ມ.2_ຄະນິດສາດ_Math

−ÕÎñ¡ (kg) 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 º¾¨÷ (-À©õº−) @?D 8k8t]k’]5,j oUltcf’g4y’0=h,6o8yf8k, v5ostr6,0v’7qow0hz6h|b’j w]pt !W ;aoD ;aomu _}_}@WW_ !W !! !@ !# !$ !& !* !(ສະຫງສ.ວວນ.ລິສຂະສິດ!) v5ostr6, 40D 38, 5D 39D 36D 40D 38D 39D 37D 37D 36, 5D ( DC) 9q’j c8h,glAoltcf’v5ostr6,0v’7qow0hD dkoltcf’0=h,6o.odyf9tdemu ! c]t mu @ gvUo;kj G dkoltg|u0=h,6oc[[glAoltcf’D dyf9tdemu $ 1j6shv’mqf]v’cs’j |bj’ gryjowfh;afcmd]aflt\\u0v’dkof6f-b,oE0v’g9hpczoj |bj’.o & okmu 3fpg]U,9kd95foE8qd]q’D okmumevyfwfh 7 mm; okmumulv’wfh 11mm; okmumulk,wfh 14 mm; okmumuluwj fh 16 mm; c]t okmumushkwfh 18mm; dD 9q’j ltcf’zqodkomqf]v’oUfh;p8k8t]k’D 0D 9qj’c8h,I6[ltcf’lt4y8yoUc[[glAoltcf’D 245

ສະຫງສ.ວວນ.ລິສຂະສິດ@D .97;k, dkoltg|u0=h,6o fh;pI6[c8h, gIqklk,kfgIafwfhs^kpI6[c[[ 8k,7;k,g\\ktlq, 0v’0=h,6o7nG • dkoltg|u0=h,6oc[[czoj ,qo gxaodkoltg|u0=h,6ofh;p;ymuc[’j goNvmuj0v’czjo,qovvdgxaolj;omugj xaovaf8klj;orq; raoda[xt]y,ko0v’0=h,6o8jk’M 3fp4ngvqk,5,.9dk’ mu,j usq;|j;pgxaovq’lk gxaos^ad .odkoc[’j D gIqkvkf.llj u s^n 0uf]kp.lcj 8j]trkdl;j omuj9tgIaf.sh9ecod7;k,]t vPf0v’0=h,6owfhw;0NoD • dkoltg|u0=h,6oc[[glAoltcf’ gxaodkoltg|u0=h,6o16j.o]t[q[glAog7Qk8A’lkdF 3fpdkoc8h,g,af8jk’M mujgxaog,af8af dao0v’glAo-nj mu0j uf9kdg,afmu[j vd7kj 8q;xPj o0v’0=h,6o0t|koda[glAog7Qk8A’ c]t glAo-n0j t|koda[glAog7QkovoD 9kdoAo gIqk0uf8+95f8kj ’Mmu]j Podao.ldj aoD dkoltg|u0=h,6oc[[oU g\\ktlq,le]a[0=h,6omuj8+gonvj ’dao s^n gxaodkoxPj ocx’ muj8+gonvj ’daoD #D [qfg/ydsaf !D lt4y8yoadIPo.o8QolqdIPo @WW_ {@W!W 0v’3I’IPo,afmtpq,8Qocs’j |b’j ,ufa’j oUG ,D! ,u9eo;o g8a, #)( 7qoF py’ !*@ 7qoS -Ao ,D@ ,u9eo;og8a, #&* 7qoF py’ !!$ 7qoS -Ao ,D# ,u9eo;og8a, $!# 7qoF py’ !$# 7qoD -Ao ,D$ ,u9eo;og8a, @@# 7qoF py’ !@& 7qoD dD 9qj’lhk’8k8t]k’ltcf’0=h,6o 0D 9q’j c8h,I6[ltcf’0=h,6ooUc[[vyflt38dik,D 7D 4k,;jk 8QolqdIPo @WW_{@W!W 0v’3I’IPofa’j djk;,uoadIPoma’\\qf9ad7qoL gxaopy’9ad7qoL ’D c8]j t-AoIPo d;,gvqk9adgxug-ao0v’oadIPoma’\\qfL 9D c8j]t-AoIPo ,uoadIPopy’ d;,gvqk9adgxug-ao0v’oadIPoma’\\qf.o-AooAoL lD 9q’j ltcf’9eo;ooadIPoc8j]t-AoIPoc[[czjo,qoD @D 0=h,6o]5,j oU 7n zqodkolv[gla’;y-k7toyflkf rkdIPomu ! 0v’shv’ ,@}0 163j I’ 246

