1. Gio n : Bi dng hc sinh gii lp7 1 Ngy son : 16/1/2012 Bui 1 kho st Cu 1: a, cho A = 4 + 22 + 23 + 24 + + 220 Hi A c chia ht cho 128 khng? b, Tnh gi tr biu thc 104.2 65.213.2 10 1212 + 49 1010 2.3 5.311.3 Bi 2 : a, Cho A = 3 + 32 + 33 + + 32009 Tm s t nhin n bit rng 2A + 3 = 3n b, Tm s t nhin c ba ch s chia ht cho 5 v 9 bit rng ch s hng chc bng trung bnh cng ca hai ch s kia Bi 3 : Cho p v p + 4 l cc s nguyn t( p > 3) . Chng minh rng p + 8 l hp s Bi 4 : Tm hai s t nhin bit tng ca chng bng 84 , CLN ca chng bng 6. Bi 5: Gi A v B l hai im trn tia Ox sao cho OA = 4 cm ; OB = 6 cm . Trn tia BA ly im C sao cho BC = 3 cm . So snh AB vi AC Hng dn chm Bi Hng dn chm im 1 a, 2A A = 221 27 A 128 b, = 104.2 78.2 10 12 + 16.3 16.3 9 10 = 3 + 3 = 6 0.5 0.5 0.5 0.5 2 a, Tm c n = 2010 b, Gi s phi tm l abc theo bi ra ta c a + b + c 9 v 1 0.5

2. Gio n : Bi dng hc sinh gii lp7 2 2b = a + c nn 3b 9 b 3 vy b 9;6;3;0 abc 5 c 5;0 Xt s abo ta c s 630 Xt s 5ab ta c s 135 ; 765 0.5 3 P c dng 3k + 1; 3k + 2 kN Dng p = 3k + 2 th p + 4 l hp s tri vi bi p = 3k + 1 p + 8 = 3k + 9 3 p + 8 l hp s 0.5 0.5 0.5 0.5 4 Gi 2 s phi tm l a v b ( ab) ta c (a,b) = 1 nn a = 6a/ b= 6b/ trong (a/ ,b/ ) = 1 ( a,b,a/ ,b/ N) a/ + b/ = 14 a/ 1 3 5 b/ 13 11 9 a 6 18 30 b 78 66 54 0.5 0.5 1 5 Hai im A v B trn tia Ox m OA< OB (41) 0.5 0.5 0.5 0.5 xO BC A 3. Gio n : Bi dng hc sinh gii lp7 3 Ngy son : 23/1/ 2012 Bui 2: n tp s hu t s thc Phn 1: L thuyt 1. Cng , tr , nhn, chia s hu t Vi x= a m , y= b m ( a,b,m Z m 0 ) a b a b x y m m m a b a b x y m m m , ( 0) . . . . . : : . . a c x y y b d a c a c x y b d b d a c a d a d x y b d b c b c 2,Gi tri tuyt i ca mt s hu t +/ Vi x Q Ta c x neu x 0 x = -x neu x < 0 Nhan xet : Vi moi x Q, ta co: x 0, x = -xva x x +/ Vi x,y Q Ta c x y x y ( Du bng xy ra khi cng du ngha l x.y 0 ) x y x y ( // .. // ) Phn II: Bi tp vn dng Bi 1. Thc hin php tnh: 1 1 1 1 1 3 5 7 ... 49 ( ... ) 4.9 9.14 14.19 44.49 89 4. Gio n : Bi dng hc sinh gii lp7 4 1 1 1 1 1 3 5 7 ... 49 ( ... ) 4.9 9.14 14.19 44.49 89 = 1 1 1 1 1 1 1 1 1 2 (1 3 5 7 ... 49) ( ... ). 5 4 9 9 14 14 19 44 49 12 = 1 1 1 2 (12.50 25) 5.9.7.89 9 ( ). 5 4 49 89 5.4.7.7.89 28 Bi 2: Thc hin php tnh: 12 5 6 2 10 3 5 2 6 3 9 32 4 5 2 .3 4 .9 5 .7 25 .49 A 125.7 5 .142 .3 8 .3 10 12 5 6 2 10 3 5 2 6 3 9 32 4 5 12 5 12 4 10 3 4 12 6 12 5 9 3 9 3 3 12 4 10 3 12 5 9 3 3 10 312 4 12 5 9 3 2 .3 4 .9 5 .7 25 .49 125.7 5 .142 .3 8 .3 2 .3 2 .3 5 .7 5 .7 2 .3 2 .3 5 .7 5 .2 .7 2 .3 . 3 1 5 .7 . 1 7 2 .3 . 3 1 5 .7 . 1 2 5 .7 . 