Tuyn chn thi hc sinh gii ton 6 S IThi gian lm bi 120 phtCu 1 : (2 im) Cho biu thc 1 2 21 22 32 3+ + + +a a aa aAa, Rt gn biu thcb, Chng minh rng nu a l s nguyn th gi tr ca biu thc tm c ca cu a, l mt phn s ti gin.Cu 2: (1 im) Tm tt c cc s t nhin c 3 ch sabcsao cho12 n abcv 2) 2 ( n cbaCu 3: (2 im)a. Tm n n2 + 2006 l mt s chnh phngb. Cho n l s nguyn t ln hn 3. Hi n2 + 2006 l s nguyn t hay l hp s.Cu 4: (2 im) a. Cho a, b, n N* Hy so snh n bn a++v bab. ChoA = 1 101 101211;B = 1 101 101110++ . So snh A v B.Cu 5: (2 im) Cho 10 s t nhin bt k : a1, a2, ....., a10. Chng minh rng th no cng c mt shoc tng mt s cc s lin tip nhau trong dy trn chia ht cho 10.Cu 6: (1 im) Cho 2006 ng thng trong bt k 2 ngthng no cng ct nhau. Khng c 3 ng thng no ng qui. Tnh s giao im ca chng.P N S ICu 1: Ta c: 1 2 21 22 32 3+ + + +a a aa aA= 11) 1 )( 1 () 1 )( 1 (2222+ + ++ + + + +a aa aa a aa a aiu kin ng a -1 ( 0,25 im).Rt gn ng cho0,75 im.b.Gi d l c chung ln nht caa2 + a 1 v a2+a +1 ( 0,25 im).V a2 + a 1 =a(a+1) 1 l s l nn d l s lMt khc, 2 =[ a2+a +1 (a2 + a 1) ] dNn d = 1 tc l a2 + a + 1v a2 + a 1 nguyn t cng nhau.( 0, 5 im)Vy biu thc A l phn s ti gin. ( 0,25 im)Cu 2: abc =100a + 10 b + c = n2-1 (1)cba = 100c + 10 b + a= n2 4n + 4 (2) (0,25 im)T (1) v (2) 99(a-c) = 4 n 5 4n 5 99 (3) (0,25 im) 1 Tuyn chn thi hc sinh gii ton 6Mt khc:100 [ n2-1 [999 101 [n2 [1000 11 [ n[ 31 39 [ 4n 5 [119 (4) ( 0, 25 im) T (3) v (4) 4n 5=99 n = 26Vy:abc= 675 ( 0 , 25 im)Cu 3: (2 im)a) Gi s n2 + 2006 l s chnh phng khi ta t n2 + 2006 = a2 ( a Z) a2 n2 = 2006 (a-n) (a+n) = 2006 (*) (0,25 im).+ Thy : Nu a,n khc tnh cht chn l th v tri ca (*) l s l nn khng tha mn (*)( 0,25 im).+ Nu a,n cng tnh chn hoc l th (a-n) 2 v (a+n)2 nn v tri chia ht cho 4 v v phi khng chia ht cho 4 nn khng tha mn (*)(0,25 im).Vy khng tn ti n n2 + 2006 l s chnh phng. (0,25 im).b) n l s nguyn t > 3 nnkhng chia ht cho 3. Vy n2 chia ht cho 3 d 1 do n2 + 2006 = 3m + 1 + 2006 = 3m+2007= 3( m+669) chia ht cho 3.Vy n2 + 2006 l hp s. ( 1 im).Bi 4: Mi cu ng cho 1 im Ta xt 3 trng hp 1 ba1 >ba1 ba a>b a+m > b+n. M n bn a++ c phn tha so vi 1 l n bb a+ba c phn tha so vi 1 l bb a, vn bb a+ < bb a nn n bn a++ < ba (0,25 im).TH3: ba x=0; y-5=12 => y=17 hoc 2x+1=3=> x=1; y-5=4=>y=9 (0,25)vy (x,y) = (0,17); (1,9) (0,25)b.(1) 3 Tuyn chn thi hc sinh gii ton 6Ta c 4n-5 = 2( 2n-1)-3(0,25) 4n-5 chia ht cho2n-1 => 3 chia ht cho2n-1 (0,25)=>* 2n-1=1 => n=1*2n-1=3=>n=2(0,25)vy n=1;2 (0,25) c. (1)Ta c 99=11.9B chia ht cho 99 => B chia ht cho 11v B chia ht cho 99(0,25)*B chia ht cho 9 => ( 6+2+4+2+7+x+y) chia ht cho 9 (x+y+3) chia ht cho 9=> x+y=6 hoc x+y =15 B chia ht cho 11=> (7+4+x+6-2-2-y) chia ht cho11=> (13+x-y)chia ht cho 11x-y=9 (loi) hoc y-x=2 (0,25)y-x=2 v x+y=6 => y=4; x=2 (0,25)y-x=2 v x+y=15 (loi) vy B=6224427(0,25)Cu2: a. Gi dl c ching ca 12n+1v 30n+2 ta c 5(12n+1)-2(30n+2)=1 chia ht cho d(0,5)vy d=1 nn 12n+1 v 30n+2 nguyn t cng nhau do 2 301 12++nnl phn s ti gin (0,5)b. Ta c 221 a = {0,1,2,3,4}.Ngha l a ={0,1,-1,2,-2,3,-3,4,-4}. Biu din trn trc s ccc s ny uln hn -5 v nh hn 5 do -5 x + 1 + x + 2 + x + 3 + . . . . . . .. . .. . . . + x + 100 =5750=> ( 1 + 2 + 3 + . .. + 100) + ( x + x + x . . . . . . . + x ) =5750 101 x 50+100 x= 5750 100 x + 5050=5750100 x = 5750 5050 100 x =700 x =7Cu2. a)eg cd ab abc + + 100 10000 deg=9999cd ab 99 ++( ) eg cd ab + + 11. b). 10 28 + 8 9.8ta c 10 28 + 8 8 (v c s tn cng l 008)nn 10 28 + 89.8 vy 10 28 + 8 72 Cu 3.Gi s giy mi lp thu c l x (Kg) th ( x-26) 11 v ( x-25)10. Do (x-15) BC(10;11) v 200 x 300=> x-15 = 220=> x = 235.S hc sinh lp 6A l:(235 26) : 11 + 1 = 20. hsS hc sinh lp 6B l:(235 25) : 10 + 1 = 22 hs.Cu 4.S th nht bng: 119: 76 = 2221 (s th hai) S th ba bng: 119: 32 = 2227 (s th hai)Tng ca 3 s bng 2227 21 22 + + (s th hai) = 2270(s th hai)S th hai l : 210 : 2270 = 66 ;s th nht l: 2221. 