{"id":552,"date":"2026-05-05T04:51:47","date_gmt":"2026-05-05T04:51:47","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ha-trung-thanh-hoa\/"},"modified":"2026-05-05T07:25:26","modified_gmt":"2026-05-05T07:25:26","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ha-trung-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-ha-trung-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 H\u00e0 Trung Thanh H\u00f3a"},"content":{"rendered":"

T\u00e0i Li\u1ec7u H\u1ecdc T\u1eadp<\/a> g\u1eedi \u0111\u1ebfn c\u00e1c b\u1ea1n \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00e0 Trung Thanh H\u00f3a<\/strong>. \u0110\u00e2y l\u00e0 t\u00e0i li\u1ec7u m\u00f4n To\u00e1n \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n nh\u1eb1m gi\u00fap c\u00e1c b\u1ea1n h\u1ecdc 12 l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi v\u00e0 bi\u1ebft \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c c\u1ee7a b\u1ea3n th\u00e2n \u0111\u1ec3 chu\u1ea9n b\u1ecb \u00f4n t\u1eadp. \u0110\u1eb7c bi\u1ec7t, \u0111\u1ec1 thi \u0111\u00e3 c\u00f3 k\u00e8m h\u01b0\u1edbng d\u1eabn c\u00e1ch gi\u1ea3i \u1edf cu\u1ed1i gi\u00fap c\u00e1c b\u1ea1n r\u00fat \u0111\u01b0\u1ee3c kinh nghi\u1ec7m trong qu\u00e1 tr\u00ecnh gi\u1ea3i \u0111\u1ec1. C\u00f9ng ch\u00fang t\u00f4i xem qua chi ti\u1ebft n\u1ed9i dung qua b\u00e0i vi\u1ebft sau.<\/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 H\u00e0 Trung 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 H\u00e0 Trung Thanh H\u00f3a<\/strong> c\u00f3 ma tr\u1eadn \u0111i\u1ec3m l\u00e0 (3 \u2013 4 \u2013 3) v\u1edbi th\u1eddi gian l\u00e0m b\u00e0i 90 ph\u00fat. N\u1ed9i dung \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025 \u0111\u01b0\u1ee3c chia l\u00e0m 3 ph\u1ea7n ch\u00ednh, b\u00e1m s\u00e1t ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc, c\u00e1c c\u00e2u h\u1ecfi ph\u00e2n b\u1ed5 \u0111\u1ec1u t\u1eeb nh\u1eadn bi\u1ebft \u2013 th\u00f4ng hi\u1ec3u \u2013 v\u1eadn d\u1ee5ng \u2013 v\u1eadn d\u1ee5ng cao. N\u1ed9i dung ch\u00ednh c\u1ee7a \u0111\u1ec1 nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 Tr\u1eafc nghi\u1ec7m l\u1ef1a ch\u1ecdn ph\u01b0\u01a1ng \u00e1n (3 \u0111i\u1ec3m)<\/strong><\/p>\n

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12. M\u1ed7i c\u00e2u ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn 1 ph\u01b0\u01a1ng \u00e1n. V\u00ed d\u1ee5 nh\u01b0:<\/p>\n

C\u00e2u 1<\/strong>. Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3^x-1 = 27 l\u00e0<\/p>\n

beginarrayll A. x = 5 & B. x = 3 C. x = 4 & D. x = 2 endarray<\/p>\n

C\u00e2u 2<\/strong>. \u0110\u01b0\u1eddng cong n\u00e0o d\u01b0\u1edbi \u0111\u00e2y l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x+1\/x-1 <\/p>\n

\"\"<\/p>\n

Ph\u1ea7n 2 \u2013 Tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 \u0111i\u1ec3m)
\n<\/strong>
\nTh\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 4. Trong m\u1ed7i \u00fd a), b), c), d), \u1edf m\u1ed7i c\u00e2u, th\u00ed sinh ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0110\u00daNG ho\u1eb7c SAI. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n

C\u00e2u 1<\/strong>. Trong h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz , cho 3 \u0111i\u1ec3m A(5; -2; 0) , B(4; 5; -2) v\u00e0 C(0; 3; 2) . \u0110i\u1ec3m M di chuy\u1ec3n tr\u00ean tr\u1ee5c Ox v\u00e0 \u0111i\u1ec3m N th\u1ecfa m\u00e3n \u0111\u1eb3ng th\u1ee9c NA\u20d7 + NB\u20d7 + 2NC\u20d7 = 0\u20d7\n<\/p>\n

a) Ho\u00e0nh \u0111\u1ed9 v\u00e0 tung \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m N b\u1eb1ng nhau.<\/p>\n

b) AB\u20d7 = (1; -7; 2) <\/p>\n

c) Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c Q = 2|MA\u20d7 + MB\u20d7 + MC\u20d7| + 3|MB\u20d7 + MC\u20d7| l\u00e0 6\u221a35 <\/p>\n

d) Tr\u1ecdng t\u00e2m tam gi\u00e1c ABC l\u00e0 \u0111i\u1ec3m G(3; 2; 0) <\/p>\n