62 .3 .2 2 .3 .4 5 .7 .9 1 10 7 6 3 2 A : Bi 3. a) Tm x bit: 2x3x2 b) Tm gi tr nh nht ca A = x20072006x Khi x thay i Gii a) Tm x bit: 2x3x2 Ta c: x + 2 0 => x - 2. + Nu x - 2 3 th 2x3x2 => 2x + 3 = x + 2 => x = - 1 (Tho mn) + Nu - 2 x < - 2 3 Th 2x3x2 => - 2x - 3 = x + 2 => x = - 3 5 (Tho mn) 5. Gio n : Bi dng hc sinh gii lp7 5 + Nu - 2 > x Khng c gi tr ca x tho mn b) Tm gi tr nh nht ca A = x20072006x Khi x thay i + Nu x < 2006 th: A = - x + 2006 + 2007 x = - 2x + 4013 Khi : - x > -2006 => - 2x + 4013 > 4012 + 4013 = 1 => A > 1 + Nu 2006 x 2007 th: A = x 2006 + 2007 x = 1 + Nu x > 2007 th A = x - 2006 - 2007 + x = 2x 4013 Do x > 2007 => 2x 4013 > 4014 4013 = 1 => A > 1. Vy A t gi tr nh nht l 1 khi 2006 x 2007 Cch 2 : Da vo hai s i nhau c gi tr tuyt i bng nhau - GV: Gi hc sinh trnh by Bi 4: Tm x bit: a. 1 4 2 3,2 3 5 5 x b. 1 11 7 7 0 x x x x - GV: Hng dn gii a, 1 2 3 1 2 3 1 72 3 3 1 52 3 3 1 4 2 1 4 16 2 3,2 3 5 5 3 5 5 5 1 4 14 3 5 5 1 2 3 x x x x x x x x b) 1 11 1 10 7 7 0 7 1 7 0 x x x x x x x 6. Gio n : Bi dng hc sinh gii lp7 6 1 10 1 10 7 0 1 ( 7) 0 7 0 7 ( 7) 1 8 7 1 7 0 10 x x x x x x x x x x Bi tp v nh : Bi 1,Cho 1,11 0,19 1,3.2 1 1 ( ): 2 2,06 0,54 2 3 7 1 23 (5 2 0,5): 2 8 4 26 A B a, Rt gn A v B b, Tm x Z A < x < B. Bi 2: Tm gi tr nh nht ca biu thc M= 2002 2001x x 7. Gio n : Bi dng hc sinh gii lp7 7 Ngy son : 2 /2/2012 Bui 3: Gi tr tuyt i ca mt s hu t. I.L thuyt 1/ nh ngha +/ Vi x Q Ta c x neu x 0 x = -x neu x < 0 2, Tnh cht : Vi moi x Q, ta co: x 0, x = -xva x x +/ Vi x,y Q Ta c x y x y ( Du bng xy ra khi cng du ngha l x.y 0 ) x y x y ( // .. // ) II.Bi tp Bi 1: Tnh gi tr ca biu thc a, A= 3x2 - 2x+1 vi x= 1 2 Ta c x= 1 2 suy ra x= 1 2 hoc x= 1 2 HS tnh gi tr trong 2 trng hp +/ Vi x= 1 2 th A= 3 4 +/ Vi x= 1 2 th A= 11 4 b, B= 3 2 6 3 2 4x x x vi x= -2/ 3 c, C= 2 3x y vi x=1/2 v y=-3 d, D=2 2 31x x vi x=4 e, E= 2 5 7 1 3 1 x x x vi x= 1 2 (v nh ) Tng t phn a gio vin yu cu hc sinh lm v cha phn b v c KQ: B=20/ 9 C= -8 D = -5 Bi 2: Tm x bit a, 6527 xx 7x =1-2x Do 7x 0 vi mi x nn xt vi 1 2x 0 2 1 x C 8. Gio n : Bi dng hc sinh gii lp7 8 Trng hp 1: x-7 = 1-2x => 3x =8 => x= 3 8 (loi do khng tho mn iu kin x 2 1 ) Trng hp 2: x 7 = 2x -1 x = - 6( tho mn iu kin ca x) b, 2 3 2x x x c, xxx 313 GV: yu cu hc sinh lm gi ln bng trnh by Bi 3: Tm x v y bit a, 1 2 2 3 2 x b, 7,5 3 5 2 4,5x c, 3 4 5 5 0x y GV: T chc cho hc sinh lm bi - Hc sinh ln bng trnh by Bi 4 Tm gi tr nh nht ca biu thc a, A=3,7 4,3 x Ta c 4,3 0x vi mi x 4,3 3,7 3,7x Hay A 3,7 Du bng xy ra khi v ch khi 4,3 0 4,3 0 4,3 x x x Vy gi tri nh nht ca A= 3,7 khi x= 4,3 Tng t gio vin cho hc sinh lm phn b, c b, B= 3 8,4 24,2x c, C= 4 3 5 7,5 17,5x y Bi tp v nh Bi 1: Tm gi tr ln nht ca biu thc sau , 5,5 2 1,5 , 10,2 3 14 , 4 5 2 3 12 a D x b E x c F x y ` 9. Gio n : Bi dng hc sinh gii lp7 9 Ngy son : 10 /2/2012 Bui 4: Gi tr tuyt i ca mt s hu t.