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 S\u00d4\u00db GD&\u00d1T TP HO\u00c0 CH\u00cd MINH \u00d1E\u00c0 THAM KHA\u00dbO TUYE\u00c5N SINH 10 NA\u00caM HO\u00cfC: 2021 - 2022 PHO\u00d8NG G\u00d1&\u00d1T QUA\u00c4N B\u00ccNH TH\u1ea0NH \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 Th\u1ea1nh - 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 = 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = \u2212x + 4 . 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 4x2 \u2212 x \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 ( )A = x1 \u2212 x2 2 . C\u00e2u 3. (1 \u0111i\u1ec3m). Trong n\u0103m 2022 , do l\u1ea1m ph\u00e1t n\u00ean kh\u00e1 nhi\u1ec1u ng\u01b0\u1eddi quan t\u00e2m t\u1edbi vi\u1ec7c g\u1eedi ti\u1ebft ki\u1ec7m khi m\u1ee9c l\u00e3i t\u0103ng cao h\u01a1n. Nh\u1edd v\u1eady, l\u01b0\u1ee3ng ti\u1ec1n g\u1eedi t\u1eeb ng\u01b0\u1eddi d\u00e2n v\u00e0o h\u1ec7 th\u1ed1ng c\u0169ng tang tr\u01b0\u1edfng, gi\u00fap \u0111\u1ea3m b\u1ea3o an to\u00e0n thanh kho\u1ea3n cho c\u00e1c ng\u00e2n h\u00e0ng. \u00d4ng Ba \u0111\u1ea7u t\u01b0 20 tri\u1ec7u v\u00e0o hai t\u00e0i kho\u1ea3n. T\u00e0i kho\u1ea3n th\u1ee9 nh\u1ea5t c\u00f3 l\u00e3i su\u1ea5t 6% \/n\u0103m v\u00e0 t\u00e0i kho\u1ea3n th\u1ee9 hai c\u00f3 l\u00e3i su\u1ea5t 8% \/n\u0103m. T\u00ednh s\u1ed1 ti\u1ec1n \u0111\u1ea7u t\u01b0 ban \u0111\u1ea7u \u1edf m\u1ed7i t\u00e0i kho\u1ea3n c\u1ee7a \u00f4ng Ba bi\u1ebft sau m\u1ed9t n\u0103m \u00f4ng nh\u1eadn \u0111\u01b0\u1ee3c 1,38 tri\u1ec7u \u0111\u1ed3ng ti\u1ec1n l\u00e3i. C\u00e2u 4. (0,75 \u0111i\u1ec3m). M\u1ed1i li\u00ean h\u1ec7 gi\u1eefa nhi\u1ec7t \u0111\u1ed9 F (Fahrenheit) v\u00e0 nhi\u1ec7t \u0111\u1ed9 C (Celsius) l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y ax b a 0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 sau: a) H\u00e3y x\u00e1c \u0111\u1ecbnh a v\u00e0 b . b) H\u00e3y t\u00ednh theo nhi\u1ec7t \u0111\u1ed9 C khi bi\u1ebft nhi\u1ec7t \u0111\u1ed9 F l\u00e0 176 F . C\u00e2u 5. (1 \u0111i\u1ec3m). \u0110\u1ed3ng h\u00e0nh v\u01b0\u1ee3t qua Covid-19. M\u1ed9t c\u1eeda h\u00e0ng \u0111\u1ed3ng lo\u1ea1t gi\u00e1 25% tr\u00ean t\u1ea5t c\u1ea3 c\u00e1c s\u1ea3n ph\u1ea9m. B\u1ea1n H\u1ea1nh \u0111\u1ebfn mua m\u1ed9t chi\u1ebfc m\u00e1y t\u00ednh Casio fx 580VN X . Do c\u00f3 gi\u1ea5y khen h\u1ecdc sinh gi\u1ecfi n\u0103m h\u1ecdc 2021\u22122022 n\u00ean b\u1ea1n H\u1ea1nh \u0111\u01b0\u1ee3c gi\u1ea3m th\u00eam 10% tr\u00ean gi\u00e1 \u0111\u00e3 gi\u1ea3m v\u00e0 ch\u1ec9 ph\u1ea3i tr\u1ea3 405 ngh\u00ecn \u0111\u1ed3ng. a) H\u1ecfi gi\u00e1 ban \u0111\u1ea7u c\u1ee7a chi\u1ebfc m\u00e1y t\u00ednh l\u00e0 bao nhi\u00eau? b) S\u1ed1 ti\u1ec1n b\u1ea1n H\u1ea1nh \u0111\u01b0\u1ee3c gi\u1ea3m chi\u1ebfm bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi gi\u00e1 ban \u0111\u1ea7u? 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 6. (1 \u0111i\u1ec3m). M\u1ed9t b\u1ec3 n\u01b0\u1edbc h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u d\u00e0i 2 m . L\u00fac \u0111\u1ea7u b\u1ec3 kh\u00f4ng c\u00f3 n\u01b0\u1edbc. Sau khi \u0111\u1ed5 v\u00e0o b\u1ec3 120 th\u00f9ng n\u01b0\u1edbc, m\u1ed7i th\u00f9ng ch\u1ee9a 20 l\u00edt th\u00ec m\u1ef1c n\u01b0\u1edbc c\u1ee7a b\u1ec3 cao 0,8 m . a) T\u00ednh chi\u1ec1u r\u1ed9ng c\u1ee7a b\u1ec3 n\u01b0\u1edbc. b) Ng\u01b0\u1eddi ta \u0111\u1ed5 th\u00eam v\u00e0o b\u1ec3 60 th\u00f9ng n\u01b0\u1edbc n\u1eefa th\u00ec \u0111\u1ea7y b\u1ec3. H\u1ecfi b\u1ec3 cao bao nhi\u00eau m\u00e9t? C\u00e2u 7. (1 \u0111i\u1ec3m). English Premier Leauge l\u00e0 gi\u1ea3i \u0111\u1ea5u b\u00f3ng \u0111\u00e1 h\u1ea5p d\u1eabn nh\u1ea5t h\u00e0nh tinh v\u1edbi nh\u1eefng m\u00e0n so k\u00e8 \u0111i\u1ec3m s\u1ed1 h\u1ea5p d\u1eabn c\u1ee7a c\u00e1c c\u00e2u l\u1ea1c b\u1ed9 h\u00e0ng \u0111\u1ea7u. Gi\u1ea3i \u0111\u1ea5u c\u00f3 20 \u0111\u1ed9i, m\u1ed7i \u0111\u1ed9i ph\u1ea3i thi \u0111\u1ea5u v\u1edbi 19 \u0111\u1ed9i c\u00f2n l\u1ea1i v\u1edbi th\u1ec3 th\u1ee9c l\u01b0\u1ee3t \u0111i v\u00e0 l\u01b0\u1ee3t v\u1ec1. Sau 38 v\u00f2ng \u0111\u1ea5u, \u0111\u1ed9i c\u00f3 s\u1ed1 \u0111i\u1ec3m cao nh\u1ea5t s\u1ebd gi\u00e0nh ch\u1ee9c v\u00f4 \u0111\u1ecbch. M\u1ed7i tr\u1eadn \u0111\u1ea5u \u0111\u01b0\u1ee3c t\u00ednh \u0111i\u1ec3m nh\u01b0 sau: \u0111\u1ed9i th\u1eafng \u0111\u01b0\u1ee3c nh\u1eadn 3 \u0111i\u1ec3m, \u0111\u1ed9i thua kh\u00f4ng c\u00f3 \u0111i\u1ec3m n\u00e0o v\u00e0 n\u1ebfu 2 \u0111\u1ed9i h\u00f2a nhau th\u00ec m\u1ed7i \u0111\u1ed9i nh\u1eadn \u0111\u01b0\u1ee3c 1 \u0111i\u1ec3m. \u1ede m\u00f9a gi\u1ea3i k\u00ec di\u1ec7u n\u0103m 2003 \u2212 2004 c\u00e1c \u201cPh\u00e1o th\u1ee7\u201d th\u00e0nh London l\u00e0 Arsenal \u0111\u00e3 l\u1eadp 1 k\u00ec t\u00edch v\u00f4 ti\u1ec1n kho\u00e1ng h\u1eadu trong l\u1ecbch s\u1eed gi\u1ea3i \u0111\u1ea5u khi tr\u1edf th\u00e0nh \u0111\u1ed9i \u0111\u1ea7u ti\u00ean gi\u00e0nh ch\u1ee9c v\u00f4 \u0111\u1ecbch m\u00e0 kh\u00f4ng \u0111\u1ec3 thua b\u1ea5t k\u00ec tr\u1eadn \u0111\u1ea5u n\u00e0o. V\u1eady b\u1ea1n c\u00f3 bi\u1ebft trong chi\u1ebfn t\u00edch l\u1eaby l\u1eebng tr\u00ean c\u1ee7a th\u1ea7y tr\u00f2 HLV Arsene Wenger th\u00ec \u0111\u1ed9i Arsenal \u0111\u00e3 gi\u00e0nh \u0111\u01b0\u1ee3c bao nhi\u00eau tr\u1eadn th\u1eafng sau 38 tr\u1eadn \u0111\u1ea5u kh\u00f4ng? Bi\u1ebft r\u1eb1ng \u0111\u1ed9i b\u00f3ng \u0111\u00e3 k\u1ebft th\u00fac gi\u1ea3i \u0111\u1ea5u v\u1edbi 90 \u0111i\u1ec3m. C\u00e2u 8. (3 \u0111i\u1ec3m). Cho \uf044ABC nh\u1ecdn n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (O) ( AB \uf03c AC) , v\u1ebd hai \u0111\u01b0\u1eddng cao AE , CH c\u1ee7a \uf044ABC v\u00e0 \u0111\u01b0\u1eddng k\u00ednh AK c\u1ee7a (O) . Tia AE c\u1eaft tia CK t\u1ea1i M . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AHEC n\u1ed9i ti\u1ebfp v\u00e0 AC2 = AE.AM . b) \u0110\u01b0\u1eddng th\u1eb3ng qua E song song v\u1edbi BK c\u1eaft AK t\u1ea1i D . Ch\u1ee9ng minh CD \u22a5 AK v\u00e0 HE = CD . c) Ch\u1ee9ng minh BE.CM = HE.BK . ----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 = 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = \u2212x + 4 . 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) \u0110\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. x \u22124 \u22122 0 2 4 y = 1 x2 8 2 0 2 8 2 x 0 1 y = \u2212x + 4 4 3 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 = \u2212x + 4 2 \uf0db 1 x2 + x \u2212 4 = 0 2 \uf0db \uf0e9x = 2 \uf0ea\uf0ebx = \u22124 Thay x = 2 v\u00e0o y = 1 x2 , ta \u0111\u01b0\u1ee3c: y = 1 .22 = 2 . 22 Thay x = \u22124 v\u00e0o y = 1 x2 , ta \u0111\u01b0\u1ee3c: y = 1 .(\u22124)2 = 8 . 22 V\u1eady (2; 2) , (\u22124; 8) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 4x2 \u2212 x \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 ( )A = x1 \u2212 x2 2 . 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 L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = (\u22121)2 \u2212 4.4.(\u22122) = 33 \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 4 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP \u22121 c = 2 .x2 = a ( )Ta c\u00f3: A = x1 \u2212 x2 2 A = x12 \u2212 2x1x2 + x22 A = x12 + x22 \u2212 2x1x2 A = S2 \u2212 4P A = \uf0e6 1 \uf0f62 \u2212 4 \uf0e6\uf0e7 \u22121 \uf0f6 = 33 \uf0e7 4 \uf0f7 \uf0e8 2 \uf0f7 16 \uf0e8 \uf0f8 \uf0f8 C\u00e2u 3. (1 \u0111i\u1ec3m). Trong n\u0103m 2022 , do l\u1ea1m ph\u00e1t n\u00ean kh\u00e1 nhi\u1ec1u ng\u01b0\u1eddi quan t\u00e2m t\u1edbi vi\u1ec7c g\u1eedi ti\u1ebft ki\u1ec7m khi m\u1ee9c l\u00e3i t\u0103ng cao h\u01a1n. Nh\u1edd v\u1eady, l\u01b0\u1ee3ng ti\u1ec1n g\u1eedi t\u1eeb ng\u01b0\u1eddi d\u00e2n v\u00e0o h\u1ec7 th\u1ed1ng c\u0169ng tang tr\u01b0\u1edfng, gi\u00fap \u0111\u1ea3m b\u1ea3o an to\u00e0n thanh kho\u1ea3n cho c\u00e1c ng\u00e2n h\u00e0ng. \u00d4ng Ba \u0111\u1ea7u t\u01b0 20 tri\u1ec7u v\u00e0o hai t\u00e0i kho\u1ea3n. T\u00e0i kho\u1ea3n th\u1ee9 nh\u1ea5t c\u00f3 l\u00e3i su\u1ea5t 6% \/n\u0103m v\u00e0 t\u00e0i kho\u1ea3n th\u1ee9 hai c\u00f3 l\u00e3i su\u1ea5t 8% \/n\u0103m. T\u00ednh s\u1ed1 ti\u1ec1n \u0111\u1ea7u t\u01b0 ban \u0111\u1ea7u \u1edf m\u1ed7i t\u00e0i kho\u1ea3n c\u1ee7a \u00f4ng Ba bi\u1ebft sau m\u1ed9t n\u0103m \u00f4ng nh\u1eadn \u0111\u01b0\u1ee3c 1,38 tri\u1ec7u \u0111\u1ed3ng ti\u1ec1n l\u00e3i. L\u1eddi gi\u1ea3i G\u1ecdi x (tri\u1ec7u \u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n t\u00e0i kho\u1ea3n th\u1ee9 nh\u1ea5t G\u1ecdi y (tri\u1ec7u \u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n t\u00e0i kho\u1ea3n th\u1ee9 hai \u0110i\u1ec1u ki\u1ec7n: x ,y 0 V\u00ec l\u00fac \u0111\u1ea7u t\u1ed5ng s\u1ed1 ti\u1ec1n trong hai t\u00e0i kho\u1ea3ng l\u00e0 20 tri\u1ec7u \u0111\u1ed3ng, n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: x + y = 20 (1) V\u00ec t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e3i sau m\u1ed9t n\u0103m, \u00f4ng Ba nh\u1eadn \u0111\u01b0\u1ee3c l\u00e0 1,38 tri\u1ec7u \u0111\u1ed3ng, n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 6%x + 8%y = 1,38 (2) T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ecx + y = 20 \uf0db \uf0ec\uf0efx = 11(n) \uf0ed\uf0ee6%x + 8%y = 1,38 \uf0ed \uf0ef\uf0ee y = 9 ( n) V\u1eady: t\u00e0i kho\u1ea3n th\u1ee9 nh\u1ea5t c\u00f3 11 tri\u1ec7u \u0111\u1ed3ng, t\u00e0i kho\u1ea3n th\u1ee9 hai c\u00f3 9 tri\u1ec7u \u0111\u1ed3ng. 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 4. (0,75 \u0111i\u1ec3m). M\u1ed1i li\u00ean h\u1ec7 gi\u1eefa nhi\u1ec7t \u0111\u1ed9 F (Fahrenheit) v\u00e0 nhi\u1ec7t \u0111\u1ed9 C (Celsius) l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y ax b a 0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 sau: a) H\u00e3y x\u00e1c \u0111\u1ecbnh a v\u00e0 b . b) H\u00e3y t\u00ednh theo nhi\u1ec7t \u0111\u1ed9 C khi bi\u1ebft nhi\u1ec7t \u0111\u1ed9 F l\u00e0 176 F . L\u1eddi gi\u1ea3i a) Theo \u0111\u1ed3 th\u1ecb, ta c\u00f3: \u2022 V\u1edbi x 0,y 32 n\u00ean 32 0.a b \u2022 V\u1edbi x 25,y 77 n\u00ean 77 25.a b Khi \u0111\u00f3, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 0a b 32 a9 25a b 77 5 b 32 V\u1eady a 9 ,b 32 v\u00e0 y 9 x 32 5 5 b) Thay y 176 F v\u00e0o y 9x 32 , ta c\u00f3: 176 9 x 32 x 80 5 5 V\u1eady nhi\u1ec7t \u0111\u1ed9 C l\u00e0 80 C . C\u00e2u 5. (1 \u0111i\u1ec3m). \u0110\u1ed3ng h\u00e0nh v\u01b0\u1ee3t qua Covid-19. M\u1ed9t c\u1eeda h\u00e0ng \u0111\u1ed3ng lo\u1ea1t gi\u00e1 25% tr\u00ean t\u1ea5t c\u1ea3 c\u00e1c s\u1ea3n ph\u1ea9m. B\u1ea1n H\u1ea1nh \u0111\u1ebfn mua m\u1ed9t chi\u1ebfc m\u00e1y t\u00ednh Casio fx 580VN X . Do c\u00f3 gi\u1ea5y khen h\u1ecdc sinh gi\u1ecfi n\u0103m h\u1ecdc 2021\u22122022 n\u00ean b\u1ea1n H\u1ea1nh \u0111\u01b0\u1ee3c gi\u1ea3m th\u00eam 10% tr\u00ean gi\u00e1 \u0111\u00e3 gi\u1ea3m v\u00e0 ch\u1ec9 ph\u1ea3i tr\u1ea3 405 ngh\u00ecn \u0111\u1ed3ng. a) H\u1ecfi gi\u00e1 ban \u0111\u1ea7u c\u1ee7a chi\u1ebfc m\u00e1y t\u00ednh l\u00e0 bao nhi\u00eau? 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 b) S\u1ed1 ti\u1ec1n b\u1ea1n H\u1ea1nh \u0111\u01b0\u1ee3c gi\u1ea3m chi\u1ebfm bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi gi\u00e1 ban \u0111\u1ea7u? L\u1eddi gi\u1ea3i a) G\u1ecdi x ( ngh\u00ecn \u0111\u1ed3ng) l\u00e0 gi\u00e1 ti\u1ec1n ban \u0111\u1ea7u c\u1ee7a chi\u1ebfc m\u00e1y t\u00ednh, (\u0110K: x 0 ) Gi\u00e1 ti\u1ec1n c\u1ee7a m\u00e1y t\u00ednh sau khi gi\u1ea3m 25% l\u00e0: 1 25% x 75%x (ngh\u00ecn \u0111\u1ed3ng) Gi\u00e1 ti\u1ec1n c\u1ee7a m\u00e1y t\u00ednh sau khi gi\u1ea3m th\u00eam 10% l\u00e0: 1 10% 75%x 0, 675x (ngh\u00ecn \u0111\u1ed3ng) Theo \u0111\u1ec1, ta c\u00f3: 0, 675x 405 x 600 (nh\u1eadn) V\u1eady gi\u00e1 ban \u0111\u1ea7u c\u1ee7a m\u00e1y t\u00ednh l\u00e0 600 ngh\u00ecn \u0111\u1ed3ng b) S\u1ed1 ti\u1ec1n b\u1ea1n H\u1ea1nh \u0111\u01b0\u1ee3c gi\u1ea3m gi\u00e1 l\u00e0: 600 405 195 (ngh\u00ecn \u0111\u1ed3ng) T\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m s\u1ed1 ti\u1ec1n \u0111\u01b0\u1ee3c gi\u1ea3m so v\u1edbi gi\u00e1 ban \u0111\u1ea7u: 195 .100% 32, 5% 600 C\u00e2u 6. (1 \u0111i\u1ec3m). M\u1ed9t b\u1ec3 n\u01b0\u1edbc h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u d\u00e0i 2 m . L\u00fac \u0111\u1ea7u b\u1ec3 kh\u00f4ng c\u00f3 n\u01b0\u1edbc. Sau khi \u0111\u1ed5 v\u00e0o b\u1ec3 120 th\u00f9ng n\u01b0\u1edbc, m\u1ed7i th\u00f9ng ch\u1ee9a 20 l\u00edt th\u00ec m\u1ef1c n\u01b0\u1edbc c\u1ee7a b\u1ec3 cao 0,8 m . a) T\u00ednh chi\u1ec1u r\u1ed9ng c\u1ee7a b\u1ec3 n\u01b0\u1edbc. b) Ng\u01b0\u1eddi ta \u0111\u1ed5 th\u00eam v\u00e0o b\u1ec3 60 th\u00f9ng n\u01b0\u1edbc n\u1eefa th\u00ec \u0111\u1ea7y b\u1ec3. H\u1ecfi b\u1ec3 cao bao nhi\u00eau m\u00e9t? L\u1eddi gi\u1ea3i a) Th\u1ec3 t\u00edch l\u01b0\u1ee3ng n\u01b0\u1edbc khi \u0111\u1ed5 v\u00e0o 120 th\u00f9ng n\u01b0\u1edbc l\u00e0: 120.20 2400 (l\u00edt) = 2, 4 m3 2, 4 1, 5 m Chi\u1ec1u r\u1ed9ng c\u1ee7a b\u1ec3 n\u01b0\u1edbc: 2.0, 8 b) Th\u1ec3 t\u00edch l\u01b0\u1ee3ng n\u01b0\u1edbc khi \u0111\u1ed5 v\u00e0o 60 th\u00f9ng n\u01b0\u1edbc 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 60.20 1200 (l\u00edt) = 1,2 m3 Th\u1ec3 t\u00edch b\u1ec3 n\u01b0\u1edbc l\u00e0: 2, 4 1,2 3, 6 m3 Chi\u1ec1u cao c\u1ee7a b\u1ec3 n\u01b0\u1edbc: 3, 6 1,2 m 2.1, 5 C\u00e2u 7. (1 \u0111i\u1ec3m). English Premier Leauge l\u00e0 gi\u1ea3i \u0111\u1ea5u b\u00f3ng \u0111\u00e1 h\u1ea5p d\u1eabn nh\u1ea5t h\u00e0nh tinh v\u1edbi nh\u1eefng m\u00e0n so k\u00e8 \u0111i\u1ec3m s\u1ed1 h\u1ea5p d\u1eabn c\u1ee7a c\u00e1c c\u00e2u l\u1ea1c b\u1ed9 h\u00e0ng \u0111\u1ea7u. Gi\u1ea3i \u0111\u1ea5u c\u00f3 20 \u0111\u1ed9i, m\u1ed7i \u0111\u1ed9i ph\u1ea3i thi \u0111\u1ea5u v\u1edbi 19 \u0111\u1ed9i c\u00f2n l\u1ea1i v\u1edbi th\u1ec3 th\u1ee9c l\u01b0\u1ee3t \u0111i v\u00e0 l\u01b0\u1ee3t v\u1ec1. Sau 38 v\u00f2ng \u0111\u1ea5u, \u0111\u1ed9i c\u00f3 s\u1ed1 \u0111i\u1ec3m cao nh\u1ea5t s\u1ebd gi\u00e0nh ch\u1ee9c