SGV TOAN 8-CTST

["Th\u1ef1c h\u00e0nh 1. T\u00ecm trong H\u00ecnh 4 c\u00e1c c\u1eb7p tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng. Gi\u1ea3i \u2206ABC v\u00e0 \u2206DEF c2\u00f35: AB= 4= 2 ; AC= 16=4 2 ; =B14C =7 2 . 3 DE 10 5 DF 15 5 EF 17,5 5 77 Suy ra DA=BE21 A=C BC . V\u1eady \u2206ABC9 \u223d \u2206DEF (c.c.c). 37 DF EF DF =8 1 AC 3 6 Th\u1ef1c h\u00e0nh 1. T\u00ecma) trong H\u00ecnh 4 c\u00e1c c\u1eb7p b) c) d) tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng. Hi\u0300nh 4 3 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c2h5\u00e0nh 1: HS th\u1ef1c h\u00e0n1h4gi\u1ea3i th1\u00ed4ch \u0111\u01b0\u1ee3c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 nh\u1ea5t c\u1ee7a hai tam gi\u00e1c, r\u00e8n luy\u1ec7n k\u0129 n\u0103ng c\u1ea7n \u0111\u1ea1t th\u00f4ng 3qua vi\u1ec7c7 gi\u1ea3i th\u00edc7h \u0111\u01b0\u1ee37c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 nh\u1ea5t c\u1ee7a hai tam gi\u00e1c. 21 9 \u2013 n\u00eau nh\u1eadn x\u00e9t m\u00e0DFkh=8\u00f413nAgC c\u1ea7n gi\u1ea3i th\u00edch. \u0110\u1ed1i G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 1: GV ch\u1ec9 c\u1ea7n m\u1edf 6rb\u1ed9) ng. c) d) v\u1edbi HS kh\u00e1 gi\u1ecfi th\u00ec xae)m nh\u01b0 l\u00e0 m\u1ed9t b\u00e0i t\u1eadp H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: H\u00ecnh 4a \u0111\u1ed3ng d\u1ea1ngHvi\u0300n\u1edbhi4H\u00ecnh 4c; H\u00ecnh 4b \u0111\u1ed3ng d\u1ea1ng v\u1edbi H\u00ecnh 4d. Nh\u1eadn x\u00e9t: N\u1ebfu tam gi\u00e1c A\u2032B\u2032C\u2032 \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c ABC theo t\u1ec9 s\u1ed1 k th\u00ec t\u1ec9 s\u1ed1 chu vi 2. Tcr\u1ee7\u01b0a\u1eddhnagi tha\u1ee3mpg\u0111i\u00e1\u1ed3cn\u0111g\u00f3dc\u0169\u1ea1nnggbt\u1eb1hn\u1ee9ghka. i (c.g.c) 2H.\u0110TKRP\u01af2\u1edcNG H\u1ee2P \u0110\u1ed2NG D\u1ea0NG TH\u1ee8 HAI (c.g.c) 2 Cho tam gi\u00e1c DEF v\u00e0 tam gi\u00e1c ABC c\u00f3 DE = 1 AB, DF = 1 AC, D D\uf0b5 = A\uf0b5 (H\u00ecnh 5). Tr\u00ean tia AB, l\u1ea5y 3 3 \u0111i\u1ec3m M sao cho AM = DE. E F Qua M k\u1ebb MN \/\/ BC (N \u2208 AC). A N a) So s\u00e1nh c\u00e1c t\u1ec9 s\u1ed1 AM v\u00e0 AN . AB AC M b) So s\u00e1nh AN v\u1edbi DF. c) Tam gi\u00e1cAMN c\u00f3 \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1cABC kh\u00f4ng? d) D\u1ef1 \u0111o\u00e1n s\u1ef1 \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c DEF v\u00e0 ABC. B C Hi\u0300nh 5 \u2013 M\u0110\u1ee5\u1ecbcnh\u0111\u00edlc\u00ed:h c\u1ee7a H\u0110KP 2: Gi\u00fap HS c\u00f3 c\u01a1 h\u1ed9i tr\u1ea3i nghi\u1ec7m, th\u1ea3o lu\u1eadn, gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai c\u1ee7a hai tam gi\u00e1c. GV\u2013\u0111G\u00e1Ncn\u01a1\u0323\u00e1hi\u1ebfcu\u00fdgcith\u1eb7\u00e1\u1ed5pa, iccchch\u1ea1\u1ea1\u1ee9\u1ed1nnchthkH\u0111ic\u00f3\u1ebf\u0110\u1ee7nbaK\u1eb1ttPnhag\u1ee9m2cn:.ghHia\u00e1Suc,ttnhh\u00e0\u1ea3\u00ecyohlatu\u1ec9i\u1eadlt\u1ec7namvn\u1edbhgi\u00f3i\u00e1hmca;i\u0111cc\u00f3\u00e1\u1ea1c\u0111n\u1ed3hnnhcg\u00f3\u1ee7mda\u1ea1tntargm\u00ecnvh\u1edbgbii\u00e1\u00e0ncyhkakiu\u1ebfa.tvq\u00e0u\u1ea3h,ali\u1edbgp\u00f3ncht\u1ead\u1ea1no xb\u00e9\u1edfti; Th\u1ef1Gc Th\u00e0nh 2\u2206.ACBhCo vta\u00e0m\u2206Ag\u2032iB\u00e1c\u2032CA\u2032, DE v\u00e0 tam A E 4F 3 A\u2032 gi\u00e1c ACF c\u2206\u00f3AcDa\u0301cEk\u223d\u00edch=\u2206tAhA\u01b0CA'\u1edbBFBc.' nhA\u01b0A=' CCtr'o,nA\uf0b5g' H\u00ecnA\uf0b5h 8. Ch\u1ee9ng minh r\u1eb1ng A 6 8 D KL \u2206A\u2032B\u2032C\u2032 \u223d \u2206ABC 200 Hi\u0300nh 8 C C\u2032 B C B\u2032 Hi\u0300nh 6 68","\u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS v\u1eadn d\u1ee5ng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai c\u1ee7a hai tam gi\u00e1c \u0111\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng. Gi\u00fap HS r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t th\u00f4ng qua vi\u1ec7c gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai c\u1ee7a hai tam gi\u00e1c. \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 2: HS th\u1ea3o lu\u1eadn nh\u00f3m; c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t; GV \u0111\u00e1nh gi\u00e1. 3. Tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 ba (g.g) H\u0110KP 3 A B\u00e0i 2 D A\u2032 BE C B\u2032 C\u2032 D D \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 3: Gi\u00fap HS c\u00f3 c\u01a1 h\u1ed9i tr\u1ea3i nghi\u1ec7m, th\u1ea3o lu\u1eadn, gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c H\u00ecnh 7 tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 ba c\u1ee7a hai tam gi\u00e1c. \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 3: HS th\u1ea3o lu\u1eadn nh\u00f3m; c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t; GV \u0111\u00e1nh gi\u00e1, ch\u1ed1t ki\u1ebfn th\u1ee9c. A\u2032 Th\u1ef1c h\u00e0nh 3. Quan s\u00e1t H\u00ecnh 12. A 79 o 79 o 6 a) Ch\u1ee9ng minh r\u1eb1ng \u2206ABC \u223d \u2206A\u2032B\u2032C\u2032. b) T\u00ednh \u0111\u1ed9 d\u00e0i ca\u0323nh B'C'. 4 60 o 6 C B\u2032 41o B C\u2032 Hi\u0300nh 12 H\u00ecnh 9 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 3: HS th\u1ef1c h\u00e0nh s\u1eed d\u1ee5ng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3Mng d\u1ea1ng th\u1ee9 ba c\u1ee7a hai tam gi\u00e1c \u0111\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng. tr\u00ecn4hcmb\u00e0y k\u1ebft qu\u1ea3, 5 cm x\u00e9t; A 3: HS bc \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh A l\u1edbp nh\u1eadn GV \u0111\u00e1nh gi\u00e1. Fa th\u1ea3o lu\u1ead2 ncmnh\u00f3m2;,5cc\u00e1mc nh\u00f3m H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: B 3,5 cm C N 7 cm P a) T\u00ednh s\u1ed1 \u0111o C\uf0b5, t\u1eeb \u0111\u00f3 suy ra \u2206ABC \u223d \u2206A\u2032B\u2032C\u2032 (gH.g\u00ecn)h. 11 b) B\u2032C\u2032 = 9. x A 201 x dE 3 cm C F","BE C B\u2032 C\u2032 D C H\u00ecnh 7 H\u00ecnh 8 V\u1eadn d\u1ee5ng 1. Cho h\u00ecnh thAan\u2032 g ABCD (AB \/\/ CD) A6B Tc\u00f3\u00edAnAhB\u0111\u1ed9=d6\u00e0im\u0111o, \u1ea1CnDth=\u1eb3n1g5OmB7,9.oOD = 8 m (H\u00ecnh 13). O 6 8 4 V\u1ead7n9 o d\u1ee5ng 2. Qua tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a c\u00e1c 15 Hi\u0300nh 13 6h0ao i tam gi\u00e1c, h\u00e3y tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi \u1edf (4t1roang 67). D C B6 C B\u2032 C\u2032 \u2013 M\u1ee5c \u0111\u00edch cH\u1ee7\u00ecanhV9\u1eadn d\u1ee5ng 1, 2: Gi\u00fap HS c\u1ee7ng c\u1ed1, kh\u1eafc s\u00e2u vH\u1ec1\u00ecnvh i1\u1ec70c \u00e1p d\u1ee5ng c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp c\u1ee5 th\u1ec3. M b\u00e0y k\u1ebft qu\u1ea3, \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u1eadn dM\u1ee5ng 1, 2: GV cho HS l\u00e0m vi\u1ec7c c\u00e1c nh\u00e2n, tr\u00ecnh 2 cml\u1edbpAHn\u01b0h2\u1edb,5\u1eadncnmgxd\u00e9\u1eabt,nG\u2013V\u0111\u0111\u00e1\u00e1p4 ncm\u00e1hng: i\u00e1. 5 cm 3b 3c A B V\u1eadn d\u1ee5nCg 1N: Ch\u1ee9ng minh7 c\u2206mAOB \u223d \u2206COD (g.g),b t\u1eeb \u0111\u00f3csuy ra OB = 3,2 m. 3,5 cm P F a EN 3a G IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp H\u00ecnh 11 H\u00ecnh 12 Tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 nh\u1ea5t (c.c.c) 1. \ta) A=F A=E AF=E 1 , do d\u00f3 \u2206AFE \u223d \u2206MNG (c.c.c). O MN MxG NG 3 3,6 cm 3 cm b) Tda c\u00f3E P\u2206AFE =1 hayF 15 1 2 cm P\u2206MNG 3 1P,\u22065McNmG = 3 . Do \u0111\u00f3 P\u2206MNCG = 45 cmx . D 1,8 cm 2. \tTa cB\u00f3 \u2206A\u2032B\u2032dC\/\u2032\/\u223dBC\u2206ABC C(gi\u1ea3 thi\u1ebft). A 7,8 cm B CD \/\/ AB Do \u0111\u00f3 A=\u2032BH\u2032 \u00ecnhA8=a\u2032,Ctr\u203294 B\u2032C\u2032 hay A=\u2032B\u2032 A=\u2032C\u2032 B\u2032C\u2032H. \u00ecnh 13, tr 95 AB AC BC 4 6 9 \u00c1p d\u1ee5ng d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3 A=\u2032B\u2032 A=\u2032C\u2032 B=\u2032C\u2032 P\u2206A=\u2032B\u2032C\u2032 6=6,5 7 . 4 6 9 P\u2206ABC 19 2 Do \u0111\u00f3 A\u2032B\u2032 = 7 . 4 = 14 (cm); A\u2032C\u2032 = 7 . 6 = 21 (cm); B\u2032C\u2032 = 7 . 9 = 31,5 (cm). 222 3. \tTa c\u00f3 \u2206ABC \u223d \u2206DEF (gi\u1ea3 thi\u1ebft). Do \u0111\u00f3 A=B A=C BC hay A=B 6=00 BC . DE DF EF 350 300 550 Suy ra AB = 700 m; BC = 1 100 m. Qu\u00e3ng \u0111\u01b0\u1eddng Nam ch\u1ea1y l\u00e0 4 . (300 + 350 + 550) = 4 800 (m). Qu\u00e3ng \u0111\u01b0\u1eddng H\u00f9ng ch\u1ea1y l\u00e0 2 . (600 + 700 + 1100) = 4 800 (m). Qu\u00e3ng \u0111\u01b0\u1eddng c\u1ee7a hai b\u1ea1n ch\u1ea1y b\u1eb1ng nhau. 202","Tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai (c.g.c) 4. \ta) Ta c\u00f3 D=E D=F 1 v\u00e0 E\uf0b7DF = B\uf0b7AC = 120o. Do \u0111\u00f3 \u2206ABC \u223d \u2206DEF (c.g.c). AB AC 2 b) Ta c\u00f3 C=E D=F 1 , E\uf0b7C=D N\uf0b7MP = 50o. Tuy nhi\u00ean, E\uf0b7CD l\u00e0 g\u00f3c kh\u00f4ng t\u1ea1o b\u1edfi NP MP 2 hai c\u1ea1nh CE v\u00e0 DE, N\uf0b7MP l\u00e0 g\u00f3c kh\u00f4ng t\u1ea1o b\u1edfi hai c\u1ea1nh NP v\u00e0 MP. Do \u0111\u00f3 \u2206DEC v\u00e0 \u2206MPN kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng. 5. \t\u2206DEF v\u00e0 \u2206MNP c\u00f3: DE= 6= 3 ; E=F 7=,8 3 . Suy ra D=E E=F 3 . MN 10 5 NP 13 5 NM NP 5 M\u1eb7t kh\u00e1c, ta c\u00f3 E\uf0b5 = N\uf0b5. Do \u0111\u00f3 \u2206DEF \u223d \u2206MNP (c.g.c). V\u1eady F\uf024 = P\uf024 = 42o. 6. \ta) Ta c\u00f3: A=E A=F 2 , A\uf0b5 l\u00e0 g\u00f3c chung. Suy ra \u2206AEF \u223d \u2206ACB (c.g.c). AC AB 3 Do \u0111\u00f3 EF = 2 , suy ra EF = BC \u0098 2 18\u0098 2 = 12 (cm). BC 3 33 b) Ta c\u00f3 FD = FC (gi\u1ea3 thi\u1ebft), do \u0111\u00f3 \u2206FDC c\u00e2n t\u1ea1i F. V\u1eady A\uf0b7CB = M\uf0b7DE. (1) \u2206ABC v\u00e0 \u2206MED c\u00f3: AC= 1=5 3 ; CB= 9= 3 . Suy ra AC = CB . (2) MD 20 4 DE 12 4 MD DE T\u1eeb (1) v\u00e0 (2) suy ra \u2206ABC \u223d \u2206MED (c.g.c). Tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 ba (g.g) 7. \ta) \u2206BNM v\u00e0 \u2206ABC c\u00f3: M\uf0b7BN = C\uf0b7AB; M\uf0b7NB = C\uf0b7BA (so le trong). Do \u0111\u00f3 \u2206BNM \u223d \u2206ABC (g.g). b) Ta c\u00f3 \u2206BNM \u223d \u2206ABC, suy ra C\uf0b5 = M\uf0b5 = 48o. 8. \ta) \u2206MNP v\u00e0 \u2206DEF c\u00f3: N\uf0b5 = E\uf0b5, M\uf0b5 = D\uf0b5. Suy ra \u2206MNP \u223d \u2206DEF (g.g). Do \u0111\u00f3 NP = MP hay a \u000e 3 18 , suy ra a = 21. EF DF 32 24 b) \u2206AMB v\u00e0 \u2206CMD c\u00f3: B\uf0b7AM = D\uf0b7CM, A\uf0b7BM = C\uf0b7DM (so le trong). Suy ra \u2206AMB \u223d \u2206CMD (g.g). Do \u0111\u00f3 A=M A=B MB hay 6= 8= y . Suy ra x = 20; y = 4. CM CD MD 15 x 10 9. \ta) \u2206OHP v\u00e0 \u2206PHE c\u00f3: H\uf0b7OP = H\uf0b7PE, H\uf0b7PO = H\uf0b7EP. Suy ra \u2206OHP \u223d \u2206PHE (g.g). Do \u0111\u00f3 HP = OH , suy ra HP2 = HE . OH = 4 . 6 = 24. HE PH V\u1eady HP = 2 6 cm. 203","b) \u2206AFM v\u00e0 \u2206AME c\u00f3: A\uf0b7FM = A\uf0b7ME, A\uf0b5 l\u00e0 g\u00f3c chung. Suy ra \u2206AFM \u223d \u2206AME (g.g) Do \u0111\u00f3 AM = AF , suy ra AM2 = AE . AF. AE AM 10. Ch\u1ee9ng minh \u2206IAB \u223d \u2206ICD, t\u1eeb \u0111\u00f3 t\u00ednh \u0111\u01b0\u1ee3c IA = 7,2 km; ID = 2,6 km. T\u1eeb nh\u00e0 anh Thanh \u0111i \u0111\u1ebfn c\u00f4ng ty c\u00f3 c\u00e1c l\u1ed9 tr\u00ecnh: M \u2192 A \u2192 I \u2192 D \u2192 N c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 4,73 + 7,2 + 2,6 + 1,16 = 15,69 (km). M \u2192 A \u2192 I \u2192 C \u2192 N c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 4,73 + 7,2 + 2,4 + 1,84 = 16,17 (km). M \u2192 B \u2192 I \u2192 D \u2192 N c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 4,27 + 7,8 + 2,6 + 1,16 = 15,83 (km). M \u2192 B \u2192 I \u2192 C \u2192 N c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 4,27 + 7,8 + 2,4 + 1,84 = 16,31 (km). V\u1eady t\u1eeb nh\u00e0 anh Thanh \u0111i \u0111\u1ebfn c\u00f4ng ty theo l\u1ed9 tr\u00ecnh M \u2192 A \u2192 I \u2192 D \u2192 N s\u1ebd c\u00f3 chi\u1ec1u d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng ng\u1eafn nh\u1ea5t. B\u00e0i 3. C\u00c1C TR\u01af\u1edcNG H\u1ee2P \u0110\u1ed2NG D\u1ea0NG C\u1ee6A HAI TAM GI\u00c1C VU\u00d4NG I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t: \u2013 Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c vu\u00f4ng. \u2013 Gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 th\u1ef1c ti\u1ec5n g\u1eafn v\u1edbi vi\u1ec7c v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1ec1 hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc; m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc; s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5, ph\u01b0\u01a1ng ti\u1ec7n h\u1ecdc to\u00e1n. