;wefzdk;rsm;cefYrSef;wefzdk;rsm;cefYrSef;wefzdk;rsm;cefYrSef;wefzdk;rsm;cefYrSef;wefzdk;rsm;
aygif;v'fudk cefYrSef;jcif;aygif;v'fudk cefYrSef;jcif;aygif;v'fudk cefYrSef;jcif;aygif;v'fudk cefYrSef;jcif;aygif;v'fudk cefYrSef;jcif;
Oyrm (1) 53 + 75 udk eD;&mq,fjynhfudef;rsm;odkY ajymif;í aygif;jcif;jzifh aygif;v'fudk
cefYrSef;yg/ aygif;v'ftrSefudk &Smyg/
cefYrSef;aygif;v'f aygif;v'ftrSef
53 + 175 53
+ 176
50 + 180 =230 229
tajz/ cefYrSef;aygif;v'f = 230
aygif;v'ftrSef = 229
Oyrm (2) 317 + 452 udkeD;&m &mjynfhudef;rsm;odkY ajymif;í aygif;jcif;jzifh aygif;v'fudk
cefYrSef;yg/ xYdkaemuf aygif;v'ftrSefudk &Smyg/
cefYrSef;aygif;v'f aygif;v'ftrSef
317 + 452 317
+ 452
300 + 500 = 800 769
tajz/ cefYrSef;aygif;v'f = 800
aygif;v'ftrSef = 769

12
Level 2 Mathematics
1/ eD;&mq,fjynfhudef;a&;í aygif;jcif;jzifh aygif;v'fudk cefYrSef;yg/
(u) 15 + 11 (c) 41 + 52
(*) 71 + 46 (C) 308 + 89
(i) 35 + 52 (p) 50 + 638
2/ txufygykpämrsm; aygif;v'ftrSefudk &Smyg/
3/ eD;&m &mjynhfudef;rsm;odkY ajymif;í aygif;jcif;jzifh aygif;v'fudk cefYrSef;yg/
(u) 421 + 128 (c) 263 + 415
(*) 201 + 526 (C) 361 + 931
(i) 205 +2733 (p) 1424 + 562
Ekwfv'fudk cefYrSef;jcif;Ekwfv'fudk cefYrSef;jcif;Ekwfv'fudk cefYrSef;jcif;Ekwfv'fudk cefYrSef;jcif;Ekwfv'fudk cefYrSef;jcif;
Oyrm (1) 116 − 32 eD;&m q,fjynhfudef;udk ajymif;í Ekwfv'fudk cefYrSef;yg/ Ekwfv'ftrSef&Smyg/
116 − 32 trSefEkwfv'f
120 − 30 = 90 116
− 32
84
tajz/ cefYrSef;Ekwfv'f = 90
Ekwfv'ftrSef = 84
+ = + =
+ = + =
+ = + =
+ = + =
+ = + =
+ =+ =

13
Level 2 Mathematics
Oyrm (2) 294 − 140 eD;&m &mjynhfudef;odkYajymif;íEkwfv'fudk cefYrSef;yg/ Ekwfv'ftrSefudk
&Smyg/
294 − 140 trSefEkwfv'f
300 − 100 = 200 294
− 140
154
tajz/ cefYrSef;Ekwfv'f = 200
Ekwfv'ftrSef = 154
1/ eD;&m q,fjynhfudef;odkY ajymif;í Ekwfv'fudk cefYrSef;yg/ xdkYaemuf trSefEkwfv'fudk &Smyg/
(u) 48 − 21 (c) 87 − 13 (*) 55 − 31
2/ eD;&m &mjynhfudef;odkY ajymif;í Ekwfv'fudk cefYrSef;yg/ xdkYaemuf trSefEkwfv'fudk &Smyg/
(u) 847 − 115 (c) 386 − 153 (*) 1632 − 801
3/ ZD;uGuf wpfaumif toufonf vaygif; 294 cefYaeEdkifí usD;uef;wpfaumif
toufonf vaygif; 180 cefY aeEdkifonf/ ZD;uGufonf usD;uef;xuf vaygif;
rnfrQcefY ydkítouf&SifaeEdkifoenf;/ (eD;&m &mjynhfudef;)

14
Level 2 Mathematics
tcef;(2)
uka#txdudef;rsm;uka#txdudef;rsm;uka#txdudef;rsm;uka#txdudef;rsm;uka#txdudef;rsm;
2 .12 .12 .12 .12 .1 udef;zwf ? udef;a&;jcif;udef;zwf ? udef;a&;jcif;udef;zwf ? udef;a&;jcif;udef;zwf ? udef;a&;jcif;udef;zwf ? udef;a&;jcif;
odef; aomif; axmif &m q,f ck
1 0 0 0 0 0
10 aomif; = 1 odef; (1 ESifh okn 5 vkHk;ygonf/)
oef; odef; aomif; axmif &m q,f ck
1 0 0 0 0 0 0
10 odef; = 1 oef; (1 ESifh okn 6 vkHk;ygonf/)
uka# oef; odef; aomif; axmif &m q,f ck
1 0 0 0 0 0 0 0
10 oef; = 1 uka# (1 ESifh okn 7 vkHk;ygonf/)
1/ atmufygwdkYudk*Pef;jzifh a&;yg/
(u) av;aomif;oHk;axmifig;&mhajcmuf
(c) &Spfodef; ckepfaomif; wpfaxmifh av;q,fhudk;
(*) ajcmufodef; wpfaomif; ig;axmifh ESpf&m
(C) oHk;uka# ig;oef; av;aomif; ESpf&mh ig;q,f
(i) q,fuka#
2/ atmufygudef;rsm;udkpmjzifh a&;yg/
(u) 6123400 (c) 38730690 (*) 20780000 (C) 10930000
2 . 22 . 22 . 22 . 22 . 2 ae&mvdkuf wefzdk;t& tus,fjzefYjcif;ae&mvdkuf wefzdk;t& tus,fjzefYjcif;ae&mvdkuf wefzdk;t& tus,fjzefYjcif;ae&mvdkuf wefzdk;t& tus,fjzefYjcif;ae&mvdkuf wefzdk;t& tus,fjzefYjcif;
1/ atmufygudef;wdkYwGif 3 ae&mvdkuf wefzdk;udk a&;yg/
Oyrm - 32547 wGif 3 ae&mtvdkuf wefzdk; 3 aomif; (30000)
(u) 13254 (c) 324578 (*) 9316040 (C) 35000000

15
Level 2 Mathematics
2/ atmufygwdkYudk ae&mvdkuf wefzdk;t& tus,fjzefYyg/
Oyrm - 21860
20000 1000 800 60 0
(u) 7042 (c) 58061 (*) 429135 (C) 1234000
(i) 2431008 (p) 86530000
3/ atmufygwdkYudk pHyHkpH jyifa&;yg/
Oyrm - 5000 + 200 + 90 + 4 = 5294
(u) 60000 + 4000 + 300 + 10 + 3
(c) 100000 + 20000 + 3000 + 400 +50 + 6
(*) 800000 + 9000 + 400 + 8
2 . 32 . 32 . 32 . 32 . 3 udef;rsm;udk EIdif;,SOfjcif; (BuD;jcif;? i,fjcif;)udef;rsm;udk EIdif;,SOfjcif; (BuD;jcif;? i,fjcif;)udef;rsm;udk EIdif;,SOfjcif; (BuD;jcif;? i,fjcif;)udef;rsm;udk EIdif;,SOfjcif; (BuD;jcif;? i,fjcif;)udef;rsm;udk EIdif;,SOfjcif; (BuD;jcif;? i,fjcif;)
Oyrm - 732980 ESifh 739261 wdkYudk EIdif;,SOfyg/
7 3 2 9 8 0 ESifh 7 3 9 2 6 1
- odef;*Pef;upí EIdif;,SOfyg/odef;*Pef;upí EIdif;,SOfyg/odef;*Pef;upí EIdif;,SOfyg/odef;*Pef;upí EIdif;,SOfyg/odef;*Pef;upí EIdif;,SOfyg/
7 csif;wlonf/
- aomif;*Pef;csif;wlonf/
- 2 axmifonf 9 axmif
atmufi,fonf/
xdkYaMumifh 732980 < 739261
(odkYr[kwf) 73926 > 732980
2 . 42 . 42 . 42 . 42 . 4 i,fpOf BuD;vdkuf pDpOfjcif;i,fpOf BuD;vdkuf pDpOfjcif;i,fpOf BuD;vdkuf pDpOfjcif;i,fpOf BuD;vdkuf pDpOfjcif;i,fpOf BuD;vdkuf pDpOfjcif;
Oyrm - 206 ? 199? 67? 45 wdkYudk i,fpOf BuD;vdkuf pOfyg/
tajz/ 45? 67? 199? 206
1/ atmufygudef;wdkYudk EIdif;,SOfí wGif < , > , = wdkYudkazmfjyyg/
(u) 9503 9103 (c) 9126 385236
(*) 79406 79406 (C) 579181 574138
(i) 10000 9999 (p) 201100 189879
+ + + +

16
Level 2 Mathematics
2/ atmufygudef;wdkYudk i,fpOfBuD;vdkuf pOfyg/
(u) 10100 ? 6800? 8900 (c) 60585? 18674? 42963
(*) 524387? 532387? 524870
2 . 42 . 42 . 42 . 42 . 4 taygif;ESifh tEkwftaygif;ESifh tEkwftaygif;ESifh tEkwftaygif;ESifh tEkwftaygif;ESifh tEkwf
Oyrm - 38565 + 23369
3 8 5 6 5
+ 2 3 3 6 9
6 1 9 3 4
tajz/ 61934
1/ atmufygwdkYudk wGufyg/
(u) 35466 (c) 67211 (*) 567214
+ 48203 + 92478 + 230826
(C) 1564 (i) 852796 (p) 64933
+ 3259 + 749415 + 6498
(q) 66822 + 4731 (Z) 13172 + 8639
(u) 239 (c) 43020 (*) 57040
54 56890 72815
3876 3140 6904
+7205 +73990 + 105
(C) 8 + 1377 + 74290 (i) 16864 + 84262 + 3516
11 1 5 + 9 = 1 4
1 + 6 + 6 = 1 3
8 + 3 = 1 1

17
Level 2 Mathematics
3/ *Pef;wGufpuf wpfzufyg avhusifhcef; rS ykpämrsm;udk *Pef;wGufpuf
jzifhwGufNyD; tajzcsdefudkufyg/
Oyrm- 8 + 1377 + 74290
yxrOD;pGm *Pef;wGufpuf&Sd ON cvkwfudk zdyg/
xdkaemuf 8 udkESdyf + 1? 3? 7? 7 + 7? 4? 2? 9? 0
= udk tpDtpOftwdkif;ESdyfygu tajz 75675 &rnf/
Oyrm- 64458 − 26524
yxrOD;pGm *Pef;wGufpuf&Sd ON cvkwfudkzdyg/
6? 4? 4? 5? 8? − 2? 6? 5? 2? 4 = udk
tpDtpOftwdkif;ESdyfygu tajz 39934 &rnf/
atmufygavhusihfcef;ykpämrsm;udk *Pef;wGufpufjzifhwGufNyD; tajzcsdefudkufyg/
Oyrm (1) 37000 − 1234 + 36
*Pef;wGufpuf ON cvkwfudk ESdyfNyD;vQif 3? 7? 0? 0? 0 − 1? 2? 3? 4 + 3? 6 = udk
tpDtpOftwdkif; ESdyfygu tajz&rnf/
Oyrm (2) NrdKUe,f wpfNrdKUe,füf ESpfpwGifaexdkifol 47521 a,muf &Sd/ xdkESpfwGif uav;
674 a,muf arG;NyD; vl 138 a,muf aoqHk;/ ESpfqHk;ü vlOD;a& rnfrQ
jzpfrnfenf;/
ay;csuf - ESpfp aexdkifol = 47521 a,muf
arG;ol = 674 a,muf
aoqHk;ol = 138 a,muf
ar;csuf - ESpfqHk;ü vlOD;a& = ?
pOf;pm;&ef - × ÷ + −
ajz&Sif;csuf - ESpfqHk;üvlOD;a& = 47521 + 674 - 138
47521 48195
+ 674 - 138
48195 48057
tajz/ ESpfqHk;üvlOD;a& = 48057 a,muf
1/ atmufygwdkYudk wGufyg/ (*Pef;wGufpufoHk;NyD;tajzcsdefudkufyg/)
(u) 62546 (c) 55346 (*) 47496
− 21304 − 21764 − 21857
(C) 80507 − 4684 (i) 53900 − 7059
2/ atmufygwdkYudk wGufyg/ (*Pef;wGufpufoHk;NyD;tajzcsdefudkufyg/)
(u) 70906 + 2527 − 40603 (c) 37000 + 3472 − 5621

18
Level 2 Mathematics
1/ OD;ponfbPf&SdpkaiGxJrS 8165 usyf xkwfNyD;aomtcgbPfüvufusefaiG 1567
usyfusef/rxkwfrDupkaiGrnfrQ&Sdoenf;/
2/ NrdKUwpfNrdKUvlOD;a&onfwpfESpfwmtwGif; 87560 a,mufrS 86214 a,mufodkY usqif;
oGm;/xdkESpftwGif;avsmhoGm;aomvlOD;a&rnfrQenf;/
3/ ausmif;wpfausmif;rdbq&mtoif; &efyHkaiG 57425 usyfrS y&dabm* jyKjyif&ef
3820 usyf wpfBudrf? 2500 usyf wpfBudrf xkwf,lvdkufaomf &efyHkaiGrnfrQusefoenf;/
4/ tkwfpufwpfckwGiftkwfvufusef 5500 &Sd/ aemufxyftkwfcsyfaygif; 257200
xkwfvkyfonf/ tkwfcsyf 145700 csyfudk a&mif;vdkufaomf tkwfpufü tkwfcsyfrnfrQ
usefoenf;/
2 . 52 . 52 . 52 . 52 . 5 eD;yg;wefzdk;rsm;eD;yg;wefzdk;rsm;eD;yg;wefzdk;rsm;eD;yg;wefzdk;rsm;eD;yg;wefzdk;rsm;
eD;&m axmifjynhf? aomif;jynhf udef;rsm;udk cefYrSef;jcif;eD;&m axmifjynhf? aomif;jynhf udef;rsm;udk cefYrSef;jcif;eD;&m axmifjynhf? aomif;jynhf udef;rsm;udk cefYrSef;jcif;eD;&m axmifjynhf? aomif;jynhf udef;rsm;udk cefYrSef;jcif;eD;&m axmifjynhf? aomif;jynhf udef;rsm;udk cefYrSef;jcif;
Oyrm (1) 6800 udk eD;&maxmifjynhfudef;odkY cefYrSef;yg/
6800
5000 6000 7000 8000
6800 onf qufwdkuf axmifjynhfudef; 6000 ESifh 7000 Mum;wGif &Sdonf/
7000 ESifh ydkeD;onf/
xdkYaMumifh 6800 cefYrSef; wefzdk; = 7000
Oyrm (2) 3500 udk eD;&maxmifjynhfudef;odkY cefYrSef;yg/
3500
2000 3000 4000 5000
3500 onf qufwdkuf axmifjynhfudef; 3000 ESifh 4000 Mum; tv,fwnhfwnhf
wGif&Sdonf/
(ydkí BuD;aom axmifjynhfudef;odkY cefYrSef;yg/)
xdkYaMumifh 3500 cefYrSef;wefzdk; = 4000

19
Level 2 Mathematics
Oyrm (3) 17500 udk eD;&maomif;jynhfodkY cefYrSef;yg/
17500
0 10000 20000
17500 onf qufwdkuf aomif;jynfhudef; 10000 ESifh 20000 Mum;wGif &Sdonf/
20000 ESifh ydkí eD;onf/
xdkYaMumifh 17500 cefYrSef;wefzdk; = 20000
1/ eD;&maxmifjynhfudef;odkY cefYrSef;yg/
(u) 8134 (c) 5280 (*) 1625 (C) 14831
2/ eD;&m aomif;jynhfudef;odkY cefYrSef;yg/
(u) 21960 (c) 31498 (*) 54671 (C) 155890
3/ atmufygZ,m;wGif jznhfpGufyg/
ay;&if;udef; eD;&m &mjynhfudef; eD;&m axmifjynhfudef; eD;&m aomif;jynhfudef;
17531 17500 18000 20000
27821
53465
39083
aygif;v'f? Ekwfv'f cefYrSef;jcif;aygif;v'f? Ekwfv'f cefYrSef;jcif;aygif;v'f? Ekwfv'f cefYrSef;jcif;aygif;v'f? Ekwfv'f cefYrSef;jcif;aygif;v'f? Ekwfv'f cefYrSef;jcif;
Oyrm - 5854 + 1107 udk eD;&maxmifjynhfudef;odkYajymif;íaygif;jcif;jzifhaygif;v'fudkcefYrSef;yg/
5854 6000
1107 +1000
7000 tajz/ cefYrSef;aygif;v'f = 7000
1/ eD;&maxmifjynhfudef;odkY ajymif;í aygif;v'f? Ekwfv'f cefYrSef;yg/
(u) 2481 + 6902 (c) 4830 + 6324 (*) 3558 − 1726
(C) 3041 − 1938