66 = 63 ; s th 3 l:2227.66 = 81Cu5: ng thng a chia mt phng ra hai na mt phng Xt 3 trng hpa). Nu c 4 im A, B, CD thuc cng mt na mt phng th a khng ct on thng no.b). Nu c 1 im ( Chng hn im A thuc na mt phng) ba im B, C, D thuc na mt phng i th ng thng a ct ba on thng AB, AC, AD 22 Tuyn chn thi hc sinh gii ton 6c). Nu c 2 im chng hn (A v B) thuc mt na mt phng hai im kia (C v D) thuc mi mt phng i th a ct bn on thng AC, AD, BC, BD HNG DN S VBi 1 (3): a) Ta c 222333 = (2.111)3.111 = 8111.(111111)2.111111(0,5)333222 = (3.111)2.111 = 9111.(111111)2 (0,5)Suy ra: 222333 > 333222b) s 2 8 1 y x36 ( 0x, y 9 , x, y N ) '+ + + +4 29 ) 2 8 1 (yy x(0,5){ 9 ; 7 ; 5 ; 3 ; 1 4 2 y y (x+y+2)9 => x+y = 7 hoc x+y = 16 => x = { 7 ; 9 ; 0 ; 2 ; 4 ; 6(0,25)Vy ta c cc s: 16812; 14832; 12852; 10872; 19872; 17892 (0,25)c) Ta c a > 28 => ( 2002 - 1960 )a => 42a (0,5) => a = 42(0,5)Bi 2 (2):a) Ta c 32S = 32 + 34 + ... + 32002 + 32004 (0,5)Suy ra: 8S = 32004 - 1 => S = 81 32004(0,5)b) S = (30 + 32 + 34 ) + 36(30 + 32 + 34 ) + ... + 31998(30 + 32 + 34 ) == (30 + 32 + 34 )( 1 + 36 + ... + 31998 ) = 91( 1 + 36 + ... + 31998 )(0,75) suy ra: S7 (0,25)Bi 3 (2):Gi s cn tm l: a Ta c a = 29q + 5 = 31p +28(0,5) 29(q - p) = 2p + 23V 2p + 23 l nn( q - p) l => q - p 1.(0,75)V a nh nht hay q - p = 1 => p = 3; => a = 121 (0,5)Vy s cn tm l 121 (0,25)Bi 4 (3): a)theogithitCnmtronggcAOB nntia OC nm gia hai tia OB v OA=> gc AOC + gc BOC = gc AOB=> gc AOC = gc AOB - gc BOC=> gc AOC = 1350 - 900 =450 23 Tuyn chn thi hc sinh gii ton 6b) v OD l tia i ca tia OC nn C, O, D thng hng. Do gc DOA + gc AOC = 1800 (hai gc k b)=> gc AOD = 1800 - gc AOC = 1800 - 450 => gc AOD = 1350gc BOD = 1800 - 900 = 900Vy gc AOD > gc BODP N S VI Bi 1: 1. Tm ch s tn cng ca cc s sau: ( 1 im ) tm ch s tn cng ca cc s ch cn xt ch s tn cng ca tng s :a) 571999 ta xt71999Ta c: 71999 = (74)499.73 = 2041499. 343 Suy ra ch s tn cng bng 3 ( 0,25 im )Vys 571999 c ch s tn cng l : 3b) 931999 ta xt 31999Ta c: 31999 = (34)499. 33 = 81499.27Suy ra ch s tn cng bng 7(0,25 im )2. Cho A = 9999931999 - 5555571997 . chng minh rng A chia ht cho 5 chng minh A chia ht cho 5 , ta xt ch s tn cng ca A bng vic xt ch s tn cng ca tng s hng.Theo cu 1b ta c: 9999931999 c ch s tn cng l 7Tng t cu 1a ta c: (74)499.7 =2041499.7 c ch s tn cng l 7( 0,25 im )Vy A c ch s tn cng l 0, do A chia ht cho 5. ( 0,25 im )3 (1 im )Theo bi ton cho a yOz = 180 aKhi ; tOy =21a t,Oy =21( 180 a) z x 26 Tuyn chn thi hc sinh gii ton 6=>tOt, = ) 180 (2121a a + = 900 O Cu 2; Gi s trong 20 im, khng c 3 im no thng hng. Khi , s ng thng v c l;19 . 20:2 = 190Trong a im, gi s khng c 3 im no thng hng.S ng thng v c l ; (a 1 ) a : 2 . Thc t, trong a im ny ta chi v c 1 ng thng. Vy ta c ;190 ( a- 1)a : 2 + 1 = 170=>a = 7P N S VIIIBi 1 : C 9 s c 1 ch s t 1 n 9 ( 0.25)C 90 s c 2 ch s t 10 n 99 (0.5)C 900 s c 3 ch s t 100 n 999 (0.5)Cc s c 4 ch s l t 1000 n 2006 c : 2006 - 1000 + 1 = 1007 s (0.5)S ch s ca s t nhin L l : 9 + 90.2 + 900.3 + 1007.4 = 6917 (ch s ) (1.25) Bi 2 : C 900 s c 3 ch s t 100 n 999 (0.25)Ta chia 900 s thnh 9 lp , mi lp c 100 s (0.25) c cng ch s hng trm .Lp th nht gm 100 s t 100 n 199 Lp th hai gm 100 s t 200 n 299 Lp th 9 gm 100 s t 900 n 999(05)Xt 9 lp th lp th 4 c 100 s u c ch s 4 hng trm .8 lp cn li hng trm khc 4 nn ch s 4 nu c th hng chc v hng n v (0.25) . Xt lp th nht th cc s c ch s 4 lm hng n vgm : 104, 114194 (c 10 s ) (05)cc s c 4 ch s lm hng chc l 140,141,142,..149 (c 10 s) (0.5)Nhng s 144 c mt trong c 2 trng hp vy lp th nht s lng s c ch s 4 l : 10 + 10 - 1 = 19 (s) (0.25)By lp cn li cng theo quy lut y . Vy s lng s c 3 ch s c ch s 4 l :100 + 19.8 = 252 s(0.5)Bi 3 : Ta dng cc s 1; 2; 3 . nh s cho cc phn u bng (0.25) .1 23 45 678 910 27 Tuyn chn thi hc sinh gii ton 628 17 19 36 28 17 19 36 28 17V cc s 4; 5; 6; 7 v 3; 4; 5; 6 nn s s 3 v s 7 bng nhau s 3 l 19 (0.5)100 - (17 + 19 + 36) = 28Vy s 1 l s 28 ( 0.25)100 - (17 + 19 + 36) = 28 . Vy s in th 5 l s 28 ( 0.25)s in s 6 cng l s 17 (0.25)Ta c : 2007 = 501.4 + 3Vy ta c 501 nhm 4 , d3 cui l th 2005; 2006; 2007 vi cc s 28; 17; 19 (0.5) a) Tng cc s trn bng l :100.501 + 28 +17 +19 = 50164(1)b) Tng cc ch s mi nhm l :2 + 8 +1 + 7 +1 +9 + 3 + 6 = 37(0.5)Tng cc ch s trn bng l : 37.501 + 2 + 8 + 1 + 7 +1 +9 = 18567 c) 19644 . vy s in th 1964 l s 36 .