{"id":488,"date":"2026-05-05T04:48:27","date_gmt":"2026-05-05T04:48:27","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-chuyen-phan-boi-chau-nghe-an\/"},"modified":"2026-05-05T07:21:39","modified_gmt":"2026-05-05T07:21:39","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-chuyen-phan-boi-chau-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-truong-chuyen-phan-boi-chau-nghe-an\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng Chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng Chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong> l\u00e0 \u0111\u1ec1 thi tham kh\u1ea3o ch\u1ea5t l\u01b0\u1ee3ng, gi\u00fap h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 v\u00e0 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i \u0111\u1ec1 b\u00e1m s\u00e1t v\u1edbi c\u1ea5u tr\u00fac c\u1ee7a B\u1ed9 GD&\u0110T. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n chi ti\u1ebft, bao qu\u00e1t c\u00e1c n\u1ed9i dung tr\u1ecdng t\u00e2m, \u0111\u1ed3ng th\u1eddi c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft. Gi\u00fap c\u00e1c em \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c v\u00e0 \u0111i\u1ec1u ch\u1ec9nh chi\u1ebfn l\u01b0\u1ee3c \u00f4n t\u1eadp ph\u00f9 h\u1ee3p, \u0111\u1ec3 t\u1ef1 tin b\u01b0\u1edbc v\u00e0o k\u1ef3 thi ch\u00ednh th\u1ee9c. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> tham kh\u1ea3o qua n\u1ed9i dung c\u1ee7a t\u1eadp t\u00e0i li\u1ec7u sau \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 Chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/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 Chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong> chu\u1ea9n c\u1ea5u tr\u00fac chung. G\u1ed3m 22 c\u00e2u h\u1ecfi chia l\u00e0m 3 ph\u1ea7n: tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n, tr\u1eafc nghi\u1ec7m \u0111\u00fang sai v\u00e0 tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn. C\u00e1c c\u00e2u h\u1ecfi c\u00f3 \u0111\u1ed9 ph\u00e2n h\u00f3a cao, t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao v\u00e0 chi ti\u1ebft n\u1ed9i dung c\u00f3 d\u1ea1ng:<\/p>\n

Ph\u1ea7n 1 \u2013 Tr\u1eafc nghi\u1ec7m 4 ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/span><\/p>\n

C\u00e1c c\u00e2u h\u1ecfi c\u1ee7a ph\u1ea7n 1 n\u00e0y ch\u1ee7 y\u1ebfu r\u01a1i v\u00e0o c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n, c\u00f3 \u0111\u1ed9 nh\u1eadn bi\u1ebft v\u00e0 v\u1eadn d\u1ee5ng, do \u0111\u00f3 c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng chi\u1ebfm tr\u1ecdng s\u1ed1 \u0111i\u1ec3m \u1edf ph\u1ea7n n\u00e0y. V\u00ed d\u1ee5 c\u00e1c c\u00e2u h\u1ecfi tham kh\u1ea3o:<\/p>\n

C\u00e2u 1:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz , cho hai vect\u01a1 a\u20d7 = (1; -2; 1), b\u20d7 = (-2; 1; 1).
\nT\u00ednh g\u00f3c gi\u1eefa a\u20d7 v\u00e0 b\u20d7 .<\/p>\n

A. 60^\u00b0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 120^\u00b0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 30^\u00b0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. -30^\u00b0 <\/p>\n

C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz , cho hai \u0111i\u1ec3m A(1; 2; 3), B(3; 8; 5). T\u1ecda \u0111\u1ed9 trung \u0111i\u1ec3m I c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB l\u00e0:<\/p>\n

A. I(2; 6; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. I(1; 3; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. I(4; 10; 8) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. I(2; 5; 4) <\/p>\n

C\u00e2u 3:<\/strong> \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = (x\u00b2 + 2x – 3)\/(x – 2) l\u00e0:<\/p>\n

A. y = x \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. x = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. y = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. y = x + 4 <\/p>\n

Ph\u1ea7n 2 \u2013 Tr\u1eafc nghi\u1ec7m ch\u1ecdn \u0111\u00fang sai<\/strong><\/span><\/p>\n

C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai l\u00e0 d\u1ea1ng c\u00e2u h\u1ecfi m\u1edbi xu\u1ea5t hi\u1ec7n trong nh\u1eefng n\u0103m g\u1ea7n \u0111\u00e2y. D\u1ea1ng n\u00e0y d\u1ec5 \u0111\u00e1nh l\u1eeba c\u00e1c b\u1ea1n h\u1ecdc sinh. Do \u0111\u00f3, c\u00e1c b\u1ea1n n\u00ean chu\u1ea9n b\u1ecb cho m\u00ecnh ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u1eefng \u0111\u1ec3 gi\u1ea3i c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u00e2y nh\u00e9:<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 SA vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y, SA = 2a , AB = a <\/p>\n

