{"id":470,"date":"2026-05-05T04:47:30","date_gmt":"2026-05-05T04:47:30","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-yen-bai\/"},"modified":"2026-05-05T07:20:33","modified_gmt":"2026-05-05T07:20:33","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-yen-bai","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-yen-bai\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Y\u00ean B\u00e1i"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Y\u00ean B\u00e1i<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c t\u1ed5ng h\u1ee3p v\u00f4 c\u00f9ng chi ti\u1ebft, b\u00e1m s\u00e1t c\u1ea5u tr\u00fac v\u00e0 y\u00eau c\u1ea7u c\u1ee7a B\u1ed9 GD & \u0110T. Gi\u00fap h\u1ecdc sinh l\u1edbp 12 l\u00e0m quen v\u1edbi c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi v\u00e0 r\u00e8n luy\u1ec7n t\u01b0 duy gi\u1ea3i \u0111\u1ec1. V\u00e0 \u0111\u00e2y c\u0169ng ch\u00ednh l\u00e0 k\u1ef3 thi quan tr\u1ecdng, kh\u00f4ng ch\u1ec9 x\u00e9t t\u1ed1t nghi\u1ec7p m\u00e0 c\u00f2n m\u1edf ra c\u01a1 h\u1ed9i ch\u1ea1m \u0111\u1ebfn c\u00e1nh c\u1ed5ng \u0110\u1ea1i h\u1ecdc m\u01a1 \u01b0\u1edbc. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> tham kh\u1ea3o qua n\u1ed9i dung c\u1ee7a t\u1eadp \u0111\u1ec1 thi th\u1eed n\u00e0y c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t nh\u00e9!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Y\u00ean B\u00e1i<\/strong><\/h2>\n

T\u1eadp \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Y\u00ean B\u00e1i<\/strong> kh\u00f4ng ch\u1ec9 c\u00f3 \u0111\u1ec1 thi m\u00e0 c\u00f2n k\u00e8m c\u00e1ch gi\u1ea3i chi ti\u1ebft, gi\u00fap h\u1ecdc sinh n\u1eafm v\u1eefng ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i v\u00e0 c\u00e1ch tr\u00ecnh b\u00e0y b\u00e0i l\u00e0m \u0111\u1ec3 \u0111\u1ea1t \u0111i\u1ec3m cao. B\u00ean c\u1ea1nh \u0111\u00f3, ph\u1ea7n l\u1eddi gi\u1ea3i c\u00f2n b\u1ed5 sung ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng, m\u1edf r\u1ed9ng c\u00e1c n\u1ed9i dung tr\u1ecdng t\u00e2m, h\u1ed7 tr\u1ee3 qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 h\u01a1n. N\u1ed9i dung chi ti\u1ebft c\u1ee7a \u0111\u1ec1 thi nh\u01b0 sau:<\/p>\n

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

\u0110\u1ec1 thi g\u1ed3m c\u00f3 12 c\u00e2u v\u1edbi 4 ph\u01b0\u01a1ng \u00e1n A, B, C, D, c\u00e1c b\u1ea1n h\u1ecdc sinh ch\u1ec9 c\u1ea7n l\u1ef1a ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t. C\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m trong \u0111\u1ec1 thi thpt to\u00e1n<\/a> c\u00f3 d\u1ea1ng sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1: \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean?\\[
\n\\begin{array}{ll}
\n\\text{A. } y = x^3 + 3x^2 \u2013 2 & \\quad \\text{B. } y = -2x^3 + 3x^2 \u2013 2 \\\\
\n\\text{C. } y = -x^3 + 3x^2 \u2013 2 & \\quad \\text{D. } y = x^3 \u2013 3x^2 \u2013 2
\n\\end{array}\\]\n<\/p>\n

\"\"<\/p>\n

C\u00e2u 2: H\u00e0m s\u1ed1 n\u00e0o sau \u0111\u00e2y \u0111\u1ed3ng bi\u1ebfn tr\u00ean mathbbR ?\\[
\n\\begin{array}{ll}
\n\\text{A. } y = 2x^2 + x + 3 & \\quad \\text{B. } y = x^4 \u2013 2x^2 + 3 \\\\
\n\\text{C. } y = x^3 + 2x + 3 & \\quad \\text{D. } y = -x^3 \u2013 3x^2 + 3
\n\\end{array}\\]\n<\/p>\n