v\u00f4 \u0111\u1ecbch. M\u1ed7i tr\u1eadn \u0111\u1ea5u \u0111\u01b0\u1ee3c t\u00ednh \u0111i\u1ec3m nh\u01b0 sau: \u0111\u1ed9i th\u1eafng \u0111\u01b0\u1ee3c nh\u1eadn 3 \u0111i\u1ec3m, \u0111\u1ed9i thua kh\u00f4ng c\u00f3 \u0111i\u1ec3m n\u00e0o v\u00e0 n\u1ebfu 2 \u0111\u1ed9i h\u00f2a nhau th\u00ec m\u1ed7i \u0111\u1ed9i nh\u1eadn \u0111\u01b0\u1ee3c 1 \u0111i\u1ec3m. \u1ede m\u00f9a gi\u1ea3i k\u00ec di\u1ec7u n\u0103m 2003 \u2212 2004 c\u00e1c \u201cPh\u00e1o th\u1ee7\u201d th\u00e0nh London l\u00e0 Arsenal \u0111\u00e3 l\u1eadp 1 k\u00ec t\u00edch v\u00f4 ti\u1ec1n kho\u00e1ng h\u1eadu trong l\u1ecbch s\u1eed gi\u1ea3i \u0111\u1ea5u khi tr\u1edf th\u00e0nh \u0111\u1ed9i \u0111\u1ea7u ti\u00ean gi\u00e0nh ch\u1ee9c v\u00f4 \u0111\u1ecbch m\u00e0 kh\u00f4ng \u0111\u1ec3 thua b\u1ea5t k\u00ec tr\u1eadn \u0111\u1ea5u n\u00e0o. V\u1eady b\u1ea1n c\u00f3 bi\u1ebft trong chi\u1ebfn t\u00edch l\u1eaby l\u1eebng tr\u00ean c\u1ee7a th\u1ea7y tr\u00f2 HLV Arsene Wenger th\u00ec \u0111\u1ed9i Arsenal \u0111\u00e3 gi\u00e0nh \u0111\u01b0\u1ee3c bao nhi\u00eau tr\u1eadn th\u1eafng sau 38 tr\u1eadn \u0111\u1ea5u kh\u00f4ng? Bi\u1ebft r\u1eb1ng \u0111\u1ed9i b\u00f3ng \u0111\u00e3 k\u1ebft th\u00fac gi\u1ea3i \u0111\u1ea5u v\u1edbi 90 \u0111i\u1ec3m. L\u1eddi gi\u1ea3i G\u1ecdi x l\u00e0 s\u1ed1 tr\u1eadn th\u1eafng v\u00e0 y l\u00e0 s\u1ed1 tr\u1eadn h\u00f2a x,y . V\u00ec t\u1ed5ng s\u1ed1 tr\u1eadn CLB \u0111\u00e3 thi \u0111\u1ea5u l\u00e0 38 , n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: x + y = 38 (1) V\u00ec t\u1ed5ng s\u1ed1 \u0111i\u1ec3m CLB \u0111\u00e3 nh\u1eadn \u0111\u01b0\u1ee3c l\u00e0 90 \u0111i\u1ec3m, n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 3x + y = 90 (2) T\u1eeb (1) , (1) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: x y 38 x 26 n 3x y 90 y 12 n V\u1eady Arsenal \u0111\u00e3 gi\u00e0nh \u0111\u01b0\u1ee3c 26 tr\u1eadn th\u1eafng sau 38 tr\u1eadn \u0111\u1ea5u. C\u00e2u 8. (3 \u0111i\u1ec3m). Cho \uf044ABC nh\u1ecdn n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (O) ( AB \uf03c AC) , v\u1ebd hai \u0111\u01b0\u1eddng cao AE , CH c\u1ee7a \uf044ABC v\u00e0 \u0111\u01b0\u1eddng k\u00ednh AK c\u1ee7a (O) . Tia AE c\u1eaft tia CK t\u1ea1i M . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AHEC n\u1ed9i ti\u1ebfp v\u00e0 AC2 = AE.AM . b) \u0110\u01b0\u1eddng th\u1eb3ng qua E song song v\u1edbi BK c\u1eaft AK t\u1ea1i D . Ch\u1ee9ng minh CD \u22a5 AK v\u00e0 HE = CD . c) Ch\u1ee9ng minh BE.CM = HE.BK . 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 T O H I ED BC K M a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AHEC n\u1ed9i ti\u1ebfp v\u00e0 AC2 = AE.AM . X\u00e9t t\u1ee9 gi\u00e1c AHEC , c\u00f3: \uf0ec\uf0efAHC = 90\uf0b0(CH \u22a5 AB) \uf0ed \uf0ef\uf0eeAEC = 90\uf0b0( AE \u22a5 BC ) M\u00e0 2 g\u00f3c n\u00e0y c\u00f9ng nh\u00ecn c\u1ea1nh AC N\u00ean AHEC n\u1ed9i ti\u1ebfp. Ta c\u00f3 ACK = 90\uf0b0 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) Suy ra: \uf044ACM vu\u00f4ng t\u1ea1i C . \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong \uf044ACM vu\u00f4ng t\u1ea1i C v\u1edbi \u0111\u01b0\u1eddng cao CE , ta \u0111\u01b0\u1ee3c: AC2 = AE.AM b) Ch\u1ee9ng minh CD \u22a5 AK . Ta c\u00f3: ED \/\/ BK \uf0de CED = CBK (\u0111\u1ed3ng v\u1ecb) M\u00e0 CBK = CAK (g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung CK ) \uf0de CED = CAK X\u00e9t t\u1ee9 gi\u00e1c AEDC , c\u00f3: CED = CAD (cmt) 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 2 g\u00f3c n\u00e0y c\u00f9ng nh\u00ecn c\u1ea1nh DC Do \u0111\u00f3 AEDC n\u1ed9i ti\u1ebfp \uf0de ADC = AEC = 90\uf0b0 (g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung CA ) N\u00ean CD \u22a5 AK Ch\u1ee9ng minh HE = CD Ta c\u00f3: AHC = AEC = ADC = 90\uf0b0 v\u00e0 c\u00f9ng nh\u00ecn c\u1ea1nh AC N\u00ean A,H,E,D,C c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. Suy ra HEDC n\u1ed9i ti\u1ebfp C\u00f3 ABK = 90\uf0b0 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) \uf0de BK \u22a5 AB M\u00e0 CH \u22a5 AB \uf0de CH \/\/ BK \uf0de ED \/\/ CH\/\/ BK X\u00e9t t\u1ee9 gi\u00e1c HEDC n\u1ed9i ti\u1ebfp, c\u00f3: ED \/\/ CH N\u00ean HE = CD . c) Ch\u1ee9ng minh BE.CM = HE.BK . V\u1ebd \u0111\u01b0\u1eddng cao BT c\u1ee7a \uf044ABC , g\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a 3 \u0111\u01b0\u1eddng cao. Ta c\u00f3: \uf0ecBI \/\/CK \uf0ed \uf0ee BK \/\/IC N\u00ean BICK l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh \uf0de IC = BK X\u00e9t t\u1ee9 gi\u00e1c BHIE , c\u00f3: \uf0ec\uf0efBHI = 90\uf0b0(CH \u22a5 AB) \uf0ed \uf0ee\uf0efBEI = 90\uf0b0( AE \u22a5 BC ) \uf0de BHI = BEI = 180\uf0b0 \uf0de T\u1ee9 gi\u00e1c BHIE n\u1ed9i ti\u1ebfp \uf0de BHE = BIE (g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung BE ) M\u00e0 BIE = IMC (so le trong) 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 \uf0de BHE = IMC (1) C\u00f3 HBE = HIA (T\u1ee9 gi\u00e1c BHIE n\u1ed9i ti\u1ebfp) M\u00e0 HIA = MIC (\u0111\u1ed1i \u0111\u1ec9nh) \uf0de HBE = MIC (2) T\u1eeb (1) , (2) suy ra: \uf044HBE \uf044MIC (g \u2013 g) \uf0de BE = IC HE MC M\u00e0 IC = BK N\u00ean BE = BK HE MC V\u1eady BE.CM = HE.BK . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 10","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 THA\u00cfNH 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 BTH - 03 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 h\u00e0m s\u1ed1 y = \u2212x2 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (P) v\u00e0 h\u00e0m s\u1ed1 y = 2x \u2212 3 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (D) . 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 12x + 2 = 0 c\u00f3 hai 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: A = x1 x12 + x2 + x2 x22 \u2212 x1 . C\u00e2u 3. (1 \u0111i\u1ec3m). M\u1ed9t x\u00ed nghi\u1ec7p \u0111ang d\u1ef1 t\u00ednh chuy\u1ec3n h\u00e0ng b\u1eb1ng hai xe t\u1ea3i v\u00e0 \u0111ang ph\u00e2n v\u00e2n gi\u1eefa vi\u1ec7c mua h\u1eb3n hai chi\u1ebfc xe t\u1ea3i ho\u1eb7c thu\u00ea hai xe t\u1ea3i. N\u1ebfu mua hai xe v\u00e0 m\u1ed7i xe gi\u00e1 200.000.000 \u0111\u1ed3ng th\u00ec m\u1ed7i ng\u00e0y x\u00ed nghi\u1ec7p ph\u1ea3i tr\u1ea3 5.000.000 \u0111\u1ed3ng cho t\u1ea5t c\u1ea3 t\u00e0i x\u1ebf v\u00e0 nhi\u00ean li\u1ec7u. C\u00f2n n\u1ebfu thu\u00ea xe th\u00ec gi\u00e1 thu\u00ea m\u1ed9t xe t\u1ea3i l\u00e0 10.000.000 \u0111\u1ed3ng\/ng\u00e0y (\u0111\u00e3 bao g\u1ed3m ti\u1ec1n c\u00f4ng cho t\u00e0i x\u1ebf v\u00e0 nhi\u00ean li\u1ec7u). a) G\u1ecdi C l\u00e0 t\u1ed5ng s\u1ed1 ti\u1ec1n x\u00ed nghi\u1ec7p b\u1ecf ra \u0111\u1ec3 v\u1eadn chuy\u1ec3n sau n ng\u00e0y. L\u1eadp h\u00e0m s\u1ed1 c\u1ee7a C theo n \u0111\u1ed1i v\u1edbi m\u1ed7i ph\u01b0\u01a1ng \u00e1n. b) Sau bao nhi\u00eau ng\u00e0y th\u00ec ph\u01b0\u01a1ng \u00e1n mua xe s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n ph\u01b0\u01a1ng \u00e1n thu\u00ea xe. C\u00e2u 4. (0,75 \u0111i\u1ec3m). Hai tr\u01b0\u1eddng THCS A v\u00e0 B c\u00f3 610 h\u1ecdc sinh d\u1ef1 thi tuy\u1ec3n sinh l\u1edbp 10. Bi\u1ebft r\u1eb1ng n\u1ebfu c\u00f3 5 s\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a tr\u01b0\u1eddng A v\u00e0 4 s\u1ed1 h\u1ecdc sinh c\u1ee7a tr\u01b0\u1eddng B tr\u00fang tuy\u1ec3n th\u00ec 65 s\u1ed1 h\u1ecdc sinh tr\u00fang tuy\u1ec3n c\u1ee7a tr\u01b0\u1eddng A nhi\u1ec1u h\u01a1n s\u1ed1 h\u1ecdc sinh tr\u00fang tuy\u1ec3n c\u1ee7a tr\u01b0\u1eddng B l\u00e0 2 h\u1ecdc sinh. T\u00ednh s\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a m\u1ed7i tr\u01b0\u1eddng. C\u00e2u 5. (0,75 \u0111i\u1ec3m). C\u00e1ch t\u00ednh thu\u1ebf ti\u00eau th\u1ee5 \u0111\u1eb7c bi\u1ec7t v\u00e0 thu\u1ebf nh\u1eadp kh\u1ea9u \u00f4 t\u00f4 \u0111\u00e3 \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh l\u1ea1i v\u00e0o ng\u00e0y 01 \/ 07 \/ 2016 , d\u1eabn t\u1edbi vi\u1ec7c thay \u0111\u1ed5i m\u1ea1nh trong c\u00e1ch t\u00ednh gi\u00e1 xe. Trong t\u1ea5t c\u1ea3 c\u00e1c lo\u1ea1i xe, th\u00ec ch\u1ec9 c\u00f3 xe c\u1ee1 nh\u1ecf ch\u1edf ng\u01b0\u1eddi d\u01b0\u1edbi 10 ch\u1ed7, dung t\u00edch xi lanh \u0111\u1ed9ng c\u01a1 t\u1eeb 1500cm3 tr\u1edf xu\u1ed1ng \u0111\u01b0\u1ee3c gi\u1ea3m thu\u1ebf su\u1ea5t so v\u1edbi hi\u1ec7n h\u00e0nh. M\u1ee9c thu\u1ebf cho lo\u1ea1i xe n\u00e0y \u0111\u01b0\u1ee3c gi\u1ea3m t\u1eeb 45% tr\u01b0\u1edbc ng\u00e0y 01 \/ 07 \/ 2016 xu\u1ed1ng c\u00f2n 40% , v\u00e0 c\u00f3 th\u1ec3 ti\u1ebfp t\u1ee5c gi\u1ea3m xu\u1ed1ng c\u00f2n 35% k\u1ec3 t\u1eeb ng\u00e0y 01 \/ 01 \/ 2018 . Ng\u00e0y 10\/10\/2017 , ch\u00fa Ba mua m\u1ed9t chi\u1ebfc \u00f4, c\u1eeda h\u00e0ng ch\u00e0o b\u00e1n v\u1edbi gi\u00e1 \u0111\u00e3 t\u00ednh thu\u1ebf l\u00e0 735 tri\u1ec7u \u0111\u1ed3ng. a) H\u1ecfi gi\u00e1 xe khi ch\u01b0a c\u00f3 thu\u1ebf l\u00e0 bao nhi\u00eau? b) N\u1ebfu ch\u00fa Ba mua xe v\u00e0o ng\u00e0y 16 \/ 06 \/ 2016 l\u00e0 bao nhi\u00eau ti\u1ec1n (\u0111\u00e3 t\u00ednh thu\u1ebf)? 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) D\u1ef1 ki\u1ebfn \u0111\u1ebfn ng\u00e0y 01 \/ 01 \/ 2018 xe \u0111\u00f3 s\u1ebd \u0111\u01b0\u1ee3c b\u00e1n v\u1edbi gi\u00e1 bao nhi\u00eau? (gi\u1ea3 s\u1eed gi\u00e1 g\u1ed1c khi ch\u01b0a t\u00ednh thu\u1ebf c\u1ee7a xe kh\u00f4ng \u0111\u1ed5i). C\u00e2u 6. (1 \u0111i\u1ec3m). M\u1ed9t chi ti\u1ebft m\u00e1y b\u1eb1ng th\u00e9p h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng t\u1ee9 gi\u00e1c c\u00f3 \u0111\u00e1y l\u00e0 m\u1ed9t h\u00ecnh thoi c\u00f3 \u0111\u1ed9 d\u00e0i hai \u0111\u01b0\u1eddng ch\u00e9o 12cm v\u00e0 16cm , chi\u1ec1u cao 10cm . a) Ng\u01b0\u1eddi ta ph\u1ee7 s\u01a1n t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t c\u1ee7a chi ti\u1ebft m\u00e1y \u0111\u00f3 \u0111\u1ec3 ch\u1ed1ng g\u1ec9 s\u00e9t. T\u00ednh di\u1ec7n t\u00edch c\u1ea7n s\u01a1n. b) \u0110\u1ec3 l\u1eafp gh\u00e9p c\u00f9ng c\u00e1c chi ti\u1ebft kh\u00e1c, ng\u01b0\u1eddi ta khoan m\u1ed9t l\u1ed7 h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh 2cm xuy\u00ean qua chi ti\u1ebft m\u00e1y \u0111\u00f3. T\u00ednh th\u1ec3 t\u00edch ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a kh\u1ed1i th\u00e9p tr\u00ean. C\u00e2u 7. (1 \u0111i\u1ec3m). M\u1ed9t xe m\u00e1y \u0111i t\u1eeb A \u0111\u1ebfn B v\u1edbi v\u1eadn t\u1ed1c 30km \/ h . Sau \u0111\u00f3 1 gi\u1edd 30 ph\u00fat xe \u00f4t\u00f4 kh\u1edfi h\u00e0nh \u0111i t\u1eeb B v\u1ec1 A v\u1edbi v\u1eadn t\u1ed1c 35km \/ h . Sau bao l\u00e2u t\u00ednh t\u1eeb l\u00fac xe m\u00e1y xu\u1ea5t ph\u00e1t th\u00ec hai xe g\u1eb7p nhau? Bi\u1ebft \u0111o\u1ea1n \u0111\u01b0\u1eddng t\u1eeb A \u0111\u1ebfn B d\u00e0i 175km . C\u00e2u 8. (3 \u0111i\u1ec3m) Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n (O; R) \u0111\u01b0\u1eddng k\u00ednh AB v\u00e0 \u0111i\u1ec3m C tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n sao cho CA = CB. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a d\u00e2y cung AC , n\u1ed1i BM c\u1eaft cung AC t\u1ea1i E , AE v\u00e0 BC k\u00e9o d\u00e0i c\u1eaft nhau t\u1ea1i D . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c DEMC n\u1ed9i ti\u1ebfp v\u00e0 DE.DA = DC.DB b) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c MOCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. c) V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m E b\u00e1n k\u00ednh EA c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 N . K\u1ebb EF \u22a5 AC , EF c\u1eaft AN t\u1ea1i I , c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 K , EB c\u1eaft AN t\u1ea1i H . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BHIK n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng tr\u00f2n. ----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 = \u2212x2 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (P) v\u00e0 h\u00e0m s\u1ed1 y = 2x \u2212 3 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (D) . 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 \u22122 \u22121 0 1 2 y = \u2212x2 \u22124 \u22121 0 \u22121 \u22124 x 01 y = 2x \u2212 3 \u22123 \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 \u2212 3 \uf0db x2 + 2x \u2212 3 = 0 \uf0db \uf0e9x = 1 \uf0ea\uf0ebx = \u22123 Thay x = 1 v\u00e0o y = \u2212x2 , ta \u0111\u01b0\u1ee3c: y = \u221212 = \u22121 . Thay x = \u22123 v\u00e0o y = \u2212x2 , ta \u0111\u01b0\u1ee3c: y = \u2212(\u22123)2 = \u22129 . V\u1eady (1; \u2212 1) , (\u22123; \u2212 9) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 3x2 \u2212 12x + 2 = 0 c\u00f3 hai 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: A = x1 x12 + x2 + x2 x22 \u2212 x1 L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = (\u221212)2 \u2212 4.3.2 = 120 \uf03e 0 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 ,x2 . 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 \uf0ec\uf0ef\uf0efS = x1 + x2 = \u2212b = \u2212 \u221212 = 4 \uf0ed = x1 a 3 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP 2 c = 3 .x2 = a ( ) ( )Ta c\u00f3: A = x1 x12 + x2 + x2 x22 \u2212 x1 A = x13 + x1x2 + x23 \u2212 x1x2 ( )( )A = x1 + x2 x12 + x22 \u2212 x1x2 ( ) ( )A = \uf0e9 2 \uf0f9 x1 + x2 \uf0ea\uf0eb x1 + x2 \u2212 3x1x2 \uf0fa\uf0fb A = ( 4 ). \uf0e9\uf0ea( 4)2 \u2212 3.