(0.5)..P N S IX:Bi 1 (1,5) a).5x = 125 5x = 53 => x= 3b) 32x = 81 => 32x = 34 => 2x = 4 => x = 2c). 52x-3 2.52 = 52.352x: 53 = 52.3 + 2.5252x: 53 = 52.552x = 52.5.53 52x = 56 => 2x = 6 => x=3Bi 2. V a l mt s t nhin vi mi a Z nn t a < 5 ta => a = {0,1,2,3,4}.Ngha l a ={0,1,-1,2,-2,3,-3,4,-4}. Biu din trn trc s ccc s ny uln hn -5 v nh hn 5 do -5 801(2)Ta c + +601601.+ 601601++801+801 +.+801801+= 127123 4413180206020+ + +(3)T (1) , (2), (3) Suy ra:801791781......431421411+ + + + + + >127Bi 2: V s trang ca mi quyn v loi 2 bng 32 s trang ca 1 quyn loi 1. Nn s trangca 3 quyn loi 2 bng s trang ca 2 quyn loi 1M s trang ca 4 quyn loi 3 bng 3 quyn loi 2.N s trang ca 2 quyn loi 1 bng s trang ca 4 quyn loi 3 Do s trang ca 8 quyn loi 1 bng : 4 .8 : 2 = 16 ( quyn loi 3)S trang ca 9 quyn loi 2 bng 9 .4 : 3 = 12 (qun loi 3)Vy 1980 chnh l s trang ca 16 + 12+ 5 = 33(quyn loi 3)Suy ra: S trang1 quyn v loi 3 l 1980 : 33 = 60 ( trang)S trang 1 quyn v loi 2 l8034 . 60 (trang)S trang 1 quyn v loi1 l; 12023 . 80 ( trang)Bi 3: T1; 2; ; nc n s hngSuy ra 1 +2 ++ n =2). 1 ( n n +M theo bi ra ta c 1 +2 +3+..+n=aaaSuy ra2). 1 ( n n + =aaa = a . 111 = a . 3.37 Suy ra: n (n+1) = 2.3.37.aV tch n(n+1) Chia ht cho s nguyn t 37 nn n hoc n+1 Chia ht cho 37V s 2). 1 ( n n +c 3 ch s Suy ra n+1 < 74 n = 37 hoc n+1 = 37+) Vi n= 37 th 703238 . 37( loi) 33 Tuyn chn thi hc sinh gii ton 6+) Vi n+1 = 37 th666237 . 36( tho mn)Vy n =36 v a=6 Ta c: 1+2+3+..+ 36 = 666Bi 4 : A, 1,5 imV mi tia vi 1 tia cn li to thnh 1 gc. Xt 1 tia, tia cng vi 5 tia cn li to thnh 5 gc. Lm nh vy vi 6 tia ta c 5.6 gc. Nhng mi gc c tnh 2 ln do c tt c l 1526 . 5 gcB, 1 im . T cu a suy ra tng qut. Vi n tia chung gc cn( 21 n)(gc).----------------------------------------------------------P N S XIVBi 1. a. 1.5.6 2.10.12 4.20.24 9.45.541.3.5 2.6.10 4.12.20 9.27.45+ + ++ + + = ( )( )1.5.6 1 2.2.2 4.4.4 9.9.91.5.621.3.5 1 2.2.2 4.4.4 9.9.9 1.3.5+ + + + + +.b.Bin i : ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 1 1 2 1 3 1 k k k k k k k k k k k k] + + + + + + ]p dng tnh : ( )( )( )( ) ( ) ( ) ( ) ( )3. 1.2 1.2.3 0.1.2.3. 2.3 2.3.4 1.2.3.3. 3.4 3.4.5 2.3.4....................................3. 1 1 2 1 1 n n n n n n n n + + + +Cng li ta c : ( ) ( )( ) ( ) 1 23. 1 23n n nS n n n S+ + + + .Bi 2. a.Tch nh sau : ( ) ( )deg 10000 100 9999 99 abc ab cd eg ab cd ab cd eg + + + + + +.Do 9999 11;99 11 M M( )9999 99 11 ab cd + MM :( )11 ab cd eg + + M (theo bi ra) nn :deg 11. abc Mb.Bin i :*A =( ) ( ) ( ) ( ) ( ) ( ) ( )2 3 4 3 4 59 60 3 592 2 2 2 2 2 ... 2 2 2 1 2 2 1 2 ... 2 1 2 + + + + + + + + + + + + + += ( )3 593 2 2 ... 2 3. + + + M*A =( ) ( ) ( )2 3 4 5 6 58 59 602 2 2 2 2 2 ... 2 2 2 + + + + + + + + + == ( ) ( ) ( )2 4 2 58 22. 1 2 2 2 . 1 2 2 ... 2 . 1 2 2 + + + + + + + + +=( )4 587 2 2 ... 2 7 + + + M. 34 Tuyn chn thi hc sinh gii ton 6*A =( ) ( ) ( )2 3 4 5 6 7 8 57 58 59 602 2 2 2 2 2 2 2 ... 2 2 2 2 + + + + + + + + + + + +== ( ) ( ) ( )2 3 5 2 3 57 2 32 1 2 2 2 2 1 2 2 2 ... 2 1 2 2 2 + + + + + + + + + + + +== ( )5 5715. 2 2 ... 2 15. + + + MBi 3. Ta c :( )21 1 1 1.1 1 n n n n n< p dng : 2 2 21 1 1 1 1 1 1 11 ; ;...; .2 2 3 2 3 1 n n n< < < 2 3 41 1 1 1...2 2 2 2n+ + + + < 11 1.n BC) AC + BC = AB AC = AB - BC = 4 cm.b. - Mi ng thng ct 100 ng thng cn li nn to ra 100 giao im.- C 101 ng thng nn c : 101.100 = 10100 giao dim.-Do mi giao im c tnh hai ln nn s giao im l :10100 : 2 = 5050 giao im.Lu :Hc sinh gii cch khc ng vn cho im ti a. Bi hnh khng v hnh khng chm im.