ຄະນິດສາດ_Math

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II. .97;k,D 15 95fryglf0v’lt4kotdkomugj xaovaf8klj;orq;rao,ufaj’oUD 12 !D mkfcmh0v’0v[g0f[aoskF 8q;1kj ’D { 0hvp-NxB,0Po !) sq;M]t @WW du[D { 0hvpgvqkw0j.l4j q’M]t !@ |j;pD { lj;oxtdv[0v’dkogIafg0Qk|q,le]a[ ( 7qodyoD { ]qf7ao|bj’dyooE,ao ( ]yf8+ !WW dy3]c,afD @D 75o]adltotltgrkt0v’dkogxaovaf8klj;orq;raoD x2 + 34678 2,4 3,2 4,8 5,6 6,4 x2 + #D dkoxtdqf,u8e]k j 7j 6oda[j j s^n j sj ko.sh j Dj ...ສະຫງສ.ວວນ.ລິສຂະສິດ ... ' 2500 8q;1jk’ G 7jk[afg0Qkg[y’j ]eg]njv’ @& WW du[ 8+ ! [afD x 2500 9eo;oxU 1 2 3 4 5 ]k7k 2500 5000 7500 10000 . . . lextlyf0v’dkogxaovaf8klj;orq;raoD $D 7;k,lk,kflhk’dik2yd.oI6[c[[8+wxoUD du[ 10000 7500 5000 2500 0 1 2 3 4 5 6 kg 150

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55[qfmu dkocdhlt4kotdkomujgxaovaf8kl;j orq;rao ສະຫງສ.ວວນ.ລິສຂະສິດ I. dyf9tdeD .odkoc]jomqo ,uoaddy]k & 7qo g0QkIj;,dkoc0’j 0aoD oaddy]kg[u # c]jow] pt * dy3]c,af .-hg;]k ! -qj;3,’S oaddy]kg[u & c]jow;d;jkoaddy]kg[u # lv’gmnjvS oaddy]kg[u @ .-hg;]k @ -q;j 3,’grnvj c]jo * dy3]c,afS oaddy]kg[u ! c]oj w;d;kj g[u # lk,gmvjn S oda dy]kg[u $ c]oj -kh d;kj g[u ! lv’gmvjn D 4kh .sh g;]k @ -qj;3,’F oaddy]kg[u & 9t-tot.odkoc]jo s^n [+ L oaddy]kg[u .fgxaoz6hc]oj wx .ow]ptwdd;\\j 6j L II. .97;k,D grnjv9tcdh[aoskdjP;da[dkogxaovaf8kl;j orq;rao gIqklhk’8k8t]k’ X s^nlhk’dik2yd? c]h;oe.-hG { lextlyf0v’dkogxaovaf8kl;j orq;raoD { 75o]adltot0v’8e]k j j 76oda[ j j s^n j j sko.sh j jD III. [qfg/ydsafD !D oEs;ko]a’|b’j ]k7k #@ WWW du[D oEs;ko * ]a’ ]k7kgmqjk.f L 9qj’0Po8nj,.lj8k8t]k’]5j,oU.sh7q[4h;oD 9}o ]a’ ! @ # $ ) !W !& !) @W ]k7k #@ WWW D D D D D D D D D D D D D D D D D D D D D D D D 152

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ສະຫງສ.ວວນ.ລິສຂະສິດII. .97;k,D ,N|b’j ,u @$ -q;j 3,’D ! -qj;3,’ = *W okmu ! okmu = *W ;yokmu 3,’c,jog7njv’,n;afcmdg;]kD III. [qfg/ydsafD !D muj7y;]qfg, gryoj 9txvj p]qfg,gxaoxqddt8yc8gj ;]k ( 3,’sk _ 3,’fa’j oU G 7aomu ! vvdg;]k ( 3,’ WW okmu 7aomu @ vvdg;]k ( 3,’ !& okmu 7aomu # vvdg;]k ( 3,’ #W okmu { 4k,;jk skj ’dao9adokmu gryoj 9b’j xjvp]qf7ao|b’j L { c8j ( 3,’ sk _ 3,’ 9t,u]qfvvd9kd7y;9ad7ao L @D dkoc0’j 0aody]kg8t[koc[j’gxao @ g7y’j g;]kF 7ng7yj’]t $& okmu c]t rad !& okmuD 4k,;kj 4hk dkoc0j’0aog]uj,8Qoc8jg;]k !* 3,’F dkoc0j’0aooao9t 9q[]q’g;]k9ad3,’L #D ,NoUc,oj ;aova’7ko;aomu $ {!@ { !__& Ivf;aomu @_ { !@ { !__& 9tc,jo;aogduf 0v’ ok’ 3vlkD 4k,;jk pa’vud9ad;ao 9bj’9tIvf;aogduf0v’]k;L $D ]qf7ao|bj’c]oj c8oj t7vos^;’;P’9ao Ivfc0;’ [+cdh; .-hg;]k ! ;ao da[ # -q;j 3,’D 4k,;kj ]qf7aooAo.-hg;]kc]jowx9ad-qj;3,’ L &D dkolv[gla’;y-k7toyflkf -Ao x$ .-hg;]k _W okmuF 4hkskddkolv[gla’ g]u,j g;]k _ 3,’D 4k,;jk 9ad3,’9bj’9tgla’c]h; L *D mhk; fe g;Qkda[ mhk; cf’ ;jkG 0hvpcdh[qfg/ydsafg]d.-hg;]k !@W okmu 9bj’c]h;F mhk; cf’ g;Qk;kj l;j o0hvp d=cdh[qfg/ydsafrkp.o @ -qj;3,’da[ & okmuD 4k,;jkz6h.fcdh[qfg/ydsafw;d;kj dao L 155