IPocs’j |b’j ,ufaj’oUG $S #S (S $S *S #S $S *S #S (S #S &S *S #S &S $S *S $S $S )S &S (S $S (S #S @S &S *S )S &S $S )S (S *S @D dD 9q’j lhk’8k8t]k’ltcf’0=h,6ofa’j dkj ;oU 0D 9q’j c8h,I6[ltcf’0=h,6oc[[czjo,qo 7D 9qj’c8h,I6[ltcf’0=h,6oc[[glAoltcf’ ’D gryjowfhc[j’]tfa[dkoIPo0v’oadIPovvdgxao $ xtgrf oadIPogda’j wfhIa[7tcoo ( 0Nowx oadIPoxkodk’ wfhIa[7tcoo & c]t * oadIPovvj o wfhIa[7tcoo # c]t $ oadIPovjvos^kp wfhIa[7tcoo W sk @ 9q’j lhk’8k8t]k’ltcf’zqodko9afxtgrfoadIPofaj’djk; rhv,ma’c8h,I6[ltcf’ zqodko9afxtgrfoU c[[vyflt38dik,D #D oU7nI6[c8h,ltcf’0=h,6oc[[vyflt38dik, 0v’9eo;ooadIPo .o3I’IPo|b’j D ສະຫງສ.ວວນ.ລິສຂະສິດ 9eo;ooadIPo Xly[7qo? 9 8,4 8 7 ¥¿ ¥¿ 6,6 −¸− −¸− À- ªñ´ À- ªñ´ 6 ¥¿ 5 −¸− ¨ò¤ ¨¤ò À- ª´ñ 4 3,2 3 2 ¨¤ò 1 ´. 1 ´. 2 ´. 3 ¢˜−»¼− dD -AoIPo.f,uoadIPos^kpd;kj L 0D 9kdI6[ltcf’0=h,6o 9q’j 7yfw]jc8j]t-AoIPo;kj ,uoadIPo9ad7qoL gxaopy’9ad7qoL 7D 9eo;ooadIPoma’\\qf0v’3I’IPocsj’oU ,u9ad7qoL gxaopy’9ad7qoL ’D oadIPo-Ao ,! s^kpd;jk-Ao ,# 9adgxug-ao0v’9eo;ooadIPoma’\\qfL 247

ສະຫງສ.ວວນ.ລິສຂະສິດ9D oadIPopy’-Ao ,! c]t ,@ s^kpd;kj oadIPopy’-Ao ,# 9ad7qoL d;,9adgxug-ao 0v’9eo;ooadIPopy’ma’\\qfLD $D 7tcoolv[gla’;y-k7toyflkfxt9erkdIPomulv’0v’shv’ , 2}0 0v’3I’IPo ,afmtpq,csj’|b’j 3fpcpd -kp{py’ fa’j oUG 7tcoooadIPopy’G *F !WF _F )F #F (F !WF *F #F *F )F !F *F *F (F )F !WF #F _F _F $F $F *F #F *F (F *F #F *F &D 7tcoooadIPo-kpG $F )F !WF )F )F !WF *F &F _F $F #F *F (F *F $F $D dD 9qj’lhk’8k8t]k’ltcf’0=h,6o0hk’gmy’oU 3fpcpd.shgsao 9eo;ooadIPo];,F 9eo;ooadIPopy’ c]t 9eo;ooadIPo-kpD 0D 9q’j ltcf’0=h,6olt4y8y0hk’gmy’fh;pglAoltcf’D 7D oadIPoshv’oUwfh7tcoo.fs^kpd;jk\\6jL ,u9ad7qoL c]t d;,gvqk9adgxug-ao0v’ oadIPoma’\\qfL ’D shv’;y-kdko3I’IPowfh;k’,kf8t4ko9afxtgrfdkoIPo0v’oadIPo w;h fa’j oUG oadIPomujwfh7tcoo.o [1;3[ 9afgxaoxtgrfvvj os^kpD oadIPomujwfh7tcoo.o [3;5[ 9afgxaoxtgrfvvj oD oadIPomujwfh7tcoo.o [5;7[ 9afgxaoxtgrfxkodk’D oadIPomuwj fh7tcoo.o [7;9[ 9afgxaoxtgrfgda’j D oadIPomuwj fh7tcoo.o [9;10] 9afgxaoxtgrfgdaj’s^kpD { 9q’j 0Po8nj,.l8j k8t]k’]5j,oU.sh7q[4h;o c]t g\\ktlq,D 7tcoo 9eo;ooadIPo 7yfgxaogxug-ao [1; 3[ [ 3;5[ [ 5; 7 [ [ 7;9[ [9;10 ] { 9qj’c8h,glAoltcf’0=h,6oc[[vyflt38cdi,D 248

7e8v[[qfg/ydsaf [qfmu ! g]dl;j o !D 1) 21 . 2) 34 . 3) 105 . 10 10 10 4) 214 . 5) 10811 . 6) 2201 1000 100 1000 *D dD 45 0D 30 7D 36 ’D 15 )D glp 90 |;j pS gs^nv 120 |;j p _D 0kp 144 kg S gs^nv 96 kg !WD dD dyoc]h; 40 dhvoS gs^nv 56 dhvoS 0D dyoc]h; 36 dhvoS gs^nv 60 dhvo [qfmu @ mt;u76o c]t v5xt76o0v’g]dl;j o !D dD !@D 0D &D 7D 12 5 ສະຫງສ.ວວນ.ລິສຂະສິດ @D 2 ; 8 21 7 #D mt;u76oI;j ,|hvpl5f0v’ 2 , 7 c]t 32 c,jo 224 3 24 45 3 $D v5xt76oI;j ,s^kpl5f0v’ 25 , 15 c]t 10 c,jo 5 3 7 9 63 &D r6fI;j ,0v’g]dl;j o 5 , 7 c]t 11 c,jo (@WD 48 40 90 [qfmu # dkosp=h c]t dko0Bor6fIj;,g]dl;j o @D dD 6 = 42 ; 72 ≠ 8 ; 100 ≠ 0 5 35 63 9 1000 10 #D dD 2; 6 ;1 0D −21 ; 1 ; − 9 7D 3; 3;9 ’D 4; 7; 3 3 11 3 3 448 582 _D dD 1 = 2 S 0D 1 = 5 S 7D 1 = 9 S ’D 1 = 15 D 2 4 2 10 2 18 2 30 249 