--------------------------------------------------------------- P N S XVCu 1. (2).a, Ta c5S = 52 + 53 +54 ++520075S S = (52 + 53 +54 ++52007) (5 + 52 + 53 + + 52006)4S = 52007-5Vy S = 20075 54b, S = (5 + 54) + (52 + 55)+(53 + 56) +.. + (52003 +52006)Bin i cS = 126.(5 + 52 + 53 ++ 52003)V 126 M126S M126Cu 2. (3) Gi s phi tm l x.Theo bi ra ta c x + 2 chia ht cho 3, 4, 5, 6. x + 2 l bi chung ca 3, 4, 5, 6BCNN(3;4;5;6) = 60 . nen x + 2 = 60.nDo x = 60.n 2(n = 1;2;3..)Mt khc xM11 ln lt cho n = 1;2;3.Ta thy n = 7 th x = 418 M11 35CBACBA Tuyn chn thi hc sinh gii ton 6Vy s nh nht phi tm l 418.Cu 3. (1). Ta c 3 2 3 3 5 3( 1) 5 531 1 1 1n n nn n n n+ + + + A c gi tr nguyn 51 n nguyn.M 51 n nguyn 5 M(n-1) hay n-1 l c ca 5Do 5 = {t1;t 5Ta tm c n =2n =0n =6n = -4Cu 4 (2) A, Tm c cc (18); (24) ; (72) ng cho 0,5C (18;24;72)= {1; 2; 3; 6b, Ta c 72 B(18)72 B(24)BCNN (18;24;72) = 72.Cu 5. (2)O DBACx V A nm gia B v C nnBA +AC = BC BA +AC =4(1)Lp. lun B nm gia A v D.Theo gt OD < OA D nm gia O v A. (0,5)M OD + DA = OA 2 + DA =5 DA =3 cmTa c DB + BA = DADB +BA =3 (2) (0,25)(1) (2) AC DB = 1 (3)(0,25)theo ra : AC = 2BD thay v (3)Ta c 2BD BD = 1 BD = 1(0,25)AC = 2BD AC = 2 cm (0,25)-------------------------------------------------------- P N S XVICu 1: Lit k cc phn t ca 2 tp hpa.A = { 0, 1, 2, 3 B ={ - 2, -1, 0, 1, 2, 0,5 imA B = { 0, 1, 2, 0,5 im.b. C 20 tch c to thnh-2 -1 0 1 20 0 0 0 0 01 -2 -1 0 1 22 -4 -2 0 2 4 36 Tuyn chn thi hc sinh gii ton 63 -6 -3 0 3 6Nhng tch l c ca 6: +1;+ 2 + 3 + 6 0,5 imCu 2: a. B= (3 + 32 + 33+ 34) ++ (397+398+399+3100)= 3 (1 + 3 + 32+33)+.+ 397(1+3+32+33) 0,5 im = 40. (3 + 35 +39 ++397 ): 40 0,5 imb. Mi s c dngabc0,abc5.Viabc0- C 5 cch chn ch s hng nghn (v ch s hng nghn khng phi l s 0).- C 6 cch chn ch s hng trm.- C cch chn ch s hng chc.Vy 5 . 6 . 6 = 180 s.Viabc5 Cch chn tng t v cng c 180 s. Vy ta thit lp c 360 s c 4 ch s chia ht cho 5 t 6 ch s cho 0,5 im.Cu 3: 1/2 tui anh th hn 3/8 tui em l 7 nm. Vy tui anh hn 6/8 tui em l 14 nm0,5 im.M 5/8 tui anh ln hn 3/4 tui em l 2 nm, nn 1-5/8 = 3/8 tui anh = 14-2 = 12 nm.1 imVy tui anh l: 12:3/8 = 32 tui. 0,5 im3/4 tui em = 32 14 = 18 tui0,5 imTui em l: 18:3/4 = 24 tui 0,5 imCu 4: a, C 2 cch v tia OZ (c hnh v)Gc XOZ = 650 hoc 13501 imb, C th din t trung im M ca on thng AB bng 3 cch khc nhauM l trung im MA+MB=AB MA=MB=AB/2Ca on thng AB MA=MB------------------------------------------------------- P N S XVIICu 1: (2,5 im)Chia ra 3 loi s:*5ab . Trong s a c 9 cch chn ( t 0 n 9, tr s 5 ). S b cng vy.Nn cc s thuc loi ny c : 9.9 = 81 ( s ) (1 im)* 5 a b. Trong s a c 8 cch chn ( t 1 n 8, tr s 5 ).S b c 9 cch chn. Nn cc s thuc loi ny c: 9.8 = 72 ( s ) (0,5 im)* 5 ab. Trong s a c 8 cch chn , s b c 9 cch chn.Nn cc s thuc loi ny c : 8.9 = 72 ( s ) (0,5 im) V 3 dng 37 Tuyn chn thi hc sinh gii ton 6trn bao gm tt c cc dng s phI m v 3 dng l phn bit.Nn s lng cc s t nhin c 3 ch s trong c ng mt ch s 5 l:81 + 72 + 72 = 225 ( s )p s: 225 ( s )(0,5 im)Cu 2: ( 2,5 im)*Ccthas5trong100! ( khi phntchccthaschiaht cho5) l: 100 100245 25+ ( tha s) (1 im)* Cc tha s 2 c trong 100! l:100 100 100 100 100 1002 4 8 16 32 64 ]]]]+ + + + + ]]]] ]]]] = 50 + 25 + 12 + 6 + 3 + 1 = 97 ( s ) (1 im)Tch ca mi cp tha s 2 v 5 tn cng bng mt ch s 0. Do : 100! C tn cng bng 24 ch s 0.Vy 20 ch s tn cng ca 100! l20 ch s 0. Cu 3: (1,5 im)a/. V 6 ngy bo ph kn ao v c sau 1 ngy din tch bo tng ln gp i nn ph kn na ao th phI sau ngy th 5. (0,5 im)b/. Sau ngy th x s phn ao b che ph l:Vi x = 5, ta c: 1: 2 = 12(ao)Vi x = 4, ta c: 12 : 2 = 14(ao)Vi x = 3, ta c: 14 : 2 = 18(ao)Vi x = 2, ta c: 18 : 2 = 116(ao)Vi x = 1, ta c: 116 : 2 = 132(ao) (0,5 im)Vy sau ngy th nht th bo ph c: 132 (ao) (0,5 im)Cu 4: (1,5 im)V CLN( a, b)= 10, suy ra : a = 10x ;b = 10y(vi x < y v CLN(x, y)= 1 ) (0,5 im)Ta c : a.b = 10x . 10y = 100xy(1)Mt khc: a.b = CLN(a, b) . BCNN(a, b) a.b = 10 . 