20
Level 2 Mathematics
2 . 62 . 62 . 62 . 62 . 6 taygif;? tEkwf pdwfwGuftaygif;? tEkwf pdwfwGuftaygif;? tEkwf pdwfwGuftaygif;? tEkwf pdwfwGuftaygif;? tEkwf pdwfwGuf
(u) q,fudef;rsm;rS pí aygif;jcif; (c) ckudef;udk q,fjynhfjzpfatmifjznhfjcif;
66 + 25 = ? 98 + 34 = ?
60 + 20 = 80 98 + 2 + 32 = ?
6 + 5 = 11 100 + 32 = 132
80 + 11 = 91 tajz/ 132
tajz/ 91
(*) ckudef;udk q,fjynhfatmif jznhfí Ekwfjcif;
34 usyfzdk; 0,f&m wpf&musyfwefay;aomfrnfrQjyeftrf;rnfenf;/ (pdwfwGuftajccH)
100 100 +6 106
- 34 34 + 6 - 40
66
tajz/ jyeftrf;aiG = 66 usyf
1/ pdwfwGuf wGufyg/
(u) 95 + 34 (c) 29 + 63 (*) 62 + 59
(C) 77 + 24 (i) 57 + 63 (p) 158 + 24
Ekwfudef;udkq,fjynhfudef;ESifhckudef;cGJjcif;/Ekwfudef;udkq,fjynhfudef;ESifhckudef;cGJjcif;/Ekwfudef;udkq,fjynhfudef;ESifhckudef;cGJjcif;/Ekwfudef;udkq,fjynhfudef;ESifhckudef;cGJjcif;/Ekwfudef;udkq,fjynhfudef;ESifhckudef;cGJjcif;/ Ekwfudef;udkq,fjynhfudef;odkYwdk;jcif;/Ekwfudef;udkq,fjynhfudef;odkYwdk;jcif;/Ekwfudef;udkq,fjynhfudef;odkYwdk;jcif;/Ekwfudef;udkq,fjynhfudef;odkYwdk;jcif;/Ekwfudef;udkq,fjynhfudef;odkYwdk;jcif;/
91 − 52 = ? 117 − 98 = ?
91 − 50 = 41 117 − 100 = 17 (2 ydkEkwfxm;onf/)
41 − 2 = 39 17 + 2 = 19

21
Level 2 Mathematics
1/ pdwfwGuf wGufyg/
(u) 47 − 23 (c) 53 − 26 (*) 39 − 36
(C) 92 − 53 (i) 96 − 79 (p) 126 − 98
2/ (u) 78 usyfzdk;0,f&m 100 usyfwefay;vdkufaomf aiGrnfrQ jyeftrf;rnfenf;/
(c) 76 usyfzdk;0,f&m 200 usyfwefay;vdkufaomf aiGrnfrQ jyeftrf;rnfenf;/
(*) 380 usyfzdk;0,f&m 500 usyfwefay;vdkufaomf aiGrnfrQ jyeftrf;rnfenf;/
(C) 457 usyfzdk;0,f&m 1000 usyfwef ay;vdkufaomf aiGrnfrQ jyeftrf;rnfenf;/
(BudKuf&m wGufenf;jzifh wGufEdkifonf/)

22
Level 2 Mathematics
tcef;(3)
*sDMoarBuDqdkif&mtajccHrsm;*sDMoarBuDqdkif&mtajccHrsm;*sDMoarBuDqdkif&mtajccHrsm;*sDMoarBuDqdkif&mtajccHrsm;*sDMoarBuDqdkif&mtajccHrsm;
3.13.13.13.13.1 trSwftrSwftrSwftrSwftrSwf
puúLay:wGif cJwHjzifh tpufi,fwpfckay:atmif axmufyg/ tqdkyg tpufi,fudk trSwftrSwftrSwftrSwftrSwf
[kac:onf/
3.23.23.23.23.2 rsOf;rsOf;rsOf;rsOf;rsOf;
vQyfppfrD;BudK;vdkif;uJhokdY 0JbufodkYvnf;aumif;? ,mbufodkYvnf;aumif;? tqkH;r½Sdajzmifhwef;
pGm wpfajzmifhwnf;oGm;aeonfh BudK;vdkif;rsKd;udk rsOf;rsOf;rsOf;rsOf;rsOf; [kac:onf/ rsOf;udktrnfay;vdkvQif
rsOf;ay:wGif trSwfESpfck ( B ESifh C ) udk,lNyD; rsOf; B C (odkYr[kwf) CB [k ac:Edkifonf/
3.33.33.33.33.3 rsOf;jywfrsOf;jywfrsOf;jywfrsOf;jywfrsOf;jywf
t0wfvSef;BudK;wef;uJhodkY ESpfbufpvkH;wdwd&d&djywfaeaomBudK;ykdif;udk rsOf;jywfrsOf;jywfrsOf;jywfrsOf;jywfrsOf;jywf [k
ac:onf/
rsOf;jywf DE (odkY) rsOf;jywf ED
1/ atmufygrsOf;wdkY trnfudk a&;yg/
(u) rsOf; AB (odkYr[kwf) rsOf; BA
(c)
(*)
tqdkygtrSwfrsKd;ukd A , B, C ........ ponfjzihf
trnfay;avh ½Sdonf/
ykHwGif trSwf A [k trnfay;xm;onf/
D E
B C
A B
M O
C D

23
Level 2 Mathematics
2/ atmufygrsOf;jywfwdkYtrnfudka&;yg/
(u) rsOf;jywf XY (odkYr[kwf) rsOf;jywf YX
(c)
(*)
rwfrsOf;ESifha&jyifnDrsOf;rwfrsOf;ESifha&jyifnDrsOf;rwfrsOf;ESifha&jyifnDrsOf;rwfrsOf;ESifha&jyifnDrsOf;rwfrsOf;ESifha&jyifnDrsOf;
cJwpfvkH;udkBudK;jzifhcsnfíykHtwdkif;qGJyg/
BudK;onf txufatmufwef;aeonf/
vuform;oHk;csdefoD;BudK;onfvnf; txufatmuf
wef;aeonf/
xdkodkY txufatmufwpfajzmifhwnf;½Sdaom
rsOf;ukd rwfrsOf;rwfrsOf;rwfrsOf;rwfrsOf;rwfrsOf; [k ac:onf/
a&xnfhxm;aom zefcGufudk ykHtwdkif; taetxm;ajymif;íudkifyg/ twGif;½Sda&rsufESmjyifonf
tNrJwapwajy;wnf;nDnDnmnm½Sdaeonf/
a&rsufESmjyifuJhodkY wajy;wnf;nDnmaeaomrsOf;udk a&jyifnDrsOf;a&jyifnDrsOf;a&jyifnDrsOf;a&jyifnDrsOf;a&jyifnDrsOf; [k ac:onf/
a&jyifnDrsOf;rsm;
X
J
Y
Q
K
R

24
Level 2 Mathematics
1/ rwfrsOf;ESifha&jyifnDrsOf;rsm;ukd a½G;yg/
tajy;NydKifyGJwpfckwGif ajy;vrf;qGJxm;aom
xkH;jzLaMumif;rsm; wpfckESifhwpfckNydKifaeonf/
rsOf;AB ESifh rsOf;CD wdkYonfrnfonfhae&m
wGifrqdk tuGmta0;wlonf/
xkdrsOf;wdkYudk rsOf;NydKifrsm;rsOf;NydKifrsm;rsOf;NydKifrsm;rsOf;NydKifrsm;rsOf;NydKifrsm; [kac:onf/
tcsif;csif;jzwfaeaomrsOf;rsm;tcsif;csif;jzwfaeaomrsOf;rsm;tcsif;csif;jzwfaeaomrsOf;rsm;tcsif;csif;jzwfaeaomrsOf;rsm;tcsif;csif;jzwfaeaomrsOf;rsm;
atmufygvrf;ESpfvrf;onf wpfckESifhwpfck jzwfaeonf/
rsOf; AB ESifh XY rsOf; wdkYonf wpfckESifhwpfckjzwfaeonf/
C D
I J
A
G
H
B E
FL
K
A B
C D
B
X
YA

25
Level 2 Mathematics
wHcg;zGifhvQif uwfaMu; rkefYydkif;vQif vufauG;vQif
toHk;jyKvQif
cJwHcRef"m;zGifhvQif
pmtkyf tzHk;zGifhvQif axmifhrsm;jzpfay:onf/
axmifht&G,ftpm; trsKd;rsKd;&Edkifonf/
avhusifhcef; (3)
rsOf;NydKifrsm; ESifh tcsif;csif;jzwfaeaom rsOf;rsm;udka&G;yg/
1/
2 / 3 /
4 / 5 / 6 /
3 .4 vSnfhjcif; ESifh axmifh

26
Level 2 Mathematics
O
M
P
F
D
E
axmifhrSef
axmifhusOf;
A
B C
Q
P
R
axmifhus,f
axmifh
axmifhrsm;axmifhrsm;axmifhrsm;axmifhrsm;axmifhrsm;
rsOf;jywfESpfaMumif;awGUqkH&mtrSwfwGif axmifhwpfck udk jzpfay:aponf/
rsOf;jywf AB ESifh BC wdkYonf B trSwfwGif awGUqkHí
jzpfay:vmonhfaxmifhudk axmifh ABC (odkYr[kwf) axmifh
CBA [ktrnfay;Edkifonf/ (axmifhudkoauFw jzifh
azmfjyEdkifonf/)
ABC (okdYr[kwf) CBA [k a&;onf/
a&jyifnDrsOf;ESifhrwfrsOf;wdkYqHkíjzpfay:vmaom
axmifhyrmPudk axmifhrSef[kac:onf/
DEF (odkYr[kwf) FED onf axmifhrSefaxmifhrSefaxmifhrSefaxmifhrSefaxmifhrSef jzpfonf/
MOP (odkYr[kwf) POM onf axmifhrSefatmufi,f
onf/
axmifhrSefwpfckatmufi,fonfhaxmifhrSefwpfckatmufi,fonfhaxmifhrSefwpfckatmufi,fonfhaxmifhrSefwpfckatmufi,fonfhaxmifhrSefwpfckatmufi,fonfhaxmifhukd axmifhusOf;axmifhusOf;axmifhusOf;axmifhusOf;axmifhusOf;
[k ac:onf/
MOP (odkYr[kwf) POM onf axmifhusOf;jzpfonf/
PQR (odkYr[kwf) RQP onf axmifhrSefxufBuD;onf/
axmifhrSefwpfckxufBuD;axmifhrSefwpfckxufBuD;axmifhrSefwpfckxufBuD;axmifhrSefwpfckxufBuD;axmifhrSefwpfckxufBuD;aom axmifhudkaxmifhus,faxmifhus,faxmifhus,faxmifhus,faxmifhus,f
[k ac:onf/
PQR (okdY) RQP onf axmifhus,fjzpfonf/
vufawGUvkyfief;
1/ puúLacguf usifwG,fudktoHk;ûyí axmifhrsm;udkvufawGUavhvmyg/
2/ ywf0ef;usif&Sdaxmifhrsm;udkajymjyí axmifhtrsKd;tpm;cGJjyyg/

27
Level 2 Mathematics
S
T
U
L
O M
Z Y
X
A
F
C
E
D
B
1/ uREfkyfwdkY aeYpOfûyvkyfaeaom tûytrlrsm;teuf rnfonhftcgwGif axmifhrsm;udk jzpfay:
oenf;/ yHkMurf;qGJyg/
2/ atmufygaxmifhrsm;udkaxmifhtrnfa&;NyD; axmifhusOf;? axmifhus,f? axmifhrSef[lícGJjyyg/
axmifh axmifhtrnf axmifhtrsKd;tpm;
(u)
(c)
(*)
(C)
(i)

28
Level 2 Mathematics
vSnhfjcif; ESifh axmifhrSefrsm;vSnhfjcif; ESifh axmifhrSefrsm;vSnhfjcif; ESifh axmifhrSefrsm;vSnhfjcif; ESifh axmifhrSefrsm;vSnhfjcif; ESifh axmifhrSefrsm;
azmfjyygyHkwGif,kefuav;jzLazG;onfuefpGef;yif
bufodkY wnfhwnfhrsufESmrlumMunfhae/
(p rSwf)
vuf0JbufwnfhwnfhodkY vSnfhvdkufaom
tcg rkefvmOudkawGUvdkuf&/
xkdrSwpfzefvuf0JbufwnfhwnfhodkY xyfvSnfh
vdkuf&m a½Tz½kHoD;ukdawGU&/
xkdrSxyfrHívuf0JbufwnfhwnfhodkY vSnfhjyef&m
yef;a*:zDudkawGU&/
vuf0JbufwnfhwnfhodkY xyfvSnfhjyef&m
uefpGef;yifukdjyefawGU&ojzifh,kefuav;jzLazG;
onf olwpfywfwdwdvSnfhaeaMumif; owdûyrd
oGm;onf/
,kefuav;jzLazG; wpfywfvSnfh&mvrf;
aMumif;udkrsOf;pufrsm;jzifhazmfjyxm;onf/
wpfBudrfvSnfhíjzpfay:vmaomaxmifhrsm;ukd
wdkif;Munfhyg/ wpfaxmifhrSefpD½Sdaeonf/
xdkYaMumifhwpfywf vSnfhvQif 1 axmifhrSef&/
1 axmifhrSef&&ef vSnfhjcif;udk vSnfhjcif;[kac:onf/
2 axmifhrSef&&efvSnfhjcif;udk vSnfhjcif; (odkYr[kwf) wpf0ufvSnfhjcif;[k ac:onf/
txufygyHkudkMunhfí ,kefuav;rnfonhf tpmudk pm;csifaeygovJ/
vuf0JbufodkY
prSwf vSnfhfrnfhaxmifhyrmP pm;vdkonhftpm
uefpGef;yif 2 axmifhrSef
rkefvmO 3 axmifhrSef
a½Tz½kHoD; 1 axmihfrSef
yef;a*:zD 2 axmifhrSef
4
1
2
1
4
1

29
Level 2 Mathematics
3.53.53.53.53.5 *sDMoarBwDykHrsm;*sDMoarBwDykHrsm;*sDMoarBwDykHrsm;*sDMoarBwDykHrsm;*sDMoarBwDykHrsm;
rsufESmjyifwpfckukd vkHatmifumEkdif&eftem;(odkYr[kwf)rsOf;jywftenf;qkH;rnfrQvdkoenf;/
«tenf;qkH;tem;(odkY)rsOf;jywfokH;ckvdkayrnf/»
Bwd*HBwd*HBwd*HBwd*HBwd*H
atmufygykHrsm;wGif½Sdaom tem;rsm;udka&wGufyg/
tem;(3)em;yg½Sdaom ykHtm;vkH;udk Bwd*H[k ac:onf/
pwk*Hpwk*Hpwk*Hpwk*Hpwk*H
atmufygykHrsm;wGif½Sdaom tem;rsm;udka&wGufyg/
tem;(4)em;yg½Sdaom ykHtm;vkH;ukd pwk*H[k ac:onf/
yOö*HyOö*HyOö*HyOö*HyOö*H
tem;(5)em;yg½Sdaom ykHtm;vkH;ukd yOö*H[k ac:onf/

30
Level 2 Mathematics
q|*Hq|*Hq|*Hq|*Hq|*H
tem;(6)em;yg½Sdaom ykHtm;vkH;ukd q|*H[k ac:onf/
A[k*HA[k*HA[k*HA[k*HA[k*H
rsOf;ajzmifhrsm;jzifh rsufESmjyifwpfckudkvHkatmifumxm;onfh yHkoP²meftrsKd;rsKd;?
trnftrsKd;rsKd;&Sdaom *sDMoarBwDyHkrsm;udk A[k*HA[k*HA[k*HA[k*HA[k*H [kac:onf/
1/ atmufygA[k*HwpfckpDESifh oufqdkifaom trnf? tem;ta&twGufESifh axmifhta&
twGufwdkYudk azmfjyyg/
A[k*H A[k*Htrnf tem;ta&twGuf axmifhta&twGuf
(u)
(c)
(*)
(C)
2/ tem;ta&twGufckepfckyg&Sdaomowå*HESifh tem;ta&twGuf&Spfckyg&Sdaomt|*HwdkY
axmifhta&twGufudk cefYrSef;yg/ yHkMurf;a&;qGJí oifcefYrSef;csuf rSef? rrSef ppfaq;yg/

31
Level 2 Mathematics
3 3
3
3 2
3.7
4
5.5
2
3 3
2
2
2
2
4
4
5
Bwd*HtrsKd;rsKd;Bwd*HtrsKd;rsKd;Bwd*HtrsKd;rsKd;Bwd*HtrsKd;rsKd;Bwd*HtrsKd;rsKd;
okH;em;nDBwd*HokH;em;nDBwd*HokH;em;nDBwd*HokH;em;nDBwd*HokH;em;nDBwd*H
tem;rsm;udkvufawGUwdkif;Munfhyg/
tem;okH;em;vHk; tvsm;rsm;wlnDaeonfukdawGU&rnf/
xdkBwd*Hudk okH;em;nDBwd*HokH;em;nDBwd*HokH;em;nDBwd*HokH;em;nDBwd*HokH;em;nDBwd*H [kac:onf/
ESpfem;nDBwd*HESpfem;nDBwd*HESpfem;nDBwd*HESpfem;nDBwd*HESpfem;nDBwd*H
tem;rsm;ukdwdkif;Munfhyg/ tem;ESpfckom tvsm;rsm;wlaeonf/
xdkBwd*Hudk ESpfem;nDBwd*HESpfem;nDBwd*HESpfem;nDBwd*HESpfem;nDBwd*HESpfem;nDBwd*H [kac:onf/
tem;rnDBwd*Htem;rnDBwd*Htem;rnDBwd*Htem;rnDBwd*Htem;rnDBwd*H
tem;rsm;ukdwdkif;Munfhyg/ tem;rsm;wpfckESifhwpfcktvsm;rwl
aMumif;awGU&onf/
xkdBwd*Hudk tem;rnDBwd*Htem;rnDBwd*Htem;rnDBwd*Htem;rnDBwd*Htem;rnDBwd*H [kac:onf/
1/ atmufygykHwkdYwGif tvsm;rsm;ukd pifwDrDwmjzifhazmfjyxm;onf/
(u) okH;em;nD Bwd*HwkdYukd a&G;cs,fyg/
(c) ESpfem;nD Bwd*HwkdYukd a&G;cs,fyg/
(*) tem;rnD Bwd*HwkdYukd a&G;cs,fyg/