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

M\u1ed7i c\u00e2u h\u1ecfi \u1edf ph\u1ea7n 2 s\u1ebd c\u00f3 4 c\u00e2u tr\u1ea3 l\u1eddi a), b), c), d). H\u1ecdc sinh c\u1ea7n ch\u1ecdn ph\u01b0\u01a1ng th\u1ee9c \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i c\u00e2u tr\u1ea3 l\u1eddi.<\/p>\n

C\u00e2u 2: T\u1ea1i m\u1ed9t c\u01a1 s\u1edf s\u1ea3n xu\u1ea5t g\u1ed1m L\u1ee5c B\u00ecnh, n\u1ebfu m\u1ed7i ng\u00e0y c\u01a1 s\u1edf n\u00e0y s\u1ea3n xu\u1ea5t x b\u00ecnh g\u1ed1m th\u00ec ph\u1ea3i chi ph\u00ed c\u00e1c kho\u1ea3n sau: \u2013 10 tri\u1ec7u \u0111\u1ed3ng chi ph\u00ed c\u1ed1 \u0111\u1ecbnh, \u2013 1,2 tri\u1ec7u \u0111\u1ed3ng cho m\u1ed7i b\u00ecnh g\u1ed1m, \u2013 0,016x\u00b2 tri\u1ec7u \u0111\u1ed3ng chi ph\u00ed b\u1ea3o d\u01b0\u1ee1ng m\u00e1y m\u00f3c. Bi\u1ebft c\u00f4ng su\u1ea5t t\u1ed1i \u0111a m\u1ed7i ng\u00e0y c\u1ee7a c\u01a1 s\u1edf n\u00e0y l\u00e0 s\u1ea3n xu\u1ea5t 40 b\u00ecnh g\u1ed1m.<\/p>\n

a) Chi ph\u00ed \u0111\u1ec3 s\u1ea3n xu\u1ea5t x b\u00ecnh g\u1ed1m l\u00e0 C(x) = 0,016x\u00b2 + 1,2x + 10 (tri\u1ec7u \u0111\u1ed3ng)\n<\/p>\n

b) Chi ph\u00ed \u0111\u1ec3 s\u1ea3n xu\u1ea5t m\u1ed7i b\u00ecnh g\u1ed1m l\u00e0 overlineC(x) = 0,016x + 10\/x (tri\u1ec7u \u0111\u1ed3ng)\n<\/p>\n

c) Khi c\u01a1 s\u1edf s\u1ea3n xu\u1ea5t 10 b\u00ecnh g\u1ed1m th\u00ec chi ph\u00ed trung b\u00ecnh s\u1ea3n xu\u1ea5t m\u1ed7i b\u00ecnh l\u00e0 1,016 tri\u1ec7u \u0111\u1ed3ng.<\/p>\n

d) \u0110\u1ec3 chi ph\u00ed trung b\u00ecnh s\u1ea3n xu\u1ea5t m\u1ed7i b\u00ecnh g\u1ed1m \u00edt nh\u1ea5t th\u00ec c\u01a1 s\u1edf ph\u1ea3i s\u1ea3n xu\u1ea5t 25 b\u00ecnh g\u1ed1m m\u1ed7i ng\u00e0y.<\/p>\n