[qfmu 57 w]ptg;]k I. dyf9tdeD !D mhk; mv’lk vkj oxB,xts;aflkf]k; c]t 0Po0=h,6ow;h3fpltgrktw]pt g;]kdko0Bo7v’czoj fyo0v’g9Qk-u;yf c8j]tvq’.ow]ptzjko,kD { 9qj’-vdskw]ptg;]k7v’czoj fyo0v’g9Qk-u;yfc8]j tvq’D -nj g9Qk-u;yf xu0Bo7v’ xulYol5fdko w]ptg;]k ສະຫງສ.ວວນ.ລິສຂະສິດ czoj fyo 7v’czoj fyo 7v’czoj fyo g9Qk 2hk’5j, g9Qk lk,clowm 1353 1373 ....... g9Qk ;y-5oot]kf 1373 1416 ....... g9Qk 3rmylt]kf 1500 1520 ....... g9Qk w-glf4kmy]kf 1520 1560 ....... g9Qk l5]ypt;q’lk 1560 1574 ....... 1638 1695 ....... @D mhk; 7es^hk wfhgIafdko16j[=]ylafxtdaowr,kc]h; @ xu ) gfnvo wfhIa[laopk .shgIaf;Pd8+vud ! xu * gfnvoD 4k,;jk mhk; 7es^hk gIafdko16[j vj ooUma’\\qf .-hg;]kgmqkj .f L #D 9qj’la’gdfg[yj’xt3spd]5j,oU c]h;[vd;jkxt3spd.f g;Qkg4y’ Xg;]k? c]t xt3spd.fg;Qkg4y’ Xw]ptg;]k?D dD !@ 3,’ de]a’dyog0QkD 0D 7;kp,uvkp5pno @W xuD 7D mhk; 7efu ,kIvf3I’IPog;]k ) 3,’ c]t da[[hko g;]k!@ 3,’D CD g0qhk3I’IPo8vog-qhkg;]k ) 3,’D 156

ສະຫງສ.ວວນ.ລິສຂະສິດII. .97;k,D w]ptg;]kc,jo-j;’g;]k0v’gsfdko.f|bj’9kd95fg]uj,8Qosk95fl5fmhkpD 8q;1jk’G { xu !#&# c,jo g;]k 0Bo7v’czoj fyo0v’g9Qk2hk’5j,D c8jxu !#&# skxu !#(# gxaow]ptg;]k @W xu c,oj w]ptg;]k7v’czjofyo0v’g9Qk2hk’5j,D { grnvj [vdw]ptg;]kgryjo.-h7eg;Qkfa’j oUG lt8t;afF mqflt;afF xuF gfnvoF vkmyfF ,nhF 3,’F okmuF ;yokmuD III. [qfg/ydsafD !D 9qj’la’gdfg[yj’xt3spd]5j,oU c]h;[vd;jkxt3spd.fg;Qkg4y’< g;]k < c]t xt3spd.fg;Qkg4y’ < w]ptg;]k<D dD g0qhk3I’IPog;]k ) 3,’D 0D rkps’a^ gdfu ,kc];h ]d6 9’y 39Xh |46 ’q ?9tvkwl1.j6 omvh ’c,xj t,ko ( sk ) gfvn oD 7D -hk’,uvkp5pno @WW xuD CD 7kj g-qkj gInv0usj ^yho.olt4komujmv’mPj ; ! -qj;3,’8=j !W WWW du[ 9D 8hv’c]h;dvj o ) 3,’D @D mhk; cdh; gdufxu !_(*D Ivfxu !__# ]k;,uvkp59adxu L Ivfxu @WWW ]k;9t,uvkp59adxu L #D 9qj’[vd;jk|a’lnry,;P’9ao.\\jlt[a[oUvvd;aomugmqjk.fL gfnvo.fL xu.fL $D oadg8t[kog/yd-hv,;ao]t ! -qj;3,’ @W okmu ]k;-hv,rkp.o ! vkmyfD 4k,;jkoadg8t[ko.-hg;]kg/yd-hv,gmqkj .f L &D c,j mhk; 7e vkp5 #& xu _ gfnvo r+0v’]k;cddj ;kj c,j # xu & gfnvo r=]j k;vkp5 gmqjk.f L *D .odkoc0’j 0aoc]oj $WW c,af mhk; lyfmygff .-hg;]k ! okmu @W ;yokmu mhk; ;y]t15f .-hg;]k ! okmu !& ;yokmu .zc]oj wfhw;dj;kdaoL w;d;jkgmqkj .fL 157