\uf0e6\uf0e7 2 \uf0f6\uf0f9 \uf0e8 3 \uf0f7\uf0fa \uf0eb \uf0f8\uf0fb A = 56 . C\u00e2u 3. (1 \u0111i\u1ec3m). M\u1ed9t x\u00ed nghi\u1ec7p \u0111ang d\u1ef1 t\u00ednh chuy\u1ec3n h\u00e0ng b\u1eb1ng hai xe t\u1ea3i v\u00e0 \u0111ang ph\u00e2n v\u00e2n gi\u1eefa vi\u1ec7c mua h\u1eb3n hai chi\u1ebfc xe t\u1ea3i ho\u1eb7c thu\u00ea hai xe t\u1ea3i. N\u1ebfu mua hai xe v\u00e0 m\u1ed7i xe gi\u00e1 200.000.000 \u0111\u1ed3ng th\u00ec m\u1ed7i ng\u00e0y x\u00ed nghi\u1ec7p ph\u1ea3i tr\u1ea3 5.000.000 \u0111\u1ed3ng cho t\u1ea5t c\u1ea3 t\u00e0i x\u1ebf v\u00e0 nhi\u00ean li\u1ec7u. C\u00f2n n\u1ebfu thu\u00ea xe th\u00ec gi\u00e1 thu\u00ea m\u1ed9t xe t\u1ea3i l\u00e0 10.000.000 \u0111\u1ed3ng\/ng\u00e0y (\u0111\u00e3 bao g\u1ed3m ti\u1ec1n c\u00f4ng cho t\u00e0i x\u1ebf v\u00e0 nhi\u00ean li\u1ec7u). a) G\u1ecdi C l\u00e0 t\u1ed5ng s\u1ed1 ti\u1ec1n x\u00ed nghi\u1ec7p b\u1ecf ra \u0111\u1ec3 v\u1eadn chuy\u1ec3n sau n ng\u00e0y. L\u1eadp h\u00e0m s\u1ed1 c\u1ee7a C theo n \u0111\u1ed1i v\u1edbi m\u1ed7i ph\u01b0\u01a1ng \u00e1n. b) Sau bao nhi\u00eau ng\u00e0y th\u00ec ph\u01b0\u01a1ng \u00e1n mua xe s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n ph\u01b0\u01a1ng \u00e1n thu\u00ea xe. L\u1eddi gi\u1ea3i a) G\u1ecdi C l\u00e0 t\u1ed5ng s\u1ed1 ti\u1ec1n x\u00ed nghi\u1ec7p b\u1ecf ra \u0111\u1ec3 v\u1eadn chuy\u1ec3n sau n ng\u00e0y. L\u1eadp h\u00e0m s\u1ed1 c\u1ee7a C theo n \u0111\u1ed1i v\u1edbi m\u1ed7i ph\u01b0\u01a1ng \u00e1n. X\u00e9t ph\u01b0\u01a1ng \u00e1n 1: mua xe Theo \u0111\u1ec1 ta c\u00f3 t\u1ed5ng s\u1ed1 ti\u1ec1n b\u1ecf ra \u0111\u1ec3 v\u1eadn chuy\u1ec3n sau n ng\u00e0y: 200000000.2 + 5000000.n = 400000000 + 5000000n (\u0111\u1ed3ng) \uf0de C = 5000000n + 400000000 (\u0111\u1ed3ng) X\u00e9t ph\u01b0\u01a1ng \u00e1n 2: thu\u00ea xe Theo \u0111\u1ec1 ta c\u00f3 t\u1ed5ng s\u1ed1 ti\u1ec1n b\u1ecf ra \u0111\u1ec3 v\u1eadn chuy\u1ec3n sau n ng\u00e0y: 10000000.2.n = 20000000n (\u0111\u1ed3ng) \uf0de C = 20000000n (\u0111\u1ed3ng) b) Sau bao nhi\u00eau ng\u00e0y th\u00ec ph\u01b0\u01a1ng \u00e1n mua xe s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n ph\u01b0\u01a1ng \u00e1n thu\u00ea xe. X\u00e9t b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: 5000000n + 400000000 \uf0a3 20000000n 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 \uf0db 400000000 \uf0a3 20000000n \u2212 5000000n \uf0db 15000000n \uf0b3 400000000 \uf0db n \uf0b3 80 \uf0bb 26,67 3 V\u1eady sau 27 ng\u00e0y th\u00ec ph\u01b0\u01a1ng \u00e1n mua xe s\u1ebd ti\u1ebft ki\u1ec7m h\u01a1n ph\u01b0\u01a1ng \u00e1n thu\u00ea xe. C\u00e2u 4. (0,75 \u0111i\u1ec3m). Hai tr\u01b0\u1eddng THCS A v\u00e0 B c\u00f3 610 h\u1ecdc sinh d\u1ef1 thi tuy\u1ec3n sinh l\u1edbp 10. Bi\u1ebft r\u1eb1ng n\u1ebfu c\u00f3 5 s\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a tr\u01b0\u1eddng A v\u00e0 4 s\u1ed1 h\u1ecdc sinh c\u1ee7a tr\u01b0\u1eddng B tr\u00fang tuy\u1ec3n th\u00ec 65 s\u1ed1 h\u1ecdc sinh tr\u00fang tuy\u1ec3n c\u1ee7a tr\u01b0\u1eddng A nhi\u1ec1u h\u01a1n s\u1ed1 h\u1ecdc sinh tr\u00fang tuy\u1ec3n c\u1ee7a tr\u01b0\u1eddng B l\u00e0 2 h\u1ecdc sinh. T\u00ednh s\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a m\u1ed7i tr\u01b0\u1eddng. L\u1eddi gi\u1ea3i G\u1ecdi: S\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a tr\u01b0\u1eddng THCS A l\u00e0: x (h\u1ecdc sinh) ( x \uf0ce \uf02a ) S\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a tr\u01b0\u1eddng THCS B l\u00e0: y (h\u1ecdc sinh) ( y \uf0ce \uf02a ) Theo \u0111\u1ec1 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ec\uf0efx + y = 610 \uf0db \uf0ecx = 300 . \uf0ed 5 4 \uf0ee\uf0edy = 310 \uf0ef\uf0ee 6 x \u2212 5 y = 2 V\u1eady: S\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a tr\u01b0\u1eddng A l\u00e0 300 h\u1ecdc sinh. S\u1ed1 h\u1ecdc sinh d\u1ef1 thi c\u1ee7a tr\u01b0\u1eddng B l\u00e0 310 h\u1ecdc sinh. C\u00e2u 5. (0,75 \u0111i\u1ec3m). C\u00e1ch t\u00ednh thu\u1ebf ti\u00eau th\u1ee5 \u0111\u1eb7c bi\u1ec7t v\u00e0 thu\u1ebf nh\u1eadp kh\u1ea9u \u00f4 t\u00f4 \u0111\u00e3 \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh l\u1ea1i v\u00e0o ng\u00e0y 01 \/ 07 \/ 2016 , d\u1eabn t\u1edbi vi\u1ec7c thay \u0111\u1ed5i m\u1ea1nh trong c\u00e1ch t\u00ednh gi\u00e1 xe. Trong t\u1ea5t c\u1ea3 c\u00e1c lo\u1ea1i xe, th\u00ec ch\u1ec9 c\u00f3 xe c\u1ee1 nh\u1ecf ch\u1edf ng\u01b0\u1eddi d\u01b0\u1edbi 10 ch\u1ed7, dung t\u00edch xi lanh \u0111\u1ed9ng c\u01a1 t\u1eeb 1500cm3 tr\u1edf xu\u1ed1ng \u0111\u01b0\u1ee3c gi\u1ea3m thu\u1ebf su\u1ea5t so v\u1edbi hi\u1ec7n h\u00e0nh. M\u1ee9c thu\u1ebf cho lo\u1ea1i xe n\u00e0y \u0111\u01b0\u1ee3c gi\u1ea3m t\u1eeb 45% tr\u01b0\u1edbc ng\u00e0y 01 \/ 07 \/ 2016 xu\u1ed1ng c\u00f2n 40% , v\u00e0 c\u00f3 th\u1ec3 ti\u1ebfp t\u1ee5c gi\u1ea3m xu\u1ed1ng c\u00f2n 35% k\u1ec3 t\u1eeb ng\u00e0y 01 \/ 01 \/ 2018 . Ng\u00e0y 10\/10\/2017 , ch\u00fa Ba mua m\u1ed9t chi\u1ebfc \u00f4, c\u1eeda h\u00e0ng ch\u00e0o b\u00e1n v\u1edbi gi\u00e1 \u0111\u00e3 t\u00ednh thu\u1ebf l\u00e0 735 tri\u1ec7u \u0111\u1ed3ng. a) H\u1ecfi gi\u00e1 xe khi ch\u01b0a c\u00f3 thu\u1ebf l\u00e0 bao nhi\u00eau? b) N\u1ebfu ch\u00fa Ba mua xe v\u00e0o ng\u00e0y 16 \/ 06 \/ 2016 l\u00e0 bao nhi\u00eau ti\u1ec1n (\u0111\u00e3 t\u00ednh thu\u1ebf)? c) D\u1ef1 ki\u1ebfn \u0111\u1ebfn ng\u00e0y 01 \/ 01 \/ 2018 xe \u0111\u00f3 s\u1ebd \u0111\u01b0\u1ee3c b\u00e1n v\u1edbi gi\u00e1 bao nhi\u00eau? (gi\u1ea3 s\u1eed gi\u00e1 g\u1ed1c khi ch\u01b0a t\u00ednh thu\u1ebf c\u1ee7a xe kh\u00f4ng \u0111\u1ed5i) L\u1eddi gi\u1ea3i a) H\u1ecfi gi\u00e1 xe khi ch\u01b0a c\u00f3 thu\u1ebf l\u00e0 bao nhi\u00eau? V\u00e0o ng\u00e0y 10\/10\/2017 , sau ng\u00e0y 01 \/ 07 \/ 2016 n\u00ean m\u1ee9c thu\u1ebf l\u00e0 40% \uf0de Gi\u00e1 xe ch\u01b0a t\u00ednh thu\u1ebf l\u00e0: 735 : (100% + 40%) = 525 (tri\u1ec7u \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 b) N\u1ebfu ch\u00fa Ba mua xe v\u00e0o ng\u00e0y 16 \/ 06 \/ 2016 l\u00e0 bao nhi\u00eau ti\u1ec1n (\u0111\u00e3 t\u00ednh thu\u1ebf)? V\u00e0o ng\u00e0y 16 \/ 06 \/ 2016 , tr\u01b0\u1edbc ng\u00e0y 01 \/ 07 \/ 2016 n\u00ean m\u1ee9c thu\u1ebf l\u00e0 45% \uf0de Gi\u00e1 xe mua v\u00e0o ng\u00e0y 16 \/ 06 \/ 2016 l\u00e0: 525.(100% + 45%) = 761,25 (tri\u1ec7u \u0111\u1ed3ng) c) D\u1ef1 ki\u1ebfn \u0111\u1ebfn ng\u00e0y 01 \/ 01 \/ 2018 xe \u0111\u00f3 s\u1ebd \u0111\u01b0\u1ee3c b\u00e1n v\u1edbi gi\u00e1 bao nhi\u00eau? (gi\u1ea3 s\u1eed gi\u00e1 g\u1ed1c khi ch\u01b0a t\u00ednh thu\u1ebf c\u1ee7a xe kh\u00f4ng \u0111\u1ed5i) V\u00e0o ng\u00e0y 01 \/ 01 \/ 2018 , m\u1ee9c thu\u1ebf l\u00e0 35% \uf0de Gi\u00e1 xe \u0111\u01b0\u1ee3c b\u00e1n v\u00e0o ng\u00e0y 01 \/ 01 \/ 2018 l\u00e0: 525.(100% + 35%) = 708,75 (tri\u1ec7u \u0111\u1ed3ng) C\u00e2u 6. (1 \u0111i\u1ec3m). M\u1ed9t chi ti\u1ebft m\u00e1y b\u1eb1ng th\u00e9p h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng t\u1ee9 gi\u00e1c c\u00f3 \u0111\u00e1y l\u00e0 m\u1ed9t h\u00ecnh thoi c\u00f3 \u0111\u1ed9 d\u00e0i hai \u0111\u01b0\u1eddng ch\u00e9o 12cm v\u00e0 16cm , chi\u1ec1u cao 10cm . a) Ng\u01b0\u1eddi ta ph\u1ee7 s\u01a1n t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t c\u1ee7a chi ti\u1ebft m\u00e1y \u0111\u00f3 \u0111\u1ec3 ch\u1ed1ng g\u1ec9 s\u00e9t. T\u00ednh di\u1ec7n t\u00edch c\u1ea7n s\u01a1n. b) \u0110\u1ec3 l\u1eafp gh\u00e9p c\u00f9ng c\u00e1c chi ti\u1ebft kh\u00e1c, ng\u01b0\u1eddi ta khoan m\u1ed9t l\u1ed7 h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh 2cm xuy\u00ean qua chi ti\u1ebft m\u00e1y \u0111\u00f3. T\u00ednh th\u1ec3 t\u00edch ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a kh\u1ed1i th\u00e9p tr\u00ean. L\u1eddi gi\u1ea3i a) Ng\u01b0\u1eddi ta ph\u1ee7 s\u01a1n t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t c\u1ee7a chi ti\u1ebft m\u00e1y \u0111\u00f3 \u0111\u1ec3 ch\u1ed1ng g\u1ec9 s\u00e9t. T\u00ednh di\u1ec7n t\u00edch c\u1ea7n s\u01a1n. ( )Di\u1ec7n t\u00edch 1 m\u1eb7t \u0111\u00e1y h\u00ecnh thoi l\u00e0: 1 .12.16 = 96 cm2 2 \uf0e6 12 \uf0f62 \uf0e6 16 \uf0f62 ( )\u0110\u1ed9 d\u00e0i c\u1ea1nh h\u00ecnh thoi m\u1eb7t \u0111\u00e1y l\u00e0: \uf0e7 2 \uf0f7 \uf0e7 2 \uf0f7 + \uf0e8 \uf0f8 = 10 cm \uf0e8 \uf0f8 ( )Di\u1ec7n t\u00edch xung quanh c\u1ee7a l\u0103ng tr\u1ee5 l\u00e0: (4.10).10 = 400 cm2 ( )Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a chi ti\u1ebft m\u00e1y l\u00e0: 2.96 + 400 = 592 cm2 V\u1eady di\u1ec7n t\u00edch c\u1ea7n s\u01a1n l\u00e0 592cm2 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) \u0110\u1ec3 l\u1eafp gh\u00e9p c\u00f9ng c\u00e1c chi ti\u1ebft kh\u00e1c, ng\u01b0\u1eddi ta khoan m\u1ed9t l\u1ed7 h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh 2cm xuy\u00ean qua chi ti\u1ebft m\u00e1y \u0111\u00f3. T\u00ednh th\u1ec3 t\u00edch ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a kh\u1ed1i th\u00e9p tr\u00ean. ( )Th\u1ec3 t\u00edch chi ti\u1ebft m\u00e1y ban \u0111\u1ea7u l\u00e0: 96.10 = 960 cm3 ( )Th\u1ec3 \uf070 .\uf0e6\uf0e7 2 \uf0f62 t\u00edch ph\u1ea7n tr\u1ee5 b\u1ecb khoan l\u00e0: \uf0e8 2 \uf0f7 .10 = 10\uf070 \uf0bb 31, 42 cm3 \uf0f8 ( )V\u1eady ph\u1ea7n th\u1ec3 t\u00edch c\u00f2n l\u1ea1i c\u1ee7a kh\u1ed1i th\u00e9p l\u00e0: 960 \u2212 31,42 = 928,58 cm3 C\u00e2u 7. (1 \u0111i\u1ec3m). M\u1ed9t xe m\u00e1y \u0111i t\u1eeb A \u0111\u1ebfn B v\u1edbi v\u1eadn t\u1ed1c 30km \/ h . Sau \u0111\u00f3 1 gi\u1edd 30 ph\u00fat xe \u00f4t\u00f4 kh\u1edfi h\u00e0nh \u0111i t\u1eeb B v\u1ec1 A v\u1edbi v\u1eadn t\u1ed1c 35km \/ h . Sau bao l\u00e2u t\u00ednh t\u1eeb l\u00fac xe m\u00e1y xu\u1ea5t ph\u00e1t th\u00ec hai xe g\u1eb7p nhau? Bi\u1ebft \u0111o\u1ea1n \u0111\u01b0\u1eddng t\u1eeb A \u0111\u1ebfn B d\u00e0i 175km . L\u1eddi gi\u1ea3i \u0110\u1ed5i \u0111\u01a1n v\u1ecb: 1 gi\u1edd 30 ph\u00fat = 1,5 gi\u1edd. G\u1ecdi: C l\u00e0 v\u1ecb tr\u1ecb g\u1eb7p nhau c\u1ee7a hai xe \u1edf gi\u1eefa A v\u00e0 B . Th\u1eddi gian xe m\u00e1y \u0111i t\u1eeb A \u0111\u1ebfn B l\u00e0: x (gi\u1edd) \uf0de Th\u1eddi gian xe \u00f4 t\u00f4 \u0111i t\u1eeb B \u0111\u1ebfn A l\u00e0: x \u2212 1,5 (gi\u1edd) Qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a xe m\u00e1y l\u00e0: AC = 30x (km \/ h) Qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a \u00f4 t\u00f4 l\u00e0: BC = 35(x \u2212 1,5) = 35x \u2212 52,5 (km \/ h) Theo \u0111\u1ec1 ta c\u00f3: 30x + 35x \u2212 52,5 = 175 \uf0db 65x = 227,5 \uf0db x = 3,5 V\u1eady sau 3,5 gi\u1edd k\u1ec3 t\u1eeb khi xe m\u00e1y xu\u1ea5t ph\u00e1t th\u00ec hai xe g\u1eb7p nhau. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n (O; R) \u0111\u01b0\u1eddng k\u00ednh AB v\u00e0 \u0111i\u1ec3m C tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n sao cho CA = CB. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a d\u00e2y cung AC , n\u1ed1i BM c\u1eaft cung AC t\u1ea1i E , AE v\u00e0 BC k\u00e9o d\u00e0i c\u1eaft nhau t\u1ea1i D . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c DEMC n\u1ed9i ti\u1ebfp v\u00e0 DE.DA = DC.DB b) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c MOCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. c) V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m E b\u00e1n k\u00ednh EA c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 N . K\u1ebb EF \u22a5 AC , EF c\u1eaft AN t\u1ea1i I , c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 K , EB c\u1eaft AN t\u1ea1i H . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BHIK n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng tr\u00f2n. 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 t\u1ee9 gi\u00e1c DEMC n\u1ed9i ti\u1ebfp v\u00e0 DE.DA = DC.DB \uf044AEB n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AB \uf0de \uf044AEB vu\u00f4ng t\u1ea1i E \uf0de BE \u22a5 DA \uf044ACB n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AB \uf0de \uf044ACB vu\u00f4ng t\u1ea1i C \uf0de AC \u22a5 DB X\u00e9t t\u1ee9 gi\u00e1c DEMC c\u00f3: \uf0ec\uf0efDEM = 90\uf0b0(BE \u22a5 DA) \uf0de DEM + DCM = 180\uf0b0 \uf0ed = 90\uf0b0( AC \u22a5 DA) \uf0ef\uf0eeDCM Suy ra t\u1ee9 gi\u00e1c DEMC n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh DM . X\u00e9t \uf044DEB vu\u00f4ng t\u1ea1i E v\u00e0 \uf044DCA vu\u00f4ng t\u1ea1i C c\u00f3: D chung Suy ra \uf044DEB\u223d\uf044DCA \uf0de DE = DB \uf0de DE.DA = DC.DB DC DA b) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c MOCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. X\u00e9t \uf044ABD c\u00f3 AC v\u00e0 BE l\u00e0 hai \u0111\u01b0\u1eddng cao c\u1eaft nhau t\u1ea1i M ( AC \u22a5 DB,BE \u22a5 DA ) N\u00ean M l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a \uf044ABD \uf0de DM l\u00e0 \u0111\u01b0\u1eddng cao v\u00e0 DM \u22a5 AB 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 \uf044CAB c\u00f3 CA = CB (gi\u1ea3 thi\u1ebft) N\u00ean \uf044CAB c\u00e2n t\u1ea1i A M\u00e0 CO l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn ( O l\u00e0 trung \u0111i\u1ec3m AB ) N\u00ean CO c\u0169ng l\u00e0 \u0111\u01b0\u1eddng cao \uf0de CO \u22a5 AB Ta c\u00f3: \uf0ecDM \u22a5 AB \uf0de DM \/\/ CO \uf0ed\uf0eeCO \u22a5 AB L\u1ea1i x\u00e9t \uf044ACB c\u00f3 + O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB + M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC Suy ra OM l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a \uf044ACB \uf0de OM \/\/ CB X\u00e9t t\u1ee9 gi\u00e1c MOCD c\u00f3 \uf0ec\uf0efDM \/\/ CO ( cmt ) \uf0ed (OM \/\/CB) \uf0ef\uf0eeOM \/\/ CD Suy ra t\u1ee9 gi\u00e1c MOCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. c) V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m E b\u00e1n k\u00ednh EA c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 N . K\u1ebb EF \u22a5 AC , EF c\u1eaft AN t\u1ea1i I , c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 K , EB c\u1eaft AN t\u1ea1i H . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BHIK n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng tr\u00f2n. X\u00e9t (E) c\u00f3 A,N \uf0ce(E) \uf0de EA = EN X\u00e9t (O) c\u00f3: + EA = EN \uf0de sdEA = sdEN \uf0ec\uf0ef\uf0efEKB = 1 sdEB = 1 sdEN \uf0ed 22 \uf0ef\uf0ef\uf0eeEHA = NHB = 1 sdEA + 2 ( ( ) )+ + sdNB sdNB M\u00e0 sdEA = sdEN \uf0de EKB = EHA ( )X\u00e9t t\u1ee9 gi\u00e1c BHIK c\u00f3: IKB = IHE EKB = EHA N\u00ean t\u1ee9 gi\u00e1c BHIK n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng tr\u00f2n (g\u00f3c ngo\u00e0i b\u1eb1ng g\u00f3c \u0111\u1ed1i trong). ----H\u1ebeT--- 9 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\u1ede GD&\u0110T TP H\u1ed2 CH\u00cd MINH \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH L\u1edaP 10 PH\u00d2NG GD&\u0110T HUY\u1ec6N C\u1ee6 CHI N\u0102M H\u1eccC: 2023 \u2013 2024 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 M\u00c3 \u0110\u1ec0: Huy\u1ec7n C\u1ee7 Chi - 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 parapol (P) y = 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = \u2212 2 x + 1 . 