[qfmu $ dkoxP[mP[g]dl;j o !D 7D 1 < 1,5 < 1,7 < 20 < 2,5 < 4 ’D 1 < 12 < 1,5 < 2 < 23 < 3 7 7 7 70 7 7 4,3 43 4,3 4,3 43 4,3 $D dD 4 < 5 < 3 < 5 < 9 ; 0D 2 < 9 < 1 < 7 < 3 16 8 4 3 2 5 20 2 10 4 &D dD 6 6 6 0D 45 7 8< 6< 5 5<5< 5 *D oadIPoshv’ ,@ ,addy]k[ko[h;’s^kpdj;kD  (D I6[lujc9lkd R1 ,u];’pk; pk;dj;kI6[lujc9lkd R2 [qfmu & dko[;d c]t dko]q[g]dl;j o !D a = 7 ; b = 12 = 3; c = 8 = 1 ; d = 1 ; e = 2 = 1 ; f = 2 = 1 5 4 16 2 5 4 2 16 8 @D a = 7, 9 ; b = 3 ; c = 10; d = 2 ; e = 2 ; f = 50 24 7 3 5 $D a = 19 ; b = 17 ; c = 1 ; d = 5 = 1 ; e = 6 ; f ສະຫງສ.ວວນ.ລິສຂະສິດ=12=4 4 13 3 15 3 7 9 3 (D a = 7 ; b = 12; c = 28 ; d = 16 5 17 [qfmu * dko[;d c]t dko]q[g]dlj;o X8+? !D a) 3 ; b) 5 ; c) 3 ; d ) 2 2 3 45 #D a) 4ndS b) 4ndS c) zyfS d) zyfS e) zyfS f ) 4ndS g) 4nd &D a = 52 ; b = 181 ; c = 158 ; d = 1 ; e = 11 ; f = 122 15 60 21 5 60 21 *D a) x = 1; b) x = 4 ; c) x = 7 ; d) x = 3 3 8 14 (D dD 4ndD 0D zyfD 7D 4ndD ’D zyfD 9D 4ndD [qfmu ( dko76og]dl;j o !D a = 4 ; b = 1 ; c = 1; d = 2 ; e =1; f =0 5 3 9 $D A = 10 ; B = 1 ; C = 1 ; D = 1 ; E = 2 10 5 2 7 250 

*D dD 4 0D 3 7D 34 ’D 10 9 10 15 3 (D 1 ; − 1 = − 10 ; − 1 = − 10 ; 1 = 1000 ; 4 ; −7 40 0,8 8 3,2 32 0,016 16 3 !WD . A = 17 ; B =1 S A = 7 ; B = 1 S A = 1 ; B = 5 24 48 4 6 18 [qfmu ) dkoskog]dl;j o !D a = 20 ; b = 3 ; c = 1 d = − 5 ; e =1; f = 2 21 4 3 6 3 #D 1 = 4; 1 = 10; 1 = 10; 1 = 50 7; 1 ; 3 ; 19 0,25 0,1 0,01 0,02 5 8 6 &D dD 35 ; 9 ; 13 0D 130 ; 47 ; 2 6 70 7 9 90 !WD 900 ]uf  !@D lq,,5f x c,oj 9eo;o0k0v’[Q’dnF gIqkwfh x = 42 ສະຫງສ.ວວນ.ລິສຂະສິດ !&D A = 23 S B = 5 ; C =1 6 6 [qfmu _ 9eo;oxqddt8y #D 4 = 1,333… = 1, 3 gIqkwfh 1,333 < 4 < 1,334 3 3 $D 25 = 3,571428… = 3, 571428 gIqkwfh 3,57 < 25 < 3,58 7 7 &D 355 = 3,14159292… = 3,141592 gIqkwfh 3,141592 < 25 < 3,141593 F 113 7 *D 1000 = 333,333… = 333, 3 S 33000 = 330 ; xhk-Nwfh4ndd;j kD 3 100 (D 15800 = 1316, 6 S -Ngxao3s^phvo;kj 1316,6 < 1450 12 [qfmu !W 9eo;oxqddt8y X8+? !D dD 16 ; 27 ; 213 0D 19 ; 41 ; 1159 5 25 1000 250 40 5000 &D x = 2,999… = 2 + 0,999… = 2 + 9 = 3 9 251 

*D dD 1, 888… = 17 ; 5,12 = 517 ; 2, 34 = 211 ; 4, 2393939… = 4197 9 99 90 990 0D 8,215 = 8133 ; 7,152 = 6437 ; 9, 2 = 83 ; 23,40 = 117 990 900 9 5 (D 1,999… = 1+ 0,999… = 1 + 9 = 2 9 [qfmu !! 9eo;ovtxqddt8y #D 2 = 1,41421356237…; 3 = 1,73205080756… ]h;oc8jc,jo9eo;ovtxqddt8yD &D [+,uD [qfmu !@ dkog7yj’7nmP[.ljg,afsobj’ q (D dD A' A 0D la’gdfI6[F ,5, AOA\" =180 180   ສະຫງສ.ວວນ.ລິສຂະສິດp  \\kp7;k,;jk g,af A'' c]t A O g7y’j 7ndaomP[.ljg,af O. A\" [qfmu !# dkog7yj’7nmP[.lgj ,af\\bj’ X8+? $D dD 0D   O          O        0=hla’gdfG l6odk’g7yj’7n O c,oj g,af8afdao0v’[aofkcdog7yj’7n0v’,aoD 252 