\"\"<\/p>\n

a) Th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.ABCD b\u1eb1ng (2a\u00b3)\/(3).\n<\/p>\n

b) Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng SA v\u00e0 BC b\u1eb1ng (2a)\/(\u221a5).\n<\/p>\n

c) SA + SC = SB + SD. <\/p>\n

d) S\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n [B, SC, D] b\u1eb1ng 103,5^\u00b0 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = ax\u00b3 + bx\u00b2 + cx + d c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 sau \u0111\u00e2y.<\/p>\n

\"\"<\/p>\n

a) Gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 y = f(x) b\u1eb1ng -1 .<\/p>\n

b) Ph\u01b0\u01a1ng tr\u00ecnh log\u2082[f(x) + 6] = 2 c\u00f3 hai nghi\u1ec7m.<\/p>\n

c) H\u00e0m s\u1ed1 y = f(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-1; 3) .<\/p>\n

d) T\u1ed5ng 2025a + b + c + d = -2025 .<\/p>\n

Ph\u1ea7n 3 \u2013 Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n

Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u1ec3 c\u00f3 c\u00e1i nh\u00ecn t\u1ed5ng qu\u00e1t v\u1ec1 ph\u1ea7n 3 trong \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a>:<\/p>\n

C\u00e2u 1:<\/strong>Trong trung t\u00e2m th\u01b0\u01a1ng m\u1ea1i Lotte th\u00e0nh ph\u1ed1 Vinh, c\u00f3 m\u1ed9t nh\u00e0 h\u00e0ng b\u00e1n buffet h\u1ea3i s\u1ea3n. Khi nh\u00e0 h\u00e0ng b\u00e1n v\u1edbi gi\u00e1 200 ngh\u00ecn \u0111\u1ed3ng m\u1ed9t su\u1ea5t th\u00ec m\u1ed7i ng\u00e0y nh\u00e0 h\u00e0ng b\u00e1n \u0111\u01b0\u1ee3c 100 su\u1ea5t. Nh\u00e0 h\u00e0ng d\u1ef1 \u0111\u1ecbnh c\u00f3 \u0111\u1ee3t gi\u1ea3m gi\u00e1 b\u00e1n \u0111\u1ec3 k\u00edch c\u1ea7u trong d\u1ecbp cu\u1ed1i n\u0103m. Theo kh\u1ea3o s\u00e1t t\u1eeb th\u1ecb tr\u01b0\u1eddng th\u00ec m\u1ed7i l\u1ea7n gi\u1ea3m gi\u00e1 10 ngh\u00ecn \u0111\u1ed3ng m\u1ed9t su\u1ea5t th\u00ec nh\u00e0 h\u00e0ng b\u00e1n th\u00eam \u0111\u01b0\u1ee3c 10 su\u1ea5t, h\u1ecfi nh\u00e0 h\u00e0ng c\u1ea7n b\u00e1n v\u1edbi gi\u00e1 m\u1edbi l\u00e0 bao nhi\u00eau ngh\u00ecn \u0111\u1ed3ng m\u1ed9t su\u1ea5t \u0111\u1ec3 doanh thu trong m\u1ed9t ng\u00e0y l\u00e0 l\u1edbn nh\u1ea5t?<\/p>\n

C\u00e2u 2:<\/strong> M\u1ed9t chi\u1ebfc m\u00e1y \u0111o \u0111\u1ea1c tr\u1eafc \u0111\u1ecba \u0111\u01b0\u1ee3c \u0111\u1eb7t tr\u00ean m\u1ed9t gi\u00e1 \u0111\u1ee1 ba ch\u00e2n. Tr\u1ecdng l\u1ef1c t\u00e1c d\u1ee5ng l\u00ean chi\u1ebfc m\u00e1y c\u00f3 \u0111\u1ed9 l\u1edbn l\u00e0 30N v\u00e0 \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed1 th\u00e0nh ba l\u1ef1c F\u20d7\u2081, F\u20d7\u2082, F\u20d7\u2083 l\u00ean ba ch\u00e2n c\u1ee7a gi\u00e1 \u0111\u1ee1. Ba l\u1ef1c F\u20d7\u2081, F\u20d7\u2082, F\u20d7\u2083 c\u00f3 \u0111\u1ed9 l\u1edbn b\u1eb1ng nhau v\u00e0 g\u00f3c t\u1ea1o b\u1edfi m\u1ed7i ch\u00e2n c\u1ee7a gi\u00e1 \u0111\u1ee1 v\u00e0 m\u1eb7t \u0111\u1ea5t l\u00e0 60^\u00b0 . H\u1ecfi \u0111\u1ed9 l\u1edbn c\u1ee7a l\u1ef1c F\u20d7\u2081 l\u00e0 bao nhi\u00eau N (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c)?<\/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 Chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng Chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3, c\u00f3 c\u1ea5u tr\u00fac s\u00e1t v\u1edbi \u0111\u1ec1 thi th\u1eadt. H\u00e3y t\u1ea3i ngay b\u1ed9 \u0111\u1ec1 thi k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y. V\u00e0 b\u1eaft \u0111\u1ea7u v\u00e0o qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp, t\u0103ng t\u1ed1c \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c th\u00e0nh t\u00edch cao trong k\u00ec thi THPT qu\u1ed1c gia m\u00f4n To\u00e1n 2025.<\/p>\n