900 = 9000(2) (0,5 im) T (1) v (2), suy ra: xy = 90Ta c cc trng hp sau: 38 Tuyn chn thi hc sinh gii ton 6X 1 2 3 5 9y 90 45 30 18 10 T suy ra a v b c cc trng hp sau: a 10 20 30 50 90y 900 450 300 180 100Cu 5: (1 im)Ta c s :----------------------------------------------------------------- P N S XVIIICu 1: (2) Ta c: p4- q4 = (p4 1 ) (q4- 1); 240 = 8 .2.3.5Chng minh p4 1 240- Do p >5 nn p l s l (0,25)+ Mt khc: p4 1= (p-1) (p+1) (p2 +1)(0,25)--> (p-1 v (p+1) l hai s chn lin tip=> (p-1) (p+1)8(0,25)+ Do p l s l nn p2l s l ->p2 +12(0,25)- p > 5 nn p c dng: + p = 3k +1 --> p 1 = 3k + 1 1= 3k 3--> p4 13 + p = 3k + 2 -->p + 1= 3k + 2 + 1= 3k +33-->p4-13 (0,25)- Mt khc, p c th l dng:+ P =5k +1 --> p 1= 5k + 1- 1= 5k 5 --> p4 - 1 5+ p = 5 k+ 2 --> p2 + 1 = (5k +2)2+1= 25k2+ 20k +55 --> p4 - 15(0,25 )+ p = 5k +3 --> p2 +1 = 25k2 + 30k +10--> p4 15+ p = 5k +4 --> p + 1 = 5k +55 --> p4 15(0,25)Vy p4 18 . 2. 3 . 5 hay p4 1240Tng t ta cng c q4- 1240 (0,25)Vy: (p4 - 1) (q4 1)= p4 q4 240Cu 2: (2)a. 3 418723 4187 ) 3 4 ( 23 4193 8++ ++ +++n nnnnA A N th 1874n + 3 => 4n +3{ 187 ; 11 ; 17(0,5)+ 4n + 3 = 11-> n = 2 + 4n +3 = 187 --> n = 46+ 4n + 3 = 17 -> 4n = 14 -> khng c n N (0,5)Vy n = 2; 46b.A l ti gin khi 187 v 4n + 3 c UCLN bng 1-> n11k + 2 (k N)-> n17m + 12 (m N)(0,5) 39 Tuyn chn thi hc sinh gii ton 6c) n = 156 -> ;1977 An = 165 -> 3989 An = 167 -> 61139 A(0,5)Cu 3: (2)Do 4 = 12 . (- 4)= 22.(-1) n c cc trng hp sau:a. ' ' ' 1311 24 31 ) 2 (2yxyxyx(0,5)hoc' ' 1111 2yxyx(0,5)b. '' ' 2422 21 32 ) 2 (2 2yxyxyx (0,5) 40 Tuyn chn thi hc sinh gii ton 6hoc '' 2022 2yxyx (0,5)Cu 4: (3)a. M, B thuc 2 tia i nhau CB v CM-> C nm gia B v M.->BM = BC + CM = 8 (cm)(0,5)b. C nm gia B,M -> Tia AC nm gia tia AB, AM ->CAM = BAM - BAC = 200 (0,75)c. C xAy = x AC+CAy= 21 BAC + 21 CAM =21 ( BAC + CAM) = 21BAM = 21.80 = 400 (0,75)d. + Nu K tia CM -> C nm gia B v K1-> BK1 = BC + CK1 = 6 (cm)(0,5)+ Nu K tia CB -> K2 nm gia B v C-> BK2= BC = CK2=4 (cm)(0,5 )Cu 5: (1)Ta c )4111(324 . 12)4111(314 . 11 );....10171(3210 . 72);7141(327 . 42 ......; )1001991(32100 . 972 (0,5)B= )1001991.....1017171414111(32 + + + + B= 503310099.32)100111(32 (0,5)--------------------------------------------------------------P N S XX Cu 1a) 510* ; 61*16 chia ht cho 3 th:5 + 1 + 0 + * chia ht cho 3; t tm c * = 0; 3; 6; 9 (1)b) 261* chia ht cho 2 v chia 3 d 1 th: 41AMBxK Cy Tuyn chn thi hc sinh gii ton 6 * chn v 2 + 6 + 1 + * chia 3 d 1; t tm c * =4 (1)Cu 2S=1.2 + 2.3 + 3.4 + ... + 99.1003.S=(1.2 + 2.3 + 3.4 + ... + 99.100).3(0,5)=1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3=1.2.3 +2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)(0,5)=1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - ... - 98.99.100 + 99.100.101 S =99.100.101: 3 = 33. 100 . 101 = 333300(0,5)Cu 3Thi gian i t A n C ca Hng l:11 - 8 = 3 (gi)Thi gian i t B n C ca Dng l: 11 - 8 = 3 (gi)Qung ng AB l 30 km do c 1 gikhong cch ca Hng v Dng bt i 10 km. V vy lc 9 gi Hng cn cch Dng l 20 km, lc Ninh gp Dng nn Ninh cng cch Hng 20 km.n 9 gi 24 pht, Ninh gp Hng do tng vn tc ca Ninh v Hng l:20 : ) / ( 502460 . 206024h km Do vn tc ca Ninh bng 1/4 vn tc ca Hng nn vn tc ca Hng l:[50 : (1 + 4)] . 4 = 40 (km/h)T suy ra qung ng BC l:40 . 3 - 30 = 90 (km)p s:BC = 90 kmCu 4: (2)Trn on thng AB c cc im A; A1; A2; A3; ...; A2004 ; B do , tng s im trn AB l 2006 im suy ra c 2006 on thng ni t M n cc im .Mi on thng (v d MA) c th kt hp vi 2005 on thng cn li v cc on thng tng ng trn AB to thnh 2005 tam gic. Do 2006 on thng s to thnh2005 . 2006 = 4022030 tam gic (nhng lu l MA kt hp vi MA1 c 1 tam gic th MA1 cng kt hp vi MA c 1 tam gic v hai tam gic ny ch l 1)Do s tam gic thc c l: 4022030 : 2 = 2011015Cu 5: (1)Tch ca hai phn s l 158. Thm 4 n v vo phn s th nht th tch mi l 1556 suy ra tch mi hn tch c l 1556 - 158 = 1548 y chnh l 4 ln phn s th hai. Suy ra phn s th hai l 1548 : 4 = 1512= 54 .T suy ra phn s th nht l: 158 : 54 = 32----------------------------------------------------------- 420,51 1 0,50,5 Tuyn chn thi hc sinh gii ton 6P N S XXICu 1:5325101 . 