{"id":574,"date":"2026-05-05T04:52:54","date_gmt":"2026-05-05T04:52:54","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-lien-truong-nghe-an\/"},"modified":"2026-05-05T07:26:45","modified_gmt":"2026-05-05T07:26:45","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-lien-truong-nghe-an","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-lien-truong-nghe-an\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Li\u00ean tr\u01b0\u1eddng Ngh\u1ec7 An"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Li\u00ean tr\u01b0\u1eddng Ngh\u1ec7 An<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac \u0111\u1ec1 minh h\u1ecda c\u1ee7a b\u1ed9 nh\u1eb1m \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c c\u1ee7a c\u00e1c b\u1ea1n h\u1ecdc sinh qua l\u1ea7n thi th\u1ee9 1. V\u00e0 \u0111\u00e2y c\u0169ng ch\u00ednh l\u00e0 c\u00e1ch gi\u00fap c\u00e1c b\u1ea1n l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1, c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi v\u00e0 c\u00e1ch tr\u00ecnh b\u00e0y b\u00e0i thi. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 n\u1ed9i dung c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t kh\u00f4ng nh\u00e9!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Li\u00ean tr\u01b0\u1eddng Ngh\u1ec7 An<\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Li\u00ean tr\u01b0\u1eddng Ngh\u1ec7 An<\/strong> c\u00f3 t\u1ea5t c\u1ea3 22 c\u00e2u h\u1ecfi chia th\u00e0nh 3 ph\u1ea7n ch\u00ednh theo quy \u0111\u1ecbnh c\u1ee7a \u0111\u1ec1 thi ch\u00ednh th\u1ee9c. N\u1ed9i dung xoay quanh ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 c\u00e1ch v\u1eadn d\u1ee5ng l\u00fd thuy\u1ebft v\u00e0o b\u00e0i t\u1eadp. \u0110i\u1ec3m \u0111\u00e1ng ch\u00fa \u00fd, l\u00e0 \u0111\u1ec1 thi c\u00f3 k\u00e8m \u0111\u00e1p v\u00e0 c\u00e1ch gi\u1ea3i th\u00edch c\u1ee7a m\u1ed7i c\u00e2u kh\u00e1 chi ti\u1ebft. Gi\u00fap c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n luy\u1ec7n v\u00e0 h\u1ecdc h\u1ecfi th\u00eam nhi\u1ec1u c\u00e1ch tr\u00ecnh b\u00e0y b\u00e0i l\u00e0m cho m\u00ecnh.<\/p>\n

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

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1ea5t c\u1ea3 12 c\u00e2u h\u1ecfi. M\u1ed7i c\u00e2u ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn m\u1ed9t ph\u01b0\u01a1ng \u00e1n ch\u00ednh x\u00e1c. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi trong \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n<\/a> nh\u01b0 sau:<\/p>\n

C\u00e2u 1.\u00a0<\/strong>Trong kh\u00f4ng gian Oxyz , cho m\u1eb7t ph\u1eb3ng (\u03b1): x + 2z – 3 = 0 . M\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng (\u03b1) l\u00e0:<\/p>\n

A. n\u20d7(1; 0; -3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. n\u20d7(1; 0; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. n\u20d7(1; 2; -3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. n\u20d7(1; 2; 0) <\/p>\n

C\u00e2u 2. <\/strong>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh log\u2083 (x\u00b2 – 1) – 3log\u2082\u2087(x + 1) = 0 l\u00e0:<\/p>\n

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

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

M\u1ed7i \u0111\u1ec1 c\u00f3 4 c\u00e2u h\u1ecfi v\u1edbi 4 \u0111\u00e1p \u00e1n a), b), c), d). Th\u00ed sinh ch\u1ec9 c\u1ea7n ch\u1ecdn gi\u00e1 tr\u1ecb \u0110\u00daNG\/SAI<\/strong> v\u00e0o m\u1ed7i \u00fd c\u1ee7a c\u00e2u tr\u1ea3 l\u1eddi. V\u1eadn d\u1ee5ng v\u00e0 gi\u1ea3i c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n

C\u00e2u 13.<\/strong>\u00a0Cho m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m t\u1ea7n s\u1ed1 th\u1ed1ng k\u00ea v\u1ec1 m\u1ee9c l\u01b0\u01a1ng c\u1ee7a hai c\u00f4ng ty A, B nh\u01b0 sau:<\/p>\n

