{"id":484,"date":"2026-05-05T04:48:15","date_gmt":"2026-05-05T04:48:15","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-bac-ninh\/"},"modified":"2026-05-05T07:21:23","modified_gmt":"2026-05-05T07:21:23","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-bac-ninh","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-bac-ninh\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh"},"content":{"rendered":"

T\u00e0i li\u1ec7u \u00d4n Thi<\/a> g\u1eedi \u0111\u1ebfn th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh<\/strong>. \u0110\u00e2y l\u00e0 t\u1eadp t\u00e0i li\u1ec7u h\u1eefu \u00edch gi\u00fap c\u00e1c em h\u1ecdc sinh ti\u1ebft ki\u1ec7m th\u1eddi gian trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1 thi. H\u00e3y c\u00f9ng ch\u00fang t\u00f4i xem qua n\u1ed9i dung c\u1ee7a m\u00e3 \u0111\u1ec1 n\u00e0y c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t n\u00e0o.<\/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 B\u1eafc Ninh<\/strong><\/h2>\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 B\u1eafc Ninh<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 thi to\u00e1n thpt m\u00e0 b\u1ed9 GD&\u0110T \u0111\u00e3 c\u00f4ng b\u1ed1 t\u1eeb tr\u01b0\u1edbc. V\u1edbi h\u00ecnh th\u1ee9c tr\u1eafc nghi\u1ec7m v\u00e0 \u0111\u01b0\u1ee3c chia th\u00e0nh 3 ph\u1ea7n nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n ( 12 c\u00e2u )<\/strong><\/span><\/p>\n

T\u01b0\u01a1ng t\u1ef1 c\u00e1c \u0111\u1ec1 thi tr\u01b0\u1edbc \u0111\u00e2y, ph\u1ea7n 1 c\u1ee7a \u0111\u1ec1 thi th\u1eed n\u00e0y s\u1ebd c\u00f3 4 \u0111\u00e1p \u00e1n A, B, C, D. C\u00e1c b\u1ea1n n\u00ean \u0111\u1ecdc k\u0129 \u0111\u1ec1 v\u00e0 l\u1ef1a ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n \u0111\u00fang.<\/p>\n

C\u00e2u 1.<\/strong> Trong kh\u00f4ng gian Oxyz , cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.A\u2019B\u2019C\u2019D\u2019 c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh b\u1eb1ng 1, \u0111i\u1ec3m A tr\u00f9ng v\u1edbi g\u1ed1c t\u1ecda \u0111\u1ed9 (nh\u01b0 h\u00ecnh v\u1ebd).<\/p>\n

\"\"<\/p>\n

T\u1ecda \u0111\u1ed9 c\u1ee7a vect\u01a1 A\u2019C\u2019\u20d7 l\u00e0:<\/p>\n

A. (1;0;1)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. (0;1;1)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. (1;1;0)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. (1;1;1)<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed7i b\u1ea1n An v\u00e0 B\u00ecnh ch\u1ecdn ng\u1eabu nhi\u00ean ba s\u1ed1 trong t\u1eadp 0;1;2;3;4;5;6;7;8;9 . X\u00e1c su\u1ea5t \u0111\u1ec3 trong hai b\u1ed9 s\u1ed1 c\u1ee7a An v\u00e0 B\u00ecnh ch\u1ecdn ra c\u00f3 \u0111\u00fang m\u1ed9t s\u1ed1 gi\u1ed1ng nhau b\u1eb1ng:<\/p>\n