Xle]a[0=h 7 c]t ’ c,oj xt8y[af7ndaoda[0=h d c]t 0?D *D I6[ Xd? ,u ) cdog7yj’7nF I6[ X0? [+,ucdog7y’j 7n c]t I6[ X7? ,u $ cdog7yj’7nD [qfmu !$ dkog7y’j 7n0v’,6,mP[.lcj doF mP[.lgj ,af $D I6[ X!? yAx' da[ xAy' S yAx da[ x'Ay' S zBx da[ x'Az' zBx' da[ xBz' S zCy da[ y'Cz' S zCy' da[ yCz' I6[ X@? xAz da[ x'Az' S zAx' da[ xAz'S yBz da[ y'Bz'S zBy' da[ yBz' &D 1 = 3 = 125 c]t 2 = 55 (D 1 = 5 = 60 S 2 = 4 = 110 c]t 3 = 6 = 70 )D dD A = 36 ; B = C = 72 A  0D 7D BDA = 108 B  D  ສະຫງສ.ວວນ.ລິສຂະສິດ BDC = 72 D F  ’D ,uI6[lk,c9mPj ’vnjo ) I6[D E  G  C  { glAo-n0j t|koda[ AB ,ulv’glAoD { glAo-nj0t|koda[ BD ,u|bj’glAoD [qfmu !& g]dde]a’ !D dF 25 F 0D (−3ab)2 F ’D (x + y)4 F 7D (x + y)4 9D ⎡⎛ − 3 ⎞ ⎛ − m ⎞ ( −t )⎤⎥⎦2 ⎣⎢⎜⎝ 4 ⎟⎠ ⎝⎜ n ⎟⎠ @D dD 27648 F 0D 54675 F 7D 69984 F ’D 1296 F 9D 1F lD 23 144 #D dD x10 F 0D y9 F 7D (ab)33 F ’D −100x7 F 9D t F lD xn -D n4a F pD x24 F fD a2xb2 yc2z $D dD 2 F 0D − 1 ⎛ x ⎞4 7D ab 5 2 ⎜ ⎟ ⎝ y ⎠ 253 

’D 1 9D 24m F lD 1 &D n = 50; m = 27; p = 15 [qfmu !* g]dde]a’ X8+? !D dD 6,95×106; 4, 602×107 F 0D 5, 2×10−3; 2,5125×101; 1, 25002×103 7D 4,3×102; 4,5×10−7; 1,55002 ×104; 7,525×10−2 @D dD 602380000000000000000000 3,g]d5oD 0D 39300 000 m F 7D 89 600 000 km2 #D 1,5×1021 dik, [qfmu !( leo;o @D dD ltcf’g4y’9eo;omujgxaomt;u76o0v’ # 0D 9eo;o7ud #D dD zqo[;d0v’[aofk]Pj ,0hk’ma’\\qf 0D goNvmujvhv,0hk’ 7D goNvmujrNo ’D [=]y,kf ສະຫງສ.ວວນ.ລິສຂະສິດ &D I6[ X!? A = bh F I6[ X@? A = h(b1 + b2 ) I6[ X#? A= AC × BD 2 2 2 [qfmu !) dko7eo;odjP;da[leo;o !D D = −1S A = 5; B = −6,8; C = −254 @D A = 20 − a; B = 2a + b; C = 3 + b; D = 8b − 2a − 25;   E = 2x + 31;   F = 16x − 8 S G = 3x −17 S H = 3y #D A = − 5 ; B = 49 ; C = − 51 ; D = 11 2 20 40 12 &D A = −40 S B = −112 S C = 90 S !WD dD 1200 0D 113 7D 160 ’D 2,75 9D 188, 4 lD 1125 98 [qfmu !_ dkocpdlj;o76o.oleo;o !D dD 5x + 5 0D 2a2 + 2a 7D 7a2 − 7 ’D 1+ y3 9D −1 @D dD 5x − 4y 1− y3 9D 3a − 9b 0D −2bx 7D 13a ’D 7m − 2m2 254 

#D dD 5 0D 3 7D 11 ’D 4 9D 2a lD 2mn -D ab pD 3ac fD 4x2 y2 8D x 4D x + y mD n(m − n) $D 9D 11a(2b + 3c − 4d) lD 5xy (2 + xy) -D 9b(4b −1) ( )pD 5a2 1− 2a + 3a2 ( )&D 7D 3xy 3x2 − 2xy + y2 ( )’D 5n n2 − 2mn + 3m2 *D dD ( x + y)(a + b) 0D (m + n)( p − q) 7D ( x + 2)( x + 5) [qfmu @W ltgs,uzqo @D dD 5a − 20 = 40 S 5a − 20 + 20 = 40 + 20 0D 5a = 60 S 5a × 1 = 60 × 1 S 7D a = 12 5 5 [qfmu @! lq,zqo0Ao|bj’mu,j u|b’j 8q;]a[ ສະຫງສ.ວວນ.ລິສຂະສິດ #D dD 4x = x + 2 S 0D 250 + x = 2500 S 7D x +15 = 3x − 3 $D 1 3 &D dD 1S 0D 4 S 7D −4 3 )D a. x = 8; b. x = 7; c. y = 35; d. y = 252; e. x = −11; f . x = 3 g. y = 2; h. z = −28; i. a = 3; j. b = −18     k. [+,u.9zqoS   l. x = −36; m. n = 27 ; n. [+,u.9zqoS o. d = −1; p. x = 1 5 !WD a. [+,u.9zqoS b. x = 3 ; c. x = 4; d. x = 2 4 !!D dD x = 1 s^n   x = −5 S 0D x = 4 s^n   x = − 1 S 2 7D x = 2 s^n   x = 3 s^n x = 4 ’D x=0 s^n   x = 1  s^n x = 1 S 9D x = 5 s^n   x = −2 S 2 lD x = 1 s^n   x = −7   255 