\"\"<\/p>\n

a) K\u00edch th\u01b0\u1edbc m\u1eabu c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m th\u1ed1ng k\u00ea m\u1ee9c l\u01b0\u01a1ng c\u00f4ng ty A l\u00e0 60.<\/p>\n

b) Kho\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m th\u1ed1ng k\u00ea m\u1ee9c l\u01b0\u01a1ng c\u00f4ng ty B l\u00e0 30.<\/p>\n

c) S\u1ed1 trung b\u00ecnh c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m th\u1ed1ng k\u00ea m\u1ee9c l\u01b0\u01a1ng c\u00f4ng ty A l\u00e0 20,5. (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c)<\/p>\n

d) Theo \u0111\u1ed9 l\u1ec7ch chu\u1ea9n th\u00ec c\u00f4ng ty A c\u00f3 m\u1ee9c l\u01b0\u01a1ng \u0111\u1ed3ng \u0111\u1ec1u h\u01a1n c\u00f4ng ty B .<\/p>\n

C\u00e2u 14.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = (ax\u00b2 – x + b)\/(x + c) (a > 0), c\u00f3 \u0111\u1ed3 th\u1ecb (C) nh\u01b0 h\u00ecnh v\u1ebd b\u00ean d\u01b0\u1edbi, bi\u1ebft \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb (C) t\u1ea1o v\u1edbi hai tr\u1ee5c t\u1ecda \u0111\u1ed9 m\u1ed9t tam gi\u00e1c c\u00e2n.<\/p>\n

\"\"<\/p>\n

a) T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 mathbbR setminus -c .<\/p>\n

b) a = 1 .<\/p>\n

c) \u0110\u1ed3 th\u1ecb c\u00f3 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb n\u1eb1m v\u1ec1 hai ph\u00eda \u0111\u1ed1i v\u1edbi tr\u1ee5c Ox .<\/p>\n

d) 24a + 4b + 2000c < 2025 .<\/p>\n

Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn
\n<\/strong><\/p>\n

C\u00e2u 17. <\/strong>Cho h\u00ecnh ch\u00f3p S.ABC c\u00f3 \u0111\u00e1y ABC l\u00e0 tam gi\u00e1c vu\u00f4ng t\u1ea1i B , BC = \u221a3 , angle BAC = 30^\u00b0 , SA perp (ABC) v\u00e0 s\u1ed1 \u0111o c\u1ee7a g\u00f3c nh\u1ecb di\u1ec7n [S,BC,A] b\u1eb1ng 60^\u00b0 . G\u1ecdi O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC , t\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng SC v\u00e0 BO . (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c).<\/p>\n

C\u00e2u 18.<\/strong>\u00a0Gi\u1ea3 s\u1eed m\u1ed9t h\u1ed9p ch\u1ee9a 3 qu\u1ea3 b\u00f3ng \u0111\u1ecf v\u00e0 6 qu\u1ea3 b\u00f3ng tr\u1eafng (c\u00e1c qu\u1ea3 b\u00f3ng c\u00f9ng m\u00e0u th\u00ec gi\u1ed1ng nhau). L\u1ea5y ng\u1eabu nhi\u00ean t\u1eebng qu\u1ea3 b\u00f3ng ra kh\u1ecfi h\u1ed9p cho \u0111\u1ebfn khi h\u1ebft b\u00f3ng. T\u00ednh x\u00e1c su\u1ea5t \u0111\u1ec3 l\u1ea5y \u0111\u01b0\u1ee3c t\u1ea5t c\u1ea3 3 qu\u1ea3 b\u00f3ng \u0111\u1ecf tr\u01b0\u1edbc khi l\u1ea5y \u0111\u01b0\u1ee3c 3 qu\u1ea3 b\u00f3ng tr\u1eafng.(k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Li\u00ean tr\u01b0\u1eddng Ngh\u1ec7 An<\/strong><\/h2>\n

\u0110\u1ec3 chinh ph\u1ee5c \u0111\u1ec1 thi THPT m\u00f4n To\u00e1n ch\u00ednh th\u1ee9c v\u1edbi \u0111i\u1ec3m s\u1ed1 10+, c\u00e1c b\u1ea1n h\u1ecdc sinh h\u00e3y chu\u1ea9n b\u1ecb cho m\u00ecnh m\u1ed9t ti\u1ebfn tr\u00ecnh \u00f4n luy\u1ec7n th\u1eadt ch\u1ec9nh chu v\u00e0 hi\u1ec7u qu\u1ea3 nh\u00e9. H\u00e3y t\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 Li\u00ean tr\u01b0\u1eddng Ngh\u1ec7 An<\/strong> qua \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y v\u00e0 luy\u1ec7n t\u1eadp \u0111\u1ec3 n\u00e2ng cao k\u1ef9 n\u0103ng t\u01b0 duy khi l\u00e0m b\u00e0i thi.<\/p>\n