(tip theo) I. L thuyt 1/ nh ngha +/ Vi x Q Ta c x nu x 0 x = -x neu x < 0 2, Tnh cht Vi moi x Q, ta co: x 0, x = -xva x x +/ Vi x,y Q Ta c x y x y ( Du bng xy ra khi cng du ngha l x.y 0 ) x y x y ( // .. // ) II. Bi tp : Bi 1: Tm tt c cc s a tho mn mt trong cc iu kin sau: a) a = |a|; b) a < |a|; c) a > |a|; d) |a| = - a; e) a |a|. Bi 2: B sung thm cc iu kin cc khng nh sau l ng: a) |a| = |b| a = b; b) a > b |a| > |b|. Bi 3: Cho |x| = |y| v x < 0, y > 0. Trong cc khng nh sau, khng nh no sai a) x2 y > 0; b) x + y = 0; c) xy < 0; d) d) Bi 4: Tm gi tr ca cc biu thc sau: a) B = 2|x| - 3|y| vi x = 1/2; y = -3. b) C = 2|x 2| - 3|1 x| vi x = 4; Bi 5: Rt gn cc biu thc sau: a) |a| + a; b) |a| - a; c) |a|.a; d) |a|:a; e) 3(x 1) 2|x + 3|; g) 2|x 3| - |4x - 1|. Bi 6: Tm x trong cc ng thc sau: a) |2x 3| = 5; b) |2x 1| = |2x + 3|; c) |x 1| + 3x = 1; d) |5x 3| - x = 7. Bi 7: Tm cc s a v b tho mn mt trong cc iu kin sau: a) a + b = |a| + |b|; b) a + b = |b| - |a|. Bi 8: C bao nhiu cp s nguyn (x; y) tho mn mt trong cc iu kin sau: a) |x| + |y| = 20; b) |x| + |y| < 20. Bi 9: in vo ch trng () cc du cc khng nh sau ng vi mi a v b. ;0 11 yx .01 y x ,, 10. Gio n : Bi dng hc sinh gii lp7 10 Hy pht biu mi khng nh thnh mt tnh cht v ch r khi no xy ra du ng thc ? a) |a + b||a| + |b|; b) |a b||a| - |b| vi |a| |b|; c) |ab||a|.|b|; d) Bi 10: Tm gi tr nh nht ca biu thc: a) A = 2|3x 2| - 1; b) B = 5|1 4x| - 1; c) C = x2 + 3|y 2| - 1; d) D = x + |x|. Bi 11: Tm gi tr ln nht ca cc biu thc: a) A = 5 - |2x 1|; b) B = Bi 12: Tm gi tr ln nht ca biu thc C = (x + 2)/|x| vi x l s nguyn. Bi 13: Cho |a c| < 3, |b c| < 2. Chng minh rng: |a b| < 5. Bi 14: a biu thc A sau y v dng khng cha du gi tr tuyt i: A = |2x + 1| + |x - 1| - |x 2|. . || || ... b a b a ; 3|1| 1 x 11. Gio n : Bi dng hc sinh gii lp7 11 Ngy son : 18 /2/ 2012 Bui 5: Lu tha ca s hu t A--L thuyt . 1, . 2, : ( 0, ) 3, ( ) 4, ( . ) . 5, ( ) ( 0) 1 6, m n m n m n m n m n m n m m m m m m n n x x x x x x x m n x x x y x y x x y y y a a - GV: Cho hc sinh ghi li ni dung cc cng thc B Bi tp Bi 1: a,C th khng nh c x2 lun lun ln hn x hay khng ? Khng khng nh c nh vy chng hn x=1/2 th 21 1 ( ) 2 2 b, Khi no x2 < x x2 < x 2 0 ( 1) 0x x x x xy ra nu x v x-1 tri du V x-1 < x nn x-1 < 0 v x > 0 suy ra 0 < x 0) tui anh cch y 5 nm l x 5 Tui ca em sau 8 nm na l y + 8 30. Gio n : Bi dng hc sinh gii lp7 30 Theo bi c TLT: 4 8 3 5 yx v x - y = 8 T tnh c: x = 20; y = 12 - Vy tui anh hin nay l 20 tui em l 12 b. (1,5) - APE = APH (CH - CG ) - AQH = AQF (CH - CG ) - gc EAF = 1800 E, A, F thng hng II. Phn ring Cu 5A (2) a. (1,5) - Bin i S = n 2 1 + ( ) 2 3 ... 