33 a) V\u1ebd (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c to\u1ea1 \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 2x2 + 4x \u2212 5 = 0 , (\u1ea9n x ). a) Ch\u1ee9ng t\u1ecf ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 2 nghi\u1ec7m x1 ,x2 ph\u00e2n bi\u1ec7t. b) T\u00ednh x1 \u2212 3 + x2 \u2212 3 . x2 + 2 x1 + 2 C\u00e2u 3. (0,75 \u0111i\u1ec3m) M\u1ed9t nh\u00e0 h\u00e0ng c\u00f3 t\u00ednh ph\u00ed d\u1ecbch v\u1ee5 10% gi\u00e1 ti\u1ec1n c\u00e1c m\u00f3n \u0103n, u\u1ed1ng. Bi\u1ebft gi\u00e1 ni\u00eam y\u1ebft (ch\u01b0a t\u00ednh ph\u00ed d\u1ecbch v\u1ee5) c\u1ee7a m\u1ed9t d\u0129a m\u00ec \u00fd l\u00e0 120 000 \u0111\u1ed3ng. Kh\u00e1ch h\u00e0ng g\u1ecdi 3 d\u0129a m\u00ec \u00fd v\u00e0 2 ly tr\u00e0 s\u1eefa, s\u1ed1 ti\u1ec1n kh\u00e1ch h\u00e0ng ph\u1ea3i tr\u1ea3 l\u00e0 495 000 \u0111\u1ed3ng (bao g\u1ed3m c\u1ea3 ph\u00ed d\u1ecbch v\u1ee5)? H\u1ecfi gi\u00e1 ti\u1ec1n ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t ly tr\u00e0 s\u1eefa bao nhi\u00eau? C\u00e2u 4. (0,75 \u0111i\u1ec3m) Nh\u00e2n d\u1ecbp t\u1ebft nguy\u00ean \u0111\u00e1n n\u0103m 2023 , m\u1ed9t tr\u01b0\u1eddng THCS t\u1ed5 ch\u1ee9c h\u1ed9i thi V\u0103n ngh\u1ec7 cho to\u00e0n tr\u01b0\u1eddng, \u0111\u01b0\u1ee3c chia l\u00e0m 2 b\u1ea3ng, b\u1ea3ng A : kh\u1ed1i 6,7 v\u00e0 b\u1ea3ng B : kh\u1ed1i 8,9 . C\u01a1 c\u1ea5u gi\u1ea3i th\u01b0\u1edfng \u1edf 2 . b\u1ea3ng l\u00e0 nh\u01b0 nhau. Bi\u1ebft s\u1ed1 ti\u1ec1n th\u01b0\u1eddng gi\u1ea3i II \u00edt h\u01a1n s\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i I l\u00e0 20% , s\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i III . \u00edt h\u01a1n gi\u1ea3i II .l\u00e0 70 000 \u0111\u1ed3ng v\u00e0 hai gi\u1ea3i khuy\u1ebfn kh\u00edch m\u1ed7i gi\u1ea3i b\u1eb1ng 1 s\u1ed1 ti\u1ec1n c\u1ee7a gi\u1ea3i nh\u1ea5t, t\u1ed5ng s\u1ed1 ti\u1ec1n ph\u00e1t th\u01b0\u1edfng \u1edf c\u1ea3 2 b\u1ea3ng l\u00e0 1840000 \u0111\u1ed3ng. H\u1ecfi s\u1ed1 ti\u1ec1n m\u1ed7i 3 gi\u1ea3i th\u01b0\u1edfng l\u00e0 bao nhi\u00eau ? C\u00e2u 5. (1 \u0111i\u1ec3m) Hai t\u1ed5 c\u1ee7a m\u1ed9t nh\u00e0 m\u00e1y s\u1ea3n xu\u1ea5t kh\u1ea9u trang trong m\u1ed9t ng\u00e0y s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 1700 chi\u1ebfc kh\u1ea9u trang. \u0110\u1ec3 \u0111\u00e1p \u1ee9ng nhu c\u1ea7u kh\u1ea9u trang trong d\u1ecbch c\u00fam do ch\u1ee7ng m\u1edbi virut Corona g\u00e2y ra n\u00ean m\u1ed7i ng\u00e0y t\u1ed5 m\u1ed9t v\u01b0\u1ee3t m\u1ee9c 65% , t\u1ed5 hai v\u01b0\u1ee3t m\u1ee9c 70% , c\u1ea3 hai t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 2850 chi\u1ebfc kh\u1ea9u trang. H\u1ecfi ban \u0111\u1ea7u trong m\u1ed9t ng\u00e0y m\u1ed7i t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c bao nhi\u00eau chi\u1ebfc kh\u1ea9u trang? ( )C\u00e2u 6. (1 \u0111i\u1ec3m) T\u1ea1i b\u1ec1 m\u1eb7t n\u01b0\u1edbc \u00e1p su\u1ea5t kh\u00ed quy\u1ec3n l\u00e0 1 atm atmosphere. B\u00ean d\u01b0\u1edbi m\u1eb7t n\u01b0\u1edbc, \u00e1p su\u1ea5t P l\u00e0 2 (atm) khi m\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u d l\u00e0 32 ( feet) Bi\u1ebft r\u1eb1ng m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa \u00e1p su\u1ea5t P (atm) v\u00e0 \u0111\u1ed9 s\u00e2u d ( feet) d\u01b0\u1edbi m\u1ef1c n\u01b0\u1edbc l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t P(d) = ad + b . a) X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b. ( )b) M\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u bao nhi\u00eau th\u00ec ch\u1ecbu \u00e1p su\u1ea5t l\u00e0 2,25 atm (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t). Bi\u1ebft feet l\u00e0 \u0111\u01a1n v\u1ecb \u0111o \u0111\u1ed9 d\u00e0i, 1 feet = 0,3048m . C\u00e2u 7. (1 \u0111i\u1ec3m) H\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 th\u1ec3 t\u00edch l\u00e0 64m3 . a) T\u00ednh \u0111\u1ed9 d\u00e0i D l\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng b) N\u1ebfu d\u00f9ng 2 v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o b\u1ec3 th\u00ec m\u1ea5t bao nhi\u00eau ph\u00fat m\u1edbi \u0111\u1ea7y b\u1ec3? (l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat). Bi\u1ebft v\u00f2i 1 sau 2 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 17 l\u00edt n\u01b0\u1edbc, v\u00f2i 2 sau 3 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 35 l\u00edt n\u01b0\u1edbc. 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 8. (3 \u0111i\u1ec3m) Cho (O) c\u00f3 t\u00e2m O , \u0111\u01b0\u1eddng k\u00ednh BC . L\u1ea5y m\u1ed9t \u0111i\u1ec3m A tr\u00ean (O) sao cho AB \uf03e AC . T\u1eeb A , v\u1ebd AH vu\u00f4ng g\u00f3c v\u1edbi BC ( H thu\u1ed9c BC ). T\u1eeb H , v\u1ebd HI vu\u00f4ng g\u00f3c v\u1edbi AB v\u00e0 HK vu\u00f4ng g\u00f3c v\u1edbi AC ( I thu\u1ed9c AB , K thu\u1ed9c AC ). a) Ch\u1ee9ng minh r\u1eb1ng t\u1ee9 gi\u00e1c AKHI l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt OA vu\u00f4ng g\u00f3c v\u1edbi IK . ( )b) \u0110\u01b0\u1eddng th\u1eb3ng IK c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n O t\u1ea1i M v\u00e0 N ( N thu\u1ed9c cung nh\u1ecf EC ). Ch\u1ee9ng minh AM2 = AI.AB Suy ra AMH l\u00e0 tam gi\u00e1c c\u00e2n. ( )c) G\u1ecdi D l\u00e0 giao \u0111i\u1ec3m c\u1ee7a MN v\u00e0 BC ; E l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AD v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n O ( E kh\u00e1c A ). K\u1ebb EK c\u1eaft BC t\u1ea1i I . Ch\u1ee9ng minh FH2 = FC.FD . ----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 parapol (P) : y = 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = \u2212 2 x + 1 33 a) V\u1ebd (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c to\u1ea1 \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 -3 0 3 y = 1 x2 3 03 3 x 03 y =\u22122x+1 1 \u22121 3 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) : \u2212 2 x + 1 = 1 x2 33 \uf0db x2 + 2x \u2212 3 = 0 \uf0db \uf0e9x = 1 \uf0ea\uf0ebx = \u22123 Thay x = 1 v\u00e0o y = 1 x2 , ta \u0111\u01b0\u1ee3c: y = 1 12 = 1 . 3 33 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 Thay x = \u22123 v\u00e0o y = 1 x2 , ta \u0111\u01b0\u1ee3c: y = 1 (\u22123)2 = 3 . 33 V\u1eady \uf0e6\uf0e7 1; 1 \uf0f6 , (\u22123; 3) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. \uf0e8 3 \uf0f7 \uf0f8 C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 2x2 + 4x \u2212 5 = 0 , (\u1ea9n x). a) Ch\u1ee9ng t\u1ecf ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 2 nghi\u1ec7m x1 ,x2 ph\u00e2n bi\u1ec7t. b) T\u00ednh x1 \u2212 3 + x2 \u2212 3 . x2 + 2 x1 + 2 L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = (4)2 \u2212 4.(\u22125).2 = 56 \uf03e 0 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 ,x2 . Theo \u0111\u1ecbnh \uf0ec\uf0ef\uf0efS = x1 + x2 = \u2212b = \u22124 = \u22122 \uf0ed = x1 a 2 l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP 5 c = 2 .x2 = a Ta c\u00f3: x1 \u2212 3 + x2 \u2212 3 x2 + 2 x1 + 2 = ( x1 \u2212 3) + ( x2 \u2212 3) ( x2 + 2) ( x1 + 2) == ( x1 \u2212 3) ( x1 + 2) + (x2 \u2212 3)( x2 + 2) (x2 + 2)(x1 + 2) ( ) ( )= x1 + x2 2 \u2212 2x1x2 \u2212 x1 + x2 \u2212 12 ( )2 x1 + x2 + x1x2 + 4 = \u221222 5 C\u00e2u 3. (0,75 \u0111i\u00ea\u0309m) M\u1ed9t nh\u00e0 h\u00e0ng c\u00f3 t\u00ednh ph\u00ed d\u1ecbch v\u1ee5 10% gi\u00e1 ti\u1ec1n c\u00e1c m\u00f3n \u0103n, u\u1ed1ng. Bi\u1ebft gi\u00e1 ni\u00eam y\u1ebft (ch\u01b0a t\u00ednh ph\u00ed d\u1ecbch v\u1ee5) c\u1ee7a m\u1ed9t d\u0129a m\u00ec \u00fd l\u00e0 120.000 \u0111\u1ed3ng. Kh\u00e1ch h\u00e0ng g\u1ecdi 3 d\u0129a m\u00ec \u00fd v\u00e0 2 ly tr\u00e0 s\u1eefa, s\u1ed1 ti\u1ec1n kh\u00e1ch h\u00e0ng ph\u1ea3i tr\u1ea3 l\u00e0 495.000 \u0111\u1ed3ng (bao g\u1ed3m c\u1ea3 ph\u00ed d\u1ecbch v\u1ee5)? H\u1ecfi gi\u00e1 ti\u1ec1n ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t ly tr\u00e0 s\u1eefa bao nhi\u00eau? L\u1eddi gi\u1ea3i S\u1ed1 ti\u1ec1n 1 d\u0129a m\u00ec \u00fd kh\u00e1ch h\u00e0ng ph\u1ea3i tr\u1ea3 l\u00e0: 120 000(1+ 10%) = 132 000 (\u0111\u1ed3ng) Gi\u00e1 2 ly tr\u00e0 s\u1eefa \u0111\u00e3 bao g\u1ed3m ph\u00ed d\u1ecbch v\u1ee5 l\u00e0: 495 000 - 3.132 000 = 99 000 (\u0111\u1ed3ng) Gi\u00e1 1 ly tr\u00e0 s\u1eefa \u0111\u00e3 bao g\u1ed3m ph\u00ed d\u1ecbch v\u1ee5 l\u00e0: 99 000 : 2 = 49 500 (\u0111\u1ed3ng) Gi\u00e1 1 ly tr\u00e0 s\u1eefa kh\u00f4ng bao g\u1ed3m ph\u00ed l\u00e0: 49 500:(1+ 10%) = 45 000 (\u0111\u1ed3ng) 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 4. (0,75 \u0111i\u1ec3m) Nh\u00e2n d\u1ecbp t\u1ebft nguy\u00ean \u0111\u00e1n n\u0103m 2023, m\u1ed9t tr\u01b0\u1eddng THCS t\u1ed5 ch\u1ee9c h\u1ed9i thi V\u0103n ngh\u1ec7 cho to\u00e0n tr\u01b0\u1eddng, \u0111\u01b0\u1ee3c chia l\u00e0m 2 b\u1ea3ng, b\u1ea3ng A: kh\u1ed1i 6,7 v\u00e0 b\u1ea3ng B: kh\u1ed1i 8,9. C\u01a1 c\u1ea5u gi\u1ea3i th\u01b0\u1edfng \u1edf 2 b\u1ea3ng l\u00e0 nh\u01b0 nhau. Bi\u1ebft s\u1ed1 ti\u1ec1n th\u01b0\u1eddng gi\u1ea3i II \u00edt h\u01a1n s\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i I l\u00e0 20% , s\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i III \u00edt h\u01a1n gi\u1ea3i II l\u00e0 70000 \u0111\u1ed3ng v\u00e0 hai gi\u1ea3i khuy\u1ebfn kh\u00edch m\u1ed7i gi\u1ea3i b\u1eb1ng 1 s\u1ed1 ti\u1ec1n c\u1ee7a gi\u1ea3i nh\u1ea5t, t\u1ed5ng s\u1ed1 3 ti\u1ec1n ph\u00e1t th\u01b0\u1edfng \u1edf c\u1ea3 2 b\u1ea3ng l\u00e0 1840000 \u0111\u1ed3ng. H\u1ecfi s\u1ed1 ti\u1ec1n m\u1ed7i gi\u1ea3i th\u01b0\u1edfng l\u00e0 bao nhi\u00eau ? L\u1eddi gi\u1ea3i G\u1ecdi s\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i I l\u00e0 x ( x \uf03e 0 , \u0111\u1ed3ng). S\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i II l\u00e0: 80%.x = 0,8x . S\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i III l\u00e0: 0,8x \u2212 70000 . S\u1ed1 ti\u1ec1n th\u01b0\u1edfng hai gi\u1ea3i khuy\u1ebfn kh\u00edch l\u00e0: 2 x . 3 Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh sau: 2. \uf0e9\uf0ea\uf0eb x + 0,8x + 0,8x \u2212 70000 + 2 x\uf0f9\uf0fa\uf0fb = 1840000 3 \uf0db 98 x = 1980000 15 \uf0db x 303000 S\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i I l\u00e0: 303000 S\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i II l\u00e0: 242400 S\u1ed1 ti\u1ec1n th\u01b0\u1edfng gi\u1ea3i III l\u00e0: 172400 C\u00e2u 5. (1 \u0111i\u00ea\u0309m) Hai t\u1ed5 c\u1ee7a m\u1ed9t nh\u00e0 m\u00e1y s\u1ea3n xu\u1ea5t kh\u1ea9u trang trong m\u1ed9t ng\u00e0y s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 1700 chi\u1ebfc kh\u1ea9u trang. \u0110\u1ec3 \u0111\u00e1p \u1ee9ng nhu c\u1ea7u kh\u1ea9u trang trong d\u1ecbch c\u00fam do ch\u1ee7ng m\u1edbi virut Corona g\u00e2y ra n\u00ean m\u1ed7i ng\u00e0y t\u1ed5 m\u1ed9t v\u01b0\u1ee3t m\u1ee9c 65% , t\u1ed5 hai v\u01b0\u1ee3t m\u1ee9c 70% , c\u1ea3 hai t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 2850 chi\u1ebfc kh\u1ea9u trang. H\u1ecfi ban \u0111\u1ea7u trong m\u1ed9t ng\u00e0y m\u1ed7i t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c bao nhi\u00eau chi\u1ebfc kh\u1ea9u trang? L\u1eddi gi\u1ea3i G\u1ecdi x l\u00e0 s\u1ed1 kh\u1ea9u trang ban \u0111\u1ea7u t\u1ed5 1 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c m\u1ed7i ng\u00e0y ( x \uf03e 0) G\u1ecdi y l\u00e0 s\u1ed1 kh\u1ea9u trang ban \u0111\u1ea7u t\u1ed5 2 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c m\u1ed7i ng\u00e0y ( y \uf03e 0) Hai t\u1ed5 c\u1ee7a m\u1ed9t nh\u00e0 m\u00e1y s\u1ea3n xu\u1ea5t kh\u1ea9u trang trong m\u1ed9t ng\u00e0y s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 1700 chi\u1ebfc kh\u1ea9u trang suy ra ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: x + y = 1700 (1) Nh\u01b0ng m\u1ed7i ng\u00e0y t\u1ed5 m\u1ed9t v\u01b0\u1ee3t m\u1ee9c 65% , t\u1ed5 hai v\u01b0\u1ee3t m\u1ee9c 70% , c\u1ea3 hai t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 2845 chi\u1ebfc kh\u1ea9u trang suy ra ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 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 x.(1+ 65%) + y.