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng. II. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 B\u00f3ng c\u1ee7a m\u1ed9t c\u1ed9t c\u1edd tr\u00ean E B m\u1eb7t \u0111\u1ea5t d\u00e0i 6 m. C\u00f9ng A th\u1eddi \u0111i\u1ec3m \u0111\u00f3 m\u1ed9t thanh s\u1eaft cao 2,4 m c\u1eafm vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u1ea5t c\u00f3 b\u00f3ng d\u00e0i 1,8 m. T\u00ednh chi\u1ec1u cao c\u1ee7a c\u1ed9t c\u1edd. 2,4 m F 1,8 m D C 6m 204","M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110K\u0110: HS c\u00f3 c\u01a1 h\u1ed9i tr\u1ea3i nghi\u1ec7m, t\u00ecm hi\u1ec3u v\u1ec1 c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c vu\u00f4ng. K\u00edch th\u00edch kh\u1ea3 n\u0103ng t\u01b0 duy s\u00e1ng t\u1ea1o, v\u1eadn d\u1ee5ng \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf. 1. \u00c1p d\u1ee5ng c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a tam gi\u00e1c v\u00e0o tam gi\u00e1c vu\u00f4ng H\u0110KP 1 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 1: Gi\u00fap HS c\u00f3 c\u01a1 h\u1ed9i tr\u1ea3i nghi\u1ec7m, th\u1ea3o lu\u1eadn t\u1eeb tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai v\u00e0 th\u1ee9 ba c\u1ee7a hai tam gi\u00e1c, HS gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c vu\u00f4ng. \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 1: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1, ch\u1ed1t ki\u1ebfn th\u1ee9c. D Th\u1ef1c h\u00e0nh 1. Cho tam gi\u00e1c DEF vu\u00f4ng t\u1ea1i D c\u00f3 DH l\u00e0 \u0111\u01b0\u1eddng cao (H\u00ecnh 3). Ch\u1ee9ng minh r\u1eb1ng DE2 = EH . EF. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: HS th\u1ef1c h\u00e0nh v\u1eadn d\u1ee5ng E H F tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c vu\u00f4ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft Hi\u0300nh 3 c\u00e1c b\u00e0i to\u00e1n c\u1ee5 th\u1ec3. Qua th\u1ef1c h\u00e0nh gi\u00fap HS r\u00e8n luy\u1ec7n k\u0129 n\u0103ng c\u1ea7n \u0111\u1ea1t. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 1: HS th\u1ef1c hi\u1ec7n b\u00e0i th\u1ef1c h\u00e0nh tr\u00ean gi\u1ea5y nh\u00e1p, tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: \u2206DHE \u223d \u2206FDE (g.g), suy ra DE2 = EH . EF. V\u1eadn d\u1ee5ng 1. T\u00ednh chi\u1ec1u cao c\u1ee7a c\u1ed9t c\u1edd trong (trang 73). \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 1: Gi\u00fap HS c\u1ee7ng c\u1ed1, kh\u1eafc s\u00e2u, gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u00f4\u0323t s\u00f4\u0301 v\u1ea5n \u0111\u1ec1 th\u01b0\u0323c ti\u00ea\u0303n g\u1eafn v\u1edbi vi\u1ec7c v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1ec1 hai tam gi\u00e1c vu\u00f4ng \u0111\u1ed3ng d\u1ea1ng. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u1eadn d\u1ee5ng 1: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: \u2206ABC \u223d \u2206DEF (g.g), suy ra AB = 8. C\u1ed9t c\u1edd cao 8 m. 205","Th\u1ef1c h\u00e0nh 1. Cho tam gi\u00e1c DEF vu\u00f4ng t\u1ea1i D c\u00f3 DH l\u00e0 \u0111\u01b0\u1eddng cao (H\u00ecnh 3). Ch\u1ee9ng minh r\u1eb1ng DE2 = EH . EF. V\u1eadn d\u1ee5ng 1. T\u00ednh chi\u1ec1u cao c\u1ee7a c\u1ed9t c\u1edd trong (trang 73). EH F 2. Th\u00eam m\u1ed9t d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft hai tam gi\u00e1c vu\u00f4ng \u0111\u1ed3ng d\u1ea1ng Hi\u0300nh 3 2H.\u0110TKHP\u00ca2M M\u1ed8T D\u1ea4U HI\u1ec6U NH\u1eacN BI\u1ebeT HAITAM GI\u00c1CVU\u00d4NG \u0110\u1ed2NG D\u1ea0NG 2 Cho hai tam gi\u00e1c vu\u00f4ng ABC v\u00e0 DEF c\u00f3 c\u00e1c k\u00edch th\u01b0\u1edbc A C nh\u01b0 H\u00ecnh 4. 6 a) H\u00e3y t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh AC v\u00e0 DF. B 10 b) So s\u00e1nh c\u00e1c t\u1ec9 s\u1ed1 AB , AC v\u00e0 BC . D DE DF EF 9 c) D\u1ef1 \u0111o\u00e1n s\u1ef1 \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c ABC v\u00e0 DEF. E 15 F Hi\u0300nh 4 tr\u01b0\u1edd\u2013nMgvN\u1ee5h\u00e0\u1ebfc\u1ee3ump\u0111c\u1ed9\u00ed\u0111\u1ea1tcn\u1ed3chhn\u1ea1cngh\u1ee7hudagy\u1ea1\u00f3\u1ec1Hnncg\u0110vvcKu\u00e0\u1ea1\u00f4Pnmnhg\u1ed92gt:c\u00f3c\u1ee7Gc\u1ea1aniv\u00fathaupmg\u00f4H\u00f3ngcgSi\u00e1vvccu\u00e0\u00f3v\u00f4cunc\u1ea1\u00f4g\u01a1nnchgh\u1ee7\u1ed9hkaiiuattyartm\u1ec1\u1ea3hni\u00ecgnhciag\u1ee7\u00e1ichatiavh\u1ec7muam\u00f4i,gntaitg\u00e1hmcn\u1ea3o\u00e0vgyuil\u00e1\u00f4utc\u1ec9n\u1eadglnv\u1ec7u\u0111gv\u00f4\u00f3i\u1edbn\u1ea3\u0111iig\u1ed3c.tn\u1ea1hgn\u00edchdh\u1ea1hn\u0111ugy\u01b0.\u1ec1\u1ee3nc \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 2: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1Vn\u00edhdg\u1ee5i\u00e12,. cChh\u1ed1ot hkaii\u1ebfntamth\u1ee9gci\u00e1.c vu\u00f4ng ABC v\u00e0 ADE c\u00f3 c\u00e1c k\u00edch B Th\u1ef1thc\u01b0h\u1edb\u00e0cnnhh\u01b02.HT\u00ecnrohn5g. Ch\u1ee9ng minh r\u1eb1ng \u2206ADE \u223d \u2206ABC. tam gi\u00e1c DEF? 20 H\u00ecnh 6, tam gi\u00e1c n\u00e0o \u0111\u1ed3ng d\u1ea1ng v\u1edbi EGi\u1ea3i \u2206ADE v\u00e0 \u2206ABC c\u00f3: AE= 6= 1215; D=E 1=0 1. E A6C 12 BC 20 2 10 6 Suy raCAACE = DE . V\u1eady \u2206ADE \u223d \u2206ABC. D A 12 C BC S Hi\u0300nh 5 D F 74 20 N 4 12 8 36 R T MP AB Hi\u0300nh 6 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS th\u1ef1c h\u00e0nh v\u1eadn d\u1ee5ng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a hai tam gi\u00e1c vu\u00f4ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n c\u1ee5 th\u1ec3. Qua th\u1ef1c h\u00e0nh gi\u00fap HS r\u00e8n luy\u1ec7n k\u0129 n\u0103ng c\u1ea7n \u0111\u1ea1t. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 2: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. V\u1eadn d\u1ee5ng 2. Trong H\u00ecnh 7, bi\u1ebft \u2206MNP \u223d \u2206ABC v\u1edbi t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng k = MN , hai \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng A M AB H B CN K P \u1ee9ng l\u00e0 MK v\u00e0 AH. Hi\u0300nh 7 a) Ch\u1ee9ng minh r\u1eb1ng \u2206MNK \u223d \u2206ABH v\u00e0 MK = k. AH 206","b) G\u1ecdi S1 l\u00e0 di\u1ec7n t\u00edch tam gi\u00e1c MNP v\u00e0 S2 l\u00e0 di\u1ec7n t\u00edch tam gi\u00e1c ABC. Ch\u1ee9ng minh r\u1eb1ng S1 = k2. S2 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 2: Gi\u00fap HS gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u00f4\u0323t s\u00f4\u0301 v\u1ea5n \u0111\u1ec1 th\u01b0\u0323c ti\u00ea\u0303n g\u1eafn v\u1edbi vi\u1ec7c v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1ec1 hai tam gi\u00e1c vu\u00f4ng \u0111\u1ed3ng d\u1ea1ng. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u1eadn d\u1ee5ng 2: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: a) \u2206MNK v\u00e0 \u2206ABH c\u00f3 K\uf0b5 = H\uf0b5 = 90o; N\uf0b5 = B\uf0b5 , suy ra \u2206MNK \u223d \u2206ABH (g.g), suy ra M=K M=N k. AH AB b) S1 1 .MK . NP MK \u0098 NP k2. S2 2 AH BC 1 . AH.BC 2 Ch\u00fa \u00fd: T\u1eeb V\u1eadn d\u1ee5ng 2, GV cho HS nh\u1eadn x\u00e9t v\u1ec1 t\u1ec9 s\u1ed1 hai \u0111\u01b0\u1eddng cao v\u00e0 t\u1ec9 s\u1ed1 di\u1ec7n t\u00edch c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng. III. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. \t\u2206ABC \u223d \u2206QPR (g.g); \u2206DEF \u223d \u2206GHI (c.g.c); \u2206TUV \u223d \u2206MKN (c\u1ea1nh huy\u1ec1n \u2013 c\u1ea1nh g\u00f3c vu\u00f4ng). 2.\t a) \u2206DEF vu\u00f4ng t\u1ea1i D v\u00e0 \u2206HDF vu\u00f4ng t\u1ea1i H c\u00f3 \uf024F l\u00e0 g\u00f3c chung. Do \u0111\u00f3: \u2206DEF \u223d \u2206HDF (g.g). b) \u2206DEF \u223d \u2206HDF, suy ra DF = EF , suy ra DF2 = HF . EF. HF DF c) DF2 = EF . HF = 15 . 5,4 = 81. V\u1eady DF = 9 cm. 3. \t\u2206ABM \u223d \u2206EFM, suy ra AB = BM , suy ra AB = 16,5. EF FM V\u1eady chi\u1ec1u cao c\u1ee7a th\u00e1p l\u00e0 16,5 m. 4. \t\u2206AEB \u223d \u2206ADC, suy ra EB = AB , suy ra AC = 12; DC AC AE2 = BE2 \u2013 AB2 = 252 \u2013 202 = 225, suy ra AE = 15; EC = AE \u2013 AC = 15 \u2013 12 = 3 (cm). 5. a) \u2206ABH vu\u00f4ng t\u1ea1i H v\u00e0 \u2206DCB vu\u00f4ng t\u1ea1i B c\u00f3 A\uf0b7BH = D\uf0b7CB (hai g\u00f3c \u0111\u1ed3ng v\u1ecb), suy ra \u2206ABH \u223d \u2206DCB (g.g). b) \u2206BCD vu\u00f4ng t\u1ea1i B v\u00e0 \u2206BEA vu\u00f4ng t\u1ea1i B c\u00f3 A\uf0b7EB = D\uf0b7CB , suy ra \u2206BCD \u223d \u2206BEA, suy ra BC = BD . 207 BE BA","6. \t\u2206ABC \u223d \u2206FEC (g.g). B AB = AC , suy ra AB = 3.28, 2 = 70,5. FE FC 1, 2 Chi\u1ec1u cao c\u1ee7a to\u00e0 nh\u00e0: 70,5 + 1,5 = 72 (m).\t 7. \ta) \u2206AMH vu\u00f4ng t\u1ea1i M v\u00e0 \u2206AHB vu\u00f4ng t\u1ea1i H c\u00f3 B\uf0b7AH E l\u00e0 g\u00f3c chung n\u00ean \u2206AMH \u223d\u2206AHB (g.g). 3m b) Ch\u1ee9ng minh AH2 = AM . AB A Ch\u1ee9ng minh AH2 = AN . AC. 27 m F 1,2 m C Suy ra AM . AB = AN. AC\t N c) \u2206ANM v\u00e0 \u2206ABC c\u00f3 A\uf0b5 l\u00e0 g\u00f3c chung v\u00e0 A C AM = AN , suy ra \u2206ANM \u223d \u2206ABC (c.g.c). M AC AB d) T\u00ednh \u0111\u01b0\u1ee3c BC = 15 cm. SABC = 1 . AB . AC = 1 . AH . BC = 54 (cm2). B H 2 2 T\u00ednh \u0111\u01b0\u1ee3c AH = 7,2 cm v\u00e0 AH2 = AM . AB, suy ra AM = 5,76 cm. SANM \u00a7 AM \u00b72 \u00a7 5, 76 \u00b72 0, 2304 , suy ra SANM = 12,4416 cm2. SABC \u00a8\u00a9 AC \u00b9\u00b8 \u00a9\u00a8 12 \u00b9\u00b8 B\u00e0i 4. HAI H\u00ccNH \u0110\u1ed2NG D\u1ea0NG I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t: \u2013 Nh\u00e2\u0323n bi\u00ea\u0301t \u0111\u01b0\u01a1\u0323c hi\u0300nh \u0111\u00f4\u0300ng da\u0323ng ph\u00f4\u0301i ca\u0309nh (hi\u0300nh vi\u0323 t\u01b0\u0323), hi\u0300nh \u0111\u00f4\u0300ng da\u0323ng qua c\u00e1c h\u00ecnh \u1ea3nh c\u1ee5 th\u1ec3. \u2013 Nh\u1eadn bi\u1ebft \u0111\u01b0\u01a1\u0323c ve\u0309 \u0111e\u0323p trong t\u01b0\u0323 nhi\u00ean, ngh\u00ea\u0323 thu\u00e2\u0323t, ki\u00ea\u0301n tru\u0301c, c\u00f4ng ngh\u00ea\u0323 ch\u00ea\u0301 ta\u0323o, ... bi\u00ea\u0309u hi\u00ea\u0323n qua hi\u0300nh \u0111\u00f4\u0300ng da\u0323ng. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5, ph\u01b0\u01a1ng ti\u1ec7n h\u1ecdc to\u00e1n. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. \u0110\u1ec3 HS d\u1ec5 d\u00e0ng nh\u1eadn bi\u1ebft h\u00ecnh \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh \u0111i t\u1eeb \u0111o\u1ea1n th\u1eb3ng, tam gi\u00e1c r\u1ed3i t\u1ee9 gi\u00e1c, GV n\u00ean th\u1ef1c hi\u1ec7n H\u0110KP 1 v\u00e0 H\u0110KP 2 c\u00f9ng l\u00fac, kh\u00f4ng t\u00e1ch bi\u1ec7t. 2. \u0110\u1ec3 \u0111\u1ea1t hi\u1ec7u qu\u1ea3 cao khi gi\u1ea3ng d\u1ea1y b\u00e0i n\u00e0y, GV n\u00ean t\u1eadn d\u1ee5ng c\u00e1c \u1ee9ng d\u1ee5ng c\u1ee7a c\u00f4ng ngh\u1ec7 th\u00f4ng tin, c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ngay \u0111i\u1ec7n tho\u1ea1i th\u00f4ng minh c\u00f3 s\u1eb5n c\u1ee7a GV v\u00e0 HS. 208","III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 Nh\u1eefng c\u00e0nh l\u00e1 nh\u01b0 h\u00ecnh b\u00ean kh\u00e1c nhau v\u1ec1 k\u00edch th\u01b0\u1edbc nh\u01b0ng gi\u1ed1ng nhau v\u1ec1 h\u00ecnh d\u1ea1ng. Em c\u00f3 th\u1ec3 n\u00eau th\u00eam nh\u1eefng s\u1ef1 v\u1eadt c\u00f3 \u0111\u1eb7c \u0111i\u1ec3m nh\u01b0 v\u1eady kh\u00f4ng? M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110K\u0110: HS c\u00f3 c\u01a1 h\u1ed9i tr\u1ea3i nghi\u1ec7m, t\u00ecm hi\u1ec3u v\u1ec1 c\u00e1c h\u00ecnh \u0111\u1ed3ng d\u1ea1ng trong t\u1ef1 nhi\u00ean v\u00e0 \u0111\u1eddi s\u1ed1ng. C\u1ea3m nh\u1eadn \u0111\u01b0\u1ee3c v\u1ebb \u0111\u1eb9p c\u1ee7a c\u00e1c h\u00ecnh \u0111\u1ed3ng d\u1ea1ng. 1. H\u00ecnh \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh H\u0110KP 1, 2 209","\u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 1, 2: Gi\u00fap HS c\u00f3 c\u01a1 h\u1ed9i tr\u1ea3i nghi\u1ec7m, th\u1ea3o lu\u1eadn nh\u1eadn bi\u1ebft h\u00ecnh \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh qua c\u00e1c h\u00ecnh \u1ea3nh \u0111\u01a1n gi\u1ea3n l\u00e0 tam gi\u00e1c v\u00e0 t\u1ee9 gi\u00e1c. \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 1, 2: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1, ch\u1ed1t ki\u1ebfn th\u1ee9c. Qua H\u0110KP 1, GV c\u1ea7n nh\u1ea5n m\u1ea1nh v\u1edbi m\u1ed7i \u0111i\u1ec3m M thu\u1ed9c h\u00ecnh F\u2032, l\u1ea5y \u0111i\u1ec3m M\u2032 thu\u1ed9c tia OM sao cho OM\u2032 = 3OM th\u00ec c\u00e1c \u0111i\u1ec3m M\u2032 \u0111\u00f3 t\u1ea1o th\u00e0nh h\u00ecnh F\u2032. Ta n\u00f3i h\u00ecnh F\u2032 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh F theo t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng k = 3. T\u01b0\u01a1ng t\u1ef1 trong H\u0110KP 2, h\u00ecnh H\u2032 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh H theo t\u1ec9 s\u1ed1 k = 1 . 2 T\u1eeb \u0111\u00f3 \u0111\u01b0a ra nh\u1eadn x\u00e9t v\u1ec1 y\u1ebfu t\u1ed1 ph\u00f3ng to ho\u1eb7c thu nh\u1ecf c\u1ee7a h\u00ecnh \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh tu\u1ef3 theo t\u1ec9 s\u1ed1 k > 1 ho\u1eb7c k < 1. Th\u1ef1c h\u00e0nh 1. Cho ba t\u1ea5m \u1ea3nh \u0111\u01b0\u1ee3c \u0111\u1eb7t tr\u00ean l\u01b0\u1edbi \u00f4 vu\u00f4ng nh\u01b0 H\u00ecnh 4. H\u00e3y ch\u1ec9 ra ba c\u1eb7p h\u00ecnh, trong m\u1ed7i c\u1eb7p h\u00ecnh c\u00f3 h\u00ecnh n\u00e0y \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh kia v\u00e0 ch\u1ec9 ra t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng t\u01b0\u01a1ng \u1ee9ng. A\u2032\u2032 D\u2032\u2032 AD A\u2032 D\u2032 O B\u2032 C\u2032 B C B\u2032\u2032 C\u2032\u2032 Hi\u0300nh 4 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: Gi\u00fap HS r\u00e8n luy\u1ec7n k\u0129 n\u0103ng c\u1ea7n \u0111\u1ea1t th\u00f4ng qua nh\u1eadn bi\u1ebft h\u00ecnh \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh \u1ee9ng v\u1edbi t\u1ec9 s\u1ed1 k > 1 ho\u1eb7c k < 1. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 1: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: H\u00ecnh ABCD \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh A\u2032B\u2032C\u2032D\u2032 theo t\u1ec9 s\u1ed1 k = 2 (ho\u1eb7c h\u00ecnh A\u2032B\u2032C\u2032D\u2032 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh ABCD theo t\u1ec9 s\u1ed1 k = 1 ). 2 H\u00ecnh A\u2033B\u2033C\u2033D\u2033 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh A\u2032B\u2032C\u2032D\u2032 theo t\u1ec9 s\u1ed1 k = 3 (ho\u1eb7c h\u00ecnh A\u2032B\u2032C\u2032D\u2032 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh A\u2033B\u2033C\u2033D\u2033 theo t\u1ec9 s\u1ed1 k = 1). 3 H\u00ecnh A\u2033B\u2033C\u2033D\u2033 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh ABCD theo t\u1ec9 s\u1ed1 k = 3 (ho\u1eb7c h\u00ecnh ABCD 2 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh A\u2033B\u2033C\u2033D\u2033 theo t\u1ec9 s\u1ed1 k = 2 ). 3 210","2. Hai h\u00ecnh \u0111\u1ed3ng d\u1ea1ng H2.\u0110HKPAI3H\u00ccNH \u0110\u1ed2NG D\u1ea0NG 3 Trong H\u00ecnh 5, bi\u1ebft h\u00ecnh H1 \u0111\u1ed3ng d\u1ea1ng ph\u1ed1i c\u1ea3nh v\u1edbi h\u00ecnh H theo t\u1ec9 s\u1ed1 k= 3. 2 a) T\u00ednh x, y. b) So s\u00e1nh h\u00ecnh H1 v\u1edbi h\u00ecnh H'. y 2 cm 5,4 cm 3,6 cm x 3 cm H H1 H' Hi\u0300nh 5 \u0111\u1ed3n\u2013gMdvH\u1ea1\u1ee5\u00e0nacigbh.\u0111\u1eb1\u00ecn\u00edncghhhHc\u00ecn\u1ee7h,aHHH'\u0110'\u0111. K\u01b0\u1ee3Pc3g:\u1ecdiGl\u00e0i\u00fa\u0111p\u1ed3nHgSd\u1ea1cn\u00f3gcn\u01a1\u1ebfuhc\u1ed9\u00f3i htr\u00ec\u1ea3nihnHgh1i\u0111\u1ec7\u1ed3mn,gtdh\u1ea1\u1ea3noglpuh\u1ead\u1ed1ni nc\u1ea3hn\u1eadhnvb\u1edbii\u1ebfht\u00ecnhh\u00ecnHh \u2013 G\u01a1\u0323i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 3: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1Nnh\u1eadgni\u00e1x,\u00e9tc:hN\u1ed1thk\u01b0i\u1ebfvn\u1eadyt,hh\u1ee9\u00eccn.h H \u0111\u1ed3ng d\u1ea1ng v\u1edbi h\u00ecnh H' n\u1ebfu H' b\u1eb1ng H ho\u1eb7c b\u1eb1ng m\u1ed9t TTh\u00ecm\u1ef1Vhhc\u00ec\u00ect\u00ednn\u1ec9hdhhs\u00e0\u1ee5\u1ed1pGn8h2\u0111h,\u00f3.\u1ed34\u0111n2Tn\u1ed3cg.gmrnoTgtdnor\u1ea1gdohn\u1ea1ncogng\u00e1\u1eb7gctcH\u01b0vht\u01a1\u1edb\u00ech\u00ecnnnuihghhn\u00ec7\u1ee9dhn\u01b0\u1ecfnhd\u1edbg\u01b0cKi.\u1ee7\u1edb\u0111ai\u00e2tH\u0111hye\u00e2, oyh.,\u00ectn\u1ec9hhs\u00e3\u1ed1y=Hkch\u0111\u1ecd\u1ed312n=n,,84rgadc\u1ea1\u00e143nc.gcv\u1eb7\u1edbpi hh\u00ec\u00ecnnhh I\u0111\u1ed3tnhgeod\u1ea1t\u1ec9nsg\u1ed1vk=\u1edbi n64h=au23. , 4 cm 4,8 cm 2,4 cm 4,8 cm 3 cm 3 cm 1,8 cm 6 cm M NP Q Hi\u0300nh 7 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7Ha Th\u1ef1c h\u00e0nh 2: Gi\u00fap HS GrH\u00e8in\u0300nhlu6y\u1ec7n k\u0129 n\u0103ng cI\u1ea7n \u0111\u1ea1t th\u00f4ng qua nhK\u1eadn bi\u1ebft h\u00ecnh \u0111T\u1ed3hn\u1ef1gcdh\u1ea1n\u00e0gn.h 2. Trong H\u00ecnh 7 d\u01b0\u1edbi \u0111\u00e2y, h\u00e3y ch\u1ecdn ra c\u00e1c c\u1eb7p h\u00ecnh \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau. \u2013 GT\u1ee3\u00ecim\u00fd tt\u1ec9\u1ed5sc\u1ed1h\u0111\u1ee9\u1ed3cnTghd\u1ef1\u1ea1cngh\u00e0tn\u01b0h\u01a1n2g: T\u1ee9hn\u1ea3go. lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. 8,4 cm H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: H\u00ecnh M \u0111\u1ed3ng d\u1ea1ng v\u1edbi h\u00ecnh P theo t4\u1ec9,8s\u1ed1cmk = 7, h\u00ecnh N4,8 c\u0111m\u1ed3ng d\u1ea1ng v\u1edbi h\u00ecnh Q theo t\u1ec9 s\u1ed1 k = 5 . 4 8 211 M N P Q 79 Hi\u0300nh 7","V\u1eadn d\u1ee5ng. Trong c\u00e1c H\u00ecnh 8b, c, d, h\u00ecnh n\u00e0o \u0111\u1ed3ng d\u1ea1ng v\u1edbi H\u00ecnh 8a? Gi\u1ea3i th\u00edch. 9 cm 7,5 cm 5 cm 5 cm a) b) 4,5 cm 12 cm 2,5 cm 4 cm c) Hi\u0300nh 8 d) \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng: Gi\u00fap HS nh\u1eadn bi\u1ebft h\u00ecnh \u0111\u1ed3ng d\u1ea1ng d\u1ef1a v\u00e0o t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u1eadn d\u1ee5ng: Th\u1ea3o lu\u1eadn nh\u00f3m, c\u00e1c nh\u00f3m tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3, l\u1edbp nh\u1eadn x\u00e9t, GV \u0111\u00e1nh gi\u00e1. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: H\u00ecnh 8c \u0111\u1ed3ng d\u1ea1ng v\u1edbi h\u00ecnh 8a theo t\u1ec9 s\u1ed1 k = 1 . 2 3. H\u00ecnh \u0111\u1ed3ng d\u1ea1ng trong t\u1ef1 nhi\u00ean v\u00e0 \u0111\u1eddi s\u1ed1ng B\u1eb1ng h\u00ecnh \u1ea3nh, GV gi\u1edbi thi\u1ec7u cho HS th\u1ea5y vai tr\u00f2 c\u1ee7a h\u00ecnh \u0111\u1ed3ng d\u1ea1ng trong t\u1ef1 nhi\u00ean v\u00e0 \u0111\u1eddi s\u1ed1ng. GV c\u00f3 th\u1ec3 s\u01b0u t\u1ea7m th\u00eam c\u00e1c h\u00ecnh \u0111\u1ed3ng d\u1ea1ng \u0111\u1ec3 gi\u1edbi thi\u1ec7u cho HS ho\u1eb7c giao cho c\u00e1c t\u1ed5, nh\u00f3m HS s\u01b0u t\u1ea7m c\u00e1c h\u00ecnh \u0111\u1ed3ng d\u1ea1ng tr\u00ean Internet v\u00e0 tr\u00ecnh b\u00e0y tr\u01b0\u1edbc l\u1edbp. IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. \tH\u00ecnh 14a v\u1edbi H\u00ecnh 14g l\u00e0 c\u1eb7p h\u00ecnh \u0111\u1ed3ng d\u1ea1ng. H\u00ecnh 14b v\u1edbi H\u00ecnh 14d l\u00e0 c\u1eb7p h\u00ecnh \u0111\u1ed3ng d\u1ea1ng. H\u00ecnh 14c v\u1edbi H\u00ecnh 14e l\u00e0 c\u1eb7p h\u00ecnh \u0111\u1ed3ng d\u1ea1ng. 2. \tH\u00ecnh 15a \u0111\u1ed3ng d\u1ea1ng v\u1edbi H\u00ecnh 15b theo t\u1ec9 s\u1ed1 k = 2 . 3 3. \tH\u00ecnh 16b \u0111\u1ed3ng d\u1ea1ng v\u1edbi H\u00ecnh 16a theo t\u1ec9 s\u1ed1 k = 3 . 2 4. \tV\u1edbi k = 1,5 th\u00ec k\u00edch th\u01b0\u1edbc H\u00ecnh 17b l\u00e0 6 \u00d7 9. 212","B\u00c0I T\u1eacP CU\u1ed0I CH\u01af\u01a0NG 8 C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M 3. D 4. D 7. C 8. C 1. B 2. A 5. B 6. B B\u00c0I T\u1eacP T\u1ef0 LU\u1eacN 9. a) X\u00e9t \u2206ABD v\u00e0 \u2206ACB c\u00f3 A\uf0b5 l\u00e0 g\u00f3c chung, A\uf0b7BD = A\uf0b7CB. Suy ra \u2206ABD \u223d \u2206ACB (g.g). b) \u2206ABD \u223d \u2206ACB, suy ra AB2 = AD . AC = 4 . 9 = 36. V\u1eady AB = 6 cm. 10. a) X\u00e9t \u2206ABD v\u00e0 \u2206BDC c\u00f3 A\uf0b7DB = D\uf0b7CB (gi\u1ea3 thi\u1ebft); A\uf0b7BD = B\uf0b7DC (so le trong). Suy ra \u2206ABD \u223d \u2206BDC (g.g), suy ra AB = BD , suy ra BD2 = AB . DC. BD DC b) X\u00e9t \u2206EFH v\u00e0 \u2206FHG c\u00f3 H\uf0b7EF = H\uf0b7FG (gi\u1ea3 thi\u1ebft); E\uf0b7FH = F\uf0b7HG (so le trong). Suy ra \u2206EFH \u223d \u2206FHG (g.g), suy ra EF = HF , suy ra HF2 = EF . HG = 9 . 16 = 144. HF HG V\u1eady HF = 12 m. 11. a) HM = 20 m. b) MN d\u00e0i kho\u1ea3ng 44 m. 12. \u2206MNE \u223d \u2206ABC (g.g), suy ra MN = ME , suy ra 2 = 1,5 . AB AC AB 6 Do \u0111\u00f3 AB = 8. Chi\u1ec1u cao ng\u00f4i nh\u00e0 l\u00e0 8 m. 13. \u2206KDE \u223d \u2206KFD (g.g), suy ra DK2 = KE . KF = 14 400. V\u1eady DK = 120 m. 14. a) \u2206AEB vu\u00f4ng t\u1ea1i E v\u00e0 \u2206AFC vu\u00f4ng t\u1ea1i F c\u00f3 A\uf0b5 l\u00e0 g\u00f3c chung, suy ra \u2206AEB\u223d\u2206AFC (g.g). b) \u2206HEC \u223d \u2206HFB (g.g), suy ra HE = HF . A E HC HB F c) Ta c\u00f3 HE = HF ; E\uf0b7HF = C\uf0b7HB (\u0111\u1ed1i \u0111\u1ec9nh). H HC HB Suy ra \u2206HEF \u223d \u2206HCB (c.g.c).\t B C 213","15. a) Ch\u1ee9ng minh \u2206AMB \u223d \u2206ANC, suy ra AM = AB . A M AN AC I Ta c\u00f3 AM = AN v\u00e0 A\uf0b5 l\u00e0 g\u00f3c chung, N AB AC suy ra \u2206AMN \u223d \u2206ABC (c.g.c). b) \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong \u2206AMN, B K C C IM AM ta c\u00f3 = . \t IN AN \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong \u2206ABC, ta c\u00f3 KB = AB . KC AC AM = AB IM KB V\u00ec n\u00ean =. AN AC IN KC 16. a) X\u00e9t \u2206ABH v\u00e0 \u2206CBA c\u00f3 A\uf0b7HB = B\uf0b7AC = 90o, AI B\uf0b5 l\u00e0 g\u00f3c chung n\u00ean \u2206ABH \u223d \u2206CBA (g.g), F suy ra AB = BH , suy ra AB2 = BH . BC. E H N CB BA B b) \u2206ABH \u223d \u2206AHE (g.g), suy ra AB = AH , AH AE suy ra AH2 = AB . AE.