32
Level 2 Mathematics
pwk*HtrsKd;rsKd;pwk*HtrsKd;rsKd;pwk*HtrsKd;rsKd;pwk*HtrsKd;rsKd;pwk*HtrsKd;rsKd;
tem;NydKifpwk*Htem;NydKifpwk*Htem;NydKifpwk*Htem;NydKifpwk*Htem;NydKifpwk*H
ay;xm;aomykHonf pwk*HykHjzpfonf/ rsufESmcsif;qdkif
tem;rsm;onfNydKifaeMuNyD; tvsm;rsm;vnf;wlMuonf/
xdkpwk*HrsKd;ukd tem;NydKifpwk*tem;NydKifpwk*tem;NydKifpwk*tem;NydKifpwk*tem;NydKifpwk*H [kac:onf/
axmifhrSefpwk*HaxmifhrSefpwk*HaxmifhrSefpwk*HaxmifhrSefpwk*HaxmifhrSefpwk*H
tem;NydKifpwk*Hyifjzpfonf/ axmifhrsm;onf 1 axmifhrSefpD
½Sdonf/ rsufESmcsif;qdkiftem;wpfpkHpDtvsm;rsm; wlnD
Muonf/ axmifhrSefpwk*HaxmifhrSefpwk*HaxmifhrSefpwk*HaxmifhrSefpwk*HaxmifhrSefpwk*H [kac:onf/
pwk&ef;pwk&ef;pwk&ef;pwk&ef;pwk&ef;
tem;NydKifpwk*Hyifjzpfonf/ axmifhrsm;onf 1 axmifhrSefpD
&Sdonf/ tem;rsm;tm;vkH;tvsm;wlMuonf/ pwk&ef;pwk&ef;pwk&ef;pwk&ef;pwk&ef; [k
ac:onf/
1/ atmufygyHkrsm;udkMunhfí trsKd;tpm;cGJay;yg/
A[k*Hrsm; tajz/ -------------------------------
Bwd*Hrsm; tajz/ ----- pwk*Hrsm; tajz/ -----------
tem;NydKifpwk*Hrsm; tajz/ --------
axmifhrSefpwk*Hrsm; tajz/ ----------
pwk&ef;rsm; tajz --------
2/ eHygwf (1) tajzrsm;udk Munhfí aumufcsufcsyg/
7 8 9 10 11
1 2 3 4 5 6

33
Level 2 Mathematics
puf0dkif;puf0dkif;puf0dkif;puf0dkif;puf0dkif;
uyfjym;i,fwpfckudk,lyg/ oifhawmfaomtuGmta0
jzifhtayguf(2)aygufazmufyg/ taygufrsm;udk(A) (B)
[k trnfay;yg/ xdktaygufygaom uyfjym;udk
pm&Gufay:wifyg/ (A) taygufwGif xnhfxm;aom
cJwHudk yHkaoaxmufNyD;uyfjym;udkvSnhfí (B) tayguf&Sd
cJwHjzifh trSwfpufrsm;csyg/
(B) tayguf&SdcJwHaMumifhjzpfay:vmaom trSwfpuf
wdkif;onf tayguf (A) &SdcJwHaMumifhjzpfay:aeaom
trSwfpufrS tuGmta0; tNrJwlaeonf/
uyfjym;udk rlv(A) ae&mwGifcJwHudkwpfxyfwnf;
usapyg/ (B) tayguf&SdcJwHjzifhuyfjym;udkvSnfhNyD;
trSwfpufrsm;udk wpfqufwnf; jzpfatmif a&;qGJyg/
uyfjym;ESifhcJwHrsm;udkz,fvdkufyg/ &Sdvmaom yHkudk
puf0dkif;yHkpuf0dkif;yHkpuf0dkif;yHkpuf0dkif;yHkpuf0dkif;yHk [kac:onf/
ykHaoaxmufxm;aom (A) ae&monf puf0dkif;yHk
A[dkA[dkA[dkA[dkA[dk jzpfonf/
ykHwGif A udk A[dk
AB udk tcsif;0uf[kac:onf/
AQ, AR wdkYonfvnf; tcsif;0uftcsif;0uftcsif;0uftcsif;0uftcsif;0uf jzpfonf/
ST onf A udk jzwfoGm;onf/
ST udk tcsif;tcsif;tcsif;tcsif;tcsif; [kac:onf/
trSwfwpfckrSwlnDpGmuGma0;aomwpfckrSwlnDpGmuGma0;aomwpfckrSwlnDpGmuGma0;aomwpfckrSwlnDpGmuGma0;aomwpfckrSwlnDpGmuGma0;aomtrSwfrsm;udkqufoG,fonfhrsOf;auG;udkpuf0dkif;puf0dkif;puf0dkif;puf0dkif;puf0dkif;[kac:onf/
vufawGUvkyfief;
puf0dkif;rsm;vufawGUa&;qGJyg/ rdrdpuf0dkif;ütcsif;? tcsif;0ufrsm;a&;qGJNyD; wdkif;wmyg/
ywf0ef;usifwGifawGU&wwfaompuf0dkif;yHkrsm;udkazmfjyyg/ (Oyrm - vSnf;bD;)
A
BR
Q
A
S
T

34
Level 2 Mathematics
E
C
A
B
F
D
O
P
QR
S
O
L
M NP Q
R
S
A
P
Q
R
1/ yHkwGifrnfonhftrSwfonf A[dktrSwfjzpfoenf;/
rnfonhfrsOf;rsm;onfomtcsif;0ufrsOf;rsm;jzpfoenf;/
tb,faMumifhenf;/
2/ rnfonfhrsOf;rsm;onf tcsif;rsOf;jzpfoenf;/
rsOf;jywf FC onf tcsif;rsOf;jzpfygovm;/
tb,faMumifhenf;/
3/
puf0dkif;ykHtkwfckHwpfcktv,fA[dk wnfhwnfhwGif
"mwfrD;wdkifwpfck½Sdonf/ tkwfckHtem;ESifhuyfí ½G,fwl
yef;tdk; A,B,C,D av;tdk;udkcsxm;&m yef;tdk; A onf
"mwfrD;wdkifrS 3 ayuGma0;/yef;tdk; B,C, D wdkYonf
"mwfrD;wdkifrSrnfrQuGma0;rnfenf;/ tb,faMumifhenf;/
4/
RS = 0. 5 pifwDrDwm MN = 0. 8 pifwDrDwm AR = 1. 5 pifwDrDwm
PQ = 1 pifwDrDwm OL = 1. 6 pifwDrDwm PQ = 3 pifwDrDwm
ay;xm;aom puf0dkif;oHk;ck twdkif;twmrsm;udk avhvmí rnfodkY aumufcsufcsEdkifoenf;/

35
Level 2 Mathematics
tcef;(4)
tajr§muftajr§muftajr§muftajr§muftajr§muf
4.14.14.14.14.1 *Pef;wpfckygaomudef;jzifh ajr§mufjcif;*Pef;wpfckygaomudef;jzifh ajr§mufjcif;*Pef;wpfckygaomudef;jzifh ajr§mufjcif;*Pef;wpfckygaomudef;jzifh ajr§mufjcif;*Pef;wpfckygaomudef;jzifh ajr§mufjcif;
Oyrm - 8716 × 4 udk wGufyg/
8 7 1 6
× 4
3 4 8 6 4
(u) 2135 (c) 1208 (*) 157 (C) 2350
× 2 × 8 × 6 × 4
(i) 10312 (p) 21078 (q) 20741 (Z) 5924
× 3 × 5 × 9 × 7
Oyrm - bDpuGwfrkefYwpfxkyfvQif rkefYcsyf 8 csyf ygaomfrkefY 1527 xkyfwGifrkefYcsyfa&rnfrQyg
oenf;/
ay;csuf - rkefYwpfxkyfwGifygaom rkefYcsyf = 8 csyf
rkefYxkyfta&twGuf = 1527 xkyf
ar;csuf - rkefYcsyfta&twGuf = ?
ajz&Sif;&ef - × ÷ + −
ajz&Sif;enf; - rkefYcsyfta&twGuf = 8 × 1527
1 5 2 7
× 8
1 2 2 1 6
tajz/ rkefYcsyfa& = 12216 csyf
1/ jcif;wpfjcif;wGif o&ufoD; 1151 vHk;&Sdaomf jcif; 6 jcif;wGif o&ufoD; rnfrQ
&Sdoenf;/
6 × 4 = 2 4
1 × 4 = 4 + 2 = 6
7 × 4 = 2 8
8 × 4 = 32 + 2 = 3 4

36
Level 2 Mathematics
2/ rufref;oD; wpfjcif;a&mif;vQif aiG 8 usyf tjrwfusef/ rufref;oD; 157 jcif;
a&mif;aomf tjrwfaiGrnfrQ&rnfenf;/
3/ rvdkifvHk;wpfxkyfvQif 9 vHk;ygaomf 2564 xkyfwGif rvdkifvHk;aygif; rnfrQygoenf;/
4/ uav;wpfa,mufvQif a&SmufcsKdoD; 3 vHk;usESifh uav; 3167 a,mufudk a0aomf
a&SmufcsKdoD;rnfrQa0&rnfenf;/
5/ vlwpfa,mufonf wpf&ufvQif aiG 7 usyf pkaomf 347 &ufwGifaiGrnfrQ
pkrdrnfenf;/
4 . 24 . 24 . 24 . 24 . 2 10? 100? 1000 wdkY qwdk;udef;rsm;jzifh ajr§mufjcif;10? 100? 1000 wdkY qwdk;udef;rsm;jzifh ajr§mufjcif;10? 100? 1000 wdkY qwdk;udef;rsm;jzifh ajr§mufjcif;10? 100? 1000 wdkY qwdk;udef;rsm;jzifh ajr§mufjcif;10? 100? 1000 wdkY qwdk;udef;rsm;jzifh ajr§mufjcif;
Oyrm (1) 6 × 100 = 600
okn 2 vHk; okn 2 vHk;
Oyrm (2) 6 × 20000 = 120000
okn 4 vHk; okn 4 vHk;
Oyrm (3) 900 × 400 = 360000
okn 2 vHk; okn 2 vHk; okn 4 vHk;
(u) 1000 × 1000 (c) 6 × 1000 (*) 100 × 38
(C) 20 × 600 (i) 700 × 600 (p) 4000 × 700
(q) 1000 × 90 (Z) 467 × 300 (ps) 540 × 1000
4 . 34 . 34 . 34 . 34 . 3 ajr§mufv'fudk cefYrSef;jcif;ajr§mufv'fudk cefYrSef;jcif;ajr§mufv'fudk cefYrSef;jcif;ajr§mufv'fudk cefYrSef;jcif;ajr§mufv'fudk cefYrSef;jcif;
Oyrm (1) 48 × 327 udk eD;&mq,fjynhfudef;rsm;odkYajymif;NyD;ajr§mufjcif;jzifh ajr§mufv'fudk
cefYrSef;yg/
48 × 327
50 × 330 = 16500
6 × 1
6 × 2
9 × 4

37
Level 2 Mathematics
Oyrm (2) 460 × 221 udk eD;&m &mjynhfudef;rsm;odkY ajymif;NyD; ajr§mufjcif;jzifh ajr§mufv'fudk
cefYrSef;yg/
460 × 221
500 × 200 = 100000
1/ atmufygwdkYdkudk eD;&mq,fjynhfudef;rsm;odkY ajymif;NyD; ajr§mufjcif;jzifh ajr§mufv'fudk cefYrSef;yg/
(u) 29 × 37 (c) 52 × 64 (*) 55 × 65
(C) 38 × 548 (i) 351 × 42 (p) 47 × 54
2/ atmufygwdkYudk eD;&m &mjynhfudef;rsm;odkY ajymif;NyD; ajr§mufjcif;jzifh ajr§mufv'fudk cefYrSef;yg/
(u) 367 × 471 (c) 541 × 678 (*) 621 ×250
3/ wpfpHkvQif 420 usyfwef pma&;cHk 485 cHk0,f&ef aiGrnfrQukefrnfenf;/ (eD;&m &mjynhfudef;odkY
ajymif;í ajr§mufv'fcefYrSef;yg/)
4 . 44 . 44 . 44 . 44 . 4 tjynhfudef; *kPfowådtjynhfudef; *kPfowådtjynhfudef; *kPfowådtjynhfudef; *kPfowådtjynhfudef; *kPfowåd
Oyrm (1) 4 × 2 × 3 udk wGufyg/
yxrenf; 4 × 2 × 3 'kwd,enf; 4 × 2 × 3
8 × 3 4 × 6
24 24
xdkwGufenf;rsm;udk tvsm;vdkuf a&;vQif
( 4 ×2 ) × 3 = 8 × 3 =24 4 × (2 × 3) = 4 × 6 = 24
xdkYaMumifh
( 4 ×2 ) × 3 = 4 × (2 × 3 )
Oyrm (2) 3 × ( 5 + 4 ) ESifh ( 3 × 5) + (3 × 4) udk avhvmyg/
3 × (5 + 4) = 3 × 9 = 27
(3 × 5) + (3 × 4 ) = 15 + 12 = 27
xdkYaMumifh
3 × (5 + 4) = (3 × 5 ) + (3 × 4)

38
Level 2 Mathematics
1/ uGufvyfjznhfyg/
(u) (24 × 5) × 2 = 24 × (5 × ---) (c) 5 × (62 ×20 ) = (5 × 62) × --
(*) (4 × 19) × 25 = 4 × (--- × 25)
2/ oifhavsmfaom udef;udk wGJí ajr§mufv'fudk &Smyg/
(u) 2 × 3 × 19 (c) 57 × 6 × 5 (*) 5 × 2 × 16
3/ uGufvyfjznhfyg/
(u) 3 × ( 10 +4 ) = ( 3 × 10) + (3 × --- )
(c) 9 × ( 10 + 8) = ( 9 × ---) + (9 × 8)
(*) 6 × ( 20 + 5 ) = ( --- × 20) + (6 × ---)
4 . 54 . 54 . 54 . 54 . 5 *Pef;ESpfvHk;yg udef;jzifh ajr§mufjcif;*Pef;ESpfvHk;yg udef;jzifh ajr§mufjcif;*Pef;ESpfvHk;yg udef;jzifh ajr§mufjcif;*Pef;ESpfvHk;yg udef;jzifh ajr§mufjcif;*Pef;ESpfvHk;yg udef;jzifh ajr§mufjcif;
Oyrm (1) 425 × 30 udk wGufyg/
425 × 30 = 12750 a'giffvdkufenf;jzifhwGufaomf
425
× 30
tajz/ 12750 12750
1/ atmufygwdkYudk a'gifvdkufenf;jzifh wGufyg/
(u) 1302 (c) 873 (*) 415
× 20 × 40 × 30
(C) 1204 × 20 (i) 743 × 50 (p) 2724 × 60
Oyrm - 2124 × 21 udk wGufyg/
2124
× 21
2124 2124 × 1
+ 42480 2124 ×20
44604 2124 ×21
tajz/ 44604
21 = 20 + 1

39
Level 2 Mathematics
(u) 2241 (c) 341 (*) 676 (C) 4380
× 20 × 36 × 58 × 45
(i) 7804 (p) 8003
× 56 × 97
(q) 2311 × 32 (Z) 45 × 5524 (ps) 75 × 1463
4 . 64 . 64 . 64 . 64 . 6 *Pef;oHk;vHk;ygaom udef;jzifh ajr§mufjcif;*Pef;oHk;vHk;ygaom udef;jzifh ajr§mufjcif;*Pef;oHk;vHk;ygaom udef;jzifh ajr§mufjcif;*Pef;oHk;vHk;ygaom udef;jzifh ajr§mufjcif;*Pef;oHk;vHk;ygaom udef;jzifh ajr§mufjcif;
Oyrm (1) 212 × 300 udk wGufyg/
212 × 300 = 63600 a'gifvdkufenf;jzifhwGufaomf
212
× 300
63600
tajz/ 63600
(u) 121 (c) 2152 (*) 934
× 400 × 300 × 600
Oyrm (2) 364 × 531 udkwGufyg/
365
× 531 (531 = 500 + 30 + 1)
365 365 × 1
+ 10950 365 × 30
182500 365 × 500
193815 365 × 531
tajz/ 193815
(u) 241 (c) 597 (*) 836 (C) 112
× 212 × 408 × 641 × 144

40
Level 2 Mathematics
(i) 2375 (p) 4609
× 450 × 254
(q) 1213 × 608 (Z) 243 × 647 (ps) 305 × 829
2/ txufyg ykpämrsm;udk *Pef;wGufpufjzifh tajzcsdefudkufyg/
Oyrm - ykpäm (1) (u) twGuf 2? 4? 1 × 2? 1? 2? = udk tpDtpOftwdkif;ESdyfyg/
Oyrm - oabFmwpfpif;vQif vl 195 a,mufwifEdkifonf/ xdkoabFmrsKd; 54 pif;wGif
vlrnfrQ wifEdkifrnfenf;/
ay;csuf - oabFmwpfpif;wGif wifEdkifaom vlOD;a& = 195 a,muf
oabFmpif;a& = 54 pif;
ar;csuf - 54 pif;wGif wifEdkifaomvlOD;a& = ?
ajz&Sif;&ef - × ÷ + −
ajz&Sif;enf; - 54 pif;wGif wifEdkifaom vlOD;a& = 195 × 54
195
× 54 (54 = 50 + 4 )
780 195 × 4
+ 9750 195 × 50
10530
tajz/ wifEdkifaomvlOD;a& = 10530 a,muf
1/ tvkyform;wpfa,mufonf wpfvvQif 225 usyfyHkrSefpkaomf 6 vtwGuf aiGrnfrQ
pkrdrnfenf;/
2/ aowåmwpfvHk;vQif iHk;O 546 vHk;xnfhEdkifaomf xdkaowåmrsKd; 27 vHk;wGif iHk;OrnfrQ
xnfhEdkif oenf;/
3/ EdkYqDaowåmwpfvHk;wGif EdkYqDbl; 48 bl;0ifonf/ aowåm 1201 vHk;wGif EdkYqDbl;aygif;
rnfrQ &Sdrnfenf;/
4/ AD½dk wpfvHk;udk 3450 usyfaps;EIef;jzifh a&mif;aomf 38 vHk;twGuf aiGrnfrQ&rnfenf;/

