TS 10 CO DAP AN 23-24

["TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH L\u1eddi gi\u1ea3i a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp v\u00e0 KF.KE = KB.KC X\u00e9t t\u1ee9 gi\u00e1c BDEM , c\u00f3: \uf0ef\uf0ecBEC = 90\uf0b0(BE \u22a5 AC) \uf0ed \uf0ee\uf0efBFC = 90\uf0b0(CF \u22a5 AB) \uf0de T\u1ee9 gi\u00e1c BDEM n\u1ed9i ti\u1ebfp v\u00ec c\u00f3 hai \u0111\u1ec9nh k\u1ec1 c\u00f9ng nh\u00ecn m\u1ed9t c\u1ea1nh g\u00f3c b\u1eb1ng nhau. \uf0de KFB = KCE (g\u00f3c ngo\u00e0i b\u1eb1ng g\u00f3c \u0111\u1ed1i trong) X\u00e9t \uf044KFB v\u00e0 \uf044KCE c\u00f3: \uf0ec\uf0efKFB = KCE (cmt) \uf0ed \uf0ef\uf0eeCKE chung \uf044KFB ~ \uf044KCE (g-g) (s\u1eeda l\u1ea1i \uf0de \uf044KFB \uf044KCE ( g \u2212 g ) \uf0de KF = KB KC KE \uf0de KF.KE = KB.KC (1) b)X\u00e9t \uf044KMB v\u00e0 \uf044KCA c\u00f3: KMB = KCA (g\u00f3c ngo\u00e0i b\u1eb1ng g\u00f3c \u0111\u1ed1i trong t\u1ee9 gi\u00e1c ACMB n\u1ed9i ti\u1ebfp) CKA chung \uf0de \uf044KMB \u223d \uf044KCA (g-g) T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 8","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH 9 \uf0de KM = KB \uf0de KM .KA = KB.KC (2) KC KA T\u1eeb (1) v\u00e0 (2) , ta c\u00f3 : KM.KA = KE.KF X\u00e9t \uf044KMF v\u00e0 \uf044KEA c\u00f3: KM.KA = KE.KF \uf0de KM = KF KE KA EKA chung \uf0de \uf044KMF \u223d \uf044KEA (c-g-c) \uf0de KMF = KEA (g\u00f3c t\u01b0\u01a1ng \u1ee9ng) \uf0de AMFE n\u1ed9i ti\u1ebfp (c\u00f3 g\u00f3c ngo\u00e0i b\u1eb1ng g\u00f3c \u0111\u1ed1i trong) c)V\u00ec BE,CF c\u1eaft t\u1ea1i H n\u00ean c\u1ea7n ch\u1ee9ng minh MN qua H Ta c\u00f3: AMFE n\u1ed9i ti\u1ebfp AEHF n\u1ed9i ti\u1ebfp ( 2 g\u00f3c \u0111\u1ed1i b\u00f9 nhau) \uf0de A, M , F, H , E c\u00f9ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AH \uf0de MH \u22a5 AM (3) D\u1ef1ng \u0111\u01b0\u1eddng k\u00ednh AI c\u1ee7a (O) . Ta c\u00f3: AMI = 90\uf0b0 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) (4) T\u1eeb (3) v\u00e0 (4) , ta c\u00f3 M , H , I th\u1eb3ng h\u00e0ng (5) Ta l\u1ea1i c\u00f3: ABI = ACI = 90\uf0b0 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) \uf0de HB\/\/CI ( c\u00f9ng vu\u00f4ng g\u00f3c AC ) v\u00e0 HC\/\/BI ( c\u00f9ng vu\u00f4ng g\u00f3c AB ) N\u00ean BHCI l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh \uf0de HI qua N l\u00e0 trung \u0111i\u1ec3m BC , hay H , N, I th\u1eb3ng h\u00e0ng (6) T\u1eeb (5) v\u00e0 (6) , ta c\u00f3 M , H , N th\u1eb3ng h\u00e0ng Hay MN, BE, CF \u0111\u1ed3ng quy t\u1ea1i N . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u00d4\u00db GD&\u00d1T TP HO\u00c0 CH\u00cd MINH \u00d1E\u00c0 THAM KHA\u00dbO TUYE\u00c5N SINH 10 PHO\u00d8NG G\u00d1&\u00d1T QUA\u00c4N TA\u00c2N B\u00ccNH NA\u00caM HO\u00cfC: 2023 - 2024 M\u00d4N: TO\u00c1N 9 \u0110\u1ec0 THAM KH\u1ea2O M\u00c3 \u0110\u1ec0: Qu\u1eadn T\u00e2n B\u00ecnh - 1 \u0110\u1ec1 thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u1ec1) C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho h\u00e0m s\u1ed1 y = 1 x2 c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (P) v\u00e0 y = \u2212 3 x + 2 c\u00f3 \u0111\u1ed3 th\u1ecb (D) . 22 a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (D) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (D) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 5x2 \u2212x \u22121= 0 c\u00f3 2 nghi\u1ec7m l\u00e0 x1 , x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, 2 5x12 \u2212 2 2 2 ( ) ( )h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A = 5x22 \u22122 . C\u00e2u 3. (0,75 \u0111i\u1ec3m) Sau nh\u1eefng v\u1ee5 va ch\u1ea1m gi\u1eefa c\u00e1c xe tr\u00ean \u0111\u01b0\u1eddng, c\u1ea3nh s\u00e1t th\u01b0\u1eddng s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng t\u1ed1c \u0111\u1ed9 v (\u0111\u01a1n v\u1ecb: d\u1eb7m\/gi\u1edd) c\u1ee7a xe t\u1eeb v\u1ebft tr\u01b0\u1ee3t tr\u00ean m\u1eb7t \u0111\u01b0\u1eddng sau khi th\u1eafng \u0111\u1ed9t ng\u1ed9t. v = 30 fd . Trong \u0111\u00f3, d l\u00e0 chi\u1ec1u d\u00e0i v\u1ebft tr\u01b0\u1ee3t c\u1ee7a b\u00e1nh xe tr\u00ean n\u1ec1n \u0111\u01b0\u1eddng t\u00ednh b\u1eb1ng feet (ft), f l\u00e0 h\u1ec7 s\u1ed1 ma s\u00e1t gi\u1eefa b\u00e1nh xe v\u00e0 m\u1eb7t \u0111\u01b0\u1eddng (l\u00e0 th\u01b0\u1edbc \u0111o s\u1ef1 \u201ctr\u01a1n tr\u01b0\u1ee3t\u201d c\u1ee7a m\u1eb7t \u0111\u01b0\u1eddng) a) \u0110\u01b0\u1eddng Cao t\u1ed1c Long Th\u00e0nh \u2013 D\u1ea7u Gi\u00e2y c\u00f3 t\u1ed1c \u0111\u1ed9 gi\u1edbi h\u1ea1n l\u00e0 100km\/h . Sau m\u1ed9t v\u1ee5 va ch\u1ea1m gi\u1eefa hai xe, c\u1ea3nh s\u00e1t \u0111o \u0111\u01b0\u1ee3c v\u1ebft tr\u01b0\u1ee3t c\u1ee7a m\u1ed9t xe l\u00e0 d = 172 ft v\u00e0 h\u1ec7 s\u1ed1 ma s\u00e1t m\u1eb7t \u0111\u01b0\u1eddng t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 f = 0,7 . Ch\u1ee7 xe \u0111\u00f3 n\u00f3i xe c\u1ee7a \u00f4ng kh\u00f4ng ch\u1ea1y qu\u00e1 t\u1ed1c \u0111\u1ed9. H\u00e3y \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean \u0111\u1ec1 \u01b0\u1edbc l\u01b0\u1ee3ng t\u1ed1c \u0111\u1ed9 chi\u1ebfc xe \u0111\u00f3 r\u1ed3i cho bi\u1ebft l\u1eddi n\u00f3i c\u1ee7a ng\u01b0\u1eddi ch\u1ee7 xe \u0111\u00fang hay sai? (bi\u1ebft 1 d\u1eb7m b\u1eb1ng 1609m ) b) N\u1ebfu xe ch\u1ea1y v\u1edbi t\u1ed1c \u0111\u1ed9 48km \/ h tr\u00ean \u0111o\u1ea1n \u0111\u01b0\u1eddng c\u00f3 h\u1ec7 s\u1ed1 ma s\u00e1t l\u00e0 0,45 th\u00ec khi th\u1eafng l\u1ea1i v\u1ebft tr\u01b0\u1ee3t tr\u00ean \u0111\u01b0\u1eddng d\u00e0i bao nhi\u00eau feet? (L\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb) C\u00e2u 4. (1 \u0111i\u1ec3m) Ch\u1ecb Ng\u00e2n l\u00e0 c\u00f4ng nh\u00e2n may c\u1ee7a x\u00ed nghi\u1ec7p may B\u00ecnh Ph\u00e1t thu\u1ed9c Th\u00e0nh Ph\u1ed1 D\u0129 An, T\u1ec9nh B\u00ecnh D\u01b0\u01a1ng. Ta nh\u1eadn th\u1ea5y s\u1ed1 \u00e1o x (c\u00e1i \u00e1o) may \u0111\u01b0\u1ee3c trong m\u1ed9t th\u00e1ng v\u00e0 s\u1ed1 ti\u1ec1n y (\u0111\u1ed3ng) nh\u1eadn \u0111\u01b0\u1ee3c trong th\u00e1ng \u0111\u00f3 li\u00ean h\u1ec7 v\u1edbi nhau b\u1edfi h\u00e0m y (\u0111\u1ed3ng) s\u1ed1 y ax b c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh v\u1ebd. 13 500 000 a) H\u00e3y x\u00e1c \u0111\u1ecbnh h\u1ec7 s\u1ed1 a , b c\u1ee7a h\u00e0m s\u1ed1 y . 9 000 b) H\u1ecfi n\u1ebfu mu\u1ed1n nh\u1eadn l\u01b0\u01a1ng 14400000 \u0111\u1ed3ng th\u00ec ch\u1ecb Ng\u00e2n O 1 500 x (c\u00e1i \u00e1o) ph\u1ea3i may bao nhi\u00eau c\u00e1i \u00e1o? (L\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb) T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 5. (0,75 \u0111i\u1ec3m) S\u00e1ng s\u1edbm b\u00e1c T\u00e2m v\u00e0 b\u00e1c Ph\u00fac c\u00f9ng nhau \u0111i l\u01b0\u1edbi b\u1eaft c\u00e1. \u0110\u1ebfn chi\u1ec1u sau khi l\u01b0\u1edbi c\u00e1 v\u1ec1, b\u00e1c T\u00e2m b\u1eaft \u0111\u01b0\u1ee3c t\u1ed5ng c\u1ed9ng 60 con c\u00e1 c\u00e1c lo\u1ea1i, trong \u0111\u00f3 c\u00f3 10 con c\u00e1 r\u00f4. C\u00f2n b\u00e1c Ph\u00fac b\u1eaft \u0111\u01b0\u1ee3c 40% t\u1ed5ng s\u1ed1 c\u00e1 l\u00e0 c\u00e1 r\u00f4. Bi\u1ebft r\u1eb1ng s\u1ed1 c\u00e1 r\u00f4 c\u1ee7a c\u1ea3 hai b\u00e1c chi\u1ebfm 30% t\u1ed5ng s\u1ed1 c\u00e1 c\u1ee7a c\u1ea3 hai. H\u1ecfi b\u00e1c Ph\u00fac b\u1eaft \u0111\u01b0\u1ee3c bao nhi\u00eau con c\u00e1? C\u00e2u 6. (1 \u0111i\u1ec3m) Nh\u00e2n d\u1ecbp t\u1ed5 ch\u1ee9c sinh nh\u1eadt cho ng\u01b0\u1eddi th\u00e2n trong nh\u00e0, C\u00f4 Hoa \u0111\u1ebfn c\u1eeda h\u00e0ng ti\u1ec7n l\u1ee3i mua m\u1ed9t th\u00f9ng Coca-cola v\u00e0 hai th\u00f9ng n\u01b0\u1edbc su\u1ed1i Aquafina v\u1edbi gi\u00e1 ni\u00eam y\u1ebft t\u1ed5ng c\u1ed9ng l\u00e0 385 ngh\u00ecn \u0111\u1ed3ng. Khi t\u00ednh ti\u1ec1n th\u00ec c\u00f4 Hoa m\u1edbi bi\u1ebft gi\u00e1 m\u1ed7i th\u00f9ng Coca-cola gi\u1ea3m 20% , c\u00f2n m\u1ed7i th\u00f9ng n\u01b0\u1edbc su\u1ed1i l\u1ea1i \u0111\u01b0\u1ee3c gi\u1ea3m 25% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft. N\u00ean c\u00f4 Hoa \u0111\u00e3 tr\u1ea3 297 ngh\u00ecn \u0111\u1ed3ng tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n. T\u00ednh gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t th\u00f9ng Coca-cola v\u00e0 m\u1ed9t th\u00f9ng n\u01b0\u1edbc su\u1ed1i Aquafina. C\u00e2u 7. (1 \u0111i\u1ec3m) T\u1eeb m\u1ed9t t\u1ea5m nh\u00f4m h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc 60cm 200cm , ng\u01b0\u1eddi ta l\u00e0m m\u1ed9t th\u00f9ng n\u01b0\u1edbc h\u00ecnh tr\u1ee5 c\u00f3 chi\u1ec1u cao b\u1eb1ng 60cm , b\u1eb1ng c\u00e1ch g\u00f2 t\u1ea5m nh\u00f4m ban \u0111\u1ea7u th\u00e0nh m\u1eb7t xung quanh c\u1ee7a th\u00f9ng (nh\u01b0 h\u00ecnh v\u1ebd), \u0111\u00e1y v\u00e0 n\u1eafp l\u00e0m b\u1eb1ng t\u1ea5m nh\u00f4m kh\u00e1c (gi\u1ea3 s\u1eed c\u00e1c m\u1ed1i n\u1ed1i c\u00f3 k\u00edch th\u01b0\u1edbc kh\u00f4ng \u0111\u00e1ng k\u1ec3). a) T\u00ednh b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh tr\u00f2n \u0111\u00e1y th\u00f9ng n\u01b0\u1edbc sau khi g\u00f2 t\u1ea5m nh\u00f4m h\u00ecnh ch\u1eef nh\u1eadt th\u00e0nh h\u00ecnh tr\u1ee5. (ghi k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn 2 ch\u1eef s\u1ed1 th\u00e2\u0323p ph\u00e2n) b) H\u1ecfi l\u01b0\u1ee3ng n\u01b0\u1edbc c\u1ee7a th\u00f9ng c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u1ea7y kho\u1ea3ng bao nhi\u00eau l\u00edt? Bi\u1ebft th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 tr\u00f2n l\u00e0: V .R2.h v\u1edbi R l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao h\u00ecnh tr\u1ee5 v\u00e0 1dm3 1l . (ghi k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). 200cm 60cm 60cm C\u00e2u 8. (3 \u0111i\u1ec3m) Cho tam gi\u00e1c ABC nh\u1ecdn (AB AC ) n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n O . Ti\u1ebfp tuy\u1ebfn t\u1ea1i A c\u1ee7a O c\u1eaft BC t\u1ea1i S . G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m BC . V\u1ebd d\u00e2y AD vu\u00f4ng g\u00f3c v\u1edbi SO t\u1ea1i H , tia AD c\u1eaft BC t\u1ea1i K . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c SAOD n\u1ed9i ti\u1ebfp v\u00e0 5 \u0111i\u1ec3m S, A, O, I, D c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. b) Ch\u1ee9ng minh SK.SI SB.SC . c) V\u1ebd \u0111\u01b0\u1eddng k\u00ednh PJ ( J thu\u1ed9c cung nh\u1ecf CD ), tia SP c\u1eaft (O) t\u1ea1i \u0111i\u1ec3m M ( M kh\u00e1c P ). Ch\u1ee9ng minh M, K, J th\u1eb3ng h\u00e0ng. ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho h\u00e0m s\u1ed1 y = 1 x2 c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (P) v\u00e0 y = \u2212 3 x + 2 c\u00f3 \u0111\u1ed3 th\u1ecb (D) . 22 a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (D) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (D) b\u1eb1ng ph\u00e9p t\u00ednh. L\u1eddi gi\u1ea3i a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (D) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. BGT: x \u22124 \u22122 0 2 4 y = 1 x2 8 2 0 2 8 2 x 02 y = \u2212 3 x+2 2 \u22121 2 b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (D) b\u1eb1ng ph\u00e9p t\u00ednh. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (D) : 1 x2 = \u2212 3 x + 2 22 \uf0db 1 x2 + 3 x \u2212 2 = 0 22 \uf0db \uf0e9x = 1 \uf0ea = \u22124 \uf0eb x Thay x =1 v\u00e0o y = \u22123 x+2, ta \u0111\u01b0\u1ee3c: y = \u2212 3 .1+ 2 = 1 . 2 2 2 Thay x = \u22124 v\u00e0o y = \u2212 3 x + 2 , ta \u0111\u01b0\u1ee3c: y = \u2212 3 .(\u22124) + 2 = 8 . 22 V\u1eady \uf0e6 1; 1 \uf0f6 , (\u22124; 8) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. \uf0e7\uf0e8 2 \uf0f7\uf0f8 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 3","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 5x2 \u2212 x \u2212 1 = 0 c\u00f3 2 nghi\u1ec7m l\u00e0 x1 , x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, 2 5x12 \u2212 2 2 2 ( ) ( )h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A = 5x22 \u22122 . L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = \uf0e6 \u2212 1 \uf0f62 \u2212 4.5.(\u22121) = 81 \uf03e0 \uf0e7\uf0e8 2 \uf0f7\uf0f8 4 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 ,x2 . S x1 x2 b1 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: a 10 P x1.x2 c 1 a 5 Ta c\u00f3: x1 l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh: 5x2 \u2212 x \u22121= 0 \uf0de 5x12 \u2212 x1 \u22121= 0 \uf0db 5x12 \u22122= x1 \u22121 3 2 2 T\u01b0\u01a1ng t\u1ef1, ta c\u00f3: 5x22 \u22122 = x2 \u22121 2 ( ) ( )Ta c\u00f3: A = 5x12 \u2212 2 2 5x22 \u2212 2 2 ( ) ( )A = 5x12 \u2212 2 2 5x22 \u2212 2 2 ( ) ( )=\uf0e95x12 \u22122 . 5x22 \u22122 \uf0f92 \uf0eb \uf0fb = \uf0e9\uf0e6 x1 \uf0f6\uf0e6 x2 \uf0f6\uf0f92 \uf0ea\uf0e7 2 \u2212 1\uf0f7.