53101 . 2553532525 (0.5)532510101 . 5310101 . 25535353252525 (0.5)Vy535353252525535325255325 (0.5)Cu 2:677300670300> m 67730067306730670300> (1) (0.5)Ta c : 673067371 v6773006773771 (2) (0.5)T (1) v (2) 6737677377>(0.5)Cu 4:Gi s i vn ngh c n ngi. Tng s tui i vn ngh tr ngi ch huy l m.Ta c: 1117+nm (1)v101 nm (2) (1)T (1) m = 11n 17(3)(2) m = 10n 10 (4) (1)T (3) v (4) 11n 17 = 10n 10 n =7 (1)p s: S ngi trong i vn ngh l: 7Cu 5:a.Tnh c yOn = 150 ; mOy = 750(1) Ch ra cch v v v ng. (0.5)b.Tnh c mOn = 900(0.5)------------------------------------------------------------------- PNSXXIICU I : 1) 1,5A = 2006 .... 3 2 163 . 373737 37 . 636363+ + + + = 2006 .... 3 2 1) 63 . 10101 .( 37 ) 37 . 10101 .( 63+ + + + = + + + +2006 .... 3 2 1) 10101 10101 .( 63 . 37 02) B = 237373735124242423.200651951755200641941744:53337331353123712191212.4161,`.|+ + ++ + + + + 43Omynx z Tuyn chn thi hc sinh gii ton 6 =1010101 . 5 . 471010101 . 3 . 41.200611911711 5200611911711 4:5313711911 35313711911 . 12.4147,`.|,`.|+ ,`.|+ + +,`.| +,`.| += 5 . 473 . 41).45. 4 .(4147 = 3(1,5)CU 2: 2-b=0 => 9+a9 => a = 0-B =5 => 14+a9 => a = 4CU III: 2 a)A =31 +32+33 + .....+ 32006 3A =32+33 +34+ .....+ 32007 3A A= 32007 -3 A = 23 32007(1)b) Ta c : 2. 23 32007+3 = 3x => 32007 -3 +3 = 3x => 32007 = 3x => x = 2007 (1)CU IV: 1A = 1 20051 200520062005++ < 2004 1 20052004 1 200520062005+ ++ += ) 1 2005 ( 2005) 1 2005 ( 200520052004++= 1 20051 200520052004++ = B VyA < B CU V : 2Gi x l s trang sch, x NNgy 1 c c l x52 trangS trang cn li l x- x52 = x53 trang Ngy 2 c c l 53.53x =x259 trangS trang cn li l x53-x259 =x256trang Ngy th 3 c c l : x256.80% +30 = 12524 x + 30Hay : x52+ x259+12524 x + 30 =x=> x =625 trang S 625 trang----------------------------------------------------------------- P N S XXIIIBi 1 (1,5):a. 308; 380; 830 (0,5)b. 380 830 (0,5)c. 803Bi 2 (2):a) (1) 44 Tuyn chn thi hc sinh gii ton 6A=50 chu so333...3123 x {50 chu so1 00..0- 1| ` . ,= { { {50 chu so 50 chu so 50 chu so33...300...0 -33...3(0,5) = {49 chu so49 chu so33 ... 33 00 ... 0033 ... 33 33 ...3266 ... 6712 3 (0,25). Vy A = {49 chu so49 chu so33 ...3266 ... 671 2 3 (0,25)b) (1 ) B= 3 + 32 + 33 + ... + 399 + 3100(1)3B= 32 + 33 + ... + 3100 + 3101(2) (0,25)Ly (2) tr (1) ta c: 2B = 3101 - 3 (0,25)Do : 2B + 3 = 3101(0,25)Theo bi 3B + 3 = 3n . Vy n = 101(0,25)Bi 3 (1,5):a) (0,75)C = 101 100 99 98 ... 3 2 1101 100 99 98 ... 3 2 1+ + + + + + + + + + +Ta c:*,101 + (100 + 99 + ... + 3 + 2 + 1)=101 + 101.100 : 2 = 101 + 5050 = 5151 (0,25)*, 101 - 100 + 99 - 98 + ... + 3 - + 1=50 cap(101 - 100) + (99 - 98) + ... + (3 - 2)+ 11 4 4 4 4 4 42 4 4 4 4 4 43= 50 + 1 = 51 (0,25)Vy C = 515110151(0,25)b) (0,75)B = 3737.43 4343.372 4 6 ... 100+ + + +Ta c: 3737.43 - 4343.37 = 34.43.101 - 43.101.37 = 0 (0,5)Vy B = 0 ( v 2 = 4 + 6 + ...+ 100 0)(0,25)Bi 4 ( 1,5):Ta c: 210 = 1024 (0,25)2100 = ( )10102= 102410 = ( )521024 (0,75)=(......76)5 = ....76 (0,5)Vy hai ch s tn cng ca 2100 l 76Bi 5 (1,5):Nu i t A n D bng con ng a1:a1 b1 c1; a1 b1 c2; a1 b1 c3; a1 b2 c1; a1 b2 c2; a1 b2 c3; (0,5)i t A n D bng con ng a2:a2 b1 c1; a2 b1 c2; a2 b1 c3; a2 b2 c1; a2 b2 c2; a2 b2 c3; (0,5)i t A n D bng con ng a3:a3 b1 c1; a3 b1 c2; a3 b1 c3; a3 b2 c1; a3 b2 c2; a3 b2 c3; (0,5) 45 Tuyn chn thi hc sinh gii ton 6Vy tp hp M:M = { a1 b1 c1; a1 b1 c2; a1 b1 c3; a1 b2 c1; a1 b2 c2; a1 b2 c3; a2 b1 c1; a2 b1 c2; a2 b1 c3; a2 b2 c1; a2 b2 c2; a2 b2 c3; a3 b1 c1; a3 b1 c2; a3 b1 c3; a3 b2 c1; a3 b2 c2; a3 b2 c3;}Bi 6 ( 2):Chn mt im. Qua im v tng im trong 99 im cn li, ta v c 99 ng thng (0,5)Lm nh vy vi 100 im ta c 99.100 ng thng(0,5)Nhng mi ng thng c tnh 2 ln, do tt c c 99.100 : 2 = 4950 ng thng(1)--------------------------------------------------------- P