41
Level 2 Mathematics
5/ bwfpum;wpfpD;onf c&D;onf 45 OD; o,faqmifEdkifaomf bufpum; 346 pD;onf
c&D;onfrnfrQ o,faqmifEdkifoenf;/
taxGaxG ykpämrsm;
Oyrm - oabFmwpfpif;wGif yxrwef;ü 10 a,muf? ½dk;½dk;wef;ü 217 a,muf
pD;Edkifonf/ xdkoabFmrsKd; 52 pif;twGuf c&D;onf pkpkaygif; rnfrQ pD;Edkifoenf;/
ay;csuf - yxrwef;üpD;EdkifolOD;a& = 10 a,muf
½dk;½dk;wef;üpD;EdkifolOD;a& = 217 a,muf
ar;csuf - oabFmpif;a& = 52 pif;
ajz&Sif;&ef - × ÷ + −
ajz&Sif;enf; - wpfpD;wGif pD;Edkifaom c&D;onf = 10 + 217
52 pif;wGif pD;Edkifaom c&D;onfaygif; = (10 + 217 ) × 52
10
+217
227
× 52
454
+ 11350
11804
tajz/ pD;Edkifaomc&D;onfaygif; = 11804 a,muf
1/ ( 498 × 47 ) + 2340 udk &Sif;yg/
2/ 21567 − (426 × 23 ) udk &Sif;yg/
3/ OD;bonf wpf&ufvQif *kefavQmf 385 ydóm0,fí OD;jronf 452 ydóm 0,fonf/
xdktav;csdeftwdkif; 3 &ufqufwdkuf 0,fvQif OD;bESifh OD;jr pkpkaygif;0,faom *kefavQmf
ydómudk&Smyg/
4/ wpfjcif;vQif vdar®mfoD; 165 vHk;ygaom jcif; 5 jcif;ESifh wpfjcif;vQif 275 vHk;ygaom
jcif; 4 jcif; &Sdonf/ vdar®mfoD; pkpkaygif; tvHk;a& rnfrQ &Sdoenf;/
5/ wpfxkyfvQif 25 csyf ygaombDpuGwfrkefY 35 xkyf&Sdonf/ rkefY 254 csyfudk
uav;rsm;tm; a0ay;vdkufvQif bDpuGwfrkefYtcsyfrnfrQusefoenf;/

42
Level 2 Mathematics
4 . 74 . 74 . 74 . 74 . 7 pdwfwGufpdwfwGufpdwfwGufpdwfwGufpdwfwGuf
tajr§mufudk pdwfwGuf prf;Munhfyg/
103 × 6 27 × 3
(100 + 3) × 6 (20 + 7 ) × 3
(100 × 6) + ( 3 × 6) (20 × 3) + (7 × 3 )
600 + 18 60 + 21
618 81
1/ atmufygwdkYudk pdwfwGuf wGufyg/
(u) 61 × 3 (c) 83 × 2 (*) 91 × 2 (C) 309 × 8
(i) 107 × 6 (p) 302 × 4 (q) 208 × 5 (Z) 2 × 46
2/ csdKcsOfwpfxkyfvQif 25 ckygaomf 3 xkyfwGif rnfrQygoenf;/
3/ jcif;wpfjcif;vQif vdar®mfoD; 205 vHk;ygaomf 4 jcif;wGif vdar®mfoD;rnfrQygoenf;/

43
Level 2 Mathematics
tcef; (5)
tpm;tpm;tpm;tpm;tpm;
5 . 15 . 15 . 15 . 15 . 1 *Pef;wpfvHk;ygaom udef;jzifh pm;jcif;*Pef;wpfvHk;ygaom udef;jzifh pm;jcif;*Pef;wpfvHk;ygaom udef;jzifh pm;jcif;*Pef;wpfvHk;ygaom udef;jzifh pm;jcif;*Pef;wpfvHk;ygaom udef;jzifh pm;jcif;
Oyrm (1) 49048 ÷ 8
6 1 3 1
8 4 9 0 4 8
− 4 8
1 0
− 8
2 4
− 2 4
8
− 8
0
tajz/ pm;v'f = 6131
t<uif; = 0
Oyrm (2) 92746 9
1 0 3 0 5
9 9 2 7 4 6
− 9
2
− 0
2 7
− 2 7
4
− 0
4 6
− 4 5
1
tajz/ pm;v'f = 10305
t<uif; = 1
csdefudkufenf;csdefudkufenf;csdefudkufenf;csdefudkufenf;csdefudkufenf;
6131 pm;v'f
× 8 pm;udef;
49048
+ 0 t<uif;
49048 wnfudef;
10305 pm;v'f
× 9 pm;udef;
92745
+ 1 t<uif;
92746 wnfudef;

44
Level 2 Mathematics
1/ pm;yg/ csdefudkufjyyg/
(u) 2 834 (c) 8 906 (*) 4 4381
(C) 3 8720 (i) 9 9074 (p) 8 65140
(q) 5 7030 (Z) 6 30290 (ps) 7 27060
2/ txufyg ykpämrsm;*Pef;rsm;udk *Pef;wGufpufjzifh wGufyg/
(Oyrm - ykpäm 1 (u) twGuf 8? 3? 4 ÷ 2 = udk tpDtpOftwdkif; ESdyfyg/)
5 . 25 . 25 . 25 . 25 . 2 q,fjynhfudef;rsm;jzifh pm;jcif;q,fjynhfudef;rsm;jzifh pm;jcif;q,fjynhfudef;rsm;jzifh pm;jcif;q,fjynhfudef;rsm;jzifh pm;jcif;q,fjynhfudef;rsm;jzifh pm;jcif;
Oyrm (1) 87 ÷ 20 udk wGufyg/
4
20 87
− 80
7
tajz/ pm;v'f = 4
t<uif; = 7
Oyrm (2) 169 ÷ 30 udkwGufyg/
5
30 169
− 150
19
tajz/ pm;v'f = 5
t<uif; = 19
1/ wGufyg/
(u) 20 54 (c) 30 120 (*) 40 283
(C) 50 222 (i) 60 360 (p) 70 359
(q) 486 ÷ 90 (Z) 1200 ÷ 50 (ps) 18956 ÷ 20

45
Level 2 Mathematics
2/ eHygwf(1)ygykpämrsm;udk *Pef;wGufpufoHk;í tajzudkcsdefudkufyg/
Oyrm (1) 97 ÷ 12
8 pm;v'f
12 97 wnfudef;
− 96
1 t<uif;
tajz/ pm;v'f = 8
t<uif; = 1
Oyrm (2) 98 vufr&SdaomBudK;wpfacsmif;rS 1 ayt&Snf&SdBudK;prsm;jzwfvQifBudK;p rnfrQ&rnfenf;/
ay;csuf - 98 vufr&Sdaom BudK;wpfacsmif;
ar;csuf - 1 ay = 12 vufr &Sdaom BudK;prsm;ta&twGuf
wGufenf; - 98 ÷ 12
8
12 98
− 96
2
tajz/ &&Sdaom BudK;p = 8 p
ydkaomBudK;p = 2 vufr
1/ atmufygwdkYudk pm;yg/ csdefudkufjyyg/
(u) 11 95 (c) 12 89 (*) 12 268
(C) 547 ÷ 11 (i) 6832 ÷ 12 (p) 2516 ÷ 11
2/ vlwpfa,mufonf 5 vwGif vpmaiGaygif; 675 usyf &&Sdaomf xdkol wpfvwGif &aom
vpm aiGudk &Smyg/
3/ tjrwfaiG28764usyfudk tzGJY0if 9 a,muftm; tnDtrQa0ay;aomf wpfa,mufvQif
rnfrQpD &rnfenf;/
4/ za,mif;wdkif 7965 wdkifudk 12 wdkifpDygaom txkyfrsm;xkyfaomf txkyfrnfrQ
&rnfenf;/ rnfrQ usefrnfenf;/
pm;v'f × pm;udef; + t<uif; = wnfudef;
8 × 12 = 96 + 1 = 97

46
Level 2 Mathematics
5/ vdar®mfoD; 1296 vHk;udk wpftdwfvQif 11 vHk;usxnhfaomf tdwfaygif;rnfrQ &rnfenf;/
rnfrQ usefoenf;/
6/ bJO 10 vHk;udk 1050 usyfay;cJh&aomf bJO wpfvHk;rnfrQenf;/
7/ ukvm;xdkif 563 vHk;udk wpfwef;vQif 9 vHk;uspDaomftwef;rnfrQ &rnfenf;/
rnfrQ ydkoenf;/
8/ qD 12 ydómudk 41760 usyf ay;&aomf wpfydómrnfrQay;&oenf;/
taxGaxGykpämrsm;
Oyrm (1) (827 × 6) + (8732 ÷ 4) udk &Sif;yg/
2 1 8 3
827 4 8 7 3 2
× 6 − 8
4962 7
− 4
3 3
− 3 2
1 2
− 1 2
0
(872 × 6) + (8732 ÷ 4)
= 4962 + 2183
= 7145
tajz/ 7145
Oyrm (2) pyg;a&mif;&aiG 28557 usyf &&Sdonfhteuf pkpkaygif;ukefusp&dwfrSm 20647 usyf
jzpfonf/ tom;wif0ifaiGwpf0ufudkvSLvdkufaomf vSLvdkufaomaiGrnfrQjzpf
rnfenf;/
ay;csuf - pyg;a&mif;&aiG = 28557 usyf
pkpkaygif;ukefusp&dwf = 20647 usyf
ar;csuf - vSLvdkufaomaiG = ?
ajz&Sif;&ef - + − × ÷
ajz&Sif;enf; - tom;wif0ifaiG = 28557 − 20647
vSLvdkufaomaiG = (28557 − 20647 ) ÷ 2

47
Level 2 Mathematics
28557 3 9 5 5
− 20647 2 7 9 1 0
7910 − 6
1 9
− 1 8
1 1
− 1 0
1 0
− 1 0
0
tajz/ vSLvdkufaomaiG = 3955 usyf
1/ ( 26341 ÷ 7 ) + 1549 udk &Sif;yg/
2/ 9346 - ( 14826 ÷ 3) udk &Sif;yg/
3/ (45 × 60) + (5424 ÷ 12 ) udk &Sif;yg/
4/ apmif 10 xnfudk 2690 usyf jzifh0,fvm/ apmifwpfxnfvQif 300 usyfjzifh
jyefa&mif;aomf wpfxnfvQif aiGrnfrQ jrwfoenf;/
5/ oMum;vHk; 145 vHk;udk armifBuD;ESifh armifi,f ESpfa,mufwdkY a0,lMu&m armifi,fonf
oMum;vHk; 15 vHk;ydk&/ armifBuD; &aom oMum;vHk; rnfrQenf;/
6/ armifb? armifvS? armifjr nDtpfudk oHk;a,mufwdkYonf ausmif;p&dwftwGuf zcifxHrS
200 usyfESifh rdcifxHrS 280 usyf &&Sdonf/ ¤if;aiGudk oHk;a,muftnDtrQ a0aomf
wpfa,mufvQif rnfrQpD&rnfenf;/

48
Level 2 Mathematics
tcef; (6)
tydkif;udef;ESifh 'orudef;tydkif;udef;ESifh 'orudef;tydkif;udef;ESifh 'orudef;tydkif;udef;ESifh 'orudef;tydkif;udef;ESifh 'orudef;
6 .16 .16 .16 .16 .1 tydkif;udef;tydkif;udef;tydkif;udef;tydkif;udef;tydkif;udef;
o½kyfjyyHk t"dyÜm,f ta&; tzwf
nDrQydkif; 3 ydkif; oHk;ydkif; wpfydkif;
teuf 1 ydkif;
nDrQydkif; 3 ydkif; oHk;ydkif; ESpfydkif;
teuf 2 ydkif;
nDrQydkif; 3 ydkif; oHk;ydkif; oHk;ydkif;
teuf 3 ydkif; (wefzdk; 1 jzpfonf/)
oHk;ydkif;wpfydkif;oHk;ydkif;wpfydkif;oHk;ydkif;wpfydkif;oHk;ydkif;wpfydkif;oHk;ydkif;wpfydkif;
cJjcpfxm;aomtydkif;ta&twGuf (ydkif;a0)(ydkif;a0)(ydkif;a0)(ydkif;a0)(ydkif;a0)
nDrQydkif; pkpkaygif; (ydkif;ajc)(ydkif;ajc)(ydkif;ajc)(ydkif;ajc)(ydkif;ajc)
nDrQydkif; 1 ydkif;pDonf wpfckvHk; oHk;yHkwpfyHkjzpfonf[k t"dyÜm,f&onf/
1
3
2
3
3
3
1
3

49
Level 2 Mathematics
1/ atmufygyHktoD;oD;wGif cJjcpfxm;onhftydkif;rsm;udk azmfjyaom tydkif;udef;udk a&G;yg/
(u) (c) (*)
? ? ? ? ? ? ? ?
(C) (i) (p)
? ? ? ? ? ? ? ? ?
2/ cJjcpfxm;aom tydkif;rsm;udk azmfjyaom tydkif;udef;udk a&;yg/
(u) (c) (*) (C)
(i) (p) (q) (Z)
1
3
1
4
2
2
1
3
1
4
1
2
2
3
1
2
1
2
1
3
3
4
3
3
1
2
2
4
2
3
1
2
1
3
2
2

50
Level 2 Mathematics
3/ atmuffyg tydkif;udef;toD;oD;twGuf oufqdkif&myHkwGif cJjcpfay;yg/
(u) (c) (*) (C)
(i) (p) (q) (Z)
4/ atmufygyHkrsm;wGif oufqdkif&m tydkif;udef;rsm;azmfjyyg/
(u) (c)
+ = + =
---- + ----- = ------- ------ + ----- = -----
(*) (C)
- = - =
------ - ----- = ------ ------ - ----- = ------
(u) + = =
(c) + =
(*) - =
(C) - =
(i) + + =
1
3
2
3
1
2
1
4
3
4 3
3
2
4
2
2
1
3
1
3
1 + 1
3
2
3
2
3
1
3
1
3
1
3
3
3
2
3
1
3
1
3
1
3

51
Level 2 Mathematics
1
3
2
6
3
9
4
9
wpfck tydkif;rsm;wpfck tydkif;rsm;wpfck tydkif;rsm;wpfck tydkif;rsm;wpfck tydkif;rsm;
Oyrm -
tpkwpfpk tydkif;udef;tpkwpfpk tydkif;udef;tpkwpfpk tydkif;udef;tpkwpfpk tydkif;udef;tpkwpfpk tydkif;udef;
Oyrm -
iSufaysmoD;ta&twGufonf toD;tm;vHk;
jzpfonf/
1/ atmufygwdkUwGif cJjc,fxm;onfrsm;udk tydkif;udef;jzifhjyyg/
(u) (c) (*) (C)
(i) (p) (q) (Z)
(ps) (n) (#)
Oyrm - ra&Tacsmonfyef;oD; 1 vkH;udk 4 pdwftnDpdwfí1 pdwfpm;vdkufonf/ usefaom
yef;oD;pdwfonf yef;oD;vkH; rnfonfhtpdwftydkif;jzpfoenf;/

52
Level 2 Mathematics
yef;oD; 1vkH; = (4 pdwf tnDpdwfonf)
pm;vdkufaomyef;oD; =
usefaomyef;oD; = - =
1/ rkefU1csyfudkom; 3 a,muftm;tnDtrQa0vQifom; 1 a,mufpD&aomrkefUonfrkefU 1 csyf
vkH; rnfonfhtpdwftydkif;jzpfoenf;/
2/ udwfrkefU 1 vkH;udkoli,fcsif;4a,muftnDtrQydkif;,lvQif 1 a,mufpD&aomrkefUonfudwfrkefU
tm;vkH; rnfonfhtpdwftydkif;jzpfoenf;/
3/ taronfrkefUcsyf udktaztm;ay;vdkuf/ usefrkefUudkom;tm;ay;aomfom;&aom
rkefUonf rkefU 1 csyfvkH;rnfonfhtpdwftydkif;jzpfoenf;/
4/ tdrf vrf;avQmuf um; ausmif;
armifarmifonf tdrfrS ausmif;okdYc&D; ukdvrf;avQmuf/ usefc&D;udkum;jzifh
oGm;aomf um;jzifhoGm;aomc&D;onfc&D;wpfckvkH;rnfonfhtpdwftydkif;jzpfoenf;/
5/ aiGwpf&mukdom; 5 a,muftm;tnDtrQa0ay;vQifwpfOD;pD&aomaiGonfrlvaiGwpf&m
rnfonfhtpdwftydkif;jzpfoenf;/
6/ jcif;awmif;xJwGif rmvumoD; 3 vHk;? yef;oD; 1 vHk;? vdar®mfoD; 4 vHk; &Sd/
rmvumoD;ta&twGufonf jcif;awmif;wGif;&SdopfoD;tm;vHk; rnfonhftpdwftydkif;
jzpfoenf;/
4
4
1
44
4
1
4
3
4
1
3
2
5

53
Level 2 Mathematics
wefzdk;wltydkif;udef;rsm;wefzdk;wltydkif;udef;rsm;wefzdk;wltydkif;udef;rsm;wefzdk;wltydkif;udef;rsm;wefzdk;wltydkif;udef;rsm;
Oyrm
= = =
= = =
1/ yHkt& wefzdk;wltydkif;udef;rsm;udk azmfjyyg/
(u)
= =
----- = ----- = -----
(c) = =
----- = ----- = -----
(*) = =
----- = ----- = -----
(C) =
----- = -----
(i) = = = =
----- = ----- = ----- = ----- = -----
1
4
2
8
3
1 2
4
1 6

