{"id":482,"date":"2026-05-05T04:48:08","date_gmt":"2026-05-05T04:48:08","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-ninh-binh\/"},"modified":"2026-05-05T07:21:14","modified_gmt":"2026-05-05T07:21:14","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-ninh-binh","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-ninh-binh\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Ninh B\u00ecnh"},"content":{"rendered":"

C\u00e1c b\u1ea1n h\u1ecdc sinh 12 b\u1ecf t\u00fai ngay t\u1eadp \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Ninh B\u00ecnh<\/strong> \u0111\u1ec3 chinh ph\u1ee5c m\u00f4n To\u00e1n trong k\u00ec thi t\u1ed1t nghi\u1ec7p THPT ch\u00ednh th\u1ee9c. B\u1ed9 t\u00e0i li\u1ec7u n\u00e0y t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00e2u h\u1ecfi tr\u1ecdng t\u00e2m, b\u00e1m s\u00e1t ki\u1ebfn th\u1ee9c To\u00e1n THPT, k\u00e8m theo \u0111\u00e1p \u00e1n chi ti\u1ebft v\u00e0 h\u01b0\u1edbng d\u1eabn tr\u00ecnh b\u00e0y khoa h\u1ecdc theo t\u1eebng ph\u1ea7n. T\u00ecm hi\u1ec3u th\u00eam th\u00f4ng tin n\u1ed9i dung c\u1ee7a \u0111\u1ec1 thi ngay sau \u0111\u00e2y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> 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 Ninh B\u00ecnh<\/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 Ninh B\u00ecnh<\/strong> c\u00f3 t\u1ea5t c\u1ea3 l\u00e0 22 c\u00e2u \u0111\u01b0\u1ee3c chia theo c\u00e1c 3 d\u1ea1ng ch\u00ednh trong \u0111\u1ec1. M\u1ed7i ph\u1ea7n s\u1ebd c\u00f3 nh\u1eefng c\u00e2u h\u1ecfi t\u1eeb nh\u1eadn bi\u1ebft, v\u1eadn d\u1ee5ng \u0111\u1ebfn n\u00e2ng cao. Nh\u1eb1m \u0111\u00e1nh gi\u00e1 m\u1ee9c \u0111\u1ed9 n\u0103ng l\u1ef1c c\u1ee7a c\u00e1c b\u1ea1n v\u00e0 t\u1eeb \u0111\u00f3 chu\u1ea9n b\u1ecb cho m\u00ecnh qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp c\u1ea3i thi\u1ec7n \u0111i\u1ec3m s\u1ed1 hi\u1ec7u qu\u1ea3. H\u00e3y xem qua c\u1ea5u tr\u00fac c\u1ee7a \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n<\/a> v\u00e0 l\u00e0m quen ngay.<\/p>\n

PH\u1ea6N 1 \u2013 TR\u1eaeC NGHI\u1ec6M 4 PH\u01af\u01a0NG \u00c1N L\u1ef0A CH\u1eccN<\/strong><\/p>\n

T\u1eeb c\u00e2u h\u1ecfi s\u1ed1 1 \u0111\u1ebfn 12 v\u1edbi n\u1ed9i dung c\u1ee7a ph\u1ea7n n\u00e0y ch\u1ee7 y\u1ebfu l\u00e0 c\u00e1c c\u00e2u h\u1ecfi v\u1ec1 x\u00e1c su\u1ea5t, h\u00ecnh h\u1ecdc kh\u00f4ng gian, gi\u1ea3i t\u00edch, h\u00e0m s\u1ed1. V\u00ed d\u1ee5 c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n

