{"id":390,"date":"2026-05-05T04:43:13","date_gmt":"2026-05-05T04:43:13","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-kiem-tra-giua-ki-2-toan-12-nam-2024-2025-truong-nguyen-binh-khiem-ha-noi\/"},"modified":"2026-05-05T07:15:58","modified_gmt":"2026-05-05T07:15:58","slug":"de-kiem-tra-giua-ki-2-toan-12-nam-2024-2025-truong-nguyen-binh-khiem-ha-noi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-kiem-tra-giua-ki-2-toan-12-nam-2024-2025-truong-nguyen-binh-khiem-ha-noi\/","title":{"rendered":"\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9i"},"content":{"rendered":"

\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9i<\/strong>\u00a0l\u00e0 t\u00e0i li\u1ec7u b\u1ed5 \u00edch gi\u00fap h\u1ecdc sinh l\u1edbp 12 l\u00e0m quen v\u1edbi \u0111\u1ec1 thi v\u00e0 v\u00e0 r\u00fat ra kinh nghi\u1ec7m l\u00e0m b\u00e0i, chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 ki\u1ec3m tra s\u1eafp t\u1edbi. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a><\/strong> b\u1eadt m\u00ed ngay c\u1ea5u tr\u00fac \u0111\u1ec1 ki\u1ec3m tra chi ti\u1ebft d\u01b0\u1edbi \u0111\u00e2y!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9i<\/strong><\/h2>\n

\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 c\u1ee7a tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9i<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t ki\u1ebfn th\u1ee9c \u0111\u00e3 h\u1ecdc, v\u1edbi c\u1ea5u tr\u00fac chu\u1ea9n theo quy \u0111\u1ecbnh. \u0110\u1ec1 thi g\u1ed3m 22 c\u00e2u h\u1ecfi, th\u1eddi gian l\u00e0m b\u00e0i 90 ph\u00fat, gi\u00fap h\u1ecdc sinh l\u00e0m quen v\u1edbi d\u1ea1ng \u0111\u1ec1 gi\u1eefa k\u1ef3 v\u00e0 chu\u1ea9n b\u1ecb v\u1eefng v\u00e0ng cho k\u1ef3 thi THPT Qu\u1ed1c gia s\u1eafp t\u1edbi. C\u00f9ng kh\u00e1m ph\u00e1 chi ti\u1ebft n\u1ed9i dung \u0111\u1ec1 ki\u1ec3m tra ngay sau \u0111\u00e2y:<\/p>\n

Ph\u1ea7n I \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m nhi\u1ec1u \u0111\u00e1p \u00e1n l\u1ef1a ch\u1ecdn ( 12 c\u00e2u )<\/strong><\/span><\/p>\n

M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong d\u1ea1ng n\u00e0y b\u1ea1n c\u1ea7n xem qua nh\u01b0 sau:<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) x\u00e1c \u0111\u1ecbnh tr\u00ean mathbbR v\u00e0 c\u00f3 f'(x) = 4 – x\u00b2 v\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c x . H\u00e0m s\u1ed1 y = f(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o sau \u0111\u00e2y?<\/p>\n

A. (-2;2) \u00a0 \u00a0 \u00a0 B. (-\u221e;-2) \u00a0 \u00a0 \u00a0 \u00a0 C. (0;+\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. (0;4) <\/p>\n

C\u00e2u 2.<\/strong> T\u1ed5ng gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 y = (2x – 1)\/(x + 1) tr\u00ean \u0111o\u1ea1n [0;2] b\u1eb1ng<\/p>\n

A. 0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. -1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 1 <\/p>\n

Ph\u1ea7n II \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai ( 4 c\u00e2u )<\/strong><\/span><\/p>\n

Ph\u1ea7n c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m c\u00f3 4 c\u00e2u v\u1edbi m\u1ed7i c\u00e2u h\u1ecfi s\u1ebd c\u00f3 4 \u0111\u00e1p \u00e1n, do \u0111\u00f3 m\u1ed7i h\u1ecdc sinh c\u1ea7n \u0111\u1ecdc th\u1eadt k\u0129 \u0111\u1ec1 v\u00e0 c\u00e2u tr\u1ea3 l\u1eddi \u0111\u1ec3 ch\u1ecdn ph\u01b0\u01a1ng \u00e1n \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i c\u00e2u. V\u00ed d\u1ee5 nh\u01b0 sau:<\/p>\n