2 3 2 3 2 3 120 n - a v dng 3S S = 2S - Bin i ta c S = 4 132 n n (n Z ) b. (0,5) - Nghim li cc gi tr 1, -1, 5, -5 vo a thc - Gi tr no lm cho a thc bng 0 th gi tr l nghim Cu 5 B (2) a. (1,5) A = 5 + 2 8 x A nguyn 2 8 x nguyn x 2 (8) Lp bng x - 2 - 8 - 4 - 2 - 1 1 2 4 8 x - 6 - 2 0 1 3 4 6 10 V x Z x = {-6; -2; 0; 1; 3; 4; 6; 10} th A Z b. (0,5) 76 + 75 74 = 74 (72 + 7 1) = 74 . 55 55 31. Gio n : Bi dng hc sinh gii lp7 31 Tun 20 Bui13 Ngy dy : 05/ 1/11 I. Mc tiu - Kin thc : - Kim tra kho st cht lng hc sinh qua thi tham kho, nh gi vic nm kin thc ca hc sinh. - K nng : - Rn cho hc sinh k nng tnh ton , k nng trnh by . - Thi : - C thc t hc t nghin cu nghim tc. II/ Chun b - Gio vin: Son kim tra. - Hc sinh: n tp li ni dung cc kin thc III/ Tin trnh tit dy : thi hc sinh gii huyn Mn: Ton 7 Thi gian lm bi: 120 pht (khng k giao ) 1.2 A/ Phn chung Cu 1 (1,5im) a. (1) Tnh tng: M = - nn 4 4 13.9 4 9.5 4 5.1 4 b. (0,5) Tm x bit: -4x(x 5) 2x(8 2x) = -3 Cu 2 (1,5im) a. (1) Tm x, y, z bit: 32. Gio n : Bi dng hc sinh gii lp7 32 216648 333 zyx v x2 + y2 + z2 = 14 b. (0,5) Cho x1 + x2 + x3 + + x50 + x51 = 0 v x1 + x2 = x3 + x4 = x5 + x6 = = x49 + x50 = 1 tnh x50 Cu 3 (2im) a. (1) Trn mt phng to , cho 2 im M(-3;2) v N(3;-2). Hy gii thch v sao gc to O v hai im M, N l 3 im thng hng? b. (1) Cho a thc: Q(x) = x 243 2 2 1 2 1 2 1 2 xxxx x a./ Tm bc ca a thc Q(x) b./ Tnh Q 2 1 c./ Chng minh rng Q(x) nhn gi tr nguyn vi mi s nguyn x Cu 4 (3im) a. (1) Ba t cng nhn A, B, C phi sn xut cng mt s sn phm nh nhau. Thi gian 3 t hon thnh k hoch theo th t l 14 ngy, 15 ngy v 21 ngy. T A nhiu hn t C l 10 ngi. Hi mi t c bao nhiu cng nhn? (Nng sut lao ng ca cc cng nhn l nh nhau) b. (2) Cho hnh vung ABCD. Trn na mt phng cha im B b l ng thng AD v tia AM (M CD) sao cho gc MAD = 200 . Cng trn na mt phng ny v tia AN (N BC) sao cho gc NAD = 650 . T B k BH AN (H AN) v trn tia i ca tia HB ly im P sao cho HB = HP chng minh: a./ Ba im N, P, M thng hng b./ Tnh cc gc ca AMN B/ Phn ring Cu 5 A. (2im) Dnh cho hc sinh chuyn a. (1) Chng minh rng: 222333 + 333222 chia ht cho 13 b. (1) Tm s d ca php chia 109345 cho 7 Cu 5 B. (2im) Dnh cho hc sinh khng chuyn a. (1) Tm s nguyn dng n bit 55 555555 555 5555 22 666666 333 4444 = 2n b. (1) Chng minh rng vi mi s nguyn dng n th: 3n+3 + 2n+3 3n+2 + 2n+2 chia ht cho 6 p n 1.2 I. Phn chung Cu 1 (1,5) a. (1)- a du ra ngoi du ngoc 33. Gio n : Bi dng hc sinh gii lp7 33 - Tch mt phn s thnh hiu 2 phn s ri rt gn c A = 1 1 n b. (0,5) Bin i ri rt gn ta c x = - 4 3 Cu 2 (1,5) a. (1)- Bin i cc mu di dng lp phng a v dng f e d c b a - p dng tnh cht dy TSBN ri tm x, y, z b. (0,5) Kt qu x50 = 26 Cu 3 (2) a. (1) Gi ng thng (d) i qua O v M(-3;2) l th hm s dng y = ax (a 0) t tnh a xc nh hm s OM l th hm s. - Kim tra im