\uf0e7 2 \u2212 1\uf0f7\uf0fa \uf0ea\uf0eb\uf0e8 \uf0f8\uf0e8 \uf0f8\uf0fa\uf0fb ( )=\uf0e9 x1 x2 \u2212 1 \uf0f92 \uf0ea 4 2 x1 + x2 + 1\uf0fa \uf0eb \uf0fb \uf0e9 \u22121 \uf0f92 \uf0ea \uf0fa =\uf0ea 5 \u2212 1 .1 + 1\uf0fa 4 2 10 \uf0fa \uf0ea \uf0ea\uf0eb \uf0fb\uf0fa = 81 100 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 4","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 3. (0,75 \u0111i\u1ec3m) Sau nh\u1eefng v\u1ee5 va ch\u1ea1m gi\u1eefa c\u00e1c xe tr\u00ean \u0111\u01b0\u1eddng, c\u1ea3nh s\u00e1t th\u01b0\u1eddng s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng t\u1ed1c \u0111\u1ed9 v (\u0111\u01a1n v\u1ecb: d\u1eb7m\/gi\u1edd) c\u1ee7a xe t\u1eeb v\u1ebft tr\u01b0\u1ee3t tr\u00ean m\u1eb7t \u0111\u01b0\u1eddng sau khi th\u1eafng \u0111\u1ed9t ng\u1ed9t. v = 30 fd . Trong \u0111\u00f3, d l\u00e0 chi\u1ec1u d\u00e0i v\u1ebft tr\u01b0\u1ee3t c\u1ee7a b\u00e1nh xe tr\u00ean n\u1ec1n \u0111\u01b0\u1eddng t\u00ednh b\u1eb1ng feet (ft), f l\u00e0 h\u1ec7 s\u1ed1 ma s\u00e1t gi\u1eefa b\u00e1nh xe v\u00e0 m\u1eb7t \u0111\u01b0\u1eddng (l\u00e0 th\u01b0\u1edbc \u0111o s\u1ef1 \u201ctr\u01a1n tr\u01b0\u1ee3t\u201d c\u1ee7a m\u1eb7t \u0111\u01b0\u1eddng) a) \u0110\u01b0\u1eddng Cao t\u1ed1c Long Th\u00e0nh \u2013 D\u1ea7u Gi\u00e2y c\u00f3 t\u1ed1c \u0111\u1ed9 gi\u1edbi h\u1ea1n l\u00e0 100km\/h . Sau m\u1ed9t v\u1ee5 va ch\u1ea1m gi\u1eefa hai xe, c\u1ea3nh s\u00e1t \u0111o \u0111\u01b0\u1ee3c v\u1ebft tr\u01b0\u1ee3t c\u1ee7a m\u1ed9t xe l\u00e0 d = 172 ft v\u00e0 h\u1ec7 s\u1ed1 ma s\u00e1t m\u1eb7t \u0111\u01b0\u1eddng t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 f = 0,7 . Ch\u1ee7 xe \u0111\u00f3 n\u00f3i xe c\u1ee7a \u00f4ng kh\u00f4ng ch\u1ea1y qu\u00e1 t\u1ed1c \u0111\u1ed9. H\u00e3y \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean \u0111\u1ec1 \u01b0\u1edbc l\u01b0\u1ee3ng t\u1ed1c \u0111\u1ed9 chi\u1ebfc xe \u0111\u00f3 r\u1ed3i cho bi\u1ebft l\u1eddi n\u00f3i c\u1ee7a ng\u01b0\u1eddi ch\u1ee7 xe \u0111\u00fang hay sai? (bi\u1ebft 1 d\u1eb7m b\u1eb1ng 1609m ) b) N\u1ebfu xe ch\u1ea1y v\u1edbi t\u1ed1c \u0111\u1ed9 48km \/ h tr\u00ean \u0111o\u1ea1n \u0111\u01b0\u1eddng c\u00f3 h\u1ec7 s\u1ed1 ma s\u00e1t l\u00e0 0,45 th\u00ec khi th\u1eafng l\u1ea1i v\u1ebft tr\u01b0\u1ee3t tr\u00ean \u0111\u01b0\u1eddng d\u00e0i bao nhi\u00eau feet? (L\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb) L\u1eddi gi\u1ea3i a) Thay d 172; f = 0,7 v\u00e0o c\u00f4ng th\u1ee9c v 30 fd , ta c\u00f3: v 30 fd 30.0,7.172 2 903 (d\u1eb7m \/h ) Ta c\u00f3: 2 903 d\u1eb7m \/h 96700,76614 m \/ h 96,7 km \/ h . V\u1eady ng\u01b0\u1eddi l\u00e1i xe \u0111\u00f3 n\u00f3i \u0111\u00fang (v\u00ec 96,7 km \/ h 100 km \/ h ). b) \u0110\u1ed5i 48km \/ h = 48000 m \/ h 48000 1609 d\u1eb7m \/h Thay v 48000 ; f = 0,45 v\u00e0o c\u00f4ng th\u1ee9c v 30 fd , ta c\u00f3: 1609 48000 30.0, 45.d 1609 48000 2 30.0,45.d 1609 d 48000 2 30.0, 45 66 (feet) 1609 : V\u1eady v\u1ebft tr\u01b0\u1ee3t tr\u00ean \u0111\u01b0\u1eddng d\u00e0i kho\u1ea3ng 66 (feet) . T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 5","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 4. (1 \u0111i\u1ec3m) Ch\u1ecb Ng\u00e2n l\u00e0 c\u00f4ng nh\u00e2n may c\u1ee7a x\u00ed nghi\u1ec7p may B\u00ecnh Ph\u00e1t thu\u1ed9c Th\u00e0nh Ph\u1ed1 D\u0129 An, T\u1ec9nh B\u00ecnh D\u01b0\u01a1ng. Ta nh\u1eadn th\u1ea5y s\u1ed1 \u00e1o x (c\u00e1i \u00e1o) may y (\u0111\u1ed3ng) \u0111\u01b0\u1ee3c trong m\u1ed9t th\u00e1ng v\u00e0 s\u1ed1 ti\u1ec1n y (\u0111\u1ed3ng) nh\u1eadn \u0111\u01b0\u1ee3c 13 500 000 trong th\u00e1ng \u0111\u00f3 li\u00ean h\u1ec7 v\u1edbi nhau b\u1edfi h\u00e0m s\u1ed1 y ax b c\u00f3 9 000 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh v\u1ebd. a) H\u00e3y x\u00e1c \u0111\u1ecbnh h\u1ec7 s\u1ed1 a , b c\u1ee7a h\u00e0m s\u1ed1 y . O 1 500 x (c\u00e1i \u00e1o) b) H\u1ecfi n\u1ebfu mu\u1ed1n nh\u1eadn l\u01b0\u01a1ng 14400000 \u0111\u1ed3ng th\u00ec ch\u1ecb Ng\u00e2n ph\u1ea3i may bao nhi\u00eau c\u00e1i \u00e1o? (L\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb) L\u1eddi gi\u1ea3i a) Thay x 0 ; y 9000 v\u00e0o c\u00f4ng th\u1ee9c y ax b , ta \u0111\u01b0\u1ee3c: 9000 a.0 b 0.a b 9000 1 Thay x 1500 ; y 13500000 v\u00e0o c\u00f4ng th\u1ee9c y ax b , ta \u0111\u01b0\u1ee3c: 13500000 a.1500 b 1500.a b 13500000 2 0.a b 9000 a 8994 T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: b 9000 1500.a b 13500000 y 8994x 9000 b\/ Thay y 14400000 v\u00e0o c\u00f4ng th\u1ee9c y 8994x 9000 , ta \u0111\u01b0\u1ee3c: 14400000 8994x 9000 x 1600,07 V\u1eady s\u1ed1 \u00e1o ch\u1ecb Ng\u00e2n ph\u1ea3i may kho\u1ea3ng 1601 \u00e1o. C\u00e2u 5. (0,75 \u0111i\u1ec3m) S\u00e1ng s\u1edbm b\u00e1c T\u00e2m v\u00e0 b\u00e1c Ph\u00fac c\u00f9ng nhau \u0111i l\u01b0\u1edbi b\u1eaft c\u00e1. \u0110\u1ebfn chi\u1ec1u sau khi l\u01b0\u1edbi c\u00e1 v\u1ec1, b\u00e1c T\u00e2m b\u1eaft \u0111\u01b0\u1ee3c t\u1ed5ng c\u1ed9ng 60 con c\u00e1 c\u00e1c lo\u1ea1i, trong \u0111\u00f3 c\u00f3 10 con c\u00e1 r\u00f4. C\u00f2n b\u00e1c Ph\u00fac b\u1eaft \u0111\u01b0\u1ee3c 40% t\u1ed5ng s\u1ed1 c\u00e1 l\u00e0 c\u00e1 r\u00f4. Bi\u1ebft r\u1eb1ng s\u1ed1 c\u00e1 r\u00f4 c\u1ee7a c\u1ea3 hai b\u00e1c chi\u1ebfm 30% t\u1ed5ng s\u1ed1 c\u00e1 c\u1ee7a c\u1ea3 hai. H\u1ecfi b\u00e1c Ph\u00fac b\u1eaft \u0111\u01b0\u1ee3c bao nhi\u00eau con c\u00e1? L\u1eddi gi\u1ea3i ( )G\u1ecdi x (con c\u00e1) l\u00e0 s\u1ed1 con c\u00e1 c\u1ee7a b\u00e1c Ph\u00fac b\u1eaft \u0111\u01b0\u1ee3c x \uf0ce * Ta c\u00f3: s\u1ed1 c\u00e1 c\u1ee7a b\u00e1c T\u00e2m v\u00e0 b\u00e1c Ph\u00fac l\u00e0: 60 x (con c\u00e1) S\u1ed1 c\u00e1 r\u00f4 c\u1ee7a b\u00e1c T\u00e2m v\u00e0 b\u00e1c Ph\u00fac l\u00e0: 10 40%.x (con c\u00e1) Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 30%. 60 x 10 40%.x T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 6","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH x 80 (nh\u1eadn) V\u1eady b\u00e1c Ph\u00fac b\u1eaft \u0111\u01b0\u1ee3c 80 con c\u00e1. C\u00e2u 6. (1 \u0111i\u1ec3m) Nh\u00e2n d\u1ecbp t\u1ed5 ch\u1ee9c sinh nh\u1eadt cho ng\u01b0\u1eddi th\u00e2n trong nh\u00e0, C\u00f4 Hoa \u0111\u1ebfn c\u1eeda h\u00e0ng ti\u1ec7n l\u1ee3i mua m\u1ed9t th\u00f9ng Coca-cola v\u00e0 hai th\u00f9ng n\u01b0\u1edbc su\u1ed1i Aquafina v\u1edbi gi\u00e1 ni\u00eam y\u1ebft t\u1ed5ng c\u1ed9ng l\u00e0 385 ngh\u00ecn \u0111\u1ed3ng. Khi t\u00ednh ti\u1ec1n th\u00ec c\u00f4 Hoa m\u1edbi bi\u1ebft gi\u00e1 m\u1ed7i th\u00f9ng Coca-cola gi\u1ea3m 20% , c\u00f2n m\u1ed7i th\u00f9ng n\u01b0\u1edbc su\u1ed1i l\u1ea1i \u0111\u01b0\u1ee3c gi\u1ea3m 25% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft. N\u00ean c\u00f4 Hoa \u0111\u00e3 tr\u1ea3 297 ngh\u00ecn \u0111\u1ed3ng tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n. T\u00ednh gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t th\u00f9ng Coca-cola v\u00e0 m\u1ed9t th\u00f9ng n\u01b0\u1edbc su\u1ed1i Aquafina. L\u1eddi gi\u1ea3i G\u1ecdi x (ngh\u00ecn \u0111\u1ed3ng) l\u00e0 gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t th\u00f9ng Coca-cola (x \uf03e 0) y (ngh\u00ecn \u0111\u1ed3ng) l\u00e0 gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t th\u00f9ng n\u01b0\u1edbc su\u1ed1i Aquafina (y \uf03e 0) Ta c\u00f3: T\u1ed5ng s\u1ed1 ti\u1ec1n ni\u00eam y\u1ebft l\u00e0 385 ngh\u00ecn \u0111\u1ed3ng: x 2y 385 1 Ta c\u00f3: T\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a h\u00f3a \u0111\u01a1n l\u00e0 297 ngh\u00ecn \u0111\u1ed3ng: 80%x 75%.2y 297 2 T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ecx + 2y = 385 \uf0ed\uf0ee80%x + 75%.2.y = 297 Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c : x 165; y 110 ( th\u1ecfa \u0111i\u1ec1u ki\u1ec7n ) V\u1eady m\u1ed9t th\u00f9ng Coca \u2013 cola gi\u00e1 165 ngh\u00ecn \u0111\u1ed3ng; m\u1ed9t th\u00f9ng n\u01b0\u1edbc su\u1ed1i Aquafina gi\u00e1 110 ngh\u00ecn \u0111\u1ed3ng. C\u00e2u 7. (1 \u0111i\u1ec3m) T\u1eeb m\u1ed9t t\u1ea5m nh\u00f4m h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc 60cm 200cm , ng\u01b0\u1eddi ta l\u00e0m m\u1ed9t th\u00f9ng n\u01b0\u1edbc h\u00ecnh tr\u1ee5 c\u00f3 chi\u1ec1u cao b\u1eb1ng 60cm , b\u1eb1ng c\u00e1ch g\u00f2 t\u1ea5m nh\u00f4m ban \u0111\u1ea7u th\u00e0nh m\u1eb7t xung quanh c\u1ee7a th\u00f9ng (nh\u01b0 h\u00ecnh v\u1ebd), \u0111\u00e1y v\u00e0 n\u1eafp l\u00e0m b\u1eb1ng t\u1ea5m nh\u00f4m kh\u00e1c (gi\u1ea3 s\u1eed c\u00e1c m\u1ed1i n\u1ed1i c\u00f3 k\u00edch th\u01b0\u1edbc kh\u00f4ng \u0111\u00e1ng k\u1ec3). a) T\u00ednh b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh tr\u00f2n \u0111\u00e1y th\u00f9ng n\u01b0\u1edbc sau khi g\u00f2 t\u1ea5m nh\u00f4m h\u00ecnh ch\u1eef nh\u1eadt th\u00e0nh h\u00ecnh tr\u1ee5. (ghi k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn 2 ch\u1eef s\u1ed1 th\u00e2\u0323p ph\u00e2n) b) H\u1ecfi l\u01b0\u1ee3ng n\u01b0\u1edbc c\u1ee7a th\u00f9ng c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u1ea7y kho\u1ea3ng bao nhi\u00eau l\u00edt? Bi\u1ebft th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 tr\u00f2n l\u00e0: V .R2.h v\u1edbi R l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao h\u00ecnh tr\u1ee5 v\u00e0 1dm3 1l . (ghi k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). 200cm 60cm 60cm T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 7","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH L\u1eddi gi\u1ea3i a) B\u00e1n k\u00ednh \u0111\u00e1y h\u1ed3 n\u01b0\u1edbc l\u00e0: R = C = 200 = 100 \uf0bb 31, 83 ( cm) 2\uf070 2\uf070 \uf070 b) Th\u1ec3 t\u00edch h\u1ed3 n\u01b0\u1edbc h\u00ecnh tr\u1ee5 l\u00e0 ( )V .\uf0e6\uf0e7\uf0e8 100 \uf0f62 = \uf070 R2h = \uf070 \uf070 \uf0f7\uf0f8 .60 \uf0bb 190985,9(c m3 ) \uf0bb 190,9859(d m3) \uf0bb 191 l V\u1eady th\u00f9ng ch\u1ee9a kho\u1ea3ng 191 l\u00edt n\u01b0\u1edbc. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho tam gi\u00e1c ABC nh\u1ecdn ( AB AC ) n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n O . Ti\u1ebfp tuy\u1ebfn t\u1ea1i A c\u1ee7a O c\u1eaft BC t\u1ea1i S . G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m BC . V\u1ebd d\u00e2yAD vu\u00f4ng g\u00f3c v\u1edbi SO t\u1ea1i H , tia AD c\u1eaft BC t\u1ea1i K . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c SAOD n\u1ed9i ti\u1ebfp v\u00e0 5 \u0111i\u1ec3m S, A, O, I, D c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. b) Ch\u1ee9ng minh SK.SI SB.SC . c) V\u1ebd \u0111\u01b0\u1eddng k\u00ednh PJ (J thu\u1ed9c cung nh\u1ecf CD ), tia SP c\u1eaft (O) t\u1ea1i \u0111i\u1ec3m M ( M kh\u00e1cP ). Ch\u1ee9ng minh M, K, J th\u1eb3ng h\u00e0ng. L\u1eddi gi\u1ea3i P A M HO S B KI C DJ a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c SAOD n\u1ed9i ti\u1ebfp v\u00e0 5 \u0111i\u1ec3m S , A , O , I , D c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. Ch\u1ee9ng minh: SAO SDO c.g.c SAO SDO (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) M\u00e0 SAO 90 (SA l\u00e0 ti\u1ebfp tuy\u1ebfn (O) ) SDO 90 M\u00e0 D O Suy ra SD l\u00e0 ti\u1ebfp tuy\u1ebfn (O) T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 8","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH X\u00e9t t\u1ee9 gi\u00e1c SAOD c\u00f3: SAO = 90\uf0b0 ( SA l\u00e0 ti\u1ebfp tuy\u1ebfn (O) ) SDO = 90\uf0b0 ( SD l\u00e0 ti\u1ebfp tuy\u1ebfn (O) ) Suy ra t\u1ee9 gi\u00e1c SAOD n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh SO X\u00e9t t\u1ee9 gi\u00e1c (O) , c\u00f3: I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC (gt) \uf0de OI \u22a5 BC t\u1ea1i I (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) Ta c\u00f3: SAO = 90\uf0b0 ( SA l\u00e0 ti\u1ebfp tuy\u1ebfn (O) ) SDO = 90\uf0b0 ( SD l\u00e0 ti\u1ebfp tuy\u1ebfn (O) ) SIO = 90\uf0b0 (cmt ) \uf0de SAO = SDO = SIO = 90\uf0b0 S, A, O, I, D c\u00f9ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh SO ( A,D,I c\u00f9ng nh\u00ecn SO d\u01b0\u1edbi m\u1ed9t g\u00f3c vu\u00f4ng) b) Ch\u1ee9ng minh SK.SI SB.SC . Ch\u1ee9ng minh: SHK \u223d SIO (g-g) Suy ra \u0111\u01b0\u1ee3c: SH.SO SK.SI . Ch\u1ee9ng minh: SH.SO SD2 (h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng). Ch\u1ee9ng minh: SB.SC SD2 T\u1eeb \u0111\u00f3 suy ra SK.SI SB.SC . c) V\u1ebd \u0111\u01b0\u1eddng k\u00ednh PJ (J thu\u1ed9c cung nh\u1ecf CD ), tia SP c\u1eaft (O) t\u1ea1i \u0111i\u1ec3m M ( M kh\u00e1cP ). Ch\u1ee9ng minh M, K, J th\u1eb3ng h\u00e0ng. Ch\u1ee9ng minh: SM.SP SB.SC . Suy ra: SM.SP SK.SI . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c IKMP n\u1ed9i ti\u1ebfp. Suy ra: PMK 90 . Suy ra: MK SP . M\u00e0 MJ SP ( JMP 90 g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) Suy ra M, K, J th\u1eb3ng h\u00e0ng. ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 9","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u00d4\u00db GD&\u00d1T TP HO\u00c0 CH\u00cd MINH \u00d1E\u00c0 THAM KHA\u00dbO TUYE\u00c5N SINH 10 PHO\u00d8NG G\u00d1&\u00d1T QUA\u00c4N B\u00ccNH TA\u00c2N NA\u00caM HO\u00cfC: 2023 - 2024 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. M\u00c3 \u0110\u1ec0: Qu\u1eadn B\u00ecnh T\u00e2n - 2 Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 3x \u2212 2 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh x2 \u2212 5x + 5 =0. G\u1ecdi x1 , x2 l\u00e0 hai nghi\u1ec7m (n\u1ebfu c\u00f3) . Kh\u00f4ng gi\u1ea3i 3 ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A = x12 + x22 x2 x1 C\u00e2u 3. (0,75 \u0111i\u1ec3m). B\u00ean c\u1ea1nh vi\u1ec7c xem \u0111ua ch\u00f3, nhi\u1ec1u ng\u01b0\u1eddi th\u00edch tham gia ch\u01b0\u01a1ng tr\u00ecnh d\u1ef1 th\u01b0\u1edfng \u0111\u1ec3 cu\u1ed9c \u0111ua th\u00eam ph\u1ea5n kh\u00edch. Tr\u01b0\u1edbc khi ch\u1ecdn ch\u00f3 \u0111\u1ec3 \u0111\u1ea1t th\u01b0\u1edfng, b\u1ea1n s\u1ebd \u0111\u01b0\u1ee3c ph\u00e1t m\u1ed9t cu\u1ed1n t\u00e0i li\u1ec7u c\u00f3 gi\u1edbi thi\u1ec7u kh\u00e1 chi ti\u1ebft v\u1ec1 t\u1eebng ch\u00fa ch\u00f3, t\u1eeb nh\u1eefng th\u00e0nh t\u00edch t\u1ed1t, x\u1ea5u \u0111\u1ebfn t\u00ecnh tr\u1ea1ng s\u1ee9c kh\u1ecfe, cu\u1ed9c \u0111ua g\u1ea7n nh\u1ea5t c\u00f3 tham gia\u2026s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng ch\u1ecdn l\u1ef1a. V\u00e0 c\u00f3 5 ki\u1ec3u th\u1eafng gi\u1ea3i \u00e1p d\u1ee5ng cho c\u00e1c \u0111\u1ee3t \u0111ua l\u00e0: - Th\u1eafng nh\u1ea5t l\u00e0 Win n\u1ebfu con ch\u00f3 m\u00e0 b\u1ea1n ch\u1ecdn v\u1ec1 nh\u1ea5t. - Th\u1eafng nh\u1ea5t \u2013 nh\u00ec (Exacta) l\u00e0 2 con ch\u00f3 b\u1ea1n ch\u1ecdn v\u1ec1 nh\u1ea5t \u2013 nh\u00ec theo \u0111\u00fang th\u1ee9 t\u1ef1. - Th\u1eafng nh\u1ea5t \u2013 nh\u00ec \u2013 ba (Trifecta) l\u00e0 c\u1ea3 3 con ch\u00f3 b\u1ea1n ch\u1ecdn \u0111\u1ec1u v\u1ec1 3 th\u1ee9 h\u1ea1ng \u0111\u1ea7u theo \u0111\u00fang th\u1ee9 t\u1ef1. C\u00e1c gi\u1ea3i ti\u1ebfp theo l\u00e0 Quartet (4) , Superfecta (6) . C\u00e0ng l\u00ean cao c\u00e0ng tr\u00fang \u0111\u1eadm. H\u1ecfi trong m\u1ed9t \u0111\u1ee3t \u0111ua c\u00f3 8 ch\u00fa khuy\u1ec3n, ta c\u00f3 bao nhi\u00eau c\u00e1ch ch\u1ecdn v\u00e9 d\u1ef1 th\u01b0\u1edfng theo gi\u1ea3i nh\u1ea5t \u2013 nh\u00ec \u2013 ba? C\u00e2u 4. (1 \u0111i\u1ec3m). Cu\u1ed1i n\u0103m 2009 , m\u1ed9t b\u1ea3n b\u00e1o c\u00e1o \u0111\u01b0\u1ee3c tr\u00ecnh l\u00ean ch\u00ednh ph\u1ee7 Anh. Theo \u0111\u00f3, n\u1ebfu nhi\u1ec7t \u0111\u1ed9 tr\u00e1i \u0111\u1ea5t t\u0103ng l\u00ean 2\uf0b0C th\u00ec t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf th\u1ebf gi\u1edbi s\u1ebd b\u1ecb gi\u1ea3m \u0111i 3% , n\u1ebfu nhi\u1ec7t \u0111\u1ed9 t\u0103ng l\u00ean 5\uf0b0C kinh t\u1ebf s\u1ebd gi\u1ea3m \u0111i 10% T\u1eeb \u0111\u00f3, th\u00f4ng