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 ( )Theo \uf0ec = x1 + x2 = \u2212b = \u2212 \u22126 =3 \uf0ef\uf0efS a 2 \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ed c \u22121 \uf0ef\uf0ef\uf0eeP = x1 .x2 = a = 2 Ta c\u00f3: A = x1 \u2212 2 + x2 \u2212 2 x2 \u2212 1 x1 \u2212 1 A = x1 \u2212 2 + x2 \u2212 2 x2 \u2212 1 x1 \u2212 1 = ( x1 \u2212 2)(x1 \u2212 1) + (x2 \u2212 2)(x2 \u2212 1) (x2 \u2212 1)(x1 \u2212 1) = x12 \u2212 x1 \u2212 2x1 + 2 + x22 \u2212 x2 \u2212 2x2 + 2 x2x1 \u2212 x2 \u2212 x1 + 1 ( ) ( )= x12 + x22 \u2212 3 x1 + x2 + 4 ( )x1x2 \u2212 x1 + x2 + 1 = S2 \u2212 2P \u2212 3S + 4 P\u2212S+1 32 \u2212 2 \uf0e6 \u2212 1 \uf0f6 \u2212 3.3 + 4 \uf0e7\uf0e8 2 \uf0f7\uf0f8 = \u22121 \u2212 3 + 1 2 = \u22122 C\u00e2u 3. V\u1edbi thi\u1ebft k\u1ebf \u0111\u1ed9c \u0111\u00e1o, c\u1ed5ng Parabol tr\u01b0\u1eddng \u0110\u1ea1i h\u1ecdc B\u00e1ch Khoa H\u00e0 N\u1ed9i \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng c\u00e1ch \u0111\u00e2y h\u01a1n 50 n\u0103m v\u00e0 \u0111\u00e3 t\u1eebng l\u00e0 ni\u1ec1m t\u1ef1 h\u00e0o c\u1ee7a tri th\u1ee9c th\u1ebf h\u1ec7 m\u1edbi. \u0110\u1ec3 \u0111o chi\u1ec1u cao c\u1ee7a c\u1ed5ng m\u1ed9t b\u1ea1n sinh vi\u00ean cao 1,6m \u0111\u1ee9ng c\u00e1ch ch\u00e2n c\u1ed5ng 0,5m th\u00ec \u0111\u1ec9nh \u0111\u1ea7u b\u1ea1n \u1ea5y v\u1eeba ch\u1ea1m v\u00e0o c\u1ed5ng. Bi\u1ebft kho\u1ea3ng c\u00e1ch gi\u1eefa hai ch\u00e2n c\u1ed5ng l\u00e0 9m. H\u00e3y t\u00ednh chi\u1ec1u cao c\u1ed5ng Parabol (l\u00e0m tr\u00f2n m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n) L\u1eddi gi\u1ea3i Ta c\u00f3: AH AB 4, 5m ; MK NH AH AN 4, 5 0, 5 4m . 2 \u0110\u1eb7t h\u1ec7 tr\u1ee5c Oxy nh\u01b0 h\u00ecnh v\u1ebd, ta th\u1ea5y \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y ax 2 \u0110\u1eb7t OH h h 0 \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111i qua hai \u0111i\u1ec3m A 9; h v\u00e0 M 4; (h 1, 6) . 2 Thay hai \u0111i\u1ec3m A v\u00e0 M v\u00e0o h\u00e0m s\u1ed1 ta c\u00f3 h\u1ec7 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 h a. 9 2 42 h 81a 16a 2 4 h 1, 6 a. 81a 1, 6 4 a 32 Ta gi\u1ea3i t\u00ecm \u0111\u01b0\u1ee3c 85 h 648 85 7, 6m V\u1eady chi\u1ec1u cao c\u1ed5ng Parabol l\u00e0 7, 6m . C\u00e2u 4. G\u1ea1ch \u1ed1ng l\u00e0 m\u1ed9t s\u1ea3n ph\u1ea9m \u0111\u01b0\u1ee3c t\u1ea1o h\u00ecnh th\u00e0nh t\u1eeb \u0111\u1ea5t s\u00e9t v\u00e0 n\u01b0\u1edbc, \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p l\u1ea1i v\u1edbi nhau theo m\u1ed9t c\u00f4ng th\u1ee9c chung h\u1ee3p l\u00fd m\u1edbi c\u00f3 th\u1ec3 t\u1ea1o ra h\u1ed7n h\u1ee3p d\u1ebbo qu\u00e1nh, sau \u0111\u00f3 ch\u00fang \u0111\u01b0\u1ee3c \u0111\u1ed5 v\u00e0o khu\u00f4n, r\u1ed3i \u0111em ph\u01a1i ho\u1eb7c s\u1ea5y kh\u00f4 v\u00e0 cu\u1ed1i c\u00f9ng l\u00e0 \u0111\u01b0a v\u00e0o l\u00f2 nung. M\u1ed9t vi\u00ean g\u1ea1ch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc d\u00e0i 20cm, r\u1ed9ng 8cm. B\u00ean trong c\u00f3 b\u1ed1n l\u1ed7 h\u00ecnh tr\u1ee5 b\u1eb1ng nhau c\u00f3 \u0111\u01b0\u1eddng k\u00ednh 2,5cm. a. T\u00ednh th\u1ec3 t\u00edch \u0111\u1ea5t s\u00e9t \u0111\u1ec3 l\u00e0m m\u1ed9t vi\u00ean g\u1ea1ch. (l\u1ea5y 3,14 ) b. Theo to\u00e1n h\u1ecdc, b\u00e1c Ba mu\u1ed1n x\u00e2y m\u1ed9t ng\u00f4i nh\u00e0 ph\u1ea3i mua 10 thi\u00ean g\u1ea1ch, gi\u00e1 m\u1ed9t vi\u00ean l\u00e0 1100 \u0111\u1ed3ng. Nh\u01b0ng khi thi c\u00f4ng, b\u00e1c Ba ph\u1ea3i mua d\u01b0 2% s\u1ed1 g\u1ea1ch c\u1ea7n d\u00f9ng d\u1ef1 ph\u00f2ng cho h\u01b0 hao. T\u00ednh s\u1ed1 ti\u1ec1n b\u00e1c Ba mua g\u1ea1ch \u0111\u1ec3 x\u00e2y c\u0103n nh\u00e0, bi\u1ebft 1 thi\u00ean g\u1ea1ch l\u00e0 1000 vi\u00ean. L\u1eddi gi\u1ea3i a) -Th\u1ec3 t\u00edch \u0111\u1ea5t s\u00e9t l\u00e0m vi\u00ean g\u1ea1ch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ch\u01b0a tr\u1eeb b\u1ed1n l\u1ed7 r\u1ed7ng b\u00ean trong l\u00e0: V 8.8.20 320 cm3 Th\u1ec3 t\u00edch c\u1ee7a b\u1ed1n l\u1ed7 h\u00ecnh tr\u1ee5 b\u1eb1ng nhau l\u00e0: V1 R2h 3,14. 2, 5 2 98,125 cm3 2 .20 Th\u1ec3 t\u00edch \u0111\u1ea5t s\u00e9t \u0111\u1ec3 l\u00e0m m\u1ed9t vi\u00ean g\u1ea1ch l\u00e0: V2 V V1 320 98,125 221, 9 cm3 b) S\u1ed1 vi\u00ean g\u1ea1ch b\u00e1c Ba c\u1ea7n mua l\u00e0: 10.1000. 1 2% 10200 (vi\u00ean g\u1ea1ch) S\u1ed1 ti\u1ec1n b\u00e1c Ba mua g\u1ea1ch \u0111\u1ec3 x\u00e2y c\u0103n nh\u00e0 l\u00e0: 10200.1100 11220000 (\u0111\u1ed3ng) C\u00e2u 5. M\u1ed9t nh\u00f3m h\u1ecdc sinh tham gia ho\u1ea1t \u0111\u1ed9ng ngo\u1ea1i kh\u00f3a \u0111\u01b0\u1ee3c chia th\u00e0nh c\u00e1c t\u1ed5 \u0111\u1ec3 sinh ho\u1ea1t. N\u1ebfu m\u1ed7i t\u1ed5 c\u00f3 7 nam v\u00e0 7 n\u1eef th\u00ec th\u1eeba 8 b\u1ea1n nam. N\u1ebfu m\u1ed7i t\u1ed5 c\u00f3 6 nam v\u00e0 5 n\u1eef th\u00ec th\u1eeba 12 n\u1eef. H\u1ecfi c\u00f3 bao nhi\u00eau h\u1ecdc sinh nam v\u00e0 bao nhi\u00eau h\u1ecdc sinh n\u1eef? L\u1eddi gi\u1ea3i G\u1ecdi x,y (s\u1ed1 t\u1ed5) l\u1ea7n l\u01b0\u1ee3t l\u00e0 s\u1ed1 t\u1ed5 trong tr\u01b0\u1eddng h\u1ee3p 1 v\u00e0 tr\u01b0\u1eddng h\u1ee3p 2 . \u0110i\u1ec1u ki\u1ec7n: x,y * 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 8 (h\u1ecdc sinh) v\u00e0 N\u1ebfu m\u1ed7i t\u1ed5 c\u00f3 7 nam v\u00e0 7 n\u1eef th\u00ec th\u1eeba 8 b\u1ea1n nam n\u00ean s\u1ed1 h\u1ecdc sinh nam l\u00e0 7x s\u1ed1 h\u1ecdc sinh n\u1eef l\u00e0 7x (h\u1ecdc sinh). N\u1ebfu m\u1ed7i t\u1ed5 c\u00f3 6 nam v\u00e0 5 n\u1eef th\u00ec th\u1eeba 12 n\u1eef th\u00ec s\u1ed1 h\u1ecdc sinh nam l\u00e0 6y (h\u1ecdc sinh) v\u00e0 s\u1ed1 h\u1ecdc sinh n\u1eef l\u00e0 5y 12 (h\u1ecdc sinh). 7x 8 6y Ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 7x 5y 12 Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c x 16;y 20 (nh\u1eadn) V\u1eady s\u1ed1 h\u1ecdc sinh nam l\u00e0 120 h\u1ecdc sinh, s\u1ed1 h\u1ecdc sinh n\u1eef l\u00e0 112 h\u1ecdc sinh. C\u00e2u 6. Trong m\u1ed9t \u0111\u1ee3t khuy\u1ebfn m\u00e3i, si\u00eau th\u1ecb gi\u1ea3m gi\u00e1 cho m\u1eb7t h\u00e0ng A l\u00e0 20% v\u00e0 m\u1eb7t h\u00e0ng B l\u00e0 15% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft. M\u1ed9t kh\u00e1ch h\u00e0ng mua 2 m\u00f3n h\u00e0ng A v\u00e0 1 m\u00f3n h\u00e0ng B ph\u1ea3i tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 362 000 \u0111\u1ed3ng. Nh\u01b0ng n\u1ebfu mua trong khung gi\u1edd v\u00e0ng th\u00ec m\u00f3n h\u00e0ng A \u0111\u01b0\u1ee3c gi\u1ea3m gi\u00e1 30% c\u00f2n m\u00f3n h\u00e0ng B \u0111\u01b0\u1ee3c gi\u1ea3m gi\u00e1 25% so v\u1edbi gi\u00e1 ni\u00eam y\u1ebft. M\u1ed9t ng\u01b0\u1eddi mua 3 m\u00f3n h\u00e0ng A v\u00e0 2 m\u00f3n h\u00e0ng B trong khung gi\u1edd v\u00e0ng n\u00ean ch\u1ec9 tr\u1ea3 s\u1ed1 ti\u1ec1n l\u00e0 552 000 \u0111\u1ed3ng. T\u00ednh gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u1ed7i m\u00f3n h\u00e0ng A v\u00e0 B. L\u1eddi gi\u1ea3i G\u1ecdi x,y (\u0111\u1ed3ng) l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u00f3n h\u00e0ng A v\u00e0 m\u00f3n h\u00e0ng B . \u0110i\u1ec1u ki\u1ec7n: x,y 0 2.x 1 20% y 1 15% 362 000 Theo \u0111\u1ec1 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 3.x. 1 30% 2.y. 1 25% 552 000 1, 6x 0, 85y 362 000 2,1x 1, 5y 552 000 x 120 000 y 200 000 n V\u1eady gi\u00e1 ni\u00eam y\u1ebft c\u1ee7a m\u00f3n h\u00e0ng A l\u00e0 120 000 \u0111\u1ed3ng, c\u1ee7a m\u00f3n h\u00e0ng B l\u00e0 200 000 \u0111\u1ed3ng. C\u00e2u 7. M\u1ed1i quan h\u1ec7 gi\u1eefa thang nhi\u1ec7t \u0111\u1ed9 y (\u0111\u1ed9 F Fahrenheit ) v\u00e0 thang nhi\u1ec7t \u0111\u1ed9 x (\u0111\u1ed9 C Celsius ) \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y ax b . a. T\u00ecm a v\u00e0 b . b. Trong kh\u00f4ng kh\u00ed, t\u1ed1c \u0111\u1ed9 \u00e2m thanh v (t\u00ednh b\u1eb1ng m\u00e9t\/gi\u00e2y) l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t theo nhi\u1ec7t \u0111\u1ed9 t (t\u00ednh b\u1eb1ng C ) \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c: v 0, 06t 331 . H\u00e3y t\u00ednh t\u1ed1c \u0111\u1ed9 \u00e2m thanh t\u1ea1i n\u01a1i c\u00f3 nhi\u1ec7t \u0111\u1ed9 kh\u00f4ng kh\u00ed l\u00e0 0 C, 77 F . 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 x0 a) Thay y 32 v\u00e0o y ax b ta c\u00f3: a.0 b 32 1 . x 10 Thay y 50 v\u00e0o y ax b ta c\u00f3: a.10 b 50 2 . T\u1eeb 1 v\u00e0 2 , gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: a 9 ;b 32 . 5 b) V\u1edbi t1 0 C thay v\u00e0o c\u00f4ng th\u1ee9c v 0, 06t1 331 ta c\u00f3 v 0, 06.0 331 331 m \/ s . V\u1edbi t2 77 F thay y 77 v\u00e0o c\u00f4ng th\u1ee9c y 9x 32 ta c\u00f3 5 77 9 x 32 x 25 C t2 25 C 5 Thay t2 25 C v\u00e0o c\u00f4ng th\u1ee9c v 0, 06t2 331ta c\u00f3 v 0, 06.25 331 332, 5 m \/ s . V\u1eady t\u1ed1c \u0111\u1ed9 \u00e2m thanh t\u1ea1i n\u01a1i c\u00f3 nhi\u1ec7t \u0111\u1ed9 kh\u00f4ng kh\u00ed 0 C l\u00e0 331m \/ s , t\u1ea1i n\u01a1i c\u00f3 nhi\u1ec7t \u0111\u1ed9 kh\u00f4ng kh\u00ed 77 F l\u00e0 332, 5m \/ s . C\u00e2u 8. Cho tam gi\u00e1c ABC c\u00f3 ba g\u00f3c nh\u1ecdn n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (O) , k\u1ebb \u0111\u01b0\u1eddng cao BE c\u1ee7a ABC . G\u1ecdi H v\u00e0 K l\u1ea7n l\u01b0\u1ee3t l\u00e0 ch\u00e2n c\u00e1c \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb E \u0111\u1ebfn AB v\u00e0 BC . a. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BHEK l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp. b. Ch\u1ee9ng minh: BH .BA BK.BC . c. K\u1ebb \u0111\u01b0\u1eddng cao CF c\u1ee7a tam gi\u00e1c ABC F AB v\u00e0 I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a EF . Ch\u1ee9ng minh ba \u0111i\u1ec3m H,I,K th\u1eb3ng h\u00e0ng. 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 BHEK n\u1ed9i ti\u1ebfp X\u00e9t t\u1ee9 gi\u00e1c BHEK , c\u00f3: \uf0ec\uf0efBHE = 90\uf0b0(EH \u22a5 AB) \uf0ed \uf0ef\uf0eeEKB = 90\uf0b0( EK \u22a5 BC ) \uf0de BHE + EKB = 180\uf0b0 \uf0de T\u1ee9 gi\u00e1c BHEK n\u1ed9i ti\u1ebfp v\u00ec c\u00f3 hai g\u00f3c \u0111\u1ed1i b\u00f9 nhau. b) Ch\u1ee9ng minh BH .BA BK.BC X\u00e9t AEB vu\u00f4ng t\u1ea1i E BE AC , c\u00f3 EH l\u00e0 \u0111\u01b0\u1eddng cao EH AB \uf0de EB2 = BH.BA (HTL) 1 X\u00e9t BEC vu\u00f4ng t\u1ea1i E BE AC , c\u00f3 EK l\u00e0 \u0111\u01b0\u1eddng cao EK BC \uf0de EB2 = BK.BC (HTL) 2 T\u1eeb 1 v\u00e0 2 , suy ra: BH.BA BK.BC EB2 c) K\u1ebb \u0111\u01b0\u1eddng cao CF c\u1ee7a tam gi\u00e1c ABC F AB v\u00e0 I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a EF . Ch\u1ee9ng minh ba \u0111i\u1ec3m H,I,K th\u1eb3ng h\u00e0ng. Ta c\u00f3: t\u1ee9 gi\u00e1c BHEK n\u1ed9i ti\u1ebfp BHK BEK ( 2 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn BK ) FHE vu\u00f4ng t\u1ea1i H EH AB c\u00f3 HI l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh EF ( I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a EF ) HI IF EF 2 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 HIF c\u00e2n t\u1ea1i I FHI IFH 3 X\u00e9t t\u1ee9 gi\u00e1c BFEC c\u00f3 BFC 90 CF AB BEC 90 BE AC BFC BEC 90 M\u00e0 hai g\u00f3c n\u00e0y li\u00ean ti\u1ebfp c\u00f9ng nh\u00ecn c\u1ea1nh BC t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp HFE ECB (g\u00f3c trong b\u1eb1ng g\u00f3c \u0111\u1ed1i ngo\u00e0i) 4 M\u1eb7t kh\u00e1c ECB BEK (c\u00f9ng ph\u1ee5 KEC ) 5 T\u1eeb 3 , 4 v\u00e0 5 , suy ra: FHI BEK BHK BEK cmt BHK FHI Ta c\u00f3: FHI BEK cmt H,I,K th\u1eb3ng h\u00e0ng. ----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 1 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 1 - 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. Cho (P) : y = \u2212 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 3x \u2212 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. Cho ph\u01b0\u01a1ng tr\u00ecnh \u2212x2 + 2(2 + m)x \u2212 m2 = 0 ( m l\u00e0 tham s\u1ed1) (1) ( )a) T\u00ecm m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 1 c\u00f3 hai nghi\u1ec7m x1; x2 ? ( )b) V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a m th\u00ec hai nghi\u1ec7m x1; x2 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 1 th\u1ecfa x1 + x2 \u2212 4 = 2x1x2 C\u00e2u 3. Trong l\u1ec5 ph\u00e1t \u0111\u1ed9ng phong tr\u00e0o