\t\t\t (1) \u2206ACH \u223d \u2206AHF (g.g), suy ra AC = AH , AH AF suy ra AH2 = AC . AF. \t\t\t (2) T\u1eeb (1) v\u00e0 (2) suy ra AE . AB = AF . AC. c) V\u00ec AE . AB = AF . AC n\u00ean AE = AF . AC AB X\u00e9t \u2206AFE v\u00e0 \u2206ABC ta c\u00f3 B\uf0b7AC l\u00e0 g\u00f3c chung v\u00e0 AE = AF , suy ra \u2206AFE\u223d\u2206ABC (c.g.c). AC AB d) \u2206HIN vu\u00f4ng t\u1ea1i N v\u00e0 \u2206HCF vu\u00f4ng t\u1ea1i F c\u00f3 I\uf0b7HC l\u00e0 g\u00f3c chung n\u00ean \u2206HIN \u223d \u2206HCF (g.g), suy ra HI HN hay HN = HF . = HC HF HI HC X\u00e9t \u2206HNF v\u00e0 \u2206HIC c\u00f3 HN = HF v\u00e0 I\uf0b7HC l\u00e0 g\u00f3c chung, suy ra \u2206HNF \u223d \u2206HIC (c.g.c). HI HC 17. a) X\u00e9t \u2206DEF v\u00e0 \u2206AMC c\u00f3 E\uf0b5 = M\uf0b5 = 36o, F = C = 76o, suy ra \u2206DEF \u223d \u2206AMC (g.g). b) \u2206DEF \u223d \u2206AMC, suy ra DF = EF . AC MC GV h\u01b0\u1edbng d\u1eabn HS \u0111o chi\u1ec1u d\u00e0i c\u1ea1nh DF tr\u00ean v\u1edf v\u00e0 t\u00ednh AC. 214","Ph\u1ea7n M\u1ed8T S\u1ed0 Y\u1ebeU T\u1ed0 TH\u1ed0NG K\u00ca V\u00c0 X\u00c1C SU\u1ea4T Ch\u01b0\u01a1ng 9 M\u1ed8T S\u1ed0 Y\u1ebeU T\u1ed0 X\u00c1C SU\u1ea4T A. M\u1ee4C TI\u00caU 1. N\u0103ng l\u01b0\u0323c chuy\u00ean m\u00f4n \u2013 S\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c t\u1ec9 s\u1ed1 \u0111\u1ec3 m\u00f4 t\u1ea3 x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t bi\u1ebfn c\u1ed1 ng\u1eabu nhi\u00ean trong m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n. \u2013 Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a m\u1ed9t bi\u1ebfn c\u1ed1 v\u1edbi x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 \u0111\u00f3 th\u00f4ng qua m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n. 2. N\u0103ng l\u01b0\u0323c chung \u2013 N\u0103ng l\u01b0\u0323c t\u01b0\u0323 chu\u0309 va\u0300 t\u01b0\u0323 ho\u0323c trong ti\u0300m to\u0300i, kha\u0301m pha\u0301. \u2013 N\u0103ng l\u01b0\u0323c giao ti\u00ea\u0301p va\u0300 h\u01a1\u0323p ta\u0301c trong tri\u0300nh ba\u0300y, tha\u0309o lu\u00e2\u0323n va\u0300 la\u0300m vi\u00ea\u0323c nho\u0301m. \u2013 N\u0103ng l\u01b0\u0323c gia\u0309i quy\u00ea\u0301t v\u00e2\u0301n \u0111\u00ea\u0300 va\u0300 sa\u0301ng ta\u0323o trong th\u01b0\u0323c ha\u0300nh va\u0300 v\u00e2\u0323n du\u0323ng. 3. Hi\u0300nh tha\u0300nh ca\u0301c ph\u00e2\u0309m ch\u00e2\u0301t \u2013 Y\u00eau n\u01b0\u01a1\u0301c, nh\u00e2n \u00e1i. \u2013 Ch\u0103m chi\u0309, trung th\u01b0\u0323c, tra\u0301ch nhi\u00ea\u0323m. B. H\u01af\u1edaNG D\u1eaaN D\u1ea0Y H\u1eccC B\u00e0i 1. M\u00d4 T\u1ea2 X\u00c1C SU\u1ea4T B\u1eb0NG T\u1ec8 S\u1ed0 I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u00e2\u0300n \u0111a\u0323t: s\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c t\u1ec9 s\u1ed1 \u0111\u1ec3 m\u00f4 t\u1ea3 x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t bi\u1ebfn c\u1ed1 ng\u1eabu nhi\u00ean trong m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u00ea\u0301p toa\u0301n ho\u0323c. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng, t\u00edch h\u1ee3p c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. \u1ede L\u1edbp 7, HS \u0111\u00e3 l\u00e0m quen v\u1edbi vi\u1ec7c d\u00f9ng x\u00e1c su\u1ea5t \u0111\u1ec3 m\u00f4 t\u1ea3 kh\u1ea3 n\u0103ng x\u1ea3y ra c\u1ee7a m\u1ed7i k\u1ebft qu\u1ea3 ri\u00eang l\u1ebb c\u1ee7a ph\u00e9p th\u1eed. Trong b\u00e0i n\u00e0y, HS s\u1ebd \u0111\u01b0\u1ee3c l\u00e0m quen v\u1edbi vi\u1ec7c m\u00f4 t\u1ea3 x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 g\u1ed3m nhi\u1ec1u k\u1ebft qu\u1ea3 th\u00f4ng qua t\u1ec9 s\u1ed1 gi\u1eefa s\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i v\u00e0 s\u1ed1 k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 x\u1ea3y ra. 215","2. GV nh\u1ea5n m\u1ea1nh cho HS c\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t trong b\u00e0i ch\u1ec9 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c khi t\u1ea5t c\u1ea3 c\u00e1c k\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p th\u1eed c\u00f3 c\u00f9ng kh\u1ea3 n\u0103ng x\u1ea3y ra. \u0110\u1ec3 bi\u1ebft c\u00e1c k\u1ebft qu\u1ea3 c\u00f3 c\u00f9ng kh\u1ea3 n\u0103ng, HS ch\u00fa \u00fd \u0111\u1ebfn c\u00e1c \u201ct\u1eeb kho\u00e1\u201d li\u00ean quan \u0111\u1ebfn ph\u00e9p th\u1eed: \u0111\u1ed3ng xu, x\u00fac x\u1eafc c\u00e2n \u0111\u1ed1i v\u00e0 \u0111\u1ed3ng ch\u1ea5t; c\u00e1c th\u1ebb c\u00f9ng lo\u1ea1i, c\u00f9ng k\u00edch th\u01b0\u1edbc; qu\u1ea3 b\u00f3ng, vi\u00ean bi c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng. III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 M\u1ed9t h\u1ed9p c\u00f3 1 qu\u1ea3 b\u00f3ng xanh v\u00e0 4 qu\u1ea3 b\u00f3ng \u0111\u1ecf c\u00f3 k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng nh\u01b0 nhau. Ch\u00e2u l\u1ea5y ra ng\u1eabu nhi\u00ean 1 qu\u1ea3 b\u00f3ng t\u1eeb h\u1ed9p. Theo em, kh\u1ea3 n\u0103ng Ch\u00e2u l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng \u0111\u1ecf b\u1eb1ng m\u1ea5y l\u1ea7n kh\u1ea3 n\u0103ng l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh? \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110K\u0110: Gi\u00fap HS nh\u1edb l\u1ea1i c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 X\u00e1c su\u1ea5t \u0111\u00e3 h\u1ecdc \u1edf c\u00e1c l\u1edbp tr\u01b0\u1edbc, \u0111\u1ed3ng th\u1eddi \u0111\u1eb7t HS v\u00e0o t\u00ecnh hu\u1ed1ng c\u00f3 v\u1ea5n \u0111\u1ec1 khi ph\u1ea3i x\u00e1c \u0111\u1ecbnh xem kh\u1ea3 n\u0103ng x\u1ea3y ra c\u1ee7a bi\u1ebfn c\u1ed1 n\u00e0y b\u1eb1ng m\u1ea5y l\u1ea7n kh\u1ea3 n\u0103ng x\u1ea3y ra c\u1ee7a bi\u1ebfn c\u1ed1 kh\u00e1c. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c H\u0110K\u0110: GV n\u00eau v\u1ea5n \u0111\u1ec1, y\u00eau c\u1ea7u HS th\u1ea3o lu\u1eadn v\u1ec1 \u00fd ngh\u0129a c\u1ee7a gi\u1ea3 thi\u1ebft c\u00e1c qu\u1ea3 b\u00f3ng c\u00f3 k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng nh\u01b0 nhau, c\u00e1ch \u0111o kh\u1ea3 n\u0103ng x\u1ea3y ra c\u1ee7a m\u1ed9t bi\u1ebfn c\u1ed1. 1. K\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i H\u0110KP 1 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 1: Gi\u00fap HS \u00f4n l\u1ea1i c\u00e1ch li\u1ec7t k\u00ea c\u00e1c k\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p th\u1eed v\u00e0 li\u1ec7t k\u00ea c\u00e1c k\u1ebft qu\u1ea3 l\u00e0m cho m\u1ed9t ph\u00e9p th\u1eed x\u1ea3y ra. Ho\u1ea1t \u0111\u1ed9ng n\u00e0y l\u00e0 b\u01b0\u1edbc \u0111\u1ec7m \u0111\u1ec3 h\u00ecnh th\u00e0nh kh\u00e1i ni\u1ec7m \u201cthu\u1eadn l\u1ee3i\u201d. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 1: GV n\u00eau v\u1ea5n \u0111\u1ec1, HS th\u1ea3o lu\u1eadn theo nh\u00f3m \u0111\u1ec3 t\u00ecm c\u00e2u tr\u1ea3 l\u1eddi. V\u00ed d\u1ee5 1. Trong ph\u00e9p th\u1eed l\u1ea5y th\u1ebb \u1edf 1, x\u00e9t c\u00e1c bi\u1ebfn c\u1ed1 sau: \t C: \u201cS\u1ed1 ghi tr\u00ean th\u1ebb l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1\u201d; \t D: \u201cS\u1ed1 ghi tr\u00ean th\u1ebb l\u00e0 s\u1ed1 l\u1ebb\u201d. H\u00e3y n\u00eau c\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho m\u1ed7i bi\u1ebfn c\u1ed1 C v\u00e0 D. 216","\u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u00ed d\u1ee5 1: HS l\u00e0m quen v\u1edbi kh\u00e1i ni\u1ec7m \u201cthu\u1eadn l\u1ee3i\u201d th\u00f4ng qua vi\u1ec7c li\u1ec7t k\u00ea c\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho m\u1ed9t bi\u1ebfn c\u1ed1. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u00ed d\u1ee5 1: GV n\u00eau v\u1ea5n \u0111\u1ec1 v\u00e0 d\u1eabn d\u1eaft HS gi\u1ea3i quy\u1ebft. GV l\u01b0u \u00fd n\u1ebfu \u0111\u1ec1 b\u00e0i y\u00eau c\u1ea7u x\u00e1c \u0111\u1ecbnh t\u1eadp h\u1ee3p c\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i th\u00ec ph\u1ea3i d\u00f9ng d\u1ea5u ngo\u1eb7c nh\u1ecdn {} \u0111\u1ec3 m\u00f4 t\u1ea3 t\u1eadp h\u1ee3p. Th\u1ef1c h\u00e0nh 1. Tr\u00ean b\u00e0n c\u00f3 m\u1ed9t t\u1ea5m b\u00eca h\u00ecnh tr\u00f2n \u0111\u01b0\u1ee3c chia 78 12 th\u00e0nh 8 h\u00ecnh qu\u1ea1t b\u1eb1ng nhau v\u00e0 \u0111\u01b0\u1ee3c \u0111\u00e1nh s\u1ed1 65 43 t\u1eeb 1 \u0111\u1ebfn 8 nh\u01b0 H\u00ecnh 1. Xoay t\u1ea5m b\u00eca quanh t\u00e2m h\u00ecnh tr\u00f2n v\u00e0 xem khi t\u1ea5m b\u00eca d\u1eebng l\u1ea1i, m\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 ghi s\u1ed1 n\u00e0o. X\u00e9t c\u00e1c bi\u1ebfn c\u1ed1 sau: A: \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 ghi s\u1ed1 ch\u1eb5n\u201d; B: \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 ghi s\u1ed1 chia h\u1ebft cho 4\u201d; C: \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 ghi s\u1ed1 nh\u1ecf h\u01a1n 3\u201d. H\u00e3y n\u00eau c\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho m\u1ed7i bi\u1ebfn c\u1ed1 tr\u00ean. Hi\u0300nh 1 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: HS c\u1ee7ng c\u1ed1 c\u00e1ch n\u00eau k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho m\u1ed7i bi\u1ebfn c\u1ed1. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 1: HS l\u00e0m vi\u1ec7c c\u00e1 nh\u00e2n. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: \u2013 C\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 A l\u00e0 2; 4; 6; 8. \u2013 C\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 B l\u00e0 4; 8. \u2013 C\u00e1c k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 C l\u00e0 1; 2. 2. M\u00f4 t\u1ea3 x\u00e1c su\u1ea5t b\u1eb1ng t\u1ec9 s\u1ed1 H\u0110KP 2 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 2: L\u00e0m quen v\u1edbi x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 c\u1ee7a ph\u00e9p th\u1eed \u0111\u01a1n gi\u1ea3n. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 2: GV \u0111\u1eb7t v\u1ea5n \u0111\u1ec1; HS th\u1ea3o lu\u1eadn theo nh\u00f3m \u0111\u1ec3 t\u00ecm c\u00e2u tr\u1ea3 l\u1eddi; GV nh\u1ea5n m\u1ea1nh hai \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a ph\u00e9p th\u1eed: s\u1ed1 k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 x\u1ea3y ra, c\u00e1c k\u1ebft qu\u1ea3 c\u00f3 c\u00f9ng kh\u1ea3 n\u0103ng x\u1ea3y ra. V\u00ed d\u1ee5 2. Trong ph\u00e9p th\u1eed gieo m\u00f4\u0323t con x\u00fac x\u1eafc \u1edf 2, t\u00ednh x\u00e1c su\u1ea5t c\u1ee7a c\u00e1c bi\u1ebfn c\u1ed1 sau: \t A: \u201cGieo \u0111\u01b0\u1ee3c m\u1eb7t c\u00f3 s\u1ed1 ch\u1ea5m l\u00e0 s\u1ed1 l\u1ebb\u201d; \t B: \u201cGieo \u0111\u01b0\u1ee3c m\u1eb7t c\u00f3 nhi\u1ec1u h\u01a1n 3 ch\u1ea5m\u201d. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u00ed d\u1ee5 2: L\u00e0m quen v\u1edbi vi\u1ec7c v\u1eadn d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 \u0111\u01a1n gi\u1ea3n. 217","\u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u00ed d\u1ee5 2: GV n\u00eau v\u1ea5n \u0111\u1ec1 v\u00e0 d\u1eabn d\u1eaft HS tr\u1ea3 l\u1eddi, GV l\u01b0u \u00fd HS c\u00e1ch l\u1eadp lu\u1eadn \u0111\u1ec3 t\u00ednh x\u00e1c su\u1ea5t, GV gi\u1edbi thi\u1ec7u kh\u00e1i ni\u1ec7m bi\u1ebfn c\u1ed1 \u201c\u0111\u1ed3ng kh\u1ea3 n\u0103ng\u201d. Th\u1ef1c h\u00e0nh 2. H\u00e3y tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi \u1edf (trang 88). \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: C\u1ee7ng c\u1ed1 c\u00e1ch v\u1eadn d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 \u0111\u01a1n gi\u1ea3n. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 2: HS th\u1ea3o lu\u1eadn nh\u00f3m. GV l\u01b0u \u00fd t\u1eeb kho\u00e1 \u201ck\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng nh\u01b0 nhau\u201d. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: Bi\u1ebfn c\u1ed1 Ch\u00e2u l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng \u0111\u1ecf c\u00f3 x\u00e1c su\u1ea5t l\u00e0 4 . 5 Bi\u1ebfn c\u1ed1 Ch\u00e2u l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh c\u00f3 x\u00e1c su\u1ea5t l\u00e0 1 . 5 Do \u0111\u00f3 kh\u1ea3 n\u0103ng Ch\u00e2u l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng \u0111\u1ecf b\u1eb1ng 4 l\u1ea7n kh\u1ea3 n\u0103ng Ch\u00e2u l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh. V\u00ed d\u1ee5 3. T\u1ec9 l\u1ec7 th\u00e0nh vi\u00ean n\u1eef c\u1ee7a m\u1ed9t c\u00e2u l\u1ea1c b\u1ed9 ngh\u1ec7 thu\u1eadt l\u00e0 60%. T\u1ed5ng s\u1ed1 th\u00e0nh vi\u00ean c\u1ee7a c\u00e2u l\u1ea1c b\u1ed9 l\u00e0 25 ng\u01b0\u01a1\u0300i. a) G\u1eb7p ng\u1eabu nhi\u00ean 1 th\u00e0nh vi\u00ean c\u1ee7a c\u00e2u l\u1ea1c b\u1ed9, t\u00ednh x\u00e1c su\u1ea5t th\u00e0nh vi\u00ean \u0111\u00f3 l\u00e0 n\u1eef. b) Em c\u00f3 nh\u1eadn x\u00e9t g\u00ec v\u1ec1 t\u1ec9 l\u1ec7 th\u00e0nh vi\u00ean n\u1eef v\u00e0 x\u00e1c su\u1ea5t tr\u00ean? \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u00ed d\u1ee5 3: B\u01b0\u1edbc \u0111\u1ea7u h\u00ecnh th\u00e0nh cho HS m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa t\u1ec9 l\u1ec7 v\u00e0 x\u00e1c su\u1ea5t. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u00ed d\u1ee5 3: GV n\u00eau v\u1ea5n \u0111\u1ec1 v\u00e0 d\u1eabn d\u1eaft HS tr\u1ea3 l\u1eddi. GV c\u00f3 th\u1ec3 \u0111\u1eb7t th\u00eam c\u00e2u h\u1ecfi: N\u1ebfu kh\u00f4ng cho t\u1ed5ng s\u1ed1 th\u00e0nh vi\u00ean c\u1ee7a c\u00e2u l\u1ea1c b\u1ed9 l\u00e0 25 ng\u01b0\u1eddi th\u00ec c\u00f3 t\u00ednh \u0111\u01b0\u1ee3c x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 th\u00e0nh vi\u00ean g\u1eb7p ng\u1eabu nhi\u00ean l\u00e0 n\u1eef kh\u00f4ng? V\u1eadn d\u1ee5ng. M\u1ed9t khu ph\u1ed1 c\u00f3 200 ng\u01b0\u1eddi lao \u0111\u1ed9ng, m\u1ed7i ng\u01b0\u1eddi l\u00e0m vi\u1ec7c \u1edf m\u1ed9t trong n\u0103m l\u0129nh v\u1ef1c l\u00e0 Kinh doanh, S\u1ea3n xu\u1ea5t, Gi\u00e1o d\u1ee5c, Y t\u1ebf v\u00e0 D\u1ecbch v\u1ee5. Bi\u1ec3u \u0111\u1ed3 trong Hi\u0300nh 2 th\u1ed1ng k\u00ea t\u1ec9 l\u1ec7 ng\u01b0\u1eddi lao \u0111\u1ed9ng thu\u1ed9c m\u1ed7i l\u0129nh v\u1ef1c ngh\u1ec1 nghi\u1ec7p. G\u1eb7p ng\u1eabu nhi\u00ean m\u1ed9t ng\u01b0\u1eddi lao \u0111\u1ed9ng c\u1ee7a khu ph\u1ed1. a) T\u00ednh x\u00e1c su\u1ea5t ng\u01b0\u1eddi \u0111\u00f3 c\u00f3 c\u00f4ng vi\u1ec7c thu\u1ed9c l\u0129nh v\u1ef1c Gi\u00e1o d\u1ee5c. b) T\u00ednh x\u00e1c su\u1ea5t ng\u01b0\u1eddi \u0111\u00f3 c\u00f3 c\u00f4ng vi\u1ec7c kh\u00f4ng thu\u1ed9c l\u0129nh v\u1ef1c Y t\u1ebf hay D\u1ecbch v\u1ee5. 24% 24% Kinh doanh 30% S\u1ea3n xu\u1ea5t 12% Gi\u00e1o d\u1ee5c 10% Y t\u1ebf D\u1ecbch v\u1ee5 218 Hi\u0300nh 2","\u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng: C\u1ee7ng c\u1ed1 m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa t\u1ec9 l\u1ec7 v\u00e0 x\u00e1c su\u1ea5t. T\u00edch h\u1ee3p gi\u1eefa bi\u1ec3u \u0111\u1ed3 Th\u1ed1ng k\u00ea v\u00e0 X\u00e1c su\u1ea5t. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u1eadn d\u1ee5ng: HS l\u00e0m vi\u1ec7c c\u00e1 nh\u00e2n sau \u0111\u00f3 th\u1ea3o lu\u1eadn k\u1ebft qu\u1ea3. IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. \tDo c\u00e1c qu\u1ea3 b\u00f3ng c\u00f3 k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng gi\u1ed1ng nhau n\u00ean ch\u00fang c\u00f3 c\u00f9ng kh\u1ea3 n\u0103ng \u0111\u01b0\u1ee3c ch\u1ecdn. Bi\u1ebfn c\u1ed1 A x\u1ea3y ra khi s\u1ed1 ghi tr\u00ean qu\u1ea3 b\u00f3ng l\u00e0 5; 13 n\u00ean c\u00f3 2 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i. V\u1eady P(A) = 2 . 5 Kh\u00f4ng c\u00f3 qu\u1ea3 b\u00f3ng n\u00e0o c\u00f3 s\u1ed1 ghi tr\u00ean qu\u1ea3 b\u00f3ng chia h\u1ebft cho 3 n\u00ean B l\u00e0 bi\u1ebfn c\u1ed1 kh\u00f4ng th\u1ec3. V\u1eady P(B) = 0. T\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 ghi tr\u00ean qu\u1ea3 b\u00f3ng \u0111\u1ec1u l\u1edbn h\u01a1n 4 n\u00ean C l\u00e0 bi\u1ebfn c\u1ed1 ch\u1eafc ch\u1eafn. V\u1eady P(C) = 1. 2. \tDo c\u00e1c vi\u00ean bi c\u00f3 k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng gi\u1ed1ng nhau n\u00ean ch\u00fang c\u00f3 c\u00f9ng kh\u1ea3 n\u0103ng \u0111\u01b0\u1ee3c ch\u1ecdn. T\u1ed5ng s\u1ed1 bi trong h\u1ed9p l\u00e0 3 + 4 + 5 = 12 (vi\u00ean). Trong h\u1ed9p c\u00f3 3 vi\u00ean bi xanh n\u00ean c\u00f3 3 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 A. V\u1eady P(A=) 3= 1 . 12 4 Trong h\u1ed9p c\u00f3 4 vi\u00ean bi \u0111\u1ecf n\u00ean s\u1ed1 bi kh\u00f4ng c\u00f3 m\u00e0u \u0111\u1ecf l\u00e0 12 \u2013 4 = 8 (vi\u00ean). S\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho B l\u00e0 8. V\u1eady P(B=) 8= 2 . 12 3 3. \tG\u1ecdi k l\u00e0 s\u1ed1 th\u1ebb ghi s\u1ed1 l\u1ebb (0 \u2264 k \u2264 10). S\u1ed1 th\u1ebb ghi s\u1ed1 ch\u1eb5n l\u00e0 10 \u2013 k. Do c\u00e1c th\u1ebb c\u00f9ng lo\u1ea1i n\u00ean ch\u00fang c\u00f3 c\u00f9ng kh\u1ea3 n\u0103ng \u0111\u01b0\u1ee3c ch\u1ecdn. X\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c th\u1ebb ghi s\u1ed1 l\u1ebb l\u00e0 k. X\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c th\u1ebb ghi s\u1ed1 ch\u1eb5n l\u00e0 10 - k. 10 10 Do x\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c th\u1ebb ghi s\u1ed1 ch\u1eb5n g\u1ea5p 4 l\u1ea7n x\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c th\u1ebb ghi s\u1ed1 l\u1ebb n\u00ean 10 - k = 4 k . 10 10 Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c k = 2. V\u1eady trong h\u1ed9p c\u00f3 2 th\u1ebb ghi s\u1ed1 l\u1ebb. 4. \tS\u1ed1 h\u1ecdc sinh n\u1eef trong C\u00e2u l\u1ea1c b\u1ed9 l\u00e0: 9 + 8 + 5 + 6 = 28 (h\u1ecdc sinh). S\u1ed1 h\u1ecdc sinh nam trong C\u00e2u l\u1ea1c b\u1ed9 l\u00e0: 8 + 6 + 4 + 4 = 22 (h\u1ecdc sinh). T\u1ed5ng s\u1ed1 h\u1ecdc sinh c\u1ee7a C\u00e2u l\u1ea1c b\u1ed9 l\u00e0: 28 + 22 = 50 (h\u1ecdc sinh). S\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 A l\u00e0 28. V\u1eady P(A=) 2=8 0,56. 50 S\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 B l\u00e0 4 + 5 = 9. V\u1eady P(B=) 9= 0,18. 50 S\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 C l\u00e0 8 + 4 + 4 = 16. V\u1eady P(C=) 1=6 0,32. 50 219","5. a) Do s\u1ed1 h\u1ecdc sinh kh\u1ed1i 9 chi\u1ebfm 24% so v\u1edbi t\u1ed5ng s\u1ed1 h\u1ecdc sinh n\u00ean x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 \u201cH\u1ecdc sinh \u0111\u01b0\u1ee3c ch\u1ecdn thu\u1ed9c kh\u1ed1i 9\u201d l\u00e0 0,24. b) T\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m h\u1ecdc sinh kh\u00f4ng thu\u1ed9c kh\u1ed1i 6 l\u00e0 100% \u2013 28% = 72%. X\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 \u201cH\u1ecdc sinh \u0111\u01b0\u1ee3c ch\u1ecdn kh\u00f4ng thu\u1ed9c kh\u1ed1i 6\u201d l\u00e0 0,72. B\u00e0i 2. X\u00c1C SU\u1ea4T L\u00cd THUY\u1ebeT V\u00c0 X\u00c1C SU\u1ea4T TH\u1ef0C NGHI\u1ec6M I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u00e2\u0300n \u0111a\u0323t: nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a m\u1ed9t bi\u1ebfn c\u1ed1 v\u1edbi x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 \u0111\u00f3 th\u00f4ng qua m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u00ea\u0301p toa\u0301n ho\u0323c. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng, t\u00edch h\u1ee3p c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. \u1ede L\u1edbp 6, HS \u0111\u00e3 h\u1ecdc c\u00e1ch t\u00ednh x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a m\u1ed9t s\u1ef1 ki\u1ec7n. T\u1eeb l\u1edbp 7, kh\u00e1i ni\u1ec7m \u201cs\u1ef1 ki\u1ec7n\u201d \u0111\u01b0\u1ee3c g\u1ecdi t\u00ean l\u1ea1i l\u00e0 \u201cbi\u1ebfn c\u1ed1\u201d. Do \u0111\u00f3 GV c\u1ea7n l\u01b0u \u00fd cho HS x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a \u201cs\u1ef1 ki\u1ec7n\u201d c\u0169ng ch\u00ednh l\u00e0 x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a \u201cbi\u1ebfn c\u1ed1\u201d t\u01b0\u01a1ng \u1ee9ng. 2. Theo Lu\u1eadt s\u1ed1 l\u1edbn trong L\u00ed thuy\u1ebft X\u00e1c su\u1ea5t, x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a m\u1ed9t bi\u1ebfn c\u1ed1 s\u1ebd g\u1ea7n b\u1eb1ng v\u1edbi x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft khi s\u1ed1 ph\u00e9p th\u1eed l\u1edbn. 3. Gi\u1ea3 s\u1eed x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft c\u1ee7a bi\u1ebfn c\u1ed1 A l\u00e0 p. Khi th\u1ef1c hi\u1ec7n ph\u00e9p th\u1eed n l\u1ea7n th\u00ec s\u1ed1 l\u1ea7n xu\u1ea5t hi\u1ec7n bi\u1ebfn c\u1ed1 A s\u1ebd g\u1ea7n b\u1eb1ng (nh\u01b0ng kh\u00f4ng nh\u1ea5t thi\u1ebft ph\u1ea3i b\u1eb1ng) np. V\u1eabn c\u00f3 kh\u1ea3 n\u0103ng s\u1ed1 l\u1ea7n xu\u1ea5t hi\u1ec7n bi\u1ebfn c\u1ed1 A c\u00e1ch xa np. Tuy nhi\u00ean, kh\u1ea3 n\u0103ng n\u00e0y l\u00e0 r\u1ea5t nh\u1ecf. III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 Tr\u01b0\u1edbc khi H\u00e0 tung m\u1ed9t \u0111\u1ed3ng xu c\u00e2n \u0111\u1ed1i v\u00e0 \u0111\u1ed3ng ch\u1ea5t 100 l\u1ea7n, Th\u1ecd d\u1ef1 \u0111o\u00e1n s\u1ebd c\u00f3 tr\u00ean 70 l\u1ea7n xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p c\u00f2n Thu\u00fd l\u1ea1i d\u1ef1 \u0111o\u00e1n s\u1ebd c\u00f3 \u00edt h\u01a1n 70 l\u1ea7n xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p. Theo em, b\u1ea1n n\u00e0o c\u00f3 kh\u1ea3 n\u0103ng \u0111o\u00e1n \u0111\u00fang cao h\u01a1n? V\u00ec sao? \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110K\u0110: T\u1ea1o c\u01a1 h\u1ed9i cho HS \u0111\u01b0\u1ee3c tr\u1ea3i nghi\u1ec7m so s\u00e1nh kh\u1ea3 n\u0103ng x\u1ea3y ra c\u1ee7a hai s\u1ef1 ki\u1ec7n khi th\u1ef1c hi\u1ec7n l\u1eb7p l\u1ea1i m\u1ed9t ph\u00e9p th\u1eed nhi\u1ec1u l\u1ea7n. T\u1eeb \u0111\u00f3 n\u1ea3y sinh nhu c\u1ea7u x\u00e1c \u0111\u1ecbnh m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m v\u00e0 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c H\u0110K\u0110: GV \u0111\u1eb7t v\u1ea5n \u0111\u1ec1, HS th\u1ea3o lu\u1eadn r\u1ed3i tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3. 220","H\u0110KP Tr\u01b0\u1edbc khi H\u00e0 tung m\u1ed9t \u0111\u1ed3ng xu c\u00e2n \u0111\u1ed1i v\u00e0 \u0111\u1ed3ng ch\u1ea5t 100 l\u1ea7n, Th\u1ecd d\u1ef1 \u0111o\u00e1n s\u1ebd c\u00f3 tr\u00ean 70 l\u1ea7n xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p c\u00f2n Thu\u00fd l\u1ea1i d\u1ef1 \u0111o\u00e1n s\u1ebd c\u00f3 \u00edt h\u01a1n 70 l\u1ea7n xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p. Theo em, b\u1ea1n n\u00e0o c\u00f3 kh\u1ea3 n\u0103ng \u0111o\u00e1n \u0111\u00fang cao h\u01a1n? V\u00ec sao? M\u1ed9t h\u1ed9p k\u00edn ch\u1ee9a 3 qu\u1ea3 b\u00f3ng xanh v\u00e0 2 qu\u1ea3 b\u00f3ng \u0111\u1ecf X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng.An l\u1ea5y ra ng\u1eabu nhi\u00ean c\u1ee7a s\u1ef1 ki\u1ec7n A sau n l\u1ea7n 1 qu\u1ea3 b\u00f3ng t\u1eeb h\u1ed9p, xem m\u00e0u r\u1ed3i tr\u1ea3 l\u1ea1i h\u1ed9p. th\u1ef1c hi\u1ec7n ph\u00e9p th\u1eed l\u00e0 a) T\u00ednh t\u1ec9 s\u1ed1 m\u00f4 t\u1ea3 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft c\u1ee7a bi\u1ebfn c\u1ed1 S\u1ed1 l\u1ea7n bi\u1ebfn c\u1ed1 A x\u1ea3y ra \u201cAn l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh\u201d. n b) Sau khi l\u1eb7p l\u1ea1i ph\u00e9p th\u1eed \u0111\u00f3 100 l\u1ea7n, An ghi l\u1ea1i s\u1ed1 l\u1ea7n m\u00ecnh l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh sau 20; 40; 60; 80 v\u00e0 100 l\u1ea7n l\u1ea5y b\u00f3ng nh\u01b0 sau: S\u1ed1 l\u1ea7n l\u1ea5y b\u00f3ng 20 40 60 80 100 S\u1ed1 l\u1ea7n l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh 9 20 32 46 59 T\u00ednh c\u00e1c x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a s\u1ef1 ki\u1ec7n \u201cAn l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh\u201d sau 20; 40; 60; 80 v\u00e0 100 l\u1ea7n th\u1eed. \u2013 MT\u1ee5acth\u0111\u1ea5\u00edcyh: c\u1ee7a H\u0110KP: HS quan s\u00e1t th\u1ea5y x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m ti\u1ebfn g\u1ea7n \u0111\u1ebfn x\u00e1c su\u1ea5t l\u00ed thuy\u2013\u1ebftXk\u00e1hci su\u1ed1\u1ea5pt hth\u00e9\u1ef1pcthn\u1eedghti\u0103\u1ec7nmg.ph\u1ee5 thu\u1ed9c v\u00e0o k\u1ebft qu\u1ea3 c\u1ee7a d\u00e3y ph\u00e9p th\u1eed v\u00e0 ch\u1ec9 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u2013 Gs\u1ee3aiu \u00fdkhti\u1ed5\u0111c\u00e3hth\u1ee9\u1ef1ccHhi\u0110\u1ec7nKdP\u00e3:yGphV\u00e9pct\u00f3h\u1eedth. \u1ec3 s\u1eed d\u1ee5ng m\u00e1y vi t\u00ednh v\u1edbi ph\u1ea7n m\u1ec1m Excel \u0111\u1ec3 m\u00f4 ph\u2013\u1ecfXng\u00e1cpshu\u00e9\u1ea5pt l\u00edthth\u1eeduyv\u1ebf\u1edbtic\u00f3s\u1ed1thl\u1ec3\u1ea7n\u0111\u01b0t\u1ee3hc\u1eedxl\u00e1\u1edbcn\u0111\u1ecbnnhh\u01b0tr\u01b0s\u1edbauc :kh\u0110i\u00e1thn\u1ef1hcsh\u1ed1i\u1ec7cn\u00e1pch\u00e9bp\u00f3nthg\u1eed.xanh l\u00e0 1, 2, 3; c\u00e1c b\u00f3\u2013nXg \u00e1\u0111c\u1ecfslu\u00e0\u1ea54t ,th5\u1ef1.cSn\u1eedgdh\u1ee5i\u1ec7nmg vh\u00e0mx\u00e1Rc AsuN\u1ea5tDl\u00edBthEuTyW\u1ebftEcE\u1ee7aNc(\u00f91n,5g)m\u0111\u1ed9\u1ec3tl\u1ea5s\u1ef1y kbi\u00f3\u1ec7nngh.ay bi\u1ebfn c\u1ed1 kh\u00f4ng nh\u1ea5t thi\u1ebft l\u00e0 b\u1eb1ng nhau. Tuy nhi\u00ean, khi th\u1ef1c hi\u1ec7n c\u00e0ng nhi\u1ec1u l\u1ea7n ph\u00e9p th\u1eed, x\u00e1c su\u1ea5t V\u00ed dth\u1ee5\u1ef11c.nMgh\u1ed7ii\u1ec7bm\u1ea1nc\u00e0Tnrg\u1ecdgn\u1ea7gn, Tx\u00e1hcu\u1ef7suv\u1ea5\u00e0t lK\u00ed thhuu\u00eay\u1ebftut.ng m\u1ed9t \u0111\u1ed3ng xu c\u00e2n \u0111\u1ed1i v\u00e0 \u0111\u1ed3ng ch\u1ea5t 20 l\u1ea7n v\u00e0 ghi l\u1ea1i k\u1ebft qu\u1ea3 \u1edf b\u1ea3ng sau: GXG\u00e1\u1ecd\u1ecdNcii mPgsu(T\u01b0T(A\u1ea5Ar\u1eddht\u1ecd)i)utnlhtl\u1ef7\u00e0g\u00e0u\u1ef1xcns\u00e1\u1ed1gncgls\u1ea7huni\u1ea5\u1ec7xtmux\u1ea5uct\u1ea5\u1ee7Shtai\u1ed1h\u1ec7binli\u1ec7\u1ea7\u1ebfnbnnib\u1ebfcxin\u1ed1\u1ebfuncA\u1ea5\u1ed1ctl1\u1ed1A\u00e08h3Aitk\u1ec7\u1ec9hnksi\u1ed1hmtihmt\u1ef1\u1eb7hm(ct\u1ef1Achs)\u1ea5i.h\u1ec7pin\u1ec7nphm\u00e9Sp\u1ed9\u1ed1tthpl\u1ea7\u1eedhn\u00e9\u0111px\u00f3tuhm\u1ea5\u1eedt.l\u1ea7h1n7i2.