qua nghi\u00ean c\u1ee9u m\u1ed9t nh\u00f3m nh\u00e0 kinh t\u1ebf h\u1ecdc \u0111\u00e3 \u0111\u01b0a ra d\u1ef1 \u0111o\u00e1n v\u1ec1 m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa nhi\u1ec7t \u0111\u1ed9 th\u1ebf gi\u1edbi v\u00e0 t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf c\u1ee7a th\u1ebf gi\u1edbi. K\u1ebft qu\u1ea3 nghi\u00ean c\u1ee9u \u0111\u01b0a ra r\u1eb1ng t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf b\u1ecb gi\u1ea3m y % l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t theo x l\u00e0 nhi\u1ec7t \u0111\u1ed9 t\u0103ng l\u00ean c\u1ee7a Tr\u00e1i \u0111\u1ea5t (t\u00ednh theo \uf0b0C ). a) X\u00e1c \u0111\u1ecbnh m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa y v\u00e0 x b) Theo nghi\u00ean c\u1ee9u \u0111\u00f3, t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf s\u1ebd gi\u1ea3m bao nhi\u00eau n\u1ebfu th\u1ebf gi\u1edbi t\u0103ng th\u00eam 10\uf0b0C (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 5. (0,75 \u0111i\u1ec3m). L\u1edbp 9A d\u1ef1 \u0111\u1ecbnh t\u1ed5 ch\u1ee9c li\u00ean hoan l\u1edbp cu\u1ed1i n\u0103m, trong ph\u1ea7n n\u01b0\u1edbc c\u1ea7n chu\u1ea9n b\u1ecb 42 ly tr\u00e0 s\u1eefa. \u0110\u1ec3 ti\u1ebft ki\u1ec7m chi ph\u00ed l\u1edbp \u0111\u00e3 t\u00ecm hi\u1ec3u gi\u00e1 c\u1ee7a hai c\u1eeda h\u00e0ng A v\u00e0 B nh\u01b0 sau: - C\u1eeda h\u00e0ng A : mua 5 ly b\u1ea5t k\u00ec s\u1ebd \u0111\u01b0\u1ee3c t\u1eb7ng 1 ly (c\u00f9ng lo\u1ea1i) v\u00e0 h\u00f3a \u0111\u01a1n tr\u00ean 400 000 \u0111\u1ed3ng th\u00ec s\u1ebd gi\u1ea3m th\u00eam 10% tr\u00ean h\u00f3a \u0111\u01a1n. - C\u1eeda h\u00e0ng B : ch\u1ec9 khuy\u1ebfn m\u00e3i khi \u0111\u1eb7t qua App Grab Food mua t\u1eeb 10 ly tr\u1edf l\u00ean th\u00ec gi\u1ea3m 30% m\u1ed7i ly so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft v\u00e0 ph\u00ed giao h\u00e0ng th\u00ec kh\u00e1ch t\u1ef1 tr\u1ea3 theo kho\u1ea3ng c\u00e1ch t\u1eeb c\u1eeda h\u00e0ng \u0111\u1ebfn n\u01a1i nh\u1eadn h\u00e0ng. H\u1ecfi l\u1edbp 9A n\u00ean mua \u1edf c\u1eeda h\u00e0ng n\u00e0o s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n v\u00e0 ti\u1ebft ki\u1ec7m h\u01a1n bao nhi\u00eau ti\u1ec1n? Bi\u1ebft gi\u00e1 ni\u00eam y\u1ebft 1 ly tr\u00e0 s\u1eefa \u1edf hai c\u1eeda h\u00e0ng \u0111\u1ec1u l\u00e0 30 000 \u0111\u1ed3ng, kho\u1ea3ng c\u00e1ch t\u1eeb \u0111\u1ecba \u0111i\u1ec3m li\u00ean hoan \u0111\u1ebfn c\u1eeda h\u00e0ng B l\u00e0 12km . Ph\u00ed giao h\u00e0ng \u0111\u01b0\u1ee3c t\u00ednh theo b\u1ea3ng sau: Kho\u1ea3ng c\u00e1ch Gi\u00e1 ti\u1ec1n (\u0111\u1ed3ng) D\u01b0\u1edbi 10km T\u1eeb 10km \u0111\u1ebfn 20km 25 000 T\u1eeb 20km \u0111\u1ebfn 40km 26 000 Tr\u00ean 40km 30 000 5% gi\u00e1 tr\u1ecb \u0111\u01a1n h\u00e0ng C\u00e2u 6. (1 \u0111i\u1ec3m). \u0110\u1ec3 l\u00e0m m\u1ed9t c\u00e1i g\u00e0u t\u00e1t n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n (h\u00ecnh 1), b\u00e1c An d\u00f9ng m\u1ed9t t\u1ea5m t\u00f4n h\u00ecnh tam gi\u00e1c OMN c\u00e2n t\u1ea1i O c\u00f3 c\u1ea1nh b\u00ean OM = 6dm , g\u00f3c MON = 120 (h\u00ecnh 2 ). B\u00e1c x\u00e1c \u0111\u1ecbnh trung \u0111i\u1ec3m H c\u1ee7a MN , v\u1ebd cung tr\u00f2n t\u00e2m O b\u00e1n k\u00ednh OH c\u1eaft c\u00e1c c\u1ea1nh OM, ON l\u1ea7n l\u01b0\u1ee3t t\u1ea1i A, B . Sau \u0111\u00f3 b\u00e1c c\u1eaft b\u1ecf ph\u1ea7n g\u1ea1ch s\u1ecdc, cu\u1ed9n ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a t\u1ea5m t\u00f4n sao cho m\u00e9p OA tr\u00f9ng kh\u00edt v\u1edbi m\u00e9p OB t\u1ea1o th\u00e0nh chi\u1ebfc g\u00e0u (gi\u1ea3 s\u1eed ph\u1ea7n di\u1ec7n t\u00edch c\u1ee7a m\u00e9p n\u1ed1i kh\u00f4ng \u0111\u00e1ng k\u1ec3). H\u1ecfi khi m\u00fac \u0111\u1ea7y th\u00ec chi\u1ebfc g\u00e0u ch\u1ee9a \u0111\u01b0\u1ee3c bao nhi\u00eau l\u00edt n\u01b0\u1edbc? (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, l\u1ea5y \uf070 \uf0bb 3,14 ) C\u00e2u 7. (1 \u0111i\u1ec3m). V\u00e0o d\u1ecbp khai tr\u01b0\u01a1ng, nh\u00e0 s\u00e1ch khuy\u1ebfn m\u00e3i m\u1ed7i c\u00e2y vi\u1ebft bi \u0111\u01b0\u1ee3c gi\u1ea3m 20% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft, c\u00f2n m\u1ed7i quy\u1ec3n t\u1eadp gi\u1ea3m 20% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft. B\u1ea1n An v\u00e0o nh\u00e0 s\u00e1ch mua 20 quy\u1ec3n t\u1eadp v\u00e0 10 c\u00e2y vi\u1ebft bi. Khi t\u00ednh ti\u1ec1n, b\u1ea1n An \u0111\u01b0a 175 000 \u0111\u1ed3ng v\u00e0 \u0111\u01b0\u1ee3c th\u1ed1i l\u1ea1i T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH 3 000 \u0111\u1ed3ng. T\u00ednh gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed7i quy\u1ec3n t\u1eadp v\u00e0 m\u1ed7i c\u00e2y vi\u1ebft bi m\u00e0 b\u1ea1n An \u0111\u00e3 mua. Bi\u1ebft r\u1eb1ng khi An nh\u00ecn v\u00e0o h\u00f3a \u0111\u01a1n, t\u1ed5ng s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 khi ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 195 000 \u0111\u1ed3ng. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho tam gi\u00e1c ABC c\u00f3 3 g\u00f3c nh\u1ecdn AB \uf03c AC . V\u1ebd \u0111\u01b0\u1eddng cao AD, BE, CF c\u1ee7a tam gi\u00e1c \u0111\u00f3. G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng cao v\u1eeba v\u1ebd. a) Ch\u1ee9ng minh: c\u00e1c t\u1ee9 gi\u00e1c AEHF v\u00e0 BFEC n\u1ed9i ti\u1ebfp. b) G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n AH, BC . Ch\u1ee9ng minh: FM.FC = FN.FA . c) G\u1ecdi P,Q l\u1ea7n l\u01b0\u1ee3t l\u00e0 ch\u00e2n c\u00e1c \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb M, N \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng DF . Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh PQ \u0111i qua giao \u0111i\u1ec3m c\u1ee7a FE v\u00e0 MN . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 3","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 3x \u2212 2 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. L\u1eddi gi\u1ea3i a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. a) BGT: x \u22122 \u22121 0 1 2 y = x2 4 1 0 1 4 x0 1 y = 3x \u2212 2 \u22122 1 b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) : x2 = 3x \u2212 2 \uf0db x2 \u2212 3x + 2 = 0 \uf0db \uf0e9x =1 \uf0ea =2 \uf0eb x Thay x = 1 v\u00e0o y = x2 , ta \u0111\u01b0\u1ee3c: y = 12 = 1. Thay x = 2 v\u00e0o y = x2 , ta \u0111\u01b0\u1ee3c: y = 22 = 4 . V\u1eady (1; 1) , (2; 4) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh x2 \u2212 5x + 5 =0. G\u1ecdi x1 , x2 l\u00e0 hai nghi\u1ec7m (n\u1ebfu c\u00f3) . Kh\u00f4ng gi\u1ea3i 3 ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A = x12 + x22 . x2 x1 L\u1eddi gi\u1ea3i Ph\u01b0\u01a1ng tr\u00ecnh: x2 \u2212 5x + 5 = 0 (a = 1, b = - 5, c = 5) 33 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 4","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH V\u00ec \uf044 = b2 \u2212 4ac = (\u22125)2 \u2212 4.1. 5 = 55 \uf03e 0 33 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 ,x2 . \uf0ec\uf0efS = x1 + x2 = \u2212b = \u2212(\u22125) = 5 \uf0ef a 1 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ed 5 \uf0ef \uf0ef\uf0eeP = x1.x2 = c = 3 = 5 a 1 3 Ta c\u00f3: A = x13 + x23 x1.x2 A = ( x1 + x2 )3 \u2212 3x1.x2 ( x1 + x2 ) x1.x2 53 \u2212 3. 5 .5 3 A= 5 = 60 3 V\u1eady A = 60 L\u01b0u \u00fd: T\u1eeb b\u00e0i n\u00e0y, c\u00e1c s\u1ed1 li\u1ec7u t\u00ednh to\u00e1n v\u1ec1 \u0111\u1ed9 d\u00e0i khi l\u00e0m tr\u00f2n (n\u1ebfu c\u00f3) l\u1ea5y \u0111\u1ebfn m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, s\u1ed1 \u0111o g\u00f3c l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat. C\u00e2u 3. (1 \u0111i\u1ec3m) B\u00ean c\u1ea1nh vi\u1ec7c xem \u0111ua ch\u00f3, nhi\u1ec1u ng\u01b0\u1eddi th\u00edch tham gia ch\u01b0\u01a1ng tr\u00ecnh d\u1ef1 th\u01b0\u1edfng \u0111\u1ec3 cu\u1ed9c \u0111ua th\u00eam ph\u1ea5n kh\u00edch. Tr\u01b0\u1edbc khi ch\u1ecdn ch\u00f3 \u0111\u1ec3 \u0111\u1ea1t th\u01b0\u1edfng, b\u1ea1n s\u1ebd \u0111\u01b0\u1ee3c ph\u00e1t m\u1ed9t cu\u1ed1n t\u00e0i li\u1ec7u c\u00f3 gi\u1edbi thi\u1ec7u kh\u00e1 chi ti\u1ebft v\u1ec1 t\u1eebng ch\u00fa ch\u00f3, t\u1eeb nh\u1eefng th\u00e0nh t\u00edch t\u1ed1t, x\u1ea5u \u0111\u1ebfn t\u00ecnh tr\u1ea1ng s\u1ee9c kh\u1ecfe, cu\u1ed9c \u0111ua g\u1ea7n nh\u1ea5t c\u00f3 tham gia\u2026s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng ch\u1ecdn l\u1ef1a. V\u00e0 c\u00f3 5 ki\u1ec3u th\u1eafng gi\u1ea3i \u00e1p d\u1ee5ng cho c\u00e1c \u0111\u1ee3t \u0111ua l\u00e0: - Th\u1eafng nh\u1ea5t l\u00e0 Win n\u1ebfu con ch\u00f3 m\u00e0 b\u1ea1n ch\u1ecdn v\u1ec1 nh\u1ea5t. - Th\u1eafng nh\u1ea5t \u2013 nh\u00ec (Exacta) l\u00e0 2 con ch\u00f3 b\u1ea1n ch\u1ecdn v\u1ec1 nh\u1ea5t \u2013 nh\u00ec theo \u0111\u00fang th\u1ee9 t\u1ef1. - Th\u1eafng nh\u1ea5t \u2013 nh\u00ec \u2013 ba (Trifecta) l\u00e0 c\u1ea3 3 con ch\u00f3 b\u1ea1n ch\u1ecdn \u0111\u1ec1u v\u1ec1 3 th\u1ee9 h\u1ea1ng \u0111\u1ea7u theo \u0111\u00fang th\u1ee9 t\u1ef1. C\u00e1c gi\u1ea3i ti\u1ebfp theo l\u00e0 Quartet (4) , Superfecta (6) . C\u00e0ng l\u00ean cao c\u00e0ng tr\u00fang \u0111\u1eadm. H\u1ecfi trong m\u1ed9t \u0111\u1ee3t \u0111ua c\u00f3 8 ch\u00fa khuy\u1ec3n, ta c\u00f3 bao nhi\u00eau c\u00e1ch ch\u1ecdn v\u00e9 d\u1ef1 th\u01b0\u1edfng theo gi\u1ea3i nh\u1ea5t \u2013 nh\u00ec \u2013 ba? L\u1eddi gi\u1ea3i Con v\u1ec1 nh\u1ea5t c\u00f3: 8 c\u00e1ch ch\u1ecdn T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 5","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH Con v\u1ec1 nh\u00ec c\u00f3: 7 c\u00e1ch ch\u1ecdn Con v\u1ec1 ba c\u00f3: 6 c\u00e1ch ch\u1ecdn V\u1eady c\u00f3: 8.7.6 = 336 c\u00e1ch ch\u1ecdn v\u00e9 d\u1ef1 th\u01b0\u1edfng theo gi\u1ea3i nh\u1ea5t \u2013 nh\u00ec \u2013 ba. C\u00e2u 4. (0,75 \u0111i\u1ec3m). Cu\u1ed1i n\u0103m 2009 , m\u1ed9t b\u1ea3n b\u00e1o c\u00e1o \u0111\u01b0\u1ee3c tr\u00ecnh l\u00ean ch\u00ednh ph\u1ee7 Anh. Theo \u0111\u00f3, n\u1ebfu nhi\u1ec7t \u0111\u1ed9 tr\u00e1i \u0111\u1ea5t t\u0103ng l\u00ean 2\uf0b0C th\u00ec t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf th\u1ebf gi\u1edbi s\u1ebd b\u1ecb gi\u1ea3m \u0111i 3% , n\u1ebfu nhi\u1ec7t \u0111\u1ed9 t\u0103ng l\u00ean 5\uf0b0C kinh t\u1ebf s\u1ebd gi\u1ea3m \u0111i 10% T\u1eeb \u0111\u00f3, th\u00f4ng qua nghi\u00ean c\u1ee9u m\u1ed9t nh\u00f3m nh\u00e0 kinh t\u1ebf h\u1ecdc \u0111\u00e3 \u0111\u01b0a ra d\u1ef1 \u0111o\u00e1n v\u1ec1 m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa nhi\u1ec7t \u0111\u1ed9 th\u1ebf gi\u1edbi v\u00e0 t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf c\u1ee7a th\u1ebf gi\u1edbi. K\u1ebft qu\u1ea3 nghi\u00ean c\u1ee9u \u0111\u01b0a ra r\u1eb1ng t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf b\u1ecb gi\u1ea3m y % l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t theo x l\u00e0 nhi\u1ec7t \u0111\u1ed9 t\u0103ng l\u00ean c\u1ee7a Tr\u00e1i \u0111\u1ea5t (t\u00ednh theo \uf0b0C ). a) X\u00e1c \u0111\u1ecbnh m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa y v\u00e0 x b) Theo nghi\u00ean c\u1ee9u \u0111\u00f3, t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf s\u1ebd gi\u1ea3m bao nhi\u00eau n\u1ebfu th\u1ebf gi\u1edbi t\u0103ng th\u00eam 10\uf0b0C (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb ) L\u1eddi gi\u1ea3i a) X\u00e1c \u0111\u1ecbnh m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa y v\u00e0 x. G\u1ecdi h\u00e0m s\u1ed1 bi\u1ec3u th\u1ecb m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa y v\u00e0 x l\u00e0: y = ax + b(a \uf0b9 0) Khi x = 2 th\u00ec y = 3 n\u00ean ta c\u00f3: 3 = a.2 + b \uf0db 2.a + b = 3 (1) Khi x =5 th\u00ec y = 10 n\u00ean ta c\u00f3: 10 = a.5 + b \uf0db 5.a + b = 10 (2) \uf0ec2a + b = 3 T\u1eeb (1) v\u00e0 (1) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ed\uf0ee5a + b = 10 a = 7 ;b = \u22125 Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: 3 3 y= 7x\u22125 V\u1eady h\u00e0m s\u1ed1 bi\u1ec3u th\u1ecb m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa y v\u00e0 x l\u00e0: 3 3 y = 7 .10 \u2212 5 \uf0bb 22 b) Thay x = 10 v\u00e0o ta \u0111\u01b0\u1ee3c: 3 3 V\u1eady t\u1ed5ng gi\u00e1 tr\u1ecb kinh t\u1ebf s\u1ebd gi\u1ea3m kho\u1ea3ng 22% n\u1ebfu th\u1ebf gi\u1edbi t\u0103ng th\u00eam 100 C C\u00e2u 5. (1 \u0111i\u1ec3m) L\u1edbp 9A d\u1ef1 \u0111\u1ecbnh t\u1ed5 ch\u1ee9c li\u00ean hoan l\u1edbp cu\u1ed1i n\u0103m, trong ph\u1ea7n n\u01b0\u1edbc c\u1ea7n chu\u1ea9n b\u1ecb 42 ly tr\u00e0 s\u1eefa. \u0110\u1ec3 ti\u1ebft ki\u1ec7m chi ph\u00ed l\u1edbp \u0111\u00e3 t\u00ecm hi\u1ec3u gi\u00e1 c\u1ee7a hai c\u1eeda h\u00e0ng A v\u00e0 B nh\u01b0 sau: - C\u1eeda h\u00e0ng A : mua 5 ly b\u1ea5t k\u00ec s\u1ebd \u0111\u01b0\u1ee3c t\u1eb7ng 1 ly (c\u00f9ng lo\u1ea1i) v\u00e0 h\u00f3a \u0111\u01a1n tr\u00ean 400 000 \u0111\u1ed3ng th\u00ec s\u1ebd gi\u1ea3m th\u00eam 10% tr\u00ean h\u00f3a \u0111\u01a1n. T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 6","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH - C\u1eeda h\u00e0ng B : ch\u1ec9 khuy\u1ebfn m\u00e3i khi \u0111\u1eb7t qua App Grab Food mua t\u1eeb 10 ly tr\u1edf l\u00ean th\u00ec gi\u1ea3m 30% m\u1ed7i ly so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft v\u00e0 ph\u00ed giao h\u00e0ng th\u00ec kh\u00e1ch t\u1ef1 tr\u1ea3 theo kho\u1ea3ng c\u00e1ch t\u1eeb c\u1eeda h\u00e0ng \u0111\u1ebfn n\u01a1i nh\u1eadn h\u00e0ng. H\u1ecfi l\u1edbp 9A n\u00ean mua \u1edf c\u1eeda h\u00e0ng n\u00e0o s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n v\u00e0 ti\u1ebft ki\u1ec7m h\u01a1n bao nhi\u00eau ti\u1ec1n? Bi\u1ebft gi\u00e1 ni\u00eam y\u1ebft 1 ly tr\u00e0 s\u1eefa \u1edf hai c\u1eeda h\u00e0ng \u0111\u1ec1u l\u00e0 30 000 \u0111\u1ed3ng, kho\u1ea3ng c\u00e1ch t\u1eeb \u0111\u1ecba \u0111i\u1ec3m li\u00ean hoan \u0111\u1ebfn c\u1eeda h\u00e0ng B l\u00e0 12km . Ph\u00ed giao h\u00e0ng \u0111\u01b0\u1ee3c t\u00ednh theo b\u1ea3ng sau: Kho\u1ea3ng c\u00e1ch Gi\u00e1 ti\u1ec1n (\u0111\u1ed3ng) D\u01b0\u1edbi 10km T\u1eeb 10km \u0111\u1ebfn 20km 25 000 T\u1eeb 20km \u0111\u1ebfn 40km 26 000 Tr\u00ean 40km 30 000 5% gi\u00e1 tr\u1ecb \u0111\u01a1n h\u00e0ng L\u1eddi gi\u1ea3i S\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 n\u1ebfu mua 42 ly tr\u00e0 s\u1eefa \u1edf c\u1eeda h\u00e0ng A l\u00e0: (42 \u2212 7).30 000.