tr\u1ed3ng c\u00e2y nh\u00e2n d\u1ecbp k\u1ef7 ni\u1ec7m ng\u00e0y sinh B\u00e1c H\u1ed3, l\u1edbp 9A \u0111\u01b0\u1ee3c giao tr\u1ed3ng 360 c\u00e2y. Khi th\u1ef1c hi\u1ec7n c\u00f3 4 b\u1ea1n \u0111\u01b0\u1ee3c \u0111i\u1ec1u \u0111i l\u00e0m vi\u1ec7c kh\u00e1c, n\u00ean m\u1ed7i h\u1ecdc sinh c\u00f2n l\u1ea1i ph\u1ea3i tr\u1ed3ng th\u00eam m\u1ed9t c\u00e2y so v\u1edbi d\u1ef1 \u0111\u1ecbnh. H\u1ecfi l\u1edbp 9A c\u00f3 bao nhi\u00eau h\u1ecdc sinh? (Bi\u1ebft s\u1ed1 c\u00e2y tr\u1ed3ng c\u1ee7a m\u1ed7i h\u1ecdc sinh nh\u01b0 nhau) C\u00e2u 4. Hai ng\u01b0\u1eddi A v\u00e0 B c\u00f9ng \u1edf m\u1ed9t ph\u00eda v\u00e0 c\u00e1ch th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh 50km . C\u1ea3 hai ng\u01b0\u1eddi c\u00f9ng nhau \u0111i tr\u00ean m\u1ed9t con \u0111\u01b0\u1eddng v\u1ec1 ph\u00eda ng\u01b0\u1ee3c h\u01b0\u1edbng v\u1edbi th\u00e0nh ph\u1ed1, ng\u01b0\u1eddi A \u0111i v\u1edbi v\u1eadn t\u1ed1c 30km \/ h v\u00e0 ng\u01b0\u1eddi B \u0111i v\u1edbi v\u1eadn t\u1ed1c 45km \/ h . G\u1ecdi d (km) l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh \u0111\u1ebfn hai ng\u01b0\u1eddi A v\u00e0 B sau khi \u0111i \u0111\u01b0\u1ee3c (t) gi\u1edd. a) L\u1eadp h\u00e0m s\u1ed1 c\u1ee7a d theo t \u0111\u1ed1i v\u1edbi m\u1ed7i ng\u01b0\u1eddi. b) H\u1ecfi n\u1ebfu hai ng\u01b0\u1eddi xu\u1ea5t ph\u00e1t c\u00f9ng m\u1ed9t l\u00fac th\u00ec v\u00e0o th\u1eddi \u0111i\u1ec3m n\u00e0o k\u1ec3 t\u1eeb l\u00fac xu\u1ea5t ph\u00e1t, kho\u1ea3ng c\u00e1ch gi\u1eefa hai ng\u01b0\u1eddi l\u00e0 30km . C\u00e2u 5. B\u00e0 T\u00e1m vay \u1edf m\u1ed9t ng\u00e2n h\u00e0ng 500 tri\u1ec7u \u0111\u1ed3ng \u0111\u1ec3 s\u1ea3n xu\u1ea5t trong th\u1eddi h\u1ea1n 1 n\u0103m. L\u1ebd ra \u0111\u00fang 1 n\u0103m sau b\u00e0 ph\u1ea3i tr\u1ea3 c\u1ea3 ti\u1ec1n v\u1ed1n l\u1eabn ti\u1ec1n l\u00e3i, song b\u00e0 \u0111\u00e3 \u0111\u01b0\u1ee3c ng\u00e2n h\u00e0ng cho k\u00e9o d\u00e0i th\u1eddi h\u1ea1n th\u00eam 1 n\u0103m n\u1eefa, s\u1ed1 ti\u1ec1n l\u00e3i c\u1ee7a n\u0103m \u0111\u1ea7u \u0111\u01b0\u1ee3c g\u1ed9p v\u00e0o v\u1edbi ti\u1ec1n v\u1ed1n \u0111\u1ec3 t\u00ednh l\u00e3i n\u0103m sau v\u00e0 l\u00e3i su\u1ea5t v\u1eabn nh\u01b0 c\u0169. H\u1ebft 2 n\u0103m b\u00e0 t\u00e1m ph\u1ea3i tr\u1ea3 t\u1ea5t c\u1ea3 605 tri\u1ec7u \u0111\u1ed3ng. H\u1ecfi l\u00e3i su\u1ea5t cho vay c\u1ee7a ng\u00e2n h\u00e0ng \u0111\u00f3 l\u00e0 bao nhi\u00eau ph\u1ea7n tr\u0103m m\u1ed9t n\u0103m? 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. D\u00e2y cu-roa l\u00e0 m\u1ed9t trong nh\u1eefng b\u1ed9 truy\u1ec1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00f4ng nghi\u1ec7p. Chi\u1ec1u d\u00e0i d\u00e2y cu-roa \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh theo c\u00f4ng th\u1ee9c: L = 2a + \uf070 (d1 + d2 ) + (d2 )\u2212 d1 2 2 4a Trong \u0111\u00f3: L : Chi\u1ec1u d\u00e0i d\u00e2y cu-roa. a : Kho\u1ea3ng c\u00e1ch t\u00e2m c\u1ee7a 2 pu-ly. d1 : \u0110\u01b0\u1eddng k\u00ednh c\u1ee7a pu-ly 1 (h\u00ecnh tr\u00f2n nh\u1ecf m\u00e0u v\u00e0ng). d2 : \u0110\u01b0\u1eddng k\u00ednh c\u1ee7a pu-ly 2 (h\u00ecnh tr\u00f2n nh\u1ecf m\u00e0u v\u00e0ng) Cho d1 = 10cm , d2 = 20cm , a = 60cm T\u00ednh chi\u1ec1u d\u00e0i c\u1ee7a m\u1ed9t \u0111o\u1ea1n d\u00e2y cu-roa. G\u1ecdi AB l\u00e0 chi\u1ec1u d\u00e0i m\u1ed9t \u0111o\u1ea1n d\u00e2y cu-roa, trong \u0111\u00f3 A, B l\u1ea7n l\u01b0\u1ee3t l\u00e0 ti\u1ebfp \u0111i\u1ec3m tr\u00ean d\u00e2y cua- roa v\u1edbi 2 \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1o b\u1edfi m\u1eb7t c\u1eaft c\u1ee7a 2 pu-ly. T\u00ednh AB C\u00e2u 7. M\u1ed9t b\u00ecnh \u0111\u1ef1ng \u0111\u1ea7y n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n (kh\u00f4ng c\u00f3 \u0111\u00e1y). Ng\u01b0\u1eddi ta th\u1ea3 v\u00e0o \u0111\u00f3 m\u1ed9t kh\u1ed1i c\u1ea7u c\u00f3 \u0111\u01b0\u1eddng k\u00ednh b\u1eb1ng chi\u1ec1u cao c\u1ee7a b\u00ecnh n\u01b0\u1edbc v\u00e0 \u0111o \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch n\u01b0\u1edbc tr\u00e0n ra ngo\u00e0i l\u00e0 18\uf070 dm3 . Bi\u1ebft r\u1eb1ng kh\u1ed1i c\u1ea7u ti\u1ebfp x\u00fac v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c \u0111\u01b0\u1eddng sinh c\u1ee7a h\u00ecnh n\u00f3n v\u00e0 \u0111\u00fang m\u1ed9t n\u1eeda c\u1ee7a kh\u1ed1i c\u1ea7u \u0111\u00e3 ch\u00ecm trong n\u01b0\u1edbc ( h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y). T\u00ednh th\u1ec3 t\u00edch n\u01b0\u1edbc c\u00f2n l\u1ea1i trong b\u00ecnh. C\u00e2u 8. Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O \u0111\u01b0\u1eddng k\u00ednh AB . K\u1ebb d\u00e2y cung CD vu\u00f4ng g\u00f3c v\u1edbi AB t\u1ea1i H ( H n\u1eb1m gi\u1eefa A v\u00e0 O , H kh\u00e1c A v\u00e0 O ). L\u1ea5y \u0111i\u1ec3m G thu\u1ed9c CH ( G kh\u00e1c C v\u00e0 H ), tia AG c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i E kh\u00e1c A . G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng BE v\u00e0 CD a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BEGH n\u1ed9i ti\u1ebfp v\u00e0 KC.KD = KE.KB . b) \u0110o\u1ea1n th\u1eb3ng AK c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m t\u1ea1i F kh\u00e1c A . Ch\u1ee9ng minh: G l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c HEF c) G\u1ecdi M,N l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a A v\u00e0 B l\u00ean \u0111\u01b0\u1eddng th\u1eb3ng EF . Ch\u1ee9ng minh: HE + HF = 1 . 2 MN 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 ----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. Cho (P) : y = \u2212 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 3x \u2212 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: x \u22128 \u22122 0 2 4 y = \u2212 1 x2 \u22128 \u22122 0 \u22122 \u22128 2 x 0 \u22122 y = 3x \u2212 4 4 \u22122 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 = 3x \u2212 4 2 \uf0db x2 + 6x \u2212 8 = 0 \uf0db \uf0e9x = \u22122 \uf0ea\uf0ebx = \u22124 Thay x = \u22122 v\u00e0o y = \u2212 1 x2 , ta \u0111\u01b0\u1ee3c: y = \u22122 . 2 Thay x = \u22124 v\u00e0o y = \u2212 1 x2 , ta \u0111\u01b0\u1ee3c: y = \u22128 . 2 V\u1eady (\u22122; \u2212 2) , (\u22124; \u2212 8) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. Cho ph\u01b0\u01a1ng tr\u00ecnh \u2212x2 + 2(2 + m)x \u2212 m2 = 0 ( m l\u00e0 tham s\u1ed1) (1) ( )a) T\u00ecm m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 1 c\u00f3 hai nghi\u1ec7m x1; x2 ? ( )b) V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a m th\u00ec hai nghi\u1ec7m x1; x2 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 1 th\u1ecfa x1 + x2 \u2212 4 = 2x1x2 L\u1eddi gi\u1ea3i 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 ( )a) T\u00ecm m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 1 c\u00f3 hai nghi\u1ec7m x1; x2 ? Ta c\u00f3: \uf044' = (2 + m)2 \u2212 m2 = 4m + 4 \u0110\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 c\u00f3 hai nghi\u1ec7m x1; x2 th\u00ec \uf044' \uf0b3 0 \uf0db 4m + 4 \uf0b3 0 \uf0db m \uf0b3 \u22121 ( )b) V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a m th\u00ec hai nghi\u1ec7m x1; x2 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 1 th\u1ecfa x1 + x2 \u2212 4 = 2x1x2 Khi m \uf0b3 \u22121 , \u00e1p d\u1ee5ng h\u1ec7 th\u1ee9c Vi-et ta c\u00f3: \uf0ec\uf0ef\uf0efS = x1 + x2 = \u2212b = 4m + 4 \uf0ed = x1x2 = a \uf0ef\uf0ef\uf0eeP c = m2 a Ta c\u00f3: x1 + x2 \u2212 4 = 2x1x2 \uf0db 4m + 4 \u2212 4 = 2m2 \uf0db 2m2 = 4m \uf0db \uf0e92m2 = 4m khi \u2212 1 \uf0a3 m \uf03c 0 \uf0ea \uf0ea\uf0eb 2m2 = \u22124m khi 0 \uf0a3 m \uf0db \uf0e9m = 0; m = 2 khi \u22121\uf0a3 m\uf03c 0 \uf0ea\uf0ebm = 0; m = \u22122 khi 0\uf0a3m \uf0dbm=0 C\u00e2u 3. Trong l\u1ec5 ph\u00e1t \u0111\u1ed9ng phong tr\u00e0o tr\u1ed3ng c\u00e2y nh\u00e2n d\u1ecbp k\u1ef7 ni\u1ec7m ng\u00e0y sinh B\u00e1c H\u1ed3, l\u1edbp 9A \u0111\u01b0\u1ee3c giao tr\u1ed3ng 360 c\u00e2y. Khi th\u1ef1c hi\u1ec7n c\u00f3 4 b\u1ea1n \u0111\u01b0\u1ee3c \u0111i\u1ec1u \u0111i l\u00e0m vi\u1ec7c kh\u00e1c, n\u00ean m\u1ed7i h\u1ecdc sinh c\u00f2n l\u1ea1i ph\u1ea3i tr\u1ed3ng th\u00eam m\u1ed9t c\u00e2y so v\u1edbi d\u1ef1 \u0111\u1ecbnh. H\u1ecfi l\u1edbp 9A c\u00f3 bao nhi\u00eau h\u1ecdc sinh? (Bi\u1ebft s\u1ed1 c\u00e2y tr\u1ed3ng c\u1ee7a m\u1ed7i h\u1ecdc sinh nh\u01b0 nhau) L\u1eddi gi\u1ea3i G\u1ecdi s\u1ed1 h\u1ecdc sinh c\u1ee7a l\u1edbp 9A l\u00e0 x (x \uf0ce N *) S\u1ed1 c\u00e2y tr\u1ed3ng m\u00e0 m\u1ed7i h\u1ecdc sinh ph\u1ea3i tr\u1ed3ng d\u1ef1 \u0111\u1ecbnh l\u00e0: 360 x Sau khi 4 b\u1ea1n \u0111\u01b0\u1ee3c \u0111i\u1ec1u \u0111i l\u00e0m vi\u1ec7c kh\u00e1c, n\u00ean m\u1ed7i h\u1ecdc sinh c\u00f2n l\u1ea1i ph\u1ea3i tr\u1ed3ng: 360 x\u22124 Ta c\u00f3: 360 + 1 = 360 x x\u22124 \uf0de 360(x \u2212 4) + x(x \u2212 4) = 360x \uf0db x2 \u2212 4x \u2212 1440 = 0 \uf0db \uf0e9 x1 = \u221236 (L) \uf0ea = 40 (N) \uf0ea\uf0ebx2 V\u1eady l\u1edbp 9A c\u00f3 40 h\u1ecdc sinh T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 5","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 4. Hai ng\u01b0\u1eddi A v\u00e0 B c\u00f9ng \u1edf m\u1ed9t ph\u00eda v\u00e0 c\u00e1ch th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh 50km . C\u1ea3 hai ng\u01b0\u1eddi c\u00f9ng nhau \u0111i tr\u00ean m\u1ed9t con \u0111\u01b0\u1eddng v\u1ec1 ph\u00eda ng\u01b0\u1ee3c h\u01b0\u1edbng v\u1edbi th\u00e0nh ph\u1ed1, ng\u01b0\u1eddi A \u0111i v\u1edbi v\u1eadn t\u1ed1c 30km \/ h v\u00e0 ng\u01b0\u1eddi B \u0111i v\u1edbi v\u1eadn t\u1ed1c 45km \/ h . G\u1ecdi d (km) l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh \u0111\u1ebfn hai ng\u01b0\u1eddi A v\u00e0 B sau khi \u0111i \u0111\u01b0\u1ee3c (t) gi\u1edd. a) L\u1eadp h\u00e0m s\u1ed1 c\u1ee7a d theo t \u0111\u1ed1i v\u1edbi m\u1ed7i ng\u01b0\u1eddi. b) H\u1ecfi n\u1ebfu hai ng\u01b0\u1eddi xu\u1ea5t ph\u00e1t c\u00f9ng m\u1ed9t l\u00fac th\u00ec v\u00e0o th\u1eddi \u0111i\u1ec3m n\u00e0o k\u1ec3 t\u1eeb l\u00fac xu\u1ea5t ph\u00e1t, kho\u1ea3ng c\u00e1ch gi\u1eefa hai ng\u01b0\u1eddi l\u00e0 30km . L\u1eddi gi\u1ea3i a) H\u00e0m s\u1ed1 c\u1ee7a d theo t \u0111\u1ed1i v\u1edbi ng\u01b0\u1eddi A l\u00e0: d = 30t + 50 H\u00e0m s\u1ed1 c\u1ee7a d theo t \u0111\u1ed1i v\u1edbi ng\u01b0\u1eddi B l\u00e0: d = 45t + 50 b) N\u1ebfu kho\u1ea3ng c\u00e1ch gi\u1eefa hai ng\u01b0\u1eddi l\u00e0 30km th\u00ec: 45t + 50 = 30t + 50 + 30 \uf0dbt=2 Hai ng\u01b0\u1eddi xu\u1ea5t ph\u00e1t c\u00f9ng m\u1ed9t l\u00fac th\u00ec sau 2h k\u1ec3 t\u1eeb l\u00fac xu\u1ea5t ph\u00e1t, kho\u1ea3ng c\u00e1ch gi\u1eefa hai ng\u01b0\u1eddi l\u00e0 30km . C\u00e2u 5. B\u00e0 T\u00e1m vay \u1edf m\u1ed9t ng\u00e2n h\u00e0ng 500 tri\u1ec7u \u0111\u1ed3ng \u0111\u1ec3 s\u1ea3n xu\u1ea5t trong th\u1eddi h\u1ea1n 1 n\u0103m. L\u1ebd ra \u0111\u00fang 1 n\u0103m sau b\u00e0 ph\u1ea3i tr\u1ea3 c\u1ea3 ti\u1ec1n v\u1ed1n l\u1eabn ti\u1ec1n l\u00e3i, song b\u00e0 \u0111\u00e3 \u0111\u01b0\u1ee3c ng\u00e2n h\u00e0ng cho k\u00e9o d\u00e0i th\u1eddi h\u1ea1n th\u00eam 1 n\u0103m n\u1eefa, s\u1ed1 ti\u1ec1n l\u00e3i c\u1ee7a n\u0103m \u0111\u1ea7u \u0111\u01b0\u1ee3c g\u1ed9p v\u00e0o v\u1edbi ti\u1ec1n v\u1ed1n \u0111\u1ec3 t\u00ednh l\u00e3i n\u0103m sau v\u00e0 l\u00e3i su\u1ea5t v\u1eabn nh\u01b0 c\u0169. H\u1ebft 2 n\u0103m b\u00e0 t\u00e1m ph\u1ea3i tr\u1ea3 t\u1ea5t c\u1ea3 605 tri\u1ec7u \u0111\u1ed3ng. H\u1ecfi l\u00e3i su\u1ea5t cho vay c\u1ee7a ng\u00e2n h\u00e0ng \u0111\u00f3 l\u00e0 bao nhi\u00eau ph\u1ea7n tr\u0103m m\u1ed9t n\u0103m? L\u1eddi gi\u1ea3i G\u1ecdi l\u00e3i su\u1ea5t c\u1ee7a ng\u00e2n h\u00e0ng l\u00e0 x% \/n\u0103m (x \uf03e 0) . S\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 c\u1ee7a b\u00e0 T\u00e1m sau m\u1ed9t n\u0103m l\u00e0: 500.