54
Level 2 Mathematics
ajr§mufjcif;jzifhwefzdk;wltydkif;udef;rsm;½Smjcif;ajr§mufjcif;jzifhwefzdk;wltydkif;udef;rsm;½Smjcif;ajr§mufjcif;jzifhwefzdk;wltydkif;udef;rsm;½Smjcif;ajr§mufjcif;jzifhwefzdk;wltydkif;udef;rsm;½Smjcif;ajr§mufjcif;jzifhwefzdk;wltydkif;udef;rsm;½Smjcif;
Oyrm (1)
= =
= =
= =
Oyrm (2)
=
=
= =
wefzdk;wltydkif;udef;&&ef tydkif;udef;wpfck ydkif;a0ESifhydkif;ajcwdkUudkwefzdk;wltydkif;udef;&&ef tydkif;udef;wpfck ydkif;a0ESifhydkif;ajcwdkUudkwefzdk;wltydkif;udef;&&ef tydkif;udef;wpfck ydkif;a0ESifhydkif;ajcwdkUudkwefzdk;wltydkif;udef;&&ef tydkif;udef;wpfck ydkif;a0ESifhydkif;ajcwdkUudkwefzdk;wltydkif;udef;&&ef tydkif;udef;wpfck ydkif;a0ESifhydkif;ajcwdkUudk
oknr[kwfaomwlnDonhf udef;wpfckjzifh ajr§mufonf/oknr[kwfaomwlnDonhf udef;wpfckjzifh ajr§mufonf/oknr[kwfaomwlnDonhf udef;wpfckjzifh ajr§mufonf/oknr[kwfaomwlnDonhf udef;wpfckjzifh ajr§mufonf/oknr[kwfaomwlnDonhf udef;wpfckjzifh ajr§mufonf/
pm;jcif;jzifh wefzdk;wltydkif;udef;rsm;½Smjcif;pm;jcif;jzifh wefzdk;wltydkif;udef;rsm;½Smjcif;pm;jcif;jzifh wefzdk;wltydkif;udef;rsm;½Smjcif;pm;jcif;jzifh wefzdk;wltydkif;udef;rsm;½Smjcif;pm;jcif;jzifh wefzdk;wltydkif;udef;rsm;½Smjcif;
Oyrm -
=
1
2
2
4
4
8
1
2
1 × 2
2 × 2
1 × 4
2 × 4
1
3
2
6
1
3
1 × 2
3 × 2
2
6
2
6
=
1
3=
2 ÷ 2
6 ÷ 2
1
3=
5 ÷ 5
15 ÷ 5
=
1
3=
5
15
5
15

55
Level 2 Mathematics
wefzdk;wltydkif;udef; &&ef tykdif;udef;wpfckydkif;a0ESifh ydkif;ajcwdkYudk oknr[kwfaomwefzdk;wltydkif;udef; &&ef tykdif;udef;wpfckydkif;a0ESifh ydkif;ajcwdkYudk oknr[kwfaomwefzdk;wltydkif;udef; &&ef tykdif;udef;wpfckydkif;a0ESifh ydkif;ajcwdkYudk oknr[kwfaomwefzdk;wltydkif;udef; &&ef tykdif;udef;wpfckydkif;a0ESifh ydkif;ajcwdkYudk oknr[kwfaomwefzdk;wltydkif;udef; &&ef tykdif;udef;wpfckydkif;a0ESifh ydkif;ajcwdkYudk oknr[kwfaom
wlnDonfh udef;wpfckjzifhpm;Edkifonf/wlnDonfh udef;wpfckjzifhpm;Edkifonf/wlnDonfh udef;wpfckjzifhpm;Edkifonf/wlnDonfh udef;wpfckjzifhpm;Edkifonf/wlnDonfh udef;wpfckjzifhpm;Edkifonf/
1/ * wGif vdktyfaomudef;jznfhyg/
(u) 1 = = = (c) = =
(*) = = (C) = =
(i) = = (p) = =
2/ (u) = = (c) = =
(*) = = (C) = =
(i) = = (p) = =
3/ (u) 1 = = = =
(c) = = = =
(*) = = = =
(C) = = =
(i) = = =
4/ ESifh wefzdk;wlaom tydkif;udef; 5 cka&;yg/
5/ ESifhwefzdk;wlaomtydkif;udef; 5 cka&;yg/
1
1
1 × *
1 × 3
3
3
1
4
1 × 2
4 × *
2
*
1 × *
3 × 3
1
3
*
9
3
5
3 × *
5 × 3
*
15
1
6
1 × 2
6 × *
2
*
1
2
1 × *
2 × 5
*
10
1
6
14
28
*
14
*
4
1
*
12
48
6
*
*
12
1
*
2
3
4
*
*
9
10
*
*
30
1
2
2
*
*
6
4
*
6
*
1
1
2
*
*
5
10
*
1
3
2
4
2 ÷ 2
4 ÷ *
1
*
8
10
8 ÷ *
10÷ 2
*
5
5
15
5 ÷ 5
15 ÷ *
1
*
3
9
3 ÷ *
9 ÷ 3
*
3
16
20
16 ÷ *
20 ÷ 2
*
10
3
6
3 ÷ 3
6 ÷ *
1
*

56
Level 2 Mathematics
6/ atmufygtydkif;udef;rsm;udk t&Sif;qkH;ykHpHjzifha&;yg/
(u) = = (c) (*) (C)
tydkif;udef;rsm;EIdif;,SOfjcif;tydkif;udef;rsm;EIdif;,SOfjcif;tydkif;udef;rsm;EIdif;,SOfjcif;tydkif;udef;rsm;EIdif;,SOfjcif;tydkif;udef;rsm;EIdif;,SOfjcif;
(u) ydkif;ajcwltydkif;udef;rsm; EIdif;,SOfjcif;
Oyrm (1)
>
Oyrm (2)
<
Oyrm (3)
3
4
2
43
4
2
4
4 = 4
3 > 2
2
4
3
42
4
3
4
4 = 4
2 < 3
3
4
1
4
3
4
1
4
>
4 = 4
3 > 1
8
40
8 ÷ 8
40 ÷ 8
1
5
10
25
14
49
18
81

57
Level 2 Mathematics
1/ rnfonfuBuD;oenf;/ > udkokH;íajzyg/
(u) ESifh (c) ESifh (*) ESifh
(C) ESifh (i) ESifh (p) ESifh
2/ rnfonfui,foenf;/ < ukdokH;íajzyg/
(c) ydkif;ajcrwlonfhtydkif;udef;rsm;EIdif;,SOfjcif;
Oyrm(1) ESifh wdkUudkEIdif;,SOfyg/
ESifh
>
>
Oyrm(2) ESifh wdkUudkEIdif;,SOfyg/
ESifh
>
>
ydkif;ajcrwlonfh tydkif;udef;rsm;udkEIdif;,SOf&mwGif ydkif;ajcwlatmifajymif;NyD;rS ydkif;a0rsm;udkydkif;ajcrwlonfh tydkif;udef;rsm;udkEIdif;,SOf&mwGif ydkif;ajcwlatmifajymif;NyD;rS ydkif;a0rsm;udkydkif;ajcrwlonfh tydkif;udef;rsm;udkEIdif;,SOf&mwGif ydkif;ajcwlatmifajymif;NyD;rS ydkif;a0rsm;udkydkif;ajcrwlonfh tydkif;udef;rsm;udkEIdif;,SOf&mwGif ydkif;ajcwlatmifajymif;NyD;rS ydkif;a0rsm;udkydkif;ajcrwlonfh tydkif;udef;rsm;udkEIdif;,SOf&mwGif ydkif;ajcwlatmifajymif;NyD;rS ydkif;a0rsm;udk
EIdif;,SOf&onf/EIdif;,SOf&onf/EIdif;,SOf&onf/EIdif;,SOf&onf/EIdif;,SOf&onf/
1
4
3
4
5
6
2
6
7
10
9
10
10
12
4
12
3
8
5
8
2
5
3
5
1
3
2
3
13
16
7
16
5
7
3
7
1
3
1
6
1 × 2
3 × 2
1
6
2
6
1
6
1
3
1
6
4
5
3
4
3 × 5
4 × 5
4 × 4
5 × 4
16
20
15
20
4
5
3
4

58
Level 2 Mathematics
1/ atmufygwdkUukd > okdYr[kwf < udkokH;íEIdif;,SOfyg/
(C) ESifh (i) ESifh (p) ESifh
ydkif;a0onfydkif;ajcxufBuD;vQifxdktydkif;udef;onf 1 xufBuD;/ydkif;a0onfydkif;ajcxufBuD;vQifxdktydkif;udef;onf 1 xufBuD;/ydkif;a0onfydkif;ajcxufBuD;vQifxdktydkif;udef;onf 1 xufBuD;/ydkif;a0onfydkif;ajcxufBuD;vQifxdktydkif;udef;onf 1 xufBuD;/ydkif;a0onfydkif;ajcxufBuD;vQifxdktydkif;udef;onf 1 xufBuD;/
Oyrm- > 1
1/ atmufyg uGufvyfwGif = odkYr[kwf > odkYr[kwf <
(u) ( ) 1 (c) ( ) 1 (*) ( ) 1
(C) ( ) 1 (i) ( ) 1 (p) ( ) 1
udef;a&mudef;a&mudef;a&mudef;a&mudef;a&m
tjynfhudef;wpfckESifhtydkif;udef;wpfckjzifhaygif;pyfazmfjyxm;jcif;udkudef;a&m[kac:onf/tjynfhudef;wpfckESifhtydkif;udef;wpfckjzifhaygif;pyfazmfjyxm;jcif;udkudef;a&m[kac:onf/tjynfhudef;wpfckESifhtydkif;udef;wpfckjzifhaygif;pyfazmfjyxm;jcif;udkudef;a&m[kac:onf/tjynfhudef;wpfckESifhtydkif;udef;wpfckjzifhaygif;pyfazmfjyxm;jcif;udkudef;a&m[kac:onf/tjynfhudef;wpfckESifhtydkif;udef;wpfckjzifhaygif;pyfazmfjyxm;jcif;udkudef;a&m[kac:onf/
1
3
1
2
3
4
2
3
5
6
2
3
1
5
1
3
5
16
3
4
2
3
3
8
7
3
5
3
8
7
7
8
3
2
1
6
3
3
2
3tjynfhudef; tydkif;udef;
1
udef;a&m

59
Level 2 Mathematics
Oyrm (1)
1 udktydkif;udef;oufoufjzifhazmfjyyg/
1 = 1 +
= +
=
=
Oyrm (2)
udk udef;a&mtjzpfazmfjyyg/
=
= 3 +
= 3
1/ tajzrSefa½G;yg/
(u) ( 3 ? 1 ? 10 )
(c) ( 7 ? 2 ? 1 )
(*) 2 ( ? ? )
(C) 2 ( ? ? )
7
2
7
2
6 + 1
2
1
2
1
2
2
3
2
3
2
3
3
3
2
3
3 + 2
3
5
3
3
2 7
- 6
1
3 1
2
13
10
1
10
3
10
1
3
15
2
1
2
1
7
2
7
1
3
6
3
7
3
3
7
1
4
9
2
9
4
6
4
_____
=

60
Level 2 Mathematics
1
3
1
6
1 × 2
3 × 2
1
6
2
6
1
6
3
6
1
2
1
2
1
2
1
5
1 × 5
2 × 5
1 × 2
5 × 2
5
10
2
10
5 - 2
10
3
10
3
10
1
3
7
12
tydkif;udef;rsm;aygif;jcif; ? Ekwfjcif;tydkif;udef;rsm;aygif;jcif; ? Ekwfjcif;tydkif;udef;rsm;aygif;jcif; ? Ekwfjcif;tydkif;udef;rsm;aygif;jcif; ? Ekwfjcif;tydkif;udef;rsm;aygif;jcif; ? Ekwfjcif;
Oyrm (1)
+ = +
= +
=
=
tajz/
Oyrm (2) - = -
= -
=
=
tajz/
1/ ½Sif;yg/
(u) + (c) + (*) +
(C) + (i) - (p) -
(q) - (Z) + (ps) -
1
4
1
2
1
4
2
3
4
5
1
3
11
12
2
3
7
10
1
6
1
10
2
5
2
3
1
9
5
6
2
3

61
Level 2 Mathematics
Oyrm (1) 3 + 1 = 3 + + 1 +
= 4 + +
= 4 + +
= 4 +
= 4
tajz/ 4
Oyrm (2) 3 - 1 = -
= -
= -
=
= 2
1/ ½Sif;yg/
(u) 9 + 3 (c) 4 + 2 (*) 1 + 2
(C) 2 - 1 (i) 1 - (p) 5 - 2
1
4
3
5
1
4
3
5
1 × 5
4 × 5
3 × 4
5 × 4
5
20
12
20
17
20
17
20
17
20
3
4
1
2
15
4
3
2
15
4
3 × 2
2 × 2
15
4
6
4
9
4
1
4
2
3
5
6
1
4
3
2
1
3
1
4
5
8
3
4
7
10
1
2
1
4
1
5

62
Level 2 Mathematics
2/ yxraeYwGif v,f{u {uxGefNyD;/ 'kwd,aeUwGif {uxGefNyD;/ wwd,aeYwGif
{uxGefNyD;/ pkpkaygif;v,f{urnfrQxGefNyD;oenf;/
3/ a&tjynfh&Sdaompnfydkif;wpfckrS a& okH;/ a&onfpnf rnfonfhtpdwftydkif;
usefao;oenf;/
6 .26 .26 .26 .26 .2 'orudef;'orudef;'orudef;'orudef;'orudef;
q,fpdwfydkif; ? &mpdwfydkif;q,fpdwfydkif; ? &mpdwfydkif;q,fpdwfydkif; ? &mpdwfydkif;q,fpdwfydkif; ? &mpdwfydkif;q,fpdwfydkif; ? &mpdwfydkif;
Oyrm -
? wdkUudk ydkif;ajc 10 (odkYr[kwf) 100 &Sdaomtydkif;udef;odkUajymif;yg/
= =
= =
1/ wGif vdkaomudef;rsm;jznfhyg/
(u) = (c) =
(*) = (C) =
2/ atmufygwdkUudkydkif;ajc 10 (odkYr[kwf) 100 &Sdaomtydkif;udef;odkYajymif;yg/
(u) (c) (*)
q,fvDpdwfq,fvDpdwfq,fvDpdwfq,fvDpdwfq,fvDpdwf
1 = q,fvDpdwf 10 pdwf
1
41
4
1
2
3
4
1
2
1 × 5
2 × 5
5
10
3
4
3 × 25
4 × 25
75
100
1
2
1
410 100
2
4
1
5 10
3
5
1
4
1
25
10
10
3
8
100
1
3

63
Level 2 Mathematics
Oyrm (1)
cJjc,fxm;aomtykdif; =
q,fckZ,m;csía&;vQif
q,f ck q,fvDpdwf
0 1
'orudef;jzifha&;vQif 0. 1 (okn'orwpf[kzwfonf/)
Oyrm (2)
q,f ck q,fvDpdwf
0 4
'orudef;jzifha&;vQif 0. 4 (okn'orav;[kzwfonf/)
Oyrm (3)
q,f ck q,fvDpdwf
2 3
'orudef;jzifha&;vQif 2. 3 (ESpf'orokH;[kzwfonf/)
avhusihfcef; (13)avhusihfcef; (13)avhusihfcef; (13)avhusihfcef; (13)avhusihfcef; (13)
1/ atmufygykHwGifcJjc,fxm;aomtydkif;rsm;udkazmfjyaom'orudef;a&;jyyg/ zwfyg/
(u) (c) (*)
( ) ( ) ( )
1
10

64
Level 2 Mathematics
(C) ( )
(i) ( )
2/ atmufygwdkUudk'orudef;jzifha&;jyyg/ zwfyg/
(u) q,f ck q,fvDpdwf (c) q,f ck q,fvDpdwf
0 7 7 3
(*) q,f ck q,fvDpdwf (C) q,f ck q,fvDpdwf
1 3 5 3 7 4
(i) q,fvDpdwf 9 pdwf (p) 9 ckESifhq,fvDpdwf 3 pdwf
(q) 2 q,fESifh 3 ckESifhq,fvDpdwf tpdwf 6 pdwf
&mvDpdwf&mvDpdwf&mvDpdwf&mvDpdwf&mvDpdwf
= =
1 = =
1 = q,fvDpdwf 10 pdwf = &mvDpdwf 100 pdwf
=
q,fvDpdwf 1 pdwf = &mvDpdwf 10 pdwf
10
10
100
100
1
10
10
100

65
Level 2 Mathematics
Oyrm (1)
ck q,fvDpdwf &mvDpdwf
0 0 1
0 . 01 [ka&;onf/ (okn'oroknwpf[kzwfonf/)
Oyrm (2)
0 5 3
0. 53 [ka&;onf/ (okn'orig;okH;[kzwfonf)
Oyrm (3)
1 2 6
1. 26 [ka&;onf/ (wpf'orESpfajcmuf[kzwfonf/)
1/ atmufygykHwdkYwGif cJjc,fxm;aomtydkif;rsm;udk 'orudef;jzifhazmfjyNyD; udef;zwfyg/
(u) (c)
( ) ( )
(*) ( )
53
100

66
Level 2 Mathematics
(C)
( )
2/ atmufygwdkUudk'orudef;jzifhazmfjyyg/
(u) ck q,fvDpdwf &mvDpdwf (c) ck q,fvDpdwf &mvDpdwf
0 1 5 2 1 7
(*) q,f ck q,fvDpdwf &mvDpdwf (C) &m q,f ck q,fvDpdwf &mvDpdwf
3 1 1 7 1 3 2 0 7
(i) q,f ck q,fvDpdwf &mvDpdwf (p)ck q,fvDpdwf &mvDpdwf
3 0 2 6 0 0 3
3/ atmufygwdkYudk 'orudef;jzifha&;yg/
(u) &mvDpdwf 9 pdwf (c) &mvDpdwf 10 pdwf (*) &mvDpdwf 17 pdwf
(C) ESpfESifh&mvDpdwf25pdwf (i) wpfESifh&mvDpdwf3pdwf (p) ESpfq,fokH;ESifh
&mvDpdwf 18 pdwf
4/ atmufygtydkif;udef;rsm;udk 'orudef;jzifha&;jyyg/
Oyrm - = &mvDpdwf 85 pdwf
= q,fvDpdwf 8 pdwfESifh &mvDpdwf 5 pdwf = 0. 85
(u) (c) (*)
(C) (i) (p)
5/ atmufygwdkUudktydkif;udef;jzifha&;jyyg/
Oyrm - 0. 25 = q,fvDpdwf 2 pdwfESifh&mvDpdwf 5 pdwf
= &mvDpdwf 20 pdwfESifh&mvDpdwf 5 pdwf
= &mvDpdwf 25 pdwf
=
(u) 0. 34 (c) 3. 4 (*) 3. 04
(C) 0. 7 (i) 2. 35 (p) 0. 05
85
100
7
10
17
100
170
100
3
10
23
100
123
100
25
100

