{"id":560,"date":"2026-05-05T04:52:11","date_gmt":"2026-05-05T04:52:11","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-khao-sat-chat-luong-mon-toan-12-nam-2024-2025-so-gd-dt-bac-ninh-lan-3\/"},"modified":"2026-05-05T07:25:54","modified_gmt":"2026-05-05T07:25:54","slug":"de-khao-sat-chat-luong-mon-toan-12-nam-2024-2025-so-gd-dt-bac-ninh-lan-3","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-khao-sat-chat-luong-mon-toan-12-nam-2024-2025-so-gd-dt-bac-ninh-lan-3\/","title":{"rendered":"\u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh l\u1ea7n 3"},"content":{"rendered":"

B\u1ecf t\u00fai ngay \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh l\u1ea7n 3<\/strong> v\u1edbi c\u1ea5u tr\u00fac v\u00e0 n\u1ed9i dung b\u00e1m kh\u00e1 s\u00e1t v\u1edbi \u0111\u1ec1 minh h\u1ecda c\u1ee7a b\u1ed9 GD&DT. \u0110\u00e2y l\u00e0 t\u00e0i li\u1ec7u gi\u00fap b\u1ea1n l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 nh\u1ea5t tr\u00e1nh b\u1ee1 ng\u1ee1 khi v\u00e0o ph\u00f2ng thi v\u1edbi \u0111\u1ec1 ch\u00ednh th\u1ee9c. Cu\u1ed1i \u0111\u1ec1 c\u00f3 k\u00e8m c\u00e1ch gi\u1ea3i chi ti\u1ebft, do \u0111\u00f3 b\u1ea1n d\u1ec5 d\u00e0ng tra c\u1ee9u k\u1ebft qu\u1ea3 v\u00e0 r\u00fat ra \u0111\u01b0\u1ee3c b\u00e0i h\u1ecdc kinh nghi\u1ec7m cho l\u1ea7n thi ch\u00ednh th\u1ee9c. C\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 n\u1ed9i dung c\u1ee7a \u0111\u1ec1 ngay sau \u0111\u00e2y.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh l\u1ea7n 3<\/strong><\/h2>\n

N\u1ed9i dung \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh l\u1ea7n 3<\/strong> g\u1ed3m 22 c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed5 bao tr\u1ecdn ki\u1ebfn th\u1ee9c To\u00e1n 12 t\u1eeb \u0111\u1ea1i s\u1ed1 \u0111\u1ebfn h\u00ecnh h\u1ecdc kh\u00f4ng gian. Gi\u00fap c\u00e1c b\u1ea1n l\u00e0m quen v\u1edbi \u0111\u1ec1 v\u00e0 \u0111\u00e1nh gi\u00e1 \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c c\u1ee7a b\u1ea3n th\u00e2n \u0111\u1ec3 chu\u1ea9n b\u1ecb qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 cho k\u00ec thi ch\u00ednh th\u1ee9c. \u0110\u1eb7c bi\u1ec7t, m\u1ed7i c\u00e2u h\u1ecfi \u0111\u1ec1u c\u00f3 l\u1eddi gi\u1ea3i th\u00edch chi ti\u1ebft, gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 b\u1ea3n ch\u1ea5t v\u1ea5n \u0111\u1ec1 v\u00e0 r\u00fat kinh nghi\u1ec7m cho b\u00e0i sau. C\u1ea5u tr\u00fac \u0110\u1ec1 Kh\u1ea3o S\u00e1t Ch\u1ea5t L\u01b0\u1ee3ng To\u00e1n 12<\/a> chi ti\u1ebft nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/p>\n

Th\u00ed sinh ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n trong 4 ph\u01b0\u01a1ng \u00e1n A, B, C, D. V\u00ed d\u1ee5:<\/p>\n

C\u00e2u 1<\/strong>. T\u1ea5t c\u1ea3 c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh sin x = 0 l\u00e0<\/p>\n