C\u00e2u 1<\/strong>: L\u1edbp 12A8 c\u1ee7a tr\u01b0\u1eddng THPT X c\u00f3 41 h\u1ecdc sinh \u0111\u01b0\u1ee3c \u0111\u00e1nh s\u1ed1 th\u1ee9 t\u1ef1 t\u1eeb 1 \u0111\u1ebfn 41. C\u00f4 gi\u00e1o ch\u1ecdn ng\u1eabu nhi\u00ean 3 b\u1ea1n \u0111\u1ec3 l\u00e0m nhi\u1ec7m v\u1ee5 ki\u1ec3m tra v\u1edf b\u00e0i t\u1eadp c\u1ee7a c\u00e1c b\u1ea1n trong l\u1edbp. X\u00e1c su\u1ea5t \u0111\u1ec3 3 b\u1ea1n \u0111\u01b0\u1ee3c ch\u1ecdn c\u00f3 s\u1ed1 th\u1ee9 t\u1ef1 l\u1eadp th\u00e0nh m\u1ed9t c\u1ea5p s\u1ed1 c\u1ed9ng l\u00e0 a\/b (v\u1edbi a\/b l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n). T\u00ednh S = 2a + b .<\/p>\n

A. 573\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. 553\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 613\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 653<\/p>\n

C\u00e2u 2<\/strong>: Cho h\u00ecnh h\u1ed9p ABCD.A\u2019B\u2019C\u2019D\u2019 (h\u00ecnh v\u1ebd). \u0110\u1eb3ng th\u1ee9c n\u00e0o sau \u0111\u00e2y sai?<\/p>\n

\"\"<\/p>\n

A. AB\u20d7 + AD\u20d7 = AC\u20d7 <\/p>\n

B. AD\u20d7 + CC\u2019\u20d7 = A\u2019D\u2019\u20d7 <\/p>\n

C. AC\u20d7 + B\u2019B\u20d7 = A\u2019C\u2019\u20d7 <\/p>\n

D. A\u2019B\u2019\u20d7 + CB\u20d7 = AC\u2019\u20d7 <\/p>\n

PH\u1ea6N 2 \u2013 TR\u1eaeC NGHI\u1ec6M CH\u1eccN \u0110\u00daNG SAI<\/strong><\/p>\n

C\u00f3 t\u1ea5t c\u1ea3 4 c\u00e2u h\u1ecfi, m\u1ed7i c\u00e2u c\u00f3 4 \u00fd tr\u1ea3 l\u1eddi, h\u1ecdc sinh c\u1ea7n ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i c\u00e2u tr\u1ea3 l\u1eddi. D\u1ea1ng n\u00e0y l\u00e0 m\u1ed9t trong d\u1ea1ng m\u1edbi c\u1ee7a \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n nh\u1eefng n\u0103m g\u1ea7n \u0111\u00e2y.<\/p>\n

C\u00e2u 1<\/strong>: Cho h\u00e0m s\u1ed1 y = f(x) = (ax\u00b2 + bx + c)\/(x + d) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong nh\u01b0 h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y, bi\u1ebft \u0111\u01b0\u1eddng ti\u1ec7m xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111i qua hai \u0111i\u1ec3m (0; 1) v\u00e0 (1; 0) .<\/p>\n

\"\"<\/p>\n

a) Kho\u1ea3ng c\u00e1ch t\u1eeb M(1; -8) \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua c\u00e1c \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eb1ng \u221a5 .<\/p>\n

b) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-4; 0) .<\/p>\n

c) Ta c\u00f3 a + b + c + d = -2 .<\/p>\n

d) T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 mathbbR setminus 2 .<\/p>\n

C\u00e2u 2<\/strong>: M\u1ed9t h\u1ea1t chuy\u1ec3n \u0111\u1ed9ng tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 g\u1eafn m\u1ed9t tr\u1ee5c t\u1ecda \u0111\u1ed9 v\u1edbi g\u1ed1c t\u1ecda \u0111\u1ed9 l\u00e0 v\u1ecb tr\u00ed h\u1ea1t b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng. T\u1ecda \u0111\u1ed9 c\u1ee7a h\u1ea1t tr\u00ean tr\u1ee5c t\u1ea1i th\u1eddi \u0111i\u1ec3m t (\u0111\u01a1n v\u1ecb: gi\u00e2y) k\u1ec3 t\u1eeb khi xu\u1ea5t ph\u00e1t \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c x(t) = 2t – 3ln(t + 1) (\u0111\u01a1n v\u1ecb: m\u00e9t), t \u2265 0 . H\u00e0m s\u1ed1 v(t) = x'(t) (\u0111\u01a1n v\u1ecb: m\u00e9t\/gi\u00e2y) bi\u1ec3u th\u1ecb v\u1eadn t\u1ed1c chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a h\u1ea1t.<\/p>\n