67
Level 2 Mathematics
'orudef;rsm;udkEIdif;,SOfjcif;'orudef;rsm;udkEIdif;,SOfjcif;'orudef;rsm;udkEIdif;,SOfjcif;'orudef;rsm;udkEIdif;,SOfjcif;'orudef;rsm;udkEIdif;,SOfjcif;
Oyrm (1)
=
q,fvDpdwf 3 pdwf = &mvDpdwf 30 pdwf
0. 3 = 0. 30
0. 3 onf 0. 30 ESifh wefzdk;wlnDonf/
Oyrm (2) 0. 2 ESifh 0. 5 EIdif;,SOfyg/
0. 2 0. 5
(0. 2 onf 0. 5 atmufi,fonf/)
0. 2 < 0. 5
Oyrm (3) 0. 7 ESifh 0. 35 udk EIdif;,SOfyg/
0. 7 0. 35
(0. 7 onf 0. 35 xufBuD;onf/)
0. 7 > 0. 35
Oyrm (4) 0. 3 ESifh 0. 37 udk EIdif;,SOfyg/
0. 3 0. 37
(0. 3 onf 0. 37 atmufi,fonf/)
0. 3 < 0. 37

68
Level 2 Mathematics
1/ atmufyguGufvyfwdkUwGif < , > , = vu©PmwdkYukd okH;íajzyg/
(u) 0. 6 ( ) 0. 9 (c)0. 08 ( ) 0. 3 (*) 0. 42 ( ) 0. 46
(C) 0. 01 ( ) 0. 06 (i)0. 5 ( ) 0. 05 (p) 5. 3 ( ) 0. 53
2/ rDwm 100 ajy;yGJwGif ajy;ol (6) OD; MumcsdefrSm atmufygtwdkif;jzpfonf/
ajy;ol rvS reD rjzL rjr rat; r0if;
Mumcsdef(puúefU) 12. 6 11. 8 12. 3 11. 9 12. 2 12. 5
ajy;yGJwGif (u) rnfolyxr&oenf;/
(c) rnfol'kwd,&oenf;/
(*) rnfolwwd,&oenf;/
(C) aemufqkH;rSyef;0ifolrnfolenf;/
'orudef;rsm;aygif;jcif;? EIwfjcif;'orudef;rsm;aygif;jcif;? EIwfjcif;'orudef;rsm;aygif;jcif;? EIwfjcif;'orudef;rsm;aygif;jcif;? EIwfjcif;'orudef;rsm;aygif;jcif;? EIwfjcif;
Oyrm (1) 0. 3 + 0. 5
0. 3
+ 0. 5
0. 8
tajz/ 0. 8
Oyrm (2) 2. 16 + 1. 6
2. 16
+1. 60 (1. 6 = 1. 60)
3. 76
tajz/ 3. 76
Oyrm (3) 1. 37 + 0. 89
1 . 3 7
+0 . 8 9
2 . 2 6
tajz/ 2 .26
11
7 + 9 = 1 6
1 + 3 + 8 = 1 2

69
Level 2 Mathematics
avhusihfcef; (16)avhusihfcef; (16)avhusihfcef; (16)avhusihfcef; (16)avhusihfcef; (16)
1/ atmufygwdkYudk &Sif;yg/
(u) 0. 4 (c) 1. 2 (*) 0. 8 (C) 1. 6
+ 0. 5 + 0. 3 + 0. 7 + 0. 4
(i) 3. 81 + 1. 1 (p) 6. 32 + 4. 7 (q) 3. 9 + 0. 8
(Z) 21. 54 + 5. 06 + 4. 74 (ps) 35. 17 + 10. 6 + 0. 32
2/ NrdKUwpfNrdKUwGif wpfywftwGif;aeYpOfrdk;½GmoGef;aomrdk;a&csdefvufrrsm;rSmatmufygtwdkif;jzpfonf/
aeU wevFm t*Fg Ak'¨[l; Mumoyaw; aomMum pae we*FaEG
rdk;a&csdef
(vufr) 2. 3 1. 9 0. 9 1. 6 3. 4 4. 6 2. 9
(u) rdk;trsm;qkH;½GmaomaeYudkazmfjyyg/
(c) rdk;tenf;qkH;½GmaomaeYudkazmfjyyg/
(*) wpfywftwGif; ½GmcJhaomrdk;a&csdefvufraygif;udk&Smyg/
Oyrm (1) 3. 58 - 1. 26
3. 58
- 1. 26
2. 32
tajz/ 2. 32
Oyrm (2) 3. 5 - 0. 8
3 . 5
- 0 . 8
2 . 7
tajz/ 2 .7
152

70
Level 2 Mathematics
Oyrm (3) 50. 8 - 47. 64
5 0 . 8 0
- 4 7 . 6 4
3 . 1 6
tajz/ 3 . 16
1/ atmufygwdkUudkwGufyg/
(u) 0. 5 - 0. 3 (c) 3. 5- 2. 3 (*) 0. 7 - 0. 35
(C) 2. 1 - 1. 35 (i) 3. 35 - 1. 7 (p) 0. 84 - 0. 64
2/ vlwpfOD;omrefudk,ftylcsdefrSm 98. 6 'D*&Dzm&if[dkufjzpf/ zsm;aeoludk,ftylcsdefonf
101. 5 'D*&Dzm&if[dkuf jzpfaomf omreftylcsdefxuf rnfrQydkaeoenf;/
3/ ZGefvtwGif;NrdKUESpfNrdKUrdk;a&csdefrSm 7. 58 ESifh 12. 18 vufrtoD;oD;jzpfaomf
NrdKUESpfNrdKUrdk;a&csdefvufrjcm;em;jcif;udk&Smyg/
'orudef;ukdtjynfhudef;wpfckjzifhajr§mufjcif;'orudef;ukdtjynfhudef;wpfckjzifhajr§mufjcif;'orudef;ukdtjynfhudef;wpfckjzifhajr§mufjcif;'orudef;ukdtjynfhudef;wpfckjzifhajr§mufjcif;'orudef;ukdtjynfhudef;wpfckjzifhajr§mufjcif;
Oyrm (1) 0. 2 × 4
0. 2
× 4
0. 8
Oyrm (2) 0. 2 × 7
0. 2
× 7
1. 4
Oyrm (3) 1. 56× 6
1. 56
× 6
9. 36
7 10104
'orudef; (wnfudef;)wGif'orwpfae&momygaomaMumifh'orudef; (wnfudef;)wGif'orwpfae&momygaomaMumifh'orudef; (wnfudef;)wGif'orwpfae&momygaomaMumifh'orudef; (wnfudef;)wGif'orwpfae&momygaomaMumifh'orudef; (wnfudef;)wGif'orwpfae&momygaomaMumifh
ajr§mufv'fwGif 'or wpfae&mom jzpfygonf/ajr§mufv'fwGif 'or wpfae&mom jzpfygonf/ajr§mufv'fwGif 'or wpfae&mom jzpfygonf/ajr§mufv'fwGif 'or wpfae&mom jzpfygonf/ajr§mufv'fwGif 'or wpfae&mom jzpfygonf/
'orudef;(wnfudef;)wGif'orESpfae&momygaomaMumifh'orudef;(wnfudef;)wGif'orESpfae&momygaomaMumifh'orudef;(wnfudef;)wGif'orESpfae&momygaomaMumifh'orudef;(wnfudef;)wGif'orESpfae&momygaomaMumifh'orudef;(wnfudef;)wGif'orESpfae&momygaomaMumifh
ajr§mufv'fwGif 'or ESpfae&m jzpfygonf/ajr§mufv'fwGif 'or ESpfae&m jzpfygonf/ajr§mufv'fwGif 'or ESpfae&m jzpfygonf/ajr§mufv'fwGif 'or ESpfae&m jzpfygonf/ajr§mufv'fwGif 'or ESpfae&m jzpfygonf/

71
Level 2 Mathematics
1/ atmufygwdkUudkwGufyg/
(u) 0. 4 × 4 (c) 0. 25 × 4 (*) 1. 5× 4
(C) 0. 25 × 8 (i) 6. 25 × 4 (p) 0. 48 × 6
2/ wGufyg/
(u) 24 .5 (c) 2 .45 (*) 2 .24
× 100 × 10 × 100
(C) 22 .4 (i) 10 .37 (p) 3 .7
× 100 × 10 × 10
(q) 0 .37 × 100 (Z) 3 .7 × 100 (ps) 23 .6 × 100
3/ 1 vufr = 2 .5 pifwDrDwmjzpfvQif 6 vufr udk pifwDrDwmjzifhjyyg/
4/ 1 uDvdk*&rf = 0 .6 ydómjzpfvQif 10 uDvdk*&rf udk ydómjzifhjyyg/
'orudef;udktjynfhudef;jzifhpm;jcif;'orudef;udktjynfhudef;jzifhpm;jcif;'orudef;udktjynfhudef;jzifhpm;jcif;'orudef;udktjynfhudef;jzifhpm;jcif;'orudef;udktjynfhudef;jzifhpm;jcif;
Oyrm (1) 0 .8 ÷ 2
0 .4
2 0 .8
-0
8
- 8
0
tajz/ 0 .4
Oyrm (2) 0 .08 ÷ 2
0 .04
2 0 .08
-0
0
- 0
8
- 8 tajz/ 0 .04
0

72
Level 2 Mathematics
Oyrm (3) 13 .38 ÷ 6
2 .23
6 13 .38
- 12
1 3
- 1 2
18
- 18
0 tajz/ 2 .23
1/ wGufyg/
(u) 3 .96 ÷ 3 (c) 1 .95 ÷ 5 (*) 13 .6 ÷ 4
(C) 4 .38 ÷ 10 (i) 36 .08 ÷ 2 (p) 1 .44 ÷ 8
(q) 6 .06 ÷ 6 (Z) 5 .35 ÷ 10 (ps) 5 .35 ÷ 100
2/ 1 .5 aygif&Sd aumfzDrIefYudk 3 xkyftnDtrQxkyfaomfwpfxkyfvQif tav;csdefrnfrQ&Sdrnfenf;/
3/ rkefY 1 ydómudk 8 a,mufcGJ,laomf wpfOD;pD &&Sdrnfh rkefYtav;csdefudk ydómjzifh jyyg/
4/ 25 rDwm t&Snf&Sdaom BudK;wpfacsmif;udk 4 ydkif;tnDtrQ ydkif;aomf wpfydkif;onf rDwm
rnfrQ &Snfrnfenf;/

73
Level 2 Mathematics
tcef;(7)
ykHjzifhukd,fpm;ûyazmfjyrIrsm;ykHjzifhukd,fpm;ûyazmfjyrIrsm;ykHjzifhukd,fpm;ûyazmfjyrIrsm;ykHjzifhukd,fpm;ûyazmfjyrIrsm;ykHjzifhukd,fpm;ûyazmfjyrIrsm;
7 .17 .17 .17 .17 .1 ½kyfjyykHrsm;½kyfjyykHrsm;½kyfjyykHrsm;½kyfjyykHrsm;½kyfjyykHrsm;
qHoqdkifwpfqdkif aeYtvdkufvmaom qHyifñSyfol ta&twGufudk azmfjyxm;onf/
aeYtvdkuf qHyifñSyfolpm&if;
wevFm
t*Fg
Ak'¨[l;
Mumoyaw;
aomMum
pae
we*FaEG
vlOD;a&
wpfckpDonf vlOD;a& 10 OD;udk ukd,fpm;jyKonf/
wpfckpDonf vlOD;a& 5 OD;udk ukd,fpm;jyKonf/
atmufygar;cGef;wdkYudk ajzyg/
(1) t*FgaeYwGif vmolOD;a& (50) OD;
(2) Mumoyaw;aeYwGif vmolOD;a& ( ) OD;
(3) paeaeYwGif vmolOD;a& ( )OD;
(4) vltenf;qkH;vmaomaeY ( ) aeY
(5) vltrsm;qkH;vmaomaeY ( ) aeY
(6) vltenf;qkH;vmaomaeYESifhvltrsm;qkH;vmaomaeYwGifvmolOD;a&jcm;em;jcif; ( ) OD;
(7) paeESifhwe*FaEGaeYrsm;wGif vmolOD;a&aygif; ( ) OD;
(8) txufyg½kyfjyykHudkMunfhí oifrnfodkY aumufcsufcsEdkifoenf;/
aeYrsm;

74
Level 2 Mathematics
7 .27 .27 .27 .27 .2 Am;*&yfAm;*&yfAm;*&yfAm;*&yfAm;*&yf
2008 - 2009 pmoifESpfwGif usKdufxkdNrdKUü NFPE pcef; (5)ck ? ppfawGNrdKUü NFPE
pcef;(3)ck? jynfNrdKUü NFPE pcef;(7)ck? yJcl;NrdKUüNFPE pcef;(4)ckESifh ykodrfNrdKUü NFPE pcef;(11)ck½Sdonf/
NFPE pcef;ta&twGufrsm;ukd atmufygtcsuftvufjyZ,m;jzifh azmfjyEdkifonf/
tcsuftvufjyZ,m;
NrdKUtrnfrsm; NFPE pcef;OD;a&
usKdufxdk 5
ppfawG 3
jynf 7
yJcl; 4
ykodrf 11
tcsuftvufjyZ,m;ukd Munfhí atmufygtwdkif; Am;*&yf wpfckudk a&;qGJEdkifonf/
NrdKUe,ftvdkuf pcef;OD;a&jy Am;*&yf
NrdKUe,ftrnf
pcef; OD;a&
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
usKdufxdk
ppfawG
jynf
yJcl;
ykodrf
123456789
123456789123456789
123456789123456789
123456789
123456789
123456789
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
123456789
123456789123456789
123456789123456789
123456789
123456789
123456789
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
12345678
1234567812345678
1234567812345678
12345678
12345678
12345678
123456789
123456789
123456789
123456789
123456789
123456789
123456789
123456789
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
123456789
123456789
123456789
123456789
123456789
123456789
123456789
123456789
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
1234567
1234567
1234567
1234567
1234567
1234567
1234567
1234567
123456789
123456789
123456789
123456789
123456789
123456789
123456789
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
123456789
123456789
123456789
123456789
123456789
123456789
123456789
123456789
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678
12345678

75
Level 2 Mathematics
1/ twef;xJ½Sdausmif;om;OD;a&udk arG;aomaeY trnfrsm;tvdkuf atmufygZ,m;wGif azmfjy
xm;onf/ xdkZ,m;udk Munfhí Am;*&yftuGufrsm;wGif jc,frIef;yg/
arG;aomaeYtrnf ausmif;om;OD;a&
we*FaEG 5
wevFm 7
t*Fg 4
Ak'¨[l; 6
Mumoyaw; 4
aomMum 5
vufawGUvkyfief;
2/ oiftwef;&Sd ausmif;om;?ausmif;olrsm; touf(ESpf)pm&if;aumufyg/
(u) &&Sdonhf tcsuftvufrsm;udk Z,m;wpfckwGif azmfjyyg/
(c) touftvdkuf ausmif;om;?ausmif;olOD;a&udk Am;*&yfwpffcka&;qGJjyyg/
wevFmaeY
t*FgaeY
Ak'¨[l;aeY
Mumoyaw;aeY
aomMumaeY
paeYaeY
we*FaEGaeY
aeYrsm;
ausmif;om;OD;a&
8
7
6
5
4
3
2
1
0

76
Level 2 Mathematics
tcef;(8)
tcsdeftwkdif;twmtcsdeftwkdif;twmtcsdeftwkdif;twmtcsdeftwkdif;twmtcsdeftwkdif;twm
8 .18 .18 .18 .18 .1 tcsdeftwkdif;twmqkdif&mqufoG,fcsuftcsdeftwkdif;twmqkdif&mqufoG,fcsuftcsdeftwkdif;twmqkdif&mqufoG,fcsuftcsdeftwkdif;twmqkdif&mqufoG,fcsuftcsdeftwkdif;twmqkdif&mqufoG,fcsuf
puúefY 60 = 1 rdepf
rdepf 60 = 1 em&D
24 em&D = 1 &uf
7 &uf = 1 oDwif; (1 ywf)
1/ atmufygem&Drsm;onf oli,fcsif;wpfpk tdyf&mxcsdefukd jyxm;/
(u) wpfOD;pD tdyf&mxcsdefukdajymyg/
(c) rnfoltapmqkH;xygoenf;/
(*) rnfolaemuf tusqkH;xygoenf;/
(u) (c) (*)
(C) (i) (p)
Oyrm (1)
1em&D30rdepf35puúefYudk puúefYjzifh jyyg/
em&D rdepf puúefY
1 30 35
× 60 + 60 + 5400
60 90 rdepf 5435 puúefY
× 60
5400 puúefY
tajz/ 5435 puúefY
rpdef rvS rjr
rtdpk rrdrd0if; r&D

77
Level 2 Mathematics
Oyrm (2)
armfawmfum;wpfpD;onf c&D;wpfckukd 7755 puúefYMumrSa&muf/ Mumcsdefukd em&D? rdepf?
puúefYjzifhajymif;zGJUjyyg/
60 7755
60 129 rdepf + 15 puúefY
2 em&D + 9 rdepf
tajz/ 2em&D 9 rdepf 15 puúefY
1/ atmufygwkdYukd puúefYzGJUyg/
(u) 1 em&D 20 rdepf 30 puúefY
(c) 2 em&D 5 rdepf 50 puúefY
2/ atmufygwkdYukd em&D? rdepf? puúefYjzifhjyyg/
(u) 7575 puúefY
(c) 6950 puúefY
3/ reDvmonf tajy;avhusifh&m tuGmta0;wpfckukd 6 rdepf 35 puúefYajy;aomf puúefY
rnfrQMumatmifajy;oenf;/
4/ v,form;wpfOD;onf v,fxJwGif 3 em&D 35 rdepf tvkyfvkyfcJhvQif rdepftm;jzifh rnfrQ
MumMumtvkyfvkyfcJhoenf;/
8 .28 .28 .28 .28 .2 tcsdefem&D rlrwl taygif;? tEkwftcsdefem&D rlrwl taygif;? tEkwftcsdefem&D rlrwl taygif;? tEkwftcsdefem&D rlrwl taygif;? tEkwftcsdefem&D rlrwl taygif;? tEkwf
Oyrm (1)
OD;bausmfonf ESJBudK;&GmrS "EkjzLokdY pufbD;pD;oGm;&m 1 em&D 45 rdepfMumonf/ tjyef
1 em&D 55 rdepfMumaomf toGm;tjyefpkpkaygif;Mumcsdefukd&Smyg/
toGm;tjyefMumcsdef = 1 em&D 45 rdepf + 1 em&D 55 rdepf
em&D rdepf
1 45
+ 1 55
3 40 ajz/ pkpkaygif;Mumcsdef = 3 em&D 40 rdepf
100 rdepf = 1 em&D 40 rdepf
1

