{"id":564,"date":"2026-05-05T04:52:24","date_gmt":"2026-05-05T04:52:24","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-trieu-son-4-thanh-hoa\/"},"modified":"2026-05-05T07:26:10","modified_gmt":"2026-05-05T07:26:10","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-trieu-son-4-thanh-hoa","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-trieu-son-4-thanh-hoa\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Tri\u1ec7u S\u01a1n 4 Thanh H\u00f3a"},"content":{"rendered":"

\u0110\u1eebng b\u1ecf l\u1ee1 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Tri\u1ec7u S\u01a1n 4 Thanh H\u00f3a<\/strong> v\u00f4 c\u00f9ng h\u1eefu d\u1ee5ng trong qu\u00e1 tr\u00ecnh \u00f4n thi chu\u1ea9n b\u1ecb cho k\u00ec thi ch\u00ednh th\u1ee9c. T\u00e0i li\u1ec7u h\u1ecdc t\u1eadp v\u00e0 \u00f4n luy\u1ec7n d\u00e0nh ri\u00eang cho c\u00e1c b\u1ea1n h\u1ecdc sinh 12 luy\u1ec7n t\u1eadp gi\u1ea3i \u0111\u1ec1, n\u00e2ng cao t\u01b0 duy logic v\u00e0 l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi. C\u00f9ng ch\u00fang t\u00f4i t\u00ecm hi\u1ec3u qua n\u1ed9i dung v\u00e0 \u00d4n Thi<\/a> ngay n\u00e0o!<\/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 Tri\u1ec7u S\u01a1n 4 Thanh H\u00f3a<\/strong><\/h2>\n

C\u1ea5u tr\u00fac \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Tri\u1ec7u S\u01a1n 4 Thanh H\u00f3a<\/strong> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi \u0111\u1ec1 thi ch\u00ednh th\u1ee9c v\u00e0 \u0111\u1ec1 minh h\u1ecda c\u1ee7a b\u1ed9. N\u1ed9i dung \u0111\u00fac k\u1ebft t\u1eeb ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 12 v\u00e0 c\u00e1c b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng b\u00ean ngo\u00e0i gi\u00fap h\u1ecdc sinh n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 t\u01b0 duy gi\u1ea3i \u0111\u1ec1. Chi ti\u1ebft nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/p>\n

Th\u00ed sinh ch\u1ecdn m\u1ed9t trong 4 ph\u01b0\u01a1ng \u00e1n A, B, C, D. Gi\u1ea3i c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n

C\u00e2u 1. <\/strong>V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, \u221a[3]a\u00b2 b\u1eb1ng<\/p>\n

A. a^3\/2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. a^2\/3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. a\u2076 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. a^1\/6 <\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 f(x) c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m nh\u01b0 sau:<\/p>\n

beginarray|c|c|c|c|c|c| hline x & -\u221e & -3 & 0 & 2 & +\u221e hline f'(x) & + & 0 & – & 0 & + & 0 & – hline 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. (0; +\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. (-3; 0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (0; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. (-\u221e; -3) <\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 c\u00e2u)<\/strong><\/p>\n

C\u00e1c b\u1ea1n l\u00e0m quen v\u1edbi d\u1ea1ng c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai trong \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a> nh\u01b0 sau:<\/p>\n

C\u00e2u 1.\u00a0<\/strong>Cho h\u00e0m s\u1ed1 f(x) c\u00f3 \u0111\u1ea1o h\u00e0m: f'(x) = (x – 1)\u00b2(x\u00b2 – 3x + 2), forall x in mathbbR\n<\/p>\n

a) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; 2) .<\/p>\n

b) H\u00e0m s\u1ed1 y = f(x\u00b2 – 4x + 1) c\u00f3 3 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u.<\/p>\n

c) H\u00e0m s\u1ed1 f(x) c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

d) \u0110i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 x = 1 .<\/p>\n

C\u00e2u 2. <\/strong>Th\u1ea7y gi\u00e1o th\u1ed1ng k\u00ea \u0111i\u1ec3m trung b\u00ecnh cu\u1ed1i n\u0103m c\u1ee7a c\u00e1c h\u1ecdc sinh l\u1edbp 11A v\u00e0 11B \u1edf b\u1ea3ng sau:<\/p>\n