A. 21\/40 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 203\/480 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 49\/60 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 17\/24 <\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi \u0111\u00fang sai ( 4 c\u00e2u )
\n<\/strong><\/span>
\n\u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng d\u1ea1ng c\u00e2u h\u1ecfi m\u1edbi so v\u1edbi \u0111\u1ec1 thi c\u1ee7a c\u00e1c n\u0103m tr\u01b0\u1edbc. V\u1edbi m\u1ed7i \u00fd a), b), a), d) c\u1ee7a m\u1ed7i c\u00e2u h\u1ecfi. B\u1ea1n c\u1ea7n ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0111\u00fang ho\u1eb7c sai cho t\u1eebng c\u00e2u tr\u1ea3 l\u1eddi. H\u00e3y gi\u1ea3i ngay c\u00e1c c\u00e2u sau \u0111\u00e2y \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 d\u1ea1ng n\u00e0y:<\/p>\n

C\u00e2u 1.<\/strong> \u0110i\u1ec3m trung b\u00ecnh m\u00f4n To\u00e1n cu\u1ed1i n\u0103m c\u1ee7a c\u00e1c h\u1ecdc sinh l\u1edbp 12A v\u00e0 12B \u0111\u01b0\u1ee3c th\u1ed1ng k\u00ea \u1edf b\u1ea3ng sau:<\/p>\n

beginarray|c|c|c|c|c|c|c| hline \u0110i\u1ec3m trung b\u00ecnh & [5;6) & [6;7) & [7;8) & [8;9) & [9;10] hline 12A & 1 & 0 & 6 & 11 & 10 12B & 0 & 6 & 7 & 14 & 2 hline endarray<\/p>\n

C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

a) L\u1edbp 12A c\u00f3 28 h\u1ecdc sinh c\u00f3 \u0111i\u1ec3m trung b\u00ecnh m\u00f4n To\u00e1n cu\u1ed1i n\u0103m t\u1eeb 8 tr\u1edf l\u00ean.<\/p>\n

b) \u0110\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u l\u1edbp 12A (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m) l\u00e0 0,72.<\/p>\n

c) S\u1ed1 trung b\u00ecnh c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u l\u1edbp 12A l\u1edbn h\u01a1n s\u1ed1 trung b\u00ecnh c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u l\u1edbp 12B.<\/p>\n

d) N\u1ebfu so s\u00e1nh theo \u0111\u1ed9 l\u1ec7ch chu\u1ea9n th\u00ec h\u1ecdc sinh l\u1edbp 12A c\u00f3 \u0111i\u1ec3m trung b\u00ecnh m\u00f4n To\u00e1n cu\u1ed1i n\u0103m \u00edt ph\u00e2n t\u00e1n h\u01a1n l\u1edbp 12B.<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = (2x + 1)\/(x – 1) (C) . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

a) H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean mathbbR setminus 1 <\/p>\n

b) H\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

c) Ti\u1ebfp tuy\u1ebfn v\u1edbi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 t\u1ea1i \u0111i\u1ec3m c\u00f3 ho\u00e0nh \u0111\u1ed9 b\u1eb1ng 2 t\u1ea1o v\u1edbi hai tr\u1ee5c t\u1ecda \u0111\u1ed9 m\u1ed9t tam gi\u00e1c c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng a\/b (v\u1edbi a,b in mathbbN^*, (a,b)=1 ). Khi \u0111\u00f3 6a – 20b = 1 .<\/p>\n

d) L\u1ea5y hai \u0111i\u1ec3m A, B thu\u1ed9c m\u1ed9t nh\u00e1nh c\u1ee7a \u0111\u1ed3 th\u1ecb sao cho x_A < x_B > 1 v\u00e0 hai \u0111i\u1ec3m C, D thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng \u0394: y = x + 1 . Khi ABCD l\u00e0 h\u00ecnh vu\u00f4ng th\u00ec di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng \u0111\u00f3 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c) l\u00e0 47.4 \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch.<\/p>\n

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

Ph\u1ea7n n\u00e0y ch\u1ee7 y\u1ebfu s\u1ebd l\u00e0 c\u00e1c c\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn, c\u00e1c b\u1ea1n c\u1ea7n \u0111\u1ecdc th\u1eadt k\u0129 \u0111\u1ec1 v\u00e0 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c c\u00e2u h\u1ecfi \u0111\u1ec3 tr\u1ea3 l\u1eddi \u0111\u00fang tr\u1ecdng t\u00e2m nh\u1ea5t v\u00e0 \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 cao.<\/p>\n