78
Level 2 Mathematics
1/ atmufygwkdYukdwGufyg/
(u) em&D rdepf (c) em&D rdepf puúefY
4 29 6 13 23
15 37 7 15 49
+ 21 35 + 9 46 36
2/ vlwpfa,mufonf NrdKUwpfNrdKUrStjcm;NrdKUwpfNrdKUokdY pufbD;jzifhoGm;&m 1 em&D 45 rdepf
MumoGm;NyD;aemuf pufbDcsdKU,Gif;oGm;ojzifh 25 rdepfMumjyifae&/ xkdYaemufqufoGm;&m
1 em&D 30 rdepfMumrS c&D;qkH;okdYa&muf/ vrf;wGif pkpkaygif;rnfrQMumoenf;/
3/ ½kyf&SifyGJwpfyGJukd n 7 em&D 45 rdepfrSpí jy/ yGJjycsdef 2 em&D 35 rdepfMumvQif rnfonfh
tcsdefwGif ½kyf&SifNyD;oenf;/
4/ um;ESpfpD;onf NrdKUwpfNrdKUrS wpfcsdefwnf;pí xGufcJh&m yxrum;onf tjcm;NrdKUwpfNrdKU okdY
5 em&D 27 rdepftMumwGifa&muf/ 'kwd,um;onf yxrum;xuf 1 em&D 35 rdepf
aemufusía&muf/ 'kwd,um;onf tcsdefrnfrQMum armif;&oenf;/
tcsdefem&DjyykHtcsdefem&DjyykHtcsdefem&DjyykHtcsdefem&DjyykHtcsdefem&DjyykH
noef;acgif 12 em&DrS rGef;wnfh 12 em&Dtxd = 12 em&D
rGef;wnfh 12 em&DrS noef;acgif 12 em&Dtxd = 12 em&D

79
Level 2 Mathematics
Oyrm -
armfawmfum;wpfpD;onf &efukefrSrGef;vGJ 2 em&D 35 rdepfrS pxGuf/ yJcl;okdY nae 6 em&D
20 rdepfwGif a&mufonf/ vrf;wGiftcsdefrnfrQMumoenf;/
&efukefrSpxGufcsdef = rGef;vTJ 2 em&D 35 rdepf
yJcl;okdYa&mufcsdef = nae 6 em&D 20 rdepf
vrf;wGifMumaomtcsdef = 6 em&D 20 rdepf - 2 em&D 35 rdepf
em&D rdepf
6 20
- 2 35
3 45
tajz/ vrf;wGifMumaomtcsdef = 3 em&D 45 rdepf
1/ atmufygwkdYukdwGufyg/
(u) em&D rdepf (c) em&D rdepf puúefY
7 20 14 35 25
- 4 35 - 2 27 45
2/ tajy;NydKifyGJwpfckwGif armif&Jvif;onf wmxGufNyD; 25 rdepf 25 puúefYtMumwGifyef;0iff/
armifEkdif0if;u 30 rdepf 15 puúefYtMumwGifyef;0if/ armif&Jvif;onf armifEkdif0if;xuf
tcsdefrnfrQapmíyef;0ifoenf;/
3/ oabFmwpfpif;onf &efukefqdyfurf;rS eHeuf 7 em&D 30 rdepfwGif xGufoGm;onf/ wGHaw;okdY
eHeuf 9 em&D 15 rdepfwGifa&mufaomf vrf;wGiftcsdefrnfrQMumoenf;/
4/ um;ESpfpD;onf ae&mwpfae&mwnf;rS NydKifwlxGufcGmvm&myxrum;onf 'kwd,um;xuf
1em&D27rdepfapma&muf/ 'kwd,a&mufaomum;onf 6 em&D 10 rdepfMum armif;cJh&aomf
yxrum;onf tcsdefrnfrQMumatmif armif;cJhoenf;/
5/ ausmif;tm;upm;yGJwpfckukd eHeuf 7 em&DrSpíusif;y&m eHeuf 11 em&D 50 rdepfwGif NyD;
eHeufpmtwGuf 30 rdepfESifh em;aecsdefwGif 25 rdepfMumaomf upm;csdefoufouf tcsdefrnfrQ
Mumoenf;/
805

80
Level 2 Mathematics
8 .38 .38 .38 .38 .3 tcsdefem&Drlrwl tajr§muf? tpm;tcsdefem&Drlrwl tajr§muf? tpm;tcsdefem&Drlrwl tajr§muf? tpm;tcsdefem&Drlrwl tajr§muf? tpm;tcsdefem&Drlrwl tajr§muf? tpm;
Oyrm (1)
um;armif;olwpfOD;onf 1 rkdifc&D;ukd 2 rdepf 30 puúefYMumarmif;aomf 50 rkdifa0;aom
c&D;ukda&muf&ef tcsdefrnfrQMumatmifarmif;&rnfenf;/
1 rkdifoGm;&efMumcsdef = 2 rdepf 30 puúefY
oGm;aomc&D;rkdif = 50 rkdif
Mumcsdef = 2 rdepf 30 puúefY × 50
em&D rdepf puúefY
0 2 30
× 50
2 5 0
tajz/ 50 rdkif c&D;odkY a&muf&ef Mumcsdef = 2 em&D 5 rdepf
Oyrm (2)
vSnf;wpfpD;onf 9 rkdifa0;aomc&D;ukd 14 em&D 15 rdepfMumatmifoGm;&aomf 1
rkdifc&D;ukd
tcsdefrnfrQMumatmifoGm;&rnfenf;/
9 rkdifc&D;ukdoGm;&efMumcsdef = 14 em&D 15 rdepf
1 rkdifc&D;ukdoGm;&efMumcsdef = 14 em&D 15 rdepf ÷ 9
1 35
em&D rdepf
9 14 15
- 9 + 300
5 315
× 60 - 27
300 rdepf 45
- 45
0
tajz/ 1 rdkifc&D;udk oGm;&efMumcsdef = 1 em&D 35 rdepf
30 × 50 = 1500 puúefY
1500 puúefY ÷ 60 = 25 rdepf
100 +25 = 125 rdepf
125 rdepf ÷ 60 = 2 em&D 5 rdepf
2^ 25^

81
Level 2 Mathematics
1/ a&pkyfpufwpfvkH;ukd wpfaeYvQif 3 em&D 35 rdepfarmif;aomf 15 &ufwGif pkpkaygif; tcsdef
rnfrQarmif;oenf;/
2/ qefpufwpfvkH;onf eHeufykdif;wGif 3 em&D 30 rdepfESifhrGef;vGJykdif;wGif 2 em&D 45 rdepfMum
aeYpOf qefBudwfcGJ/ 45 &ufwGif qefBudwfcGJcsdef pkpkaygif;rnfrQ&Sdrnfenf;/
3/ armfawmfum;wpfpD;onf rkdif 50 a0;aomc&D;wpfckukd 2 em&D 30 rdepfMum oGm;&aomf
1 rkdif c&D;ukd rnfrQMumatmif oGm;&rnfenf;/
4/ tvkyform;wpfOD; 5 &uftwGif; pkpkaygif;tvkyfvkyfcsdefrSm 3 em&D 30 rdepfjzpfvQif
(u) 1 &ufwGif tcsdefrnfrQtvkyfvkyf&oenf;/
(c) 3 &ufwGif tcsdefrnfrQtvkyfvkyf&oenf;/
8 .48 .48 .48 .48 .4 Mumcsdef&Smjcif;Mumcsdef&Smjcif;Mumcsdef&Smjcif;Mumcsdef&Smjcif;Mumcsdef&Smjcif;
Oyrm (1)
aomMumaeYeHeuf 8 em&DrS rGef;wnfhcsdeftxd tcsdefrnfrQMumoenf;/
Mumaomtcsdef = 12 em&D - 8 em&D
em&D rdepf
12 00
- 8 00
4 00
tajz/ Mumcsdef = 4 em&D
Oyrm (2)
paeaeYrGef;vTJ 2 em&D 30 rdepfrS xkdaeY oef;acgif;csdeftxd rnfrQMumoenf;/
Mumaomtcsdef = 12 em&D - 2 em&D 30 rdepf
em&D rdepf
12 00
- 2 30
9 30
tajz/ Mumcsdef = 9 em&D 30 rdepf
6011

82
Level 2 Mathematics
1/ ausmif;olwpfOD;onf n 8 em&D 15 rdepfrS xkdaeYn oef;acgiftxd pmMunfhaomf
pmMunfhcsdefpkpkaygif;ukd&Smyg/
2/ eHeuf 6 em&D 45 rdepfwGif ausmif;wufí rGef;wnfh 12 em&DwGif ausmif;qif;aomf
eHeufykdif;ausmif;csdefrnfrQMumoenf;/
3/ jr0wD½kyfjrifoHMum;tpDtpOfwGif AGD'D,kdZmwfvrf;rsm;ukd paeaeY rGef;wnfh 12 em&DrS rGef;vGJ
2 em&Dtxdjyoygonf/ AGD'D,kd Zmwfvrf;jyocsdefrnfrQMumygoenf;/
Oyrm (1)
we*FaEGaeYeHeuf 9 em&D 25 rdepfrS rGef;vGJ 5 em&D 40 rdepftxd rnfrQMumoenf;/
eHeuf 9 em&D 25 rdepfrS rGef;wnfhcsdefxdMumcsdef = 12 em&D - 9 em&D 25 rdepf
em&D rdepf
12 00
- 9 25
rGef;wnfhxdMumcsdef 2 35
rGef;vGJykdif;Mumcsdef + 5 40
8 15
wpfenf;/wpfenf;/wpfenf;/wpfenf;/wpfenf;/ rGef;vGJ 5 em&D 40 rdepf = 17 em&D 40 rdepf
em&D rdepf
17 40
- 9 25
8 15
tajz? Mumcsdef = 8 em&D 15 rdepf
Oyrm (2)
we*FaEGaeY eHeuf 6 em&DrS wevFmaeY eHeuf 3 em&Dtxd pkpkaygif;Mumcsdefukd&Smyg/
we*FaEGaeY eHeuf 6 em&DrS xkdaeYrGef;wnfhxdMumcsdef (12 - 6 ) 6 em&D
we*FaEGaeYrGef;wnfhrS xkdaeYoef;acgifxdMumcsdef 12 em&D
we*FaEGaeY oef;acgifrSwevFmaeY eHeuf 3 em&DxdMumcsdef + 3 em&D
pkpkaygif;Mumcsdef 21 em&D
tajz/ pkpkaygif;Mumcsdef = 21 em&D
6011
35 + 40 = 75 rdepf = 1 em&D 15 rdepf
1 + 2 + 5 = 8 em&D

83
Level 2 Mathematics
Oyrm (3)
oabFmwpfpif;onf &efukefNrdKUrS wevFmaeYnae 6 em&D 30 rdepfwGifpíxGufcJh&m
BuHcif;NrdKUokdY Mumoyaw;aeY eHeuf 8 em&D 15 rdepfwGifa&muf/ pkpkaygif;Mumcsdefukd &uf?
em&D? rdepfjzifhjyyg/
wevFmaeYnae 6 em&D 30 rdepfrS xkdaeYoef;acgifxdMumcsdef= 12 em&D - 6 em&D 30 rdepf
em&D rdepf
12 00
- 6 30
5 30
&uf em&D rdepf
wevFmaeYnae 6 em&D 30 rdepfrSxkdaeYoef;acgifxdMumcsdef 5 30
wevFmaeYoef;acgifrSt*FgaeYoef;acgifxdMumcsdef 1
t*FgaeYoef;acgifrSAk'¨[l;aeYoef;acgifxdMumcsdef 1
Ak'¨[l;aeYoef;acgifrSMumoyaw;aeYeHeuf 8 em&D 15rdepfxdMumcsdef + 8 15
pkpkaygif;Mumcsdef 2 13 45
tajz/ pkpkaygif;Mumcsdef = 2 &uf 13 em&D 45 rdepf
1/ um;wpfpD;onf &efukefNrdKUrS eHeuf 6 em&D 30 rdepfwGif pNyD;xGufcJh&m jynfNrdKUokdY rGef;vGJ
2 em&DwGifa&muf vrf;wGifrnfrQMumcJhoenf;/
2/ &xm;wpfpif;onf rEÅav;NrdKUrSMumoyaw;aeYn 7 em&D 30 rdepfrSpíxGufvm&m rkd;ñSif;
blwmokdY aomMumaeYeHeuf 11 em&D 50 rdepfwGif qkdufa&muf/ vrf;wGiftcsdef
rnfrQMumcJhoenf;/
3/ vlwpfa,mufonf c&D;wpfckukd Ak'¨[l;aeYeHeuf 5 em&D 30 rdepfrSpxGuf&m aomMumaeY
eHeuf 9 em&D 15 rdepfwGifa&muf/ pkpkaygif;Mumcsdefukd &uf? em&D? rdepfjzifhjyyg/
4/ atmufyg[if;rsm;ukd rD;zkdwpfvkH;jzifh tjrefNyD;atmifcsuf&ef tenf;qkH;tcsdefrnfrQvkdygoenf;/
aqmif&Gufrnfhvkyfief;pOf tqifhqifhukdazmfjyxm;onf/
yJESyf csOfaygifausmf ig;yd&nf
yJa&aq; 5 rdepf csOfaygif&Gufoif 10 rdepf ig;ydaumifa&azsmf 5 rdepf
qDowf 5 rdepf csOfaygif&Gufaq; 10 rdepf usdK 20 rdepf
ESyf 40 rdepf ykZGefoif 20 rdepf
aMumf 30 rdepf
6011

84
Level 2 Mathematics
8 .58 .58 .58 .58 .5 jrefrmjyu©'defjrefrmjyu©'defjrefrmjyu©'defjrefrmjyu©'defjrefrmjyu©'def
trSwf vtrnf vqef;1&ufrSvjynfhaeY vqkwf1&ufrSvuG,faeY pkpkaygif;&uf
pOf txd&ufaygif; txd&ufaygif;
1 wefcl; 15 14 29
2 uqkef 15 15 30
3 e,kef 15 14 29
4 0gqdk 15 15 30
5 0gacgif 15 14 29
6 awmfovif; 15 15 30
7 oDwif;uRwf 15 14 29
8 wefaqmifrkef; 15 15 30
9 ewfawmf 15 14 29
10 jymodk 15 15 30
11 wydkYwGJ 15 14 29
12 waygif; 15 15 30
jrefrmvrsm;udk
vqef;1&ufrSvjynfhaeYtxdvqef;ydkif;ESifh vjynfhausmf1&ufrSvuG,faeYtxd vqkwfydkif;
[lí ESpfykdif;cGJxm;ygonf/
vqef;ydkif;wGif vwdkif; 15 &uf&Sdonf/
pkH*Pef;trSwfpOf&Sdaom (2?4? 6? 8? 10? 12)vrsm;onfvqkwfydkif;wGifvnf;(15)&ufpD
&Sdonf/
r*Pef;trSwfpOf&Sdaomvrsm;wGif vqkwfydkif;wGif (14)&ufpDom&Sdonf/
Oyrm -
0gacgifvqkwf3&ufrS0gacgifvuG,faeYtxd tpESifhtqkH;&uftygt0if&ufaygif;rnfrQ&Sdoenf;/
0gacgifvqkwf 1&ufrS vuG,faeYtxd = 14 &uf
0gacgifvqkwf 1&ufrS 2&ufaeYtxd = 2 &uf
0gacgifvqkwf 3 &ufrS vuG,faeYtxd&ufaygif; = 14 - 2 = 12 &uf
tajz/ &ufaygif; = 12 &uf
atmufygtydkif;tjcm;rsm;wGiftpESifhtqkH;&uftygt0if &ufaygif;rnfrQ&Sdoenf;/
1/ e,kefvqef; 3 &ufrS e,kefvjynfhaeYtxd
2/ 0gqdkvqkwf 3 &ufrS 0gqdkvuG,faeYtxd
3/ wefaqmifrkef; vqef; 5 &ufrS wefaqmifrkef;vjynfhaeYtxd
4/ oDwif;uRwfvjynfhausmf 7 &ufrS oDwif;uRwfvuG,faeYtxd

85
Level 2 Mathematics
8 .68 .68 .68 .68 .6 t*Fvdyfjyu©'deft*Fvdyfjyu©'deft*Fvdyfjyu©'deft*Fvdyfjyu©'deft*Fvdyfjyu©'def
trSwfpOftrSwfpOftrSwfpOftrSwfpOftrSwfpOf vtrnfvtrnfvtrnfvtrnfvtrnf &ufaygif;&ufaygif;&ufaygif;&ufaygif;&ufaygif;
1 Zefe0g&D 31
2 azazmf0g&D 28
3 rwf 31
4 {NyD 30
5 ar 31
6 ZGef 30
7 Zlvdkif 31
8 Mo*kwf 31
9 pufwifbm 30
10 atmufwdkbm 31
11 Edk0ifbm 30
12 'DZifbm 31
1 ESpf = 12v
7 &uf = 1 oDwif;(1ywf)
½dk;½dk;ESpf 1ESpf = 365 &uf
&ufxyfESpf 1ESpf = 366 &uf
we*FaEGaeYrSpí paeaeYtxd &ufaygif; = 7 &uf = 1 oDwif; (1ywf)
&ufxyfESpfjzpfvQifazazmf0g&DvwGif (29) &uf&Sdonf/
c&pfouú&mZfudk 4 jzifhpm;íjywfaomESpfudk &ufxyfESpf[kac:onf/
Oyrm 1984 ckESpfudk 4 jzifhpm;íjywfonf/ xdkESpfwGif azazmf0g&Dvü 29 &uf&Sdonf/
Oyrm -
ZGefv 9 &ufaeYrS vukefaomaeYtxd tpESifhtqkH;&uftygt0if &ufaygif;rnfrQ&Sd
oenf;/
ZGefv 1 &ufrS vukefonfhaeYtxd = 30 &uf
ZGefv 1 &ufrS 8 &ufaeYtxd = 8 &uf
ZGefv 9 &ufrS vukefonfhaeYtxd&ufaygif; = 30 - 8 = 22 &uf
1/ atmufygumvtydkif;tjcm;wGif tpESifhtqkH;&uftygt0if &ufaygif;rnfrQ&Sdoenf;/
(u) Zefe0g&Dv 4 &ufrS Zefe0g&DvukefaomaeYtxd
(c) rwfv 27 &ufrS rwfvukefaomaeYtxd
(*) Edk0ifbmv 21 &ufrS Edk0ifbmvukefaomaeYtxd