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

C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m d\u1ea1ng n\u00e0y t\u01b0\u01a1ng t\u1ef1 nh\u01b0 c\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn c\u1ee7a c\u00e1c \u0111\u1ec1 thi c\u0169. H\u00e3y c\u00f9ng tham kh\u1ea3o m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi \u1edf ph\u1ea7n n\u00e0y ngay sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1: Ta coi n\u0103m l\u1ea5y l\u00e0m m\u1ed1c \u0111\u1ec3 t\u00ednh d\u00e2n s\u1ed1 c\u1ee7a m\u1ed9t v\u00f9ng (ho\u1eb7c c\u1ee7a m\u1ed9t qu\u1ed1c gia) l\u00e0 n\u0103m 0. Khi \u0111\u00f3, d\u00e2n s\u1ed1 c\u1ee7a v\u00f9ng (ho\u1eb7c qu\u1ed1c gia) \u0111\u00f3 \u1edf n\u0103m th\u1ee9 t l\u00e0 h\u00e0m s\u1ed1 theo bi\u1ebfn t \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c: S = A e^rt. Trong \u0111\u00f3 A l\u00e0 d\u00e2n s\u1ed1 c\u1ee7a v\u00f9ng (ho\u1eb7c qu\u1ed1c gia) \u0111\u00f3 \u1edf n\u0103m 0 v\u00e0 r l\u00e0 t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u1eb1ng n\u0103m (Ngu\u1ed3n: Gi\u1ea3i t\u00edch 12 NXBGD Vi\u1ec7t Nam, 2021). Bi\u1ebft r\u1eb1ng d\u00e2n s\u1ed1 Vi\u1ec7t Nam n\u0103m 2020 \u01b0\u1edbc t\u00ednh l\u00e0 97338579 ng\u01b0\u1eddi v\u00e0 t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u1eb1ng n\u0103m 0,91%\/n\u0103m (Ngu\u1ed3n: https:\/\/danso.org.viet-nam). Nh\u01b0 v\u1eady, n\u1ebfu t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u1eb1ng n\u0103m kh\u00f4ng \u0111\u1ed5i th\u00ec t\u1ed1i thi\u1ec3u \u0111\u1ebfn n\u0103m bao nhi\u00eau s\u1ed1 d\u00e2n c\u1ee7a Vi\u1ec7t Nam c\u00f3 kho\u1ea3ng 104689000 ng\u01b0\u1eddi?<\/p>\n

C\u00e2u 2: M\u1ed9t doanh nghi\u1ec7p s\u1ea3n xu\u1ea5t v\u00e0 b\u00e1n m\u1ed9t lo\u1ea1i s\u1ea3n ph\u1ea9m v\u1edbi gi\u00e1 45 ngh\u00ecn \u0111\u1ed3ng m\u1ed7i s\u1ea3n ph\u1ea9m. T\u1ea1i m\u1ee9c gi\u00e1 n\u00e0y, doanh nghi\u1ec7p b\u00e1n \u0111\u01b0\u1ee3c 66 s\u1ea3n ph\u1ea9m m\u1ed7i th\u00e1ng. Doanh nghi\u1ec7p d\u1ef1 \u0111\u1ecbnh t\u0103ng gi\u00e1 b\u00e1n v\u00e0 \u01b0\u1edbc t\u00ednh r\u1eb1ng n\u1ebfu t\u0103ng 2 ngh\u00ecn \u0111\u1ed3ng trong gi\u00e1 b\u00e1n th\u00ec s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m b\u00e1n \u0111\u01b0\u1ee3c s\u1ebd gi\u1ea3m \u0111i 6 s\u1ea3n ph\u1ea9m m\u1ed7i th\u00e1ng. Bi\u1ebft r\u1eb1ng chi ph\u00ed s\u1ea3n xu\u1ea5t m\u1ed7i s\u1ea3n ph\u1ea9m l\u00e0 27 ngh\u00ecn \u0111\u1ed3ng. Doanh nghi\u1ec7p n\u00ean b\u00e1n s\u1ea3n ph\u1ea9m v\u1edbi gi\u00e1 bao nhi\u00eau \u0111\u1ec3 l\u1ee3i nhu\u1eadn thu \u0111\u01b0\u1ee3c l\u00e0 l\u1edbn nh\u1ea5t?<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Y\u00ean B\u00e1i<\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Y\u00ean B\u00e1i<\/strong> l\u00e0 t\u1eadp t\u00e0i li\u1ec7u v\u00f4 c\u00f9ng h\u1eefu \u00edch, t\u0103ng kh\u1ea3 n\u0103ng chinh ph\u1ee5c k\u00ec thi quan tr\u1ecdng s\u1eafp t\u1edbi. H\u00e3y t\u1ea3i ngay \u0111\u1ec1 thi k\u00e8m \u0111\u00e1p \u00e1n theo \u0111\u01b0\u1eddng link sau \u0111\u00e2y v\u00e0 luy\u1ec7n t\u1eadp ngay h\u00f4m nay nh\u00e9!<\/p>\n