C\u00e2u 3.<\/strong> C\u1eaft m\u1ed9t chi\u1ebfc tr\u1ed1ng \u0111\u1ed3ng c\u00f3 d\u1ea1ng kh\u1ed1i tr\u00f2n xoay b\u1edfi m\u1ed9t m\u1eb7t ph\u1eb3ng \u0111i qua t\u00e2m c\u1ee7a \u0111\u00e1y v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y \u0111\u01b0\u1ee3c m\u1eb7t c\u1eaft l\u00e0 ph\u1ea7n h\u00ecnh ph\u1eb3ng. Bi\u1ebft r\u1eb1ng hai \u0111\u01b0\u1eddng cong th\u00e0nh b\u00ean l\u1ea7n l\u01b0\u1ee3t l\u00e0 m\u1ed9t ph\u1ea7n c\u1ee7a \u0111\u01b0\u1eddng parabol y = f(x) v\u00e0 y = g(x) .<\/p>\n

a) f(x) = 1\/100x\u00b2 + 24 .<\/p>\n

b) g(x) = f(-x) .<\/p>\n

c) Di\u1ec7n t\u00edch c\u1ee7a ph\u1ea7n m\u1eb7t c\u1eaft b\u1eb1ng 7040\/3 cm \u00b2 .<\/p>\n

d) Th\u1ec3 t\u00edch c\u1ee7a chi\u1ebfc tr\u1ed1ng \u0111\u1ed3ng b\u1eb1ng 70656\u03c0 cm \u00b3 .<\/p>\n

C\u00e2u 4.<\/strong> Trong kh\u00f4ng gian Oxyz , cho hai \u0111i\u1ec3m A(0;-2;1) , B(1;0;2) v\u00e0 m\u1eb7t ph\u1eb3ng (P): x – 2y + 2z – 2 = 0 . G\u1ecdi (Q) l\u00e0 m\u1eb7t ph\u1eb3ng \u0111i qua hai \u0111i\u1ec3m A, B v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (P) .<\/p>\n

a) Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng (P) l\u00e0 n\u20d7_(P) = (1;-2;2) .<\/p>\n

b) AB\u20d7 v\u00e0 n\u20d7_(P) l\u00e0 c\u1eb7p vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a m\u1eb7t ph\u1eb3ng (Q) .<\/p>\n

c) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng (Q) l\u00e0: 6x – y – 4z – 4 = 0 .<\/p>\n

d) Kho\u1ea3ng c\u00e1ch t\u1eeb g\u1ed1c t\u1ecda \u0111\u1ed9 O \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (Q) b\u1eb1ng (\u221a53)\/(53) .<\/p>\n

Ph\u1ea7n III \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn ( 6 c\u00e2u )<\/strong><\/span><\/p>\n