(1+ 70%) = 2850 (2) T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ec x + y = 1700 \uf0db \uf0ec\uf0efx = 800 (N ) \uf0ed\uf0ee1, 65x + 1,7y = 2850 \uf0ed\uf0ef\uf0eey = 900 (N ) V\u1eady ban \u0111\u1ea7u trong m\u1ed9t ng\u00e0y t\u1ed5 1 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 800 chi\u1ebfc kh\u1ea9u trang, t\u1ed5 2 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 900 chi\u1ebfc kh\u1ea9u trang. C\u00e2u 6. (1 \u0111i\u00ea\u0309m) T\u1ea1i b\u1ec1 m\u1eb7t n\u01b0\u1edbc \u00e1p su\u1ea5t kh\u00ed quy\u1ec3n l\u00e0 1 (atm) atmosphere. B\u00ean d\u01b0\u1edbi m\u1eb7t n\u01b0\u1edbc, \u00e1p su\u1ea5t P l\u00e0 2 atm khi m\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u d l\u00e0 32 feet. Bi\u1ebft r\u1eb1ng m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa \u00e1p su\u1ea5t P (atm) v\u00e0 \u0111\u1ed9 s\u00e2u d (feet) d\u01b0\u1edbi m\u1ef1c n\u01b0\u1edbc l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t P(d) = ad + b . a) X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b. b) M\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u bao nhi\u00eau th\u00ec ch\u1ecbu \u00e1p su\u1ea5t l\u00e0 2,25 atm (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u00e2\u0323p ph\u00e2n th\u1ee9 nh\u1ea5t). Bi\u1ebft feet l\u00e0 \u0111\u01a1n v\u1ecb \u0111o \u0111\u1ed9 d\u00e0i, 1 feet = 0,3048m . L\u1eddi gi\u1ea3i a) X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b . T\u1ea1i b\u1ec1 m\u1eb7t n\u01b0\u1edbc \u00e1p xu\u1ea5t kh\u00ed quy\u1ec3n l\u00e0 1(atm) . Thay P = 1,d = 0 v\u00e0o h\u00e0m s\u1ed1 P(d) = ad + b Ta c\u00f3: 1 = 0.a + b \uf0de b = 1 B\u00ean d\u01b0\u1edbi m\u1eb7t n\u01b0\u1edbc, \u00e1p su\u1ea5t P l\u00e0 2(atm) khi m\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u d l\u00e0 32( feet) Thay P = 2;d = 32,b = 1 v\u00e0o h\u00e0m s\u1ed1 P(d) = ad + b Ta c\u00f3 2 = 32.a + 1 \uf0de a = 1 32 V\u1eady a = 1 ;b = 1 32 b) M\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u bao nhi\u00eau th\u00ec ch\u1ecbu \u00e1p su\u1ea5t l\u00e0 2,25(atm) (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u00e2\u0323p ph\u00e2n th\u1ee9 nh\u1ea5t). Bi\u1ebft feet l\u00e0 \u0111\u01a1n v\u1ecb \u0111o \u0111\u1ed9 d\u00e0i, 1 feet = 0,3048m . Thay P = 2,25 v\u00e0o h\u00e0m s\u1ed1 P(d) = ad + b Ta c\u00f3: 2,25 = 1 .d + 1 Do \u0111\u00f3 d = 1,25 : 1 = 40( feet) 32 32 \u0110\u1ed5i 40( feet) = 40.0,3048 = 12,192m \uf0bb 12,2m V\u1eady m\u1ed9t ng\u01b0\u1eddi th\u1ee3 l\u1eb7n \u1edf \u0111\u1ed9 s\u00e2u 12,2m th\u00ec ch\u1ecbu \u00e1p su\u1ea5t l\u00e0 2,25(atm) . C\u00e2u 7. (1 \u0111i\u00ea\u0309m) 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 H\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 th\u1ec3 t\u00edch l\u00e0 64m3 . a) T\u00ednh \u0111\u1ed9 d\u00e0i D l\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng. b) N\u1ebfu d\u00f9ng 2 v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o b\u1ec3 th\u00ec m\u1ea5t bao nhi\u00eau ph\u00fat m\u1edbi \u0111\u1ea7y b\u1ec3? (l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat). Bi\u1ebft v\u00f2i 1 sau 2 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 17 l\u00edt n\u01b0\u1edbc, v\u00f2i 2 sau 3 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 35 l\u00edt n\u01b0\u1edbc. L\u1eddi gi\u1ea3i a) T\u00ednh \u0111\u1ed9 d\u00e0i D l\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng. \u0110\u1ed9 d\u00e0i c\u1ea1nh a c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 4(m) \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o m\u1ed9t m\u1eb7t c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0: d a2 a2 32 4 2 m \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0: D a2 d2 4 3 m . b) N\u1ebfu d\u00f9ng 2 v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o b\u1ec3 th\u00ec m\u1ea5t bao nhi\u00eau ph\u00fat m\u1edbi \u0111\u1ea7y b\u1ec3? (l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat). Bi\u1ebft v\u00f2i 1 sau 2 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 17 l\u00edt n\u01b0\u1edbc, v\u00f2i 2 sau 3 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 35 l\u00edt n\u01b0\u1edbc. V\u00f2i 1 trong 1 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 17 8, 5(l) 2 V\u00f2i 2 trong 1 gi\u00e2y ch\u1ea3y \u0111\u01b0\u1ee3c 35 (l) 3 Trong 1 giay c\u1ea3 2 v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c: 35 8, 5 121 (l ) . 3 6 \u0110\u1ed5i 64m3 64000(l). Ch\u1ea3y \u0111\u1ea7y b\u1ec3 c\u1ea7n: 64000 : 121 3137, 55(s) 53 ph\u00fat. 6 C\u00e2u 8. (3 \u0111i\u00ea\u0309m) Cho (O) c\u00f3 t\u00e2m O, \u0111\u01b0\u1eddng k\u00ednh BC. L\u1ea5y m\u1ed9t \u0111i\u1ec3m A tr\u00ean (O) sao cho AB > AC. T\u1eeb A, v\u1ebd AH vu\u00f4ng g\u00f3c v\u1edbi BC (H thu\u1ed9c BC). T\u1eeb H, v\u1ebd HI vu\u00f4ng g\u00f3c v\u1edbi AB v\u00e0 HK vu\u00f4ng g\u00f3c v\u1edbi AC (I thu\u1ed9c AB, K thu\u1ed9c AC). a) Ch\u1ee9ng minh r\u1eb1ng t\u1ee9 gi\u00e1c AKHI l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt OA vu\u00f4ng g\u00f3c v\u1edbi IK. b) \u0110\u01b0\u1eddng th\u1eb3ng IK c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i M v\u00e0 N (N thu\u1ed9c cung nh\u1ecf EC). Ch\u1ee9ng minh AM2 = AI.AB . Suy ra AMH l\u00e0 tam gi\u00e1c c\u00e2n. c) G\u1ecdi D l\u00e0 giao \u0111i\u1ec3m c\u1ee7a MN v\u00e0 BC; E l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AD v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n (O) (E kh\u00e1c A). K\u1ebb EK c\u1eaft BC t\u1ea1i I. Ch\u1ee9ng minh FH2 = FC.FD . L\u1eddi gi\u1ea3i A M1 1E I1 12 T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 7 K N","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH a) Ch\u1ee9ng minh r\u1eb1ng t\u1ee9 gi\u00e1c AKHI l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt OA vu\u00f4ng g\u00f3c v\u1edbi IK Ch\u1ee9ng minh t\u1ee9 gi\u00e1c c\u00f3 3 g\u00f3c vu\u00f4ng l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt: Ta c\u00f3: I1 = AHK = ACK v\u00e0 AB0 = BAO ( tam gi\u00e1c ABO c\u00e2n t\u1ea1i O ). M\u00e0 AB0 + ACH = 900 \uf0de I1 + OAB = 900 V\u1eady OA \u22a5 IK b) Ch\u1ee9ng minh AM2 = AI.AB . Suy ra AMH l\u00e0 tam gi\u00e1c c\u00e2n. X\u00e9t \uf044AMI v\u00e0 \uf044ABM A Chung, M1 = B1 ( c\u00f9ng ch\u1eafn 2 cung b\u1eb1ng nhau) \uf0de \uf044AMI \uf044ABM (g.g) \uf0de AM = AI AB AM \uf0de AM2 = AI.AB \uf0de AH2 = AI.AB \uf0de AM2 = AH2 \uf0de AM = AH V\u1eady AMH l\u00e0 tam gi\u00e1c c\u00e2n c) Ch\u1ee9ng minh FH2 = FC.FD . Cm: t\u1ee9 gi\u00e1c IAEK n\u1ed9i ti\u1ebfp v\u00ec I1 = E2 . M\u1eb7t kh\u00e1c h\u00ecnh ch\u1eef nh\u1eadt IAKH n\u1ed9i ti\u1ebfp. \uf0de I, A,E,K,H c\u00f9ng thu\u1ed9c 1 \u0111\u01b0\u1eddng tr\u00f2n. Ta ch\u1ee9ng minh FHK FEH(g.g) \uf0de FH2 = FK.FE Ch\u1ee9ng minh FKC FEH(g.g) \uf0de FK.FE = FC.FD V\u1eady FH2 = FC.FD . 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 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 HUY\u1ec6N C\u1ee6 CHI NA\u00caM HO\u00cfC: 2021 - 2022 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 M\u00c3 \u0110\u1ec0: Huy\u1ec7n C\u1ee7 Chi - 2 \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 h\u00e0m s\u1ed1 y = \u2212 1 x2 c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ( P) v\u00e0 y = 3 x \u2212 2 c\u00f3 \u0111\u1ed3 th\u1ecb (D) . 22 a) V\u1ebd \u0111\u1ed3 th\u1ecb ( P) v\u00e0 (D) tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1ea9ng t\u1ecda \u0111\u1ed9 Oxy . 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 + 2x \u2212 1 = 0 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh h\u00e3y t\u00ednh bi\u1ec3u th\u1ee9c A = x12 + x22 x2 + 2 x1 + 2 C\u00e2u 3. (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 ph\u1ea3i 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 quan 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 v\u00e0 b bi\u1ebft r\u1eb1ng nh\u00e0 b\u1ea1n Nam trong th\u00e1ng 3 \u0111\u00e3 g\u1ecdi 120 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 80 ngh\u00ecn \u0111\u1ed3ng v\u00e0 trong th\u00e1ng 4 \u0111\u00e3 g\u1ecdi \u00edt h\u01a1n th\u00e1ng ba 40 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 58 000 \u0111\u1ed3ng. C\u00e2u 4. (1 \u0111i\u1ec3m). Ch\u1ecb Thu d\u1ef1 \u0111\u1ecbnh mua v\u00e9 m\u00e1y bay h\u1ea1ng th\u01b0\u1eddng \u0111i t\u1eeb th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh ra H\u00e0 N\u1ed9i \u0111\u1ec3 \u0111i c\u00f4ng t\u00e1c v\u1edbi s\u1ed1 h\u00e0nh l\u00fd d\u1ef1 tr\u00f9 t\u1eeb 12 kg \u0111\u1ebfn 25 kg . Bi\u1ebft r\u1eb1ng: - H\u00e3ng A : Ti\u1ec1n v\u00e9 cho m\u1ed7i kh\u00e1ch h\u00e0ng \u1edf khoang th\u01b0\u1eddng l\u00e0 900 000 \u0111\u1ed3ng v\u00e0 quy \u0111\u1ecbnh m\u1ed7i h\u00e0nh kh\u00e1ch ch\u1ec9 \u0111\u01b0\u1ee3c mang 7 kg h\u00e0nh l\u00fd. N\u1ebfu s\u1ed1 l\u01b0\u1ee3ng h\u00e0nh l\u00fd v\u01b0\u1ee3t qu\u00e1 quy \u0111\u1ecbnh, m\u1ed7i kh\u00e1ch h\u00e0ng c\u1ea7n ph\u1ea3i tr\u1ea3 th\u00eam 40 000 \u0111\u1ed3ng\/kg h\u00e0nh l\u00fd. - H\u00e3ng B : Ti\u1ec1n v\u00e9 cho m\u1ed7i kh\u00e1ch h\u00e0ng \u1edf khoang th\u01b0\u1eddng l\u00e0 120 000 \u0111\u1ed3ng v\u00e0 quy \u0111\u1ecbnh m\u1ed7i h\u00e0nh kh\u00e1ch ch\u1ec9 \u0111\u01b0\u1ee3c mang 12 kg h\u00e0nh l\u00fd. N\u1ebfu s\u1ed1 l\u01b0\u1ee3ng h\u00e0nh l\u00fd v\u01b0\u1ee3t qu\u00e1 quy \u0111\u1ecbnh, m\u1ed7i kh\u00e1ch h\u00e0ng c\u1ea7n ph\u1ea3i tr\u1ea3 th\u00eam 20 000 \u0111\u1ed3ng\/kg h\u00e0nh l\u00fd. a) H\u00e3y l\u1eadp h\u00e0m s\u1ed1 bi\u1ec3u di\u1ec5n s\u1ed1 ti\u1ec1n ch\u1ecb Thu ph\u1ea3i tr\u1ea3 cho m\u1ed7i h\u00e3ng theo kh\u1ed1i l\u01b0\u1ee3ng h\u00e0nh l\u00fd d\u1ef1 tr\u00f9 x . b) H\u1ecfi v\u1edbi 23 kg , ch\u1ecb Thu n\u00ean l\u1ef1a ch\u1ecdn \u0111i h\u00e3ng n\u00e0o cho ti\u1ebft ki\u1ec7m chi ph\u00ed? C\u00e2u 5. (1 \u0111i\u1ec3m). Nh\u1eb1m chia s\u1ebb, h\u1ed7 tr\u1ee3 cho h\u1ecdc sinh c\u00f3 ho\u00e0n c\u1ea3nh kh\u00f3 kh\u0103n nh\u00e2n d\u1ecbp t\u1ebft \u0111\u1ebfn xu\u00e2n v\u1ec1, tr\u01b0\u1eddng THCS A t\u1ed5 ch\u1ee9c ch\u01b0\u01a1ng tr\u00ecnh 'Xu\u00e2n lan t\u1ecfa y\u00eau th\u01b0\u01a1ng' v\u00e0o ng\u00e0y h\u1ed9i xu\u00e2n truy\u1ec1n th\u1ed1ng h\u1eb1ng n\u0103m. \u0110\u1ec3 chu\u1ea9n b\u1ecb cho ch\u01b0\u01a1ng tr\u00ecnh, ngay t\u1eeb \u0111\u1ea7u th\u00e1ng 10 nh\u00e0 tr\u01b0\u1eddng \u0111\u00e3 ph\u00e1t \u0111\u1ed9ng phong tr\u00e0o \u0111\u1ebfn t\u1eadp th\u1ec3 h\u1ecdc sinh v\u00e0 khuy\u1ebfn kh\u00edch m\u1ed7i l\u1edbp th\u1ef1c hi\u1ec7n ti\u1ebft ki\u1ec7m \u0111\u1ec3 mua 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 qu\u00e0 h\u1ed7 tr\u1ee3 b\u1ea1n c\u00f3 ho\u00e0n c\u1ea3nh kh\u00f3 kh\u0103n trong l\u1edbp. Trong bu\u1ed5i h\u1ecdp l\u1edbp, b\u1ea1n l\u1edbp tr\u01b0\u1edfng c\u1ee7a l\u1edbp 9A \u0111\u1ec1 ngh\u1ecb l\u1edbp th\u1ef1c hi\u1ec7n ti\u1ebft ki\u1ec7m b\u1eaft \u0111\u1ea7u t\u1eeb th\u1ee9 hai ng\u00e0y 31 \/ 10 \/ 2022 v\u00e0 k\u1ebft th\u00fac v\u00e0o ng\u00e0y 25 \/ 12 \/ 2022 . C\u00e1c b\u1ea1n ti\u1ebft ki\u1ec7m b\u1eb1ng hai h\u00ecnh th\u1ee9c: \u27a2 Thu gom gi\u1ea5y v\u1ee5n h\u1eb1ng ng\u00e0y \u27a2 Nu\u00f4i heo \u0111\u1ea5t : M\u1ed7i b\u1ea1n tr\u00edch 2000 \u0111\u1ed3ng ti\u1ec1n \u0103n s\u00e1ng m\u1ed7i ng\u00e0y \u0111\u1ebfn tr\u01b0\u1eddng \u0111\u1ec3 b\u1ecf v\u00e0o heo \u0111\u1ea5t (Tr\u1eeb th\u1ee9 b\u1ea3y v\u00e0 ch\u1ee7 nh\u1eadt) \u0110\u1ebfn 25 \/ 12 sau khi t\u1ed5ng k\u1ebft l\u1ea1i c\u00e1c b\u1ea1n l\u1edbp 9A thu \u0111\u01b0\u1ee3c: t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 3 560 000 \u0111\u1ed3ng bao g\u1ed3m ti\u1ec1n khui heo \u0111\u1ea5t v\u00e0 ti\u1ec1n b\u00e1n gi\u1ea5y v\u1ee5n. Em h\u00e3y t\u00ednh xem l\u1edbp 9A c\u00f3 bao nhi\u00eau b\u1ea1n tham gia ch\u01b0\u01a1ng tr\u00ecnh ti\u1ebft ki\u1ec7m, bi\u1ebft r\u1eb1ng c\u00e1c b\u1ea1n thu th\u1eadp \u0111\u01b0\u1ee3c 200 kg gi\u1ea5y v\u1ee5n trong \u0111\u00f3 s\u1ed1 gi\u1ea5y b\u1ecb \u1ea9m \u01b0\u1edbt kh\u00f4ng b\u00e1n \u0111\u01b0\u1ee3c chi\u1ebfm 10% v\u00e0 gi\u00e1 m\u1ed7i kg gi\u1ea5y l\u00e0 2000 \u0111\u1ed3ng C\u00e2u 6. (1 \u0111i\u1ec3m). \u0110\u1ec3 chu\u1ea9n b\u1ecb cho bu\u1ed5i li\u00ean hoan cu\u1ed1i n\u0103m c\u1ee7a l\u1edbp 9A , gi\u00e1o vi\u00ean ch\u1ee7 nhi\u1ec7m \u0111\u01b0a cho l\u1edbp tr\u01b0\u1edfng 1, 5 tri\u1ec7u \u0111\u1ed3ng \u0111\u1ec3 \u0111i mua 45 c\u00e1i b\u00e1nh ng\u1ecdt cho l\u1edbp. H\u00f4m \u0111\u00f3 ti\u1ec7m b\u00e1nh c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i, t\u1eeb c\u00e1i b\u00e1nh th\u1ee9 16 m\u1ed7i c\u00e1i b\u00e1nh \u0111\u01b0\u1ee3c gi\u1ea3m 5% gi\u00e1 ni\u00eam y\u1ebft. Sau khi tr\u1ea3 ti\u1ec1n b\u00e1nh th\u00ec l\u1edbp tr\u01b0\u1edfng \u0111\u01b0a l\u1ea1i cho gi\u00e1o vi\u00ean ch\u1ee7 nhi\u1ec7m 195 000 \u0111\u1ed3ng ti\u1ec1n th\u1eeba. H\u1ecfi gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t c\u00e1i b\u00e1nh l\u00e0 bao nhi\u00eau? C\u00e2u 7. (0,75 \u0111i\u1ec3m). M\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y l\u00e0 3 cm , chi\u1ec1u cao 4 cm \u0111\u01b0\u1ee3c \u0111\u1eb7t \u0111\u1ee9ng tr\u00ean m\u1eb7t b\u00e0n. M\u1ed9t ph\u1ea7n c\u1ee7a h\u00ecnh tr\u1ee5 b\u1ecb c\u1eaft r\u1eddi ra theo b\u00e1n k\u00ednh OA , OB v\u00e0 theo chi\u1ec1u th\u1eb3ng \u0111\u1ee9ng t\u1eeb tr\u00ean xu\u1ed1ng d\u01b0\u1edbi v\u1edbi AOB = 30\uf0b0 . (nh\u01b0 h\u00ecnh v\u1ebd). H\u00e3y t\u00ednh: a) Th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 ban \u0111\u1ea7u. b) Th\u1ec3 t\u00edch ph\u1ea7n c\u00f2n l\u1ea1i. ( )C\u00e2u 8. (3 \u0111i\u1ec3m) Cho \u0111\u01b0\u1eddng tr\u00f2n O v\u00e0 \u0111i\u1ec3m A n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n. V\u1ebd c\u00e1c ti\u1ebfp tuy\u1ebfn AM, AN v\u1edbi (O) ( M, N l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m ). Qua A v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i hai \u0111i\u1ec3m B v\u00e0 C ph\u00e2n bi\u1ec7t ( B n\u1eb1m gi\u1eefa A v\u00e0 C ). G\u1ecdi H l\u00e0 trung \u0111i\u1ec3m BC . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AMHN n\u1ed9i ti\u1ebfp v\u00e0 AM2 = AB.AC . 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 ( )b) G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AO v\u00e0 O . Ch\u1ee9ng minh K l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \uf044AMN . c) \u0110\u01b0\u1eddng th\u1eb3ng qua B song song AM v\u1edbi c\u1eaft \u0111o\u1ea1n th\u1eb3ng t\u1ea1i E . Ch\u1ee9ng minh EH \/\/ MC . ----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 h\u00e0m s\u1ed1 y = \u2212 1 x2 c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ( P) v\u00e0 y = 3 x \u2212 2 c\u00f3 \u0111\u1ed3 th\u1ecb (D) . 22 a) V\u1ebd \u0111\u1ed3 th\u1ecb ( P) v\u00e0 (D) tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1ea9ng t\u1ecda \u0111\u1ed9 Oxy. 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 = \u2212 1 x2 \u22128 \u22121 0 \u22121 \u22128 2 x 02 y= 3x\u22122 \u22122 1 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) : \u2212 1 x2 = 3 x \u2212 2 22 \uf0db x2 + 3x \u2212 4 = 0 \uf0db \uf0e9x = 1 \uf0ea\uf0ebx = \u22124 Thay x =1 v\u00e0o y = \u2212 1 x2 , ta \u0111\u01b0\u1ee3c: y = \u2212 \uf0e6 1 \uf0f62 = \u2212 1 . 