C\u00e2u 1.<\/strong> Trong h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxy , cho \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (C): y = (x\u00b2 + x + 1)\/(x – 1) m\u00f4 t\u1ea3 chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a hai t\u00e0u \u0111\u00e1nh c\u00e1 A v\u00e0 B (\u0111\u01a1n v\u1ecb tr\u00ean m\u1ed7i tr\u1ee5c t\u1ecda \u0111\u1ed9 t\u00ednh b\u1eb1ng km ). Bi\u1ebft qu\u1ef9 \u0111\u1ea1o chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a hai t\u00e0u lu\u00f4n thu\u1ed9c v\u1ec1 hai nh\u00e1nh kh\u00e1c nhau c\u1ee7a \u0111\u1ed3 th\u1ecb (C) . T\u00ednh kho\u1ea3ng c\u00e1ch ng\u1eafn nh\u1ea5t (\u0111\u01a1n v\u1ecb km ) gi\u1eefa hai t\u00e0u \u0111\u00e1nh c\u00e1 A v\u00e0 B (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t c\u00f4ng ty x\u00e2y d\u1ef1ng \u0111\u1ea5u th\u1ea7u 3 d\u1ef1 \u00e1n X, Y, Z . X\u00e1c su\u1ea5t \u0111\u1ec3 ba d\u1ef1 \u00e1n X, Y, Z tr\u00fang th\u1ea7u t\u01b0\u01a1ng \u1ee9ng l\u00e0 a, b, 0.8 (v\u1edbi a > b ). Bi\u1ebft r\u1eb1ng x\u00e1c su\u1ea5t \u0111\u1ec3 \u00edt nh\u1ea5t m\u1ed9t trong ba d\u1ef1 \u00e1n tr\u00fang th\u1ea7u l\u00e0 0.964 v\u00e0 x\u00e1c su\u1ea5t \u0111\u1ec3 c\u1ea3 ba d\u1ef1 \u00e1n \u0111\u1ec1u tr\u00fang th\u1ea7u l\u00e0 0.224 . Gi\u1ea3 s\u1eed vi\u1ec7c tr\u00fang th\u1ea7u c\u1ee7a ba d\u1ef1 \u00e1n X, Y, Z l\u00e0 \u0111\u1ed9c l\u1eadp v\u1edbi nhau. T\u00ednh 2a + b ?<\/p>\n

B\u00ean c\u1ea1nh \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh<\/strong>, c\u00e1c b\u1ea1n h\u1ecdc sinh 12 c\u00f3 th\u1ec3 tham kh\u1ea3o c\u00e1c \u0111\u1ec1 thi th\u1eed to\u00e1n thpt<\/a> kh\u00e1c \u0111\u1ec3 \u00f4n t\u1eadp v\u1eefng ki\u1ebfn th\u1ee9c v\u00e0 n\u00e2ng cao t\u01b0 duy gi\u1ea3i \u0111\u1ec1.<\/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 B\u1eafc Ninh<\/strong><\/h2>\n

B\u1ed9 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T B\u1eafc Ninh<\/strong> c\u00f3 n\u1ed9i dung kh\u00e1 s\u00e1t v\u1edbi \u0111\u1ec1 thi ch\u00ednh th\u1ee9c v\u00e0 k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng tra c\u1ee9u v\u00e0 c\u1ea3i thi\u1ec7n c\u00e1ch tr\u00ecnh b\u00e0y b\u00e0i thi. H\u00e3y t\u1ea3i ngay \u0111\u1ec1 thi qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y v\u00e0 \u00f4n t\u1eadp nh\u00e9!<\/p>\n