N S XXIVBi 1a. S = 270.450 270.550 270(450 550) 2700003000(2 18).990 902+ + +b. Ta c nu 1ab < th *( )a a nn Nb b n+< + 2006 20062007 20072006 1 2006 1 20052006 1 2006 2005 1A+ + + 8100 Nn 3200 > 2300 b) A = 101 : 1717101 : 40417210101 : 17171710101 : 1212121717404172171717121212 + + +174 2 121741721712 + + AVy A = 1710 hay A =B = 17103). Bi 3. s c 4 ch s*26* , 4ch s khc nhau m 4 ch s*26* chia ht cho c 4 s 2; 5;3;9.Ta cn tho mn : S m bo chia ht cho 2 nn s l s chn.S chia ht cho 5 nn s phi c ch s tn cng l s 0 hoc 5.S va chia ht cho 3 v9 .Nn s phi c tng cc ch s chia ht cho 9.Vy : Ch s tn cng ca s l 0 *260. Ch s u l s 1Do s cho l 12604 ) Bi 4. Tm s t nhin n. M 1! +2!+3! +...+n! l bnh phng ca mt s t nhin. Xt : n = 1 1! = 12 n = 2 1! +2! = 3 n=3 1! + 2! + 3! = 9 =32 n = 41!+ 2! +3! + 4! =33Vi n >4 thn! = 1.2.3.........n l mi s chn .Nn 1!+2!+......+n! =33 cng vi mt s chn bngsc ch s tn cng ca tng l ch s 3 .Nn n khng phi l s chnh phng. Vy chc hai gi tr n=1 hoc n=3 th 1! +2! + 3! +4! +.......+n!l s chnh phng.5 )Gii 47 Tuyn chn thi hc sinh gii ton 61 gi xe th nht i c21qung ng AB.1 gi xe th 2 i c 31 qung ng AB .1 gi c 2 xe i c 21+31= 65 qung ng AB. Sau 10 pht = 61gi: Xe th nht i c61. 21=121qung ng AB.Qung ng cn li l: 1 - 121 1211 (ca AB)Thi gian hai xe cng i qung ng cn li l:1211:65= 1011 gi = 1 gi 6 pht.Hai xe gp nhau lc 7 gi 10 pht + 1 gi 6 pht = 8 gi 16 pht .p n: 8 gi 16 pht.(0,25) 6) Hnh hc. (t v hnh) (2)V : xOy= 1200 ,AOy = 750, im A nm trong gc xOy nn tia OA nm gia hai tia Ox v Oy.Ta c : 0 0 0 xOA = xOy - AOy =120- 75= 45im B c th hai v tr : B v B. (0,75) +, Ti B th tia OB nm ngoi hai tia Ox, OA nn 0 0 0 BOx + xOA = 135+ 45= 180 . Do 0BOA = BOx +xOA =180. Nn 3 im A,O,B thng hng. (0,75) +, Cn ti B th : xOB' = 1350< 1800, 0 0 0AOB'=xOB' - xOA = 135- 45= 90 . Nn 3 im A,O, B khng thng hng.(0,5) ------------------------------------------------------------------------------- HNG DN GII S XXVICu 1: Ta c 3A = 1 + 1/3 + 1/32 + ... + 1/399vy: 3A-A = (1 + 1/3 + 1/32 + ... + 1/399)-(1/3 + 1/32 + ... + 1/3100) 2A= 1-1/3100 = (3100-1)/ 3100 suy raA= (3100-1) )/ 2.3100Cu 2: Ta c 12/21= 4/7, cc phn s 3/5, 4/5,6/11 ti gin nn tn ti cc s t nhin k, l, m sao cho a=3k, b=5k, b=4n, c=7n, c= 6m, d=11m. T cc ng thc 5k=4n, v 7k = 6m ta c 4n 5 v 7n6 m (4,5)=1; (7,6)=1 nn n 5, n6 mt khc (5,6) =1 do n30 cc s t nhin a, b, c, d nh nht v phi khc 0 , ta chn n nh nht bng 30 suy ra: k =24, m=35vy a=72, b=120, c=210, d=385.cu 3:Gi a v b l hai s bt k thuc dy 1, 2, 3, ..., 50. Gi s a>b. 48 Tuyn chn thi hc sinh gii ton 6a.Gi d thuc C(a,b) th a-bd ta s chng minh d 25 tht vy gi s d>25 th b>25 ta c a 50 m b>25 nn0< a-b < 25, khng th xy ra a-bd ; d=25 xy ra khi a=50; b=25 vy hai s c CLN t gi tr ln nht l 50 v 25b. BCNN(a,b) a.b 50.49=2450 vy hai s c BCNN t gi tr ln nht l 50 v 49cu 4: (Hc sinh t v hnh) Ta thy : 0AOB+BOC + AOD >180v nu tri li th gc AOD c im trong chung vi ba gc kia. t AOB= ta c: 0AOB+BOC + AOD + COD = 360 +3+5+6=3600 = 240. Vy: 0 0 0 0AOB = 24 ;BOC =72 ; COD = 120 ;DOA = 144---------------------------------------------------------- P N S XXVIICu 1: (3).a. V c s cho (1,5).- S hc sinh thch ng 2 mn bng v bi: 14 10 = 4 (hs)- S hc sinh thch ng hai mn bi v bng chuyn: 13 10 = 3 (hs).- S hc sinh thch ng hai mn bng v bng chuyn: 15 10 = 5 (hs)- S hc sinh ch thch bng : 20 (4 + 10 + 5) = 1 (hs)- S hc sinh ch thch bi: 17 (4 + 10 + 3) = 0 (hs).- S hc sinh ch thch bng chuyn: 36 (5 + 10 + 3) = 18 (hs).Vy: S hc sinh ca lp l: 1 + 0 + 18 + 4 + 10 + 5 + 3 + 12 + = 53 (hs).b. (1,5 )A = 1 2 3 4 5 6 7 8 9 10 11 12 58 59 60.* T 1 n 9 c : 9 ch s T 10 n 60 c: 51 . 2 = 102 ch s.Vy: S A c 9 + 102 = 111 ch s.(0,5)* Nu xa 100 ch s trong s A th s A cn 11 ch s. Trong s A c 6 ch s 0 nhng c 5 ch s 0 ng trc cc ch s 51 52 53 . 58 59 60. Trong s nh nht c 5 ch s 0 ng trc s nh nht l s c 6 ch s. S nh nht l 00000123450 = 123450 (0,5).