2 \uf0e7\uf0e8 2 \uf0f7\uf0f8 2 Thay x = \u22124 v\u00e0o y = \u2212 1 x2 , ta \u0111\u01b0\u1ee3c: y = \u2212 1 (\u22124)2 = \u22128 . 22 V\u1eady \uf0e6 1; \u2212 1 \uf0f6 , ( \u22124; \u22128) 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 4","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 3x2 + 2x \u2212 1 = 0 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh h\u00e3y t\u00ednh bi\u1ec3u th\u1ee9c A = x12 + x22 x2 + 2 x1 + 2 L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = 22 \u2212 4.3.(\u22121) = 16 \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 = \u2212 2 \uf0ed = x1 a 3 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP =\u22121 c .x2 = a 3 Ta c\u00f3: A = x12 + x22 x2 + 2 x1 + 2 ( )( )A = x13 + 2x12 + x23 + 2x22 x2 + 2 x1 + 2 ( )( )A = x13 + x23 + 2x12 + 2x22 x2 + 2 x1 + 2 ( x1 + x2 )3 \u2212 (3x1x2 x1 + x2 ) + 2 \uf0e9\uf0eb\uf0ea(x1 + x2 )2 \u2212 2x1x2 \uf0f9 2 (x1 + x2 ) + 4 \uf0fb\uf0fa A = x1x2 + \uf0e6 \u22122 \uf0f63 \u2212 3. \uf0e6 \u22121 \uf0f6 .\uf0e8\uf0e7\uf0e6 \u22122 \uf0f6 + 2 \uf0e9\uf0eb\uf0ea\uf0ea\uf0e8\uf0e7\uf0e6 \u22122 \uf0f62 \u2212 2.\uf0e7\uf0e8\uf0e6 \u22121 \uf0f7\uf0f8\uf0f6\uf0fa\uf0fa\uf0f9\uf0fb \uf0e7\uf0e8 3 \uf0f8\uf0f7 \uf0e8\uf0e7 3 \uf0f7\uf0f8 3 \uf0f7\uf0f8 3 \uf0f8\uf0f7 3 34 A = = \u22121 2.\uf0e6\uf0e8\uf0e7 \u22122 \uf0f6 63 3 + 3 \uf0f8\uf0f7 + 4 C\u00e2u 3. (1 \u0111i\u1ec3m) \u00c1p 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 ph\u1ea3i 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 quan 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 v\u00e0 b bi\u1ebft r\u1eb1ng nh\u00e0 b\u1ea1n Nam trong th\u00e1ng 3 \u0111\u00e3 g\u1ecdi 120 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 80 000 \u0111\u1ed3ng v\u00e0 trong th\u00e1ng 4 \u0111\u00e3 g\u1ecdi \u00edt h\u01a1n th\u00e1ng ba 40 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 58 000 \u0111\u1ed3ng. L\u1eddi gi\u1ea3i V\u00ec trong th\u00e1ng 3 nh\u00e0 b\u1ea1n Nam \u0111\u00e3 g\u1ecdi 120 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 80 000 \u0111\u1ed3ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 80 000 = a.120 + b (1) S\u1ed1 ph\u00fat nh\u00e0 b\u1ea1n Nam \u0111\u00e3 g\u1ecdi trong th\u00e1ng 4 l\u00e0: 120 \u2212 40 = 80 (ph\u00fat). 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 V\u00ec trong th\u00e1ng 4 nh\u00e0 b\u1ea1n Nam \u0111\u00e3 g\u1ecdi 80 ph\u00fat v\u1edbi s\u1ed1 ti\u1ec1n l\u00e0 58 000 \u0111\u1ed3ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 58 000 = a.80 + b (2) T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ec80 000 = 120a + b \uf0db \uf0eca = 550 \uf0ed\uf0ee58 000 = 80a + b \uf0ed\uf0eeb = 14 000 V\u1eady a = 550 v\u00e0 b = 14 000 . C\u00e2u 4. (1 \u0111i\u1ec3m). Ch\u1ecb Thu d\u1ef1 \u0111\u1ecbnh mua v\u00e9 m\u00e1y bay h\u1ea1ng th\u01b0\u1eddng \u0111i t\u1eeb th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh ra H\u00e0 N\u1ed9i \u0111\u1ec3 \u0111i c\u00f4ng t\u00e1c v\u1edbi s\u1ed1 h\u00e0nh l\u00fd d\u1ef1 tr\u00f9 t\u1eeb 12 kg \u0111\u1ebfn 25 kg. Bi\u1ebft r\u1eb1ng: - H\u00e3ng A: Ti\u1ec1n v\u00e9 cho m\u1ed7i kh\u00e1ch h\u00e0ng \u1edf khoang th\u01b0\u1eddng l\u00e0 900 000 \u0111\u1ed3ng v\u00e0 quy \u0111\u1ecbnh m\u1ed7i h\u00e0nh kh\u00e1ch ch\u1ec9 \u0111\u01b0\u1ee3c mang 7 kg h\u00e0nh l\u00fd. N\u1ebfu s\u1ed1 l\u01b0\u1ee3ng h\u00e0nh l\u00fd v\u01b0\u1ee3t qu\u00e1 quy \u0111\u1ecbnh, m\u1ed7i kh\u00e1ch h\u00e0ng c\u1ea7n ph\u1ea3i tr\u1ea3 th\u00eam 40 000 \u0111\u1ed3ng\/kg h\u00e0nh l\u00fd. - H\u00e3ng B: Ti\u1ec1n v\u00e9 cho m\u1ed7i kh\u00e1ch h\u00e0ng \u1edf khoang th\u01b0\u1eddng l\u00e0 120 000 \u0111\u1ed3ng v\u00e0 quy \u0111\u1ecbnh m\u1ed7i h\u00e0nh kh\u00e1ch ch\u1ec9 \u0111\u01b0\u1ee3c mang 12 kg h\u00e0nh l\u00fd. N\u1ebfu s\u1ed1 l\u01b0\u1ee3ng h\u00e0nh l\u00fd v\u01b0\u1ee3t qu\u00e1 quy \u0111\u1ecbnh, m\u1ed7i kh\u00e1ch h\u00e0ng c\u1ea7n ph\u1ea3i tr\u1ea3 th\u00eam 20 000 \u0111\u1ed3ng\/kg h\u00e0nh l\u00fd. a) H\u00e3y l\u1eadp h\u00e0m s\u1ed1 bi\u1ec3u di\u1ec5n s\u1ed1 ti\u1ec1n ch\u1ecb Thu ph\u1ea3i tr\u1ea3 cho m\u1ed7i h\u00e3ng theo kh\u1ed1i l\u01b0\u1ee3ng h\u00e0nh l\u00fd d\u1ef1 tr\u00f9 x . b) H\u1ecfi v\u1edbi 23 kg, ch\u1ecb Thu n\u00ean l\u1ef1a ch\u1ecdn \u0111i h\u00e3ng n\u00e0o cho ti\u1ebft ki\u1ec7m chi ph\u00ed? L\u1eddi gi\u1ea3i a) H\u00e0m s\u1ed1 bi\u1ec3u di\u1ec5n s\u1ed1 ti\u1ec1n ch\u1ecb Thu ph\u1ea3i tr\u1ea3 n\u1ebfu \u0111i h\u00e3ng A l\u00e0: y = 900 000 + 40 000(x \u2212 7) = 40 000x + 620 000 H\u00e0m s\u1ed1 bi\u1ec3u di\u1ec5n s\u1ed1 ti\u1ec1n ch\u1ecb Thu ph\u1ea3i tr\u1ea3 n\u1ebfu \u0111i h\u00e3ng B l\u00e0: y = 120 000 + 20 000(x \u2212 12) = 20 000x \u2212 120 000 b) S\u1ed1 ti\u1ec1n ch\u1ecb Thu ph\u1ea3i tr\u1ea3 n\u1ebfu \u0111i h\u00e3ng A l\u00e0: y = 40 000.23 + 620 000 = 1540 000 (\u0111\u1ed3ng). S\u1ed1 ti\u1ec1n ch\u1ecb Thu ph\u1ea3i tr\u1ea3 n\u1ebfu \u0111i h\u00e3ng B l\u00e0: y = 20 000.23 \u2212 120 000 = 340 000 (\u0111\u1ed3ng). V\u1eady ch\u1ecb Thu n\u00ean \u0111i H\u00e3ng B \u0111\u1ec3 ti\u1ebft ki\u1ec7m chi ph\u00ed h\u01a1n. C\u00e2u 5. (1 \u0111i\u1ec3m). Nh\u1eb1m chia s\u1ebb, h\u1ed7 tr\u1ee3 cho h\u1ecdc sinh c\u00f3 ho\u00e0n c\u1ea3nh kh\u00f3 kh\u0103n nh\u00e2n d\u1ecbp t\u1ebft \u0111\u1ebfn xu\u00e2n v\u1ec1, tr\u01b0\u1eddng THCS A t\u1ed5 ch\u1ee9c ch\u01b0\u01a1ng tr\u00ecnh 'Xu\u00e2n lan t\u1ecfa y\u00eau th\u01b0\u01a1ng' v\u00e0o ng\u00e0y h\u1ed9i xu\u00e2n truy\u1ec1n th\u1ed1ng h\u1eb1ng n\u0103m. \u0110\u1ec3 chu\u1ea9n b\u1ecb cho ch\u01b0\u01a1ng tr\u00ecnh, ngay t\u1eeb \u0111\u1ea7u th\u00e1ng 10 nh\u00e0 tr\u01b0\u1eddng \u0111\u00e3 ph\u00e1t \u0111\u1ed9ng phong tr\u00e0o \u0111\u1ebfn t\u1eadp th\u1ec3 h\u1ecdc sinh v\u00e0 khuy\u1ebfn kh\u00edch m\u1ed7i l\u1edbp th\u1ef1c hi\u1ec7n ti\u1ebft ki\u1ec7m \u0111\u1ec3 mua qu\u00e0 h\u1ed7 tr\u1ee3 b\u1ea1n c\u00f3 ho\u00e0n c\u1ea3nh kh\u00f3 kh\u0103n trong l\u1edbp. Trong bu\u1ed5i h\u1ecdp l\u1edbp, b\u1ea1n l\u1edbp tr\u01b0\u1edfng c\u1ee7a l\u1edbp 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 9A \u0111\u1ec1 ngh\u1ecb l\u1edbp th\u1ef1c hi\u1ec7n ti\u1ebft ki\u1ec7m b\u1eaft \u0111\u1ea7u t\u1eeb th\u1ee9 hai ng\u00e0y 31 \/ 10 \/ 2022 v\u00e0 k\u1ebft th\u00fac v\u00e0o ng\u00e0y 25 \/ 12 \/ 2022 . C\u00e1c b\u1ea1n ti\u1ebft ki\u1ec7m b\u1eb1ng hai h\u00ecnh th\u1ee9c: \u27a2 Thu gom gi\u1ea5y v\u1ee5n h\u1eb1ng ng\u00e0y \u27a2 Nu\u00f4i heo \u0111\u1ea5t : M\u1ed7i b\u1ea1n tr\u00edch 2000 \u0111\u1ed3ng ti\u1ec1n \u0103n s\u00e1ng m\u1ed7i ng\u00e0y \u0111\u1ebfn tr\u01b0\u1eddng \u0111\u1ec3 b\u1ecf v\u00e0o heo \u0111\u1ea5t (Tr\u1eeb th\u1ee9 b\u1ea3y v\u00e0 ch\u1ee7 nh\u1eadt) \u0110\u1ebfn 25 \/ 12 sau khi t\u1ed5ng k\u1ebft l\u1ea1i c\u00e1c b\u1ea1n l\u1edbp 9A thu \u0111\u01b0\u1ee3c: t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 3 560 000 \u0111\u1ed3ng bao g\u1ed3m ti\u1ec1n khui heo \u0111\u1ea5t v\u00e0 ti\u1ec1n b\u00e1n gi\u1ea5y v\u1ee5n. Em h\u00e3y t\u00ednh xem l\u1edbp 9A c\u00f3 bao nhi\u00eau b\u1ea1n tham gia ch\u01b0\u01a1ng tr\u00ecnh ti\u1ebft ki\u1ec7m, bi\u1ebft r\u1eb1ng c\u00e1c b\u1ea1n thu th\u1eadp \u0111\u01b0\u1ee3c 200 kg gi\u1ea5y v\u1ee5n trong \u0111\u00f3 s\u1ed1 gi\u1ea5y b\u1ecb \u1ea9m \u01b0\u1edbt kh\u00f4ng b\u00e1n \u0111\u01b0\u1ee3c chi\u1ebfm 10% v\u00e0 gi\u00e1 m\u1ed7i kg gi\u1ea5y l\u00e0 2000 \u0111\u1ed3ng. L\u1eddi gi\u1ea3i S\u1ed1 kg gi\u1ea5y v\u1ee5n l\u1edbp 9A b\u00e1n \u0111\u01b0\u1ee3c l\u00e0: 200.(100% \u2212 10%) = 180 kg . S\u1ed1 ti\u1ec1n l\u1edbp 9A thu \u0111\u01b0\u1ee3c sau khi b\u00e1n gi\u1ea5y v\u1ee5n l\u00e0: 180.2000 = 360 000 (\u0111\u1ed3ng). S\u1ed1 ti\u1ec1n l\u1edbp 9A thu \u0111\u01b0\u1ee3c t\u1eeb h\u00ecnh th\u1ee9c nu\u00f4i heo \u0111\u1ea5t l\u00e0: 3 560 000 \u2212 360 000 = 3 200 000 (\u0111\u1ed3ng). T\u1ed5ng s\u1ed1 ng\u00e0y l\u1edbp 9A thu ti\u1ec1n heo t\u00ednh t\u1eeb 31 \/ 10 \/ 2022 \u0111\u1ebfn 25 \/ 12 \/ 2022 (kh\u00f4ng t\u00ednh th\u1ee9 b\u00e0y v\u00e0 ch\u1ee7 nh\u1eadt) l\u00e0 40 ng\u00e0y. S\u1ed1 ti\u1ec1n thu \u0111\u01b0\u1ee3c t\u1eeb heo \u0111\u1ea5t trong m\u1ed9t ng\u00e0y l\u00e0: 3 200 000 : 40 = 80 000 (\u0111\u1ed3ng). S\u1ed1 h\u1ecdc sinh l\u1edbp 9A l\u00e0: 80 000 : 2000 = 40 h\u1ecdc sinh. C\u00e2u 6. (1 \u0111i\u1ec3m). \u0110\u1ec3 chu\u1ea9n b\u1ecb cho bu\u1ed5i li\u00ean hoan cu\u1ed1i n\u0103m c\u1ee7a l\u1edbp 9A, gi\u00e1o vi\u00ean ch\u1ee7 nhi\u1ec7m \u0111\u01b0a cho l\u1edbp tr\u01b0\u1edfng 1,5 tri\u1ec7u \u0111\u1ed3ng \u0111\u1ec3 \u0111i mua 45 c\u00e1i b\u00e1nh ng\u1ecdt cho l\u1edbp. H\u00f4m \u0111\u00f3 ti\u1ec7m b\u00e1nh c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i, t\u1eeb c\u00e1i b\u00e1nh th\u1ee9 16 m\u1ed7i c\u00e1i b\u00e1nh \u0111\u01b0\u1ee3c gi\u1ea3m 5% gi\u00e1 ni\u00eam y\u1ebft. Sau khi tr\u1ea3 ti\u1ec1n b\u00e1nh th\u00ec l\u1edbp tr\u01b0\u1edfng \u0111\u01b0a l\u1ea1i cho gi\u00e1o vi\u00ean ch\u1ee7 nhi\u1ec7m 195 000 \u0111\u1ed3ng ti\u1ec1n th\u1eeba. H\u1ecfi gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t c\u00e1i b\u00e1nh l\u00e0 bao nhi\u00eau? L\u1eddi gi\u1ea3i G\u1ecdi x l\u00e0 gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed9t c\u00e1i b\u00e1nh (khi ch\u01b0a khuy\u1ebfn m\u00e3i), x \uf03e 0 S\u1ed1 ti\u1ec1n l\u1edbp tr\u01b0\u1edfng ph\u1ea3i tr\u1ea3 khi mua 45 c\u00e1i b\u00e1nh l\u00e0: 15.x + 30x.0,95 (vnd) Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 15.x + 30x.0,95 = 1500000 \u2212 195000 \uf0db 43.5x = 1305000 \uf0db x = 30000 (Nh\u1eadn) V\u1eady gi\u00e1 ti\u1ec1n m\u1ed7i c\u00e1i b\u00e1nh l\u00e0 30 000 \u0111\u1ed3ng 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 C\u00e2u 7. (0,75 \u0111i\u1ec3m). M\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y l\u00e0 3cm, chi\u1ec1u cao 4cm \u0111\u01b0\u1ee3c \u0111\u1eb7t \u0111\u1ee9ng tr\u00ean m\u1eb7t b\u00e0n. M\u1ed9t ph\u1ea7n c\u1ee7a h\u00ecnh tr\u1ee5 b\u1ecb c\u1eaft r\u1eddi ra theo b\u00e1n k\u00ednh OA, OB v\u00e0 theo chi\u1ec1u th\u1eb3ng \u0111\u1ee9ng t\u1eeb tr\u00ean xu\u1ed1ng d\u01b0\u1edbi v\u1edbi AOB = 30 . (nh\u01b0 h\u00ecnh v\u1ebd). H\u00e3y t\u00ednh: a) Th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 ban \u0111\u1ea7u. b) Th\u1ec3 t\u00edch ph\u1ea7n c\u00f2n l\u1ea1i. L\u1eddi gi\u1ea3i ( )a) Th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 ban \u0111\u1ea7u l\u00e0: V = h.S = 4.\uf070 .32 = 36\uf070 cm3 ( )b) 30 3 Di\u1ec7n t\u00edch h\u00ecnh qu\u1ea1t OAB l\u00e0: SOAB = \uf070 .32. 360 = 4 .\uf070 cm3 ( )Th\u1ec3 t\u00edch ph\u1ea7n b\u1ecb c\u1eaft l\u00e0: 3 .\uf070 .4 = 3\uf070 cm3 4 ( )Th\u1ec3 t\u00edch ph\u1ea7n tr\u1ee5 c\u00f2n l\u1ea1i: 36\uf070 \u2212 3\uf070 = 33\uf070 cm3 ( )C\u00e2u 8. (3 \u0111i\u1ec3m) Cho \u0111\u01b0\u1eddng tr\u00f2n O v\u00e0 \u0111i\u1ec3m A n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n. V\u1ebd c\u00e1c ti\u1ebfp tuy\u1ebfn AM, AN v\u1edbi (O) ( M, N l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m ). Qua A v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n (O) t\u1ea1i hai \u0111i\u1ec3m B v\u00e0 C ph\u00e2n bi\u1ec7t ( B n\u1eb1m gi\u1eefa A v\u00e0 C ). G\u1ecdi H l\u00e0 trung \u0111i\u1ec3m BC . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AMHN n\u1ed9i ti\u1ebfp v\u00e0 AM2 = AB.AC . ( )b) G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AO v\u00e0 O . Ch\u1ee9ng minh K l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \uf044AMN c) \u0110\u01b0\u1eddng th\u1eb3ng qua B song song AM v\u1edbi c\u1eaft \u0111o\u1ea1n th\u1eb3ng t\u1ea1i E . Ch\u1ee9ng minh EH \/\/ MC L\u1eddi gi\u1ea3i 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 a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AMHN n\u1ed9i ti\u1ebfp v\u00e0 AM2 = AB.AC . Ta c\u00f3 H l\u00e0 trung \u0111i\u1ec3m BC \uf0de OH \u22a5 BC M\u00e0 AM \u22a5 MO, AN \u22a5 NO \uf0de AHO = AMO = ANO = 90\uf0b0 \uf0de H, M, N c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AO . \uf0de H, M, N,O, A c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. \uf0de t\u1ee9 gi\u00e1c AMHN n\u1ed9i ti\u1ebfp. X\u00e9t \uf044AMN v\u00e0 \uf044AMN c\u00f3 MAB chung AMB = ACM (g\u00f3c n\u1ed9i ti\u1ebfp v\u00e0 g\u00f3c t\u1ea1o b\u1edfi ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung c\u00f9ng ch\u1eafn cung MB) \uf0de \uf044AMB \uf044ACM (g \u2013 g). \uf0de AM = AB AC AM \uf0de AM2 = AB.AC ( )b) G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AO v\u00e0 O . Ch\u1ee9ng minh K l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \uf044AMN Ta c\u00f3 AM = AN,OM = ON \uf0de AO l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a MN M\u00e0 K \uf0ce AO \uf0de KM = KN 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 \uf0de s\u0111 KM = s\u0111 KN AMK = 1 s\u0111 KM ( g\u00f3c t\u1ea1o b\u1edfi ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung KM ) 2 KMN = 1 s\u0111 KN ( g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn KN ) 2 \uf0de AMK = KMN (1) \uf0de MK l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a AMN X\u00e9t \uf044AMO vu\u00f4ng t\u1ea1i M v\u00e0 \uf044ANO vu\u00f4ng t\u1ea1i N c\u00f3 AM = AN,OM = ON \uf0de \uf044AMO = \uf044ANO(c.g.c) \uf0de MAO = NAO (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) \uf0de AK l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a MAN (2) T\u1eeb (1) , (2) \uf0de K l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \uf044AMN c) \u0110\u01b0\u1eddng th\u1eb3ng qua B song song AM v\u1edbi c\u1eaft \u0111o\u1ea1n th\u1eb3ng t\u1ea1i E . Ch\u1ee9ng minh EH \/\/ MC . Ta c\u00f3 BE \/\/ AM \uf0de EBH = MAH (hai g\u00f3c \u0111\u1ed3ng v\u1ecb) ( )M\u00e0 MAH = ENH (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung EH c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n AMHON ) \uf0de EBH = ENH \uf0de t\u1ee9 gi\u00e1c BEHN n\u1ed9i ti\u1ebfp. \uf0de BHE = BNM ( )M\u00e0 BNM = BCM (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung BM c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O ) \uf0de BHE = BCM M\u00e0 BHE v\u00e0 BCM l\u00e0 hai g\u00f3c \u0111\u1ed3ng v\u1ecb \uf0de EH \/\/ MC . ----H\u1ebeT--- 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 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 HUYE\u00c4N C\u1ee6 CHI NA\u00caM HO\u00cfC: 2023 - 2024 M\u00d4N: TO\u00c1N 9 \u0110\u1ec0 THAM KH\u1ea2O M\u00c3 \u0110\u1ec0: Qu\u1eadn CC - 3 \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 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng d :y 1x 2. 