\u1ec7n m\u1eb7t ng\u1eeda Khi mKc\u00e0hnug\u00ea l\u1edbn, x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m11c\u1ee7a bi\u1ebfn c\u1ed1 A c\u00e0ng g\u1ea7n P(A). 9 G\u1ecdiVA\u00ed dl\u00e0\u1ee5b1i.\u1ebfMn c\u1ed7\u1ed1i b\u201c\u1ea1XnuT\u1ea5rt\u1ecdhnig\u1ec7,nTmhu\u1eb7\u1ef7t sv\u1ea5\u00e0pK\u201d.hu\u00ea tung m\u1ed9t \u0111\u1ed3ng xu c\u00e2n \u0111\u1ed1i v\u00e0 \u0111\u1ed3ng ch\u1ea5t 20 l\u1ea7n a) Tv\u00ed\u00e0nhghci\u00e1lc\u1ea1ixk\u00e1\u1ebfct squu\u1ea5\u1ea3t\u1edfthb\u1ef1\u1ea3cngngsahui\u1ec7: m c\u1ee7a bi\u1ebfn c\u1ed1 A sau 20 l\u1ea7n tung c\u1ee7a t\u1eebng b\u1ea1n. b) T\u00ednh xN\u00e1cg\u01b0su\u1edd\u1ea5ittuthn\u1ef1gc nghi\u1ec7mS\u1ed1c\u1ee7l\u1ea7anbix\u1ebfun\u1ea5ct \u1ed1hiA\u1ec7nsamu\u1eb76t0s\u1ea5lp\u1ea7n tunSg\u1ed1cl\u1ea7\u1ee7na xc\u1ea3u\u1ea53t bh\u1ea1i\u1ec7nn. m\u1eb7t ng\u1eeda cx)\u00e1cT\u00edsnuh\u1ea5txt\u00e1hc\u1ef1sTcKTurhnh\u1ea5\u1ecdugutn\u1ef7\u00eahlg\u00edi\u1ec7thmuyv\u1ebf\u1eebtact\u1ee7\u00edanhb,i\u1ebfenmcc\u1ed1\u00f3Ankh118h\u1ead13ni txu\u00e9ntgg\u0111\u00ec?\u1ed3ng x\u00e1c1s72u\u1ea5t xu. So s\u00e1nh 9 n\u00e0y v\u1edbi c\u00e1c bi9\u1ebf2\u2013n M\u1ee5c \u0111\u00edch c\u1ee7a V\u00ed d\u1ee5 1: HS \u0111\u01b0\u1ee3c c\u1ee7ng c\u1ed1 c\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a c\u1ed1 v\u00e0 tr\u1ea3i nghi\u1ec7m s\u1ef1 h\u1ed9i t\u1ee5 c\u1ee7a x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m \u0111\u1ebfn x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u00ed d\u1ee5 1: GV n\u00eau v\u1ea5n \u0111\u1ec1, HS l\u00e0m vi\u1ec7c nh\u00f3m \u0111\u1ec3 th\u1ea3o lu\u1eadn r\u1ed3i tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3. Ch\u00fa \u00fd: GV nh\u1ea5n m\u1ea1nh hai nh\u1eadn x\u00e9t: \u2013 X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 A c\u00f3 th\u1ec3 l\u1edbn h\u01a1n ho\u1eb7c nh\u1ecf h\u01a1n x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft. \u2013 Khi s\u1ed1 l\u00e2\u0300n th\u01b0\u0323c hi\u00ea\u0323n ph\u00e9p th\u1eed l\u1edbn (60 l\u1ea7n) th\u00ec x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 A l\u00e0 0,53 g\u1ea7n b\u1eb1ng x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft l\u00e0 0,5. 221","\u2013 C\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u1ea7n m\u1ec1m Excel \u0111\u1ec3 m\u00f4 ph\u1ecfng ph\u00e9p th\u1eed nh\u01b0 sau: Quy \u01b0\u1edbc \u0111\u1ed3ng xu xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p l\u00e0 1, \u0111\u1ed3ng xu xu\u1ea5t hi\u1ec7n m\u1eb7t ng\u1eeda l\u00e0 2. S\u1eed d\u1ee5ng h\u00e0m RANDBETWEEN(1, 2) \u0111\u1ec3 tung \u0111\u1ed3ng xu. V\u00ed d\u1ee5 2. \u1ede m\u1ed9t trang tr\u1ea1i nu\u00f4i g\u00e0, ng\u01b0\u1eddi ta nh\u1eadn th\u1ea5y x\u00e1c su\u1ea5t m\u1ed9t qu\u1ea3 tr\u1ee9ng g\u00e0 c\u00f3 c\u00e2n n\u1eb7ng tr\u00ean 42 g l\u00e0 0,4. H\u00e3y \u01b0\u1edbc l\u01b0\u1ee3ng xem trong m\u1ed9t l\u00f4 2 000 qu\u1ea3 tr\u1ee9ng g\u00e0 c\u1ee7a trang tr\u1ea1i c\u00f3 kho\u1ea3ng bao nhi\u00eau qu\u1ea3 tr\u1ee9ng c\u00f3 c\u00e2n n\u1eb7ng tr\u00ean 42 g. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u00ed d\u1ee5 2: HS s\u1eed d\u1ee5ng m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m v\u00e0 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng s\u1ed1 ph\u00e9p th\u1eed th\u00e0nh c\u00f4ng. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u00ed d\u1ee5 2: GV n\u00eau v\u1ea5n \u0111\u1ec1, HS l\u00e0m vi\u1ec7c nh\u00f3m \u0111\u1ec3 th\u1ea3o lu\u1eadn r\u1ed3i tr\u00ecnh b\u00e0y k\u1ebft qu\u1ea3. Ch\u00fa \u00fd: GV c\u00f3 th\u1ec3 \u0111\u1eb7t th\u00eam c\u00e2u h\u1ecfi: C\u00f3 th\u1ec3 x\u1ea3y ra kh\u1ea3 n\u0103ng trong 2 000 qu\u1ea3 tr\u1ee9ng g\u00e0, c\u00f3 1 000 qu\u1ea3 tr\u1ee9ng c\u00e2n n\u1eb7ng tr\u00ean 42 g hay kh\u00f4ng? C\u00e2u tr\u1ea3 l\u1eddi l\u00e0 c\u00f3 th\u1ec3, nh\u01b0ng kh\u1ea3 n\u0103ng x\u1ea3y ra l\u00e0 r\u1ea5t th\u1ea5p. Th\u1ef1c h\u00e0nh 1. H\u00e3y tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi \u1edf (trang 92). \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: HS \u0111\u01b0\u1ee3c c\u1ee7ng c\u1ed1 vi\u1ec7c s\u1eed d\u1ee5ng m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m v\u00e0 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng s\u1ed1 ph\u00e9p th\u1eed th\u00e0nh c\u00f4ng. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 1: GV n\u00eau v\u1ea5n \u0111\u1ec1, HS th\u1ea3o lu\u1eadn nh\u00f3m. GV c\u00f3 th\u1ec3 \u0111\u1eb7t c\u00e2u h\u1ecfi: C\u00f3 ph\u1ea3i l\u00e0 Thu\u00fd ch\u1eafc ch\u1eafn \u0111o\u00e1n \u0111\u00fang c\u00f2n Th\u1ecd ch\u1eafc ch\u1eafn \u0111o\u00e1n sai hay kh\u00f4ng? Tr\u1ea3 l\u1eddi: Thu\u00fd v\u1eabn c\u00f3 kh\u1ea3 n\u0103ng sai v\u00e0 Th\u1ecd v\u1eabn c\u00f3 kh\u1ea3 n\u0103ng \u0111\u00fang. Tuy nhi\u00ean kh\u1ea3 n\u0103ng \u0111\u00f3 l\u00e0 r\u1ea5t nh\u1ecf. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: V\u00ec \u0111\u1ed3ng xu c\u00e2n \u0111\u1ed1i v\u00e0 \u0111\u1ed3ng ch\u1ea5t n\u00ean x\u00e1c su\u1ea5t xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p l\u00e0 1 . Nh\u01b0 v\u1eady, khi th\u1ef1c hi\u1ec7n 100 ph\u00e9p th\u1eed th\u00ec s\u1ed1 l\u1ea7n xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p s\u1ebd v\u00e0o kho\u1ea3ng 2 100 \u22c5 1 =50 l\u1ea7n. V\u1eady Thu\u00fd c\u00f3 kh\u1ea3 n\u0103ng \u0111o\u00e1n \u0111\u00fang cao h\u01a1n. 2 Th\u1ef1c h\u00e0nh 2. M\u1ed9t h\u1ed9p ch\u1ee9a m\u1ed9t s\u1ed1 qu\u1ea3 b\u00f3ng xanh v\u00e0 b\u00f3ng \u0111\u1ecf c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc v\u00e0 kh\u1ed1i l\u01b0\u1ee3ng. Linh l\u1ea5y ra ng\u1eabu nhi\u00ean 1 qu\u1ea3 b\u00f3ng t\u1eeb h\u1ed9p, xem m\u00e0u r\u1ed3i tr\u1ea3 b\u00f3ng l\u1ea1i h\u1ed9p. L\u1eb7p l\u1ea1i ph\u00e9p th\u1eed \u0111o\u0301 200 l\u1ea7n, Linh th\u1ea5y c\u00f3 62 l\u1ea7n l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh v\u00e0 138 l\u1ea7n l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng \u0111\u1ecf. a) T\u00ednh x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cL\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh\u201d sau 200 l\u1ea7n th\u1eed. b) Bi\u1ebft s\u1ed1 b\u00f3ng xanh trong h\u1ed9p l\u00e0 20, h\u00e3y \u01b0\u1edbc l\u01b0\u1ee3ng s\u1ed1 b\u00f3ng \u0111\u1ecf trong h\u1ed9p. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS \u0111\u01b0\u1ee3c c\u1ee7ng c\u1ed1 vi\u1ec7c s\u1eed d\u1ee5ng m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m v\u00e0 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 2: HS th\u1ea3o lu\u1eadn nh\u00f3m. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: a) X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cL\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh\u201d sau 200 l\u1ea7n th\u1eed l\u00e0 62 = 0,31. 200 222","b) G\u1ecdi N l\u00e0 s\u1ed1 qu\u1ea3 b\u00f3ng trong h\u1ed9p. X\u00e1c su\u1ea5t l\u00ed thuy\u1ebft l\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh trong m\u1ed7i l\u1ea7n th\u1eed l\u00e0 20 . Do s\u1ed1 ph\u00e9p th\u1eed l\u1edbn n\u00ean x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m v\u00e0 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft c\u1ee7a bi\u1ebfn c\u1ed1 N \u201cL\u1ea5y \u0111\u01b0\u1ee3c b\u00f3ng xanh\u201d l\u00e0 g\u1ea7n b\u1eb1ng nhau. Do \u0111\u00f3 20 \u2248 0,31 hay N \u2248 65. N V\u1eady trong h\u1ed9p c\u00f3 kho\u1ea3ng 65 \u2013 20 = 45 qu\u1ea3 b\u00f3ng \u0111\u1ecf. V\u1eadn d\u1ee5ng. X\u00e1c su\u1ea5t n\u1ea3y m\u1ea7m c\u1ee7a m\u1ed9t lo\u1ea1i h\u1ea1t gi\u1ed1ng l\u00e0 0,8. Ng\u01b0\u1eddi ta \u0111em gieo 1000 h\u1ea1t gi\u1ed1ng \u0111\u00f3. H\u00e3y \u01b0\u1edbc l\u01b0\u1ee3ng xem c\u00f3 kho\u1ea3ng bao nhi\u00eau h\u1ea1t trong s\u1ed1 \u0111\u00f3 s\u1ebd n\u1ea3y m\u1ea7m. Hi\u0300nh 1 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng: HS v\u1eadn d\u1ee5ng m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m v\u00e0 x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft \u0111\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 th\u1ef1c ti\u1ec5n. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c V\u1eadn d\u1ee5ng: HS l\u00e0m vi\u1ec7c c\u00e1 nh\u00e2n sau \u0111\u00f3 thuy\u1ebft tr\u00ecnh l\u1eddi gi\u1ea3i tr\u01b0\u1edbc l\u1edbp. IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. \tX\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cGieo \u0111\u01b0\u1ee3c m\u1eb7t c\u00f3 s\u1ed1 ch\u1ea5m l\u00e0 s\u1ed1 l\u1ebb\u201d l\u00e0 21+ 8 +18 = 47 . 120 120 2. \tS\u1ed1 chuy\u1ebfn bay trong ng\u00e0y h\u00f4m \u0111\u00f3 m\u1ecdi ng\u01b0\u1eddi mua v\u00e9 \u0111\u1ec1u c\u00f3 m\u1eb7t l\u00e0 kho\u1ea3ng \t\t\t\t\t\t\t\t 0,9 . 120 = 108 (chuy\u1ebfn bay). S\u1ed1 chuy\u1ebfn bay trong ng\u00e0y h\u00f4m \u0111\u00f3 c\u00f3 ng\u01b0\u1eddi mua v\u00e9 nh\u01b0ng kh\u00f4ng l\u00ean m\u00e1y bay l\u00e0 kho\u1ea3ng \t\t\t\t\t\t\t 120 \u2013 108 = 12 (chuy\u1ebfn bay). 3. \ta) X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cL\u1ea5y \u0111\u01b0\u1ee3c vi\u00ean bi m\u00e0u \u0111en\u201d l\u00e0 80 \u2212 24 = 0,7. 80 b) X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cL\u1ea5y \u0111\u01b0\u1ee3c vi\u00ean bi m\u00e0u tr\u1eafng\u201d l\u00e0 24 = 0,3. 80 V\u1eady c\u00f3 kho\u1ea3ng 0,3 . 10 = 3 vi\u00ean bi tr\u1eafng trong h\u1ed9p. 4. \tX\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cNg\u01b0\u1eddi \u0111\u01b0\u1ee3c l\u1ef1a ch\u1ecdn \u1ee7ng h\u1ed9 vi\u1ec7c t\u1eaft \u0111i\u1ec7n\u201d l\u00e0 255 = 0,85. 300 Do s\u1ed1 ng\u01b0\u1eddi \u0111\u01b0\u1ee3c ph\u1ecfng v\u1ea5n l\u00e0 t\u01b0\u01a1ng \u0111\u1ed1i l\u1edbn n\u00ean bi\u1ebfn c\u1ed1 \u201cM\u1ed9t ng\u01b0\u1eddi \u0111\u01b0\u1ee3c l\u1ef1a ch\u1ecdn ng\u1eabu nhi\u00ean trong khu d\u00e2n c\u01b0 \u1ee7ng h\u1ed9 vi\u1ec7c t\u1eaft \u0111\u00e8n \u0111i\u1ec7n trong s\u1ef1 ki\u1ec7n Gi\u1edd Tr\u00e1i \u0110\u1ea5t\u201d x\u1ea5p x\u1ec9 b\u1eb1ng 0,85. 223","B\u00c0I T\u1eacP CU\u1ed0I CH\u01af\u01a0NG 9 C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M 1. C 2. C 3. C 4. A 5. B B\u00c0I T\u1eacP T\u1ef0 LU\u1eacN 6. \tP(A) = 1 ; \t P(B) = 2;\t P(C) = 0. 3 3 7. \tP(A) = 1 ; \tP(B) = 1 . 22 8. \tX\u00e1c su\u1ea5t v\u1eadn \u0111\u1ed9ng vi\u00ean \u0111\u1ea1t huy ch\u01b0\u01a1ng l\u00e0 0,21. 