a) V\u1eadn t\u1ed1c ban \u0111\u1ea7u c\u1ee7a h\u1ea1t l\u00e0 1 m\/s .<\/p>\n

b) H\u1ea1t \u0111\u1ee9ng y\u00ean t\u1ea1i th\u1eddi \u0111i\u1ec3m t = 0,5 s .<\/p>\n

c) v(t) = 2 – (3)\/(t + 1) <\/p>\n

d) Qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 h\u1ea1t \u0111i \u0111\u01b0\u1ee3c trong 3 gi\u00e2y \u0111\u1ea7u ti\u00ean l\u00e0 1,84 m (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

PH\u1ea6N 3 \u2013 TR\u1eaeC NGHI\u1ec6M TR\u1ea2 L\u1edcI NG\u1eaeN<\/strong><\/p>\n

M\u1eddi qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh tham kh\u1ea3o qua c\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1<\/strong>: Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh thoi t\u00e2m O , SO vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y. Bi\u1ebft c\u1ea1nh h\u00ecnh thoi b\u1eb1ng 2024 , g\u00f3c angle BAD = 120^\u00b0 , kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m C \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (SBD) b\u1eb1ng bao nhi\u00eau?<\/p>\n

C\u00e2u 2<\/strong>: Trong kh\u00f4ng gian Oxyz , m\u1ed9t khinh kh\u00ed c\u1ea7u \u1edf t\u1ecda \u0111\u1ed9 A(-16; -10; 10) b\u1eaft \u0111\u1ea7u bay v\u1edbi vect\u01a1 v\u1eadn t\u1ed1c kh\u00f4ng \u0111\u1ed5i v\u20d7 = (4; 3; -1) (\u0111\u01a1n v\u1ecb v\u1eadn t\u1ed1c l\u00e0 km\/h) v\u00e0 d\u1ef1 ki\u1ebfn bay trong th\u1eddi gian 10 gi\u1edd. Bi\u1ebft tr\u1ea1m ki\u1ec3m so\u00e1t kh\u00f4ng l\u01b0u \u0111\u1eb7t \u1edf v\u1ecb tr\u00ed g\u1ed1c t\u1ecda \u0111\u1ed9 O ki\u1ec3m so\u00e1t \u0111\u01b0\u1ee3c c\u00e1c v\u1eadt th\u1ec3 c\u00e1ch tr\u1ea1m m\u1ed9t kho\u1ea3ng t\u1ed1i \u0111a b\u1eb1ng 12 km . Th\u1eddi gian k\u1ec3 t\u1eeb khi tr\u1ea1m ki\u1ec3m so\u00e1t ph\u00e1t hi\u1ec7n ra khinh kh\u00ed c\u1ea7u \u0111\u1ebfn khi khinh kh\u00ed c\u1ea7u ra kh\u1ecfi v\u00f9ng ki\u1ec3m so\u00e1t l\u00e0 bao nhi\u00eau ph\u00fat?<\/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 Ninh B\u00ecnh<\/strong><\/h2>\n

V\u1edbi \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Ninh B\u00ecnh<\/strong>, c\u00e1c b\u1ea1n h\u1ecdc sinh l\u1edbp 12 s\u1ebd c\u00f3 c\u01a1 h\u1ed9i \u00f4n t\u1eadp v\u00e0 l\u00e0m quen tr\u01b0\u1edbc v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi m\u00f4n To\u00e1n. \u0110\u00e2y l\u00e0 t\u00e0i li\u1ec7u kh\u00f4ng th\u1ec3 b\u1ecf qua nh\u1eb1m c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c, n\u00e2ng cao n\u0103ng l\u1ef1c gi\u1ea3i \u0111\u1ec1 v\u00e0 c\u00e1ch tr\u00ecnh b\u00e0y b\u00e0i l\u00e0m th\u1eadt ho\u00e0n ch\u1ec9nh. H\u00e3y t\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Ninh B\u00ecnh qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y v\u00e0 luy\u1ec7n t\u1eadp ngay nh\u00e9!<\/p>\n