\"\"<\/p>\n

a) So s\u00e1nh \u0111\u1ed9 l\u1ec7ch chu\u1ea9n th\u00ec c\u00e1c h\u1ecdc sinh l\u1edbp 11A h\u1ecdc \u0111\u1ed3ng \u0111\u1ec1u h\u01a1n l\u1edbp 11B.<\/p>\n

b) \u0110i\u1ec3m trung b\u00ecnh c\u1ee7a l\u1edbp 11A nh\u1ecf h\u01a1n l\u1edbp 11B.<\/p>\n

c) Ph\u01b0\u01a1ng sai c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u l\u1edbp 11B l\u00e0 1,05 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

d) \u0110i\u1ec3m trung b\u00ecnh c\u1ee7a l\u1edbp 11A l\u00e0 8,3 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb).<\/p>\n

Ph\u1ea7n 3 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ea1o h\u00e0m li\u00ean t\u1ee5c tr\u00ean mathbbR v\u00e0 c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a \u0111\u1ea1o h\u00e0m nh\u01b0 h\u00ecnh v\u1ebd.<\/p>\n

\"\"<\/p>\n

\u0110\u1eb7t g(x) = f( (x\u00b2 + 1)\/(x) ) T\u00ecm s\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = g(x) .<\/p>\n

C\u00e2u 2.<\/strong> \u0110\u1ed9 d\u1ed1c c\u1ee7a m\u00e1i nh\u00e0 (m\u1eb7t s\u00e0n, con \u0111\u01b0\u1eddng th\u1eb3ng,\u2026) l\u00e0 tang c\u1ee7a g\u00f3c t\u1ea1o b\u1edfi m\u00e1i nh\u00e0 (m\u1eb7t s\u00e0n, con \u0111\u01b0\u1eddng th\u1eb3ng,\u2026) \u0111\u00f3 v\u1edbi m\u1eb7t ph\u1eb3ng n\u1eb1m ngang. Cho bi\u1ebft kim t\u1ef1 th\u00e1p Memphis t\u1ea1i bang Tennessee (M\u1ef9) c\u00f3 d\u1ea1ng h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, bi\u1ebft r\u1eb1ng di\u1ec7n t\u00edch \u0111\u1ec3 l\u00e1t t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t c\u1ee7a kim t\u1ef1 th\u00e1p b\u1eb1ng 80300 m\u00b2 v\u00e0 \u0111\u1ed9 d\u1ed1c c\u1ee7a m\u1eb7t b\u00ean kim t\u1ef1 th\u00e1p b\u1eb1ng 49\/45 . T\u00ednh chi\u1ec1u cao (\u0111\u01a1n v\u1ecb m) c\u1ee7a kim t\u1ef1 th\u00e1p (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb).<\/p>\n

\"\"<\/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 Tri\u1ec7u S\u01a1n 4 Thanh H\u00f3a<\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Tri\u1ec7u S\u01a1n 4 Thanh H\u00f3a<\/strong> l\u00e0 t\u00e0i li\u1ec7u tham kh\u1ea3o v\u00e0 \u00f4n t\u1eadp h\u1eefu \u00edch d\u00e0nh cho h\u1ecdc sinh 12. Ngo\u00e0i ra, \u0111\u1ec1 thi c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch tr\u00ecnh b\u00e0y chi ti\u1ebft m\u1ed7i c\u00e2u, gi\u00fap b\u1ea1n hi\u1ec3u \u0111\u01b0\u1ee3c b\u1ea3n ch\u1ea5t v\u00e0 c\u00e1ch l\u00e0m \u0111\u00fang cho m\u1ed7i c\u00e2u c\u1ee7a \u0111\u1ec1 thi. H\u00e3y t\u1ea3i \u0111\u1ec1 thi + \u0111\u00e1p \u00e1n qua \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y!<\/p>\n