[qfmu @@ dkocdh39fdPj ;da[lq,zqo0Ao|bj’muj,u|b’j 8q;]a[ !D 29 xu   @D oadIPo.oshv’,u !* 7qoD *D g0Qk9u|j bj’dhvo]k7k &WW du[D (D 7kj ;afcmd0v’lk,,5,c,oj G 30 ; 50 ; 100 8k,]efa[D [qfmu @# vtltg\\uzqozqo @D d? 3210 g = 3, 210 kg 0? 2 kg 7g = 2, 07 kg #D d? 0; 1; 5; 6; 7 ; 14 F 0? − 18 ; − 1; 4; 11 ; 15 ; 22 7 7 7 7 77 11 11 11 11 11 11 &D −7, 437 < − 7, 436 < −7, 435 [qfmu @$ vtlq,zqo0Ao|bj’mu,j u|bj’8q;]a[ !D dD x > −1 0D x > 1 7D x > 14 ’D x > 0 9D 5 < x ສະຫງສ.ວວນ.ລິສຂະສິດ4 lD x < −9 -D x > 15 pD x < −5 fD x > 11 8D x < 5 2 4D x > 58 = 29 mD x < −14 oD x ≤ −6 8 4 [D x < 9 xD x ≥ 4 zD x ≤ 10 = 5 4 2  ‐2  ‐1  0  1 2 3 4 56 7 x    @D dD x ≥ 2 0D x ≤ 2 7D m c,jom5dM9eo;o9y’ 'D x c,oj m5dM9eo;o9y’ -D x ≥ 6 pD [+,u.9zqo fD [+,u.9zqo 8D x c,oj m5dM9eo;o9y’ #D lD x < − 16 -D x> 7 pD x < 42 fD x ≤ 55 8D x ≥ −19 23 6 7 $D dD x < − 10b 0D x> 4c 7D x ≤ − c ’D x> b a e 10b a *D dD x > 7 0D x < 8 7D x > −2 ’D x > 5 9D x < 3 256 

[qfmu @& dkocdh39fdPj ;da[vtlq,zqo0aho|bj’muj,u|bj’8q;]a[ @D x > 8 #D ]k;wfh0kpwxc]h;s^kpd;jk 400 sq;D $D 5 < x < 15F &D x > 34 F *D x < 34 F )D 40,5 < x < 43 _D 2 < AB < 6 [qfmu @* lq,zqomu,j u7kj le[6o !D x = −4 s^n x = 4 x = 3 s^n x = − 3 x = 3,5 s^n x = 3,5 2 2 @D x = 6 s^n x = −4 $D dD x = 3 F x=3 s^n x = − 7 3 0D x −1 = 4 F 7D x −1 = 5 [qfmu @( vtlq,zqomuj,u7jkle[6o !D dD − 8 < x < 8 S − 0,7 < x < 0,7 S − 7 < x < 7 ສະຫງສ.ວວນ.ລິສຂະສິດ 2 2 @D dD x < −18 s^n x > 18 S     x < −5,4 s^n x > 5,4; x < − 8 s^n x> 8 5 5 #D dD −7< x<9S 7D x < − 3 s^n x > 13 ; 9D − 5 ≤ x ≤ 1S lD   x ≤ −4 s^n x ≥ 6; 2 2 $D dD 7 ≤ x ≤ 9 ,u.9zqoc,joG − 9; − 8; − 7; 7; 8; 9. 0D .9zqoc,oj G 0 ; 4; 5. &D dD − 5 < x < 5 ; − 14 < x < 14 F 0D  x < − 2 s^n x > 2 ; x < −4 s^n x > 4 2 2 3 3 3 3 [qfmu @) I6[lujc90hk’0t|ko !D * I6[F @D !W I6[ 0D $D dD A 5cm  B A 5cm  B 70   4cm  70   4cm  4cm  D  D  5cm  C  257 

7D A = C = 70 ; B = D = 110 0=h-Uc9’G B = O = E *D C  F  fa’j oAo B = E B  E  O  A  D  (D dD x = 3; y = 4 0D x = 7; y = 18 7D x = 13; y = 5 ’D x = 10; y = 16 [qfmu @_ I6[lucj 9lkd !D a. x = 2; b. x = 2; y = 5; c. x = 45; y = 15; d. x = 1; y = 5 @D dD AB = 7 cm c]t BC = 5cm D A B  ;ymulhk’G 7cm  5cm  { lhk’mvj o-nj AB = 7 cm ສະຫງສ.ວວນ.ລິສຂະສິດ C  { lhk’g7yj’glAo-nj [Bx) ⊥ ABF;k’g,af x  C 16j [Bx) 3fp;kj BC = 5cm D y  D E { lhk’g7y’j glAo-nj [Cy) ⊥ BC 16jmujg,af C D { ;k’g,af D 16j [Cy) 3fp;kj CD = 7 cm { 0uf8+ D sk A 9twfhI6[lucj 9lkd ABCD mu8j hv’dkolhk’D [qfmu #W I6[fvd9ao c]t I6[9t85]af d @D { ;k’mjvo-nj AI = 3cm B  { 16gj ,af I F lhk’glAo-nj d ⊥ AI { 0ufmjvodq’j muj,ug,af.9dk’16j A 5cm  fh;p]aflt|u 5cm S mvj odqj’8af d A 3cm  I 16jg,af B c]t D 8k,]efa[D 5cm  { 0uflv’mvj odqj’mu,j ug,af.9dk’16j B c]t D fh;p]aflt|u 5cm S D 258 

