{"id":566,"date":"2026-05-05T04:52:30","date_gmt":"2026-05-05T04:52:30","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-le-loi-thanh-hoa\/"},"modified":"2026-05-05T07:26:18","modified_gmt":"2026-05-05T07:26:18","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-le-loi-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-le-loi-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 L\u00ea L\u1ee3i Thanh H\u00f3a"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Tr\u01b0\u1eddng THPT L\u00ea L\u1ee3i Thanh H\u00f3a<\/strong> l\u00e0 t\u00e0i nguy\u00ean \u00f4n luy\u1ec7n v\u00f4 c\u00f9ng hi\u1ec7u qu\u1ea3 cho c\u00e1c b\u1ea1n h\u1ecdc sinh \u0111ang chu\u1ea9n b\u1ecb ki\u1ebfn th\u1ee9c v\u00e0 t\u00e2m l\u00fd cho k\u00ec thi s\u1eafp t\u1edbi. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n c\u00f3 c\u1ea5u tr\u00fac b\u00e1m s\u00e1t v\u1edbi \u0111\u1ec1 minh h\u1ecda c\u1ee7a b\u1ed9 v\u00e0 c\u00f3 k\u00e8m l\u1eddi \u0111\u00e1p \u00e1n. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u th\u00eam 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 L\u1ee3i Thanh H\u00f3a<\/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 L\u1ee3i Thanh H\u00f3a<\/strong> g\u1ed3m 22 c\u00e2u h\u1ecfi v\u1edbi h\u00ecnh th\u1ee9c l\u00e0 tr\u1eafc nghi\u1ec7m v\u1edbi nhi\u1ec1u d\u1ea1ng kh\u00e1c nhau v\u00e0 c\u00f3 th\u1eddi gian 90 ph\u00fat \u0111\u1ec3 l\u00e0m. N\u1ed9i dung chi ti\u1ebft \u0111\u01b0\u1ee3c chia th\u00e0nh c\u00e1c ph\u1ea7n nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n<\/strong><\/p>\n

Tr\u00edch m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 thi nh\u01b0 sau:<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong (xem h\u00ecnh).<\/p>\n

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ed3ng bi\u1ebfn trong kho\u1ea3ng n\u00e0o?<\/p>\n

A. (0;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. (-\u221e; 0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. (1; +\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. (-1; 0) <\/p>\n

C\u00e2u 2.<\/strong> H\u00e0m s\u1ed1 f(x) c\u00f3 \u0111\u1ea1o h\u00e0m f'(x) = x(x – 1), forall x in mathbbR . H\u00e0m s\u1ed1 f(x) c\u00f3 bao nhi\u00eau \u0111i\u1ec3m c\u1ef1c tr\u1ecb?<\/p>\n

A. 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 3<\/p>\n

C\u00e2u 3.<\/strong>T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh log\u2082(x – 1) \u2264 1 l\u00e0<\/p>\n

A. [1; 3] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. [1; 3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (1; 5) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. [3; 5] <\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n

Th\u00ed sinh ch\u1ec9 c\u1ea7n tick ch\u1ecdn gi\u00e1 tr\u1ecb \u0110\u00daNG\/SAI<\/strong> cho m\u1ed7i c\u00e2u: V\u00ed d\u1ee5:<\/p>\n

C\u00e2u 1<\/strong>.\u00a0Cho h\u00e0m s\u1ed1 f(x) = 2 sin 2x + 2x .<\/p>\n

a) Ph\u01b0\u01a1ng tr\u00ecnh f'(x) = 0 c\u00f3 hai nghi\u1ec7m thu\u1ed9c [0; \u03c0] . [ 0; \u03c0\/2 ] v\u00e0 [ 2\u03c0\/3; \u221a3 ]\n<\/p>\n

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

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

d) f(\u03c0) = \u03c0 <\/p>\n

C\u00e2u 2.\u00a0<\/strong>H\u00ecnh v\u1ebd sau m\u00f4 t\u1ea3 v\u1ecb tr\u00ed c\u1ee7a m\u00e1y bay v\u00e0o th\u1eddi \u0111i\u1ec3m 9 gi\u1edd 30 ph\u00fat. Bi\u1ebft c\u00e1c \u0111\u01a1n v\u1ecb tr\u00ean h\u00ecnh t\u00ednh theo \u0111\u01a1n v\u1ecb km. M\u1eb7t ph\u1eb3ng (Oxy) tr\u00f9ng v\u1edbi m\u1eb7t \u0111\u1ea5t, O tr\u00f9ng v\u1edbi v\u1ecb tr\u00ed trung t\u00e2m \u0111i\u1ec1u khi\u1ec3n.<\/p>\n

\"\"<\/p>\n

a) Phi c\u00f4ng \u0111\u1ec3 m\u00e1y bay \u1edf ch\u1ebf \u0111\u1ed9 t\u1ef1 \u0111\u1ed9ng bay th\u1eb3ng theo h\u01b0\u1edbng \u0111\u00f4ng v\u1edbi v\u1eadn t\u1ed1c l\u00e0 750 km\/h , \u0111\u1ed9 cao kh\u00f4ng \u0111\u1ed5i th\u00ec t\u1ea1i th\u1eddi \u0111i\u1ec3m 10 gi\u1edd 30 ph\u00fat m\u00e1y bay \u1edf t\u1ecda \u0111\u1ed9: (150; 1050; 9)\n<\/p>\n

b) T\u1ea1i th\u1eddi \u0111i\u1ec3m 9 gi\u1edd 30 ph\u00fat, m\u00e1y bay c\u00e1ch trung t\u00e2m \u0111i\u1ec1u khi\u1ec3n m\u1ed9t kho\u1ea3ng (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi) l\u00e0: 335,6 km\n<\/p>\n

c) T\u1ea1i th\u1eddi \u0111i\u1ec3m 9 gi\u1edd 30 ph\u00fat, t\u1ecda \u0111\u1ed9 c\u1ee7a m\u00e1y bay l\u00e0: (300; 150; 9)\n<\/p>\n

d) T\u1ea1i th\u1eddi \u0111i\u1ec3m 9 gi\u1edd 30 ph\u00fat, m\u00e1y bay \u0111ang \u1edf \u0111\u1ed9 cao: 9 km so v\u1edbi m\u1eb7t \u0111\u1ea5t\n<\/p>\n

Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n

T\u01b0\u01a1ng t\u1ef1 c\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn c\u1ee7a c\u00e1c n\u0103m tr\u01b0\u1edbc, ph\u1ea7n n\u00e0y th\u00ed sinh n\u00ean t\u00ecm th\u1eadt nhi\u1ec1u \u0111\u1ec1 gi\u1ea3i v\u00e0 h\u1ecdc h\u1ecfi c\u00e1ch tr\u00ecnh b\u00e0y t\u1eebng c\u00e2u c\u1ee7a m\u1ed7i \u0111\u1ec1 \u0111\u1ec3 \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 t\u1ed1i \u0111a. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n

C\u00e2u 1.<\/strong>\u00a0M\u1ed9t trang tr\u1ea1i rau s\u1ea1ch \u1edf \u0110\u00e0 L\u1ea1t m\u1ed7i ng\u00e0y thu ho\u1ea1ch \u0111\u01b0\u1ee3c 1 t\u1ea5n rau. M\u1ed7i ng\u00e0y, n\u1ebfu gi\u00e1 b\u00e1n rau l\u00e0 30 000 \u0111\u1ed3ng\/kg th\u00ec b\u00e1n h\u1ebft rau, n\u1ebfu gi\u00e1 b\u00e1n rau t\u0103ng 1 000 \u0111\u1ed3ng\/kg th\u00ec s\u1ed1 rau th\u1eeba t\u0103ng 20 kg . S\u1ed1 rau th\u1eeba n\u00e0y \u0111\u01b0\u1ee3c thu mua h\u1ebft \u0111\u1ec3 l\u00e0m th\u1ee9c \u0103n ch\u0103n nu\u00f4i v\u1edbi gi\u00e1 2 000 \u0111\u1ed3ng\/kg . H\u1ecfi \u0111\u1ec3 m\u1ed7i ng\u00e0y thu \u0111\u01b0\u1ee3c s\u1ed1 ti\u1ec1n b\u00e1n rau l\u1edbn nh\u1ea5t th\u00ec trang tr\u1ea1i \u0111\u00f3 n\u00ean b\u00e1n rau v\u1edbi gi\u00e1 bao nhi\u00eau ngh\u00ecn \u0111\u1ed3ng?<\/p>\n

C\u00e2u 2. <\/strong>M\u1ed9t nh\u00f3m g\u1ed3m 3 h\u1ecdc sinh l\u1edbp 10; 3 h\u1ecdc sinh l\u1edbp 11 v\u00e0 3 h\u1ecdc sinh l\u1edbp 12 \u0111\u01b0\u1ee3c x\u1ebfp ng\u1ed3i v\u00e0o m\u1ed9t h\u00e0ng c\u00f3 9 gh\u1ebf, m\u1ed7i h\u1ecdc sinh 1 gh\u1ebf. T\u00ednh x\u00e1c su\u1ea5t \u0111\u1ec3 3 h\u1ecdc sinh l\u1edbp 10 kh\u00f4ng ng\u1ed3i 3 gh\u1ebf li\u1ec1n nhau. (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

\u0110\u1ec3 chu\u1ea9n b\u1ecb k\u1ef9 n\u0103ng v\u00e0 t\u00e2m l\u00fd th\u1eadt v\u1eefng khi l\u00e0m \u0111\u1ec1 thi to\u00e1n thpt qu\u1ed1c gia<\/a> ch\u00ednh th\u1ee9c. C\u00e1c b\u1ea1n h\u1ecdc sinh n\u00ean tham kh\u1ea3o qua \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Tr\u01b0\u1eddng THPT L\u00ea L\u1ee3i Thanh H\u00f3a<\/strong> v\u00e0 nhi\u1ec1u \u0111\u1ec1 thi kh\u00e1c. Ch\u1eafc h\u1eb3n, \u0111i\u1ec1u n\u00e0y s\u1ebd gi\u00fap b\u1ea1n v\u01b0\u1ee3t qua k\u00ec thi th\u1eadt t\u1ed1t v\u1edbi \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t.<\/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 L\u1ee3i 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 L\u00ea L\u1ee3i Thanh H\u00f3a<\/strong> s\u1ebd l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u h\u1ecdc t\u1eadp v\u00e0 \u00f4n luy\u1ec7n \u0111\u1eafc l\u1ef1c d\u00e0nh cho h\u1ecdc sinh 12. H\u00e3y t\u1ea3i b\u1ed9 \u0111\u1ec1 thi v\u00e0 \u0111\u00e1p \u00e1n theo \u0111\u01b0\u1eddng d\u1eabn sau v\u00e0 b\u1eaft tay v\u00e0o gi\u1ea3i \u0111\u1ec1 ngay h\u00f4m nay nh\u00e9! Ch\u00fac c\u00e1c b\u1ea1n \u0111\u1ea1t th\u00e0nh t\u00edch cao trong k\u00ec thi THPT qu\u1ed1c gia m\u00f4n To\u00e1n s\u1eafp t\u1edbi.<\/p>\n