(1\u221210%) = 945 000 (\u0111\u1ed3ng) S\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 n\u1ebfu mua 42 ly tr\u00e0 s\u1eefa \u1edf c\u1eeda h\u00e0ng B l\u00e0: 42.30 000.(1\u2212 30%) + 26 000 = 908 000 (\u0111\u1ed3ng) L\u1edbp 9A n\u00ean mua \u1edf c\u1eeda h\u00e0ng B s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n v\u00ec 908 000 < 945 000 V\u00e0 ti\u1ebft ki\u1ec7m h\u01a1n: 908 000 \u2212945 000 = 37 000 (\u0111\u1ed3ng) C\u00e2u 6. (1 \u0111i\u1ec3m) \u0110\u1ec3 l\u00e0m m\u1ed9t c\u00e1i g\u00e0u t\u00e1t n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n (h\u00ecnh 1), b\u00e1c An d\u00f9ng m\u1ed9t t\u1ea5m t\u00f4n h\u00ecnh tam gi\u00e1c OMN c\u00e2n t\u1ea1i O c\u00f3 c\u1ea1nh b\u00ean OM = 6dm , g\u00f3c MON = 120 (h\u00ecnh 2 ). B\u00e1c x\u00e1c \u0111\u1ecbnh trung \u0111i\u1ec3m H c\u1ee7a MN , v\u1ebd cung tr\u00f2n t\u00e2m O b\u00e1n k\u00ednh OH c\u1eaft c\u00e1c c\u1ea1nh OM, ON l\u1ea7n l\u01b0\u1ee3t t\u1ea1i A, B . Sau \u0111\u00f3 b\u00e1c c\u1eaft b\u1ecf ph\u1ea7n g\u1ea1ch s\u1ecdc, cu\u1ed9n ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a t\u1ea5m t\u00f4n sao cho m\u00e9p OA tr\u00f9ng kh\u00edt v\u1edbi m\u00e9p OB t\u1ea1o th\u00e0nh chi\u1ebfc g\u00e0u (gi\u1ea3 s\u1eed ph\u1ea7n di\u1ec7n t\u00edch c\u1ee7a m\u00e9p n\u1ed1i kh\u00f4ng \u0111\u00e1ng k\u1ec3). H\u1ecfi khi m\u00fac \u0111\u1ea7y th\u00ec chi\u1ebfc g\u00e0u ch\u1ee9a \u0111\u01b0\u1ee3c bao nhi\u00eau l\u00edt n\u01b0\u1edbc? (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, l\u1ea5y \uf070 \uf0bb 3,14 ) L\u1eddi gi\u1ea3i 7 Tam gi\u00e1c OMN c\u00e2n, H l\u00e0 trung \u0111i\u1ec3m T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH \uf0de OH l\u00e0 \u0111\u01b0\u1eddng cao, l\u00e0 ph\u00e2n gi\u00e1c X\u00e9t tam gi\u00e1c OHM vu\u00f4ng t\u1ea1i H , ta c\u00f3: cos 600 = OH \uf0de OH = 6.cos 600 = 3(dm) OM \u0110\u1ed9 d\u00e0i cung tr\u00f2n AB l\u00e0: l = \uf070 R.n = \uf070 .3.120 = 2\uf070 (dm) 180 180 B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n mi\u1ec7ng c\u1ee7a chi\u1ebfc g\u00e0u l\u00e0: R = C : 2\uf070 = 2\uf070 : 2\uf070 = 1(dm) Chi\u1ec1u cao c\u1ee7a chi\u1ebfc g\u00e0u l\u00e0: h = 32 \u221212 = 2 2 (dm) Khi m\u00fac \u0111\u1ea7y th\u00ec chi\u1ebfc g\u00e0u ch\u1ee9a \u0111\u01b0\u1ee3c s\u1ed1 l\u00edt n\u01b0\u1edbc l\u00e0: V = 1 \uf070 R2h = 1 .3,14.12.2 2 = 3,0(dm3) = 3(l) 33 C\u00e2u 7. (1 \u0111i\u1ec3m) V\u00e0o d\u1ecbp khai tr\u01b0\u01a1ng, nh\u00e0 s\u00e1ch khuy\u1ebfn m\u00e3i m\u1ed7i c\u00e2y vi\u1ebft bi \u0111\u01b0\u1ee3c gi\u1ea3m 20% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft, c\u00f2n m\u1ed7i quy\u1ec3n t\u1eadp gi\u1ea3m 20% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft. B\u1ea1n An v\u00e0o nh\u00e0 s\u00e1ch mua 20 quy\u1ec3n t\u1eadp v\u00e0 10 c\u00e2y vi\u1ebft bi. Khi t\u00ednh ti\u1ec1n, b\u1ea1n An \u0111\u01b0a 175 000 \u0111\u1ed3ng v\u00e0 \u0111\u01b0\u1ee3c th\u1ed1i l\u1ea1i 3 000 \u0111\u1ed3ng. T\u00ednh gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed7i quy\u1ec3n t\u1eadp v\u00e0 m\u1ed7i c\u00e2y vi\u1ebft bi m\u00e0 b\u1ea1n An \u0111\u00e3 mua. Bi\u1ebft r\u1eb1ng khi An nh\u00ecn v\u00e0o h\u00f3a \u0111\u01a1n, t\u1ed5ng s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 khi ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 195 000 \u0111\u1ed3ng. L\u1eddi gi\u1ea3i G\u1ecdi gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed7i quy\u1ec3n t\u1eadp l\u00e0 x ( x \uf03e 0 ; \u0111\u1ed3ng) Gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed7i c\u00e2y vi\u1ebft bi l\u00e0 y ( y \uf03e 0 ; \u0111\u1ed3ng) V\u00ec t\u1ed5ng s\u1ed1 ti\u1ec1n mua 20 quy\u1ec3n t\u1eadp v\u00e0 10 c\u00e2y vi\u1ebft bi khi ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 195 000 \u0111\u1ed3ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 20x +10 y = 195000 (1) V\u00ec t\u1ed5ng s\u1ed1 ti\u1ec1n mua 20 quy\u1ec3n t\u1eadp v\u00e0 10 c\u00e2y vi\u1ebft bi khi \u0111\u00e3 gi\u1ea3m gi\u00e1 l\u00e0 175000 \u2212 3000 =172000 \u0111\u1ed3ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 20(1\u221210%)x +10(1\u2212 20%)y =172000 \uf0db 18x + 8y = 172000 (2) \uf0ec20x +10y = 195000 T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ee\uf0ed18x + 8y = 172000 Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c: \uf0ecx = 8000(n) \uf0ed \uf0ee y = 3500(n) V\u1eady gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed7i quy\u1ec3n t\u1eadp l\u00e0 8000 \u0111\u1ed3ng v\u00e0 m\u1ed7i c\u00e2y vi\u1ebft bi 3500 \u0111\u1ed3ng. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho tam gi\u00e1c ABC c\u00f3 3 g\u00f3c nh\u1ecdn AB \uf03c AC. V\u1ebd \u0111\u01b0\u1eddng cao AD, BE, CF c\u1ee7a tam gi\u00e1c \u0111\u00f3. G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng cao v\u1eeba v\u1ebd. a) Ch\u1ee9ng minh: c\u00e1c t\u1ee9 gi\u00e1c AEHF v\u00e0 BFEC n\u1ed9i ti\u1ebfp. b) G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n AH, BC . Ch\u1ee9ng minh: FM.FC = FN.FA . c) G\u1ecdi P,Q l\u1ea7n l\u01b0\u1ee3t l\u00e0 ch\u00e2n c\u00e1c \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb M, N \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng DF . Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh PQ \u0111i qua giao \u0111i\u1ec3m c\u1ee7a FE v\u00e0 MN . T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 8","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH L\u1eddi gi\u1ea3i a) Ch\u1ee9ng minh: c\u00e1c t\u1ee9 gi\u00e1c AEHF v\u00e0 BFEC n\u1ed9i ti\u1ebfp. Ch\u1ee9ng minh: T\u1ee9 gi\u00e1c AEHF n\u1ed9i ti\u1ebfp X\u00e9t t\u1ee9 gi\u00e1c AEHF c\u00f3: \uf0ec = 90 (V\u00ec CF, BE l\u00e0 \u0111\u01b0\u1eddng cao) \uf0ef AEH \uf0ed \uf0ef\uf0ee AFH = 90 AEH + AFH = 90 + 90 = 180 \uf0f0 T\u1ee9 gi\u00e1c AEHF n\u1ed9i ti\u1ebfp Ch\u1ee9ng minh: T\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp \uf0ec = 90 \uf0efBEC X\u00e9t t\u1ee9 gi\u00e1c BFEC c\u00f3: \uf0ed (V\u00ec CF, BE l\u00e0 \u0111\u01b0\u1eddng cao) \uf0ef\uf0eeBFC = 90 \uf0f0 BEC = BFC \uf0f0 T\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n AH,BC . Ch\u1ee9ng minh: FM.FC = FN.FA Tam gi\u00e1c AFH vu\u00f4ng t\u1ea1i F,FM l\u00e0 trung tuy\u1ebfn \uf0f0 MF = MA (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) \uf0f0 \uf044AMF c\u00e2n t\u1ea1i M \uf0f0 MAF = MFA Tam gi\u00e1c BFC vu\u00f4ng t\u1ea1i F,FN l\u00e0 trung tuy\u1ebfn \uf0f0 NF = NC (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 9","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH \uf0f0 \uf044CNF c\u00e2n t\u1ea1i N \uf0f0 NCF = NFC \u2022 X\u00e9t t\u1ee9 gi\u00e1c AFCD c\u00f3: \uf0ec = 90 (V\u00ec CF,BE l\u00e0 \u0111\u01b0\u1eddng cao) \uf0ef AFC \uf0ed \uf0ee\uf0ef ADC = 90 \uf0f0 AFC = ADC \uf0f0 T\u1ee9 gi\u00e1c AFCD n\u1ed9i ti\u1ebfp \uf0f0 FAD = FCD (c\u00f9ng ch\u1eafn cung FD ) \uf0f0 MAF = MFA = NCF = NFC \u2022 X\u00e9t \uf044AFM v\u00e0 \uf044CFN c\u00f3: \uf0ec\uf0efFAM = FCN \uf0ed \uf0ef\uf0ee AFM = CFN \uf0f0 \uf044AFM \u223d \uf044CFN (g \u2013 g) \uf0f0 FM = FA =\uf03e FM .FC = FN.FA FN FC d) G\u1ecdi P, Q l\u1ea7n l\u01b0\u1ee3t l\u00e0 ch\u00e2n c\u00e1c \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb M, N \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng DF. Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh PQ \u0111i qua giao \u0111i\u1ec3m c\u1ee7a FE v\u00e0 MN. G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a EF v\u00e0 MN Ta c\u00f3 \uf044 MAF \u223d \uf044 NCF Suy ra: MFA = NFC M\u00e0 AFC = 900 \uf0de MFN = 90 \uf0de MFP + NFQ = 90 Ta l\u1ea1i c\u00f3 MFP + FMQ = 90 Suy ra NFQ = FMP (1) V\u00ec M l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp t\u1ee9 gi\u00e1c AEHF , N l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp t\u1ee9 gi\u00e1c BCEF do \u0111\u00f3 MN \u22a5 EF t\u1ea1i K Suy ra t\u1ee9 gi\u00e1c MKFP n\u1ed9i ti\u1ebfp \uf0de FMP = PKF (2) T\u1eeb (1),(2) suy ra NFQ = PKF V\u00e0 t\u1ee9 gi\u00e1c NKFQ n\u1ed9i ti\u1ebfp \uf0de QNF = QKF M\u00e0 QNF + NFQ = 90 suy ra QKF + PKF = 90 10 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH Suy ra QKP = 90 Do \u0111\u00f3 K thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh PQ . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 11","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u1ede GD&\u0110T TP H\u1ed2 CH\u00cd MINH \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 PH\u00d2NG GD&\u0110T QU\u1eacN T\u00c2N N\u0102M H\u1eccC: 2023 - 2024 M\u00d4N: TO\u00c1N B\u00ccNH \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. \u0110\u1ec0 THAM KH\u1ea2O Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) M\u00c3 \u0110\u1ec0: Qu\u1eadn T\u00e2n B\u00ecnh - 3 C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d ) : y = 1 x + 2 . 42 a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 4x2 \u2212 5x \u2212 3 = 0 c\u00f3 hai nghi\u1ec7m x1; x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00ecm x1; x2 , t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c M = 5x1 \u2212 3 + 5x2 \u2212 3 x2 x1 C\u00e2u 3. (0,75 \u0111i\u1ec3m). C\u00e1c nh\u00e0 khoa h\u1ecdc v\u1ec1 th\u1ed1ng k\u00ea \u0111\u00e3 thi\u1ebft l\u1eadp \u0111\u01b0\u1ee3c h\u00e0m s\u1ed1 \u0111\u1ec3 t\u00ednh v\u1ec1 \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u c\u1ee7a th\u1ebf gi\u1edbi nh\u01b0 sau: A(t ) = 0, 08t +19, 7 . Trong \u0111\u00f3: A(t ) l\u00e0 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u c\u1ee7a th\u1ebf gi\u1edbi, t l\u00e0 n\u0103m k\u1ebft h\u00f4n v\u1edbi g\u1ed1c th\u1eddi gian t\u00ednh t\u1eeb n\u0103m 1950 ngh\u0129a l\u00e0 n\u0103m 1950 th\u00ec t = 0 , n\u0103m 1951 t =1,\u2026 a) H\u00e3y t\u00ednh \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u tr\u00ean th\u1ebf gi\u1edbi l\u1ea7n l\u01b0\u1ee3t v\u00e0o c\u00e1c n\u0103m 1980, 2005 . b) V\u00e0o n\u0103m bao nhi\u00eau th\u00ec \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u l\u00e0 25, 7 tu\u1ed5i? C\u00e2u 4. (0,75 \u0111i\u1ec3m). C\u01b0\u1edbc \u0111i\u1ec7n tho\u1ea1i y (ngh\u00ecn \u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n m\u00e0 ng\u01b0\u1eddi s\u1eed d\u1ee5ng \u0111i\u1ec7n tho\u1ea1i c\u1ea7n tr\u1ea3 h\u00e0ng th\u00e1ng, n\u00f3 ph\u1ee5 thu\u1ed9c v\u00e0o l\u01b0\u1ee3ng th\u1eddi gian g\u1ecdi x (ph\u00fat) c\u1ee7a ng\u01b0\u1eddi \u0111\u00f3 trong th\u00e1ng. M\u1ed1i li\u00ean h\u1ec7 gi\u1eefa hai \u0111\u1ea1i l\u01b0\u1ee3ng n\u00e0y l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y = ax + b . H\u00e3y t\u00ecm a,b bi\u1ebft r\u1eb1ng nh\u00e0 b\u1ea1n An trong th\u00e1ng 5 \u0111\u00e3 g\u1ecdi 100 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 40 ngh\u00ecn \u0111\u1ed3ng v\u00e0 trong th\u00e1ng 6 g\u1ecdi 40 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 28 ngh\u00ecn \u0111\u1ed3ng. C\u00e2u 5. (1 \u0111i\u1ec3m). H\u00f4m qua m\u1eb9 c\u1ee7a Lan \u0111i ch\u1ee3 mua 2 kg t\u00e1o v\u00e0 2 kg xo\u00e0i th\u00ec ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 220000 \u0111\u1ed3ng. H\u00f4m nay m\u1eb9 Lan mua 4 kg t\u00e1o v\u00e0 5 kg xo\u00e0i th\u00ec ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 505000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 c\u1ee7a t\u00e1o v\u00e0 xo\u00e0i l\u00e0 bao nhi\u00eau \u0111\u1ed3ng\/kg? (bi\u1ebft gi\u00e1 t\u00e1o v\u00e0 xo\u00e0i kh\u00f4ng thay \u0111\u1ed5i) C\u00e2u 6. (1 \u0111i\u1ec3m). M\u1ed9t x\u00f4 n\u01b0\u1edbc h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 28cm v\u00e0 chi\u1ec1u cao 30cm , \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 l\u1ea5y n\u01b0\u1edbc t\u1eeb m\u1ed9t h\u1ed3 tr\u1eef n\u01b0\u1edbc h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 c\u1ea1nh l\u00e0 1,8m . H\u1ed3 \u0111ang ch\u1ee9a \u0111\u1ea7y n\u01b0\u1edbc. a) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a x\u00f4 n\u01b0\u1edbc. Bi\u1ebft r\u1eb1ng th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c V = 3,14R2h . Trong \u0111\u00f3 l\u00e0 R b\u00e1n k\u00ednh m\u1eb7t \u0111\u00e1y; h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh tr\u1ee5. T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH b) Gi\u1ea3 s\u1eed m\u1ed9i ng\u00e0y gia \u0111\u00ecnh b\u1ea1n A s\u1eed d\u1ee5ng 30 x\u00f4 n\u01b0\u1edbc l\u1ea5y t\u1eeb h\u1ed3. H\u1ecfi trong ng\u00e0y h\u1ed3 h\u1ebft n\u01b0\u1edbc, n\u01b0\u1edbc trong h\u1ed3 s\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c \u0111\u1ebfn x\u00f4 th\u1ee9 bao nhi\u00eau th\u00ec h\u1ebft n\u01b0\u1edbc (b\u1ecf qua th\u1ec3 t\u00edch th\u00e0nh h\u1ed3, m\u1ed7i l\u1ea7n m\u00fac \u0111\u1ea7y x\u00f4 n\u01b0\u1edbc). C\u00e2u 7. (1 \u0111i\u1ec3m). M\u1ed9t c\u1eeda h\u00e0ng nh\u1eadp v\u1ec1 20 c\u00e1i tivi v\u00e0 b\u00e1n v\u1edbi gi\u00e1 t\u0103ng 40% so v\u1edbi gi\u00e1 nh\u1eadp. Nh\u01b0ng sau khi b\u00e1n \u0111\u01b0\u1ee3c 12 c\u00e1i th\u00ec c\u1eeda h\u00e0ng mu\u1ed1n t\u0103ng l\u1ee3i nhu\u1eadn n\u00ean \u0111\u00e3 t\u0103ng 20% gi\u00e1 b\u00e1n so v\u1edbi gi\u00e1 \u0111ang b\u00e1n. Sau khi b\u00e1n h\u1ebft 20 c\u00e1i tivi c\u1eeda h\u00e0ng thu \u0111\u01b0\u1ee3c 272160000 \u0111\u1ed3ng. H\u1ecfi c\u1eeda h\u00e0ng \u0111\u00e3 nh\u1eadp m\u1ed7i c\u00e1c tivi v\u1edbi gi\u00e1 l\u00e0 bao nhi\u00eau \u0111\u1ed3ng? C\u00e2u 8. (3 \u0111i\u1ec3m). Cho AB, AC l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a (O) v\u1edbi B,C l\u00e0 ti\u1ebfp \u0111i\u1ec3m. G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OA v\u00e0 BC . L\u1ea5y \u0111i\u1ec3m E thu\u1ed9c cung l\u1edbn BC c\u1ee7a (O) sao cho EB \uf03c EC c\u1eaft (O) t\u1ea1i D . ( D kh\u00e1c E ) . V\u1ebd CI \u22a5 AE t\u1ea1i I . a) Ch\u1ee9ng minh OA \u22a5 BD t\u1ea1i H v\u00e0 t\u1ee9 gi\u00e1c AIHC n\u1ed9i ti\u1ebfp. b) V\u1ebd CF \u22a5 BD t\u1ea1i F v\u00e0 FI c\u1eaft BE t\u1ea1i G . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c IDFC n\u1ed9i ti\u1ebfp v\u00e0 CG \u22a5 BE . c) Ch\u1ee9ng minh I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a GF . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d ) : y = 1 x + 2 . 42 a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. L\u1eddi gi\u1ea3i a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. BGT: x \u22124 \u22122 0 2 4 x 0 2 (d) : y = 1 x + 2 2 1 y = x2 41014 4 2 b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) : x2 = 1 x + 2 42 \uf0db x2 \u2212 1 x \u2212 2 = 0 42 \uf0db x = 4 hay x = \u22122 Thay x = 4 v\u00e0o y = x2 , ta \u0111\u01b0\u1ee3c:. y = 42 = 4 44 Thay x = \u22122 v\u00e0o y= x2 , ta \u0111\u01b0\u1ee3c:. ( \u22122 )2 =1 y= 44 V\u1eady (4, 4) v\u00e0 (\u22122,1) l\u00e0 giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 3","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 4x2 \u2212 5x \u2212 3 = 0 c\u00f3 hai nghi\u1ec7m x1; x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00ecm x1; x2 , t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c M = 5x1 \u2212 3 + 5x2 \u2212 3 x2 x1 L\u1eddi gi\u1ea3i V\u00ec a.c = 4.(\u22123) = \u221212 \uf03c 0 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 , x2 . \uf0ec\uf0ef\uf0efS = x1 + x2 = \u2212b = 5 \uf0ed = a 4 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: c \u22123 \uf0ef P x1.x2 = a = 4 \uf0ef\uf0ee Ta c\u00f3: M = 5x1 \u2212 3 + 5x2 \u2212 3 x2 x1 M = x1 (5x1 \u2212 3) + x2 (5x2 \u2212 3) x2 x1 x1x2 \uf0db M = 5x12 \u2212 3x1 + 5x22 \u2212 3x2 x1x2 ( )5 \u2212 3( x1 + x2 ) \uf0dbM = x12 + x22 x1x2 5(S 2 \u2212 2P) \u2212 3S \uf0dbM = P 5 \uf0e6 \uf0e6 5 \uf0f62 \u2212 2.\uf0e6\uf0e7\uf0e8 \u22123 \uf0f6 \uf0f6 \u2212 3. 5 \uf0e7\uf0e7\uf0e8 \uf0e7\uf0e8 4 \uf0f7\uf0f8 4 \uf0f7\uf0f8 \uf0f7\uf0f7\uf0f8 4 \uf0db M = = \u2212185 \uf0e6 \u22123 \uf0f6 12 \uf0e7\uf0e8 4 \uf0f7\uf0f8 C\u00e2u 3. (0,75 \u0111i\u1ec3m) C\u00e1c nh\u00e0 khoa h\u1ecdc v\u1ec1 th\u1ed1ng k\u00ea \u0111\u00e3 thi\u1ebft l\u1eadp \u0111\u01b0\u1ee3c h\u00e0m s\u1ed1 \u0111\u1ec3 t\u00ednh v\u1ec1 \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u c\u1ee7a th\u1ebf gi\u1edbi nh\u01b0 sau: A(t ) = 0, 08t +19, 7 . Trong \u0111\u00f3: A(t ) l\u00e0 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u c\u1ee7a th\u1ebf gi\u1edbi, t l\u00e0 n\u0103m k\u1ebft h\u00f4n v\u1edbi g\u1ed1c th\u1eddi gian t\u00ednh t\u1eeb n\u0103m 1950 ngh\u0129a l\u00e0 n\u0103m 1950 th\u00ec t = 0 , n\u0103m 1951 t =1,\u2026 a) H\u00e3y t\u00ednh \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u tr\u00ean th\u1ebf gi\u1edbi l\u1ea7n l\u01b0\u1ee3t v\u00e0o c\u00e1c n\u0103m 1980, 2005 . V\u00e0o n\u0103m bao nhi\u00eau th\u00ec \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u l\u00e0 25, 7 tu\u1ed5i. L\u1eddi gi\u1ea3i a) V\u00e0o n\u0103m 1980th\u00ec t =1980 \u22121950 = 30 th\u1ebf v\u00e0o c\u00f4ng th\u1ee9c ta \u0111\u01b0\u1ee3c: A(t ) = 0,08.30 +19,7 = 22,1 V\u00e0o n\u0103m 2005 th\u00ec t = 2005 \u22121950 = 55 th\u1ebf v\u00e0o c\u00f4ng th\u1ee9c ta \u0111\u01b0\u1ee3c: 4 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH A(t ) = 0,08.55 +19,7 = 24,1 V\u1eady \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u tr\u00ean th\u1ebf gi\u1edbi l\u1ea7n l\u01b0\u1ee3t v\u00e0o c\u00e1c n\u0103m 1980 l\u00e0 22,1 tu\u1ed5i; 2005 l\u00e0 24,1tu\u1ed5i. b) Ta c\u00f3 A(t ) = 25, 7 th\u1ebf v\u00e0o c\u00f4ng th\u1ee9c ta \u0111\u01b0\u1ee3c: 25, 7 = 0, 08t +19, 7 \uf0de t = 75 V\u1eady v\u00e0o n\u0103m 2025 th\u00ec \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u00e1c ph\u1ee5 n\u1eef k\u1ebft h\u00f4n l\u1ea7n \u0111\u1ea7u l\u00e0 25, 7 tu\u1ed5i. C\u00e2u 4. (0,75 \u0111i\u1ec3m) C\u01b0\u1edbc \u0111i\u1ec7n tho\u1ea1i y (ngh\u00ecn \u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n m\u00e0 ng\u01b0\u1eddi s\u1eed d\u1ee5ng \u0111i\u1ec7n tho\u1ea1i c\u1ea7n tr\u1ea3 h\u00e0ng th\u00e1ng, n\u00f3 ph\u1ee5 thu\u1ed9c v\u00e0o l\u01b0\u1ee3ng th\u1eddi gian g\u1ecdi x (ph\u00fat) c\u1ee7a ng\u01b0\u1eddi \u0111\u00f3 trong th\u00e1ng. M\u1ed1i li\u00ean h\u1ec7 gi\u1eefa hai \u0111\u1ea1i l\u01b0\u1ee3ng n\u00e0y l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y = ax + b . H\u00e3y t\u00ecm a,b bi\u1ebft r\u1eb1ng nh\u00e0 b\u1ea1n An trong th\u00e1ng 5 \u0111\u00e3 g\u1ecdi 100 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 40 ngh\u00ecn \u0111\u1ed3ng v\u00e0 trong th\u00e1ng 6 g\u1ecdi 40 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 28 ngh\u00ecn \u0111\u1ed3ng. L\u1eddi gi\u1ea3i Th\u1ebf x =100 v\u00e0 y = 40 v\u00e0o h\u00e0m s\u1ed1 ta \u0111\u01b0\u1ee3c: 40 = a.100 + b (1) Th\u1ebf x = 40 v\u00e0 y = 28 v\u00e0o h\u00e0m s\u1ed1 ta \u0111\u01b0\u1ee3c: 28 = a.40 + b (2) T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ec40 = a.100 + b \uf0ed\uf0ee28 = a.40 + b \uf0db \uf0ec\uf0efa = 1 \uf0ed 5 \uf0ef\uf0eeb = 20 V\u1eady a = 1 v\u00e0 b = 20 5 C\u00e2u 5. (1 \u0111i\u1ec3m) H\u00f4m qua m\u1eb9 c\u1ee7a Lan \u0111i ch\u1ee3 mua 2 kg t\u00e1o v\u00e0 2 kg xo\u00e0i th\u00ec ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 220000 \u0111\u1ed3ng. H\u00f4m nay m\u1eb9 Lan mua 4 kg t\u00e1o v\u00e0 5 kg xo\u00e0i th\u00ec ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 505000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 c\u1ee7a t\u00e1o v\u00e0 xo\u00e0i l\u00e0 bao nhi\u00eau \u0111\u1ed3ng\/kg? (bi\u1ebft gi\u00e1 t\u00e1o v\u00e0 xo\u00e0i kh\u00f4ng thay \u0111\u1ed5i) G\u1ecdi x l\u00e0 s\u1ed1 ti\u1ec1n 1kg t\u00e1o L\u1eddi gi\u1ea3i ( x, y \uf03e 0) T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 5","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH y l\u00e0 s\u1ed1 ti\u1ec1n 1kg xo\u00e0i Theo b\u00e0i ra: mua 2 kg t\u00e1o v\u00e0 2 kg xo\u00e0i th\u00ec ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 220000 \u0111\u1ed3ng. \uf0de 2x + 2y = 220000 (1) Mua 4 kg t\u00e1o v\u00e0 5 kg xo\u00e0i th\u00ec ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 505000 \u0111\u1ed3ng. \uf0de 4x + 5y = 505000 (2) T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ec2x + 2y = 220000 \uf0ed\uf0ee4x + 5y = 505000 \uf0db \uf0ecx = 45000 (nh\u1eadn) \uf0ed = 65000 \uf0ee y V\u1eady gi\u00e1 1kg t\u00e1o l\u1ea3 45000 \u0111\u1ed3ng, gi\u00e1 1kg xo\u00e0i l\u00e0 65000 \u0111\u1ed3ng. C\u00e2u 6. (1 \u0111i\u1ec3m) M\u1ed9t x\u00f4 n\u01b0\u1edbc h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 28cm v\u00e0 chi\u1ec1u cao 30cm , \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 l\u1ea5y n\u01b0\u1edbc t\u1eeb m\u1ed9t h\u1ed3 tr\u1eef n\u01b0\u1edbc h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 c\u1ea1nh l\u00e0 1,8m . H\u1ed3 \u0111ang ch\u1ee9a \u0111\u1ea7y n\u01b0\u1edbc. a) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a x\u00f4 n\u01b0\u1edbc. Bi\u1ebft r\u1eb1ng th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c V = 3,14R2h . Trong \u0111\u00f3 l\u00e0 R b\u00e1n k\u00ednh m\u1eb7t \u0111\u00e1y; h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh tr\u1ee5. b) Gi\u1ea3 s\u1eed m\u1ed9i ng\u00e0y gia \u0111\u00ecnh b\u1ea1n A s\u1eed d\u1ee5ng 30 x\u00f4 n\u01b0\u1edbc l\u1ea5y t\u1eeb h\u1ed3. H\u1ecfi trong ng\u00e0y h\u1ed3 h\u1ebft n\u01b0\u1edbc, n\u01b0\u1edbc trong h\u1ed3 s\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c \u0111\u1ebfn x\u00f4 th\u1ee9 bao nhi\u00eau th\u00ec h\u1ebft n\u01b0\u1edbc (b\u1ecf qua th\u1ec3 t\u00edch th\u00e0nh h\u1ed3, m\u1ed7i l\u1ea7n m\u00fac \u0111\u1ea7y x\u00f4 n\u01b0\u1edbc). L\u1eddi gi\u1ea3i 6 a) B\u00e1n k\u00ednh x\u00f4 n\u01b0\u1edbc: R = d = 28 = 14cm . 22 ( )Th\u1ec3 t\u00edch x\u00f4 n\u01b0\u1edbc: V = 3,14R2h = 3,14.142.30 = 18463, 2 cm3 ( )b) Th\u1ec3 t\u00edch h\u1ed3 n\u01b0\u1edbc: V = a3 = 1,83 = 5,832 m3 \u0110\u1ed5i: 5,832m3 = 5832000cm3 . S\u1ed1 ng\u00e0y s\u1eed d\u1ee5ng h\u1ebft n\u01b0\u1edbc trong h\u1ed3: T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH ( )5832000 :18463, 2 : 30 =10 (ng\u00e0y) d\u01b0 293040 cm3 . S\u1ed1 x\u00f4 n\u01b0\u1edbc d\u01b0 trong ng\u00e0y: 293040 :18463, 2 \uf0bb 15,87 (x\u00f4) V\u1eady trong ng\u00e0y h\u1ed3 h\u1ebft n\u01b0\u1edbc, n\u01b0\u1edbc trong h\u1ed3 s\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c \u0111\u1ebfn x\u00f4 th\u1ee9 16 . C\u00e2u 7. (1 \u0111i\u1ec3m) M\u1ed9t c\u1eeda h\u00e0ng nh\u1eadp v\u1ec1 20 c\u00e1i tivi v\u00e0 b\u00e1n v\u1edbi gi\u00e1 t\u0103ng 40% so v\u1edbi gi\u00e1 nh\u1eadp. Nh\u01b0ng sau khi b\u00e1n \u0111\u01b0\u1ee3c 12 c\u00e1i th\u00ec c\u1eeda h\u00e0ng mu\u1ed1n t\u0103ng l\u1ee3i nhu\u1eadn n\u00ean \u0111\u00e3 t\u0103ng 20% gi\u00e1 b\u00e1n so v\u1edbi gi\u00e1 \u0111ang b\u00e1n. Sau khi b\u00e1n h\u1ebft 20 c\u00e1i tivi c\u1eeda h\u00e0ng thu \u0111\u01b0\u1ee3c 272160000 \u0111\u1ed3ng. H\u1ecfi c\u1eeda h\u00e0ng \u0111\u00e3 nh\u1eadp m\u1ed7i c\u00e1c tivi v\u1edbi gi\u00e1 l\u00e0 bao nhi\u00eau \u0111\u1ed3ng? L\u1eddi gi\u1ea3i G\u1ecdi x l\u00e0 gi\u00e1 nh\u1eadp c\u1ee7a m\u1ed9t c\u00e1i tivi. (x \uf03e 0) \uf0de x (1+ 40%) = 1, 4x l\u00e0 gi\u00e1 b\u00e1n l\u00fac \u0111\u1ea7u c\u1ee7a m\u1ed9t c\u00e1i tivi. \uf0de1, 4x (1+ 20%) = 1, 68x l\u00e0 gi\u00e1 b\u00e1n l\u00fac sau c\u1ee7a m\u1ed9t c\u00e1i tivi. Theo b\u00e0i ra: t\u1ed5ng s\u1ed1 ti\u1ec1n b\u00e1n h\u1ebft 20 c\u00e1i tivi l\u00e0 272160000 \u0111\u1ed3ng. \uf0de1, 4x.12 + 8.1, 68x = 272160000 \uf0db 30, 24x = 272160000 \uf0db x = 9000000 (nh\u1eadn) V\u1eady gi\u00e1 nh\u1eadp m\u1ed9t c\u00e1i tivi l\u00e0 9000000 \u0111\u1ed3ng. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho AB, AC l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a (O) v\u1edbi B,C l\u00e0 ti\u1ebfp \u0111i\u1ec3m. G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OA v\u00e0 BC . L\u1ea5y \u0111i\u1ec3m E thu\u1ed9c cung l\u1edbn BC c\u1ee7a (O) sao cho EB \uf03c EC c\u1eaft (O) t\u1ea1i D ( D kh\u00e1c E ) . V\u1ebd CI \u22a5 AE t\u1ea1i I . a) Ch\u1ee9ng minh OA \u22a5 BD t\u1ea1i H v\u00e0 t\u1ee9 gi\u00e1c AIHC n\u1ed9i ti\u1ebfp. b) V\u1ebd CF \u22a5 BD t\u1ea1i F v\u00e0 FI c\u1eaft BE t\u1ea1i G . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c IDFC n\u1ed9i ti\u1ebfp v\u00e0 CG \u22a5 BE c) Ch\u1ee9ng minh I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a GF . T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 7","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH L\u1eddi gi\u1ea3i 8 a) Ta c\u00f3 OB = OC (b\u00e1n k\u00ednh) AB = AC (t\u00ednh ch\u1ea5t 2 ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) \uf0de OA l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a BC . \uf0de OA \u22a5 BC X\u00e9t tg AIHC c\u00f3: AIC = AHC = 90\uf0b0 v\u00e0 c\u00f9ng nh\u00ecn c\u1ea1nh AC . V\u1eady tg AIHC n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n. b) X\u00e9t tg IDFC c\u00f3: DFC = 90\uf0b0 DIC = 90\uf0b0 \uf0de DFC + DFC = 180\uf0b0 V\u1eady tg IDFC n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n. Ta c\u00f3: CDI = CFI (c\u00f9ng ch\u1eafn CI ) M\u00e0 CDI = CBE (c\u00f9ng ch\u1eafn CE ) \uf0de CFI = CBE \uf0de Tg CFBG n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n. \uf0de CFB + CGB = 180\uf0b0 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH M\u00e0 CFB = 90\uf0b0 \uf0de CGB = 90\uf0b0 \uf0de CG \u22a5 BE c) Ta c\u00f3: FIC = FDC (tg IDFC n\u1ed9i ti\u1ebfp) (1) X\u00e9t \uf044ADC v\u00e0 \uf044ACE c\u00f3: (2) CAE chung (3) ACD = AEC (c\u00f9ng ch\u1eafn CD ) ADC ACE (g.g) \uf0de ADC = ACE \uf0db ADF + FDC = ACB + BCF \uf0db DFC + BCE = ACB + BCE M\u00e0 BCE = BCE (c\u00f9ng ch\u1eafn BE ) \uf0db DFC = ACB Ta c\u00f3: \uf0de CIH = HAC (tg AIHC n\u1ed9i ti\u1ebfp) M\u00e0 HAC + ACH = 90\uf0b0 T\u1eeb (1),(2),(3) \uf0de CIH + FIC = 90\uf0b0 \uf0de IH \u22a5 FG Ta c\u00f3: \uf044BGC vu\u00f4ng t\u1ea1i G , H l\u00e0 trung \u0111i\u1ec3m BC . \uf0de GH = 1 BC 2 Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta \u0111\u01b0\u1ee3c: FH = 1 BC 2 \uf0de GH = FH \uf0de \uf044HGF c\u00e2n t\u1ea1i H . M\u00e0 IH \u22a5 FG \uf0de IH c\u0169ng l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn. \uf0de I l\u00e0 trung \u0111i\u1ec3m FG . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 9","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u00d4\u00db GD&\u00d1T TP HO\u00c0 CH\u00cd MINH \u00d1E\u00c0 THAM KHA\u00dbO TUYE\u00c5N SINH 10 PHO\u00d8NG G\u00d1&\u00d1T QUA\u00c4N TA\u00c2N B\u00ccNH NA\u00caM HO\u00cfC: 2023 - 2024 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. M\u00c3 \u0110\u1ec0: Qu\u1eadn TB - 4 Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (D) : y = 2x \u2212 1 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (D) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (D) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 3x2 \u2212 2x \u2212 2 = 0 c\u00f3 2 nghi\u1ec7m l\u00e0 x1 , x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c D = x1 + x2 x2 \u2212 1 x1 \u2212 1 C\u00e2u 3. (1 \u0111i\u1ec3m). M\u1ed9t phi h\u00e0nh gia n\u1eb7ng 70kg khi c\u00f2n \u1edf Tr\u00e1i \u0110\u1ea5t. Khi bay v\u00e0o kh\u00f4ng gian, c\u00e2n n\u1eb7ng f (h) c\u1ee7a phi h\u00e0nh gia n\u00e0y khi c\u00e1ch Tr\u00e1i \u0110\u1ea5t m\u1ed9t \u0111\u1ed9 cao h m\u00e9t, \u0111\u01b0\u1ee3c t\u00ednh theo h\u00e0m s\u1ed1 c\u00f3 c\u00f4ng th\u1ee9c: f ( h ) = 70.