lv’mvj odqj’8afdao16gj ,af E D { 0uf8+ E sk B c]t D 9twfhI6[fvd9aomu8j hv’dkoD (D dD x = 4 0D x = 10 7D x = 15 ’D x = 7 9D x = 25 3 [qfmu #! I6[7k’\\6 @D dD MN = 6+9 = 7,5cm 0D MN = 10 cm 2 #D 100 c]t 135 $D dD AB = 8,5 0D EN = 4,5 7D MN = 7x+2y ’D B = 100 &D x = 7 S A = 50 c]t B = 130 [qfmu #@ I6[lk,c9 !D Xd? wfFh grkt;kj 5 + 6 >10 X0? [+ grkt;kj 5 + 6 =11 X7? [+F grkt;kj 5 + 6 < 12 X’? wfh grkt;jk 7 + 7 > 7 ສະຫງສ.ວວນ.ລິສຂະສິດ &D dD 4hk;kj ];’pk;0v’lv’0hk’0v’I6[lk,c9c,jo 15 c]t 20.  ];’pk;0v’0hk’mulk, 9t8hv’16j]ts;jk’ & sk #&D 0D x ,u7jk16]j ts;jk’ @ sk !@D A  7D x 8hv’s^kpd;kj @D B  *D la’gdfI6[ gIqk,uG D  • AB + BC > AC • CD + DA > AC faj’oAo AB + BC + CD + DA > 2AC C  [qfmu ## glAomujle7ao.oI6[lk,c9 @D S   0=h-Uc9’G I6[lucj 9 RICH ,u I = C = H = R = 90 I  C  fa’j oAo RICH c,joI6[lujc9lkdD R   H  T  (1)  259 

X  0=h-Uc9’G g-ajofP;daoda[I6[ X!?F c8jI6[lucj 9lkd O  R  WORD ,u WO = OR = RD = DW fa’j oAo WORD c,oj I6[9t85]afD W  D  Y  I6[lk,c9 AMC c]t BMD (2)  B  ,ug,af4j;’ |adfP;dao X G c]t G' g8a’dao? !@D A  C  G  M  G'   D  [qfmu #$ ];’Iv[ c]t goNvmuj0v’I6[lujc9lkdF I6[9t85]afສະຫງສ.ວວນ.ລິສຂະສິດ c]t I6[fvd9ao #D • Amk' = 375 m2 • Al;j o =1125m2 XgoNvmumj ujpa’gs^nv9kddkogIafmk’? $D dD 200 m2 0D 4 4a’ &D ];’d;hk’gmqkj 5,5cm. *D A(1) = 45; A(2) = 78 m2 (D • Amk' = 173,5 m2 • Al;o = 906,5m2 XgoNvmujmujpa’gs^nv9kddkogIafmk’?D [qfmu #& ];’Iv[ c]t goNvmuj0v’I6[lucj 90k’0|koF I6[lk,c9 c]t I6[7k’\\6 #D dD • APQRS = 240 • APSR = 120 • AOSR = 60 • APSO = 60 0D • AABC = 8×5 = 20 • ABCE = 8×5 = 20 2 2 260 

&D AGROS = 972 [qfmu #* ,5,.o c]t ,5,ovd0v’I6[lk,c9 #D B = C = 132 = 66 $D 90 &D 55 2 * dD A = 30 ; B = 60 c]t C = 90 X ABC c,oj I6[lk,c9lkd? 0D A = 45 ; B = 60 ; C = 75 7D A = 50 ; B = 60 ; C = 70 (D 62 c]t 28 )D CAD = 62 c]t CDA = 62 [qfmu #( ,5,.o0v’I6[lujc9l;f @D 36 ; 72 ; 108 ; 144 #D 105 ; 75 ; 105 ; 75 $D RSO = 100 ສະຫງສ.ວວນ.ລິສຂະສິດ *D 40 ; 60 ; 120 ; 140 (D dD HEF = 110 0D EHF = 32 7D x = 35 )D I6[ X!?G x = 34,5 ; y = 16 S I6[ X@?G x = 3; y = 5 I6[ X#? x = 13; y = 78S I6[ X$? x = 110 S I6[ X&? x = 143; y = 118 _D XZY = 90 !WD ADX = 19 c]t DBX = 101 D !!D ABC = 100 c]t ECD = 20 !@D a) x = a + b + c [qfmu #) ;q’,qo c]t czo,qo $D A 27,14 m2 &D dD 9900 m 0D 10000 Iv[D *D A = 9,12 cm2 261 