86
Level 2 Mathematics
Oyrm (1)
Zefe0g&Dv 13&ufrS Zefe0g&Dv 18 &uftxd &ufaygif; rnfrQ&Sdoenf;/
Zefe0g&Dv 1 &ufrS 18 &uftxd 18 &uf
Zefe0g&Dv 1 &ufrS 12 &uftxd - 12 &uf
Zefe0g&Dv 13 &ufrS 18 &uftxd 6 &uf
Oyrm (2)
arv25&ufrS Zlvdkifv6&uftxd&ufaygif;rnfrQ&Sdoenf;/
arvwGifygaom&ufaygif; (31 - 24) 7 &uf
ZGefvwGifygaom&ufaygif; 30 &uf
ZlvdkifvwGifygaom&ufaygif; + 6 &uf
arv25&ufrSZlvdkifv6&uftxd&ufaygif; 43 &uf
1/ uGufvyfjznfhyg/ (pdwfwGuf)
(u) rwfv 1 &ufrS 17 &uftxd &ufaygif; = ( ) &uf
(c) arv 5 &uf 14 &uftxd&ufaygif; = ( ) &uf
(*) ZGefv 3 &ufrS vukefaomaeYtxd&ufaygif; = ( ) &uf
(C) wevFmaeYrS ----------- aeYtxd&ufaygif; = 7 &uf (1 ywf)
(i) Mumoyaw;aeYrS --------- aeYtxd&ufaygif; = 7 &uf (1 ywf)
(p) Ak'¨[l;aeYrS --------- aeYtxd&ufaygif; = 7 &uf (1 ywf)
2/ atmufazmfjyyg tcsdefumvrsm;twGif; &ufaygif;rnfrQ&Sdoenf;/
(u) Zlvdkifv 8 &ufrS pufwifbmv 28 &uftxd
(c) arv 15 &ufrS ZGefv 10 &uftxd
(*) 1980 ckESpf? azazmf0g&Dv 26 &ufrS rwfv 25 &uftxd

87
Level 2 Mathematics
Oyrm - 1999 ckESpf pufwifbmv 25 &uf rS 2001 ckESpf 'DZifbmv 3 &uftxd Mumaomtcsdefudk
ESpf? v &ufjzifhjyyg/
ESpf v &uf
1999 ckESpf pufwifbmv25 &ufrS2001 ckESpf pufwifbmv25&ufxd 2 0 0
2001 ckESpf pufwifbmv 26 &ufrS vukefxd&ufaygif; (30 - 25) 0 0 5
2001 ckESpf atmufwdkbmv 0 1 0
2001 ckESpf Edk0ifbmv 0 1 0
2001 ckESpf 'DZifbmv 1 &ufrS 'DZifbmv 3 &ufxd&ufaygif; + 0 0 3
Mumaomtcsdef 2 2 8
tajz/ Mumaomtcsdef = 2 ESpf 2 v 8 &uf
1/ 1983 ckESpf ZGefv15&ufaeYwGif arG;aomuav;wpfOD;onf 1999 ckESpf 'DZifbmv6&ufaeYwGif
toufrnfrQ&Sdrnfenf;/
2/ 1949 ckESpf Mo*kwfv26 &ufwGifarG;cJhaom vlwpfa,mufonf 2000 ckESpf Ekd0ifbmv
15 &uf wGiftoufrnfrQ&Sdrnfenf;/
3/ oifonf 2001 ckESpf? Zlvdkifv9&ufwGif toufrnfrQ&Sdrnfenf;/

88
Level 2 Mathematics
tcef;(9)
tav;csdefESifhtjcift0iftav;csdefESifhtjcift0iftav;csdefESifhtjcift0iftav;csdefESifhtjcift0iftav;csdefESifhtjcift0if
9 .19 .19 .19 .19 .1 jrefrmtav;csdefjrefrmtav;csdefjrefrmtav;csdefjrefrmtav;csdefjrefrmtav;csdef
jrefrmtav;csdefqdkif&mqufoG,fcsufZ,m;
1 ydóm = 100 usyfom;
50 usyfom; 50 usyfom;
25 usyfom; 25 usyfom; 25 usyfom; 25 usyfom;
usyfom; usyfom; usyfom; usyfom; usyfom; usyfom; usyfom; usyfom;
10 10 10 10 10 10 10 10 10 10
usyfom; usyfom; usyfom; usyfom; usyfom; usyfom; usyfom; usyfom; usyfom; usyfom;
1 ydóm = 100 usyfom;
ydóm = 50 usyfom;
ydóm = 2 5 usyfom; (tpdwfom;)
ydóm = usyfom;(12usyfcJGom;^t0ufom;)
ydóm = 10 usyfom;
1/ txufygZ,m;udkMunfhí atmufyguGufvyfrsm;udkjznfhyg/
(u) 1 ydómrSm 50usyfom; ( ) Budrf
(c) 1 ydómrSm 25 usyfom; ( ) Budrf
(*) 1 ydómrSm usyfom; ( ) Budrf
(C) 1 ydómrSm 10 usyfom; ( ) Budrf
(i) 1 ydómrSm 5 usyfom; ( ) Budrf
(p) 1 ydómrSm tpdwfom; ( ) Budrf
(q) 1 ydómrSm t0ufom; ( ) Budrf
12 1
2
12 1
2
12 1
2
12 1
2
12 1
2
12 1
2
12 1
2
12 1
2
1
4
1
2
1
8
1
10
12 1
2
1
212

89
Level 2 Mathematics
2/ trsKd;orD;wpfa,mufonf aps;rSig; 75 usyfom;? Muufom; 60 usyfom;? ig;yd10usyfom;?
c&rf;csOfoD; 1 ydóm50usyfom; 0,fvmaomf ypönf;rsm; tav;csdefudk&Smyg/
3/ awmif;wpfvkH;jzifhxef;vsufcsdef&m 8 ydóm 25 usyfom;&Sd/ awmif;tav;csdefonf
60 usyfom; jzpfaomfxef;vsuf tav;csdefudk&Smyg/
ydóm? usyfom; rlrwl tajr§muf? tpm;ydóm? usyfom; rlrwl tajr§muf? tpm;ydóm? usyfom; rlrwl tajr§muf? tpm;ydóm? usyfom; rlrwl tajr§muf? tpm;ydóm? usyfom; rlrwl tajr§muf? tpm;
Oyrm (1)
ydóm usyfom;
1 25
× 9
11 25
Oyrm (2)
0 70
ydóm usyfom;
4 2 80
× 100 + 200
200 280
- 28
0
- 0
0
tajz/ 70 usyfom;
1/ qm; 1 tdwfvQif 62 ydóm 75 usyfom; ygaom 9 tdwf twGuftav;csdefudk&Smyg/
2/ c&rf;csOfoD; 122 ydóm 50 usyfom; udkjcif; 7 jcif; wGif tav;csdef tnDtrQcGJxnfhaomf
1 jcif;vQif c&rf;csOfoD;tav;csdefrnfrQygrnfenf;/
3/ 1 ykH;vQifiHjym&nf 13 ydóm20 usyfom; ygaomf 11 ykH; wGifiHjym&nftav;csdefrnfrQygoenf;/
4/ MuufoGefeD 335 ydóm udktdwf 12 tdwfwGif tnDtrQcGJíxnfhxm;/ MuufoGef 1
tdwftav;csdefudk&Smyg/
25 × 9 = 225 usyfom;
= 2 ydóm 25 usyfom;
1 × 9 + 2 = 11 ydóm

90
Level 2 Mathematics
Oyrm (1)
Muufom;1ydómvQif 3800 usyfaps;jzifh Muufom; 10 usyfom; wefzdk;udk&Smyg/
1ydóm = 10 usyfom; 10Budrf
Muufom; 10 usyfom; 10Budrf wefzdk; = 3800 usyf
Muufom; 10 usyfom; wefzdk; = 3800 usyf ÷ 10
380 00
usyf jym;
10 3800 00
- 30 - 0
80 0
- 80 - 0
0 0
tajz/ 380 usyf
Oyrm (2)
oMum; 25 usyfom;ukd 210 usyf aps;ay;&aomf oMum; 1 ydómaps;EIef;udk&Smyg/
oMum; 25usyfom;zdk; = 210 usyf
oMum; 25 usyfom; 4Budrfwefzdk; = 210 usyf × 4
oMum;1ydómwefzdk; = 210 usyf × 4
usyf jym;
210 00
× 4
840 00
tajz/ oMum; 1 ydómaps; = 840 usyf
(pdwfwGuf)
atmufygukefypönf;rsm; wefzdk;toD;oD;udk&Smyg/
1/ a*:zD 1 ydómvQif 1800 usyfaps;jzifh 10 usyfom;
2/ ukvm;yJ 1 ydómvQif 2000 usyfaps;jzifh 50 usyfom;
3/ 1 ydómvQif 18000 usyfaps;jzifh ig;&HUajcmuf 25 usyfom;
4/ yJeDav; 10 usyfom;vQif 250 usyfaps;jzifh 30 usyfom;
5/ MuufoGefjzL 25 usyfom;udk 500 usyfay;&vQif 1 ydómwefzdk;
6/ qD 50 usyfom;udk 1600 usyfay;&vQif 1ydómwefzdk;
7/ i½kwfoD;ajcmuf 10 usyfom; vQif 220 usyfaps;jzifh 5usyfom;wefzdk;
pdwfwGuf
3800 usyf ÷ 10
380 ^0 = 380 usyf
wpfq,fom;zdk;twGuf
'orwpfvHk;jzwfonhf oabm

91
Level 2 Mathematics
9 .29 .29 .29 .29 .2 t*Fvdyftav;csdeft*Fvdyftav;csdeft*Fvdyftav;csdeft*Fvdyftav;csdeft*Fvdyftav;csdef
16 atmifp = 1 aygif
2240 aygif = 1 wef
aygifESifhatmifpqufoG,fcsufaygifESifhatmifpqufoG,fcsufaygifESifhatmifpqufoG,fcsufaygifESifhatmifpqufoG,fcsufaygifESifhatmifpqufoG,fcsuf
1 aygif
8 atmifp 8 atmifp
4 atmifp 4 atifp 4 atmifp 4 atmifp
1 aygif = 16 atmifp
aygif = 8 atmifp (aygif0uf)
aygif = 4 atmifp (aygif wpfpdwf)
Oyrm (1) 3 aygif 10 atmifpudk atmifpzGJUyg/
aygif atmifp
3 10
× 16 +48
48atmifp 58 atmifp
tajz = 58 atmifp
Oyrm (2) 75 atmifpudk aygif?atmifp zGJUyg/
4 aygif
16 75 atmifp
-64
11 atmifp
tajz/ 4 aygif 11 atmifp
1
2
1
4

92
Level 2 Mathematics
1/ uGufvyfjznfhyg/
(u) 1 aygifrSm 8 atmifp = ( ) Budrf
(c) 1 aygifrSm 4 atmifp = ( ) Budrf
(*) 1 aygifrSm 1 atmifp = ( ) Budrf
(C) aygif0uf = ( ) atmifp
(i) aygifwpfpdwf = ( ) atmifp
(p) aygif = ( ) atmifp
2/ atmufygwdkYukdatmifpzGJUyg/
(u) 2 aygif 13 atmifp (c) 9 aygif 6 atmifp
3/ atmufygwdkYukdaygif?atmifpzGJUyg/
(u) 144 atmifp (c) 207 atmifp
4/ uGufvyfjznfhyg/
(u) vufzufajcmuf 5 aygifukd 1atmifp0iftdwfrsm;jzifhxnfhvQif ( )tdwf&rnf/
(c) axmywf 3aygif ukd 8 atmifp 0if txkyfrsm;xkyfaomftxkyfaygif; ( ) &rnf/
(*) aumfzDrIefY 2 aygifukd 4atmifp 0ifxkyfrsm;xkyfaomf ( )xkyf&rnf/
(C) tu,fíaumfzDrIefY 2 aygifudk 2atmifp 0iftxkyfrsm;xkyfygu ( )xkyf&rnf/
Oyrm (1) 3 wef 110 aygif ukdaygifzGJUyg/
wef aygif
3 110
× 2240 + 6720
6720 6830 aygif
tajz/ 6830 aygif
Oyrm (2) 2595 aygifudk wef? aygifzGJUyg/
2240 2595
1 wef + 355 aygif
tajz/ 1 wef 233 aygif
3
4

93
Level 2 Mathematics
1/ aygifzGJYyg/
(u) 5 wef 750 aygif (c) 10 wef 800 aygif
2/ wef?aygifzGJYyg/
(u) 3645 aygif (c) 4535 aygif
3/ 1 wif;vQif 46 aygifav;aom pyg;wif;aygif; 100tav;csdefudk wef?aygif jzifhjyyg/
t*Fvdyftav;csdefrlrwl taygif;? tEkwft*Fvdyftav;csdefrlrwl taygif;? tEkwft*Fvdyftav;csdefrlrwl taygif;? tEkwft*Fvdyftav;csdefrlrwl taygif;? tEkwft*Fvdyftav;csdefrlrwl taygif;? tEkwf
Oyrm (1) aygif atmifp
18 9
20 14
+ 19 5
58 12
Oyrm (2) wef aygif
3 1100
+ 7 1200
11 60
Oyrm (3) aygif atmifp
29 7
- 7 12
21 11
Oyrm (4) wef aygif
5 1000
- 3 2000
1 1240
9 + 14 + 5 = 28 aygif
= 1 aygif 12 atmifp
1
1100 + 1200 = 2300 aygif
= 1 wef 60 aygif
2328 aygifrS 1 aygif,l
1 aygif = 16 atmifp
16 + 7 = 23 atmifp
32404
wefrS 1 wef,l
1 wef = 2240 aygif
2240 + 1000 = 3240 aygif
1

94
Level 2 Mathematics
1/ wGufyg/
(u) aygif atmifp (c) wef aygif
13 9 56 1500
+ 7 8 + 12 2000
(*) aygif atmifp (C) wef aygif
43 5 24 500
- 12 15 - 13 1200
2/ yxraowåmwGifodk;arT; 12 aygif 8 atmifp? 'kwd,aowåmwGif 19aygif 15atmifp?
wwd,aowåmwGif 21 aygif 7 atmifp ygaomfpkpkaygif;okd;arT;tav;csdefrnfrQenf;/
3/ yvwfpwpf 18 aygif 1 atmifp teuf 8 aygif 7atmifp a&mif;vdkufaomfrnfrQusefrnfenf;/
4/ arG;puav;trTm 2 a,mufteufyxruav;tav;csdefonf 7 aygif 3 atmifp ESifh
'kwd, uav;tav;csdefrSm 5 aygif 7 atmifp&Sd/ yxruav;onf 'kwd,uav;xuf
tav;csdef rnfrQydkoenf;/
5/ 3 wefum;wpfpD;ay:wGif ukefwifNyD;aemuf pkpkaygif;tav;csdef 5 wef 115 aygif&Sdaomf
ukef tav;csdefudk&Smyg/
6/ rD;&xm;ukefwGJ 2 wGJay:wGif ausmufrD;aoG; 8 wef 180 aygif ESifh 10 wef 2100 aygif
toD;oD;&Sdaomf pkpkaygif;ausmufrD;aoG; tav;csdefudk&Smyg/
7/ aumfzDrIefY 1aygif vQif 3000 usyfjzpfaomf atmufygwdkY wefzdk;udk&Smyg/
(u) aumfzDrIefYaygif0uf
(c) aumfzDrIefYaygifwpfpdwf
(*) aumfzDrIefY aygif
(C) aumfzDrIefY aygif
1
2
2
1
2
3

95
Level 2 Mathematics
jrefrmtav;csdefESifht*Fvdyftav;csdefqufoG,fcsufrefrmtav;csdefESifht*Fvdyftav;csdefqufoG,fcsufrefrmtav;csdefESifht*Fvdyftav;csdefqufoG,fcsufrefrmtav;csdefESifht*Fvdyftav;csdefqufoG,fcsufrefrmtav;csdefESifht*Fvdyftav;csdefqufoG,fcsuf
1 ydóm = 3 .6 aygif
10 ydóm = 36 aygif
1/ uGufvyfjznfhyg/
(u) 50 usyfom; = ( ) aygif
(c) 25 usyfom; = ( ) aygif
(*) 10 usyfom; = ( ) aygif
(C) 5 usyfom; = ( ) aygif
(i) 2 ydóm = ( ) aygif
9 .39 .39 .39 .39 .3 rufx&pftav;csdefrufx&pftav;csdefrufx&pftav;csdefrufx&pftav;csdefrufx&pftav;csdef
1000 *&rf = 1 uDvdk*&rf
jrefrmtav;csdefESifhrufx&pftav;csdefqufoG,frIjrefrmtav;csdefESifhrufx&pftav;csdefqufoG,frIjrefrmtav;csdefESifhrufx&pftav;csdefqufoG,frIjrefrmtav;csdefESifhrufx&pftav;csdefqufoG,frIjrefrmtav;csdefESifhrufx&pftav;csdefqufoG,frI
1 uDvdk*&rf = 61 usyfom;
1 *&rf = usyfom;
ajryJawmifhtav;csdef = 1 *&rfcefY&Sdonf/
oHy&moD; tav;csdef = 100 *&rfcefY&Sdonf/
1
4
6
100
ajryJawmifh oHy&moD;
1 *&rf 100 *&rf

Level 2 mathematics

Recommended

Recommended

More Related Content

What's hot

What's hot (17)

More from Hujjathullah

More from Hujjathullah (20)

Level 2 mathematics