N(3;-2) c thuc th hm s khng? kt lun: O, M, N thng hng b. (1) - Thu gn Q(x) = 2 23 xx bc Q(x) l 3 (0,25) - Q(- 2 1 ) = 2 ) 2 1 () 2 1 ( 23 = 16 3 2 4 1 8 1 (0,25) - Q(x) = 2 )1(2 xx l mt s chn Q(x) Z (0,5) Cu 4(3) a. (1) Gi s ngi t A, t B, t C ln lt l x, y,z t l nghch vi 14, 15, 21 x, y, z TLT vi 21 1 ; 15 1 ; 14 1 T tnh c x = 30; y = 28; z = 20 b. (2) * - BNA = PNA (c.c.c) gc NPA = 900 (1) - DAM = PAM (c.g.c) gc APM = 900 (2) T (1) v (2) gc NPM = 1800 Kt lun * Gc NAM = 450 ; gc ANP = 650 ; gc AMN = 700 II. phn ring Cu 5 A (2) a. (1) 222333 + 333222 = 111333 .2333 + 111222 .3222 = 111222 [(111.23 )111 + (32 )111 ] = 111222 (888111 + 9111 ) V 888111 + 9111 = (888 + 9)(888110 888109 .9 + - 888.9109 + 9110 ) = 13.69 (888110 888109 .9 + - 888109 + 9110 )13 KL b. (1) Ta c 109345 = (109345 4345 ) + (4345 1) + 1. v 109345 4345 7 4345 1 7 109345 chia ht cho 7 d 1 Cu 5 B (2) p n 2 a. (1) 34. Gio n : Bi dng hc sinh gii lp7 34 VT: - a tng cc lu tha bng nhau di dng tch v bin i c 212 n = 12 b. (1) - Nhm s hng th nht vi s hng th 3 ri t TSC. S hng th 2 vi s hng th 4 ri t TS C - a v mt tng c cc s hng cho 2 v 3 m UCLN(2;3) = 1 tng 6 Tun 21 Bui14 Ngy dy : 12/1/11 I. Mc tiu - Kin thc : - Kim tra kho st cht lng hc sinh qua thi tham kho, nh gi vic nm kin thc ca hc sinh. - K nng : - Rn cho hc sinh k nng tnh ton , k nng trnh by . - Thi : - C thc t hc t nghin cu nghim tc. II/ Chun b - Gio vin: Son kim tra. - Hc sinh: n tp li ni dung cc kin thc III/ Tin trnh tit dy : thi hc sinh gii Mn: Ton 7 Thi gian lm bi: 120 pht (khng k giao ) 1.3 A/ Phn chung Cu 1 (2,5im): a. (1,75) Tnh tng: M = 3 1 1 1 761 4 5 4 417 762 139 762 417.762 139 b. (0,75) Tnh gi tr ca a thc sau ti x = -1 x2 + x4 + x6 + x8 + + x100 Cu 2 (1im): a. (0,5) Cho t l thc 4 33 yx yx tnh gi tr ca y x b. (0,5) Cho t l thc d c b a chng minh rng dc dc ba ba 32 32 32 32 Cu 3 (2,5im): a. (1,5) Cho hm s y = - x 3 1 v hm s y = x -4 * V th hm s y = - 3 1 x 35. Gio n : Bi dng hc sinh gii lp7 35 * Chng t M(3;-1) l giao ca hai th hm s trn * Tnh di OM (O l gc to ) b. (1) Mt t ti v mt t con cng khi hnh t A B, vn tc t con l 40km/h, vn tc t ti l 30km/h. Khi t ti n B th t con n B trc 45 pht. Tnh di qung ng AB. Cu 4 (2im): Cho ABC c gc A = 900 , v phn gic BD v CE (DAC ; E AB) chng ct nhau ti O. a. (0,5) Tnh s o gc BOC b. (1) Trn BC ly im M v N sao cho BM = BA; CN = CA chng minh EN// DM c. (0,5) Gi I l giao ca BD v AN chng minh AIM cn. B/ Phn ring Cu 5 A (2im): Dnh cho hc sinh chuyn b. (1) Chng minh rng a thc sau khng c nghim: P(x) = 2x2 + 2x + 4 5 c. (1) Chng minh rng: 2454 .5424 .210 chia ht cho 7263 Cu 5 B (2im): Dnh cho hc sinh khng chuyn a. (1) Tm nghim ca a thc 5x2 + 10x b. (1) Tm x bit: 5(x-2)(x+3) = 