9. \tX\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cHai \u0111\u1ed3ng xu \u0111\u1ec1u xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ea5p sau 100 l\u1ea7n tung\u201d l\u00e0 14 = 0,14. 100 10. G\u1ecdi s\u1ed1 vi\u00ean bi \u0111\u1ecf trong t\u00fai l\u00e0 n. X\u00e1c su\u1ea5t l\u00ed thuy\u1ebft c\u1ee7a bi\u1ebfn c\u1ed1 \u201cL\u1ea5y \u0111\u01b0\u1ee3c bi \u0111\u1ecf\u201d t\u1eeb t\u00fai l\u00e0 n . n+9 X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cL\u1ea5y \u0111\u01b0\u1ee3c bi \u0111\u1ecf trong 100 l\u1ea7n l\u1ea5y bi\u201d l\u00e0 40 = 0,4. 100 Do s\u1ed1 ph\u00e9p th\u1eed l\u1edbn n\u00ean x\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m g\u1ea7n b\u1eb1ng v\u1edbi x\u00e1c su\u1ea5t l\u00ed thuy\u1ebft, suy ra n \u2248 0,4 hay n \u2248 6. n+9 V\u1eady c\u00f3 kho\u1ea3ng 6 vi\u00ean bi \u0111\u1ecf trong h\u1ed9p. 11. a) X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 c\u00f3 m\u00e0u tr\u1eafng\u201d l\u00e0 15 + 23 = 38 . 120 120 b) X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 s\u1ed1 5\u201d l\u00e0 32 . 120 X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 s\u1ed1 2\u201d l\u00e0 9 . 120 Do 9 ch\u00eanh l\u1ec7ch nhi\u1ec1u so v\u1edbi 32 n\u00ean c\u00f3 th\u1ec3 d\u1ef1 \u0111o\u00e1n x\u00e1c su\u1ea5t m\u0169i t\u00ean ch\u1ec9 v\u00e0o 120 120 c\u00e1c \u00f4 kh\u00f4ng b\u1eb1ng nhau. c) X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 c\u00f3 m\u00e0u xanh\u201d l\u00e0 9 + 32 = 41 . 120 120 X\u00e1c su\u1ea5t th\u1ef1c nghi\u1ec7m c\u1ee7a bi\u1ebfn c\u1ed1 \u201cM\u0169i t\u00ean ch\u1ec9 v\u00e0o \u00f4 c\u00f3 m\u00e0u \u0111\u1ecf\u201d l\u00e0 16 + 25 = 41 . 120 120 Do 38 v\u00e0 41 ch\u00eanh l\u1ec7ch r\u1ea5t nh\u1ecf n\u00ean k\u1ebft qu\u1ea3 th\u1ef1c nghi\u1ec7m ph\u00f9 h\u1ee3p v\u1edbi nh\u1eadn \u0111\u1ecbnh 120 120 \u0111\u00e3 cho. 224","ho\u1ea1t \u0111\u1ed9ng th\u1ef1c h\u00e0nh v\u00e0 tr\u1ea3i nghi\u1ec7m Ho\u1ea1t \u0111\u1ed9ng 4. V\u1ebc \u0110\u1ed2 TH\u1eca H\u00c0M S\u1ed0 B\u1eacC NH\u1ea4T y = ax + b B\u1eb0NG PH\u1ea6N M\u1ec0M GEOGEBRA A. M\u1ee4C TI\u00caU 1. N\u0103ng l\u1ef1c chuy\u00ean m\u00f4n \u2013 V\u1eadn du\u0323ng c\u00e1c ki\u1ebfn th\u1ee9c v\u00e0 k\u0129 n\u0103ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 th\u1ef1c ti\u1ec5n. \u2013 Th\u1ef1c h\u00e0nh t\u00edch h\u1ee3p li\u00ean m\u00f4n gi\u1eefa To\u00e1n h\u1ecdc v\u1edbi c\u00e1c m\u00f4n Khoa h\u1ecdc t\u1ef1 nhi\u00ean. \u2013 Th\u1ef1c h\u00e0nh gi\u00e1o du\u0323c STEM trong tr\u1ea3i nghi\u1ec7m To\u00e1n. 2. N\u0103ng l\u1ef1c chung \u2013 N\u0103ng l\u1ef1c t\u1ef1 ch\u1ee7 v\u00e0 t\u1ef1 h\u1ecdc trong t\u00ecm t\u00f2i, kh\u00e1m ph\u00e1. \u2013 N\u0103ng l\u1ef1c giao ti\u1ebfp v\u00e0 h\u1ee3p t\u00e1c trong tr\u00ecnh b\u00e0y, th\u1ea3o lu\u1eadn v\u00e0 l\u00e0m vi\u1ec7c nh\u00f3m. \u2013 N\u0103ng l\u1ef1c gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 v\u00e0 s\u00e1ng t\u1ea1o trong th\u1ef1c h\u00e0nh v\u00e0 v\u1eadn d\u1ee5ng. 3. H\u00ecnh th\u00e0nh c\u00e1c ph\u1ea9m ch\u1ea5t \u2013 Y\u00eau n\u01b0\u1edbc, nh\u00e2n \u00e1i. \u2013 Ch\u0103m ch\u1ec9, trung th\u1ef1c, tr\u00e1ch nhi\u1ec7m. B. H\u01af\u1edaNG D\u1eaaN D\u1ea0Y H\u1eccC I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t: \u2013 Th\u1ef1c h\u00e0nh s\u1eed d\u1ee5ng ph\u1ea7n m\u1ec1m GeoGebra \u0111\u1ec3 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y = ax + b tr\u00ean m\u1eb7t ph\u1eb3ng to\u1ea1 \u0111\u1ed9. \u2013 Xem x\u00e9t s\u1ef1 thay \u0111\u1ed5i c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b khi thay \u0111\u1ed5i h\u1ec7 s\u1ed1 a, b trong c\u00f4ng th\u1ee9c h\u00e0m s\u1ed1. \u2013 \u00d4n t\u1eadp v\u00e0 minh ho\u1ea1 c\u00e1c t\u00ednh ch\u1ea5t \u0111\u00e3 h\u1ecdc v\u1ec1 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u1ebfp to\u00e1n h\u1ecdc, s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5, ph\u01b0\u01a1ng ti\u1ec7n h\u1ecdc to\u00e1n. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 Tin h\u1ecdc. II. Chu\u1ea9n b\u1ecb \u2013 S\u00e1ch gi\u00e1o khoa To\u00e1n 8, t\u1eadp hai \u2013 Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o. \u2013 D\u1ee5ng c\u1ee5 h\u1ecdc t\u1eadp th\u00f4ng th\u01b0\u1eddng. \u2013 M\u00e1y t\u00ednh c\u1ea7m tay, m\u00e1y t\u00ednh c\u00e1 nh\u00e2n c\u00f3 k\u1ebft n\u1ed1i m\u1ea1ng Internet, ti vi ho\u1eb7c m\u00e1y chi\u1ebfu, ph\u1ea7n m\u1ec1m GeoGebra. 225","III. T\u1ed5 ch\u1ee9c ho\u1ea1t \u0111\u1ed9ng 1. H\u01b0\u1edbng d\u1eabn c\u00e1ch l\u00e0m a) N\u1ed9i dung nhi\u1ec7m v\u1ee5: \u2013 GV vi\u00ean h\u01b0\u1edbng d\u1eabn HS c\u00e1c ch\u1ee9c n\u0103ng v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a ph\u1ea7n m\u1ec1m GeoGebra. Vu\u0300ng ch\u01b0\u0301a ca\u0301c thanh c\u00f4ng cu\u0323 Vu\u0300ng hi\u00ea\u0309n thi\u0323 Vu\u0300ng la\u0300m vi\u00ea\u0323c danh sa\u0301ch \u0111\u00f4\u0301i t\u01b0\u01a1\u0323ng Vu\u0300ng nh\u00e2\u0323p l\u00ea\u0323nh b) Bi\u1ec7n ph\u00e1p ki\u1ec3m tra HS hi\u1ec3u r\u00f5 nhi\u1ec7m v\u1ee5: \u2013 Y\u00eau c\u1ea7u HS quan s\u00e1t v\u00e0 gi\u1ea3i th\u00edch c\u00e1c nh\u1eadn x\u00e9t v\u00e0 t\u00ednh ch\u1ea5t \u0111\u00e3 h\u1ecdc v\u1ec1 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng. \u2013 GV \u0111i\u1ec1u ch\u1ec9nh, b\u1ed5 sung c\u00e1c thi\u1ebfu s\u00f3t. 2. T\u1ed5 ch\u1ee9c th\u1ef1c hi\u1ec7n a) HS th\u1ef1c hi\u1ec7n: HS th\u1ef1c h\u00e0nh hai thao t\u00e1c ch\u00ednh: \u2013 V\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = ax + b v\u1edbi a, b \u0111\u01b0\u1ee3c nh\u1eadp t\u1eeb b\u00e0n ph\u00edm. \u2013 V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b v\u1edbi a, b thay \u0111\u1ed5i tr\u00ean thanh tr\u01b0\u1ee3t. b) GV h\u1ed7 tr\u1ee3 (kh\u1eafc ph\u1ee5c kh\u00f3 kh\u0103n HS d\u1ef1 ki\u1ebfn s\u1ebd g\u1eb7p): GV ki\u1ec3m tra v\u00e0 h\u01b0\u1edbng d\u1eabn c\u00e1c thao t\u00e1c kh\u00f3. 226","3. Ki\u1ec3m tra \u0111\u00e1nh gi\u00e1 a) GV d\u1ef1 ki\u1ebfn m\u1ee9c \u0111\u1ed9 ho\u00e0n th\u00e0nh c\u1ee7a HS: M\u1ee9c \u0111\u1ed9 N\u1ed9i dung ho\u00e0n th\u00e0nh \u2013 V\u1ebd \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = ax + b b\u1eb1ng ph\u1ea7n m\u1ec1m. T\u1ed1t \u2013 T\u1ef1 t\u1ea1o \u0111\u01b0\u1ee3c thanh tr\u01b0\u1ee3t bi\u1ec3u di\u1ec5n s\u1ef1 thay \u0111\u1ed5i c\u1ee7a a, b. \u2013 Li\u00ean h\u1ec7 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c t\u00ednh ch\u1ea5t gi\u1eefa l\u00ed thuy\u1ebft \u0111\u00e3 h\u1ecdc v\u00e0 bi\u1ec3u di\u1ec5n \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1. \u2013 V\u1ebd \u0111\u01b0\u1ee3c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = ax + b b\u1eb1ng ph\u1ea7n m\u1ec1m. \u2013 T\u1ea1o \u0111\u01b0\u1ee3c thanh tr\u01b0\u1ee3t bi\u1ec3u di\u1ec5n s\u1ef1 thay \u0111\u1ed5i c\u1ee7a a, b v\u1edbi s\u1ef1 tr\u1ee3 \u0110\u1ea1t gi\u00fap c\u1ee7a GV. \u2013 C\u00f3 c\u1ed1 g\u1eafng li\u00ean h\u1ec7 gi\u1eefa l\u00ed thuy\u1ebft \u0111\u00e3 h\u1ecdc v\u00e0 bi\u1ec3u di\u1ec5n \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1. Ch\u01b0a \u0111\u1ea1t \u2013 Thi\u1ebfu m\u1ed9t trong c\u00e1c n\u1ed9i dung c\u1ee7a m\u1ee9c \u0111\u1ed9 \u0110\u1ea1t. b) GV h\u01b0\u1edbng d\u1eabn b\u00e1o c\u00e1o, th\u1ea3o lu\u1eadn: Gi\u1ea3i ph\u00e1p l\u1ef1a ch\u1ecdn nh\u00f3m HS b\u00e1o c\u00e1o: \u0110\u1ea1i di\u1ec7n c\u00e1c nh\u00f3m l\u1ea7n l\u01b0\u1ee3t l\u00ean b\u00e1o c\u00e1o. HS b\u00e1o c\u00e1o th\u1ea3o lu\u1eadn: Thuy\u1ebft tr\u00ecnh tr\u01b0\u1edbc l\u1edbp v\u1edbi s\u1ea3n ph\u1ea9m k\u00e8m theo. 4. K\u1ebft lu\u1eadn, nh\u1eadn \u0111\u1ecbnh a) Ph\u00e2n t\u00edch s\u1ea3n ph\u1ea9m: GV ph\u00e2n t\u00edch d\u1ef1a theo b\u1ea3ng ti\u00eau ch\u00ed \u0111\u00e3 thi\u1ebft l\u1eadp. b) \u0110\u00e1nh gi\u00e1 c\u00e1c m\u1ee9c \u0111\u1ed9 ho\u00e0n th\u00e0nh c\u1ee7a HS: GV \u0111\u00e1nh gi\u00e1 d\u1ef1a theo b\u1ea3ng ti\u00eau ch\u00ed. c) \u0110\u1ec1 xu\u1ea5t ph\u00e1t tri\u1ec3n: S\u1eed d\u1ee5ng Internet t\u00ecm hi\u1ec3u th\u00eam c\u00e1c \u1ee9ng d\u1ee5ng kh\u00e1c c\u1ee7a ph\u1ea7n m\u1ec1m GeoGebra. 227","Ho\u1ea1t \u0111\u1ed9ng 5. D\u00d9NG PH\u01af\u01a0NG TR\u00ccNH B\u1eacC NH\u1ea4T \u0110\u1ec2 T\u00cdNH N\u1ed2NG \u0110\u1ed8 PH\u1ea6N TR\u0102M C\u1ee6A DUNG D\u1ecaCH TH\u1ef0C H\u00c0NH PHA CH\u1ebe N\u01af\u1edaC MU\u1ed0I SINH L\u00cd C% = ? I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t: \u2013 V\u1eadn d\u1ee5ng \u0111\u01b0\u01a1\u0323c ki\u1ebfn th\u1ee9c \u0111\u1ea1i s\u1ed1 \u0111\u1ec3 gi\u1ea3i th\u00edch m\u1ed9t s\u1ed1 quy t\u1eafc trong Ho\u00e1 h\u1ecdc. \u2013 \u1ee8ng d\u1ee5ng ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t trong c\u00e1c b\u00e0i to\u00e1n v\u1ec1 x\u00e1c \u0111\u1ecbnh n\u1ed3ng \u0111\u1ed9 ph\u1ea7n tr\u0103m. \u2013 Th\u1ef1c h\u00e0nh pha ch\u1ebf dung d\u1ecbch n\u01b0\u1edbc mu\u1ed1i sinh l\u00ed theo t\u00ednh to\u00e1n \u0111\u00e3 h\u1ecdc. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 to\u00e1n h\u1ecdc, giao ti\u1ebfp to\u00e1n h\u1ecdc, s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5, ph\u01b0\u01a1ng ti\u1ec7n h\u1ecdc to\u00e1n. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 Khoa h\u1ecdc t\u1ef1 nhi\u00ean. II. Chu\u1ea9n b\u1ecb \u2013 S\u00e1ch gi\u00e1o khoa To\u00e1n 8, t\u1eadp hai \u2013 Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o; s\u00e1ch gi\u00e1o khoa Khoa h\u1ecdc t\u1ef1 nhi\u00ean 8 \u2013 Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o. \u2013 V\u00e0i chai n\u01b0\u1edbc mu\u1ed1i sinh l\u00ed NaCl 0,9% (lo\u1ea1i 10 ml ho\u1eb7c 500 ml). \u2013 L\u1edbp chia th\u00e0nh b\u1ed1n nh\u00f3m, m\u1ed7i nh\u00f3m chu\u1ea9n b\u1ecb 300 ml dung d\u1ecbch NaCl 6%. \u2013 D\u1ee5ng c\u1ee5 \u0111o \u0111\u1ed9 m\u1eb7n c\u1ee7a dung d\u1ecbch mu\u1ed1i \u0103n (n\u1ebfu c\u00f3). \u2013 B\u00ecnh th\u1ee7y tinh c\u00f3 chia v\u1ea1ch, n\u01b0\u1edbc tinh khi\u1ebft. III. T\u1ed5 ch\u1ee9c ho\u1ea1t \u0111\u1ed9ng 1. H\u01b0\u1edbng d\u1eabn c\u00e1ch l\u00e0m a) N\u1ed9i dung nhi\u1ec7m v\u1ee5: \u2013 HS xem l\u1ea1i c\u00e1ch t\u00ednh n\u1ed3ng \u0111\u1ed9 ph\u1ea7n tr\u0103m c\u1ee7a dung d\u1ecbch trong m\u00f4n h\u1ecdc Khoa h\u1ecdc t\u1ef1 nhi\u00ean l\u1edbp 8. \u2013 GV y\u00eau c\u1ea7n HS nh\u1eafc l\u1ea1i c\u00f4ng th\u1ee9c t\u00ednh n\u1ed3ng \u0111\u1ed9 ph\u1ea7n tr\u0103m c\u1ee7a dung d\u1ecbch. \u2013 GV gi\u1edbi thi\u1ec7u n\u01b0\u1edbc mu\u1ed1i sinh l\u00ed v\u00e0 vai tr\u00f2 c\u1ee7a n\u01b0\u1edbc mu\u1ed1i trong \u0111\u1eddi s\u1ed1ng. 228","b) Bi\u1ec7n ph\u00e1p ki\u1ec3m tra HS hi\u1ec3u r\u00f5 nhi\u1ec7m v\u1ee5: \u2013 Y\u00eau c\u1ea7u \u0111\u1ea1i di\u1ec7n nh\u00f3m nh\u1eafc l\u1ea1i t\u00f3m t\u1eaft n\u1ed9i dung c\u1ee7a SGK v\u00e0 c\u00e1c ki\u1ebfn th\u1ee9c \u0111\u00e3 h\u1ecdc c\u00f3 li\u00ean quan \u0111\u1ebfn n\u1ed3ng \u0111\u1ed9 ph\u1ea7n tr\u0103m c\u1ee7a dung d\u1ecbch v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t. \u2013 GV \u0111i\u1ec1u ch\u1ec9nh, b\u1ed5 sung c\u00e1c thi\u1ebfu s\u00f3t. 2. T\u1ed5 ch\u1ee9c th\u1ef1c hi\u1ec7n a) HS th\u1ef1c hi\u1ec7n: \u2013 HS th\u1ea3o lu\u1eadn nh\u00f3m v\u1ec1 t\u00ecnh hu\u1ed1ng c\u1ea7n pha ch\u1ebf bao nhi\u00eau n\u01b0\u1edbc v\u00e0o dung d\u1ecbch n\u01b0\u1edbc mu\u1ed1i c\u00f3 n\u1ed3ng \u0111\u1ed9 6% \u0111\u1ec3 \u0111\u01b0\u1ee3c n\u01b0\u1edbc mu\u1ed1i sinh l\u00ed 0,9%. \u2013 HS \u0111\u1eb7t \u1ea9n