[qfmu #_ |hkrP’8q;xtlko !D (1; 2), (2; 4), (3;6), (4;8), (5;10), (6;12), (7;14), (8,16). @D (1;12), (2;8), (3;7), (4;10), (5;15), (6;17), (7;6), (8,8), (9,10), (10,15). #D A(3;8), B(6; 4), C(−3;8), D(−8; 2), E((−5; −6), F(−9; −8), G(5; −5), H(10; −9). *D P(−5;1), Q(−2; −2), R(2; −6),S(2;12), M(−3;7), N(−15; −5), T(−10;0). (D D(2; −1). )D D(−2; −3). _D (2a;a), (2a, −a) s^n (−2a;a), (−2a, −a). !@D 0D (0; 0), (1; 2), (3; 6), (4; 8), (5;10), (6;12), (6 1 ;13), (7 1 ;15), (8;16). 2 2 !#D 0D (−30; −2), (−20; −4), (−10;14),(0;32), (10;50), (20;68), (30;86). [qfmu $W dkogxaovaf8kl;j orq;raodq’ !D a). y gxaovaf8kl;j odq’da[ x D b). y [+gxaovaf8kl;j odq’da[ x D c). y gxaovaf8klj;odq’da[ x D d). y [+gxaovaf8kl;j odq’da[ x D #D k=4 $D y = 17 . &D s = 300 . ສະຫງສ.ວວນ.ລິສຂະສິດ 2 7 )D dD g;]k 16 : 30 z6hmu0j u]j qf4u[wxwfh @& dy3]c,afD 0D g;]k 16 : 30 z6hmu0j u]j qf9adwxwfh #W dy3]c,afD 7D z6hmu0j u]j qf9adIvf[hkog;]k 17 : 00 3,’D ’D z6hmuj0u]j qf4u[Ivf[hkog;]k 18: 00 3,’D 9D z6hmu0j u]j qf9adwxmaoz6hmuj0u]j qf4u[g;]k16 : 00 3,’ c]t sjk’9kd3I’IPo 20km [qfmu $! dkogxaovaf8klj;orq;raoxUo !D dD a). y gxaovaf8klj;orq;raoxUoda[ xD y = 12 . x b). y [+gxaovaf8klj;orq;raoxUoda[ x D 0D a). y gxaovaf8klj;orq;raoxUoda[ x c]h; x D x = 12 D y c). x gxaovaf8klj;orq;raoxUoda[ yD x = − 4 y 7D d=]toumq;j wxF 4hk y gxaovaf8klj;orq;raoxUoda[ x c]h; x d=gxaovaf8kl;j o rq;raoxUoda[ y D 262 

’D 4hk y gxaovaf8kl;j orq;raoxUoda[ x c]h;gIqklk,kfg;Qkwfh;jk y gxaovaf8k lj;orq;dq’da[ 1 D x #D dD y = 24 0D 1 D 7D 9ts^5f]q’ 16.7 %. $D 6 vkmyfD x 2 &D 12km / h. [qfmu $@ g]dl;j oIhvp #D !?D 19 @?D 7 #?D 1 $?D 1 20 50 20 100 $D dD $F)D 0D @&:D 7D ##F##D &D 5000 du[D *D && 7qoD (D 90%. )D 96 km. _D 3 d;fD !WD (#F&( : !!D *$WWWWdu[D [qfmu $# ,kf8klj;o ສະຫງສ.ວວນ.ລິສຂະສິດ !D 4800 m. @D dD 37,5cm 0D 3300 km. #D dD 9cm 0D 15cm 7D ];’pk; = 10,8cm F ];’d;hk’ = 6cm ’D ];’pk; = 7,5cm F ];’d;hk’ = 6cm 9D 0hk’’pk; = 9,6cm F rNopk; = 6cm D $D 1 D *D dD 5cm 0D 1. 250 2500 [qfmu $$ dkolkp8k,];’mu.j sh,k @D dD O gxaog,afg7yj’dk’0v’mjvo-nj [AB] , A' c]t B' c,jog’qk0v’ A c]t B .lgj lAo-nj (d ) 8k,];’fP;daoD fa’j oAo O 9b’j c,jog,afg7y’j dk’0v’mvj o-nj [A'B'] 0D I6[lucj 9 AB’BA’ gxaoI6[lujc90hk’0t|koD &D I gxaog,afg7y’j dk’0v’0hk’ [AB] , J c,oj g,afg7y’j dk’0v’ [AC] D faj’oAoglAo-nj (IJ) 9b’j 0t|koda[glAo-nj (BC) F glAo-nj (AM) 8afglAo-nj (IJ) 16j K D g,af M 1j6glAo-nj (BC) D faj’oAo K 9b’j gxaog,afg7y’j dk’0v’mjvo-nj [AM] D 263 