(1 + x%) = 500 + 5x . S\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 c\u1ee7a b\u00e0 T\u00e1m sau hai n\u0103m l\u00e0: (500 + 5x)(1 + x%) = 500 + 5x + 5x + 0,05x2 . Theo \u0111\u1ec1: sau hai n\u0103m b\u00e0 T\u00e1m ph\u1ea3i tr\u1ea3 t\u1ea5t c\u1ea3 605 tri\u1ec7u \u0111\u1ed3ng n\u00ean ta c\u00f3: 0,05x2 + 10x + 500 = 605 \uf0db 0,05x2 + 10x \u2212 105 = 0 \uf0db \uf0e9 x1 = \u2212210 (L) \uf0ea (N) \uf0ea\uf0ebx2 = 10 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 V\u1eady l\u00e3i su\u1ea5t cho vay c\u1ee7a ng\u00e2n h\u00e0ng \u0111\u00f3 l\u00e0 10% \/n\u0103m. C\u00e2u 6. D\u00e2y cu-roa l\u00e0 m\u1ed9t trong nh\u1eefng b\u1ed9 truy\u1ec1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00f4ng nghi\u1ec7p. Chi\u1ec1u d\u00e0i d\u00e2y cu-roa \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh theo c\u00f4ng th\u1ee9c: L = 2a + \uf070 (d1 + d2 ) + (d2 )\u2212 d1 2 2 4a Trong \u0111\u00f3: L : Chi\u1ec1u d\u00e0i d\u00e2y cu-roa. a : Kho\u1ea3ng c\u00e1ch t\u00e2m c\u1ee7a 2 pu-ly. d1 : \u0110\u01b0\u1eddng k\u00ednh c\u1ee7a pu-ly 1 (h\u00ecnh tr\u00f2n nh\u1ecf m\u00e0u v\u00e0ng) d2 : \u0110\u01b0\u1eddng k\u00ednh c\u1ee7a pu-ly 2 (h\u00ecnh tr\u00f2n nh\u1ecf m\u00e0u v\u00e0ng) Cho d1 = 10cm , d2 = 20cm , a = 60cm T\u00ednh chi\u1ec1u d\u00e0i c\u1ee7a m\u1ed9t \u0111o\u1ea1n d\u00e2y cu-roa. G\u1ecdi AB l\u00e0 chi\u1ec1u d\u00e0i m\u1ed9t \u0111o\u1ea1n d\u00e2y cu-roa, trong \u0111\u00f3 A, B l\u1ea7n l\u01b0\u1ee3t l\u00e0 ti\u1ebfp \u0111i\u1ec3m tr\u00ean d\u00e2y cua- roa v\u1edbi 2 \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1o b\u1edfi m\u1eb7t c\u1eaft c\u1ee7a 2 pu-ly. T\u00ednh AB L\u1eddi gi\u1ea3i d2 \u2212 d1 2 4a ( ) ( )\uf070 Thay d1 = 10cm , d2 = 20cm , a = 60cm v\u00e0o L = 2a + d1 + d2 + 2 L = 2.60 + \uf070 (10 + 20) (20 \u2212 10)2 + 2 4.60 2.60 + \uf070 (10 + 20) + (20 \u2212 10)2 \u2212 \uf070 .20 \u2212 \uf070 .10 2 4.60 2 2 \uf0bb 60,21cm Chi\u1ec1u d\u00e0i \u0111o\u1ea1n AB l\u00e0: 2 V\u1eady chi\u1ec1u d\u00e0i \u0111o\u1ea1n AB l\u00e0 60,21cm . C\u00e2u 7. M\u1ed9t b\u00ecnh \u0111\u1ef1ng \u0111\u1ea7y n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n (kh\u00f4ng c\u00f3 \u0111\u00e1y). Ng\u01b0\u1eddi ta th\u1ea3 v\u00e0o \u0111\u00f3 m\u1ed9t kh\u1ed1i c\u1ea7u c\u00f3 \u0111\u01b0\u1eddng k\u00ednh b\u1eb1ng chi\u1ec1u cao c\u1ee7a b\u00ecnh n\u01b0\u1edbc v\u00e0 \u0111o \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch n\u01b0\u1edbc tr\u00e0n ra ngo\u00e0i l\u00e0 18\uf070 dm3 . Bi\u1ebft r\u1eb1ng kh\u1ed1i c\u1ea7u ti\u1ebfp x\u00fac v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c \u0111\u01b0\u1eddng sinh c\u1ee7a h\u00ecnh n\u00f3n v\u00e0 \u0111\u00fang m\u1ed9t n\u1eeda c\u1ee7a kh\u1ed1i c\u1ea7u \u0111\u00e3 ch\u00ecm trong n\u01b0\u1edbc ( h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y). T\u00ednh th\u1ec3 t\u00edch n\u01b0\u1edbc c\u00f2n l\u1ea1i trong b\u00ecnh. 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 G\u1ecdi R l\u00e0 b\u00e1n k\u00ednh c\u1ee7a kh\u1ed1i c\u1ea7u. Th\u1ec3 t\u00edch n\u01b0\u1edbc tr\u00e0n ra l\u00e0: 1 \uf0d7 4 \uf070 R3 = 18\uf070 \uf0db R = 3dm . 23 Chi\u1ec1u cao c\u1ee7a b\u00ecnh n\u01b0\u1edbc l\u00e0: h = 2R = 6dm . G\u1ecdi r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y c\u1ee7a b\u00ecnh h\u00ecnh n\u00f3n th\u00ec 1 +1 =1 \uf0der=2 3dm . r3 h2 R2 Th\u1ec3 t\u00edch b\u00ecnh h\u00ecnh n\u00f3n: V = 1 \uf070 r2h = 24\uf070 dm3 . 3 Th\u1ec3 t\u00edch n\u01b0\u1edbc tr\u00e0n ra l\u00e0: 24\uf070 \u2212 18\uf070 = 6\uf070 dm3 . C\u00e2u 8. Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O \u0111\u01b0\u1eddng k\u00ednh AB . K\u1ebb d\u00e2y cung CD vu\u00f4ng g\u00f3c v\u1edbi AB t\u1ea1i H ( H n\u1eb1m gi\u1eefa A v\u00e0 O , H kh\u00e1c A v\u00e0 O ). L\u1ea5y \u0111i\u1ec3m G thu\u1ed9c CH ( G kh\u00e1c C v\u00e0 H ), tia AG c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i E kh\u00e1c A . G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng BE v\u00e0 CD a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BEGH n\u1ed9i ti\u1ebfp v\u00e0 KC.KD = KE.KB . b) \u0110o\u1ea1n th\u1eb3ng AK c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m t\u1ea1i F kh\u00e1c A . Ch\u1ee9ng minh: G l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c HEF c) G\u1ecdi M,N l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a A v\u00e0 B l\u00ean \u0111\u01b0\u1eddng th\u1eb3ng EF . Ch\u1ee9ng minh: HE + HF = 1 . MN T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 8","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BEGH n\u1ed9i ti\u1ebfp v\u00e0 KC.KD = KE.KB . X\u00e9t t\u1ee9 gi\u00e1c BEGH , c\u00f3: \uf0ec\uf0efBHG = 90\uf0b0(GT ) \uf0ed \uf0ee\uf0efBEG = 90\uf0b0 ( AB = 2R) \uf0de BHG + BEG = 180\uf0b0 M\u00e0 BHG ; BEG \u0111\u1ed1i nhau \uf0de T\u1ee9 gi\u00e1c t\u1ee9 gi\u00e1c BEGH n\u1ed9i ti\u1ebfp. X\u00e9t \uf044KDE v\u00e0 \uf044KCB ta c\u00f3: KBC = KDE (c\u00f9ng ch\u1eafn EC ) K chung \uf0de \uf044KDE \uf044KBC (g \u2212 g) \uf0de KD = KE (t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng) KB KC \uf0de KD.KC = KE.KB . b) \u0110o\u1ea1n th\u1eb3ng AK c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m t\u1ea1i F kh\u00e1c A . Ch\u1ee9ng minh: G l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c HEF Ta c\u00f3: \uf044KAB c\u00f3 ba \u0111\u01b0\u1eddng cao AE,BF,KH \u0111\u1ed3ng quy t\u1ea1i G . Suy ra G l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a \uf044KAB . Ta c\u00f3: GHE = GBE = 1 sdGE ( trong \u0111\u01b0\u1eddng tr\u00f2n BEGH ) 2 Ta c\u00f3: GBE = GAF = 1 sdEF 2 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 Ta c\u00f3: GAF = GHF = 1 sdEG (t\u1ee9 gi\u00e1c AFGH n\u1ed9i ti\u1ebfp) 2 Suy ra: GHE = GHF \uf0de HG l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a EHF T\u01b0\u01a1ng t\u1ef1 EG l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a FEG Ta c\u00f3: \uf044EHF c\u00f3 2 tia ph\u00e2n gi\u00e1c HG v\u00e0 EG n\u00ean G l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \uf044EHF . c) G\u1ecdi M,N l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a A v\u00e0 B l\u00ean \u0111\u01b0\u1eddng th\u1eb3ng EF . Ch\u1ee9ng minh: HE + HF = 1 . MN G\u1ecdi Q l\u00e0 giao \u0111i\u1ec3m c\u1ee7a tia EH v\u00e0 (O) Ta c\u00f3: EOB = 2BFE = sdEB; 2BFE = EFO (do FG l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a EFH ) \uf0de EOB = EFH \uf0de t\u1ee9 gi\u00e1c EFHO n\u1ed9i ti\u1ebfp \uf0de FOH = FEH = 1 sdQE = 1 FOQ \uf0de FOH = 1 FOQ 22 2 \uf0de OH l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a FOQ Ta c\u00f3: \uf044OFH ; \uf044OQH c\u00f3 OH chung, OF = OQ, FOH = QOH \uf0de \uf044OFH = \uf044OQH \uf0de HF = HQ Do \u0111\u00f3: HE + HF = HE + HQ = EQ Ta c\u00f3: AMN = MNT = NTA = 90\uf0b0 \uf0de t\u1ee9 gi\u00e1c AMNT l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt, n\u00ean AT = MN \uf0de AQ = FA = ET \uf0de AE\/\/QT m\u00e0 AETQ n\u1ed9i ti\u1ebfp (O) \uf0de AETQ l\u00e0 h\u00ecnh thang c\u00e2n \uf0de EQ = AT = MN \uf0de HE + HF = MN hay HE + HF = 1 MN 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\u1ede GD&\u0110T TP. H\u1ed2 CH\u00cd MINH \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 PH\u00d2NG GD&\u0110T QU\u1eacN 1 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 1- 3 Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 3x \u2212 2 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. C\u00e2u 2. (1 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh x(3x \u2212 4) = 2x2 + 1 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 = x12 + x22 + 3x1x2 . 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). N\u01b0\u1edbc bi\u1ec3n l\u00e0 dung d\u1ecbch c\u00f3 n\u1ed3ng \u0111\u1ed9 mu\u1ed1i l\u00e0 3, 5% (gi\u1ea3 s\u1eed kh\u00f4ng c\u00f3 t\u1ea1p ch\u1ea5t). C\u00f3 10kg n\u01b0\u1edbc bi\u1ec3n. H\u1ecfi ph\u1ea3i th\u00eam bao nhi\u00eau kg n\u01b0\u1edbc (nguy\u00ean ch\u1ea5t) \u0111\u1ec3 \u0111\u01b0\u1ee3c dung d\u1ecbch c\u00f3 n\u1ed3ng \u0111\u1ed9 2% . C\u00e2u 4. (0,75 \u0111i\u1ec3m). Nh\u00e2n d\u1ecbp L\u1ec5 gi\u1ed7 t\u1ed5 H\u00f9ng V\u01b0\u01a1ng, m\u1ed9t si\u00eau th\u1ecb \u0111i\u1ec7n m\u00e1y \u0111\u00e3 gi\u1ea3m gi\u00e1 nhi\u1ec1u m\u1eb7t h\u00e0ng \u0111\u1ec3 k\u00edch c\u1ea7u mua s\u1eafm. Gi\u00e1 ni\u00eam y\u1ebft m\u1ed9t t\u1ee7 l\u1ea1nh v\u00e0 m\u1ed9t m\u00e1y gi\u1eb7t c\u00f3 t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 25, 4 tri\u1ec7u \u0111\u1ed3ng nh\u01b0ng trong d\u1ecbp n\u00e0y gi\u00e1 m\u1ed9t t\u1ee7 l\u1ea1nh gi\u1ea3m 40% gi\u00e1 b\u00e1n v\u00e0 gi\u00e1 m\u1ed9t m\u00e1y gi\u1eb7t gi\u1ea3m 20% gi\u00e1 b\u00e1n n\u00ean c\u00f4 Li\u00ean \u0111\u00e3 mua hai m\u00f3n \u0111\u1ed3 tr\u00ean v\u1edbi t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 16, 77 tri\u1ec7u \u0111\u1ed3ng. H\u1ecfi gi\u00e1 m\u1ed7i m\u00f3n \u0111\u1ed3 tr\u00ean khi ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 bao nhi\u00eau ti\u1ec1n? C\u00e2u 5. (1 \u0111i\u1ec3m). Ng\u01b0\u1eddi ta nu\u00f4i c\u00e1 trong m\u1ed9t b\u1ec3 x\u00e2y, m\u1eb7t b\u1ec3 l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt chi\u1ec1u d\u00e0i 60m , chi\u1ec1u r\u1ed9ng 40m . Tr\u00ean m\u1ed7i \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch m\u1eb7t b\u1ec3 ng\u01b0\u1eddi ta th\u1ea3 12 con c\u00e1 gi\u1ed1ng, \u0111\u1ebfn m\u1ed7i k\u1ef3 thu ho\u1ea1ch, trung b\u00ecnh m\u1ed7i con c\u00e1 c\u00e2n n\u1eb7ng 240g . Khi b\u00e1n kho\u1ea3ng 30000 \u0111\u1ed3ng\/kg v\u00e0 th\u1ea5y l\u00e3i qua k\u1ef3 thu ho\u1ea1ch n\u00e0y l\u00e0 100 tri\u1ec7u. H\u1ecfi v\u1ed1n mua c\u00e1 gi\u1ed1ng v\u00e0 c\u00e1c chi ph\u00ed trong \u0111\u1ee3t n\u00e0y chi\u1ebfm bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi gi\u00e1 b\u00e1n (l\u00e0m tr\u00f2n 1 ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n). C\u00e2u 6. (1 \u0111i\u1ec3m). \u0110\u1ec3 t\u00ednh to\u00e1n th\u1eddi gian m\u1ed9t chu k\u1ef3 \u0111ong \u0111\u01b0a (m\u1ed9t chu k\u1ef3 \u0111ong \u0111\u01b0a d\u00e2y \u0111u \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb l\u00fac d\u00e2y \u0111u b\u1eaft \u0111\u1ea7u \u0111\u01b0\u1ee3c \u0111\u01b0a l\u00ean cao \u0111\u1ebfn khi d\u1eebng h\u1eb3n) c\u1ee7a m\u1ed9t d\u00e2y \u0111u, ng\u01b0\u1eddi ta s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c T 2 L . Trong \u0111\u00f3, T l\u00e0 th\u1eddi gian m\u1ed9t chu k\u1ef3 \u0111ong \u0111\u01b0a s , L l\u00e0 chi\u1ec1u g d\u00e0i c\u1ee7a d\u00e2y \u0111u m , g 9, 81 m \/ s2 . a) M\u1ed9t s\u1ee3i d\u00e2y \u0111u c\u00f3 chi\u1ec1u d\u00e0i 2 3 m , h\u1ecfi chu k\u1ef3 \u0111ong \u0111\u01b0a d\u00e0i bao nhi\u00eau gi\u00e2y? T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH b) M\u1ed9t ng\u01b0\u1eddi mu\u1ed1n thi\u1ebft k\u1ebf m\u1ed9t d\u00e2y \u0111u sao cho m\u1ed9t chu k\u1ef3 \u0111\u00f4ng \u0111\u01b0a k\u00e9o d\u00e0i 4 gi\u00e2y. H\u1ecfi ng\u01b0\u1eddi \u0111\u00f3 ph\u1ea3i l\u00e0m m\u1ed9t s\u1ee3i d\u00e2y \u0111u d\u00e0i bao nhi\u00eau? C\u00e2u 7. (1 \u0111i\u1ec3m). M\u00e1y k\u00e9o n\u00f4ng nghi\u00eap c\u00f3 hai b\u00e1nh sau to h\u01a1n hai b\u00e1nh tr\u01b0\u1edbc. Khi b\u01a1m c\u0103ng, b\u00e1nh xa sau c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 1, 672m v\u00e0 b\u00e1nh xe tr\u01b0\u1edbc c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 88cm . H\u1ecfi khi b\u01a1m c\u0103ng, b\u00e1nh xe sau l\u0103n \u0111\u01b0\u1ee3c 10 v\u00f2ng th\u00ec b\u00e1nh xe tr\u01b0\u1edbc l\u0103n \u0111\u01b0\u1ee3c m\u1ea5y v\u00f2ng? C\u00e2u 8. (3 \u0111i\u1ec3m) Cho tam gi\u00e1c ABC ( AB \uf03c AC) c\u00f3 ba g\u00f3c nh\u1ecdn n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (O) . C\u00e1c \u0111\u01b0\u1eddng cao AD, BE, CF c\u1eaft nhau t\u1ea1i H . Tia EF c\u1eaft tia CB t\u1ea1i K . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp v\u00e0 KF.KE = KB.KC . b) \u0110\u01b0\u1eddng th\u1eb3ng KA c\u1eaft O t\u1ea1i M . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AEFM n\u1ed9i ti\u1ebfp. c) G\u1ecdi N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC . Ch\u1ee9ng minh M, H, N th\u1eb3ng h\u00e0ng. ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho (P) : y = x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 3x \u2212 2 . a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. L\u1eddi gi\u1ea3i a) V\u1ebd \u0111\u1ed3 th\u1ecb (P) v\u00e0 (d) tr\u00ean c\u00f9ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9. a) BGT: y x \u22122 \u22121 0 1 2 4 y = x2 4 1 0 1 4 x 01 1 x y = 3x \u2212 2 \u22122 1 \u20132 \u20131 0 1 2 b) T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) b\u1eb1ng ph\u00e9p t\u00ednh. \u20132 Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (P) v\u00e0 (d) : x2 = 3x \u2212 2 \uf0db x2 \u2212 3x + 2 = 0 \uf0db \uf0e9x = 1 \uf0ea\uf0ebx = 2 Thay x = 1 v\u00e0o y = x2 , ta \u0111\u01b0\u1ee3c: y = 12 = 1. Thay x = \u22124 v\u00e0o y = x2 , ta \u0111\u01b0\u1ee3c: y = 22 = 4 . V\u1eady (1; 1) , (2; 4) l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh x(3x \u2212 4) = 2x2 + 1 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 = x12 + x22 + 3x1x2 . L\u1eddi gi\u1ea3i Ta c\u00f3: x(3x \u2212 4) = 2x2 + 1 \uf0db 3x2 \u2212 4x = 2x2 + 1 \uf0db 3x2 \u2212 4x \u2212 2x2 \u2212 1 = 0 \uf0db x2 \u2212 4x \u2212 1 = 0 (a = 1, b = \u22124, c = \u22121) V\u00ec a.c 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 = \u2212 b = \u2212 \u22124 = 4 \uf0ed = x1 a 2 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP c \u22121 = \u22121 .x2 = a = 1 Ta c\u00f3: A = x12 + x22 + 3x1x2 A = S2 \u2212 2P + 3P A = S2 + P A = 42 + (\u22121) A = 15 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). N\u01b0\u1edbc bi\u1ec3n l\u00e0 dung d\u1ecbch c\u00f3 n\u1ed3ng \u0111\u1ed9 mu\u1ed1i l\u00e0 3, 5% (gi\u1ea3 s\u1eed kh\u00f4ng c\u00f3 t\u1ea1p ch\u1ea5t). C\u00f3 10kg n\u01b0\u1edbc bi\u1ec3n. H\u1ecfi ph\u1ea3i th\u00eam bao nhi\u00eau kg n\u01b0\u1edbc (nguy\u00ean ch\u1ea5t) \u0111\u1ec3 \u0111\u01b0\u1ee3c dung d\u1ecbch c\u00f3 n\u1ed3ng \u0111\u1ed9 2% ? L\u1eddi gi\u1ea3i Kh\u1ed1i l\u01b0\u1ee3ng mu\u1ed1i trong dung d\u1ecbch n\u01b0\u1edbc bi\u1ec3n 10kg l\u00e0: 3, 5%.10 0, 35 kg . Kh\u1ed1i l\u01b0\u1ee3ng n\u01b0\u1edbc bi\u1ec3n c\u00f3 n\u1ed3ng \u0111\u1ed9 2% l\u00e0: 0, 35 : 2% 17, 5 kg . Kh\u1ed1i l\u01b0\u1ee3ng n\u01b0\u1edbc \u0111\u01b0\u1ee3c th\u00eam v\u00e0o \u0111\u1ec3 \u0111\u01b0\u1ee3c dung d\u1ecbch c\u00f3 n\u1ed3ng \u0111\u1ed9 2% l\u00e0: 17, 5 10 7, 5 kg . C\u00e2u 4. (0,75 \u0111i\u1ec3m) Nh\u00e2n d\u1ecbp L\u1ec5 gi\u1ed7 t\u1ed5 H\u00f9ng V\u01b0\u01a1ng, m\u1ed9t si\u00eau th\u1ecb \u0111i\u1ec7n m\u00e1y \u0111\u00e3 gi\u1ea3m gi\u00e1 nhi\u1ec1u m\u1eb7t h\u00e0ng \u0111\u1ec3 k\u00edch c\u1ea7u mua s\u1eafm. Gi\u00e1 ni\u00eam y\u1ebft m\u1ed9t t\u1ee7 l\u1ea1nh v\u00e0 m\u1ed9t m\u00e1y gi\u1eb7t c\u00f3 t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 25, 4 tri\u1ec7u \u0111\u1ed3ng nh\u01b0ng trong d\u1ecbp n\u00e0y gi\u00e1 m\u1ed9t t\u1ee7 l\u1ea1nh gi\u1ea3m 40% gi\u00e1 b\u00e1n v\u00e0 gi\u00e1 m\u1ed9t m\u00e1y gi\u1eb7t gi\u1ea3m 20% gi\u00e1 b\u00e1n n\u00ean c\u00f4 Li\u00ean \u0111\u00e3 mua hai m\u00f3n \u0111\u1ed3 tr\u00ean v\u1edbi t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 16, 77 tri\u1ec7u \u0111\u1ed3ng. H\u1ecfi gi\u00e1 m\u1ed7i m\u00f3n \u0111\u1ed3 tr\u00ean khi ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 bao nhi\u00eau ti\u1ec1n? L\u1eddi gi\u1ea3i G\u1ecdi x,y (\u0111\u1ed3ng) l\u1ea7n l\u01b0\u1ee3t l\u00e0 s\u1ed1 ti\u1ec1n c\u1ee7a m\u1ed9t t\u1ee7 l\u1ea1nh, m\u1ed9t m\u00e1y gi\u1eb7t khi ch\u01b0a gi\u1ea3m gi\u00e1 x,y 0 V\u00ec gi\u00e1 ni\u00eam y\u1ebft m\u1ed9t t\u1ee7 l\u1ea1nh v\u00e0 m\u1ed9t m\u00e1y gi\u1eb7t c\u00f3 t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 25, 4 tri\u1ec7u \u0111\u1ed3ng n\u00ean c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x y 25, 4 (1) T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 4","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH V\u00ec trong d\u1ecbp n\u00e0y gi\u00e1 m\u1ed9t t\u1ee7 l\u1ea1nh gi\u1ea3m 40% gi\u00e1 b\u00e1n v\u00e0 gi\u00e1 m\u1ed9t m\u00e1y gi\u1eb7t gi\u1ea3m 20% gi\u00e1 b\u00e1n n\u00ean c\u00f4 Li\u00ean \u0111\u00e3 mua hai m\u00f3n \u0111\u1ed3 tr\u00ean v\u1edbi t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e0 16, 77 tri\u1ec7u \u0111\u1ed3ng n\u00ean c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh 1 40% x 1 20% y 16, 77 0, 6x 0, 8y 16, 77 2 T\u1eeb 1 v\u00e0 2 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh x y 25, 4 x 17, 75 (n) 0, 6x 0, 8y 16, 77 y 7, 65 (n) . V\u1eady s\u1ed1 ti\u1ec1n c\u1ee7a m\u1ed9t t\u1ee7 l\u1ea1nh khi ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 17, 75 tri\u1ec7u \u0111\u1ed3ng, s\u1ed1 ti\u1ec1n c\u1ee7a m\u1ed9t t\u1ee7 l\u1ea1nh ch\u01b0a gi\u1ea3m gi\u00e1 l\u00e0 7, 65 tri\u1ec7u \u0111\u1ed3ng. C\u00e2u 5. (1 \u0111i\u1ec3m) Ng\u01b0\u1eddi ta nu\u00f4i c\u00e1 trong m\u1ed9t b\u1ec3 x\u00e2y, m\u1eb7t b\u1ec3 l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt chi\u1ec1u d\u00e0i 60m , chi\u1ec1u r\u1ed9ng 40m . Tr\u00ean m\u1ed7i \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch m\u1eb7t b\u1ec3 ng\u01b0\u1eddi ta th\u1ea3 12 con c\u00e1 gi\u1ed1ng, \u0111\u1ebfn m\u1ed7i k\u1ef3 thu ho\u1ea1ch, trung b\u00ecnh m\u1ed7i con c\u00e1 c\u00e2n n\u1eb7ng 240g . Khi b\u00e1n kho\u1ea3ng 30000 \u0111\u1ed3ng\/kg v\u00e0 th\u1ea5y l\u00e3i qua k\u1ef3 thu ho\u1ea1ch n\u00e0y l\u00e0 100 tri\u1ec7u. H\u1ecfi v\u1ed1n mua c\u00e1 gi\u1ed1ng v\u00e0 c\u00e1c chi ph\u00ed trong \u0111\u1ee3t n\u00e0y chi\u1ebfm bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi gi\u00e1 b\u00e1n (l\u00e0m tr\u00f2n 1 ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n). L\u1eddi gi\u1ea3i Di\u1ec7n t\u00edch c\u1ee7a b\u1ec3 nu\u00f4i c\u00e1 l\u00e0: 60.40 2400 m2 . S\u1ed1 con c\u00e1 gi\u1ed1ng \u0111\u01b0\u1ee3c th\u1ea3 v\u00e0o b\u1ec3 l\u00e0: 2400.12 28800 con . S\u1ed1 kg c\u00e1 \u0111\u01b0\u1ee3c b\u00e1n l\u00e0: 240.28800 6912000 g 6912 kg . S\u1ed1 ti\u1ec1n b\u00e1n c\u00e1 l\u00e0: 6912.30000 207360000 (\u0111\u1ed3ng) 207, 36 (tri\u1ec7u \u0111\u1ed3ng). S\u1ed1 ti\u1ec1n v\u1ed1n v\u00e0 c\u00e1c chi ph\u00ed l\u00e0: 207, 36 100 107, 36 (tri\u1ec7u \u0111\u1ed3ng). Ph\u1ea7n tr\u0103m v\u1ed1n mua c\u00e1 gi\u1ed1ng v\u00e0 c\u00e1c chi ph\u00ed so v\u1edbi gi\u00e1 b\u00e1n chi\u1ebfm: 107, 36 : 207, 36 0, 518 51, 8% . C\u00e2u 6. (1 \u0111i\u1ec3m) \u0110\u1ec3 t\u00ednh to\u00e1n th\u1eddi gian m\u1ed9t chu k\u1ef3 \u0111ong \u0111\u01b0a (m\u1ed9t chu k\u1ef3 \u0111ong \u0111\u01b0a d\u00e2y \u0111u \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb l\u00fac d\u00e2y \u0111u b\u1eaft \u0111\u1ea7u \u0111\u01b0\u1ee3c \u0111\u01b0a l\u00ean cao \u0111\u1ebfn khi d\u1eebng h\u1eb3n) c\u1ee7a m\u1ed9t d\u00e2y \u0111u, ng\u01b0\u1eddi ta s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c T 2 L . Trong \u0111\u00f3, T l\u00e0 th\u1eddi gian m\u1ed9t chu k\u1ef3 \u0111ong \u0111\u01b0a s ,L l\u00e0 chi\u1ec1u d\u00e0i c\u1ee7a g d\u00e2y \u0111u m , g 9, 81 m \/ s2 . a) M\u1ed9t s\u1ee3i d\u00e2y \u0111u c\u00f3 chi\u1ec1u d\u00e0i 2 3 m , h\u1ecfi chu k\u1ef3 \u0111ong \u0111\u01b0a d\u00e0i bao nhi\u00eau gi\u00e2y? b) M\u1ed9t ng\u01b0\u1eddi mu\u1ed1n thi\u1ebft k\u1ebf m\u1ed9t d\u00e2y \u0111u sao cho m\u1ed9t chu k\u1ef3 \u0111\u00f4ng \u0111\u01b0a k\u00e9o d\u00e0i 4 gi\u00e2y. H\u1ecfi ng\u01b0\u1eddi \u0111\u00f3 ph\u1ea3i l\u00e0m m\u1ed9t s\u1ee3i d\u00e2y \u0111u d\u00e0i 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 L\u1eddi gi\u1ea3i a) Thay L 2 3, g 9, 81 v\u00e0o c\u00f4ng th\u1ee9c T 2 L , ta \u0111\u01b0\u1ee3c T 2 23 3, 9 g 9, 81 V\u1eady m\u1ed9t s\u1ee3i d\u00e2y \u0111u c\u00f3 chi\u1ec1u d\u00e0i 2 3 m c\u00f3 chu k\u1ef3 \u0111ong \u0111\u01b0a d\u00e0i kho\u1ea3ng 3, 9 gi\u00e2y. b) Thay T 4, g 9, 81 v\u00e0o c\u00f4ng th\u1ee9c T 2 L , ta \u0111\u01b0\u1ee3c 4 2 L g 9, 81 4 L 22 L L 2 2 4m 2 9, 81 9, 81 .9, 81 V\u1eady m\u1ed9t ng\u01b0\u1eddi mu\u1ed1n thi\u1ebft k\u1ebf m\u1ed9t d\u00e2y \u0111u sao cho m\u1ed9t chu k\u1ef3 \u0111\u00f4ng \u0111\u01b0a k\u00e9o d\u00e0i 4 gi\u00e2y, ng\u01b0\u1eddi \u0111\u00f3 ph\u1ea3i l\u00e0m m\u1ed9t s\u1ee3i d\u00e2y \u0111u d\u00e0i kho\u1ea3ng 4m . C\u00e2u 7. (1 \u0111i\u1ec3m) M\u00e1y k\u00e9o n\u00f4ng nghi\u00eap c\u00f3 hai b\u00e1nh sau to h\u01a1n hai b\u00e1nh tr\u01b0\u1edbc. Khi b\u01a1m c\u0103ng, b\u00e1nh xe sau c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 1, 672m v\u00e0 b\u00e1nh xe tr\u01b0\u1edbc c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 88cm . H\u1ecfi khi b\u01a1m c\u0103ng, b\u00e1nh xe sau l\u0103n \u0111\u01b0\u1ee3c 10 v\u00f2ng th\u00ec b\u00e1nh xe tr\u01b0\u1edbc l\u0103n \u0111\u01b0\u1ee3c m\u1ea5y v\u00f2ng? L\u1eddi gi\u1ea3i \u0110\u1ed5i \u0111\u01a1n v\u1ecb: 1, 672m 167,2cm . Chu vi c\u1ee7a b\u00e1nh xe sau l\u00e0: C d .162, 7 162, 7 cm . Chu vi c\u1ee7a b\u00e1nh xe tr\u01b0\u1edbc l\u00e0: C d .88 88 cm . Qu\u00e3ng \u0111\u01b0\u1eddng xe di chuy\u1ec3n \u0111\u01b0\u1ee3c l\u00e0: 10.167,2 1672 cm . S\u1ed1 v\u00f2ng m\u00e0 b\u00e1nh xe tr\u01b0\u1edbc l\u0103n \u0111\u01b0\u1ee3c l\u00e0: 1672 : 88 19 (v\u00f2ng). C\u00e2u 8. (3 \u0111i\u1ec3m) Cho tam gi\u00e1c ABC ( AB \uf03c AC) c\u00f3 ba g\u00f3c nh\u1ecdn n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (O) . C\u00e1c \u0111\u01b0\u1eddng cao AD, BE, CF c\u1eaft nhau t\u1ea1i H . Tia EF c\u1eaft tia CB t\u1ea1i K . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp v\u00e0 KF.KE = KB.KC . b) \u0110\u01b0\u1eddng th\u1eb3ng KA c\u1eaft O t\u1ea1i M . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AEFM n\u1ed9i ti\u1ebfp. c) G\u1ecdi N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC . Ch\u1ee9ng minh M, H, N th\u1eb3ng h\u00e0ng. L\u1eddi gi\u1ea3i 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 A M E F O H K B DN C L a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp v\u00e0 KF.KE = KB.KC . X\u00e9t t\u1ee9 gi\u00e1c BFEC c\u00f3 BEC BFC 90 ( BE,CF l\u00e0 \u0111\u01b0\u1eddng cao) Suy ra t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp ( 2 \u0111\u1ec9nh li\u1ec1n k\u1ec1 c\u00f9ng nh\u00ecn c\u1ea1nh BC ). X\u00e9t \uf044KEB v\u00e0 \uf044KCF c\u00f3: K l\u00e0 g\u00f3c chung KEB KCF 1 S\u0111 BF (t\u1ee9 gi\u00e1c BFEC n\u1ed9i ti\u1ebfp) 2 V\u1eady \uf044KEB \uf044KCF (g.g). KE KB KE.KF KB.KC . KC KF b) \u0110\u01b0\u1eddng th\u1eb3ng KA c\u1eaft O t\u1ea1i M . Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AEFM n\u1ed9i ti\u1ebfp. X\u00e9t \uf044KMB v\u00e0 \uf044KCA c\u00f3: K l\u00e0 g\u00f3c chung KMB KCA (g\u00f3c ngo\u00e0i b\u1eb1ng g\u00f3c \u0111\u1ed1i trong c\u1ee7a t\u1ee9 gi\u00e1c AMBC n\u1ed9i ti\u1ebfp) V\u1eady \uf044KMB \uf044KCA (g.g). KM KB KM.KA KB.KC . KC KA M\u00e0 KE.KF KB.KC (cmt) Suy ra KM.KA KE.KF . X\u00e9t \uf044KMF v\u00e0 \uf044KEA c\u00f3: 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 K l\u00e0 g\u00f3c chung KM KF KM.KA KE.KF KE KA V\u1eady \uf044KMF \uf044KEA (g.g) KMF KEA (2 g\u00f3c t\u01b0\u01a1ng \u1ee9ng) V\u1eady t\u1ee9 gi\u00e1c AEFM n\u1ed9i ti\u1ebfp (g\u00f3c ngo\u00e0i b\u1eb1ng g\u00f3c \u0111\u1ed1i trong). c) G\u1ecdi N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC . Ch\u1ee9ng minh M, H, N th\u1eb3ng h\u00e0ng. K\u1ebb \u0111\u01b0\u1eddng k\u00ednh AL c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O \uf0de ABL = 90\uf0b0 ; ACL = 90\uf0b0 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) \uf0de AB \u22a5 BL, AC \u22a5 CL Ta c\u00f3: AB BL,CF AB BL \/\/CF AC CL,BE AC CL\/\/BE \uf0de T\u1ee9 gi\u00e1c BHCL l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh M\u00e0 N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC \uf0de N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a HL \uf0de H, N, L th\u1eb3ng h\u00e0ng (1) X\u00e9t t\u1ee9 gi\u00e1c AFHE c\u00f3 AFH AEH 90 (CF, BE l\u00e0 \u0111\u01b0\u1eddng cao) AFH AEH 90 90 180 V\u1eady t\u1ee9 gi\u00e1c AFHE n\u1ed9i ti\u1ebfp M\u00e0 t\u1ee9 gi\u00e1c AEFM n\u1ed9i ti\u1ebfp (cmt) \uf0de 5 \u0111i\u1ec3m A,M,F,H,E c\u00f9ng thu\u1ed9c 1 \u0111\u01b0\u1eddng tr\u00f2n. \uf0de T\u1ee9 gi\u00e1c AMHE n\u1ed9i ti\u1ebfp \uf0de AMH = AEH = 90\uf0b0 \uf0de HM AM M\u00e0 AM ML ( v\u00ec LMA = 90\uf0b0 l\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) \uf0de M,H,L th\u1eb3ng h\u00e0ng 2 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 T\u1eeb 1 , 2 suy ra H,M,N th\u1eb3ng h\u00e0ng. ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 9","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\u00d4\u00db GD&\u00d1T TP HO\u00c0 CH\u00cd MINH \u00d1E\u00c0 THAM KHA\u00dbO TUYE\u00c5N SINH 10 PHO\u00d8NG G\u00d1&\u00d1T QUA\u00c4N 3 NA\u00caM HO\u00cfC: 2022 \u2013 2023 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 M\u00c3 \u0110\u1ec0: Qu\u1eadn 3 - 1 \u0110\u00ea thi g\u1ed3m 8 c\u00e2u ho\u0309i t\u01b0\u0323 lu\u00e2\u0323n. Th\u01a1\u0300i gian: 120 phu\u0301t (kh\u00f4ng k\u00ea\u0309 th\u01a1\u0300i gian pha\u0301t \u0111\u00ea\u0300) C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho (P) : y = \u2212x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 2x \u2212 3 . 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. (1,0 \u0111i\u1ec3m). Cho ph\u01b0\u01a1ng tr\u00ecnh 2x2 \u2212 x \u2212 3 = 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 = x12 + x22 \u2212 x12x22 . C\u00e2u 3. (1,0 \u0111i\u1ec3m). N\u1ed3ng \u0111\u1ed9 c\u1ed3n trong m\u00e1u (BAC \u2013 Blood Alcohol Conentration) l\u00e0 t\u1ec9 l\u1ec7 l\u01b0\u1ee3ng r\u01b0\u1ee3u (gam) trong 100 mililit m\u00e1u. V\u00ed d\u1ee5: BAC 0, 03ngh\u0129a l\u00e0 0, 03g r\u01b0\u1ee3u trong 100ml. m\u00e1u. U\u1ed1ng c\u00e0ng nhi\u1ec1u r\u01b0\u1ee3u bia th\u00ec n\u1ed3ng \u0111\u1ed9 c\u1ed3n trong m\u00e1u c\u00e0ng cao v\u00e0 c\u00e0ng d\u1ec5 g\u00e2y ra tai n\u1ea1n khi \u0111i\u1ec1u khi\u1ec3n ph\u01b0\u01a1ng ti\u1ec7n giao th\u00f4ng. V\u1edbi m\u1ed9t ng\u01b0\u1eddi \u0111\u00e3 u\u1ed1ng kho\u1ea3ng 100g r\u01b0\u1ee3u (r\u01b0\u1ee3u ethyl ho\u1eb7c ethanol) th\u00ec n\u1ed3ng \u0111\u1ed9 BAC sau t gi\u1edd \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n qua \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh 2 . a) G\u1ecdi y l\u00e0 n\u1ed3ng \u0111\u1ed9 BAC c\u1ee7a m\u1ed9t ng\u01b0\u1eddi sau khi u\u1ed1ng kho\u1ea3ng 100g r\u01b0\u1ee3u trong t gi\u1edd. Vi\u1ebft c\u00f4ng th\u1ee9c bi\u1ec3u th\u1ecb y theo t , bi\u1ebft y l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t c\u1ee7a t . b) Theo ngh\u1ecb \u0111\u1ecbnh 100 \/ 2019 \/ N\u0110-CP ng\u00e0y 30 \/12 \/ 2019 c\u1ee7a ch\u00ednh ph\u1ee7 n\u01b0\u1edbc C\u1ed9ng h\u00f2a x\u00e3 h\u1ed9i ch\u1ee7 ngh\u0129a Vi\u1ec7t Nam v\u1ec1 quy \u0111\u1ecbnh x\u1eed ph\u1ea1t vi ph\u1ea1m h\u00e0nh ch\u00ednh trong l\u0129nh v\u1ef1c giao th\u00f4ng \u0111\u01b0\u1eddng b\u1ed9 v\u00e0 \u0111\u01b0\u1eddng s\u1eaft; m\u1ee9c x\u1eed ph\u1ea1t c\u00e1c l\u1ed7i vi ph\u1ea1m giao th\u00f4ng \u0111\u1ed1i v\u1edbi ng\u01b0\u1eddi \u0111i\u1ec1u khi\u1ec3n xe m\u00e1y \u0111\u01b0\u1ee3c t\u00ednh theo b\u1ea3ng 1 . H\u1ecfi sau khi u\u1ed1ng 100g r\u01b0\u1ee3u kho\u1ea3ng 2 gi\u1edd, n\u1ebfu ng\u01b0\u1eddi n\u00e0y \u0111i\u1ec1u khi\u1ec3n xe m\u00e1y tham gia giao th\u00f4ng \u0111\u01b0\u1eddng b\u1ed9 th\u00ec s\u1ebd b\u1ecb x\u1eed ph\u1ea1t \u1edf m\u1ee9c n\u00e0o? B\u1ea3ng 1 : Tra c\u1ee9u m\u1ee9c ph\u1ea1t c\u00e1c l\u1ed7i vi ph\u1ea1m giao th\u00f4ng. STT L\u1ed7i vi ph\u1ea1m M\u1ee9c ph\u1ea1t ti\u1ec1n v\u00e0 h\u00ecnh ph\u1ea1t 1 N\u1ed3ng \u0111\u1ed9 ch\u01b0a v\u01b0\u1ee3t qu\u00e1 BAC \u2022 02 \u2212 03 tri\u1ec7u \u0111\u1ed3ng. \u2022 Thu b\u1eb1ng l\u00e1i xe t\u1eeb 10 \u221212 th\u00e1ng. 0, 05 \u2022 04 \u2212 05 tri\u1ec7u \u0111\u1ed3ng. \u2022 Thu b\u1eb1ng l\u00e1i xe t\u1eeb 16 \u221218 th\u00e1ng. 2 N\u1ed3ng \u0111\u1ed9 t\u1eeb BAC 0, 05\u0111\u1ebfn BAC 0, 08 \u2022 06 \u2212 08 tri\u1ec7u \u0111\u1ed3ng. \u2022 Thu b\u1eb1ng l\u00e1i xe t\u1eeb 22 \u2212 24 th\u00e1ng. 3 N\u1ed3ng \u0111\u1ed9 l\u1edbn h\u01a1n BAC 0, 08 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 4. (1,0 \u0111i\u1ec3m). M\u1ed9t ng\u01b0\u1eddi cao 175cm \u0111\u1ee9ng tr\u00ean b\u1edd h\u1ed3 v\u00e0 nh\u00ecn l\u00ean \u0111\u1ec9nh m\u1ed9t t\u00f2a cao \u1ed1c 159m x\u00e2y gi\u1eefa h\u1ed3 (m\u1eb7t h\u1ed3 c\u00f3 d\u1ea1ng h\u00ecnh tr\u00f2n, cao \u1ed1c xem nh\u01b0 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t h\u00ecnh tr\u00f2n t\u1ea1i t\u00e2m h\u00ecnh tr\u00f2n) d\u01b0\u1edbi m\u1ed9t g\u00f3c 58 . Em h\u00e3y t\u00ednh di\u1ec7n t\u00edch v\u00e0 chu vi c\u1ee7a h\u1ed3 n\u00e0y bi\u1ebft chu vi C v\u00e0 di\u1ec7n t\u00edch S c\u1ee7a h\u00ecnh tr\u00f2n \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c C 3,14.d v\u00e0 S 3,14.R2 trong \u0111\u00f3 d l\u00e0 \u0111\u01b0\u1eddng k\u00ednh v\u00e0 R l\u00e0 b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh tr\u00f2n (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai). C\u00e2u 5. (1,0 \u0111i\u1ec3m). Trong th\u00e1ng gi\u00eang c\u1ea3 hai t\u1ed5 I v\u00e0 II s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 720 chi ti\u1ebft m\u00e1y. Trong th\u00e1ng hai, t\u1ed5 I s\u1ea3n xu\u1ea5t v\u01b0\u1ee3t15% , t\u1ed5 II s\u1ea3n xu\u1ea5t v\u01b0\u1ee3t 12% so v\u1edbi th\u00e1ng gi\u00eang n\u00ean c\u1ea3 hai t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c t\u1ea5t c\u1ea3 l\u00e0 819 chi ti\u1ebft m\u00e1y. T\u00ednh xem trong th\u00e1ng gi\u00eang m\u1ed7i t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c bao nhi\u00eau chi ti\u1ebft m\u00e1y. C\u00e2u 6. (0,75 \u0111i\u1ec3m). M\u1ed9t v\u00e9 xem phim \u0111ang c\u00f3 gi\u00e1 l\u00e0 120 000 \u0111\u1ed3ng. Trong \u0111\u1ee3t gi\u1ea3m gi\u00e1 cu\u1ed1i n\u0103m2022 , s\u1ed1 l\u01b0\u1ee3ng ng\u01b0\u1eddi xem phim t\u0103ng th\u00eam 50% n\u00ean t\u1ed5ng doanh thu c\u0169ng t\u0103ng l\u00ean 20% (so v\u1edbi l\u00fac ch\u01b0a gi\u1ea3m gi\u00e1). H\u1ecfi gi\u00e1 m\u1ed7i v\u00e9 khi \u0111\u00e3 gi\u1ea3m l\u00e0 bao nhi\u00eau \u0111\u1ed3ng? C\u00e2u 7. (0,75 \u0111i\u1ec3m). M\u1ed9t xe b\u1ed3n ch\u1edf n\u01b0\u1edbc s\u1ea1ch cho m\u1ed9t khu d\u00e2n c\u01b0 c\u00f3 200 h\u1ed9 d\u00e2n. B\u1ed3n xe c\u00f3 h\u00ecnh d\u1ea1ng v\u00e0 k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd b\u00ean d\u01b0\u1edbi, m\u1ed7i \u0111\u1ea7u c\u1ee7a b\u1ed3n xe l\u00e0 n\u1eeda h\u00ecnh c\u1ea7u. Xe ch\u1edf \u0111\u1ea7y n\u01b0\u1edbc v\u00e0 l\u01b0\u1ee3ng n\u01b0\u1edbc chia \u0111\u1ec1u cho t\u1eebng h\u1ed9 d\u00e2n. T\u00ednh xem m\u1ed7i h\u1ed9 d\u00e2n \u0111\u01b0\u1ee3c nh\u1eadn bao nhi\u00eau l\u00edt n\u01b0\u1edbc s\u1ea1ch. C\u00e2u 8. (3,0 \u0111i\u1ec3m) T\u1eeb \u0111i\u1ec3m M n\u1eb1m \u1edf ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n O;R v\u1ebd hao ti\u1ebfp tuy\u1ebfn MA,MC v\u01a1i \u0111\u01b0\u1eddng tr\u00f2n ( A,C l\u00e0 hai ti\u1ebfp \u0111i\u1ec3m). V\u1ebd \u0111\u01b0\u1eddng k\u00ednh AB c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AMCO n\u1ed9i ti\u1ebfp v\u00e0 OM \/ \/BC . b) K\u1ebb CD AB D AB . BM c\u1eaft O t\u1ea1i N N B . Ch\u1ee9ng minh MAO v\u00e0 CDB MN CN 2 AB , t\u00ednh \u0111\u1ed3ng d\u1ea1ng v\u00e0 MB CB2 . c) G\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OM v\u00e0 AC ; K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a BM v\u00e0 CD . Khi OM theo R di\u1ec7n t\u00edch MIK . 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\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 3","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH H\u01af\u1edaNG D\u1eaaN GI\u1ea2I C\u00e2u 1. (1,5 \u0111i\u1ec3m) Cho (P) : y = \u2212x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 2x \u2212 3 . 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 = 3x \u2212 4 \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 \u2212x2 \u2212 2x + 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 . C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 2x2 \u2212 x \u2212 3 = 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 = x12 + x22 \u2212 x12x22 . L\u1eddi gi\u1ea3i V\u00ec \uf044 = b2 \u2212 4ac = (\u22121)2 \u2212 4.2.(\u22123) = 25 \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 4","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 = 1 \uf0ed = a 2 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP \u22123 c = 2 x1.x2 = a Ta c\u00f3: A = x12 + x22 \u2212 x12x22 ( ) ( )A = x1 + x2 2 \u2212 2x1x2 \u2212 x1x2 2 A = \uf0e6 1 \uf0f62 \u2212 2.\uf0e6\uf0e7\uf0e8 \u22123 \uf0f6 \u2212 \uf0e6 \u22123 \uf0f62 \uf0e7\uf0e8 2 \uf0f7\uf0f8 2 \uf0f7\uf0f8 \uf0e7\uf0e8 2 \uf0f7\uf0f8 A=1 C\u00e2u 3. (1 \u0111i\u1ec3m) N\u1ed3ng \u0111\u1ed9 c\u1ed3n trong m\u00e1u (BAC \u2013 Blood Alcohol Conentration) l\u00e0 t\u1ec9 l\u1ec7 l\u01b0\u1ee3ng r\u01b0\u1ee3u (gam) trong 100 mililit m\u00e1u. V\u00ed d\u1ee5: BAC 0, 03 ngh\u0129a l\u00e0 0,03g r\u01b0\u1ee3u trong 100ml. m\u00e1u. U\u1ed1ng c\u00e0ng nhi\u1ec1u r\u01b0\u1ee3u bia th\u00ec n\u1ed3ng \u0111\u1ed9 c\u1ed3n trong m\u00e1u c\u00e0ng cao v\u00e0 c\u00e0ng d\u1ec5 g\u00e2y ra tai n\u1ea1n khi \u0111i\u1ec1u khi\u1ec3n ph\u01b0\u01a1ng ti\u1ec7n giao th\u00f4ng. V\u1edbi m\u1ed9t ng\u01b0\u1eddi \u0111\u00e3 u\u1ed1ng kho\u1ea3ng 100g r\u01b0\u1ee3u (r\u01b0\u1ee3u ethyl ho\u1eb7c ethanol) th\u00ec n\u1ed3ng \u0111\u1ed9 BAC sau t gi\u1edd \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n qua \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh 2 . a) G\u1ecdi y l\u00e0 n\u1ed3ng \u0111\u1ed9 BAC c\u1ee7a m\u1ed9t ng\u01b0\u1eddi sau khi u\u1ed1ng kho\u1ea3ng 100g r\u01b0\u1ee3u trong t gi\u1edd. Vi\u1ebft c\u00f4ng th\u1ee9c bi\u1ec3u th\u1ecb y theo t , bi\u1ebft y l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t c\u1ee7a t . b) Theo ngh\u1ecb \u0111\u1ecbnh 100 \/ 2019 \/ N\u0110-CP ng\u00e0y 30 \/12 \/ 2019 c\u1ee7a ch\u00ednh ph\u1ee7 n\u01b0\u1edbc C\u1ed9ng h\u00f2a x\u00e3 h\u1ed9i ch\u1ee7 ngh\u0129a Vi\u1ec7t Nam v\u1ec1 quy \u0111\u1ecbnh x\u1eed ph\u1ea1t vi ph\u1ea1m h\u00e0nh ch\u00ednh trong l\u0129nh v\u1ef1c giao th\u00f4ng \u0111\u01b0\u1eddng b\u1ed9 v\u00e0 \u0111\u01b0\u1eddng s\u1eaft; m\u1ee9c x\u1eed ph\u1ea1t c\u00e1c l\u1ed7i vi ph\u1ea1m giao th\u00f4ng \u0111\u1ed1i v\u1edbi ng\u01b0\u1eddi \u0111i\u1ec1u khi\u1ec3n xe m\u00e1y \u0111\u01b0\u1ee3c t\u00ednh theo b\u1ea3ng 1. H\u1ecfi sau khi u\u1ed1ng 100g r\u01b0\u1ee3u kho\u1ea3ng 2 gi\u1edd, n\u1ebfu ng\u01b0\u1eddi n\u00e0y \u0111i\u1ec1u khi\u1ec3n xe m\u00e1y tham gia giao th\u00f4ng \u0111\u01b0\u1eddng b\u1ed9 th\u00ec s\u1ebd b\u1ecb x\u1eed ph\u1ea1t \u1edf m\u1ee9c n\u00e0o? B\u1ea3ng 1: Tra c\u1ee9u m\u1ee9c ph\u1ea1t c\u00e1c l\u1ed7i vi ph\u1ea1m giao th\u00f4ng. STT L\u1ed7i vi ph\u1ea1m M\u1ee9c ph\u1ea1t ti\u1ec1n v\u00e0 h\u00ecnh ph\u1ea1t 1 N\u1ed3ng \u0111\u1ed9 ch\u01b0a v\u01b0\u1ee3t qu\u00e1 BAC \u2022 02 \u2212 03 tri\u1ec7u \u0111\u1ed3ng. 0, 05 \u2022 Thu b\u1eb1ng l\u00e1i xe t\u1eeb 10 \u221212 th\u00e1ng. \u2022 04 \u2212 05 tri\u1ec7u \u0111\u1ed3ng. 2 N\u1ed3ng \u0111\u1ed9 t\u1eeb BAC 0, 05\u0111\u1ebfn \u2022 Thu b\u1eb1ng l\u00e1i xe t\u1eeb 16 \u221218 th\u00e1ng. BAC 0, 08 \u2022 06 \u2212 08 tri\u1ec7u \u0111\u1ed3ng. 3 N\u1ed3ng \u0111\u1ed9 l\u1edbn h\u01a1n BAC 0, 08 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 \u2022 Thu b\u1eb1ng l\u00e1i xe t\u1eeb 22 \u2212 24 th\u00e1ng. L\u1eddi gi\u1ea3i a) V\u00ec y l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t c\u1ee7a t . N\u00ean h\u00e0m s\u1ed1 c\u1ee7a y c\u00f3 d\u1ea1ng: y = at + b Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: V\u1edbi \uf0ect = 0 \uf0de 0,074 = 0.a + b . (1) \uf0ed\uf0eey = 0,074 V\u1edbi \uf0ect = 1 \uf0de 0,065 = a + b . (2) \uf0ed\uf0eey = 0,065 T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: \uf0ec0a + b = 0,074 \uf0db \uf0eca = \u22120,009 \uf0ed\uf0ee12a + b = 0,065 \uf0ed\uf0eeb = 0,074 . V\u1eady: a = \u22120,009 , b = 0,074 v\u00e0 y = \u22120,009t + 0,074 . b) Thay t = 2v\u00e0o y = \u22120, 009t + 0, 074 \uf0de y = 0, 056 . So v\u1edbi b\u1ea3ng m\u1ee9c ph\u1ea1t th\u00ec ng\u01b0\u1eddi n\u00e0y b\u1ecb ph\u1ea1t \u1edf m\u1ee9c th\u1ee9 2. C\u00e2u 4. (0,75 \u0111i\u1ec3m). M\u1ed9t ng\u01b0\u1eddi cao 175cm \u0111\u1ee9ng tr\u00ean b\u1edd h\u1ed3 v\u00e0 nh\u00ecn l\u00ean \u0111\u1ec9nh m\u1ed9t t\u00f2a cao \u1ed1c 159m x\u00e2y gi\u1eefa h\u1ed3 (m\u1eb7t h\u1ed3 c\u00f3 d\u1ea1ng h\u00ecnh tr\u00f2n, cao \u1ed1c xem nh\u01b0 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t h\u00ecnh tr\u00f2n t\u1ea1i t\u00e2m h\u00ecnh tr\u00f2n) d\u01b0\u1edbi m\u1ed9t g\u00f3c 58o . Em h\u00e3y t\u00ednh di\u1ec7n t\u00edch v\u00e0 chu vi c\u1ee7a h\u1ed3 n\u00e0y bi\u1ebft chu vi C v\u00e0 di\u1ec7n t\u00edch S c\u1ee7a h\u00ecnh tr\u00f2n \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c C 3,14.d v\u00e0 S 3,14.R2 trong \u0111\u00f3 d l\u00e0 \u0111\u01b0\u1eddng k\u00ednh v\u00e0 R l\u00e0 b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh tr\u00f2n (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai). L\u1eddi gi\u1ea3i \u0110\u1ed5i 175cm 1, 75m Chi\u1ec1u cao c\u1ee7a t\u00f2a nh\u00e0 t\u00ednh t\u1eeb \u0111\u1ea7u c\u1ee7a ng\u01b0\u1eddi \u0111\u00f3 \u0111\u1ebfn \u0111\u1ec9nh c\u1ee7a t\u00f2a nh\u00e0: 159 1, 75 157,25 m B\u00e1n k\u00ednh c\u1ee7a h\u1ed3: R 157,25 m Di\u1ec7n t\u00edch c\u1ee7a h\u1ed3: S tan 58o 3,14.R2 3,14. 