s\u1ed1, l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh. \u2013 HS ti\u1ebfn h\u00e0nh pha ch\u1ebf theo k\u1ebft qu\u1ea3 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh. b) GV h\u1ed7 tr\u1ee3 (kh\u1eafc ph\u1ee5c kh\u00f3 kh\u0103n HS d\u1ef1 ki\u1ebfn s\u1ebd g\u1eb7p): GV ki\u1ec3m tra k\u1ebft qu\u1ea3 v\u00e0 h\u01b0\u1edbng d\u1eabn c\u00e1ch pha ch\u1ebf. 3. Ki\u1ec3m tra \u0111\u00e1nh gi\u00e1 a) GV D\u1ef1 ki\u1ebfn m\u1ee9c \u0111\u1ed9 ho\u00e0n th\u00e0nh c\u1ee7a HS: M\u1ee9c \u0111\u1ed9 N\u1ed9i dung ho\u00e0n th\u00e0nh T\u1ed1t \u2013 \u0110\u1eb7t \u0111\u01b0\u1ee3c \u1ea9n s\u1ed1. \u0110\u1ea1t \u2013 Gi\u1ea3i \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh. Ch\u01b0a \u0111\u1ea1t \u2013 Pha ch\u1ebf \u0111\u01b0\u1ee3c n\u01b0\u1edbc mu\u1ed1i sinh l\u00ed v\u1edbi n\u1ed3ng \u0111\u1ed9 ch\u00ednh x\u00e1c. \u2013 \u0110\u1eb7t \u0111\u01b0\u1ee3c \u1ea9n s\u1ed1. \u2013 Gi\u1ea3i \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh. \u2013 Bi\u1ebft c\u00e1ch th\u1ef1c hi\u1ec7n v\u00e0 pha ch\u1ebf n\u01b0\u1edbc mu\u1ed1i sinh l\u00ed (ch\u01b0a c\u1ea7n ch\u00ednh x\u00e1c n\u1ed3ng \u0111\u1ed9). \u2013 Thi\u1ebfu m\u1ed9t trong c\u00e1c n\u1ed9i dung c\u1ee7a m\u1ee9c \u0111\u1ed9 \u0110\u1ea1t. b) GV h\u01b0\u1edbng d\u1eabn b\u00e1o c\u00e1o, th\u1ea3o lu\u1eadn: Gi\u1ea3i ph\u00e1p l\u1ef1a ch\u1ecdn nh\u00f3m HS b\u00e1o c\u00e1o: \u0110\u1ea1i di\u1ec7n c\u00e1c nh\u00f3m l\u1ea7n l\u01b0\u1ee3t l\u00ean b\u00e1o c\u00e1o. HS b\u00e1o c\u00e1o th\u1ea3o lu\u1eadn: Thuy\u1ebft tr\u00ecnh tr\u01b0\u1edbc l\u1edbp v\u1edbi s\u1ea3n ph\u1ea9m k\u00e8m theo. 4. K\u1ebft lu\u1eadn, nh\u1eadn \u0111\u1ecbnh a) Ph\u00e2n t\u00edch s\u1ea3n ph\u1ea9m: GV ph\u00e2n t\u00edch d\u1ef1a theo b\u1ea3ng ti\u00eau ch\u00ed \u0111\u00e3 thi\u1ebft l\u1eadp. b) \u0110\u00e1nh gi\u00e1 c\u00e1c m\u1ee9c \u0111\u1ed9 ho\u00e0n th\u00e0nh c\u1ee7a HS: GV \u0111\u00e1nh gi\u00e1 d\u1ef1a theo b\u1ea3ng ti\u00eau ch\u00ed. c) \u0110\u1ec1 xu\u1ea5t ph\u00e1t tri\u1ec3n: S\u1eed d\u1ee5ng Internet t\u00ecm hi\u1ec3u th\u00eam c\u00e1c \u1ee9ng d\u1ee5ng kh\u00e1c c\u1ee7a gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t. 229","Ho\u1ea1t \u0111\u1ed9ng 6. \u1ee8NG D\u1ee4NG \u0110\u1ecaNH L\u00cd THAL\u00c8S \u0110\u1ec2 \u01af\u1edaC L\u01af\u1ee2NG T\u1ec8 L\u1ec6 GI\u1eeeA CHI\u1ec0U NGANG V\u00c0 CHI\u1ec0U D\u1eccC C\u1ee6A M\u1ed8T V\u1eacT M M\u2032 M M\u2032 d d\u2032 Or r\u2032 O d' = OM' = r' \u21d2d = d' . d OM r r r' I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t: \u2013 V\u1eadn d\u1ee5ng \u0111\u1ecbnh l\u00ed Thal\u00e8s \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh t\u1ec9 l\u1ec7 gi\u1eefa chi\u1ec1u cao v\u00e0 chi\u1ec1u ngang c\u1ee7a m\u1ed9t v\u1eadt \u1edf xa. \u2013 V\u1eadn d\u1ee5ng To\u00e1n h\u1ecdc v\u00e0o th\u1ef1c ti\u1ec5n \u0111o \u0111\u1ea1c, \u01b0\u1edbc l\u01b0\u1ee3ng \u0111\u1ed9 d\u00e0i v\u00e0 v\u1ebd ph\u00e1c th\u1ea3o trong h\u1ed9i ho\u1ea1. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 to\u00e1n h\u1ecdc, giao ti\u1ebfp to\u00e1n h\u1ecdc, s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5, ph\u01b0\u01a1ng ti\u1ec7n h\u1ecdc to\u00e1n. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng. II. Chu\u1ea9n b\u1ecb \u2013 S\u00e1ch gi\u00e1o khoa To\u00e1n 8, t\u1eadp hai \u2013 Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o. \u2013 V\u1eadt m\u1eabu h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ho\u1eb7c h\u00ecnh tr\u1ee5 \u0111\u1ec3 tr\u00ean b\u00e0n. \u2013 Th\u01b0\u1edbc th\u1eb3ng, b\u00fat ch\u00ec ho\u1eb7c m\u1ed9t que g\u1ed7 th\u1eb3ng. III. T\u1ed5 ch\u1ee9c ho\u1ea1t \u0111\u1ed9ng 1. H\u01b0\u1edbng d\u1eabn c\u00e1ch l\u00e0m a) N\u1ed9i dung nhi\u1ec7m v\u1ee5: \u2013 \u0110o chi\u1ec1u cao v\u00e0 chi\u1ec1u ngang c\u1ee7a v\u1eadt m\u1eabu tr\u00ean b\u00e0n GV nh\u01b0 h\u00ecnh v\u1ebd h\u01b0\u1edbng d\u1eabn trong SGK. \u2013 T\u00ednh \u0111\u01b0\u1ee3c t\u1ec9 l\u1ec7 gi\u1eefa chi\u1ec1u cao v\u00e0 chi\u1ec1u ngang c\u1ee7a m\u1ed9t v\u1eadt \u1edf xa b\u1eb1ng c\u00e1c \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Thal\u00e8s. 230","b) Bi\u1ec7n ph\u00e1p ki\u1ec3m tra HS hi\u1ec3u r\u00f5 nhi\u1ec7m v\u1ee5: \u2013 Y\u00eau c\u1ea7u \u0111\u1ea1i di\u1ec7n nh\u00f3m nh\u1eafc l\u1ea1i t\u00f3m t\u1eaft n\u1ed9i dung c\u1ee7a SGK v\u00e0 c\u00e1c ki\u1ebfn th\u1ee9c \u0111\u00e3 h\u1ecdc c\u00f3 li\u00ean quan \u0111\u1ebfn \u0111\u1ecbnh l\u00ed Thal\u00e8s. \u2013 GV \u0111i\u1ec1u ch\u1ec9nh, b\u1ed5 sung c\u00e1c thi\u1ebfu s\u00f3t. 2. T\u1ed5 ch\u1ee9c th\u1ef1c hi\u1ec7n a) HS th\u1ef1c hi\u1ec7n: Nh\u00f3m tr\u01b0\u1edfng ph\u00e2n c\u00f4ng HS th\u1ef1c hi\u1ec7n \u0111o \u0111\u1ea1c, t\u00ednh to\u00e1n theo h\u01b0\u1edbng d\u1eabn trong SGK. b) GV h\u1ed7 tr\u1ee3 (kh\u1eafc ph\u1ee5c kh\u00f3 kh\u0103n HS d\u1ef1 ki\u1ebfn s\u1ebd g\u1eb7p): GV ki\u1ec3m tra c\u00e1ch \u0111o \u0111\u00fang v\u00e0 h\u01b0\u1edbng d\u1eabn c\u00e1ch t\u00ednh t\u1ec9 l\u1ec7. 3. Ki\u1ec3m tra \u0111\u00e1nh gi\u00e1 a) GV d\u1ef1 ki\u1ebfn m\u1ee9c \u0111\u1ed9 ho\u00e0n th\u00e0nh c\u1ee7a HS: M\u1ee9c \u0111\u1ed9 N\u1ed9i dung ho\u00e0n th\u00e0nh T\u1ed1t \u2013 T\u00ecm \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c t\u1ec9 l\u1ec7 gi\u1eefa chi\u1ec1u cao v\u00e0 chi\u1ec1u ngang c\u1ee7a v\u1eadt. \u2013 Gi\u1ea3i th\u00edch \u0111\u1ea7y \u0111\u1ee7 c\u01a1 s\u1edf to\u00e1n h\u1ecdc c\u1ee7a ph\u00e9p \u0111o. \u0110\u1ea1t \u2013 Ph\u00e2n c\u00f4ng \u0111\u1ea7y \u0111\u1ee7 v\u00e0 h\u1ee3p l\u00ed. Ch\u01b0a \u0111\u1ea1t \u2013 T\u00ecm \u0111\u01b0\u1ee3c t\u01b0\u01a1ng \u0111\u1ed1i ch\u00ednh x\u00e1c t\u1ec9 l\u1ec7 gi\u1eefa chi\u1ec1u cao v\u00e0 chi\u1ec1u ngang c\u1ee7a v\u1eadt. \u2013 C\u00f3 gi\u1ea3i th\u00edch c\u01a1 s\u1edf to\u00e1n h\u1ecdc c\u1ee7a ph\u00e9p \u0111o. \u2013 C\u00f3 ph\u00e2n c\u00f4ng trong nh\u00f3m. \u2013 Thi\u1ebfu m\u1ed9t trong c\u00e1c n\u1ed9i dung c\u1ee7a m\u1ee9c \u0111\u1ed9 \u0110\u1ea1t. b) GV h\u01b0\u1edbng d\u1eabn b\u00e1o c\u00e1o, th\u1ea3o lu\u1eadn: Gi\u1ea3i ph\u00e1p l\u1ef1a ch\u1ecdn nh\u00f3m HS b\u00e1o c\u00e1o: \u0110\u1ea1i di\u1ec7n c\u00e1c nh\u00f3m l\u1ea7n l\u01b0\u1ee3t l\u00ean b\u00e1o c\u00e1o. HS b\u00e1o c\u00e1o th\u1ea3o lu\u1eadn: Thuy\u1ebft tr\u00ecnh tr\u01b0\u1edbc l\u1edbp v\u1edbi s\u1ea3n ph\u1ea9m k\u00e8m theo. 4. K\u1ebft lu\u1eadn, nh\u1eadn \u0111\u1ecbnh a) Ph\u00e2n t\u00edch s\u1ea3n ph\u1ea9m: GV ph\u00e2n t\u00edch d\u1ef1a theo b\u1ea3ng ti\u00eau ch\u00ed \u0111\u00e3 thi\u1ebft l\u1eadp. b) \u0110\u00e1nh gi\u00e1 c\u00e1c m\u1ee9c \u0111\u1ed9 ho\u00e0n th\u00e0nh c\u1ee7a HS: GV \u0111\u00e1nh gi\u00e1 d\u1ef1a theo b\u1ea3ng ti\u00eau ch\u00ed. c) \u0110\u1ec1 xu\u1ea5t ph\u00e1t tri\u1ec3n: GV h\u01b0\u1edbng d\u1eabn HS th\u1ef1c hi\u1ec7n \u0111o \u0111\u1ea1c c\u00e1c c\u00f4ng tr\u00ecnh ngo\u00e0i l\u1edbp h\u1ecdc. 231","Nh\u00e0 xu\u1ea5t b\u1ea3n Gi\u00e1o d\u1ee5c Vi\u1ec7t Nam xin tr\u00e2n tr\u1ecdng c\u1ea3m \u01a1n c\u00e1c t\u00e1c gi\u1ea3 c\u00f3 t\u00e1c ph\u1ea9m, t\u01b0 li\u1ec7u \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng, tr\u00edch d\u1eabn trong cu\u1ed1n s\u00e1ch n\u00e0y. Ch\u1ecbu tr\u00e1ch nhi\u1ec7m xu\u1ea5t b\u1ea3n: T\u1ed5ng Gi\u00e1m \u0111\u1ed1c HO\u00c0NG L\u00ca B\u00c1CH Ch\u1ecbu tr\u00e1ch nhi\u1ec7m n\u1ed9i dung: T\u1ed5ng bi\u00ean t\u1eadp PH\u1ea0M V\u0128NH TH\u00c1I Bi\u00ean t\u1eadp: NGUY\u1ec4N TH\u1eca PH\u01af\u1edaC TH\u1ecc \u2013 \u0110\u0102NG TH\u1eca THU\u00dd \u2013 NGUY\u1ec4N TH\u1eca THANH DUY\u00caN Bi\u00ean t\u1eadp m\u0129 thu\u1eadt: B\u00d9I XU\u00c2N D\u01af\u01a0NG Thi\u1ebft k\u1ebf s\u00e1ch: B\u00d9I XU\u00c2N D\u01af\u01a0NG Tr\u00ecnh b\u00e0y b\u00eca: \u0110\u1eb6NG NG\u1eccC H\u00c0 Minh ho\u1ea1: NGUY\u1ec4N M\u1ea0NH H\u00d9NG S\u1eeda b\u1ea3n in: NGUY\u1ec4N TH\u1eca PH\u01af\u1edaC TH\u1ecc \u2013 \u0110\u0102NG TH\u1eca THU\u00dd \t NGUY\u1ec4N TH\u1eca THANH DUY\u00caN \u2013 HO\u00c0NG TH\u1eca THU DUNG Ch\u1ebf b\u1ea3n: C\u00d4NG TY C\u1ed4 PH\u1ea6N D\u1ecaCH V\u1ee4 XU\u1ea4T B\u1ea2N GI\u00c1O D\u1ee4C GIA \u0110\u1ecaNH B\u1ea3n quy\u1ec1n thu\u1ed9c Nh\u00e0 xu\u1ea5t b\u1ea3n Gi\u00e1o d\u1ee5c Vi\u1ec7t Nam. T\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n c\u1ee7a n\u1ed9i dung cu\u1ed1n s\u00e1ch n\u00e0y \u0111\u1ec1u kh\u00f4ng \u0111\u01b0\u1ee3c sao ch\u00e9p, l\u01b0u tr\u1eef, chuy\u1ec3n th\u1ec3 d\u01b0\u1edbi b\u1ea5t k\u00ec h\u00ecnh th\u1ee9c n\u00e0o khi ch\u01b0a c\u00f3 s\u1ef1 cho ph\u00e9p b\u1eb1ng v\u0103n b\u1ea3n c\u1ee7a Nh\u00e0 xu\u1ea5t b\u1ea3n Gi\u00e1o d\u1ee5c Vi\u1ec7t Nam. TO\u00c1N 8 - S\u00c1CH GI\u00c1O VI\u00caN (CH\u00c2N TR\u1edcI S\u00c1NG T\u1ea0O) M\u00e3 s\u1ed1: G2HG8T001M23 In\u2026\u2026\u2026b\u1ea3n, (Q\u0110 in s\u1ed1\u2026.) Kh\u1ed5 19 \u00d7 26,5 cm. \u0110\u01a1n v\u1ecb in:\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.. C\u01a1 s\u1edf in:\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026 S\u1ed1 \u0110KXB: 10-2023\/CXBIPH\/62-2157\/GD S\u1ed1 Q\u0110XB:......... ng\u00e0y \u2026. th\u00e1ng\u2026. n\u0103m 20 ... In xong v\u00e0 n\u1ed9p l\u01b0u chi\u1ec3u th\u00e1ng \u2026.n\u0103m 20\u2026. M\u00e3 s\u1ed1 ISBN: 978-604-0-35264-4 232","HU\u00c2N CH\u01af\u01a0NG H\u1ed2 CH\u00cd MINH B\u1ed8 S\u00c1CH GI\u00c1O VI\u00caN L\u1edaP 8 \u2013 CH\u00c2N TR\u1edcI S\u00c1NG T\u1ea0O 1. NG\u1eee V\u0102N 8, T\u1eacP M\u1ed8T 9. GI\u00c1O D\u1ee4C TH\u1ec2 CH\u1ea4T 8 S\u00e1ch gi\u00e1o vi\u00ean S\u00e1ch gi\u00e1o vi\u00ean 2. NG\u1eee V\u0102N 8, T\u1eacP HAI 10. \u00c2M NH\u1ea0C 8 S\u00e1ch gi\u00e1o vi\u00ean S\u00e1ch gi\u00e1o vi\u00ean 3. TO\u00c1N 8 11. M\u0128 THU\u1eacT 8 (1) S\u00e1ch gi\u00e1o vi\u00ean S\u00e1ch gi\u00e1o vi\u00ean 4. TI\u1ebeNG ANH 8 12. M\u0128 THU\u1eacT 8 (2) Friends Plus - Teacher\u2019s Guide S\u00e1ch gi\u00e1o vi\u00ean 5. GI\u00c1O D\u1ee4C C\u00d4NG D\u00c2N 8 13. HO\u1ea0T \u0110\u1ed8NG TR\u1ea2I NGHI\u1ec6M, S\u00e1ch gi\u00e1o vi\u00ean H\u01af\u1edaNG NGHI\u1ec6P 8 (1) S\u00e1ch gi\u00e1o vi\u00ean 6. L\u1ecaCH S\u1eec V\u00c0 \u0110\u1ecaA L\u00cd 8 S\u00e1ch gi\u00e1o vi\u00ean 14. HO\u1ea0T \u0110\u1ed8NG TR\u1ea2I NGHI\u1ec6M, H\u01af\u1edaNG NGHI\u1ec6P 8 (2) 7. TIN H\u1eccC 8 S\u00e1ch gi\u00e1o vi\u00ean S\u00e1ch gi\u00e1o vi\u00ean 8. C\u00d4NG NGH\u1ec6 8 S\u00e1ch gi\u00e1o vi\u00ean C\u00e1c \u0111\u01a1n v\u1ecb \u0111\u1ea7u m\u1ed1i ph\u00e1t h\u00e0nh \u2022 Mi\u1ec1n B\u1eafc: CTCP \u0110\u1ea7u t\u01b0 v\u00e0 Ph\u00e1t tri\u1ec3n Gi\u00e1o d\u1ee5c H\u00e0 N\u1ed9i CTCP S\u00e1ch v\u00e0 Thi\u1ebft b\u1ecb Gi\u00e1o d\u1ee5c mi\u1ec1n B\u1eafc \u2022 Mi\u1ec1n Trung: CTCP \u0110\u1ea7u t\u01b0 v\u00e0 Ph\u00e1t tri\u1ec3n Gi\u00e1o d\u1ee5c \u0110\u00e0 N\u1eb5ng CTCP S\u00e1ch v\u00e0 Thi\u1ebft b\u1ecb Gi\u00e1o d\u1ee5c mi\u1ec1n Trung \u2022 Mi\u1ec1n Nam: CTCP \u0110\u1ea7u t\u01b0 v\u00e0 Ph\u00e1t tri\u1ec3n Gi\u00e1o d\u1ee5c Ph\u01b0\u01a1ng Nam CTCP S\u00e1ch v\u00e0 Thi\u1ebft b\u1ecb Gi\u00e1o d\u1ee5c mi\u1ec1n Nam CTCP S\u00e1ch v\u00e0 Thi\u1ebft b\u1ecb Gi\u00e1o d\u1ee5c C\u1eedu Long S\u00e1ch \u0111i\u1ec7n t\u1eed: http:\/\/hanhtrangso.nxbgd.vn K\u00edch ho\u1ea1t \u0111\u1ec3 m\u1edf h\u1ecdc li\u1ec7u \u0111i\u1ec7n t\u1eed: C\u00e0o l\u1edbp nh\u0169 tr\u00ean tem \u0111\u1ec3 nh\u1eadn m\u00e3 s\u1ed1. Truy c\u1eadp http:\/\/hanhtrangso.nxbgd.vn v\u00e0 nh\u1eadp m\u00e3 s\u1ed1 t\u1ea1i bi\u1ec3u t\u01b0\u1ee3ng ch\u00eca kho\u00e1. Gi\u00e1: ....... \u0111"]