\uf0e6\uf0e7 3960 h \uf0f62 \uf0e8 3960 + \uf0f7 \uf0f8 a) C\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia l\u00e0 bao nhi\u00eau khi c\u00e1ch Tr\u00e1i \u0110\u1ea5t 100 m\u00e9t b) \u1ede \u0111\u1ed9 cao 250m , c\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia n\u00e0y thay \u0111\u1ed5i bao nhi\u00eau so v\u1edbi c\u00e2n n\u1eb7ng c\u00f3 \u0111\u01b0\u1ee3c \u1edf m\u1eb7t \u0111\u1ea5t (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t) C\u00e2u 4. (1 \u0111i\u1ec3m). B\u1ea1n H\u00f9ng mua b\u00e1nh li\u00ean hoan cu\u1ed1i n\u0103m h\u1ecdc cho l\u1edbp. T\u1ea1i c\u1eeda h\u00e0ng b\u00e1nh A gi\u00e1 b\u00e1nh H\u00f9ng mu\u1ed1n mua l\u00e0 15000 \u0111\u1ed3ng 1c\u00e1i b\u00e1nh, nh\u01b0ng n\u1ebfu mua tr\u00ean 10 c\u00e1i b\u00e1nh s\u1ebd \u0111\u01b0\u1ee3c c\u1eeda h\u00e0ng b\u00e1nh gi\u1ea3m 10% tr\u00ean t\u1ed5ng s\u1ed1 ti\u1ec1n mua b\u00e1nh. a) N\u1ebfu b\u1ea1n H\u00f9ng mua 44 c\u00e1i b\u00e1nh n\u00f3i tr\u00ean \u1edf c\u1eeda h\u00e0ng b\u00e1nh A th\u00ec ph\u1ea3i tr\u1ea3 bao nhi\u00eau ti\u1ec1n? b) T\u1ea1i c\u1eeda h\u00e0ng B (g\u1ea7n c\u1eeda h\u00e0ng A ) b\u00e1n c\u00f9ng lo\u1ea1i b\u00e1nh n\u00f3itr\u00ean (ch\u1ea5t l\u01b0\u1ee3ng nh\u01b0 nhau) \u0111\u1ed3ng gi\u00e1 15000 \u0111\u1ed3ng 1 c\u00e1i b\u00e1nh nh\u01b0ng n\u1ebfu mua 3 c\u00e1i b\u00e1nh ch\u1ec9 ph\u1ea3i tr\u1ea3 40000 \u0111\u1ed3ng. B\u1ea1n H\u00f9ng mua 44 c\u00e1i b\u00e1nh n\u00f3i tr\u00ean \u1edf c\u1eeda h\u00e0ng n\u00e0o \u0111\u1ec3 t\u1ed5ng s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 \u00edt h\u01a1n? C\u00e2u 5. (1 \u0111i\u1ec3m). M\u1ed9t c\u00e1i th\u00f9ng c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c 14kg thanh long ho\u1eb7c 21kg nh\u00e3n. N\u1ebfu ch\u1ee9a \u0111\u1ea7y th\u00f9ng \u0111\u00f3 b\u1eb1ng c\u1ea3 thanh long v\u00e0 nh\u00e3n m\u00e0 gi\u00e1 ti\u1ec1n c\u1ee7a thanh long b\u1eb1ng gi\u00e1 ti\u1ec1n c\u1ee7a nh\u00e3n th\u00ec s\u1ed1 tr\u00e1i c\u00e2y trong th\u00f9ng l\u00e0 s\u1ebd c\u00e2n n\u1eb7ng 18kg v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 480000 \u0111\u1ed3ng. T\u00ecm gi\u00e1 ti\u1ec1n 1kg thanh long, 1kg nh\u00e3n. C\u00e2u 6. (1 \u0111i\u1ec3m). N\u01b0\u1edbc gi\u1ea3i kh\u00e1t th\u01b0\u1eddng \u0111\u1ef1ng trong lon nh\u00f4m v\u00e0 c\u1ee1 lon ph\u1ed5 bi\u1ebfn ch\u1ee9a \u0111\u01b0\u1ee3c kho\u1ea3ng 330ml ch\u1ea5t l\u1ecfng, \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf h\u00ecnh tr\u1ee5 v\u1edbi chi\u1ec1u cao kho\u1ea3ng 10,2cm (ph\u1ea7n ch\u1ee9a ch\u1ea5t l\u1ecfng), \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y kho\u1ea3ng 6,42cm . Nh\u01b0ng hi\u1ec7n nay c\u00e1c nh\u00e0 s\u1ea3n xu\u1ea5t c\u00f3 xu h\u01b0\u1edbng t\u1ea1o ra nh\u1eefng lon nh\u00f4m v\u1edbi ki\u1ec3u d\u00e1ng cao thon h\u01a1n. Tuy chi ph\u00ed s\u1ea3n xu\u1ea5t nh\u1eefng chi\u1ebfc lon cao n\u00e0y t\u1ed1n k\u00e9m h\u01a1n, nh\u01b0ng n\u00f3 l\u1ea1i d\u1ec5 \u0111\u00e1nh l\u1eeba th\u1ecb gi\u00e1c v\u00e0 \u0111\u01b0\u1ee3c ng\u01b0\u1eddi ti\u00eau d\u00f9ng \u01b0a chu\u1ed9ng h\u01a1n. T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH a) M\u1ed9t lon n\u01b0\u1edbc ng\u1ecdt cao 13,41cm (ph\u1ea7n ch\u1ee9a ch\u1ea5t l\u1ecfng), \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y l\u00e0 5,6cm . H\u1ecfi lon n\u01b0\u1edbc ng\u1ecdt cao n\u00e0y c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c h\u1ebft l\u01b0\u1ee3ng n\u01b0\u1edbc ng\u1ecdt c\u1ee7a m\u1ed9t lon c\u00f3 c\u1ee1 ph\u1ed5 bi\u1ebfn kh\u00f4ng ? V\u00ec sao ? Bi\u1ebft th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5: V = \uf070 R2.h , v\u1edbi \uf070 \uf0bb 3,14 . b) Bi\u1ebft chi ph\u00ed s\u1ea3n xu\u1ea5t m\u1ed9t chi\u1ebfc lon t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a lon. H\u1ecfi chi ph\u00ed s\u1ea3n xu\u1ea5t chi\u1ebfc lon cao t\u0103ng bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi chi ph\u00ed s\u1ea3n xu\u1ea5t chi\u1ebfc lon c\u1ee1 ph\u1ed5 bi\u1ebfn? (l\u00e0m tr\u00f2n 1ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n). Bi\u1ebft di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c: Sxq = 2\uf070 R.h v\u00e0 Stp = Sxq + 2S\u00f1a\u00f9y C\u00e2u 7. (1 \u0111i\u1ec3m). C\u00f3 hai h\u00e3ng \u0111i\u1ec7n tho\u1ea1i c\u1ed1 \u0111\u1ecbnh t\u00ednh ph\u00ed g\u1ecdi cho c\u00e1c thu\u00ea bao nh\u01b0 sau: H\u00e3ng Thu\u00ea bao (ng\u00e0n \u0111\u1ed3ng) G\u1ecdi n\u1ed9i h\u1ea1t (ng\u00e0n \u0111\u1ed3ng\/ 30 ph\u00fat) H\u00e3ng A 10 6 H\u00e3ng B 15 5 G\u1ecdi y l\u00e0 gi\u00e1 ti\u1ec1n m\u00e0 kh\u00e1ch h\u00e0ng ph\u1ea3i tr\u1ea3 sau x l\u1ea7n 30 ph\u00fat (x \uf0ce *) . Bi\u1ebft c\u01b0\u1edbc ph\u00ed h\u00e0ng th\u00e1ng b\u1eb1ng t\u1ed5ng ti\u1ec1n thu\u00ea bao v\u00e0 c\u01b0\u1edbc ph\u00ed g\u1ecdi n\u1ed9i h\u1ea1t. a) H\u00e3y bi\u1ec3u di\u1ec5n y theo x c\u1ee7a t\u1eebng h\u00e3ng. C\u00e2u 8. b) H\u00e3y cho bi\u1ebft v\u1edbi c\u00e1ch t\u00ednh ph\u00ed nh\u01b0 tr\u00ean th\u00ec m\u1ed9t kh\u00e1ch h\u00e0ng m\u1ed7i th\u00e1ng g\u1ecdi b\u00ecnh qu\u00e2n 6 gi\u1edd n\u00ean s\u1eed d\u1ee5ng m\u1ea1ng c\u1ee7a h\u00e3ng n\u00e0o s\u1ebd r\u1ebb h\u01a1n? (3 \u0111i\u1ec3m) Cho (O; R) v\u00e0 \u0111i\u1ec3m P \u1edf ngo\u00e0i (O) . M\u1ed9t c\u00e1t tuy\u1ebfn qua P c\u1eaft (O) t\u1ea1i M , N ( PMN kh\u00f4ng qua t\u00e2m O ). Hai ti\u1ebfp tuy\u1ebfn t\u1ea1i M , N c\u1ee7a (O) c\u1eaft nhau t\u1ea1i A . V\u1ebd AE vu\u00f4ng g\u00f3c OP t\u1ea1i E . a) Ch\u1ee9ng minh: A , M , E , O , N c\u00f9ng thu\u1ed9c 1\u0111\u01b0\u1eddng tr\u00f2n. ( )b) Tia AE c\u1eaft O t\u1ea1i I , K ( I n\u1eb1m gi\u1eefa A v\u00e0 K ). Ch\u1ee9ng minh: AM2 = AI.AK v\u00e0 AI = MI 2 AK MK2 c) Ch\u1ee9ng minh: PI l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a (O) . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho P : y x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng D : y 2x 1 . a) V\u1ebd \u0111\u1ed3 th\u1ecb P v\u00e0 D tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a P v\u00e0 D b\u1eb1ng ph\u00e9p t\u00ednh. L\u1eddi gi\u1ea3i a) V\u1ebd \u0111\u1ed3 th\u1ecb P v\u00e0 D tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. BGT: 2 10 1 2 x 4 1 01 4 y x2 x 01 y 2x 1 1 1 b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a P v\u00e0 D b\u1eb1ng ph\u00e9p t\u00ednh. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a P v\u00e0 D : x2 2x 1 x2 2x 1 0 x1 Thay x 1 v\u00e0o y x2 , ta \u0111\u01b0\u1ee3c: y 1. V\u1eady 1; 1 l\u00e0 giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 3x2 2x 2 0 c\u00f3 2 nghi\u1ec7m l\u00e0 x1, x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c D x1 x2 . x2 1 x1 1 L\u1eddi gi\u1ea3i V\u00ec a.c 3. 2 6 0 n\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1, x2 . S x1 x2 b2 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: a3 P c 2 x1.x2 a 3 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 3","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH Ta c\u00f3: D x1 x2 x2 1 x1 1 D x1. x1 1 x2. x2 1 x2 1 . x1 1 x2 1 . x1 1 D x12 x1 x22 x2 x1x2 x2 x1 1 D x12 x22 x1 x2 x1x2 x1 x2 1 D x1 x2 2 2x1x2 x1 x2 x1x2 x1 x2 1 2 2 2 2 2 10 10 D3 33 9 3 2 21 1 33 3 L\u01b0u \u00fd: T\u1eeb b\u00e0i n\u00e0y, c\u00e1c s\u1ed1 li\u1ec7u t\u00ednh to\u00e1n v\u1ec1 \u0111\u1ed9 d\u00e0i khi l\u00e0m tr\u00f2n (n\u1ebfu c\u00f3) l\u1ea5y \u0111\u1ebfn m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, s\u1ed1 \u0111o g\u00f3c l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat. C\u00e2u 3. (1 \u0111i\u1ec3m) M\u1ed9t phi h\u00e0nh gia n\u1eb7ng 70kg khi c\u00f2n \u1edf Tr\u00e1i \u0110\u1ea5t. Khi bay v\u00e0o kh\u00f4ng gian, c\u00e2n n\u1eb7ng f h c\u1ee7a phi h\u00e0nh gia n\u00e0y khi c\u00e1ch Tr\u00e1i \u0110\u1ea5t m\u1ed9t \u0111\u1ed9 cao h m\u00e9t, \u0111\u01b0\u1ee3c t\u00ednh theo h\u00e0m s\u1ed1 c\u00f3 c\u00f4ng th\u1ee9c: f h 3960 2 70. 3960 h a) C\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia l\u00e0 bao nhi\u00eau khi c\u00e1ch Tr\u00e1i \u0110\u1ea5t 100 m\u00e9t b) \u1ede \u0111\u1ed9 cao 250m , c\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia n\u00e0y thay \u0111\u1ed5i bao nhi\u00eau so v\u1edbi c\u00e2n n\u1eb7ng c\u00f3 \u0111\u01b0\u1ee3c \u1edf m\u1eb7t \u0111\u1ea5t (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t) L\u1eddi gi\u1ea3i a) C\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia khi c\u00e1ch Tr\u00e1i \u0110\u1ea5t 100 m\u00e9t l\u00e0: f 100 70. 3960 2 66,6 kg 3960 100 V\u1eady c\u00e2n n\u1eb7ng c\u1ea7n t\u00ecm l\u00e0 66,6kg . b) C\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia \u1edf \u0111\u1ed9 cao 250 m\u00e9t l\u00e0: f (250) 70. 3960 2 61,9 kg 3960 250 C\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia khi \u1edf \u0111\u1ed9 cao 250 m\u00e9t nh\u1eb9 h\u01a1n so v\u1edbi c\u00e2n n\u1eb7ng c\u00f3 \u0111\u01b0\u1ee3c \u1edf m\u1eb7t \u0111\u1ea5t l\u00e0: T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 4","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH 70 61,9 8,1 kg V\u1eady khi \u1edf \u0111\u1ed9 cao 250m th\u00ec c\u00e2n n\u1eb7ng c\u1ee7a phi h\u00e0nh gia nh\u1eb9 h\u01a1n 8,1kg so v\u1edbi \u1edf m\u1eb7t \u0111\u1ea5t. C\u00e2u 4. (1 \u0111i\u1ec3m). B\u1ea1n H\u00f9ng mua b\u00e1nh li\u00ean hoan cu\u1ed1i n\u0103m h\u1ecdc cho l\u1edbp. T\u1ea1i c\u1eeda h\u00e0ng b\u00e1nh A gi\u00e1 b\u00e1nh H\u00f9ng mu\u1ed1n mua l\u00e0 15000 \u0111\u1ed3ng1 c\u00e1i b\u00e1nh, nh\u01b0ng n\u1ebfu mua tr\u00ean 10 c\u00e1i b\u00e1nh s\u1ebd \u0111\u01b0\u1ee3c c\u1eeda h\u00e0ng b\u00e1nh gi\u1ea3m 10% tr\u00ean t\u1ed5ng s\u1ed1 ti\u1ec1n mua b\u00e1nh. a)N\u1ebfu b\u1ea1n H\u00f9ng mua 44 c\u00e1i b\u00e1nh n\u00f3i tr\u00ean \u1edf c\u1eeda h\u00e0ng b\u00e1nh A th\u00ec ph\u1ea3i tr\u1ea3 bao nhi\u00eau ti\u1ec1n? b)T\u1ea1i c\u1eeda h\u00e0ng B (g\u1ea7n c\u1eeda h\u00e0ng A ) b\u00e1n c\u00f9ng lo\u1ea1i b\u00e1nh n\u00f3itr\u00ean (ch\u1ea5t l\u01b0\u1ee3ng nh\u01b0 nhau) \u0111\u1ed3ng gi\u00e1 15000 \u0111\u1ed3ng 1 c\u00e1i b\u00e1nh nh\u01b0ng n\u1ebfu mua 3 c\u00e1i b\u00e1nh ch\u1ec9 ph\u1ea3i tr\u1ea3 40000 \u0111\u1ed3ng. B\u1ea1n H\u00f9ng mua 44 c\u00e1i b\u00e1nh n\u00f3i tr\u00ean \u1edf c\u1eeda h\u00e0ng n\u00e0o \u0111\u1ec3 t\u1ed5ng s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 \u00edt h\u01a1n? L\u1eddi gi\u1ea3i a) S\u1ed1 ti\u1ec1n b\u1ea1n H\u00f9ng c\u1ea7n tr\u1ea3 khi mua 44 c\u00e1i b\u00e1nh t\u1ea1i c\u1eeda h\u00e0ng A l\u00e0: 15 000.44 .90% 594 000 \u0111\u1ed3ng b) S\u1ed1 ti\u1ec1n b\u1ea1n H\u00f9ng c\u1ea7n tr\u1ea3 khi mua 44 c\u00e1i b\u00e1nh t\u1ea1i c\u1eeda h\u00e0ng B l\u00e0: 14.40 000 2.15 000 590 000 \u0111\u1ed3ng V\u1eady b\u1ea1n H\u00f9ng mua 44 c\u00e1i b\u00e1nh \u1edf c\u1eeda h\u00e0ng B th\u00ec t\u1ed5ng s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 \u00edt h\u01a1n. C\u00e2u 5. (1 \u0111i\u1ec3m) M\u1ed9t c\u00e1i th\u00f9ng c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c 14kg thanh long ho\u1eb7c 21kg nh\u00e3n. N\u1ebfu ch\u1ee9a \u0111\u1ea7y th\u00f9ng \u0111\u00f3 b\u1eb1ng c\u1ea3 thanh long v\u00e0 nh\u00e3n m\u00e0 gi\u00e1 ti\u1ec1n c\u1ee7a thanh long b\u1eb1ng gi\u00e1 ti\u1ec1n c\u1ee7a nh\u00e3n th\u00ec s\u1ed1 tr\u00e1i c\u00e2y trong th\u00f9ng l\u00e0 s\u1ebd c\u00e2n n\u1eb7ng 18kg v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 480000 \u0111\u1ed3ng. T\u00ecm gi\u00e1 ti\u1ec1n 1kg thanh long, 1kg nh\u00e3n. L\u1eddi gi\u1ea3i G\u1ecdi x kg l\u00e0 s\u1ed1 thanh long c\u00f3 trong th\u00f9ng 0 x 18 y kg l\u00e0 s\u1ed1 nh\u00e3n c\u00f3 trong th\u00f9ng 0 y 18 18 V\u00ec t\u1ed5ng s\u1ed1 thanh long v\u00e0 nh\u00e3n c\u00f3 trong th\u00f9ng l\u00e0 18kg n\u00ean ta c\u00f3: x y x kg thanh long chi\u1ebfm x th\u00f9ng v\u00e0 y kg nh\u00e3n chi\u1ebfm y th\u00f9ng 14 21 C\u1ea3 th\u00f9ng \u0111\u01b0\u1ee3c ch\u1ea5t \u0111\u1ea7y thanh long v\u00e0 nh\u00e3n n\u00ean ta c\u00f3: x y 1 14 21 x y 18 x y 18 x 6n Theo gt, ta c\u00f3: x y 1 21x 14 y 294 y 12 n 14 21 Do s\u1ed1 ti\u1ec1n c\u1ee7a thanh long v\u00e0 nh\u00e3n b\u1eb1ng nhau n\u00ean gi\u00e1 ti\u1ec1n m\u1ed7i lo\u1ea1i l\u00e0: 480000 : 2 240000 \u0111\u1ed3ng. V\u1eady gi\u00e1 ti\u1ec1n 1kg thanh long l\u00e0: 240000 : 6 40000 \u0111\u1ed3ng. Gi\u00e1 ti\u1ec1n 1kg nh\u00e3n l\u00e0: 240000 :12 20 000\u0111\u1ed3ng. T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 5","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 6. (1 \u0111i\u1ec3m) N\u01b0\u1edbc gi\u1ea3i kh\u00e1t th\u01b0\u1eddng \u0111\u1ef1ng trong lon nh\u00f4m v\u00e0 c\u1ee1 lon ph\u1ed5 bi\u1ebfn ch\u1ee9a \u0111\u01b0\u1ee3c kho\u1ea3ng 330ml ch\u1ea5t l\u1ecfng, \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf h\u00ecnh tr\u1ee5 v\u1edbi chi\u1ec1u cao kho\u1ea3ng 10,2cm (ph\u1ea7n ch\u1ee9a ch\u1ea5t l\u1ecfng), \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y kho\u1ea3ng 6,42cm . Nh\u01b0ng hi\u1ec7n nay c\u00e1c nh\u00e0 s\u1ea3n xu\u1ea5t c\u00f3 xu h\u01b0\u1edbng t\u1ea1o ra nh\u1eefng lon nh\u00f4m v\u1edbi ki\u1ec3u d\u00e1ng cao thon h\u01a1n. Tuy chi ph\u00ed s\u1ea3n xu\u1ea5t nh\u1eefng chi\u1ebfc lon cao n\u00e0y t\u1ed1n k\u00e9m h\u01a1n, nh\u01b0ng n\u00f3 l\u1ea1i d\u1ec5 \u0111\u00e1nh l\u1eeba th\u1ecb gi\u00e1c v\u00e0 \u0111\u01b0\u1ee3c ng\u01b0\u1eddi ti\u00eau d\u00f9ng \u01b0a chu\u1ed9ng h\u01a1n. a) M\u1ed9t lon n\u01b0\u1edbc ng\u1ecdt cao 13,41cm (ph\u1ea7n ch\u1ee9a ch\u1ea5t l\u1ecfng), \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y l\u00e0 5,6cm . H\u1ecfi lon n\u01b0\u1edbc ng\u1ecdt cao n\u00e0y c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c h\u1ebft l\u01b0\u1ee3ng n\u01b0\u1edbc ng\u1ecdt c\u1ee7a m\u1ed9t lon c\u00f3 c\u1ee1 ph\u1ed5 bi\u1ebfn kh\u00f4ng ? V\u00ec sao ? Bi\u1ebft th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5: V R2.h , v\u1edbi 3,14 . b) Bi\u1ebft chi ph\u00ed s\u1ea3n xu\u1ea5t m\u1ed9t chi\u1ebfc lon t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a lon. H\u1ecfi chi ph\u00ed s\u1ea3n xu\u1ea5t chi\u1ebfc lon cao t\u0103ng bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi chi ph\u00ed s\u1ea3n xu\u1ea5t chi\u1ebfc lon c\u1ee1 ph\u1ed5 bi\u1ebfn? (l\u00e0m tr\u00f2n 1 ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n). Bi\u1ebft di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c: Sxq 2 R.h v\u00e0 Stp Sxq 2S\u00f1a\u00f9y L\u1eddi gi\u1ea3i a) Th\u1ec3 t\u00edch lon n\u01b0\u1edbc ng\u1ecdt cao n\u00e0y ch\u1ee9a \u0111\u01b0\u1ee3c: V R2.h 3,14.2,82.13, 41 330,1ml V\u1eady lon n\u01b0\u1edbc ng\u1ecdt cao \u0111\u00e3 cho c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c h\u1ebft l\u01b0\u1ee3ng n\u01b0\u1edbc ng\u1ecdt c\u1ee7a m\u1ed9t lon c\u1ee1 ph\u1ed5 bi\u1ebfn. b) Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a chi\u1ebfc lon c\u1ee1 ph\u1ed5 bi\u1ebfn l\u00e0: Stp1 Sxq1 2S\u00f1a\u00f9y1 2 R1.h1 2 R12 2.3,14.3, 21.10, 2 2.3,14.3, 212 270, 3cm2 Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a chi\u1ebfc lon cao l\u00e0: Stp2 Sxq2 2S\u00f1a\u00f9y2 2 R2.h2 2 R22 2.3,14.2,8.13,41 2.3,14.2,82 285cm2 Chi ph\u00ed s\u1ea3n xu\u1ea5t chi\u1ebfc lon cao t\u0103ng so v\u1edbi chi ph\u00ed s\u1ea3n xu\u1ea5t chi\u1ebfc lon c\u1ee1 ph\u1ed5 bi\u1ebfn l\u00e0: T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 6","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH 285 .100% 100% 5, 4% 270,3 V\u1eady chi ph\u00ed s\u1ea3n xu\u1ea5t t\u0103ng 5,4% C\u00e2u 7. (1 \u0111i\u1ec3m) C\u00f3 hai h\u00e3ng \u0111i\u1ec7n tho\u1ea1i c\u1ed1 \u0111\u1ecbnh t\u00ednh ph\u00ed g\u1ecdi cho c\u00e1c thu\u00ea bao nh\u01b0 sau: H\u00e3ng Thu\u00ea bao (ng\u00e0n \u0111\u1ed3ng) G\u1ecdi n\u1ed9i h\u1ea1t (ng\u00e0n \u0111\u1ed3ng\/ ph\u00fat) H\u00e3ng A 10 6 H\u00e3ng B 15 5 G\u1ecdi y l\u00e0 gi\u00e1 ti\u1ec1n m\u00e0 kh\u00e1ch h\u00e0ng ph\u1ea3i tr\u1ea3 sau x l\u1ea7n 30 ph\u00fat x * . Bi\u1ebft c\u01b0\u1edbc ph\u00ed h\u00e0ng th\u00e1ng b\u1eb1ng t\u1ed5ng ti\u1ec1n thu\u00ea bao v\u00e0 c\u01b0\u1edbc ph\u00ed g\u1ecdi n\u1ed9i h\u1ea1t. a) H\u00e3y bi\u1ec3u di\u1ec5n y theo x c\u1ee7a t\u1eebng h\u00e3ng. b) H\u00e3y cho bi\u1ebft v\u1edbi c\u00e1ch t\u00ednh ph\u00ed nh\u01b0 tr\u00ean th\u00ec m\u1ed9t kh\u00e1ch h\u00e0ng m\u1ed7i th\u00e1ng g\u1ecdi b\u00ecnh qu\u00e2n 6 gi\u1edd n\u00ean s\u1eed d\u1ee5ng m\u1ea1ng c\u1ee7a h\u00e3ng n\u00e0o s\u1ebd r\u1ebb h\u01a1n?. L\u1eddi gi\u1ea3i a) H\u00e3y bi\u1ec3u di\u1ec5n y theo x c\u1ee7a t\u1eebng h\u00e3ng. H\u00e3ng A : y 10 6x H\u00e3ng B : y 15 5x b) M\u1ed7i th\u00e1ng g\u1ecdi b\u00ecnh qu\u00e2n 6 gi\u1edd 12 l\u1ea7n 30 ph\u00fat Chi ph\u00ed ph\u1ea3i tr\u1ea3 cho th\u1eddi gian s\u1eed d\u1ee5ng n\u00eau tr\u00ean l\u00e0: H\u00e3ng A : y 10 6.12 82 ng\u00e0n \u0111\u1ed3ng. H\u00e3ng B : y 15 5.12 75 ng\u00e0n \u0111\u1ed3ng. V\u1eady kh\u00e1ch h\u00e0ng n\u00ean s\u1eed d\u1ee5ng m\u1ea1ng c\u1ee7a h\u00e3ng B s\u1ebd r\u1ebb h\u01a1n. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho (O; R) v\u00e0 \u0111i\u1ec3m P \u1edf ngo\u00e0i (O). M\u1ed9t c\u00e1t tuy\u1ebfn qua P c\u1eaft (O) t\u1ea1i M, N (PMN kh\u00f4ng qua t\u00e2m O). Hai ti\u1ebfp tuy\u1ebfn t\u1ea1i M, N c\u1ee7a (O) c\u1eaft nhau t\u1ea1i A. V\u1ebd AE vu\u00f4ng g\u00f3c OP t\u1ea1i E. AI.AK v\u00e0 a) Ch\u1ee9ng minh: A, M, E, O, N c\u00f9ng thu\u1ed9c 1 \u0111\u01b0\u1eddng tr\u00f2n. b) Tia AE c\u1eaft (O) t\u1ea1i I, K (I n\u1eb1m gi\u1eefa A v\u00e0 K). Ch\u1ee9ng minh: AM 2 AI MI 2 AK MK 2 c) Ch\u1ee9ng minh: PI l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a (O). L\u1eddi gi\u1ea3i T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 7","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH a) Ta c\u00f3: ONA 90 OMA 90 OEA 90 3 g\u00f3c n\u00e0y \u0111\u1ec1u nh\u00ecn OA d\u01b0\u1edbi m\u1ed9t g\u00f3c l\u00e0 90 O , E , A , M , N c\u00f9ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh OA. b) X\u00e9t AMI v\u00e0 AKM ta c\u00f3: A chung AKM AMI (cu\u00f8ng cha\u00e9n IM) AMI \u223d AKM g.g AI AM AM 2 AI.AK AM AK AI IM AMI \u223d AKM AM MK AI 2 IM 2 m\u00e0 AM 2 AI.AK AM 2 MK 2 AI 2 IM 2 AI MI 2 AI.AK MK 2 AK MK 2 c) G\u1ecdi F AO MN OMA vu\u00f4ng t\u1ea1i M OA.OF OM 2 (h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng) Ta th\u1ea5y OEMA l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp (do OEA OMA 90 ) OEM ONM 180 OMP OMN 180 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 8","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH M\u00e0 OMN c\u00e2n t\u1ea1i O ONM OMN OMP OEM OE.OP OM 2 OMP\u223d OEM (g.g) OE.OP OA.OF POI \u223d IEO (c.g.c) OIP OEI 90 PI la\u00f8 tie\u00e1p tuye\u00e1n cu\u00fba O ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 9","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u1ede GD & \u0110T TP H\u1ed2 CH\u00cd MINH \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 PH\u00d2NG GI\u00c1O D\u1ee4C & \u0110T QU\u00c2N T\u00c2N B\u00ccNH N\u0102M H\u1eccC: 2023 - 2024 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 M\u00c3 \u0110\u1ec0: Qu\u1eadn T\u00e2n B\u00ecnh - 5 \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = \u2212x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 2x + 1 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh x2 \u2212 x \u2212 2 = 0 . G\u1ecdi x1 , x2 l\u00e0 2 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (n\u1ebfu c\u00f3). Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A = x12 + x22 x2 x1 C\u00e2u 3. (0,75 \u0111i\u1ec3m). C\u00f4ng ty \u0111\u1ed3 ch\u01a1i Bingbon v\u1eeba cho ra \u0111\u1eddi m\u1ed9t \u0111\u1ed3 ch\u01a1i t\u00e0u \u0111i\u1ec7n \u0111i\u1ec1u khi\u1ec3n t\u1eeb xa. Trong \u0111i\u1ec1u ki\u1ec7n ph\u00f2ng th\u00ed nghi\u1ec7m, qu\u00e3ng \u0111\u01b0\u1eddng s(cm) \u0111i \u0111\u01b0\u1ee3c c\u1ee7a \u0111o\u00e0n t\u00e0u c\u1ee7a \u0111\u1ed3 ch\u01a1i l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 c\u1ee7a th\u1eddi gian t ( gi\u00e2y) h\u00e0m s\u1ed1 \u0111\u00f3 l\u00e0 s = 6t + 9 . Trong \u0111i\u1ec1u ki\u1ec7n th\u1ef1c t\u1ebf ng\u01b0\u1eddi ta th\u1ea5y r\u1eb1ng n\u1ebfu \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i di chuy\u1ec3n qu\u00e3ng \u0111\u01b0\u1eddng 12cm th\u00ec m\u1ea5t 2 gi\u00e2y, v\u00e0 c\u1ee9 trong m\u1ed7i 10 gi\u00e2y th\u00ec n\u00f3 \u0111i \u0111\u01b0\u1ee3c 52cm . a) Trong \u0111i\u1ec1u ki\u1ec7n ph\u00f2ng th\u00ed nghi\u1ec7m, sau 5 ( gi\u00e2y) \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i di chuy\u1ec3n \u0111\u01b0\u1ee3c bao nhi\u00eau xen ti m\u00e9t? b) M\u1eb9 b\u00e9 An mua \u0111\u1ed3 ch\u01a1i v\u1ec1 cho b\u00e9 ch\u01a1i, b\u00e9 ng\u1ed3i c\u00e1ch m\u1eb9 2 m\u00e9t. H\u1ecfi c\u1ea7n bao nhi\u00eau gi\u00e2y \u0111\u1ec3 \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i \u0111i t\u1eeb ch\u1ed7 b\u00e9 t\u1edbi ch\u1ed7 m\u1eb9? C\u00e2u 4. (0,75 \u0111i\u1ec3m). Sau bu\u1ed5i t\u1ed5ng k\u1ebft, l\u1edbp 9A \u0111i \u0103n kem \u1edf m\u1ed9t qu\u00e1n g\u1ea7n tr\u01b0\u1eddng. Do qu\u00e1n m\u1edbi khai tr\u01b0\u01a1ng n\u00ean c\u00f3 khuy\u1ebfn m\u00e3i, b\u1eaft \u0111\u1ea7u t\u1eeb ly th\u1ee9 5 gi\u00e1 m\u1ed7i ly kem gi\u1ea3m 3000 \u0111\u1ed3ng so v\u1edbi gi\u00e1 ban \u0111\u1ea7u. L\u1edbp 9A mua 44 ly kem, khi t\u00ednh ti\u1ec1n ch\u1ee7 c\u1eeda h\u00e0ng th\u1ea5y l\u1edbp mua nhi\u1ec1u n\u00ean gi\u1ea3m th\u00eam 5 0 s\u1ed1 ti\u1ec1n tr\u00ean h\u00f3a \u0111\u01a1n, v\u00ec v\u1eady s\u1ed1 ti\u1ec1n l\u1edbp 9A ch\u1ec9 ph\u1ea3i tr\u1ea3 l\u00e0 513000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 0 c\u1ee7a m\u1ed7i ly kem ban \u0111\u1ea7u l\u00e0 bao nhi\u00eau? C\u00e2u 5. (1 \u0111i\u1ec3m). Trong n\u0103m h\u1ecdc 2022 2023 , Tr\u01b0\u1eddng THCS A , H\u1ecdc k\u00ec I c\u00f3 500 h\u1ecdc sinh \u0111\u1ea1t lo\u1ea1i kh\u00e1, Gi\u1ecfi. Qua h\u1ecdc k\u00ec II , s\u1ed1 h\u1ecdc sinh \u0111\u1ea1t lo\u1ea1i kh\u00e1 t\u0103ng 2 0 , s\u1ed1 h\u1ecdc sinh \u0111\u1ea1t lo\u1ea1i Gi\u1ecfi t\u0103ng 0 4 0 n\u00ean t\u1ed5ng s\u1ed1 h\u1ecdc sinh lo\u1ea1i kh\u00e1, Gi\u1ecfi l\u00e0 513 h\u1ecdc sinh. Nh\u00e0 tr\u01b0\u1eddng ph\u00e1t th\u01b0\u1edfng cho h\u1ecdc 0 sinh nh\u01b0 sau: m\u1ed7i h\u1ecdc sinh Gi\u1ecfi l\u00e0 20 quy\u1ec3n, m\u1ed7i h\u1ecdc sinh Kh\u00e1 l\u00e0 10 quy\u1ec3n t\u1eadp. Bi\u1ebft gi\u00e1 m\u1ed7i quy\u1ec3n t\u1eadp tr\u00ean th\u1ecb tr\u01b0\u1eddng l\u00e0 7500 \u0111\u1ed3ng\/ quy\u1ec3n. Do mua s\u1ed1 l\u01b0\u1ee3ng l\u1edbn n\u00ean c\u00f4ng ty cung c\u1ea5p c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i nh\u01b0 sau: N\u1ebfu mua h\u00f3a \u0111\u01a1n tr\u00ean 40000000 \u0111\u1ed3ng th\u00ec \u0111\u01b0\u1ee3c gi\u1ea3m 5 0 tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n; N\u1ebfu mua h\u00f3a \u0111\u01a1n tr\u00ean 50000000 \u0111\u1ed3ng th\u00ec \u0111\u01b0\u1ee3c gi\u1ea3m 8 0 tr\u00ean t\u1ed5ng 0 0 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH h\u00f3a \u0111\u01a1n; N\u1ebfu mua h\u00f3a \u0111\u01a1n tr\u00ean 60000000 \u0111\u1ed3ng th\u00ec \u0111\u01b0\u1ee3c gi\u1ea3m 10 0 tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n. H\u1ecfi 0 nh\u00e0 tr\u01b0\u1eddng ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n bao nhi\u00eau \u0111\u1ec3 mua t\u1eadp ph\u00e1t th\u01b0\u1edfng cho h\u1ecdc sinh n\u0103m h\u1ecdc \u0111\u00f3? C\u00e2u 6. (1 \u0111i\u1ec3m). \u0110\u1ec3 l\u00e0m th\u00ed nghi\u1ec7m v\u1ec1 s\u1ef1 n\u1ed5i c\u1ee7a v\u1eadt kh\u00f4ng ch\u1ee9a n\u01b0\u1edbc. Nam chu\u1ea9n b\u1ecb m\u1ed9t ly n\u01b0\u1edbc th\u1ee7y tinh v\u1edbi d\u1ea1ng l\u00f2ng trong c\u1ee7a ly l\u00e0 m\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y l\u00e0 6cm ; chi\u1ec1u cao l\u00e0 10cm v\u00e0 m\u1ed9t qu\u1ea3 b\u00f3ng b\u00e0n ti\u00eau chu\u1ea9n qu\u1ed1c t\u1ebf c\u00f3 d\u1ea1ng h\u00ecnh c\u1ea7u v\u1edbi \u0111\u01b0\u1eddng k\u00ednh 40mm . Minh ti\u1ebfn h\u00e0nh b\u1ecf qu\u1ea3 b\u00f3ng b\u00e0n v\u00e0o trong ly r\u1ed3i r\u00f3t 200cm3 n\u01b0\u1edbc t\u1eeb t\u1eeb v\u00e0o ly v\u00e0 \u0111o d\u01b0\u1ee3c m\u1ef1c n\u01b0\u1edbc d\u00e2ng cao 7,2cm . a) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a qu\u1ea3 b\u00f3ng b\u00e0n. b) T\u00ednh th\u1ec3 t\u00edch ph\u1ea7n n\u1ed5i c\u1ee7a qu\u1ea3 b\u00f3ng b\u00e0n trong th\u00ed nghi\u1ec7m c\u1ee7a Minh.( Bi\u1ebft th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u b\u00e1n k\u00ednh R l\u00e0 V 4 R3 ; c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 v\u1edbi b\u00e1n k\u00ednh r l\u00e0V r 2h ,l\u1ea5y 3 3,14 v\u00e0 k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai) C\u00e2u 7. (1 \u0111i\u1ec3m). Nh\u00e0 tr\u01b0\u1eddng t\u1ed5 ch\u1ee9c gi\u1ea3i b\u00f3ng \u0111\u00e1 mini m\u1eebng Xu\u00e2n cho h\u1ecdc sinh kh\u1ed1i 9 . M\u1ed7i l\u1edbp c\u1eed m\u1ed9t \u0111\u1ed9i tham gia, m\u1ed7i \u0111\u1ed9i \u0111\u1ea5u v\u1edbi m\u1ed9t \u0111\u1ed9i c\u1ee7a l\u1edbp b\u1ea1n m\u1ed9t l\u1ea7n. N\u1ebfu t\u1ed5ng s\u1ed1 tr\u1eadn \u0111\u1ea5u l\u00e0 28 th\u00ec kh\u1ed1i l\u1edbp 9 c\u00f3 bao nhi\u00eau \u0111\u1ed9i tham gia? C\u00e2u 8. (3 \u0111i\u1ec3m) Cho M n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n (O) , k\u1ebb hai ti\u1ebfp tuy\u1ebfn MA , MB v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n (O) ( A,B l\u00e0 hai ti\u1ebfp \u0111i\u1ec3m). L\u1ea5y \u0111i\u1ec3m N thu\u1ed9c cung l\u1edbn AB (NB NA) . MN c\u1eaft (O) t\u1ea1i E . a) Ch\u1ee9ng minh: ME.MN MA2 b) G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OM v\u00e0 AB , OM c\u1eaft (O) l\u1ea7n l\u01b0\u1ee3t t\u1ea1i hai \u0111i\u1ec3m I, K ( K n\u1eb1m gi\u1eefa M v\u00e0 I ). Ch\u1ee9ng minh: OH .HM HK .HI v\u00e0 1 1 2 HK HI HM c) Ch\u1ee9ng minh: t\u1ee9 gi\u00e1c OHEN n\u1ed9i ti\u1ebfp v\u00e0 KH .IM KM .IH . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = \u2212x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 2x + 1 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. L\u1eddi gi\u1ea3i a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. 3 a) BGT: x \u22122 \u22121 0 1 2 y = \u2212x2 \u22124 \u22121 0 \u22121 \u22124 x 01 y = 2x + 1 1 \u22121 b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) : \u2212x2 = 2x + 1 \uf0db x2 + 2x + 1 = 0 \uf0db (x + 1)2 = 0 \uf0db x = \u22121 Thay x = \u22121 v\u00e0o y = \u2212x2 , ta \u0111\u01b0\u1ee3c: y = \u2212(\u22121)2 = \u22121 . T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH V\u1eady (1; \u2212 1) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh x2 \u2212 x \u2212 2 = 0 . G\u1ecdi x1 , x2 l\u00e0 2 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (n\u1ebfu c\u00f3). Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A = x12 + x22 x2 x1 L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = (\u22121)2 \u2212 4.(1).