4 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 2x 2 13x 6 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 A x1 x2 2 4x1x2 . 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. (0,75 \u0111i\u1ec3m). M\u1ed9t c\u1eeda h\u00e0ng Pizza c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i: gi\u1ea3m 30% cho b\u00e1nh Pizza h\u1ea3i s\u1ea3n c\u00f3 gi\u00e1 b\u00e1n ban \u0111\u1ea7u l\u00e0 210000 \u0111\u1ed3ng\/c\u00e1i. N\u1ebfu kh\u00e1ch h\u00e0ng c\u00f3 th\u1ebb VIP th\u00ec s\u1ebd \u0111\u01b0\u1ee3c gi\u1ea3m th\u00eam 5% tr\u00ean gi\u00e1 \u0111\u00e3 gi\u1ea3m. H\u1ecfi m\u1ed9t nh\u00f3m nh\u00e2n vi\u00ean v\u0103n ph\u00f2ng \u0111\u1eb7t mua 60 c\u00e1i b\u00e1nh Pizza h\u1ea3i s\u1ea3n \u1edf c\u1eeda h\u00e0ng trong \u0111\u00f3 c\u00f3 25 c\u00e1i d\u00f9ng th\u1ebb VIP th\u00ec ph\u1ea3i tr\u1ea3 t\u1ea5t c\u1ea3 bao nhi\u00eau ti\u1ec1n (l\u00e0m tr\u00f2n ngh\u00ecn \u0111\u1ed3ng)? C\u00e2u 4. (0,75 \u0111i\u1ec3m). Ch\u1ecb An l\u00e0 c\u00f4ng nh\u00e2n may m\u1eb7c c\u1ee7a X\u00ed nghi\u1ec7p A . Ng\u01b0\u1eddi 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 s\u1ed1 y ax b c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh v\u1ebd sau: H\u1ecfi n\u1ebfu mu\u1ed1n nh\u1eadn l\u01b0\u01a1ng 14000000 \u0111\u1ed3ng th\u00ec ch\u1ecb An ph\u1ea3i may bao nhi\u00eau c\u00e1i \u00e1o? C\u00e2u 5. (1 \u0111i\u1ec3m). B\u1ea1n B\u00ecnh mu\u1ed1n mua m\u1ed9t \u0111\u00f4i gi\u00e0y th\u1ec3 thao m\u1edbi. Hi\u1ec7n t\u1ea1i b\u1ea1n \u0111ang c\u00f3 s\u1eb5n m\u1ed9t s\u1ed1 ti\u1ec1n nh\u01b0ng kh\u00f4ng \u0111\u1ee7 \u0111\u1ec3 mua. V\u00ec v\u1eady b\u1ea1n l\u00ean k\u1ebf ho\u1ea1ch ti\u1ebft ki\u1ec7m ti\u1ec1n t\u1eeb ng\u00e0y 01\/02\/2020 \u0111\u1ebfn ng\u00e0y 31\/03\/2020 . Th\u00e1ng T\u01b0, B\u00ecnh r\u1ee7 An \u0111\u1ebfn c\u1eeda h\u00e0ng \u0111\u1ec3 mua gi\u00e0y. Sau khi mua gi\u00e0y xong, B\u00ecnh mua hai th\u00eam hai ly tr\u00e0 s\u1eefa v\u1edbi gi\u00e1 30000 \u0111\u1ed3ng m\u1ed9t ly th\u00ec B\u00ecnh c\u00f2n d\u01b0 l\u1ea1i 60000 \u0111\u1ed3ng. G\u1ecdi y (\u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n b\u1ea1n B\u00ecnh c\u00f3 s\u1eb5n, x (\u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n b\u1ea1n \u0111\u1ec3 d\u00e0nh m\u1ed7i ng\u00e0y t\u1eeb 01\/02\/2020 \u0111\u1ebfn 31\/03\/2020 . a) L\u1eadp h\u00e0m s\u1ed1 y theo x bi\u1ebft gi\u00e1 \u0111\u00f4i gi\u00e0y b\u1ea1n mua l\u00e0 680000 \u0111\u1ed3ng. b) Bi\u1ebft s\u1ed1 ti\u1ec1n b\u1ea1n B\u00ecnh c\u00f3 s\u1eb5n do \u00f4ng b\u00e0 l\u00ec x\u00ec T\u1ebft l\u00e0 200000 \u0111\u1ed3ng. H\u1ecfi \u0111\u1ec3 c\u00f3 ti\u1ec1n mua gi\u00e0y th\u00ec m\u1ed7i ng\u00e0y B\u00ecnh ph\u1ea3i ti\u1ebft ki\u1ec7m bao nhi\u00eau ti\u1ec1n? 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 6. (1 \u0111i\u1ec3m). M\u1ed9t th\u00e1p \u0111\u1ed3ng h\u1ed3 c\u00f3 ph\u1ea7n d\u01b0\u1edbi c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh d\u00e0i 5m , chi\u1ec1u cao c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt l\u00e0 12m . Ph\u1ea7n tr\u00ean c\u1ee7a th\u00e1p c\u00f3 d\u1ea1ng h\u00ecnh ch\u00f3p \u0111\u1ec1u, c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n chung \u0111\u1ec9nh (h\u00ecnh v\u1ebd). M\u1ed7i c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p d\u00e0i 8 m . a) T\u00ednh theo m\u00e9t chi\u1ec1u cao c\u1ee7a th\u00e1p \u0111\u1ed3ng h\u1ed3? (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t). b) Cho bi\u1ebft th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c V S.h , trong \u0111\u00f3 S l\u00e0 di\u1ec7n t\u00edch m\u1eb7t \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt. Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c V 1 S .h , trong \u0111\u00f3 S l\u00e0 di\u1ec7n t\u00edch m\u1eb7t \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh ch\u00f3p. 3 T\u00ednh th\u1ec3 t\u00edch c\u1ee7a th\u00e1p \u0111\u1ed3ng h\u1ed3 n\u00e0y? (L\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). C\u00e2u 7. (1 \u0111i\u1ec3m). Ba b\u1ea1n T\u00e2m, B\u00ecnh, An \u0111\u00e3 \u0111\u1ec3 d\u00e0nh \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 ti\u1ec1n chu\u1ea9n b\u1ecb cho chuy\u1ebfn \u0111i t\u1eeb thi\u1ec7n do tr\u01b0\u1eddng t\u1ed5 ch\u1ee9c s\u1eafp t\u1edbi. Bi\u1ebft t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m v\u00e0 B\u00ecnh l\u00e0 700000 \u0111\u1ed3ng. S\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m b\u1eb1ng 1 t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh v\u00e0 An. S\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh b\u1eb1ng 1 t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m v\u00e0 An. 3 2 H\u1ecfi m\u1ed7i b\u1ea1n \u0111\u1ec3 d\u00e0nh \u0111\u01b0\u1ee3c bao nhi\u00eau ti\u1ec1n? C\u00e2u 8. (3 \u0111i\u1ec3m) T\u1eeb m\u1ed9t \u0111i\u1ec3m A \u1edf b\u00ean ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n O , v\u1ebd ti\u1ebfp tuy\u1ebfn AB,AC v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n O ( B,C l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OA v\u00e0 BC . V\u1ebd \u0111\u01b0\u1eddng k\u00ednh CD c\u1ee7a O , AD c\u1eaft O t\u1ea1i M (M kh\u00e1c D ). a) Ch\u1ee9ng minh r\u1eb1ng OA vu\u00f4ng g\u00f3c BC t\u1ea1i H v\u00e0 t\u1ee9 gi\u00e1c AMHC n\u1ed9i ti\u1ebfp. b) BM c\u1eaft AO t\u1ea1i N . Ch\u1ee9ng minh N l\u00e0 trung \u0111i\u1ec3m AH . c) G\u1ecdi I v\u00e0 K l\u00e0 c\u00e1c giao \u0111i\u1ec3m c\u1ee7a AO v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n O ( I n\u1eb1m gi\u1eefa A v\u00e0 K ). Ch\u1ee9ng minh: 1 1 1 . AN AI AK ----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 1x 2. 4 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. BGT: 4 20 2 4 4 1014 x y x2 4 x 24 y 1x 2 1 0 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 1x 2 42 x 2 2x 8 0 x2 x4 Thay x 2 v\u00e0o y 1x 2 , ta \u0111\u01b0\u1ee3c: y 1. Thay x 2 4 v\u00e0o y 1 x 2 , ta \u0111\u01b0\u1ee3c: y 4. 2 V\u1eady 2; 1 , 4; 4 l\u00e0 hai 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 2x 2 13x 6 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 A x1 x2 2 4x1x2 . L\u1eddi gi\u1ea3i S x1 x2 b 13 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: a 2 c P x1.x2 a 3 Ta c\u00f3: A x1 x2 2 4x1x2 A x 2 2x1x2 x 2 4x1x2 1 2 A x1 x2 2 8x1x2 A 13 2 8.( 3) 2 A 265 . 4 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 c\u1eeda h\u00e0ng Pizza c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i: gi\u1ea3m 30% cho b\u00e1nh Pizza h\u1ea3i s\u1ea3n c\u00f3 gi\u00e1 b\u00e1n ban \u0111\u1ea7u l\u00e0 210000 \u0111\u1ed3ng\/c\u00e1i. N\u1ebfu kh\u00e1ch h\u00e0ng c\u00f3 th\u1ebb VIP th\u00ec s\u1ebd \u0111\u01b0\u1ee3c gi\u1ea3m th\u00eam 5% tr\u00ean gi\u00e1 \u0111\u00e3 gi\u1ea3m. H\u1ecfi m\u1ed9t nh\u00f3m nh\u00e2n vi\u00ean v\u0103n ph\u00f2ng \u0111\u1eb7t mua 60 c\u00e1i b\u00e1nh Pizza h\u1ea3i s\u1ea3n \u1edf c\u1eeda h\u00e0ng trong \u0111\u00f3 c\u00f3 25 c\u00e1i d\u00f9ng th\u1ebb VIP th\u00ec ph\u1ea3i tr\u1ea3 t\u1ea5t c\u1ea3 bao nhi\u00eau ti\u1ec1n (l\u00e0m tr\u00f2n ngh\u00ecn \u0111\u1ed3ng)? L\u1eddi gi\u1ea3i Gi\u00e1 m\u1ed9t c\u00e1i b\u00e1nh Pizza h\u1ea3i s\u1ea3n trong ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i: 100% \u2013 30% .210000 147000 (\u0111\u1ed3ng) Gi\u00e1 m\u1ed9t c\u00e1i b\u00e1nh Pizza h\u1ea3i h\u1ea3i trong ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i v\u00e0 c\u00f3 d\u00f9ng th\u1ebb VIP: 100% \u2013 5% .147000 139650 (\u0111\u1ed3ng) Nh\u00f3m nh\u00e2n vi\u00ean v\u0103n ph\u00f2ng \u0111\u1eb7t mua 60 c\u00e1i b\u00e1nh Pizza h\u1ea3i s\u1ea3n trong \u0111\u00f3 c\u00f3 25 c\u00e1i d\u00f9ng th\u1ebb VIP th\u00ec s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 l\u00e0: 147000. 60 25 139650.25 8636250 (\u0111\u1ed3ng) 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 4. (0,75 \u0111i\u1ec3m). Ch\u1ecb An l\u00e0 c\u00f4ng nh\u00e2n may m\u1eb7c c\u1ee7a X\u00ed nghi\u1ec7p A . Ng\u01b0\u1eddi 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 s\u1ed1 y ax b c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh v\u1ebd sau: H\u1ecfi n\u1ebfu mu\u1ed1n nh\u1eadn l\u01b0\u01a1ng 14000000 \u0111\u1ed3ng th\u00ec ch\u1ecb An ph\u1ea3i may bao nhi\u00eau c\u00e1i \u00e1o? L\u1eddi gi\u1ea3i X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b . Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: x 0 8000000 0.a b 1 V\u1edbi y 8000000 x 1300 13200000 1300.a b 2 V\u1edbi y 13200000 T\u1eeb 1 v\u00e0 2 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 0a b 8000000 a 4000 1300a b 13200000 b 8000000 V\u1eady: a 4000 , b 8000000 v\u00e0 y 4000x 8000000 . Thay y 14000000 v\u00e0o y 4000x 8000000 ta suy ra x 1500 . V\u1eady ch\u1ecb A ph\u1ea3i may 1500 c\u00e1i \u00e1o. C\u00e2u 5. (1 \u0111i\u1ec3m) B\u1ea1n B\u00ecnh mu\u1ed1n mua m\u1ed9t \u0111\u00f4i gi\u00e0y th\u1ec3 thao m\u1edbi. Hi\u1ec7n t\u1ea1i b\u1ea1n \u0111ang c\u00f3 s\u1eb5n m\u1ed9t s\u1ed1 ti\u1ec1n nh\u01b0ng kh\u00f4ng \u0111\u1ee7 \u0111\u1ec3 mua. V\u00ec v\u1eady b\u1ea1n l\u00ean k\u1ebf ho\u1ea1ch ti\u1ebft ki\u1ec7m ti\u1ec1n t\u1eeb ng\u00e0y 01\/02\/2020 \u0111\u1ebfn ng\u00e0y 31\/03\/2020 . Th\u00e1ng T\u01b0, B\u00ecnh r\u1ee7 An \u0111\u1ebfn c\u1eeda h\u00e0ng \u0111\u1ec3 mua gi\u00e0y. Sau khi mua gi\u00e0y xong, B\u00ecnh mua hai th\u00eam hai ly tr\u00e0 s\u1eefa v\u1edbi gi\u00e1 30000 \u0111\u1ed3ng m\u1ed9t ly th\u00ec B\u00ecnh c\u00f2n d\u01b0 l\u1ea1i 60000 \u0111\u1ed3ng. G\u1ecdi y (\u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n b\u1ea1n B\u00ecnh c\u00f3 s\u1eb5n, x (\u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n b\u1ea1n \u0111\u1ec3 d\u00e0nh m\u1ed7i ng\u00e0y t\u1eeb 01\/02\/2020 \u0111\u1ebfn 31\/03\/2020 . a) L\u1eadp h\u00e0m s\u1ed1 y theo x bi\u1ebft gi\u00e1 \u0111\u00f4i gi\u00e0y b\u1ea1n mua l\u00e0 680000 \u0111\u1ed3ng. b) Bi\u1ebft s\u1ed1 ti\u1ec1n b\u1ea1n B\u00ecnh c\u00f3 s\u1eb5n do \u00f4ng b\u00e0 l\u00ec x\u00ec T\u1ebft l\u00e0 200000 \u0111\u1ed3ng. H\u1ecfi \u0111\u1ec3 c\u00f3 ti\u1ec1n mua gi\u00e0y th\u00ec m\u1ed7i ng\u00e0y B\u00ecnh ph\u1ea3i ti\u1ebft ki\u1ec7m bao nhi\u00eau ti\u1ec1n? 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 L\u1eddi gi\u1ea3i a) T\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh: 680000 30000.2 60000 800000 \u0111\u1ed3ng t\u1eeb 01\/02\/2020 \u0111\u1ebfn 31\/03\/2020 c\u00f3: 29 31 60 ng\u00e0y. H\u00e0m s\u1ed1 y theo x l\u00e0: y 800000 \u2013 60x . b) V\u1edbi y 200000 ta \u0111\u01b0\u1ee3c: 800000 \u2013 60x 200000 x 10000 V\u1eady \u0111\u1ec3 c\u00f3 \u0111\u1ee7 s\u1ed1 ti\u1ec1n th\u00ec m\u1ed7i ng\u00e0y \u0111\u1ec3 d\u00e0nh 10000 \u0111\u1ed3ng. C\u00e2u 6. (1 \u0111i\u1ec3m) M\u1ed9t th\u00e1p \u0111\u1ed3ng h\u1ed3 c\u00f3 ph\u1ea7n d\u01b0\u1edbi c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh d\u00e0i 5m , chi\u1ec1u cao c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt l\u00e0 12m . Ph\u1ea7n tr\u00ean c\u1ee7a th\u00e1p c\u00f3 d\u1ea1ng h\u00ecnh ch\u00f3p \u0111\u1ec1u, c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n chung \u0111\u1ec9nh (h\u00ecnh v\u1ebd). M\u1ed7i c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p d\u00e0i 8 m . a) T\u00ednh theo m\u00e9t chi\u1ec1u cao c\u1ee7a th\u00e1p \u0111\u1ed3ng h\u1ed3? (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t). b) Cho bi\u1ebft th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c V S.h , trong \u0111\u00f3 S l\u00e0 di\u1ec7n t\u00edch m\u1eb7t \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt. Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c V 1 S.h , trong \u0111\u00f3 S l\u00e0 di\u1ec7n t\u00edch m\u1eb7t \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh ch\u00f3p. 3 T\u00ednh th\u1ec3 t\u00edch c\u1ee7a th\u00e1p \u0111\u1ed3ng h\u1ed3 n\u00e0y? (L\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). L\u1eddi gi\u1ea3i a) \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o A C c\u1ee7a h\u00ecnh vu\u00f4ng A B C D l\u00e0: A C 5 2 m . Suy ra O C AC 5 2 m . 