1 p n 1.3 I. Phn chung Cu 1 (2,5) a. (2) - Bin i M di dng mt tng ri t a = 1 417 ; b = 762 1 ; c = 139 1 - Rt gn ri thay gi tr a, b, c vo ta tnh c M = 762 3 b. (0,5) (-1)2 + (-1)4 + (-1)6 + + (-1)100 = 1 + 1 +1 + + 1 = 50 Cu 2 (1) a. (0,5) p dng tnh cht ca t l thc bcad d c b a 9 7 y x b. (0,5) T dc dc ba ba dc ba dc ba d b c a d b c a d c b a 32 32 32 32 32 32 32 32 3 3 2 2 Cu 3 (2,5) a. (1,5) * V th hm s y = - 3 1 x * T 2 hm s trn ta c phng trnh honh - 3 1 x = x -4 36. Gio n : Bi dng hc sinh gii lp7 36 - Thay im M(3; -1) vo phng trnh honh ta c - 3 1 . 3 = 3 4 = -1 M(3; -1) l giao ca 2 th hm s trn. * Trn mt phng to ta thy OMP vung ti P 22222 31 PMOPOM 1091 OM (vd) b. (1) - i 45 pht = hh 4 3 60 45 - Gi vn tc ca t ti v t con l v1 v v2 (km/h) tng ng vi thi gian l t1 v t2 (h). Ta c v1.t1 = v2.t2 - V vn tc v thi gian l hai i lng TLN 1 2 2 1 t t v v ; t2 t1 = 4 3 - Tnh c t2 = 4 3 . 4 = 3 (h) T1 = )( 4 9 3 4 3 h S = v2 . t2 = 3 . 30 = 90km Cu 4 (2) a. (0,5) C gc B + gc C = 900 gc OBC + gc BCO = 0 0 45 2 90 (BD, CE l phn gic) gc BOC = 1800 450 = 1350 b. (1) ABD = MBD (c.g.c) gc A = gc M = 900 DM BC (1) ECN = ECA (c.g.c) gc A = gc N = 900 EN BC (2) T (1) v (2) EN // DM c. (0,5) IBA = IBM (c.g.c) IA = IM thay IAM cn ti I II. Phn ring Cu 5 A (2) O I E A D C M N B 37. Gio n : Bi dng hc sinh gii lp7 37 a. (1) P(x) = (x+1)2 + x2 + 4 1 4 1 vi x vy P(x) khng c nghim b. (1) 2454 . 5424 . 210 = (23 .3)54 . (2.33 )24 . 210 = 2196 . 3126 7263 = (23 . 32 )63 = 2189 . 3126 T suy ra 2454 . 5424 . 210 7263 Cu 5 B (2) a. (1) Cho 5x2 + 10x = 0 5x(x + 10) = 0 010 05 x x 10 0 x x Nghim ca a thc l x = 0 hoc x = -10 b. (1) 5(x-2)(x+3) = 1 = 50 (x-2)(x+3) = 0 3 2 03 02 x x x x Vy x = 2 hoc x = -3 Tun 22 Bui15 Ngy dy : 19/1/11 38. Gio n : Bi dng hc sinh gii lp7 38 I. Mc tiu - Kin thc : - Kim tra kho st cht lng hc sinh qua thi tham kho, nh gi vic nm kin thc ca hc sinh. - K nng : - Rn cho hc sinh k nng tnh ton , k nng trnh by . - Thi : - C thc t hc t nghin cu nghim tc. II/ Chun b - Gio vin: Son kim tra. - Hc sinh: n tp li ni dung cc kin thc III/ Tin trnh tit dy : thi hc sinh gii huyn Mn: Ton 7 Thi gian lm bi: 120 pht (khng k giao ) 1.4 A/ Phn chung Cu 1 (1,5im): a. (0,75) Tnh tng M = 5 ) 23 4 5( 47 3 4 47 3 27 23 4 b. (0,75) Cho cc s a1, a2, a3 an mi s nhn gi tr l 1 hoc -1 Bit rng a1a2 + a2a3 + + ana1 = 0. Hi n c th bng 2002 c hay khng? Cu 2 (2 im) a. (1) Tm x bit x yyy 6 61 24 41 18 21 b. (1) Tm x, y, z bit 3x = 2y; 7y = 5z v x y + z = 32 Cu 3 (1,5im) Cho hnh v, ng thng OA l th hm s y = f(x) = ax (a 0) a. Tnh t s 4 2 o o x y b. Gi s x0 = 5 tnh din tch OBC Cu 4 (3im) a. (1) Mt t ti v mt t con cng khi hnh t A B, vn tc t con l 40km/h, vn tc t