[qfmu 58 dkodeoqfmu8j A’.o8k|jk’ I. dyf9tdeD 9qj’la’gdfg[y’j dkodeoqfg,af8kj ’M.o8k|jk’]5j,oUG 18 ສະຫງສ.ວວນ.ລິສຂະສິດ 17 16 15 14 .13 F 12 .11 C 10 .9 B .8 G 7 6 .5 A .4 D .3 H 2 .1 E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 dD 9qj’deoqfmuj8A’0v’g,af C, D, E, F, c]t H g,nvj I6h;jk G A (7 , 5 ) ; B (12 , 9 ) ; G ( 3, 8 ) 0D 9qj’\\kpg,af8=jwxoU.lj8k|jk’ I X @ S # ? J X!# S * ? K XW S ( ? L X !! S ! ? M X!) S ( ? II. .97;k,D dkodeoqfmuj8A’0v’g,af.f|bj’16j.o8k|jk’c,jogIqk8hv’0Po8q;g]d16jglAo g7Qkovodvj o c]h;9b’j 0Po8q;g]d16gj lAog7Qk8A’8k,s^a’D 8q;1kj ’G A X( S & ? X( c,jo8q;g]d1j6glAog7Qkovo ? X& c,jo8q;g]d16jglAog7Qk8A’ ? 158

III. [qfg/ydsafD !D 9qj’lhk’I6[.o8k|jk’oU 8k,g,af8jk’Mmujdeoqf.shfaj’oUG 10 . .. . .. .9 . . . 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 9qj’\\kpg,afgs^qkj oU.l8j k|kj ’ A (1 ; 8 ) ; B ( 12 ; 7 ) ; C (4 ; 8 ) ; D ( 10 ; 4 ) ; E (10 ; 7 ) ; F(4;4) ; G (10 ; 9 ) ; H ( 4 ; 2 ) ; I (12 ; 9 ) ; J ( 10 ; 2 ) . ສະຫງສ.ວວນ.ລິສຂະສິດ 9q’j 0uf8+ A .lj B F .lj C D .lj E B .lj C C .lj G G .lj H C .lj D G .lj J E .lj F H .lj I c]t H .lj B c]h;gsao;jkgxaoI6[spa’ L @D 9qj’deoqfmu8j A’0v’g,af8jk’M.oI6[oUD .10 A 9 8 7 6 .5 .C .D 4B 3 2 . .1 F E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 159

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[qfmu 60 dkog7njvophkp I. dyf9tdeD !D 9q’j ]vdc[[I6[]5,j oU.ljxB,0Poc]h;.ljlu8=j8k,8q;1jk’D @D 9qj’la’gdfI6[]j5,oUc]h;c8h,8+D ສະຫງສ.ວວນ.ລິສຂະສິດ 162

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@D 9’jq ]vdc[[I[6 o.U lgj 9ph 0k; XI[6 $ c9lkd ABCD ? c];h lkh ’I[6 lcju 9lkdvoa .\\j fh;p;ymug7nvj ophkpI6[lujc9lkdoAo wxmk’g[nhv’-hkp ) 8kdk3i 8k,glAo AE .shwfhI6[ EFGH . EA D B C #D 9q’j [vd;ymumuj 21 2 ສະຫງສ.ວວນ.ລິສຂະສິດ lk,kfc8h, 20 I6[mu @ .sh7n 19 da[I6[mu ! wfh 18 .sh-afg9o.o8k 17 dk3iohvp0hk’ 16 0;koUD 15 14 13 1 12 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 $D dkog7nvj ophkpI6[9kd d sk 0D 9q’j c8h,8+I6[ ! .sh7nda[I6[ d c]t c8h,8+I6[ @ .sh7nda[I6[ 0F s^a’9kdc8h,c]h; 9tlts^5[wfhco;.f L 0 ! d @ 165

[qfmu 61 m;o7no I. dyf9tdeD 5 9 6, 3 8 + 2 0 7, 5 4 !D 9qj’7yfw]jg]d]5,j oUD 1 3 5, 6 4 6 5, 4 2 2 8 3, 4 6 3 + 2 7, 4 + 3 0 4, 2 8 + 5 1, 2 7 5 _ 4 5 6, 3 7 _ 6 4 8, 4 5 _ 5 9 2, 8 9 _ 8 6 5, 7 8 2 4 9, 2 7 1 5 7, 3 5 1 5, 4 8 5 6 4, 2 3 8, 4 6 2, 4 4, 6 5 9, 0 4 V 24 V 2, 8 V 2, 7 V 3, 2 3684 12 1525 25 9144 36 5440 64ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9q’j 0Po8n,j .l8j k8t]k’]5,j oUD 8q;8aA’sko 8q;sko zqosko 8q;glf 8859 36 2847 23 7959 34 11610 128 16384 130 #D 9qj’la’gdf8q;1jk’dko76o]5,j oUc]h;oe.-h76o8+wxD 18 x 3,25 = (18 x 3 ) + ( 18 x 0,2 ) + ( 18 x 0,05 ) = 54 + 3,6 + 0,9 = 58,5 166

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