* Trong s A c 6 ch s 9. Nu s ln nht c 6 ch s 9 ng lin nhau th s l: 99999960 S ny ch c 8 ch skhng tha mn. S ln nht ch c 5 ch s 9 lin nhau s c dng 99999. Cc ch s cn li 78 59 60.Vy s ln nht: 99999785860.Cu 2: (2,5).a.(1,5). A = 5 + 52 + + 596 5A =52 + 53 + + 596 + 597 49 Tuyn chn thi hc sinh gii ton 6 5A A = 597 - 5A = 975 - 54Tac: 597 c ch s tn cng l 5 597 5 c ch s tn cng l 0.Vy: Ch s tn cng ca A l 0.b. (1).C: 6n + 3 = 2(3n + 6) 96n + 3chia ht 3n + 6 2(3n + 6) 9 chia ht 3n + 69 chia ht 3n + 63n + 6 = t 1 ; t3 ;t 93n + 6 - 9 - 3 - 1 1 3 9n - 5 - 3 - 7/3 - 5/3 - 1 1Vy; Vi n = 1 th 6n + 3 chia ht cho 3n + 6.Cu 3: (2,5).a. (1).Gi s t nhin cn tm l a (a > 0, a N)Theo bi ra ta c:- a chia cho 3 d 2a 2 chia ht cho 3- a chia cho 4 d 3a 3 chia ht cho 4- a chia cho 5 d 4a 4 chia ht cho 5- a chia cho 10 d 9a 9 chia ht cho 10a = BCNN(3, 4, 5, 10) = 60.b.(1,5).11n + 2 + 122n + 1 = 121 . 11n + 12 . 144n=(133 12) . 11n + 12 . 144n = 133 . 11n + (144n 11n) . 12Tac: 133 . 11n chia ht 133;144n 11n chia ht (144 11) 144n 11n chia ht 133 11n + 1 + 122n + 1Cu 4: (2).S ng thng v c qua n im: ( ) 11052n n n .(n 1) = 210 = 2 . 5 . 3 . 7 = 10 . 14n. (n 1) = 6 . 35 = 15 . 14.V n v n 1 l 2 s t nhin lin tip nn: n = 14Vy n = 14.-----------------------------------------------------P N S XXVIIIBi 1:(2,25 im)a) x=7 1 225 5 25 ;b) x=5 4 45 44 8911 9 99 99+ ;c) x = 32Bi 2:(2,25 im) Tnh tng sau bng cch hp l nht: 50 Tuyn chn thi hc sinh gii ton 6a) A = (11 + 20) + (12 + 19) + (13 + 18) + (14 + 17) + (15+ 16) =31 + 31 + 31 +31+ 31 = 31.5= 155b) B = (11+25)+(13+23)+(15 + 21)+(17 +19) = 36.4 = 144.c) C = (12 +26)+(14+24)+(16 +22)+(18 +20) = 38.4 = 152.Bi 3:(2,25 im) Tnh:a) A= 1 1 1 1 1 1 1 1 1 1 5...11 16 16 21 21 26 61 66 11 66 66 + + + + b) B= 1 1 1 1 1 1 1 1 1 1 1 1 61 12 2 3 3 4 4 5 5 6 6 7 7 7 + + + + + c) C = 1 1 1 1 1 1 1 1 20061 ... ... 12 2 3 1989 1990 2006 2007 2007 2007 + + + + + Bi 4:(1 im)Ta c:10A = 20022002 200210 10 9 = 1 +10 1 10 1++ +(1)Tng t: 10B = 20032003 200310 10 9 = 1 +10 1 10 1++ +(2)T (1) v (2) ta thy : 2002 20039 910 1 10 1>+ + 10A > 10BA > B Bi 5:(2,25 im)a) Trn tia BA ta c BK = 2 cm. BA = 7cm nn BK< BA do im K nm gia A v B. Suy ra AK + KB = ABhay AK + 2 = 7 AK = 5 cm. Trn tia AB c im I v K m AI < AK (v 4 n+2 ( 18) = { 18 ; 9 ; 6 ; 3 ; 2 ; 1 (0,25 im)+, n + 2= 1 n= - 1 (loi)+,n + 2= 2 n= 0 +, n + 2= 3 n= 1 +, n + 2= 6 n= 4 +, n + 2= 9 n= 7 +,n + 2= 18 n= 16Vy n { 16 ; 7 ; 4 ; 1 ; 0 th B N(0,25im )c. (1 im)Ta c 55 =5.11 m (5 ;1) = 1 (0,25 im)Do C = y x199555 '115CC( )( ) 12 (0.25 im)(1) => y = 0 hoc y = 5+, y= 0 : (2)=> x+ 9+5 ( 1+9 +0)11 => x = 7(0,25 im)+, y =5 : (2)= > x+9 +5 (1+9+5 ) 11 => x = 1(0,25 im)Ba 2 (2 im)a( 1im) M = 140010...26010140105610+ + + + = 28 . 255...13 . 10510 . 757 . 45+ + + +(0,25 im)=,`.| + + + + 281251...131101101717141.35( 0, 25 im)= 145286.3528141.35 ,`.| ( 0,5 im)b. (1 im) S = 153153153153153143133123113103+ + + + > + + + +=> S > 11515 (1) ( 0,5im) S=103103103103103143133123113103+ + + + < + + + + => S < 210201015 1 < S < 2Bi 3: Gigi go np l a (ng/kg) ; khi lng go np mua l b (kg)(0,25 im)Suy ra gi go t l a .1080; khi lng go t mua l b .100120 ( 0,25 im)S tin ngi th nht phi tr l a.b (ng)(0,25 im)S ting ngi thhai phi tr l 10096. .100120. .10080 b a a.b (0.75im)Vy ngi th hai tr t tin hn ngi th nht . T l % t hn l:% 4 . : . .10096. ,`.| b a b a b a (0,5 im)BI 4 V hnh chnh xc(0,5 im) 52 Tuyn chn thi hc sinh gii ton 6a.Bn im A,B, M, N thng hng v chng cng nm trn ng thng MN (0,5 im)b. (1 im)BM = AB AM = 2 (cm) (0,25im)M,N tia AB m BM > BN ( 2 > 1) => N nm gia B v M.( 0,25 im)MN = BM BN = 1 cm = BN.=> N l ng trung im ca BM .(0,5 im).c. ng trn tm N i qua B nn CN = NB = 1 cm (0,25 im) ng trn tm A i qua N nnAC = AN = AM + MN = 4 cm(0.25 im)Chu vi CAN = AC + CN = NA = 4 + 4+1= 9 (cm) (0,5 im)-------------------------------------------------------------------- 53