{"id":486,"date":"2026-05-05T04:48:21","date_gmt":"2026-05-05T04:48:21","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-le-thanh-tong-tp-hcm\/"},"modified":"2026-05-05T07:21:30","modified_gmt":"2026-05-05T07:21:30","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-le-thanh-tong-tp-hcm","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-le-thanh-tong-tp-hcm\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u00ea Th\u00e1nh T\u00f4ng TP HCM"},"content":{"rendered":"

C\u00e1c b\u1ea1n h\u1ecdc sinh 12 l\u01b0u ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u00ea Th\u00e1nh T\u00f4ng TP HCM<\/strong> v\u00e0 b\u1eaft tay v\u00e0o luy\u1ec7n t\u1eadp ngay h\u00f4m nay n\u00e0o. \u0110\u00e2y ch\u00ednh l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p c\u00e1c ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m, c\u00e1c d\u1ea1ng to\u00e1n t\u1eeb v\u1eadn d\u1ee5ng \u0111\u1ebfn n\u00e2ng cao, gi\u00fap c\u00e1c b\u1ea1n \u0111\u00e1nh gi\u00e1 \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c c\u1ee7a b\u1ea3n th\u00e2n tr\u01b0\u1edbc k\u00ec thi quan tr\u1ecdng s\u1eafp t\u1edbi. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 n\u1ed9i dung qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u00ea Th\u00e1nh T\u00f4ng TP HCM<\/strong><\/h2>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u00ea Th\u00e1nh T\u00f4ng TP HCM<\/strong> t\u1eadp h\u1ee3p c\u00e1c c\u00e2u h\u1ecfi v\u1ec1 x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea, h\u00ecnh h\u1ecdc kh\u00f4ng gian, \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1, v\u00e0 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n c\u1ea5p 3. \u0110\u1eb7c bi\u1ec7t b\u1ed9 t\u00e0i li\u1ec7u \u0111\u00e3 c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch gi\u1ea3i chi ti\u1ebft t\u1eebng ph\u1ea7n, h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n trong qu\u00e1 tr\u00ecnh l\u00e0m v\u00e0 s\u1eeda b\u00e0i, r\u00fat ra \u0111\u01b0\u1ee3c b\u00e0i h\u1ecdc qu\u00fd b\u00e1u v\u00e0 \u0111\u00fac k\u1ebft k\u0129 n\u0103ng cho k\u00ec thi ch\u00ednh th\u1ee9c. N\u1ed9i dung chi ti\u1ebft c\u1ee7a \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n<\/a> nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m<\/strong><\/span><\/p>\n

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12, m\u1ed7i c\u00e2u h\u1ecfi s\u1ebd c\u00f3 4 ph\u01b0\u01a1ng \u00e1n, c\u00e1c b\u1ea1n c\u1ea7n \u0111\u1ecdc th\u1eadt k\u0129 v\u00e0 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t. V\u00ed d\u1ee5 c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau:<\/p>\n

beginarrayc|cccccc x & -\u221e & & -1 & & 0 & +\u221e hline f'(x) & & – & 0 & + & 0 & – hline f(x) & searrow & -\u221e & nearrow & 2 & searrow & -2 endarray<\/p>\n

H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n

A. (-2;2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. (-1;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. (-2;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. (-1; +\u221e) <\/p>\n

C\u00e2u 2.<\/strong> Trong kh\u00f4ng gian Oxyz , cho hai \u0111i\u1ec3m A(1; -1; 2) v\u00e0 B(3; -1; 2) . T\u1ecda \u0111\u1ed9 c\u1ee7a vect\u01a1 BA\u20d7 l\u00e0:<\/p>\n

A. (2; -2; 4) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. (2; 0; 0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. (-1; -1; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. (-2; -2; -4) <\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi \u0111\u00fang sai<\/strong><\/span><\/p>\n