(\u22121) = 5 \uf03e 0 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 ,x2 . \uf0ec\uf0ef\uf0efS = x1 + x2 = \u2212b = 1 \uf0ed = x1 a Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ee\uf0ef\uf0efP c = \u22122 a .x2 = Ta c\u00f3: A = x12 + x22 x2 x1 A = x12 + x22 x2 x1 A = x13 + x23 x1x2 ( ) ( )A = x1 + x2 3 \u2212 3x1x2 x1 + x2 x1x2 A = (1)3 \u2212 3(\u22122) \uf0d71 = \u2212 7 . \u22122 2 L\u01b0u \u00fd: T\u1eeb b\u00e0i n\u00e0y, c\u00e1c s\u1ed1 li\u1ec7u t\u00ednh to\u00e1n v\u1ec1 \u0111\u1ed9 d\u00e0i khi l\u00e0m tr\u00f2n (n\u1ebfu c\u00f3) l\u1ea5y \u0111\u1ebfn m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, s\u1ed1 \u0111o g\u00f3c l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat. C\u00e2u 9. (0,75 \u0111i\u1ec3m). C\u00f4ng ty \u0111\u1ed3 ch\u01a1i Bingbon v\u1eeba cho ra \u0111\u1eddi m\u1ed9t \u0111\u1ed3 ch\u01a1i t\u00e0u \u0111i\u1ec7n \u0111i\u1ec1u khi\u1ec3n t\u1eeb xa. Trong \u0111i\u1ec1u ki\u1ec7n ph\u00f2ng th\u00ed nghi\u1ec7m, qu\u00e3ng \u0111\u01b0\u1eddng s (cm) \u0111i \u0111\u01b0\u1ee3c c\u1ee7a \u0111o\u00e0n t\u00e0u c\u1ee7a \u0111\u1ed3 ch\u01a1i l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 c\u1ee7a th\u1eddi gian t ( gi\u00e2y) h\u00e0m s\u1ed1 \u0111\u00f3 l\u00e0 s = 6t + 9 . Trong \u0111i\u1ec1u ki\u1ec7n th\u1ef1c t\u1ebf ng\u01b0\u1eddi ta th\u1ea5y r\u1eb1ng n\u1ebfu \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i di chuy\u1ec3n qu\u00e3ng \u0111\u01b0\u1eddng 12cm th\u00ec m\u1ea5t 2 gi\u00e2y, v\u00e0 c\u1ee9 trong m\u1ed7i 10 gi\u00e2y th\u00ec n\u00f3 \u0111i \u0111\u01b0\u1ee3c 52 cm. a) Trong \u0111i\u1ec1u ki\u1ec7n ph\u00f2ng th\u00ed nghi\u1ec7m, sau 5 ( gi\u00e2y) \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i di chuy\u1ec3n \u0111\u01b0\u1ee3c bao nhi\u00eau xen ti m\u00e9t? T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 4","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH b) M\u1eb9 b\u00e9 An mua \u0111\u1ed3 ch\u01a1i v\u1ec1 cho b\u00e9 ch\u01a1i, b\u00e9 ng\u1ed3i c\u00e1ch m\u1eb9 2 m\u00e9t. H\u1ecfi c\u1ea7n bao nhi\u00eau gi\u00e2y \u0111\u1ec3 \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i \u0111i t\u1eeb ch\u1ed7 b\u00e9 t\u1edbi ch\u1ed7 m\u1eb9? L\u1eddi gi\u1ea3i a) Trong \u0111i\u1ec1u ki\u1ec7n ph\u00f2ng th\u00ed nghi\u1ec7m, sau 5 ( gi\u00e2y) \u0111o\u00e0n t\u00e0u \u0111\u1ed3 ch\u01a1i di chuy\u1ec3n \u0111\u01b0\u1ee3c: s = 6t + 9\uf0de s = 6 \uf0d7 5 + 9 = 39(cm) b) Trong \u0111i\u1ec1u ki\u1ec7n th\u1ef1c t\u1ebf ta c\u00f3 qu\u00e3ng \u0111\u01b0\u1eddng: s = at + b V\u1edbi s 12;t 2 ta c\u00f3 2a + b= 12 (1) V\u1edbi s 52;t 10 ta c\u00f3 10a + b= 52 (2) T\u1eeb (1 v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 2a b 12 10a b 52 a5 b2 V\u1eady qu\u00e3ng \u0111\u01b0\u1eddng th\u1ef1c t\u1ebf: s = 5t + 2 V\u1edbi s 2m 200m ta c\u00f3 : 200 = 5t + 2 \uf0db t = 39,6 (s) V\u1eady t\u00e0u \u0111\u1ed3 ch\u01a1i \u0111i h\u1ebft 39, 6 (s) C\u00e2u 3. (0,75 \u0111i\u1ec3m). Sau bu\u1ed5i t\u1ed5ng k\u1ebft, l\u1edbp 9A \u0111i \u0103n kem \u1edf m\u1ed9t qu\u00e1n g\u1ea7n tr\u01b0\u1eddng. Do qu\u00e1n m\u1edbi khai tr\u01b0\u01a1ng n\u00ean c\u00f3 khuy\u1ebfn m\u00e3i, b\u1eaft \u0111\u1ea7u t\u1eeb ly th\u1ee9 5 gi\u00e1 m\u1ed7i ly kem gi\u1ea3m 3000 \u0111\u1ed3ng so v\u1edbi gi\u00e1 ban \u0111\u1ea7u. L\u1edbp 9A mua 44 ly kem, khi t\u00ednh ti\u1ec1n ch\u1ee7 c\u1eeda h\u00e0ng th\u1ea5y l\u1edbp mua nhi\u1ec1u n\u00ean gi\u1ea3m th\u00eam 5% s\u1ed1 ti\u1ec1n tr\u00ean h\u00f3a \u0111\u01a1n, v\u00ec v\u1eady s\u1ed1 ti\u1ec1n l\u1edbp 9A ch\u1ec9 ph\u1ea3i tr\u1ea3 l\u00e0 513 000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 c\u1ee7a m\u1ed7i ly kem ban \u0111\u1ea7u l\u00e0 bao nhi\u00eau? L\u1eddi gi\u1ea3i G\u1ecdi x (\u0111\u1ed3ng) l\u00e0 gi\u00e1 ti\u1ec1n ly kem ban \u0111\u1ea7u x * Gi\u00e1 ti\u1ec1n m\u1ed9t ly kem sau gi\u1ea3m l\u00e0: 3000 x (\u0111\u1ed3ng) Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 4x 40(x 3000) 95% 513000 ( nh\u1eadn ) x 15000 V\u1eady gi\u00e1 ban \u0111\u1ea7u c\u1ee7a ly kem l\u00e0 15 000( \u0111\u1ed3ng ) C\u00e2u 4. (1 \u0111i\u1ec3m). Trong n\u0103m h\u1ecdc 2022 \u2013 2023, Tr\u01b0\u1eddng THCS A, H\u1ecdc k\u00ec I c\u00f3 500 h\u1ecdc sinh \u0111\u1ea1t lo\u1ea1i kh\u00e1, Gi\u1ecfi. Qua h\u1ecdc k\u00ec II, s\u1ed1 h\u1ecdc sinh \u0111\u1ea1t lo\u1ea1i kh\u00e1 t\u0103ng 2%, s\u1ed1 h\u1ecdc sinh \u0111\u1ea1t lo\u1ea1i Gi\u1ecfi t\u0103ng 4% n\u00ean t\u1ed5ng s\u1ed1 h\u1ecdc sinh lo\u1ea1i kh\u00e1, Gi\u1ecfi l\u00e0 513 h\u1ecdc sinh. Nh\u00e0 tr\u01b0\u1eddng ph\u00e1t th\u01b0\u1edfng cho h\u1ecdc sinh nh\u01b0 sau: m\u1ed7i h\u1ecdc sinh Gi\u1ecfi l\u00e0 20 quy\u1ec3n, m\u1ed7i h\u1ecdc sinh Kh\u00e1 l\u00e0 10 quy\u1ec3n t\u1eadp. Bi\u1ebft gi\u00e1 m\u1ed7i quy\u1ec3n t\u1eadp T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 5","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH tr\u00ean th\u1ecb tr\u01b0\u1eddng l\u00e0 7500 \u0111\u1ed3ng\/ quy\u1ec3n. Do mua s\u1ed1 l\u01b0\u1ee3ng l\u1edbn n\u00ean c\u00f4ng ty cung c\u1ea5p c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i nh\u01b0 sau: N\u1ebfu mua h\u00f3a \u0111\u01a1n tr\u00ean 40 000 000 \u0111\u1ed3ng th\u00ec \u0111\u01b0\u1ee3c gi\u1ea3m 5% tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n; N\u1ebfu mua h\u00f3a \u0111\u01a1n tr\u00ean 50 000 000 \u0111\u1ed3ng th\u00ec \u0111\u01b0\u1ee3c gi\u1ea3m 8% tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n; N\u1ebfu mua h\u00f3a \u0111\u01a1n tr\u00ean 60 000 000 \u0111\u1ed3ng th\u00ec \u0111\u01b0\u1ee3c gi\u1ea3m 10% tr\u00ean t\u1ed5ng h\u00f3a \u0111\u01a1n. H\u1ecfi nh\u00e0 tr\u01b0\u1eddng ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n bao nhi\u00eau \u0111\u1ec3 mua t\u1eadp ph\u00e1t th\u01b0\u1edfng cho h\u1ecdc sinh n\u0103m h\u1ecdc \u0111\u00f3? L\u1eddi gi\u1ea3i G\u1ecdi x,y ( h\u1ecdc sinh) l\u1ea7n l\u01b0\u1ee3t l\u00e0 s\u1ed1 h\u1ecdc sinh kh\u00e1 v\u00e0 gi\u1ecfi \u1edf H\u1ecdc k\u00ec 1 x,y * S\u1ed1 h\u1ecdc sinh kh\u00e1 v\u00e0 gi\u1ecfi \u1edf HKI l\u00e0 500 ta c\u00f3 pt: x y 500 1 S\u1ed1 h\u1ecdc sinh kh\u00e1 v\u00e0 gi\u1ecfi \u1edf HKII l\u00e0 513 ta c\u00f3 pt: 102%x 104%y 513 2 T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: x y 500 513 102%x 102%y (nh\u1eadn) x 350 y 150 S\u1ed1 ti\u1ec1n mua t\u1eadp \u1edf HKI: 350 10 7500 150 20 7500 48750000 (\u0111\u1ed3ng) S\u1ed1 ti\u1ec1n mua t\u1eadp \u1edf HKII: 350 1, 02 10 7500 150 1, 04 20 7500 50175000 (\u0111\u1ed3ng) S\u1ed1 ti\u1ec1n t\u1eadp nh\u00e0 tr\u01b0\u1eddng tr\u1ea3 cho n\u0103m h\u1ecdc \u0111\u00f3 l\u00e0: 48750000 50175000 0, 9 89032500 ( \u0111\u1ed3ng) C\u00e2u 5. (1 \u0111i\u1ec3m). \u0110\u1ec3 l\u00e0m th\u00ed nghi\u1ec7m v\u1ec1 s\u1ef1 n\u1ed5i c\u1ee7a v\u1eadt kh\u00f4ng ch\u1ee9a n\u01b0\u1edbc. Nam chu\u1ea9n b\u1ecb m\u1ed9t ly n\u01b0\u1edbc th\u1ee7y tinh v\u1edbi d\u1ea1ng l\u00f2ng trong c\u1ee7a ly l\u00e0 m\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y l\u00e0 6cm; chi\u1ec1u cao l\u00e0 10cm v\u00e0 m\u1ed9t qu\u1ea3 b\u00f3ng b\u00e0n ti\u00eau chu\u1ea9n qu\u1ed1c t\u1ebf c\u00f3 d\u1ea1ng h\u00ecnh c\u1ea7u v\u1edbi \u0111\u01b0\u1eddng k\u00ednh 40mm. Minh ti\u1ebfn h\u00e0nh b\u1ecf qu\u1ea3 b\u00f3ng b\u00e0n v\u00e0o trong ly r\u1ed3i r\u00f3t 200cm3 n\u01b0\u1edbc t\u1eeb t\u1eeb v\u00e0o ly v\u00e0 \u0111o d\u01b0\u1ee3c m\u1ef1c n\u01b0\u1edbc d\u00e2ng cao 7,2cm. a) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a qu\u1ea3 b\u00f3ng b\u00e0n. b) T\u00ednh th\u1ec3 t\u00edch ph\u1ea7n n\u1ed5i c\u1ee7a qu\u1ea3 b\u00f3ng b\u00e0n trong th\u00ed nghi\u1ec7m c\u1ee7a Minh.( Bi\u1ebft th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u b\u00e1n k\u00ednh R l\u00e0 V 4 R3 ; c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 v\u1edbi b\u00e1n k\u00ednh r l\u00e0V r 2h ,l\u1ea5y 3 3,14 v\u00e0 k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai) L\u1eddi gi\u1ea3i 4 \uf070 R3 4 \uf0d7 3,14.23 3 3 ( )a) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a qu\u1ea3 b\u00f3ng b\u00e0n: Vb = = = 33, 49 cm3 . T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 6","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH ( )b) Th\u1ec3 t\u00edch n\u01b0\u1edbc d\u00e2ng: Vtr = \uf070 R2.h = 3,14.32.7,2 = 203,472 cm3 . Th\u1ec3 t\u00edch ph\u1ea7n b\u00f3ng ch\u00ecm: 203, 472 200 3, 472(cm3) ( )V\u1eady th\u1ec3 t\u00edch ph\u1ea7n n\u1ed5i qu\u1ea3 b\u00f3ng: V = Vb \u2212 Vc = 33,49 \u2212 3,472 \uf0bb 30,02 cm3 . C\u00e2u 10. (1,0 \u0111i\u1ec3m) Nh\u00e0 tr\u01b0\u1eddng t\u1ed5 ch\u1ee9c gi\u1ea3i b\u00f3ng \u0111\u00e1 mini m\u1eebng Xu\u00e2n cho h\u1ecdc sinh kh\u1ed1i 9. M\u1ed7i l\u1edbp c\u1eed m\u1ed9t \u0111\u1ed9i tham gia, m\u1ed7i \u0111\u1ed9i \u0111\u1ea5u v\u1edbi m\u1ed9t \u0111\u1ed9i c\u1ee7a l\u1edbp b\u1ea1n m\u1ed9t l\u1ea7n. N\u1ebfu t\u1ed5ng s\u1ed1 tr\u1eadn \u0111\u1ea5u l\u00e0 28 th\u00ec kh\u1ed1i l\u1edbp 9 c\u00f3 bao nhi\u00eau \u0111\u1ed9i tham gia? G\u1ecdi x ( \u0111\u1ed9i) l\u00e0 s\u1ed1 \u0111\u1ed9i b\u00f3ng x L\u1eddi gi\u1ea3i * C\u1ee9 1 \u0111\u1ed9i \u0111\u1ea5u v\u1edbi x 1 \u0111\u1ed9i kh\u00e1c t\u1ea1o ra x 1 tr\u1eadn \u0111\u1ea5u C\u00f3 t\u1ea5t c\u1ea3 x \u0111\u1ed9i v\u00e0 m\u1ed7i tr\u1eadn l\u1eb7p l\u1ea1i 1 l\u1ea7n n\u00ean t\u1ed5ng s\u1ed1 tr\u1eadn l\u00e0: x(x 1) 2 (tr\u1eadn \u0111\u1ea5u) V\u00ec t\u1ed5ng s\u1ed1 tr\u1eadn l\u00e0 28 ta c\u00f3: x(x 1) 28 0 2 x 2 x 56 x 8(n) x 7(l) V\u1eady c\u00f3 8 \u0111\u1ed9i thi \u0111\u1ea5u. C\u00e2u 6. (3 \u0111i\u1ec3m) Cho M n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n (O), k\u1ebb hai ti\u1ebfp tuy\u1ebfn MA, MB v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n (O)(A, B l\u00e0 hai ti\u1ebfp \u0111i\u1ec3m).L\u1ea5y \u0111i\u1ec3m N thu\u1ed9c cung l\u1edbn AB( NB > NA). MN c\u1eaft (O) t\u1ea1i E. a) Ch\u1ee9ng minh: ME.MN MA2 b) G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OM v\u00e0 AB, MO c\u1eaft (O) l\u1ea7n l\u01b0\u1ee3t t\u1ea1i hai \u0111i\u1ec3m I, K( K n\u1eb1m gi\u1eefa M v\u00e0 I). Ch\u1ee9ng minh: OH .HM HK .HI v\u00e0 1 1 2 HK HI HM c) Ch\u1ee9ng minh: t\u1ee9 gi\u00e1c OHEN n\u1ed9i ti\u1ebfp v\u00e0 KH .IM KM .IH L\u1eddi gi\u1ea3i T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 7","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH a. Ch\u1ee9ng minh: ME.MN MA2 X\u00e9t \uf044MEA v\u00e0 \uf044MNA c\u00f3 \uf0ec\uf0efAME = AMN = \uf0e6 1 sd AE \uf0f6 \uf0ed = MNA \uf0e7 2 \uf0f7 \uf0efMEA \uf0e8 \uf0f8 \uf0ee Suy ra \uf044MAE \u0111\u1ed3ng d\u1ea1ng \uf044MNA (g.g), suy ra MA = ME \uf0db MA2 = MN.ME . (\u0111pcm) MN MA b. G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OM v\u00e0 AB, MO c\u1eaft (O) l\u1ea7n l\u01b0\u1ee3t t\u1ea1i hai \u0111i\u1ec3m I, K( K n\u1eb1m gi\u1eefa M v\u00e0 I). Ch\u1ee9ng minh: OH .HM HK .HI v\u00e0 1 1 2 HK HI HM MA MB Ta c\u00f3: OA OB( R) OM l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a AB OM AB t\u1ea1i H v\u00e0 H l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB. X\u00e9t \uf044MAO vu\u00f4ng t\u1ea1i A, c\u00f3 \u0111\u01b0\u1eddng cao AH: AH 2 OH.HM(HTL) (1) Ta c\u00f3: IAK 900 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda (O)) IAK vu\u00f4ng \u1edf A , m\u00e0 AH l\u00e0 \u0111\u01b0\u1eddng cao AH 2 HK HI(HTL) (2) (1),(2) OH HM HK HI Ta c\u00f3: T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 8","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH 1 1 HI HK (OI OH ) (OK OH ) HK HI HI HK OH HM OH OK OH OI 2OH 2 OH HM OH HM HM c. Ch\u1ee9ng minh: t\u1ee9 gi\u00e1c OHEN n\u1ed9i ti\u1ebfp v\u00e0 KH .IM KM .IH Ta c\u00f3: MA2 ME MN (cmt) MA2 MH MO ME MN MH MO ME MH MO MN X\u00e9t \uf044MEH v\u00e0 \uf044MON c\u00f3 \uf0ec\uf0efHME = OMN \uf0ed ME MH \uf0ef\uf0ee MO = MN (cmt) Suy ra \uf044MAE \u0111\u1ed3ng d\u1ea1ng \uf044MNA (c.g,c) Suy ra MHE MNO OHEN n\u1ed9i ti\u1ebfp ( g\u00f3c ngo\u00e0i = g\u00f3c trong \u0111\u1ed1i di\u1ec7n) Ta c\u00f3: \uf0ec\uf0ef\uf0ef\uf0edHMAAKK++HHKAAK = 90\uf0b0 = 90\uf0b0 \uf0ef\uf0ee\uf0efOAK = HKA \uf0de MAK = HAK AK l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a MAH KH AH (1) (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong) KM AM M\u00e0 AK IA(cmt) N\u00ean IA l\u00e0 ph\u00e2n gi\u00e1c ngo\u00e0i c\u1ee7a AHM IH AH (2) IM AM (1);(2) KH IH KM IM KH IM KM IH ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 9","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u00d4\u00db GD&\u00d1T TP HO\u00c0 CH\u00cd MINH \u00d1E\u00c0 THAM KHA\u00dbO TUYE\u00c5N SINH 10 PHO\u00d8NG G\u00d1&\u00d1T QUA\u00c4N TA\u00c2N PH\u00da NA\u00caM HO\u00cfC: 2023 - 2024 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. M\u00c3 \u0110\u1ec0: Qu\u1eadn T\u00e2n Ph\u00fa - 1 Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 2x \u2212 7 . 44 a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 4x2 \u2212 2x \u2212 5 = 0 c\u00f3 2 nghi\u1ec7m l\u00e0 x1 , x2 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, h\u00e3y t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c B = x1 + x2 x2 \u2212 1 x1 \u2212 1 C\u00e2u 3. (1 \u0111i\u1ec3m). M\u1ed7i n\u01a1i tr\u00ean th\u1ebf gi\u1edbi c\u00f3 m\u1ed9t m\u00fai gi\u1edd. Gi\u1edd m\u1ed7i ng\u00e0y t\u1ea1i m\u1ed7i n\u01a1i \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c T = GMT + H , trong \u0111\u00f3 T l\u00e0 gi\u1edd t\u1ea1i n\u01a1i \u0111\u00f3, GMT l\u00e0 gi\u1edd g\u1ed1c, gi\u1edd \u1edf m\u00fai gi\u1edd l\u00e0 0 , H \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi b\u1ea3ng sau: a M\u00fai gi\u1edd 0 1 2 3 4 5 6 7 H 0 12 3 4 5 6 7 M\u00fai gi\u1edd 8 9 10 11 12 13 14 15 HH 8 9 10 11 12 \u221211 \u221210 \u22129 M\u00fai M\u00fai gi\u1edd 16 17 18 19 20 21 22 23 H \u22128 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 Nh\u01b0 v\u1eady khi bi\u1ebft gi\u1edd \u1edf m\u1ed9t n\u01a1i c\u00f3 m\u00fai gi\u1edd n\u00e0y, ta c\u00f3 th\u1ec3 t\u00ednh gi\u1edd \u1edf n\u01a1i c\u00f3 m\u00fai gi\u1edd kh\u00e1c. M\u00fai gi\u1edd c\u1ee7a m\u1ed9t s\u1ed1 th\u00e0nh ph\u1ed1 \u0111\u01b0\u1ee3c cho b\u1edfi b\u1ea3ng sau: Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh New York Moscow Los Angeles M\u00fai gi\u1edd 7 19 3 16 D\u1ef1a v\u00e0o c\u00e1ch t\u00ednh tr\u00ean em h\u00e3y t\u00ednh xem: a) L\u00fac 11 gi\u1edd ng\u00e0y 03 \/ 06 \u1edf NewYork th\u00ec \u1edf Moscow l\u00e0 m\u1ea5y gi\u1edd ng\u00e0y n\u00e0o? b) Qu\u1ef3nh \u0111i chuy\u1ebfn bay t\u1eeb Tp.HCM \u0111\u1ebfn Moscow c\u1ee7a h\u00e3ng h\u00e0ng kh\u00f4ng Aeroflot. Chuy\u1ebfn bay xu\u1ea5t ph\u00e1t l\u00fac 14 gi\u1edd 30 ph\u00fat ng\u00e0y 01 \/ 09 theo gi\u1edd t\u1ea1i Tp.HCM. Em h\u00e3y t\u00ednh xem chuy\u1ebfn bay k\u00e9o d\u00e0i bao l\u00e2u bi\u1ebft Qu\u1ef3nh \u0111\u1ebfn s\u00e2n bay qu\u1ed1c t\u1ebf Sheremetyevo c\u1ee7a Moscow l\u00fac 21 gi\u1edd ng\u00e0y 01 \/ 09 ? C\u00e2u 4. (0,75 \u0111i\u1ec3m). Nh\u00e2n d\u1ecbp k\u1ec9 ni\u1ec7m 1 n\u0103m th\u00e0nh l\u1eadp, m\u1ed9t c\u1eeda h\u00e0ng th\u1eddi trang \u0111\u01b0a ra ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i: \u0111\u1ee3t 1 : Gi\u1ea3m 20% tr\u00ean t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t h\u00e0ng t\u1eeb ng\u00e0y 01 \/ 10 \/ 2020 \u0111\u1ebfn 05 \/ 10 \/ 2020 ; \u0111\u1ee3t 2 : gi\u1ea3m 5% t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t h\u00e0ng tr\u00ean gi\u00e1 \u0111\u00e3 gi\u1ea3m c\u1ee7a \u0111\u1ee3t 1 t\u1eeb ng\u00e0y 06 \/ 10 \/ 2020 \u0111\u1ebfn 10 \/ 10 \/ 2020 bi\u00eat gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a \u00e1o thun l\u00e0 400000 \u0111\u1ed3ng\/ \u00e1o, \u00e1o kho\u00e1c 500000 \u0111\u1ed3ng\/ \u00e1o. T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1"]