C\u00e2u 2<\/strong>. Cho hai h\u00e0m s\u1ed1 f(x) = sin x – x v\u00e0 g(x) = sin x – x + m\u00b2 + 2m – 3 . G\u1ecdi S l\u00e0 t\u1eadp c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m \u0111\u1ec3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m y = g(x) tr\u00ean \u0111o\u1ea1n [0; \u03c0] b\u1eb1ng -4 <\/p>\n

a) T\u1eadp S c\u00f3 hai ph\u1ea7n t\u1eed.<\/p>\n

b) Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f'(x) = 0 l\u00e0 x = \u03c0 + k2\u03c0 (k in mathbbZ) <\/p>\n

c) | f( \u03c0\/2 ) | – \u03c0\/2 <\/p>\n

d) H\u00e0m s\u1ed1 y = f(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/p>\n

Ph\u1ea7n 3 \u2013 Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (3 \u0111i\u1ec3m)
\n<\/strong>
\nC\u00f3 t\u1ea5t c\u1ea3 6 c\u00e2u h\u1ecfi, th\u00ed sinh \u0111\u1ecdc \u0111\u1ec1 v\u00e0 tr\u00ecnh b\u00e0y b\u00e0i l\u00e0m r\u00f5 r\u00e0ng, m\u1ea1ch l\u1ea1c:<\/p>\n

C\u00e2u 1<\/strong>. An v\u00e0 B\u00ecnh thi \u0111\u1ea5u v\u1edbi nhau m\u1ed9t tr\u1eadn b\u00f3ng b\u00e0n, ng\u01b0\u1eddi n\u00e0o th\u1eafng tr\u01b0\u1edbc 3 s\u00e9c s\u1ebd gi\u00e0nh chi\u1ebfn th\u1eafng chung cu\u1ed9c. X\u00e1c su\u1ea5t An th\u1eafng m\u1ed7i s\u00e9c l\u00e0 0,4 (kh\u00f4ng c\u00f3 h\u00f2a). T\u00ednh x\u00e1c su\u1ea5t An th\u1eafng chung cu\u1ed9c. (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

C\u00e2u 2<\/strong>. Cho t\u1ee9 di\u1ec7n ABCD c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh AB = 3 , AC = 4 , AD = 6 v\u00e0 c\u00e1c g\u00f3c widehatBAC = widehatBAD = 60^\u00b0 , widehatCAD = 90^\u00b0 . T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 CD . (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u1ea7n tr\u0103m).<\/p>\n

C\u00e2u 3<\/strong>. Ba chi\u1ebfc m\u00e1y bay kh\u00f4ng ng\u01b0\u1eddi l\u00e1i c\u00f9ng bay l\u00ean m\u1ed9t \u0111\u1ecba \u0111i\u1ec3m. Sau m\u1ed9t th\u1eddi gian bay, chi\u1ebfc m\u00e1y bay th\u1ee9 nh\u1ea5t c\u00e1ch \u0111i\u1ec3m xu\u1ea5t ph\u00e1t v\u1ec1 ph\u00eda \u0110\u00f4ng 60 (km) v\u00e0 v\u1ec1 ph\u00eda Nam 40 (km) , \u0111\u1ed3ng th\u1eddi c\u00e1ch m\u1eb7t \u0111\u1ea5t 2 (km) . Chi\u1ebfc m\u00e1y bay th\u1ee9 hai c\u00e1ch \u0111i\u1ec3m xu\u1ea5t ph\u00e1t v\u1ec1 ph\u00eda B\u1eafc 80 (km) v\u00e0 v\u1ec1 ph\u00eda T\u00e2y 50 (km) , \u0111\u1ed3ng th\u1eddi c\u00e1ch m\u1eb7t \u0111\u1ea5t 4 (km) . Chi\u1ebfc m\u00e1y bay th\u1ee9 ba ch\u00ednh gi\u1eefa c\u1ee7a chi\u1ebfc m\u00e1y bay th\u1ee9 nh\u1ea5t v\u00e0 th\u1ee9 hai, \u0111\u1ed3ng th\u1eddi ba chi\u1ebfc m\u00e1y bay n\u00e0y th\u1eb3ng h\u00e0ng. X\u00e1c \u0111\u1ecbnh kho\u1ea3ng c\u00e1ch c\u1ee7a chi\u1ebfc m\u00e1y bay th\u1ee9 ba v\u1edbi v\u1ecb tr\u00ed t\u1ea1i \u0111i\u1ec3m xu\u1ea5t ph\u00e1t c\u1ee7a n\u00f3.<\/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 H\u00e0 Trung 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 H\u00e0 Trung Thanh H\u00f3a<\/strong> l\u00e0 tr\u1ee3 th\u1ee7 \u0111\u1eafc l\u1ef1c h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n h\u1ecdc sinh trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1. V\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a> chu\u1ea9n c\u1ee7a b\u1ed9 k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft, gi\u00fap c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n luy\u1ec7n v\u00e0 chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t. H\u00e3y t\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00e0 Trung Thanh H\u00f3a<\/strong> qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y v\u00e0 b\u1eaft tay v\u00e0o \u00f4n t\u1eadp ngay h\u00f4m nay nh\u00e9.<\/p>\n