ti l 30km/h. Khi t ti n B th t con n B trc 45 pht. Tnh di qung ng AB. b. (2) Cho ABC, gi M v N theo th t l trung im ca AC v AB. Trn tia i ca tia MB ly im D sao cho MD = MB, trn tia i ca tia NC ly im E sao cho NE = NC. Chng minh rng: Ba im E, A, D thng hng A l trung im ca ED y0 2 1 X0 C B A xo 1 2 3 4 5 y 39. Gio n : Bi dng hc sinh gii lp7 39 B/ Phn ring Cu 5 A (2im) Dnh cho hc sinh chuyn a. (1) So snh 8 v 5 + 1 b. (1) Cho hai a thc P(x) = x2 + 2mx + m2 v Q(x) = x2 + (2m+1)x + m2 Tm m bit P(1) = Q(-1) Cu 5 B (2im) Dnh cho hc sinh khng chuyn a. (1) So snh 2300 v 3200 b. (1) Tnh tng A = 1 + 2 + 22 + + 22010 p n 1.4 I. Phn chung Cu 1 (1,5) a. (0,75) - Bin i M di dng mt tng - t a 23 1 ; b 47 1 - Rt gn ri thay gi tr ca a, b vo c A = 119 b. (0,75) Xt gi tr ca mi tch a1a2, a2a3, ana1 s tch c gi tr bng 1 bng s tch c gi tr bng -1 v bng 2 n v 2002 2 n = 2002 Cu 2 (2) a. (1) Tm x bit x yyy 6 61 24 41 18 21 )3()2()1( - p dng tnh cht dy TSBN cho t s (1) v (3) c t s (4) - Xt mi quan h gia t s (4) v (2) 6x = 2 . 24 = 48 x = 8 b. (1) - a v dng f e d c b a - p dng tnh cht dy TSBN tnh x, y, z Cu 3 (1,5) a. (0,75) - Trn mt phng to ta thy im B(x0;y0) th hm s y = f(x) = ax y0 = ax0 0 0 x y = a M A(2;1) a = 0 0 2 1 x y 4 2 4 2 0 0 0 0 x y x y b. (0,75) - OBC vung ti C S OBC = BCOC. 2 1 = 0. 2 1 yOC Vi x0 = 5 2 5 5 2 1 OBCS = 6,25 (vdt) 40. Gio n : Bi dng hc sinh gii lp7 40 Cu 4 (3) a. (1) - i 45 pht = hh 4 3 60 45 - Gi vn tc ca t ti v t con l v1 v v2 (km/h) tng ng vi thi gian l t1 v t2 (h). Ta c v1.t1 = v2.t2 - V vn tc v thi gian l hai i lng TLN 1 2 2 1 t t v v ; t2 t1 = 4 3 - Tnh c t2 = 4 3 . 4 = 3 (h) t1 = )( 4 9 3 4 3 h S = v2 . t2 = 3 . 30 = 90km b. (2) - MAD = MCB (c.g.c) gc D = gc B AD // BC (1) - NAE = NBC (c.g.c) gc E = gc C AE // BC (2) T (1) v (2) E, A, D thng hng - T chng minh trn A l trung im ca ED II. Phn ring Cu 5 A (2) a. (1) So snh 8 v 15 ta c 2 < 5 2 + 6 < 5 + 6 = 5 + 5 + 1 8 < ( 2 )15 58 + 1 b. (1) - Thay gi tr ca x vo 2 a thc - Cho 2 a thc bng nhau ta tnh c m = - 4 1 Cu 5 B (2) a. (1) Ta c 2 1003300 )2( 3 1002200 )3( 3200 > 2300 b. (1) - Nhn hai v ca tng vi A vi 2 - Ly 2A A rt gn c A = 2 122010 A B N M C E D 41. Gio n : Bi dng hc sinh gii lp7 41 Tun 23 Bui16 Ngy dy : 26/1/11 I. Mc tiu - Kin thc : - Kim tra kho st cht lng hc sinh qua thi tham kho, nh gi vic nm kin thc ca hc sinh. - K nng : - Rn cho hc sinh k nng tnh ton , k nng trnh by . - Thi : - C thc t hc t nghin cu nghim tc. II/ Chun b - Gio vin: Son kim tra. - Hc sinh: n tp li ni dung cc kin thc III/ Tin trnh tit dy : thi hc sinh gii huyn Mn: Ton 7 Thi gian lm bi: 120 pht (khng k giao ) 42. Gio n : Bi dng hc sinh gii lp7 42 1.5 A/ Phn chung Cu 1 (1,5 im): (1) Tnh tng: A = 11 4 7 4 9 4 11 1 7 1 9 1 + 625 4 125 4 16,0 5 4 625 3 125 3 25 3 6,0 a. (0,5) Tm cc s a1, a2, a3, a9 bit 1 9 ... 