A. x = \u03c0\/2 + k\u03c0, ; k in mathbbZ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. x = k2\u03c0, ; k in mathbbZ <\/p>\n

C. x = \u03c0 + k2\u03c0, ; k in mathbbZ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. x = k\u03c0, ; k in mathbbZ <\/p>\n

C\u00e2u 2.<\/strong> Trong kh\u00f4ng gian Oxyz , cho hai \u0111i\u1ec3m A(1;2;3), B(-2;4;0). Trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB c\u00f3 tung \u0111\u1ed9 l\u00e0<\/p>\n

A. 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. -1<\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 c\u00e2u)<\/strong><\/p>\n

Th\u00ed sinh \u0111\u00e1nh d\u1ea5u v\u00e0o \u00f4 gi\u00e1 tr\u1ecb \u0110\u00daNG ho\u1eb7c SAI c\u1ee7a m\u1ed7i c\u00e2u sau:<\/p>\n

C\u00e2u 1.<\/strong> Kh\u1ea3o s\u00e1t m\u1ed9t nh\u00f3m 50 h\u1ecdc sinh \u1edf m\u1ed9t tr\u01b0\u1eddng trung h\u1ecdc, ng\u01b0\u1eddi ta th\u1ea5y r\u1eb1ng: c\u00f3 20 h\u1ecdc sinh gi\u1ecfi Ngo\u1ea1i ng\u1eef, 15 h\u1ecdc sinh gi\u1ecfi Tin h\u1ecdc, 10 h\u1ecdc sinh gi\u1ecfi c\u1ea3 Ngo\u1ea1i ng\u1eef v\u00e0 Tin h\u1ecdc. Ch\u1ecdn ng\u1eabu nhi\u00ean m\u1ed9t h\u1ecdc sinh t\u1eeb nh\u00f3m \u0111\u00f3.<\/p>\n

a) X\u00e1c su\u1ea5t \u0111\u1ec3 ch\u1ecdn \u0111\u01b0\u1ee3c h\u1ecdc sinh gi\u1ecfi Ngo\u1ea1i ng\u1eef ho\u1eb7c Tin h\u1ecdc b\u1eb1ng 0,7 .<\/p>\n

b) X\u00e1c su\u1ea5t \u0111\u1ec3 ch\u1ecdn \u0111\u01b0\u1ee3c h\u1ecdc sinh gi\u1ecfi Tin h\u1ecdc b\u1eb1ng 0,3 .<\/p>\n

c) X\u00e1c su\u1ea5t \u0111\u1ec3 ch\u1ecdn \u0111\u01b0\u1ee3c h\u1ecdc sinh gi\u1ecfi Ngo\u1ea1i ng\u1eef b\u1eb1ng 0,4 .<\/p>\n

d) X\u00e1c su\u1ea5t \u0111\u1ec3 ch\u1ecdn \u0111\u01b0\u1ee3c h\u1ecdc sinh kh\u00f4ng gi\u1ecfi Ngo\u1ea1i ng\u1eef ho\u1eb7c Tin h\u1ecdc b\u1eb1ng 0,3 .<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f(x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y.<\/p>\n

\"\"<\/p>\n

a) H\u00e0m s\u1ed1 y = f(x) c\u00f3 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

b) H\u00e0m s\u1ed1 y = f(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean (-3; 5) .<\/p>\n

c) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 g(x) = (x – 4)\/(f(x) – 5) c\u00f3 3 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn.<\/p>\n

d) Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 g(x) = f(4x – x\u00b2) + 1\/3x\u00b3 – 3x\u00b2 + 8x + 1\/3 tr\u00ean \u0111o\u1ea1n [1;3] b\u1eb1ng 12 .<\/p>\n

Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)
\n<\/strong><\/p>\n

C\u00e2u 1<\/strong>. M\u1ed9t \u0111\u01b0\u1eddng d\u00e2y \u0111i\u1ec7n \u0111\u01b0\u1ee3c n\u1ed1i t\u1eeb m\u1ed9t nh\u00e0 m\u00e1y \u0111i\u1ec7n \u1edf A (n\u1eb1m t\u1ea1i b\u1edd bi\u1ec3n l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng AB ) \u0111\u1ebfn m\u1ed9t h\u00f2n \u0111\u1ea3o C , kho\u1ea3ng c\u00e1ch ng\u1eafn nh\u1ea5t t\u1eeb \u0111\u1ea3o v\u1ec1 b\u1edd bi\u1ec3n l\u00e0 \u0111o\u1ea1n BC d\u00e0i 1 km, kho\u1ea3ng c\u00e1ch t\u1eeb B \u0111\u1ebfn A l\u00e0 4 km \u0111\u01b0\u1ee3c minh h\u1ecda b\u1eb1ng h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y.<\/p>\n

\"\"<\/p>\n

Bi\u1ebft r\u1eb1ng m\u1ed7i km d\u00e2y \u0111i\u1ec7n \u0111\u1eb7t d\u01b0\u1edbi n\u01b0\u1edbc chi ph\u00ed m\u1ea5t 5000 USD, c\u00f2n \u0111\u1eb7t d\u01b0\u1edbi \u0111\u1ea5t chi ph\u00ed m\u1ea5t 3000 USD. H\u1ecfi \u0111i\u1ec3m S tr\u00ean b\u1edd c\u00e1ch A bao nhi\u00eau \u0111\u1ec3 khi m\u1eafc d\u00e2y \u0111i\u1ec7n t\u1eeb A qua S r\u1ed3i \u0111\u1ebfn C c\u00f3 chi ph\u00ed l\u00e0 \u00edt nh\u1ea5t?<\/p>\n

C\u00e2u 2.<\/strong> \u00d4ng An g\u1eedi ti\u1ebft ki\u1ec7m 50 tri\u1ec7u \u0111\u1ed3ng v\u00e0o ng\u00e2n h\u00e0ng v\u1edbi l\u00e3i su\u1ea5t 0,5% \/th\u00e1ng theo h\u00ecnh th\u1ee9c l\u00e3i k\u00e9p. Sau khi g\u1eedi \u0111\u01b0\u1ee3c 3 th\u00e1ng, \u00f4ng r\u00fat to\u00e0n b\u1ed9 g\u1ed1c v\u00e0 l\u00e3i r\u1ed3i g\u1eedi ti\u1ebfp s\u1ed1 ti\u1ec1n \u0111\u00f3 v\u1edbi l\u00e3i su\u1ea5t 6% \/n\u0103m c\u0169ng theo h\u00ecnh th\u1ee9c l\u00e3i k\u00e9p. T\u1ed5ng s\u1ed1 ti\u1ec1n \u00f4ng An thu \u0111\u01b0\u1ee3c sau 4 n\u0103m 3 th\u00e1ng k\u1ec3 t\u1eeb l\u00fac b\u1eaft \u0111\u1ea7u ti\u1ebft ki\u1ec7m l\u00e0 bao nhi\u00eau tri\u1ec7u \u0111\u1ed3ng? (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb)<\/p>\n

T\u1ea3i \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh l\u1ea7n 3<\/strong><\/h2>\n

\u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh l\u1ea7n 3<\/strong> gi\u00fap b\u1ea1n r\u00e8n luy\u1ec7n k\u0129 n\u0103ng l\u00e0m b\u00e0i, l\u00e0m quen v\u1edbi \u00e1p l\u1ef1c th\u1eddi gian trong ph\u00f2ng thi v\u00e0 t\u1ef1 tin h\u01a1n v\u1edbi \u0111\u1ec1 thi ch\u00ednh th\u1ee9c. T\u1ea3i ngay \u0111\u1ec1 v\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y. Ch\u00fac b\u1ea1n \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3 v\u00e0 \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t.<\/p>\n