157,25 2 30317,22 m2 tan 58o 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 Chu vi c\u1ee7a h\u1ed3: C 3,14.d 3,14.2.R 3,14.2. 157,25 617, 08 m tan 58o C\u00e2u 5. (1 \u0111i\u1ec3m) Trong th\u00e1ng gi\u00eang c\u1ea3 hai t\u1ed5 I v\u00e0 II s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 720 chi ti\u1ebft m\u00e1y. Trong th\u00e1ng hai, t\u1ed5 I s\u1ea3n xu\u1ea5t v\u01b0\u1ee3t15% , t\u1ed5 II s\u1ea3n xu\u1ea5t v\u01b0\u1ee3t 12% so v\u1edbi th\u00e1ng gi\u00eang n\u00ean c\u1ea3 hai t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c t\u1ea5t c\u1ea3 l\u00e0 819 chi ti\u1ebft m\u00e1y. T\u00ednh xem trong th\u00e1ng gi\u00eang m\u1ed7i t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c bao nhi\u00eau chi ti\u1ebft m\u00e1y. L\u1eddi gi\u1ea3i G\u1ecdi s\u1ed1 chi ti\u1ebft m\u00e1y trong th\u00e1ng gi\u00eang c\u1ee7a t\u1ed5 I v\u00e0 II l\u1ea7n l\u01b0\u1ee3t l\u00e0 x;y 0 x,y 720 V\u00ec trong th\u00e1ng gi\u00eang c\u1ea3 hai t\u1ed5 I v\u00e0 II s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 720 chi ti\u1ebft m\u00e1y, n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: x y 720 1 Trong th\u00e1ng hai c\u1ea3 hai t\u1ed5 I v\u00e0 II s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c 819 chi ti\u1ebft m\u00e1y, n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 115%x 112%y 819 2 x y 720 x 420 T\u1eeb 1 v\u00e0 2 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: 115%x 112%y 819 y 300 (th\u1ecfa m\u00e3n) V\u1eady s\u1ed1 chi ti\u1ebft m\u00e1y trong th\u00e1ng gi\u00eang c\u1ee7a t\u1ed5 I v\u00e0 II l\u1ea7n l\u01b0\u1ee3t l\u00e0 420; 300 chi ti\u1ebft m\u00e1y. C\u00e2u 6. (1 \u0111i\u1ec3m) M\u1ed9t v\u00e9 xem phim \u0111ang c\u00f3 gi\u00e1 l\u00e0 120 000 \u0111\u1ed3ng. Trong \u0111\u1ee3t gi\u1ea3m gi\u00e1 cu\u1ed1i n\u0103m 2022 , s\u1ed1 l\u01b0\u1ee3ng ng\u01b0\u1eddi xem phim t\u0103ng th\u00eam 50% n\u00ean t\u1ed5ng doanh thu c\u0169ng t\u0103ng l\u00ean 20% (so v\u1edbi l\u00fac ch\u01b0a gi\u1ea3m gi\u00e1). H\u1ecfi gi\u00e1 m\u1ed7i v\u00e9 khi \u0111\u00e3 gi\u1ea3m l\u00e0 bao nhi\u00eau \u0111\u1ed3ng? L\u1eddi gi\u1ea3i G\u1ecdi s\u1ed1 l\u01b0\u1ee3ng ng\u01b0\u1eddi xem tr\u01b0\u1edbc khi gi\u1ea3m gi\u00e1 v\u00e9 l\u00e0 x x * Doanh thu l\u00fac tr\u01b0\u1edbc:120 000x (\u0111\u1ed3ng) S\u1ed1 l\u01b0\u1ee3ng ng\u01b0\u1eddi xem sau khi gi\u1ea3m gi\u00e1 v\u00e9: 150%.x 1, 5x (ng\u01b0\u1eddi) Doanh thu l\u00fac sau:120 000x.120% 144 000x (\u0111\u1ed3ng) Gi\u00e1 m\u1ed7i v\u00e9 sau khi \u0111\u00e3 gi\u1ea3m:144 000x : 1, 5x 96000 (\u0111\u1ed3ng) V\u1eady gi\u00e1 m\u1ed7i v\u00e9 sau khi \u0111\u00e3 gi\u1ea3m l\u00e0 96000 (\u0111\u1ed3ng) C\u00e2u 7. (1 \u0111i\u1ec3m) M\u1ed9t xe b\u1ed3n ch\u1edf n\u01b0\u1edbc s\u1ea1ch cho m\u1ed9t khu d\u00e2n c\u01b0 c\u00f3 200 h\u1ed9 d\u00e2n. B\u1ed3n xe c\u00f3 h\u00ecnh d\u1ea1ng v\u00e0 k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd b\u00ean d\u01b0\u1edbi, m\u1ed7i \u0111\u1ea7u c\u1ee7a b\u1ed3n xe l\u00e0 n\u1eeda h\u00ecnh c\u1ea7u. Xe ch\u1edf \u0111\u1ea7y 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 n\u01b0\u1edbc v\u00e0 l\u01b0\u1ee3ng n\u01b0\u1edbc chia \u0111\u1ec1u cho t\u1eebng h\u1ed9 d\u00e2n. T\u00ednh xem m\u1ed7i h\u1ed9 d\u00e2n \u0111\u01b0\u1ee3c nh\u1eadn bao nhi\u00eau l\u00edt n\u01b0\u1edbc s\u1ea1ch. L\u1eddi gi\u1ea3i Th\u1ec3 t\u00edch c\u1ee7a b\u1ed3n ch\u1edf n\u01b0\u1edbc l\u00e0 : V = \uf070 R2h + 4 \uf070 R3 3 V = 3,14. \uf0e6 1, 8 \uf0f62 .3, 62 + 4 .3,14. \uf0e6 1, 8 \uf0f63 \uf0e7\uf0e8 2 \uf0f7\uf0f8 3 \uf0e7\uf0e8 2 \uf0f7\uf0f8 V \uf0bb 12, 259 (m3 ) \u0110\u1ed5i 12, 259 m3 = 12259 l S\u1ed1 l\u00edt n\u01b0\u1edbc m\u1ed7i h\u1ed9 d\u00e2n nh\u1eadn \u0111\u01b0\u1ee3c l\u00e0 : 12259 : 200 = 61, 295 (l ) C\u00e2u 8. (3 \u0111i\u1ec3m) T\u1eeb \u0111i\u1ec3m M n\u1eb1m \u1edf ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n O;R v\u1ebd hao ti\u1ebfp tuy\u1ebfn MA,MC v\u01a1i \u0111\u01b0\u1eddng tr\u00f2n ( A,C l\u00e0 hai ti\u1ebfp \u0111i\u1ec3m). V\u1ebd \u0111\u01b0\u1eddng k\u00ednh AB c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AMCO n\u1ed9i ti\u1ebfp v\u00e0 OM \/ \/BC . b) K\u1ebb CD AB D AB . BM c\u1eaft O t\u1ea1i N N B . Ch\u1ee9ng minh MAO v\u00e0 CDB MN CN 2 AB , t\u00ednh \u0111\u1ed3ng d\u1ea1ng v\u00e0 MB CB2 . c) G\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OM v\u00e0 AC ; K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a BM v\u00e0 CD . Khi OM theo R di\u1ec7n t\u00edch MIK . 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 MI O ND H K B C a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c AMCO n\u1ed9i ti\u1ebfp v\u00e0 OM \/ \/BC . X\u00e9t t\u1ee9 gi\u00e1c AMCO , c\u00f3: \uf0ec\uf0efMAO = 90\uf0b0( MA \u22a5 OA) \uf0ed \uf0ef\uf0eeMCO = 90\uf0b0( MC \u22a5 OC ) \uf0de MAO + MCO = 180\uf0b0 \uf0de T\u1ee9 gi\u00e1c BDEM n\u1ed9i ti\u1ebfp v\u00ec c\u00f3 hai g\u00f3c \u0111\u1ed1i b\u00f9 nhau. Ta c\u00f3 : + MA MC ( t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) + OA OC R MO l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n AC MO AC Ta l\u1ea1i c\u00f3 : ACB 90 (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n ) CB AC V\u00ec v\u1eady : MO \/ \/BC b) K\u1ebb CD AB D AB . BM c\u1eaft O t\u1ea1i N N B . Ch\u1ee9ng minh MAO v\u00e0 CDB MN CN 2 \u0111\u1ed3ng d\u1ea1ng v\u00e0 MB CB2 . X\u00e9t MAO v\u00e0 CDB c\u00f3 : + MAO CDB 90 + MOA CBD ( hai g\u00f3c \u0111\u1ed3ng v\u1ecb) MAO \u223d CDB g.g 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 X\u00e9t MCN v\u00e0 MBC c\u00f3 : + NMN l\u00e0 g\u00f3c chung + MCN MBC ( c\u00f9ng ch\u1eafn CN ) MCN \u223d MBC(g.g) MC MN CN MB MC CB ( t\u1ec9 l\u1ec7 \u0111\u1ed3ng d\u1ea1ng) MC MN MC 2 MN .MB V\u00ec MB MC MC CN MC 2 CN 2 MN.MB CN 2 MN CN 2 V\u00e0 v\u00ec MB CB MB2 CB2 MB CB2 MB2 CB 2 c) G\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a OM v\u00e0 AC ; K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a BM v\u00e0 CD . Khi OM AB , t\u00ednh theo R di\u1ec7n t\u00edch MIK . V\u00ec MO l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a AC v\u00e0 c\u1eaft AC t\u1ea1i I N\u00ean AI MO v\u00e0 I l\u00e0 trung \u0111i\u1ec3m AC X\u00e9t MAO vu\u00f4ng t\u1ea1i A c\u00f3 \u0111\u01b0\u1eddng cao AI + MO2 MA2 AO2 ( \u0111\u1ecbnh l\u00ed Py-ta-go) 4R2 MA2 R2 MA R 3 + MA2 MI.MO ( H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng) 3R2 MI .2R MI 3R 2 Ta c\u00f3 : S MOB 1 BO.MA 1 .R.R 3 R2 3 2 2 2 G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AM v\u00e0 BC . V\u00ec MO \/ \/BC MO \/ \/BH X\u00e9t BAH c\u00f3 : + O l\u00e0 trung \u0111i\u1ec3m AB + MO \/ \/BC M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n AH. MA MH 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 X\u00e9t BAM c\u00f3 DK \/ \/AM BD DK BM AM ( H\u1ec7 qu\u1ea3 \u0111\u1ecbnh l\u00ed Ta l\u00e9t) X\u00e9t BMH c\u00f3 CK \/ \/MH BK CK BM MH ( H\u1ec7 qu\u1ea3 \u0111\u1ecbnh l\u00ed Ta l\u00e9t) DK CK T\u1eeb \u0111\u00f3 suy ra : AM MH M\u00e0 AM MH cmt N\u00ean KD CK K l\u00e0 trung \u0111i\u1ec3m CD X\u00e9t CDA c\u00f3 + K l\u00e0 trung \u0111i\u1ec3m CD + I l\u00e0 trung \u0111i\u1ec3m AC IK l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a CDA IK \/ \/AD IK \/ \/OB X\u00e9t MIK v\u00e0 MOB c\u00f3 : + BMO l\u00e0 g\u00f3c chung. + MKI MBO ( hai g\u00f3c \u0111\u1ed3ng v\u1ecb) MIK \u223d MOB g.g S MIK MI 2 9 R2 9 S MOB MO 2 4 16 4R2 S MIK 9S MOB 9 . R2 3 9R2 3 16 16 2 32 (\u0111vdt). ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 11","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH S\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 3 NA\u00caM HO\u00cfC: 2021 - 2022 \u0110\u1ec0 THAM KH\u1ea2O M\u00d4N: TO\u00c1N 9 M\u00c3 \u0110\u1ec0: Qu\u1eadn 3 - 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) Gi\u00e1o vi\u00ean s\u1eeda ph\u1ea7n m\u00e0u \u0111\u1ecf theo m\u00e3 \u0111\u1ec1 c\u1ee7a m\u00ecnh ( ) ( )C\u00e2u 1. (1,5 \u0111i\u1ec3m). Cho h\u00e0m s\u1ed1 y = x2 c\u00f3 \u0111\u1ed3 th\u1ecb P v\u00e0 h\u00e0m s\u1ed1 y = x + 2 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 d . ( ) ( )a) V\u1ebd P v\u00e0 d tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1eb3ng 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 5x2 \u2212 7x + 1 = 0 1 (x l\u00e0 \u1ea9n s\u1ed1). a) Ch\u1ee9ng minh ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1, x2 . b) T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c A x1 7 x1 1 x 2 . 5 2 25x 2 2 L\u01b0u \u00fd: T\u1eeb b\u00e0i n\u00e0y, c\u00e1c s\u1ed1 li\u1ec7u t\u00ednh to\u00e1n v\u1ec1 \u0111\u1ed9 d\u00e0i khi l\u00e0m tr\u00f2n (n\u1ebfu c\u00f3) l\u1ea5y \u0111\u1ebfn m\u1ed9t ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, s\u1ed1 \u0111o g\u00f3c l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat. C\u00e2u 3. (1 \u0111i\u1ec3m). Tr\u00ean m\u1ed9t kh\u00fac s\u00f4ng, v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y (c\u1ee7a n\u01b0\u1edbc) \u1edf b\u1ec1 m\u1eb7t l\u1edbn h\u01a1n v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng. G\u1ecdi v km \/ h l\u00e0 v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng, f km \/ h l\u00e0 v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng, c\u00e1c nh\u00e0 khoa h\u1ecdc \u0111\u00e3 t\u00ecm \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c th\u1ec3 hi\u1ec7n m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa v\u1eadn t\u1ed1c n\u00e0y l\u00e0: f v 1, 31 . a) N\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 9, 31km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ph\u1ea7n tr\u0103m km \/ h ) b) N\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 20, 32km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ph\u1ea7n tr\u0103m km \/ h ) C\u00e2u 4. (1 \u0111i\u1ec3m). Th\u1edbt l\u00e0 d\u1ee5ng c\u1ee5 s\u1eed d\u1ee5ng trong b\u1ebfp c\u1ee7a m\u1ed7i gia \u0111\u00ecnh. X\u00e9t m\u1ed9t c\u00e1i th\u1edbt b\u1eb1ng g\u1ed7 c\u00f3 h\u00ecnh tr\u1ee5 v\u1edbi \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y 22cm , chi\u1ec1u cao 4cm . a) T\u00ednh t\u1ed5ng di\u1ec7n t\u00edch hai m\u1eb7t th\u1edbt (l\u00e0m tr\u00f2n \u0111\u1ebfn \u0111\u01a1n v\u1ecb cm2 ). b) Cho bi\u1ebft lo\u1ea1i g\u1ed7 l\u00e0m th\u1edbt c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang l\u00e0 500kg \/ m3 . T\u00ednh kh\u1ed1i l\u01b0\u1ee3ng (theo \u0111\u01a1n v\u1ecb gam) c\u1ee7a c\u00e1i th\u1edbt tr\u00ean. Bi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V c\u1ee7a h\u00ecnh tr\u1ee5 l\u00e0 V S.h ( S l\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 h l\u00e0 chi\u1ec1u cao h\u00ecnh