7 3 8 2 9 1 9321 aaaa v a1 + a2 + a3 + + a9 = 90 Cu 2 (2 im) a. (1) Tm x, y bit x y x yy 4 71 5 51 12 31 b. (1) Ch ra cc cp (x;y) tho mn 92 22 yxx = 0 Cu 3 (1,5im) a. (1) Cho hm s y = f(x) = x + 1 vi x -1 -x 1 vi x < -1 * Vit biu thc xc nh f * Tm x khi f(x) = 2 b. (0,5) Cho hm s y = x 5 2 * V th hm s * Tm trn th im M c tung l (-2), xc nh honh M (gii bng tnh ton). Cu 4 (3im) a. (1) Mt t d nh i t A n B trong mt thi gian d nh vi vn tc 40km/h. Sau khi i c 1/2 qung ng AB th t tng vn tc ln 50km/h trn qung ng cn li. Do t n B sm hn d nh 18 pht. Tnh qung ng AB. b. (2) Cho ABC vung cn A, M l trung im ca BC, im E nm gia M v C. K BH, CK vung gc vi AE (H v K thuc ng thng AE). Chng minh rng: * BH = AK * MBH = MAK * MHK l tam gic vung cn B/ Phn ring Cu 5 A (2im) Dnh cho hc sinh chuyn a. (1) Tm cc s x, y, z tho mn ng thc 2 )2( x + 2 )2( y + zyx = 0 b. (1) Tm x, y, z bit: x + y = x : y = 3(x y) 43. Gio n : Bi dng hc sinh gii lp7 43 Cu 5 B (2im) Dnh cho hc sinh khng chuyn a. (1) Tm x bit: 2x + 2x+1 + 2x+2 + 2x+3 = 120 b. (1) Rt gn biu thc sau mt cch hp l: A = 343 4 7 2 7 4 2 64 )77( 1 49 1 49 1 1 2 2 p n 1.5 I. phn chung Cu 1 (1,5: mi ng 0,75) a. A = 1 b. p dng tnh cht ca dy TSBN ta tnh c a1 = a2 = = a9 = 10 Cu 2 (2im: mi ng 1) a. - p dng tnh cht dy TSBN cho t s (1) v (3) c t s (4) - T t s (4) v t s (2) 12 + 4x = 2.5x x = 2 - T tnh c y = - 15 1 b. - V 022 xx v 092 y x2 + 2x = 0 v y2 9 = 0 t tm cc cp (x;y) Cu 3 (1,5) a. (1) - Biu thc xc nh f(x) = 1x - Khi f(x) = 2 1x = 2 t tm x b. (0,5) - V th hm s y = x 5 2 x 0 5 O (0;0) y 0 2 A (5;2) - Biu din O(0;0); A(5;2) trn mt phng to OA l th hm s y = x 5 2 - M th y = x 5 2 -2 = x 5 2 x = -5 Cu 4 (3im) a. (1) 18 pht = )( 10 3 60 18 h - Gi vn tc v thi gian d nh i na qung ng trc l v1; t1, vn tc v thi gian i na qung ng sau l v2; t2. - Cng mt qung ng vn tc v thi gian l 2 i lng TLN do : V1t1 = v2t2 3 100 21 12 2 1 1 2 tt vv t v t v 2 3 1 t (gi) thi gian d nh i M K B E 44. Gio n : Bi dng hc sinh gii lp7 44 c qung ng AB l 3 gi - Qung ng AB di 40 . 3 = 120 (km) b. (2) - HAB = KCA (CH GN) BH = AK - MHB = MKA (c.g.c) MHK cn v MH = MK (1) C MHA = MKC (c.c.c) gc AMH = gc CMK t gc HMK = 900 (2) T (1) v (2) MHK vung cn ti M II. Phn ring Cu 5 A (2) a. (1) V 2 )2(x 0 vi x 2 )2( y 0 vi y zyx 0 vi x, y, z ng thc xy ra 0 0)2( 0)2( 2 2 xyx y x 0 2 2 z y x b. (1)T x + y = 3(x-y) = x : y 2y(2y x) = 0 m y 0 nn 2y x = 0 x = 2y T x = 3 4 ; y = 3 2 Cu 5 B (2) a. (1) - t 2x lm TSC rt gn - Bin i 120 di dng lu tha c s 2 ri tm x b. (1) Bin i t vo mu ri rt gn c A = 4 1 45. Gio n : Bi dng hc sinh gii lp7 45