[qfmu $& glAo-njzkj og,afg7y’j dk’0v’lv’0hk’0v’I6[lk,c9 !D dD I c,oj g,afg7yj’dk’0v’0hk’ [AB] , J c,jog,afg7y’j dk’0v’0hk’ [AC] S faj’oAo glAo-nj (IJ) c]t glAo-nj (BC) 9bj’0t|kodaoD 0D IJ = 7 2 @D 0D I6[lujc9 ABEC gxaoI6[lucj 90hk’0t|koD 7D BE = AC = 2cm &D O'C' = 2; CD = 2; OC = 4; C'D' = 4 [qfmu $* s^adgdo8kc]af !D dD zyfD 0D zyfD 7D 4ndD $D dD x = 9cm; y = 16 cm; 0D x = 15 cm ; y = 24 cm 3 2 5 &D FE = 1 (BD+DC) = 5 cm ; EC = 1 AC = 6 cm; CI = 4cm 2 2 _D   dD AB = 3,75cm S AE = 3, 24cm 0D AB = 3,84cm S AE = 75 cm   ສະຫງສ.ວວນ.ລິສຂະສິດ32 !@D AB = 3000m = 3km !#D dD RM = 25 0D AT = 14 ; RM = 70 4 3 9 !(D MN = 10 cm; AP = MN = 10 cm ; NP = AM = 2cm 3 3 [qfmu $( I6[lk,c97hkp7ndao  @D gIqk,u AB = 4 = 1 ; AC = 5 = 1 AD 8 2 AE 10 2 gsao;kj AB = AC = 1 ltcf’;kj (DE) //(BC) F faj’oAolv’I6[lk,c9 ABC AD AE 2 c]t ADE 9b’j 7hkp7ndaoD #D SABC 1 × 40 × AC 4800 4 AC SA'B'C' 2 7500 5 A'C' = 1 ⇔ = 2 × 50 × A'C' 264 

⇔ 4 = AC B’ 5 A'C' 50cm B C A’ fhko|bj’ AB = 40 = 4 A'B' 50 5 gsao;jk AB = AC = 4 40cm A'B' A'C' 5 fa’j oAolv’I6[lk,c9 ABC c]t A C’ A'B'C' 9bj’7hkp7ndaoD $D dD I6[lk,c9 ODE, (AB) //(DE) OA = OB = AB D OD OE DE AB E { I6[lk,c9 OFE, (BC) //(EF) C F OC = OB = BC O OF OE EF ສະຫງສ.ວວນ.ລິສຂະສິດ faj’oAo OA = OC OD OF 0D OA = OC ⇔ OA = OD faj’oAo (AC) //(DF) OD OF OC OF 7D AB = BC = AC fa’j oAolv’I6[lk,c9 ABC c]t DEF 9bj’7hkp7ndaoD DE EF DF [qfmu $) d=]tou7hkp7n0v’I6[lk,c9 !D I6[lk,c9 A'B'C' c]t ABC 7hkp7ndaoF AB = 225000 mm = 225 m. @D I6[lk,c9 OKB c]t OHA 7hkp7ndaoF BK = 2AH c]t OK = 2×OH [qfmu $_ dkogda[de0=h,6o c]t dkoltg\\u0=h,6ofh;p8k8t]k’ !D 0D # 7qoD 7D * 7qoD ’D @( 7qoD #D dD wm F @** F @!F#$) :D 0D !!WF )F)@):D 7D ##F !WF&(*:F @&F *F*)$:F &@F !WF$:D D $D dD 7kj x5pc,joG 43315804 du[D { 7jk1k0hkc,’w,hc,joG 9281958 du[D { 7jkcI’’koc,oj G 58235692 du[D { 7jkco;raoc,joG 11825902 du[D   { 7jkoE-qo]txtmkoG 14782377 du[D 265 

&D 0D -AoIPo x ! ,u9eo;oshv’IPos^kpmujl5f c]t ,u9eo;ooadIPo $) *(* 7qoD 7D -AoIPo x & ,u9eo;oshv’IPo|hvpmujl5fF ,u )$# shv’ c]t |hvpd;kj -AoIPo mu,j u9eo;ooadIPos^kpl5f @)_ shv’D ’D { -AoIPo x ! [ao95oadIPo3fpltg]pj shv’]t $# 7qoD { -AoIPo x @ [ao95oadIPo3fpltg]pj shv’]t $& 7qoD { -AoIPo x # [ao95oadIPo3fpltg]jpshv’]t $# 7qoD { -AoIPo x $ [ao95oadIPo3fpltg]jpshv’]t $& 7qoD { -AoIPo x & [ao95oadIPo3fpltg]jpshv’]t $# 7qoD *D 0D !$ 7qoD 7D @! 7qoD [qfmu &W dkoltg\\u0=h,6ofh;pI6[c8h, ສະຫງສ.ວວນ.ລິສຂະສິດ !D 0D zqo[;dmuxj tdqfvvds^kp7A’d;kj |6cj ,jo ( c]t ,u !& 7A’D 7D 9eo;o & c]t s^kpd;jk # 7A’D @D 7D !# 7A’D ’D c8h,muxj kdqfvvds^kpd;kj |6j c,oj & c]t ,u * 7A’ c]t s^kp d;kj c8h,mujxkdqfvvd|hvpd;jk\\j6 $ 7A’D #D 7D .o-k;|5j, @&W 7qo ,u _@ 7qomujl6’ 170cm 0Nowx c]t ,u !## 7qomuj 8ej dkj ; 170cm ]q’,kg4y’ 160cm D $D ’D #_W! 7qoF py’ !))! 7qoD 9D 32,99% F 20,66% F 23, 40% F 22,94%. lD 14, 41% D 10, 61% D 11,36% D 11,84% D [qfmu &! dkoltg\\u0=h,6ofh;pI6[c8h, X8+? !D 7D 8QolqdIPo @WW_{@W!W 0v’3I’IPof’ja dkj ;,uoadIPoma’|qf !#(_ 7qo gxaopy’ &$$ 7qoD $D 7D oadIPoshv’oUwfh7tcoo * s^kpd;kj \\6j ,u !@ 7qo c]t d;,gvqk 26,9% 0v’oadIPoma’\\qfD   266