\u0110\u1ec3 chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao trong k\u1ef3 thi s\u1eafp t\u1edbi, h\u00e3y c\u00f9ng nhau luy\u1ec7n t\u1eadp v\u1edbi b\u1ed9 \u0111\u1ec1 thi gi\u1eefa k\u1ef3 2 To\u00e1n 12<\/strong><\/a> v\u1edbi nhi\u1ec1u d\u1ea1ng b\u00e0i t\u1eadp t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn n\u00e2ng cao sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1:<\/strong> M\u1ed9t c\u00f4ng ty s\u1ea3n xu\u1ea5t \u0111\u1ed3 ch\u01a1i d\u1ef1 ki\u1ebfn s\u1ea3n xu\u1ea5t kh\u00f4ng qu\u00e1 1000 b\u1ed9 \u0111\u1ed3 ch\u01a1i m\u1ed7i th\u00e1ng \u0111\u1ec3 \u0111\u00e1p \u1ee9ng nhu c\u1ea7u th\u1ecb tr\u01b0\u1eddng. N\u1ebfu s\u1ea3n xu\u1ea5t x b\u1ed9 \u0111\u1ed3 ch\u01a1i, doanh thu c\u00f3 th\u1ec3 \u0111\u1ea1t khi b\u00e1n h\u1ebft l\u00e0:
\n F(x) = 2x\u00b3 – 6 000x\u00b2 + 3 000 000x + 8 000 000 (\u0111\u1ed3ng). Chi ph\u00ed trung b\u00ecnh cho m\u1ed7i b\u1ed9 l\u00e0: overlineC(x) = 1,5x + 1800 + (5 000 000)\/(x) (\u0111\u1ed3ng). H\u1ecfi c\u00f4ng ty c\u1ea7n s\u1ea3n xu\u1ea5t bao nhi\u00eau b\u1ed9 \u0111\u1ed3 ch\u01a1i \u0111\u1ec3 thu \u0111\u01b0\u1ee3c l\u1ee3i nhu\u1eadn l\u1edbn nh\u1ea5t?<\/p>\n

C\u00e2u 2:<\/strong> Vi khu\u1ea9n E. coli s\u1ed1ng ch\u1ee7 y\u1ebfu \u1edf \u0111\u01b0\u1eddng ru\u1ed9t v\u00e0 c\u00f3 s\u1ed1 l\u01b0\u1ee3ng l\u1edbn nh\u1ea5t trong h\u1ec7 vi sinh v\u1eadt c\u1ee7a c\u01a1 th\u1ec3. M\u1ed9t qu\u1ea7n th\u1ec3 vi khu\u1ea9n E. coli \u0111\u01b0\u1ee3c quan s\u00e1t trong \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p, c\u00f3 t\u1ed1c \u0111\u1ed9 sinh s\u1ea3n \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1: f(t) = 480.2^t ln 2. Trong \u0111\u00f3 t t\u00ednh b\u1eb1ng gi\u1edd ( t > 0 ), f(t) t\u00ednh b\u1eb1ng c\u00e1 th\u1ec3\/gi\u1edd. Bi\u1ebft t\u1ea1i th\u1eddi \u0111i\u1ec3m b\u1eaft \u0111\u1ea7u quan s\u00e1t, s\u1ed1 l\u01b0\u1ee3ng c\u00e1 th\u1ec3 \u0111\u01b0\u1ee3c \u01b0\u1edbc t\u00ednh m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c kho\u1ea3ng 480 c\u00e1 th\u1ec3. H\u1ecfi sau 3 gi\u1edd s\u1ed1 l\u01b0\u1ee3ng c\u00e1 th\u1ec3 b\u1eb1ng bao nhi\u00eau?<\/p>\n

Ngo\u00e0i \u0111\u1ec1 \u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9<\/strong>i b\u1ea1n c\u0169ng c\u00f3 th\u1ec3 tham kh\u1ea3o qua nhi\u1ec1u t\u00e0i li\u1ec7u, d\u1ea1ng \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp kh\u00e1c trong \u0111\u1ec1 thi gi\u1eefa k\u00ec 2 to\u00e1n 12<\/a>. \u0110i\u1ec1u n\u00e0y s\u1ebd gi\u00fap b\u1ea1n \u00f4n t\u1eadp ki\u1ebfn th\u1ee9c v\u00e0 r\u00e8n luy\u1ec7n t\u00ednh ph\u1ea3n x\u1ea1 t\u1ed1t tr\u01b0\u1edbc khi b\u1eaft \u0111\u1ea7u k\u00ec thi \u0111\u1ea5y.<\/p>\n

T\u1ea3i \u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9i<\/strong><\/h2>\n

T\u1ea3i \u0111\u1ea7y \u0111\u1ee7 t\u00e0i li\u1ec7u v\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft c\u1ee7a \u0110\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng Nguy\u1ec5n B\u1ec9nh Khi\u00eam \u2013 H\u00e0 N\u1ed9<\/strong>i qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y.<\/p>\n