tr\u1ee5). T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 1","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH C\u00e2u 5. (1 \u0111i\u1ec3m). Trong m\u00f4n b\u00f3ng \u0111\u00e1, ban \u0111\u1ea7u c\u00e1c qu\u1ea3 b\u00f3ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c l\u00e0m b\u1eb1ng b\u00e0ng quang ho\u1eb7c d\u1ea1 d\u00e0y c\u1ee7a \u0111\u1ed9ng v\u1eadt. Nh\u1eefng qu\u1ea3 b\u00f3ng n\u00e0y d\u1ec5 b\u1ecb v\u1ee1. \u0110\u1ebfn th\u1ec3 k\u1ef7 19, v\u1edbi nh\u1eefng kh\u00e1m ph\u00e1 v\u1ec1 l\u01b0u h\u00f3a c\u1ee7a Charles Goodyear, b\u00f3ng \u0111\u01b0\u1ee3c l\u00e0m b\u1eb1ng cao su. Cu\u1ed1i th\u1ec3 k\u1ef7 20, qu\u1ea3 b\u00f3ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c l\u00e0m t\u1eeb 32 m\u1ea3nh gh\u00e9p nh\u1ecf do Eigil Nielsen ph\u00e1t tri\u1ec3n v\u00e0o n\u0103m 1962. Cho \u0111\u1ebfn h\u00f4m nay, ng\u01b0\u1eddi ta \u0111\u00e3 \u1ee9ng d\u1ee5ng th\u00eam nhi\u1ec1u c\u00f4ng ngh\u1ec7 kh\u00e1c n\u1eefa \u0111\u1ec3 l\u00e0m qu\u1ea3 b\u00f3ng. X\u00e9t m\u1ed9t qu\u1ea3 b\u00f3ng \u0111\u01b0\u1ee3c gh\u00e9p t\u1eeb 32 m\u1ea3nh da g\u1ed3m c\u00e1c m\u1ea3nh h\u00ecnh l\u1ee5c gi\u00e1c m\u00e0u tr\u1eafng v\u00e0 h\u00ecnh ng\u0169 gi\u00e1c m\u00e0u \u0111en. M\u1ed7i m\u1ea3nh m\u00e0u \u0111en r\u00e1p v\u1edbi 5 m\u1ea3nh m\u00e0u tr\u1eafng. M\u1ed7i m\u1ea3nh m\u00e0u tr\u1eafng r\u00e1p v\u1edbi 3 m\u1ea3nh m\u00e0u \u0111en v\u00e0 3 m\u1ea3nh m\u00e0u tr\u1eafng (H\u00ecnh 1). H\u1ecfi qu\u1ea3 b\u00f3ng n\u00e0y c\u00f3 bao nhi\u00eau m\u1ea3nh m\u00e0u tr\u1eafng? C\u00e2u 6. (0,75 \u0111i\u1ec3m). M\u1ed9t c\u1eeda h\u00e0ng th\u1ef1c hi\u1ec7n ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i m\u1ed9t s\u1ea3n ph\u1ea9m b\u00e1nh kem: Mua 4 t\u1eb7ng 1. Gi\u00e1 b\u00e1n 1 b\u00e1nh l\u00e0 50 000 \u0111\u1ed3ng. B\u00ecnh mua 12 b\u00e1nh, Mai mua 13 b\u00e1nh. B\u00ecnh n\u00f3i v\u1edbi Mai gh\u00f3p ti\u1ec1n mua chung s\u1ebd t\u1ed1n \u00edt ti\u1ec1n h\u01a1n khi t\u1eebng ng\u01b0\u1eddi mua ri\u00eang. H\u00e3y t\u00ednh xem khi Mai v\u00e0 B\u00ecnh mua chung th\u00ec s\u1ebd \u0111\u1ee1 t\u1ed1n h\u01a1n bao nhi\u00eau ti\u1ec1n v\u00e0 m\u1ed7i ng\u01b0\u1eddi s\u1ebd chi tr\u1ea3 bao nhi\u00eau. C\u00e2u 7. (0,75 \u0111i\u1ec3m). C\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ee7a l\u1edbp 9A d\u1ef1 \u0111\u1ecbnh \u0111\u00f3ng gh\u00f3p m\u1ed9t s\u1ed1 ti\u1ec1n \u0111\u1ec3 mua t\u1eb7ng cho m\u1ed7i em \u1edf M\u00e1i \u1ea5m t\u00ednh th\u01b0\u01a1ng ba m\u00f3n qu\u00e0 (gi\u00e1 ti\u1ec1n c\u00e1c m\u00f3n qu\u00e0 \u0111\u1ec1u nh\u01b0 nhau). Khi c\u00e1c b\u1ea1n \u0111\u00f3ng \u0111\u1ee7 s\u1ed1 ti\u1ec1n nh\u01b0 d\u1ef1 \u0111\u1ecbnh th\u00ec M\u00e1i \u1ea5m \u0111\u00e3 nh\u1eadn ch\u0103m s\u00f3c th\u00eam 9 em v\u00e0 gi\u00e1 ti\u1ec1n m\u1ed7i m\u00f3n qu\u00e0 l\u1ea1i t\u0103ng th\u00eam 5% n\u00ean s\u1ed1 ti\u1ec1n c\u00f3 \u0111\u01b0\u1ee3c ch\u1ec9 v\u1eeba \u0111\u1ee7 \u0111\u1ec3 t\u1eb7ng m\u1ed7i em hai m\u00f3n qu\u00e0. H\u1ecfi hi\u1ec7n t\u1ea1i M\u00e1i \u1ea5m c\u00f3 bao nhi\u00eau em? C\u00e2u 8. (3 \u0111i\u1ec3m) Cho AB v\u00e0 CD l\u00e0 hai \u0111\u01b0\u1eddng k\u00ednh vu\u00f4ng g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O;R . G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a b\u00e1n k\u00ednh OD . Tia AI c\u1eaft O t\u1ea1i P P A . Ti\u1ebfp tuy\u1ebfn t\u1ea1i P c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O c\u1eaft tia AB t\u1ea1i T . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c PIOB n\u1ed9i ti\u1ebfp v\u00e0 BTP + 2TPB = 90\uf0b0 . b) K\u1ebb PK AB K AB . G\u1ecdi Q l\u00e0 giao \u0111i\u1ec3m c\u1ee7a TP v\u00e0 CD . Ch\u1ee9ng minh PQI 2 11 c\u00e2n v\u00e0 KT KB KA . c) T\u00ednh theo R di\u1ec7n t\u00edch ACP . ----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 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 = x2 c\u00f3 \u0111\u1ed3 th\u1ecb P v\u00e0 h\u00e0m s\u1ed1 y = x + 2 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 d . ( ) ( )a) V\u1ebd P v\u00e0 d tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1eb3ng 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 P v\u00e0 d tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy . BGT: x \u22122 \u22121 0 1 2 y = x2 4 1 0 1 4 x 01 y=x+2 2 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 : x2 = x + 2 \uf0db x2 \u2212 x \u2212 2 = 0 \uf0db \uf0e9x = \u22121 \uf0ea\uf0ebx = 2 Thay x 1 v\u00e0o y x 2 , ta \u0111\u01b0\u1ee3c: y 1 2 1. Thay x = 2 v\u00e0o y x 2 , ta \u0111\u01b0\u1ee3c: y 22 4 . V\u1eady 1; 1 , 2; 4 l\u00e0 hai giao \u0111i\u1ec3m c\u1ea7n t\u00ecm. C\u00e2u 2. (1 \u0111i\u1ec3m) Cho ph\u01b0\u01a1ng tr\u00ecnh 5x2 \u2212 7x + 1 = 0 1 (x l\u00e0 \u1ea9n s\u1ed1). a) Ch\u1ee9ng minh ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1, x2 . b) T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c A x1 7 x1 1 x 2 . 5 2 25x 2 2 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 L\u1eddi gi\u1ea3i a) Ch\u1ee9ng minh ph\u01b0\u01a1ng tr\u00ecnh 1 c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1, x2 . Ph\u01b0\u01a1ng tr\u00ecnh 5x2 \u2212 7x + 1 = 0 1 ( x l\u00e0 \u1ea9n s\u1ed1). V\u00ec \uf044 = b2 \u2212 4ac = (\u22127 )2 \u2212 4.5.1 = 29 \uf03e 0 N\u00ean ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 ,x2 . b) T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c A x1 7 x1 1 x 2 . 5 2 25x 2 2 \uf0ec\uf0ef\uf0efS = x1 + x2 = \u2212b = 7 \uf0ed = x1 a 5 Theo \u0111\u1ecbnh l\u00ed Vi-et, ta c\u00f3: \uf0ef\uf0ef\uf0eeP 1 c = 5 .x2 = a Ta c\u00f3: A x1 7 x1 1 x 2 5 2 25x 2 2 ( )A = \uf0e9\uf0ebx1 \u2212 \uf0f9\uf0fb x1 \uf0e6 1 \uf0f62 1 x22 x1 + x2 + \uf0e7 5 \uf0f7 . x22 + \uf0f8 \uf0e8 ( )A = \u2212x2.x1 + 2 1 + x22 x1 .x2 . x22 A = \u2212x1.x2 + x12 + x22 ( )A = x1 + x2 2 \u2212 3x1.x2 A = \uf0e6 7 \uf0f62 \u2212 3. 1 \uf0e7 5 \uf0f7 5 \uf0e8 \uf0f8 A = 49 \u2212 3 25 5 A = 34 25 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) Tr\u00ean m\u1ed9t kh\u00fac s\u00f4ng, v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y (c\u1ee7a n\u01b0\u1edbc) \u1edf b\u1ec1 m\u1eb7t l\u1edbn h\u01a1n v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng. G\u1ecdi v km \/ h l\u00e0 v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng, f km \/ h l\u00e0 v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng, c\u00e1c nh\u00e0 khoa h\u1ecdc \u0111\u00e3 t\u00ecm \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c th\u1ec3 hi\u1ec7n m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa v\u1eadn t\u1ed1c n\u00e0y l\u00e0: f v 1, 31 . a) N\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 9, 31km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ph\u1ea7n tr\u0103m km \/ h ) 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 v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 20, 32km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ph\u1ea7n tr\u0103m km \/ h ) L\u1eddi gi\u1ea3i a) N\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 9, 31km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ph\u1ea7n tr\u0103m km \/ h ) Ta c\u00f3: v 9, 31km \/ h thay v\u00e0o c\u00f4ng th\u1ee9c f v 1, 31 f 9, 31 1, 31 2 f 9, 31 1, 31 3, 03 km \/ h V\u1eady n\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 9, 31km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 3, 03 km \/ h . b) N\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 20, 32km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ph\u1ea7n tr\u0103m km \/ h ) Ta c\u00f3: f 20, 32km \/ h thay v\u00e0o c\u00f4ng th\u1ee9c f v 1, 31 20, 32 v 1, 31 v 20, 32 1, 31 2 v 20, 32 1, 31 v 33, 85 km \/ h V\u1eady n\u1ebfu v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf \u0111\u00e1y s\u00f4ng l\u00e0 20, 32km \/ h th\u00ec v\u1eadn t\u1ed1c d\u00f2ng ch\u1ea3y \u1edf b\u1ec1 m\u1eb7t s\u00f4ng l\u00e0 33, 85 km \/ h . C\u00e2u 4. (1 \u0111i\u1ec3m) Th\u1edbt l\u00e0 d\u1ee5ng c\u1ee5 s\u1eed d\u1ee5ng trong b\u1ebfp c\u1ee7a m\u1ed7i gia \u0111\u00ecnh. X\u00e9t m\u1ed9t c\u00e1i th\u1edbt b\u1eb1ng g\u1ed7 c\u00f3 h\u00ecnh tr\u1ee5 v\u1edbi \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y 22cm , chi\u1ec1u cao 4cm . a) T\u00ednh t\u1ed5ng di\u1ec7n t\u00edch hai m\u1eb7t th\u1edbt (l\u00e0m tr\u00f2n \u0111\u1ebfn \u0111\u01a1n v\u1ecb cm2 ). b) Cho bi\u1ebft lo\u1ea1i g\u1ed7 l\u00e0m th\u1edbt c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang l\u00e0 500kg \/ m3 . T\u00ednh kh\u1ed1i l\u01b0\u1ee3ng (theo \u0111\u01a1n v\u1ecb gam) c\u1ee7a c\u00e1i th\u1edbt tr\u00ean. Bi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V c\u1ee7a h\u00ecnh tr\u1ee5 l\u00e0 V S.h ( S l\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 h l\u00e0 chi\u1ec1u cao h\u00ecnh tr\u1ee5). L\u1eddi gi\u1ea3i a) T\u00ednh t\u1ed5ng di\u1ec7n t\u00edch hai m\u1eb7t th\u1edbt (l\u00e0m tr\u00f2n \u0111\u1ebfn \u0111\u01a1n v\u1ecb cm2 ). 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\u00e1n k\u00ednh \u0111\u00e1y th\u1edbt l\u00e0: r 22 : 2 11 cm T\u1ed5ng di\u1ec7n t\u00edch hai m\u1eb7t th\u1edbt l\u00e0: 2 r2 2 .112 760 cm2 b) Cho bi\u1ebft lo\u1ea1i g\u1ed7 l\u00e0m th\u1edbt c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang l\u00e0 500kg \/ m3 . T\u00ednh kh\u1ed1i l\u01b0\u1ee3ng (theo \u0111\u01a1n v\u1ecb gam) c\u1ee7a c\u00e1i th\u1edbt tr\u00ean. Bi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V c\u1ee7a h\u00ecnh tr\u1ee5 l\u00e0 V S.h ( S l\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 h l\u00e0 chi\u1ec1u cao h\u00ecnh tr\u1ee5). Th\u1ec3 t\u00edch c\u1ee7a th\u1edbt l\u00e0: V S.h .r2.h .112.4 1520,53 cm3 0,00152053 m3 Kh\u1ed1i l\u01b0\u1ee3ng c\u1ee7a th\u1edbt l\u00e0: 0, 00152053.500 0, 76 kg 760 g C\u00e2u 5. (1 \u0111i\u1ec3m) Trong m\u00f4n b\u00f3ng \u0111\u00e1, ban \u0111\u1ea7u c\u00e1c qu\u1ea3 b\u00f3ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c l\u00e0m b\u1eb1ng b\u00e0ng quang ho\u1eb7c d\u1ea1 d\u00e0y c\u1ee7a \u0111\u1ed9ng v\u1eadt. Nh\u1eefng qu\u1ea3 b\u00f3ng n\u00e0y d\u1ec5 b\u1ecb v\u1ee1. \u0110\u1ebfn th\u1ec3 k\u1ef7 19, v\u1edbi nh\u1eefng kh\u00e1m ph\u00e1 v\u1ec1 l\u01b0u h\u00f3a c\u1ee7a Charles Goodyear, b\u00f3ng \u0111\u01b0\u1ee3c l\u00e0m b\u1eb1ng cao su. Cu\u1ed1i th\u1ec3 k\u1ef7 20, qu\u1ea3 b\u00f3ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c l\u00e0m t\u1eeb 32 m\u1ea3nh gh\u00e9p nh\u1ecf do Eigil Nielsen ph\u00e1t tri\u1ec3n v\u00e0o n\u0103m 1962. Cho \u0111\u1ebfn h\u00f4m nay, ng\u01b0\u1eddi ta \u0111\u00e3 \u1ee9ng d\u1ee5ng th\u00eam nhi\u1ec1u c\u00f4ng ngh\u1ec7 kh\u00e1c n\u1eefa \u0111\u1ec3 l\u00e0m qu\u1ea3 b\u00f3ng. X\u00e9t m\u1ed9t qu\u1ea3 b\u00f3ng \u0111\u01b0\u1ee3c gh\u00e9p t\u1eeb 32 m\u1ea3nh da g\u1ed3m c\u00e1c m\u1ea3nh h\u00ecnh l\u1ee5c gi\u00e1c m\u00e0u tr\u1eafng v\u00e0 h\u00ecnh ng\u0169 gi\u00e1c m\u00e0u \u0111en. M\u1ed7i m\u1ea3nh m\u00e0u \u0111en r\u00e1p v\u1edbi 5 m\u1ea3nh m\u00e0u tr\u1eafng. M\u1ed7i m\u1ea3nh m\u00e0u tr\u1eafng r\u00e1p v\u1edbi 3 m\u1ea3nh m\u00e0u \u0111en v\u00e0 3 m\u1ea3nh m\u00e0u tr\u1eafng (H\u00ecnh 1). H\u1ecfi qu\u1ea3 b\u00f3ng n\u00e0y c\u00f3 bao nhi\u00eau m\u1ea3nh m\u00e0u tr\u1eafng? L\u1eddi gi\u1ea3i G\u1ecdi s\u1ed1 m\u1ea3nh m\u00e0u tr\u1eafng l\u00e0 x (m\u1ea3nh) s\u1ed1 m\u1ea3nh m\u00e0u \u0111en l\u00e0 y (m\u1ea3nh) \u0110k: x,y * T\u1ed5ng s\u1ed1 m\u1ea3nh gh\u00e9p l\u00e0 32 x y 32 1 V\u00ec m\u1ed7i m\u1ea3nh m\u00e0u \u0111en r\u00e1p v\u1edbi 5 m\u1ea3nh m\u00e0u tr\u1eafng v\u00e0 m\u1ed7i m\u1ea3nh m\u00e0u tr\u1eafng r\u00e1p v\u1edbi 3 m\u1ea3nh m\u00e0u \u0111en 3x 5y 2 T\u1eeb 1 , 2 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: x y 32 x y 32 x 20 3x 5y 3x 5y 0 y 12 (nh\u1eadn) V\u1eady qu\u1ea3 b\u00f3ng n\u00e0y c\u00f3 20 m\u1ea3nh m\u00e0u tr\u1eafng. 