2 2 \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pytago cho SO C vu\u00f4ng t\u1ea1i O ta c\u00f3 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 SC 2 SO 2 O C 2 82 SO 2 2 52 2 SO 2 103 2 SO 7,2 V\u1eady chi\u1ec1u cao c\u1ee7a th\u00e1p kho\u1ea3ng 19,2m . b) Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt: V1 S.h 5.5.12 300 m3 Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p: V2 1 S.h 1 5.5.7, 2 60m3 Th\u1ec3 t\u00edch c\u1ee7a th\u00e1p \u0111\u1ed3ng h\u1ed3: 3 3 V V1 V2 300 60 360 m3 C\u00e2u 7. (1 \u0111i\u1ec3m) Ba b\u1ea1n T\u00e2m, B\u00ecnh, An \u0111\u00e3 \u0111\u1ec3 d\u00e0nh \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 ti\u1ec1n chu\u1ea9n b\u1ecb cho chuy\u1ebfn \u0111i t\u1eeb thi\u1ec7n do tr\u01b0\u1eddng t\u1ed5 ch\u1ee9c s\u1eafp t\u1edbi. Bi\u1ebft t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m v\u00e0 B\u00ecnh l\u00e0 700000 \u0111\u1ed3ng. S\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m b\u1eb1ng 1 t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh v\u00e0 An. S\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh b\u1eb1ng 1 t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m v\u00e0 An. H\u1ecfi 3 2 m\u1ed7i b\u1ea1n \u0111\u1ec3 d\u00e0nh \u0111\u01b0\u1ee3c bao nhi\u00eau ti\u1ec1n? L\u1eddi gi\u1ea3i G\u1ecdi x (ngh\u00ecn \u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n c\u1ee7a An v\u00e0 y (ngh\u00ecn \u0111\u1ed3ng) l\u00e0 s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m. (\u0110K: x,y 0) S\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh l\u00e0: 700 \u2013 x (ngh\u00ecn \u0111\u1ed3ng) S\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m b\u1eb1ng 1 t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh v\u00e0 An 3 n\u00ean y 1 700 y x (1) 3 S\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh b\u1eb1ng 1 t\u1ed5ng s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m v\u00e0 An 2 n\u00ean 700 \u2013 y 1y x (2) 2 y 1 700 y x 3 x T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 1y 700 \u2013 y 2 1x 4y 700 x 500 33 3 y 300 (nh\u1eadn) 1 3 2 x 2 y 700 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 V\u1eady s\u1ed1 ti\u1ec1n c\u1ee7a An l\u00e0: 500 ng\u00ecn \u0111\u1ed3ng. s\u1ed1 ti\u1ec1n c\u1ee7a T\u00e2m l\u00e0: 300 ng\u00ecn \u0111\u1ed3ng. s\u1ed1 ti\u1ec1n c\u1ee7a B\u00ecnh l\u00e0: 400 ng\u00ecn \u0111\u1ed3ng. C\u00e2u 8. (3 \u0111i\u1ec3m) T\u1eeb m\u1ed9t \u0111i\u1ec3m A \u1edf b\u00ean ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n O , v\u1ebd ti\u1ebfp tuy\u1ebfn AB,AC v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n O ( B,C l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OA v\u00e0 BC . V\u1ebd \u0111\u01b0\u1eddng k\u00ednh CD c\u1ee7a O , AD c\u1eaft O t\u1ea1i M (M kh\u00e1c D ). a) Ch\u1ee9ng minh r\u1eb1ng OA vu\u00f4ng g\u00f3c BC t\u1ea1i H v\u00e0 t\u1ee9 gi\u00e1c AMHC n\u1ed9i ti\u1ebfp. b) BM c\u1eaft AO t\u1ea1i N . Ch\u1ee9ng minh N l\u00e0 trung \u0111i\u1ec3m AH . c) G\u1ecdi I v\u00e0 K l\u00e0 c\u00e1c giao \u0111i\u1ec3m c\u1ee7a AO v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n O ( I n\u1eb1m gi\u1eefa A v\u00e0 K ). Ch\u1ee9ng 1 11 minh: AN AI AK . L\u1eddi gi\u1ea3i BD M A NI HO K C 8 a) Ch\u1ee9ng minh r\u1eb1ng OA vu\u00f4ng g\u00f3c BC t\u1ea1i H v\u00e0 t\u1ee9 gi\u00e1c AMHC n\u1ed9i ti\u1ebfp. Ta c\u00f3: AB AC (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) OB OC (hai b\u00e1n k\u00ednh) OA l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a BC OA BC t\u1ea1i H . Ta c\u00f3: DMC 90 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) AMC 90 (k\u1ec1 b\u00f9 v\u1edbi DMC ) M\u00e0 AHC 90 ( v\u00ec OA BC t\u1ea1i H ) AHC AMC 90 T\u1ee9 gi\u00e1c AMHC n\u1ed9i ti\u1ebfp. 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 b) BM c\u1eaft AO t\u1ea1i N . Ch\u1ee9ng minh N l\u00e0 trung \u0111i\u1ec3m AH . X\u00e9t NAM v\u00e0 NBA c\u00f3: \uf096 ANM chung \uf096 MAN ABM (= MCB ) NAM NBA (g-g) NA NM NA2 NM.NB . NB NA T\u01b0\u01a1ng t\u1ef1 c\/m \u0111\u01b0\u1ee3c: NH 2 MN.NB ( NHM NBH ). NA2 NH 2 NA NH V\u1eady N l\u00e0 trung \u0111i\u1ec3m AH . c) G\u1ecdi I v\u00e0 K l\u00e0 c\u00e1c giao \u0111i\u1ec3m c\u1ee7a AO v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n O ( I n\u1eb1m gi\u1eefa A v\u00e0 K ). 11 1 Ch\u1ee9ng minh: AN AI AK Ta c\u00f3: 1 1 AK AI AO OK AO OI 2.OA AI AK AK .AI AK .AI AK .AI Ch\u1ee9ng minh \u0111\u01b0\u1ee3c ABI AKB (g.g) AB2 AK.AI H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong ABO vu\u00f4ng BA2 AH.AO AK.AI AH.AO Suy ra 1 1 2.OA 2 AI AK AH .AO AH M\u00e0 AH 2.AN ( v\u00ec N l\u00e0 trung \u0111i\u1ec3m AH ) Suy ra: 1 1 1 . AI AK AN ----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 L\u1edaP 10 PH\u00d2NG GD & \u0110T QU\u1eacN G\u00d2 V\u1ea4P N\u0102M H\u1eccC: 2023 - 2024 M\u00d4N: TO\u00c1N 9 \u0110\u1ec0 THAM KH\u1ea2O \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. M\u00c3 \u0110\u1ec0: Qu\u1eadn G\u00f2 V\u1ea5p - 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 = \u22121 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = \u22123 x . 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 3x2 \u2212 5x \u2212 4 = 0 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh. T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A= (2x13x2 \u2212 2023) + 2 x2 ( 3x1 \u2212 2023 ) 3 3 C\u00e2u 3. (1 \u0111i\u1ec3m). B\u1ebfn xe Mi\u1ec1n \u0110\u00f4ng m\u1edbi \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf theo m\u00f4 h\u00ecnh Transit Oriented Development (vi\u1ebft t\u1eaft l\u00e0 TOD) \u2013 l\u00e0 m\u00f4 h\u00ecnh \u0111\u1ecbnh h\u01b0\u1edbng ph\u00e1t tri\u1ec3n giao th\u00f4ng c\u00f4ng c\u1ed9ng l\u00e0m c\u01a1 s\u1edf quy ho\u1ea1ch ph\u00e1t tri\u1ec3n c\u1ee7a \u0111\u00f4 th\u1ecb, l\u1ea5y giao th\u00f4ng l\u00e0m \u0111i\u1ec3m t\u1eadp trung d\u00e2n c\u01b0 \u0111\u1ec3 t\u1eeb \u0111\u00f3 h\u00ecnh th\u00e0nh h\u1ec7 th\u1ed1ng giao th\u00f4ng ph\u00e2n t\u00e1n, m\u00f4 h\u00ecnh n\u00e0y r\u1ea5t ph\u00e1t tri\u1ec3n tr\u00ean th\u1ebf gi\u1edbi. M\u1ed9t xe \u00f4 t\u00f4 ch\u1edf kh\u00e1ch \u0111i t\u1eeb b\u1ebfn xe Mi\u1ec1n \u0110\u00f4ng m\u1edbi h\u01b0\u1edbng v\u1ec1 Mi\u1ec1n Trung; qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a xe c\u00e1ch Trung t\u00e2m Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh l\u00e0 (s) v\u00e0 th\u1eddi gian xe ch\u1ea1y (t ) \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t s = at + b v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 sau: (L\u01b0u \u00fd: H\u1ecdc sinh kh\u00f4ng c\u1ea7n v\u1ebd h\u00ecnh) a) X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean. b) Sau 4 gi\u1edd, xe \u0111\u00e3 c\u00e1ch trung t\u00e2m Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh bao nhi\u00eau km; bi\u1ebft xe c\u00f3 gh\u00e9 ngh\u1ec9 ng\u01a1i t\u1ea1i tr\u1ea1m d\u1eebng ch\u00e2n 45 ph\u00fat C\u00e2u 4. (0,75 \u0111i\u1ec3m). Cu\u1ed1i tu\u1ea7n, m\u1ed9t nh\u00f3m b\u1ea1n mu\u1ed1n \u0111i th\u01b0 gi\u00e3n b\u1eb1ng c\u00e1ch c\u1eafm tr\u1ea1i ngo\u00e0i tr\u1eddi. \u0110\u1ec3 che n\u1eafng che m\u01b0a trong l\u00fac c\u1eafm tr\u1ea1i, c\u00e1c b\u1ea1n quy\u1ebft \u0111\u1ecbnh d\u1ef1ng l\u1ec1u ch\u1eef A . Theo t\u00ednh to\u00e1n c\u1ee7a nh\u00f3m, c\u00e1c b\u1ea1n c\u00f3 s\u1eb5n hai c\u00e2y c\u1ecdc c\u00f3 chi\u1ec1u cao 2m . Nh\u00f3m c\u00f3 t\u1ea5m b\u1ea1t d\u00e0i 6m th\u00ec c\u00f3 th\u1ec3 d\u1ef1ng l\u1ec1u ch\u1eef A v\u1edbi g\u00f3c t\u1ea1o b\u1edfi t\u1ea5m b\u1ea1t v\u00e0 m\u1eb7t \u0111\u1ea5t l\u00e0 bao nhi\u00eau \u0111\u1ed9? A 2m BHC C\u00e2u 5. (1 \u0111i\u1ec3m). M\u1ed9t ng\u01b0\u1eddi \u0111i si\u00eau th\u1ecb mua hai m\u00f3n h\u00e0ng. M\u00f3n th\u1ee9 nh\u1ea5t c\u00f3 gi\u00e1 ni\u00eam y\u1ebft l\u00e0 4 tri\u1ec7u. Nh\u01b0ng \u0111\u00fang v\u00e0o \u0111\u1ee3t khuy\u1ebfn m\u00e3i n\u00ean m\u00f3n h\u00e0ng th\u1ee9 nh\u1ea5t \u0111\u01b0\u1ee3c gi\u1ea3m 10% , c\u00f2n m\u00f3n h\u00e0ng th\u1ee9 hai \u0111\u01b0\u1ee3c gi\u1ea3m 8% n\u00ean ng\u01b0\u1eddi \u0111\u00f3 ph\u1ea3i tr\u1ea3 6,36 tri\u1ec7u \u0111\u1ed3ng. H\u1ecfi gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u00f3n h\u00e0ng th\u1ee9 hai l\u00e0 bao nhi\u00eau? 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 6. (1 \u0111i\u1ec3m). M\u1ed9t qu\u00e1n tr\u00e0 s\u1eefa c\u00f3 ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i mua 4 t\u1eb7ng 1 v\u1edbi m\u1eb7t hang tr\u00e0 s\u1eefa gi\u00e1 30000 \u0111\u1ed3ng \/ly Trong m\u1ed9t ng\u00e0y, s\u1ed1 l\u01b0\u1ee3ng ng\u01b0\u1eddi mua tr\u00e0 s\u1eefa \u0111\u01b0\u1ee3c th\u1ed1ng k\u00ea l\u1ea1i qua b\u1ea3ng sau: S\u1ed1 ly S\u1ed1 ng\u01b0\u1eddi 1 ly 15 2 ly 20 3 ly 10 4 ly 20 5 ly 10 6 ly 5 a) T\u00ednh s\u1ed1 ly tr\u00e0 s\u1eefa m\u00e0 qu\u00e1n \u0111\u00e3 l\u00e0m cho kh\u00e1ch h\u00e0ng? b) N\u1ebfu gi\u00e1 v\u1ed1n \u0111\u1ec3 l\u00e0m m\u1ed9t ly tr\u00e0 s\u1eefa l\u00e0 25000 \u0111\u1ed3ng, thu\u1ebf ph\u1ea3i n\u1ed9p l\u00e0 10% tr\u00ean t\u1ed5ng s\u1ed1 ti\u1ec1n b\u00e1n th\u00ec ng\u00e0y h\u00f4m \u0111\u00f3 qu\u00e1n c\u00f3 l\u1eddi hay kh\u00f4ng? V\u00e0 l\u1eddi bao nhi\u00eau ti\u1ec1n? C\u00e2u 7. (1 \u0111i\u1ec3m). Tr\u00f2 Ch\u01a1i X\u00c2Y TH\u00c1P WOODY TOWER WD012 bao g\u1ed3m 48 thanh 6 m\u00e0u \u0111\u01b0\u1ee3c l\u00e0m t\u1eeb ch\u1ea5t li\u1ec7u g\u1ed7, c\u00f3 th\u1ec3 ch\u01a1i m\u1ed9t ho\u1eb7c nhi\u1ec1u ng\u01b0\u1eddi, m\u1ed7i l\u01b0\u1ee3t ng\u01b0\u1eddi ch\u01a1i r\u00fat ra m\u1ed9t thanh g\u1ed7 t\u1eeb t\u00f2a th\u00e1p v\u00e0 \u0111\u1eb7t thanh g\u1ed7 r\u00fat ra \u0111\u00f3 l\u00ean tr\u00ean \u0111\u1ec9nh m\u00e0 kh\u00f4ng l\u00e0m \u0111\u1ed5 th\u00e1p. Tr\u00f2 ch\u01a1i ti\u1ebfp t\u1ee5c nh\u01b0 v\u1eady, v\u1edbi m\u1ed7i l\u01b0\u1ee3t c\u1ee7a t\u1eebng ng\u01b0\u1eddi ch\u01a1i cho \u0111\u1ebfn khi th\u00e1p \u0111\u1ed5. M\u1ed7i thanh l\u00e0 m\u1ed9t h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc 1,5cm x 2cm x 7,5cm ; \u0111\u01b0\u1ee3c \u0111\u1ef1ng v\u00e0o m\u1ed9t h\u1ed9p c\u00f3 k\u00edch th\u01b0\u1edbc 8cm x 8cm x 27cm . a) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u1ed9p \u0111\u1ef1ng 48 thanh g\u1ed7? b) H\u1ecfi th\u1ec3 t\u00edch c\u00e1c thanh g\u1ed7 m\u00e0u \u0111\u1ecf v\u00e0 t\u00edm trong h\u1ed9p chi\u1ebfm bao nhi\u00eau ph\u1ea7n tr\u0103m th\u1ec3 t\u00edch h\u1ed9p (C\u00e1c k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai sau d\u1ea5u ph\u1ea9y) C\u00e2u 8. (3 \u0111i\u1ec3m) Cho \u0111\u01b0\u1eddng tr\u00f2n (O) v\u00e0 \u0111i\u1ec3m A n\u1eb1m ngo\u00e0i (O) . T\u1eeb A v\u1ebd hai ti\u1ebfp tuy\u1ebfn AB, AC c\u1ee7a (O) ( B,C l\u00e0 hai ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AO v\u00e0 BC . Qua A v\u1ebd c\u00e1t tuy\u1ebfn ADE c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n (O) (D, E thu\u1ed9c (O)) sao cho \u0111\u01b0\u1eddng th\u1eb3ng AE c\u1eaft \u0111o\u1ea1n th\u1eb3ng HB t\u1ea1i I . G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m d\u00e2y cung DE . a) Ch\u1ee9ng minh: 5 \u0111i\u1ec3m A, B,O, M ,C c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n; suy ra MA l\u00e0 tia ph\u00e2n gi\u00e1c g\u00f3c BMC . b) Ch\u1ee9ng minh: t\u1ee9 gi\u00e1c OHDE n\u1ed9i ti\u1ebfp. c) Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia HD l\u1ea5y \u0111i\u1ec3m F sao cho H l\u00e0 trung \u0111i\u1ec3m DF . Tia AO c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng EF t\u1ea1i K . Ch\u1ee9ng minh: IK \/ \/DF . ----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 = \u22121 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = \u22123 x . 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. 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 = \u2212 1 x2 \u22124 \u22121 0 \u22121 \u22124 4 x 04 y = \u22123 x 0 \u22123 4 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) : \u2212 1 x2 = \u22123 x 44 \uf0db x2 \u2212 3x = 0 \uf0db \uf0e9x = 0 \uf0ea\uf0ebx = 3 Thay x = 0 v\u00e0o y = \u2212 1 x2 , ta \u0111\u01b0\u1ee3c: y = 0 . 4 Thay x = 3 v\u00e0o y = \u2212 1 x2 , ta \u0111\u01b0\u1ee3c: y = \u22129 . 44 V\u1eady ( 0; 0 ), \uf0e6 3; \u2212 9 \uf0f6 l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. \uf0e7 4 \uf0f7 \uf0e8 \uf0f8 C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 3x2 \u2212 5x \u2212 4 = 0 . Kh\u00f4ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh. 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 T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c A= (2 x1 3x2 \u2212 2023) + (2x23x1 \u2212 2023) 3 3 L\u1eddi gi\u1ea3i V\u00ec a.c = 3.(\u22124) = \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 = x1 a3 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP c =\u22124 a .x2 = 3 Ta c\u00f3: A= (2x1 3x2 \u2212 2023) + (2 x2 3x1 \u2212 2023) 3 3 A = 2x1x2 \u2212 4046 x1 + 2x1x2 \u2212 4046 x2 3 3 ( )A = 4046 4x1x2 \u2212 3 x1 + x2 A = 4. \u22124 \u2212 4046 \uf0e6 5 \uf0f6 = \u221220278 3 3 \uf0e7 3 \uf0f7 9 \uf0e8 \uf0f8 C\u00e2u 3. (1 \u0111i\u1ec3m). B\u1ebfn xe Mi\u1ec1n \u0110\u00f4ng m\u1edbi \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf theo m\u00f4 h\u00ecnh Transit Oriented Development (vi\u1ebft t\u1eaft l\u00e0 TOD) \u2013 l\u00e0 m\u00f4 h\u00ecnh \u0111\u1ecbnh h\u01b0\u1edbng ph\u00e1t tri\u1ec3n giao th\u00f4ng c\u00f4ng c\u1ed9ng l\u00e0m c\u01a1 s\u1edf quy ho\u1ea1ch ph\u00e1t tri\u1ec3n c\u1ee7a \u0111\u00f4 th\u1ecb, l\u1ea5y giao th\u00f4ng l\u00e0m \u0111i\u1ec3m t\u1eadp trung d\u00e2n c\u01b0 \u0111\u1ec3 t\u1eeb \u0111\u00f3 h\u00ecnh th\u00e0nh h\u1ec7 th\u1ed1ng giao th\u00f4ng ph\u00e2n t\u00e1n, m\u00f4 h\u00ecnh n\u00e0y r\u1ea5t ph\u00e1t tri\u1ec3n tr\u00ean th\u1ebf gi\u1edbi. M\u1ed9t xe \u00f4 t\u00f4 ch\u1edf kh\u00e1ch \u0111i t\u1eeb b\u1ebfn xe Mi\u1ec1n \u0110\u00f4ng m\u1edbi h\u01b0\u1edbng v\u1ec1 Mi\u1ec1n Trung; qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a xe c\u00e1ch Trung t\u00e2m Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh l\u00e0 (s) v\u00e0 th\u1eddi gian xe ch\u1ea1y (t ) \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t s = at + b v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 sau: (L\u01b0u \u00fd: H\u1ecdc sinh kh\u00f4ng c\u1ea7n v\u1ebd h\u00ecnh) a) X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean b) Sau 4 gi\u1edd, xe \u0111\u00e3 c\u00e1ch trung t\u00e2m Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh bao nhi\u00eau km; bi\u1ebft xe c\u00f3 gh\u00e9 ngh\u1ec9 ng\u01a1i t\u1ea1i tr\u1ea1m d\u1eebng ch\u00e2n 45 ph\u00fat L\u1eddi gi\u1ea3i a) X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a v\u00e0 b c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean. Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 4"]