Bao g\u1ed3m 4 c\u00e2u h\u1ecfi ch\u00ednh v\u00e0 m\u1ed7i c\u00e2u c\u00f3 4 c\u00e2u tr\u1ea3 l\u1eddi. Th\u00ed sinh ch\u1ec9 c\u1ea7n ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0111\u00fang ho\u1eb7c sai \u0111i\u1ec1n v\u00e0o c\u00e1c c\u00e2u tr\u1ea3 l\u1eddi. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi sau sau:<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = 4sin x cos x + 2x <\/p>\n

a) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 f'(x) = 4sin 2x + 2 <\/p>\n

b) H\u00e0m s\u1ed1 y = f(x) c\u00f3 4 \u0111i\u1ec3m c\u1ef1c tr\u1ecb thu\u1ed9c [-\u03c0; \u03c0] <\/p>\n

c) H\u00e0m s\u1ed1 y = f(x) ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng ( -\u03c0\/2; \u03c0\/2 ) <\/p>\n

d) Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a f(x) tr\u00ean \u0111o\u1ea1n [ 0; \u03c0\/2 ] l\u00e0 2\u03c0\/3 + \u221a3 <\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t ng\u01b0\u1eddi \u0111i\u1ec1u khi\u1ec3n \u00f4 t\u00f4 \u0111ang \u1edf \u0111\u01b0\u1eddng d\u1eabn mu\u1ed1n nh\u1eadp l\u00e0n v\u00e0o \u0111\u01b0\u1eddng cao t\u1ed1c. Khi \u00f4 t\u00f4 c\u00e1ch \u0111i\u1ec3m nh\u1eadp l\u00e0n 200 m , t\u1ed1c \u0111\u1ed9 c\u1ee7a \u00f4 t\u00f4 l\u00e0 36 km\/h . Hai gi\u00e2y sau \u0111\u00f3, \u00f4 t\u00f4 b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c v\u1edbi t\u1ed1c \u0111\u1ed9 v(t) = at + b (a, b in mathbbR, a > 0) , trong \u0111\u00f3 t l\u00e0 th\u1eddi gian t\u00ednh b\u1eb1ng gi\u00e2y k\u1ec3 t\u1eeb khi b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c. Bi\u1ebft r\u1eb1ng \u00f4 t\u00f4 nh\u1eadp l\u00e0n cao t\u1ed1c sau 12 gi\u00e2y v\u00e0 duy tr\u00ec s\u1ef1 t\u0103ng t\u1ed1c trong 24 gi\u00e2y k\u1ec3 t\u1eeb khi b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c, sau 24s \u0111\u00f3 \u00f4 t\u00f4 duy tr\u00ec t\u1ed1c \u0111\u1ed9 cao nh\u1ea5t trong th\u1eddi gian c\u00f2n l\u1ea1i tr\u00ean cao t\u1ed1c.<\/p>\n

a) Qu\u00e3ng \u0111\u01b0\u1eddng \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c t\u1eeb khi b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c \u0111\u1ebfn khi nh\u1eadp l\u00e0n l\u00e0 180 m .<\/p>\n

b) V\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 t\u1ea1i th\u1eddi \u0111i\u1ec3m nh\u1eadp l\u00e0n l\u00e0 72 km\/h .<\/p>\n

c) Qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c trong th\u1eddi gian 30 gi\u00e2y k\u1ec3 t\u1eeb khi \u00f4 t\u00f4 c\u00e1ch \u0111i\u1ec3m nh\u1eadp l\u00e0n 200 m l\u00e0 620 m .<\/p>\n

d) Sau 24 gi\u00e2y k\u1ec3 t\u1eeb khi t\u0103ng t\u1ed1c, \u00f4 t\u00f4 duy tr\u00ec t\u1ed1c \u0111\u1ed9 cao nh\u1ea5t trong v\u00f2ng 5s th\u00ec ph\u00e1t hi\u1ec7n ch\u01b0\u1edbng ng\u1ea1i v\u1eadt c\u00e1ch \u0111\u00f3 300 m , ng\u01b0\u1eddi \u0111i\u1ec1u khi\u1ec3n l\u1eadp t\u1ee9c \u0111\u1ea1p phanh v\u00e0 \u00f4 t\u00f4 chuy\u1ec3n \u0111\u1ed9ng ch\u1eadm d\u1ea7n \u0111\u1ec1u v\u1edbi a(t) = -3 (m\/s\u00b2) . Khi \u0111\u00f3 \u00f4 t\u00f4 d\u1eebng l\u1ea1i c\u00e1ch ch\u01b0\u1edbng ng\u1ea1i v\u1eadt 10 m .<\/p>\n

Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn ng\u1eafn<\/strong><\/span><\/p>\n

T\u01b0\u01a1ng t\u1ef1 nh\u01b0 c\u00e1c \u0111\u1ec1 thi c\u1ee7a c\u00e1c n\u0103m tr\u01b0\u1edbc, ph\u1ea7n 3 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn bao g\u1ed3m c\u00e1c c\u00e2u h\u1ecfi c\u00f3 n\u1ed9i dung t\u1eeb h\u00ecnh h\u1ecdc, x\u00e1c su\u1ea5t, ph\u01b0\u01a1ng tr\u00ecnh logarit. Th\u00ed sinh c\u1ea7n t\u01b0 duy v\u00e0 hi\u1ec3u \u0111\u01b0\u1ee3c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n \u0111\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i b\u00e0i nhanh v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABC.A\u2019B\u2019C\u2019 c\u00f3 \u0111\u00e1y ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh \u221a2 . C\u1ea1nh BA\u2019 = \u221a6 . Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng A\u2019B v\u00e0 B\u2019C l\u00e0 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t c\u1ed1c h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y b\u1eb1ng 7 cm , chi\u1ec1u cao 15 cm . Trong c\u1ed1c ch\u1ee9a m\u1ed9t l\u01b0\u1ee3ng n\u01b0\u1edbc b\u1eb1ng 2\/3 th\u1ec3 t\u00edch c\u1ed1c. M\u1ed9t con qu\u1ea1 mu\u1ed1n u\u1ed1ng \u0111\u01b0\u1ee3c n\u01b0\u1edbc trong c\u1ed1c th\u00ec m\u1eb7t n\u01b0\u1edbc ph\u1ea3i c\u00e1ch mi\u1ec7ng c\u1ed1c kh\u00f4ng qu\u00e1 3 cm . Con qu\u1ea1 th\u00f4ng minh \u0111\u00e3 m\u1ed5 nh\u1eefng vi\u00ean s\u1ecfi h\u00ecnh c\u1ea7u c\u00f3 b\u00e1n k\u00ednh 0,9 cm th\u1ea3 v\u00e0o c\u1ed1c \u0111\u1ec3 m\u1ef1c n\u01b0\u1edbc d\u00e2ng l\u00ean. H\u1ecfi \u0111\u1ec3 u\u1ed1ng \u0111\u01b0\u1ee3c n\u01b0\u1edbc, con qu\u1ea1 c\u1ea7n th\u1ea3 \u00edt nh\u1ea5t bao nhi\u00eau vi\u00ean s\u1ecfi?<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u00ea Th\u00e1nh T\u00f4ng TP HCM<\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u00ea Th\u00e1nh T\u00f4ng TP HCM<\/strong> ch\u00ednh l\u00e0 t\u00e0i li\u1ec7u \u00f4n t\u1eadp b\u1ed5 \u00edch d\u00e0nh cho h\u1ecdc sinh l\u1edbp 12 trong qu\u00e1 tr\u00ecnh chu\u1ea9n b\u1ecb cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi. H\u00e3y nhanh ch\u00f3ng t\u1ea3i v\u1ec1 tr\u1ecdn b\u1ed9 \u0111\u1ec1 thi k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft \u0111\u1ec3 luy\u1ec7n t\u1eadp, x\u00e2y d\u1ef1ng cho b\u1ea3n th\u00e2n l\u1ed9 tr\u00ecnh \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3 v\u00e0 chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t.<\/p>\n