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 6. (0,75 \u0111i\u1ec3m) M\u1ed9t c\u1eeda h\u00e0ng th\u1ef1c hi\u1ec7n ch\u01b0\u01a1ng tr\u00ecnh khuy\u1ebfn m\u00e3i m\u1ed9t s\u1ea3n ph\u1ea9m b\u00e1nh kem: Mua 4 t\u1eb7ng 1. Gi\u00e1 b\u00e1n 1 b\u00e1nh l\u00e0 50 000 \u0111\u1ed3ng. B\u00ecnh mua 12 b\u00e1nh, Mai mua 13 b\u00e1nh. B\u00ecnh n\u00f3i v\u1edbi Mai gh\u00f3p ti\u1ec1n mua chung s\u1ebd t\u1ed1n \u00edt ti\u1ec1n h\u01a1n khi t\u1eebng ng\u01b0\u1eddi mua ri\u00eang. H\u00e3y t\u00ednh xem khi Mai v\u00e0 B\u00ecnh mua chung th\u00ec s\u1ebd \u0111\u1ee1 t\u1ed1n h\u01a1n bao nhi\u00eau ti\u1ec1n v\u00e0 m\u1ed7i ng\u01b0\u1eddi s\u1ebd chi tr\u1ea3 bao nhi\u00eau. L\u1eddi gi\u1ea3i TH1. Hai b\u1ea1n mua b\u00e1nh ri\u00eang B\u00ecnh mua 12 b\u00e1nh n\u00ean B\u00ecnh ch\u1ec9 c\u1ea7n mua 10 b\u00e1nh (v\u00ec mua 8 t\u1eb7ng 2 ) S\u1ed1 ti\u1ec1n B\u00ecnh ph\u1ea3i tr\u1ea3 l\u00e0: 10.50 000 500 000 (\u0111\u1ed3ng) Mai mua 13 b\u00e1nh n\u00ean Mai ch\u1ec9 c\u1ea7n mua 11 b\u00e1nh (v\u00ec mua 8 t\u1eb7ng 2 ) S\u1ed1 ti\u1ec1n Mai ph\u1ea3i tr\u1ea3 l\u00e0: 11.50 000 550 000 (\u0111\u1ed3ng) T\u1ed5ng s\u1ed1 ti\u1ec1n mua ri\u00eang ph\u1ea3i tr\u1ea3 c\u1ee7a 2 b\u1ea1n l\u00e0: 500 000 550 000 1050 000 (\u0111\u1ed3ng) TH2. Hai b\u1ea1n gh\u00f3p ti\u1ec1n mua b\u00e1nh chung T\u1ed5ng s\u1ed1 b\u00e1nh 2 b\u1ea1n mua chung l\u00e0 25 b\u00e1nh n\u00ean 2 b\u1ea1n ch\u1ec9 c\u1ea7n mua 20 b\u00e1nh (v\u00ec mua 20 t\u1eb7ng 5 ) T\u1ed5ng s\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 khi 2 b\u1ea1n mua chung l\u00e0: 20.50 000 1000 000 (\u0111\u1ed3ng) S\u1ed1 ti\u1ec1n ti\u1ebft ki\u1ec7m khi 2 b\u1ea1n mua chung l\u00e0: 1050 000 1000 000 50 000 (\u0111\u1ed3ng) S\u1ed1 ti\u1ec1n B\u00ecnh ph\u1ea3i tr\u1ea3 khi mua chung l\u00e0: 1000 000.12 480 000 (\u0111\u1ed3ng) 25 S\u1ed1 ti\u1ec1n Mai ph\u1ea3i tr\u1ea3 khi mua chung l\u00e0: 1000 000.13 520 000 (\u0111\u1ed3ng) 25 C\u00e2u 7. (0,75 \u0111i\u1ec3m) C\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ee7a l\u1edbp 9A d\u1ef1 \u0111\u1ecbnh \u0111\u00f3ng gh\u00f3p m\u1ed9t s\u1ed1 ti\u1ec1n \u0111\u1ec3 mua t\u1eb7ng cho m\u1ed7i em \u1edf M\u00e1i \u1ea5m t\u00ecnh th\u01b0\u01a1ng ba m\u00f3n qu\u00e0 (gi\u00e1 ti\u1ec1n c\u00e1c m\u00f3n qu\u00e0 \u0111\u1ec1u nh\u01b0 nhau). Khi c\u00e1c b\u1ea1n \u0111\u00f3ng \u0111\u1ee7 s\u1ed1 ti\u1ec1n nh\u01b0 d\u1ef1 \u0111\u1ecbnh th\u00ec M\u00e1i \u1ea5m \u0111\u00e3 nh\u1eadn ch\u0103m s\u00f3c th\u00eam 9 em v\u00e0 gi\u00e1 ti\u1ec1n m\u1ed7i m\u00f3n qu\u00e0 l\u1ea1i t\u0103ng th\u00eam 5% n\u00ean s\u1ed1 ti\u1ec1n c\u00f3 \u0111\u01b0\u1ee3c ch\u1ec9 v\u1eeba \u0111\u1ee7 \u0111\u1ec3 t\u1eb7ng m\u1ed7i em hai m\u00f3n qu\u00e0. H\u1ecfi hi\u1ec7n t\u1ea1i M\u00e1i \u1ea5m c\u00f3 bao nhi\u00eau em? L\u1eddi gi\u1ea3i G\u1ecdi s\u1ed1 em l\u00fac ban \u0111\u1ea7u \u1edf M\u00e1i \u1ea5m l\u00e0 x (em) S\u1ed1 em l\u00fac t\u1eb7ng qu\u00e0 \u1edf M\u00e1i \u1ea5m l\u00e0 x 9 (em) \u0110k: x * 8 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 Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: x.3 x 9 .2.105% 3x x 9 .2,1 3x 2,1x 18, 9 0, 9x 18, 9 x 21 nh ?n V\u1eady hi\u1ec7n t\u1ea1i M\u00e1i \u1ea5m c\u00f3: 21 9 30 (em) C\u00e2u 8. (3 \u0111i\u1ec3m) Cho AB v\u00e0 CD l\u00e0 hai \u0111\u01b0\u1eddng k\u00ednh vu\u00f4ng g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O;R . G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a b\u00e1n k\u00ednh OD . Tia AI c\u1eaft O t\u1ea1i P P A . Ti\u1ebfp tuy\u1ebfn t\u1ea1i P c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n O c\u1eaft tia AB t\u1ea1i T . a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c PIOB n\u1ed9i ti\u1ebfp v\u00e0 BTP + 2TPB = 90\uf0b0 . b) K\u1ebb PK AB K AB . G\u1ecdi Q l\u00e0 giao \u0111i\u1ec3m c\u1ee7a TP v\u00e0 CD . Ch\u1ee9ng minh PQI 2 11 c\u00e2n v\u00e0 KT KB KA . c) T\u00ednh theo R di\u1ec7n t\u00edch ACP . L\u1eddi gi\u1ea3i 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 a) Ch\u1ee9ng minh t\u1ee9 gi\u00e1c PIOB n\u1ed9i ti\u1ebfp v\u00e0 BTP + 2TPB = 90\uf0b0 . X\u00e9t t\u1ee9 gi\u00e1c PIOB , c\u00f3: IOB 90 AB CD IPB 90 AP PB \uf0de IOB + IPB = 180\uf0b0 T\u1ee9 gi\u00e1c PIOB n\u1ed9i ti\u1ebfp v\u00ec c\u00f3 hai g\u00f3c \u0111\u1ed1i b\u00f9 nhau. X\u00e9t OPT c\u00f3: OP PT (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn ) OPT vu\u00f4ng t\u1ea1i P POT PTO 90 M\u00e0 POT 2TPB (G\u00f3c \u1edf t\u00e2m, g\u00f3c t\u1ea1o b\u1edfi ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung c\u00f9ng ch\u1eafn BP ) BTP 2.TPB 90 b) K\u1ebb PK AB K AB . G\u1ecdi Q l\u00e0 giao \u0111i\u1ec3m c\u1ee7a TP v\u00e0 CD . Ch\u1ee9ng minh PQI 2 11 c\u00e2n v\u00e0 KT KB KA . Ta c\u00f3: t\u1ee9 gi\u00e1c PIOB n\u1ed9i ti\u1ebfp PIQ OBP (g\u00f3c ngo\u00e0i = g\u00f3c \u0111\u1ed1i trong) M\u00e0 ABP APQ (G\u00f3c n\u1ed9i ti\u1ebfp, g\u00f3c t\u1ea1o b\u1edfi ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung c\u00f9ng ch\u1eafn AP ) PIQ APQ X\u00e9t PQI c\u00f3: PIQ IPQ PQI c\u00e2n t\u1ea1i Q . 2 11 Ta c\u00f3: KT KB KA 2 KA KB KT KA.KB 2KA.KB KT. KA KB 2KA.KB KT. OA OK KB 2KA.KB KT. OA KB OK 2KA.KB KT. OK OK 2KA.KB KT.2OK KA.KB KT.OK X\u00e9t APB vu\u00f4ng t\u1ea1i P c\u00f3 \u0111\u01b0\u1eddng cao PK 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 KA.KB KP 2 1 X\u00e9t OPT vu\u00f4ng t\u1ea1i P c\u00f3 \u0111\u01b0\u1eddng cao PK KT.KO KP2 2 T\u1eeb 1 , 2 KA.KB KT.KO 2 11 5R2 R 5 V\u1eady KT KB KA . 42 c) T\u00ednh theo R di\u1ec7n t\u00edch ACP . K\u1ebb PN OD t\u1ea1i N X\u00e9t t\u1ee9 gi\u00e1c OKPN c\u00f3: PKO KON ONP 90 T\u1ee9 gi\u00e1c OKPN l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt OK PN X\u00e9t AOI vu\u00f4ng t\u1ea1i O AI AO2 OI 2 R2 R 2 2 X\u00e9t AOI v\u00e0 APB c\u00f3: A chung AOI APB 90 \uf0de \uf044AOI #\uf044APB (g \u2013 g) AO AI OI (TS\u0110D) AP AB PB AO AI Ta c\u00f3: AP AB R5 R2 AP 2R AP R.2R R5 2 AP 4R 5 X\u00e9t APB vu\u00f4ng t\u1ea1i P c\u00f3 d\u01b0\u1eddng cao PK T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 11","TUY\u1ec2N T\u1eacP \u0110\u1ec0 THAM KH\u1ea2O TUY\u1ec2N SINH 10 TP H\u1ed2 CH\u00cd MINH AP 2 AK.AB 4R 2 AK.2R 5 16R2 AK.2R 5 AK 16R2 : 2R 5 AK 8R 5 V\u1eady S ACP S ACI S CPI S ACP 1 AO.CI 1 PN .CI S ACP 2 2 S ACP 1 S ACP 2 CI AO PN S ACP 1CI AO OK 2 1CI .AK 2 6R2 dvdt 1 R 8R 1 3R 8R 5 2 R 2 . 5 2 2 . 5 ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 12","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 3 NA\u00caM HO\u00cfC: 2023 - 2024 M\u00d4N: TO\u00c1N 9 \u0110\u1ec0 THAM KH\u1ea2O M\u00c3 \u0110\u1ec0: Qu\u1eadn 3 - 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 parabol (P) : y = 1 x2 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = x + 4 . 2 a) V\u1ebd (P) v\u00e0 (d) tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy . b) X\u00e1c \u0111\u1ecbnh 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 6x2 + 6x \u2212 13 = 0 c\u00f3 2 nghi\u1ec7m l\u00e0 x1 v\u00e0 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 \u2212 1 + x2 \u2212 x1 \u2212 1 . x2 x1 C\u00e2u 3. (1 \u0111i\u1ec3m). C\u00f3 hai h\u00e3ng \u0111i\u1ec7n tho\u1ea1i c\u1ed1 \u0111\u1ecbnh t\u00ednh ph\u00ed g\u1ecdi cho c\u00e1c thu\u00ea bao nh\u01b0 sau: H\u00e3ng Thu\u00ea bao (ng\u00e0n \u0111\u1ed3ng\/th\u00e1ng) G\u1ecdi n\u1ed9i h\u1ea1t (ng\u00e0n \u0111\u1ed3ng\/ 30 ph\u00fat) H\u00e3ng A 10 6 H\u00e3ng B 15 5 G\u1ecdi y (ng\u00e0n \u0111\u1ed3ng) l\u00e0 gi\u00e1 ti\u1ec1n m\u00e0 kh\u00e1ch h\u00e0ng ph\u1ea3i tr\u1ea3 sau x l\u1ea7n 30 ph\u00fat x * Bi\u1ebft c\u01b0\u1edbc ph\u00ed h\u00e0ng th\u00e1ng b\u1eb1ng t\u1ed5ng ti\u1ec1n thu\u00ea bao v\u00e0 c\u01b0\u1edbc ph\u00ed g\u1ecdi n\u1ed9i h\u1ea1t. a) H\u00e3y bi\u1ec3u di\u1ec5n y theo x c\u1ee7a t\u1eebng h\u00e3ng, bi\u1ebft r\u1eb1ng y ax b (a,b l\u00e0 s\u1ed1 x\u00e1c \u0111\u1ecbnh). b) H\u00e3y cho bi\u1ebft v\u1edbi c\u00e1ch t\u00ednh ph\u00ed nh\u01b0 tr\u00ean th\u00ec m\u1ed9t kh\u00e1ch h\u00e0ng m\u1ed7i th\u00e1ng g\u1ecdi b\u00ecnh qu\u00e2n 6 gi\u1edd n\u00ean s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 c\u1ee7a h\u00e3ng n\u00e0o s\u1ebd r\u1ebb h\u01a1n? C\u00e2u 4. (1 \u0111i\u1ec3m). M\u1ed9t chi\u1ebfc n\u00f3n l\u00e1 c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n nh\u01b0 h\u00ecnh b\u00ean: \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng sinh l\u00e0 25cm , b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y l\u00e0 15cm . T\u00ednh th\u1ec3 t\u00edch c\u1ee7a chi\u1ebfc n\u00f3n; bi\u1ebft V 1 S.h , v\u1edbi V 3 l\u00e0 th\u1ec3 t\u00edch, S l\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh n\u00f3n. C\u00e2u 5. (1 \u0111i\u1ec3m). Th\u00e1ng tr\u01b0\u1edbc, hai t\u1ed5 c\u00f4ng nh\u00e2n s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c t\u1ed5ng c\u1ed9ng 750 chi ti\u1ebft m\u00e1y. Do k\u0129 thu\u1eadt \u0111\u01b0\u1ee3c c\u1ea3i ti\u1ebfn, th\u00e1ng n\u00e0y s\u1ed1 l\u01b0\u1ee3ng chi ti\u1ebft m\u00e1y t\u1ed5 1 v\u00e0 t\u1ed5 2 s\u1ea3n xu\u1ea5t l\u1ea7n l\u01b0\u1ee3t t\u0103ng 7% v\u00e0 8% so v\u1edbi th\u00e1ng tr\u01b0\u1edbc, \u0111\u1ea1t t\u1ed5ng c\u1ed9ng 806 chi ti\u1ebft m\u00e1y. H\u1ecfi th\u00e1ng tr\u01b0\u1edbc m\u1ed7i t\u1ed5 s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c bao nhi\u00eau chi ti\u1ebft m\u00e1y? C\u00e2u 6. (0,75 \u0111i\u1ec3m). Ng\u01b0\u1eddi h\u00fat thu\u1ed1c l\u00e1 th\u01b0\u1eddng xuy\u00ean s\u1ebd b\u1ecb gi\u1ea3m tu\u1ed5i th\u1ecd, d\u1ec5 m\u1eafc c\u00e1c lo\u1ea1i b\u1ec7nh nguy hi\u1ec3m nh\u01b0: vi\u00eam ph\u1ed5i, vi\u00eam \u0111\u01b0\u1eddng h\u00f4 h\u1ea5p, ung th\u01b0, \u2026 Gi\u1ea3 s\u1eed khi h\u00fat m\u1ed9t \u0111i\u1ebfu thu\u1ed1c th\u00ec ng\u01b0\u1eddi h\u00fat b\u1ecb gi\u1ea3m 15 ph\u00fat tu\u1ed5i th\u1ecd. T\u00ednh xem m\u1ed9t ng\u01b0\u1eddi h\u00fat thu\u1ed1c trung b\u00ecnh m\u1ed7i ng\u00e0y 2 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 g\u00f3i trong c\u1ea3 n\u0103m 2023 th\u00ec ng\u01b0\u1eddi \u0111\u00f3 s\u1ebd b\u1ecb gi\u1ea3m bao nhi\u00eau tu\u1ed5i th\u1ecd? Bi\u1ebft r\u1eb1ng m\u1ed7i g\u00f3i thu\u1ed1c c\u00f3 20 \u0111i\u1ebfu thu\u1ed1c l\u00e1. C\u00e2u 7. (0,75 \u0111i\u1ec3m). K\u00ednh \u0111eo m\u1eaft c\u1ee7a ng\u01b0\u1eddi gi\u00e0 th\u01b0\u1eddng l\u00e0 lo\u1ea1i th\u1ea5u k\u00ednh h\u1ed9i t\u1ee5. B\u1ea1n An \u0111\u00e3 d\u00f9ng m\u1ed9t chi\u1ebfc k\u00ednh c\u1ee7a \u00f4ng ngo\u1ea1i (lo\u1ea1i th\u1ea5u k\u00ednh h\u1ed9i t\u1ee5) \u0111\u1ec3 t\u1ea1o ra h\u00ecnh \u1ea3nh c\u1ee7a m\u1ed9t c\u00e2y n\u1ebfn tr\u00ean m\u1ed9t t\u1ea5m m\u00e0n. X\u00e9t c\u00e2y n\u1ebfn l\u00e0 m\u1ed9t v\u1eadt s\u00e1ng c\u00f3 h\u00ecnh d\u1ea1ng l\u00e0 \u0111o\u1ea1n AB \u0111\u1eb7t vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c ch\u00ednh c\u1ee7a m\u1ed9t th\u1ea5u k\u00ednh h\u1ed9i t\u1ee5, c\u00e1ch th\u1ea5u k\u00ednh m\u1ed9t \u0111o\u1ea1n OA 4m . Th\u1ea5u k\u00ednh c\u00f3 quang t\u00e2m O v\u00e0 ti\u00eau \u0111i\u1ec3m F, F ' . V\u1eadt AB cho \u1ea3nh th\u1eadt A ' B ' g\u1ea5p 3 l\u1ea7n AB . T\u00ednh ti\u00eau c\u1ef1 c\u1ee7a th\u1ea5u k\u00ednh. Bi\u1ebft r\u1eb1ng \u0111\u01b0\u1eddng \u0111i c\u1ee7a c\u00e1c tia s\u00e1ng \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 nh\u01b0 trong h\u00ecnh v\u1ebd tr\u00ean. C\u00e2u 8. (3 \u0111i\u1ec3m) Cho \uf044ABC nh\u1ecdn ( AB \uf03c AC) . \u0110\u01b0\u1eddng tr\u00f2n t\u00e2m O \u0111\u01b0\u1eddng k\u00ednh BC c\u1eaft AC v\u00e0 AB l\u1ea7n l\u01b0\u1ee3t t\u1ea1i E v\u00e0 F , BE v\u00e0 CF c\u1eaft nhau t\u1ea1i H , AH c\u1eaft BC t\u1ea1i D , EF c\u1eaft CB t\u1ea1i M . a) Ch\u1ee9ng minh AD BC v\u00e0 MF.ME MB.MC . b) Tia FD c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n O t\u1ea1i N ( N kh\u00e1c F ). Ch\u1ee9ng minh t\u1ee9 gi\u00e1c OFMN n\u1ed9i ti\u1ebfp. c) G\u1ecdi I v\u00e0 K l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a B v\u00e0 C tr\u00ean EF . Cho BC 8cm ; ABC 75 . T\u00ednh SEIB SCKE . ----H\u1ebeT--- T\u00c0I LI\u1ec6U \u0110\u01af\u1ee2C NH\u00d3M TO\u00c1N THCS TP HCM BI\u00caN SO\u1ea0N 2"]