{"id":568,"date":"2026-05-05T04:52:36","date_gmt":"2026-05-05T04:52:36","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-vo-thi-sau-vinh-phuc\/"},"modified":"2026-05-05T07:26:26","modified_gmt":"2026-05-05T07:26:26","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-vo-thi-sau-vinh-phuc","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-vo-thi-sau-vinh-phuc\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u00f5 Th\u1ecb S\u00e1u V\u0129nh Ph\u00fac"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u00f5 Th\u1ecb S\u00e1u V\u0129nh Ph\u00fac<\/strong> l\u00e0 m\u1ed9t trong nh\u1eefng t\u00e0i li\u1ec7u luy\u1ec7n thi s\u00e1t v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi ch\u00ednh th\u1ee9c c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 thi gi\u00fap h\u1ecdc sinh \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c hi\u1ec7n t\u1ea1i v\u00e0 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i \u0111\u1ec1, l\u00e0m quen v\u1edbi \u0111a d\u1ea1ng d\u1ea1ng b\u00e0i t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. C\u00f9ng T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> t\u00ecm hi\u1ec3u v\u1ec1 \u0111\u1ec1 thi n\u00e0y trong b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u00f5 Th\u1ecb S\u00e1u V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u00f5 Th\u1ecb S\u00e1u V\u0129nh Ph\u00fac <\/strong><\/span>gi\u00fap h\u1ecdc sinh l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac v\u00e0 \u0111\u1ed9 kh\u00f3 c\u1ee7a k\u1ef3 thi ch\u00ednh th\u1ee9c, cung c\u1ea5p \u0111a d\u1ea1ng d\u1ea1ng b\u00e0i t\u1eadp \u0111\u1ec3 ki\u1ec3m tra to\u00e0n di\u1ec7n c\u00e1c k\u1ef9 n\u0103ng to\u00e1n h\u1ecdc. C\u1ea5u tr\u00fac \u0111\u1ec1 thi g\u1ed3m 3 ph\u1ea7n l\u1edbn v\u1edbi t\u1ed5ng th\u1eddi gian l\u00e0m b\u00e0i l\u00e0 90 ph\u00fat:<\/p>\n

Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Ph\u01b0\u01a1ng tr\u00ecnh sin x = sin \u03b1 c\u00f3 nghi\u1ec7m l\u00e0<\/p>\n

A. \\( \\left\\{ \\begin{array}{l}
\nx = \\alpha + k2\\pi \\\\
\nx = \\pi \u2013 \\alpha + k2\\pi
\n\\end{array} ;\\, k \\in \\mathbb{Z} \\right. \\)<\/p>\n

B. \\(\\left\\{ \\begin{array}{l}
\nx = \\alpha + k\\pi \\\\
\nx = \\pi \u2013 \\alpha + k\\pi
\n\\end{array} ;\\, k \\in \\mathbb{Z} \\right. \\)<\/p>\n

C. \\(\\left\\{ \\begin{array}{l}
\nx = \\alpha + k\\pi \\\\
\nx = -\\alpha + k\\pi
\n\\end{array} ;\\, k \\in \\mathbb{Z} \\right. \\)<\/p>\n

D. \\(\\left\\{ \\begin{array}{l}
\nx = \\alpha + k2\\pi \\\\
\nx = -\\alpha + k2\\pi
\n\\end{array} ;\\, k \\in \\mathbb{Z} \\right. \\)<\/p>\n

C\u00e2u 2.<\/strong> Cho c\u1ea5p s\u1ed1 nh\u00e2n (u_n) v\u1edbi u\u2081 = -1\/2, u\u2087 = -32 . T\u00ecm q ?<\/p>\n

A. q = \u00b1 1\/2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. q = \u00b1 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. q = \u00b1 4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. q = \u00b1 1 <\/p>\n

Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u, m\u1ed7i c\u00e2u g\u1ed3m 4 \u00fd nh\u1ecf)<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ea1o h\u00e0m y\u2019 = f'(x) = x(x – 2), forall x in mathbbR . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

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

b) Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean [1;2] l\u00e0 f(2) <\/p>\n

c) H\u00e0m s\u1ed1 y = f(x) ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; 1) <\/p>\n

d) Ph\u01b0\u01a1ng tr\u00ecnh f(x) = m c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t khi m \u2265 f(0) ho\u1eb7c m \u2264 f(2) <\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = x\u00b2 .<\/p>\n

a) H\u00e0m s\u1ed1 F(x) = (x\u00b3)\/(3) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) .<\/p>\n

b) intlimits\u2080\u00b2 (f(x) + 1) dx = 14\/3 .<\/p>\n

c) intlimits\u2082\u2080\u2082\u2084^a (f\u00b2(x)) dx = 0, a \u2265 2024 . Khi \u0111\u00f3 2a – 1 = 4047 <\/p>\n

d) Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh thang cong gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f(x) , tr\u1ee5c ho\u00e0nh, tr\u1ee5c tung v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = 2 b\u1eb1ng 3.<\/p>\n

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

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = x\u00b3 + 6x\u00b2 + (1 – m)x – 3 . C\u00f3 t\u1ea5t c\u1ea3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m thu\u1ed9c kho\u1ea3ng (-20; 20) \u0111\u1ec3 h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ed3ng bi\u1ebfn tr\u00ean mathbbR ?<\/p>\n

C\u00e2u 2.<\/strong> D\u0169ng l\u00e0 h\u1ecdc sinh r\u1ea5t gi\u1ecfi ch\u01a1i rubik, b\u1ea1n c\u00f3 th\u1ec3 gi\u1ea3i nhi\u1ec1u lo\u1ea1i kh\u1ed1i rubik kh\u00e1c nhau. Trong m\u1ed9t l\u1ea7n t\u1eadp luy\u1ec7n gi\u1ea3i kh\u1ed1i rubik 3 \u00d7 3 , b\u1ea1n D\u0169ng \u0111\u00e3 t\u1ef1 th\u1ed1ng k\u00ea l\u1ea1i th\u1eddi gian gi\u1ea3i rubik trong 25 l\u1ea7n gi\u1ea3i li\u00ean ti\u1ebfp \u1edf b\u1ea3ng sau:<\/p>\n

\"\"<\/p>\n

Kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m l\u00e0 bao nhi\u00eau?<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u00f5 Th\u1ecb S\u00e1u V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed to\u00e1n 12<\/a> c\u00f3 b\u1ea3ng \u0111\u00e1p \u00e1n chi ti\u1ebft cho t\u1eebng c\u00e2u h\u1ecfi, gi\u00fap h\u1ecdc sinh t\u1ef1 ki\u1ec3m tra v\u00e0 \u0111\u00e1nh gi\u00e1 k\u1ebft qu\u1ea3 sau khi luy\u1ec7n t\u1eadp. T\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u00f5 Th\u1ecb S\u00e1u V\u0129nh Ph\u00fac<\/strong> <\/span>\u0111\u1ec3 luy\u1ec7n t\u1eadp qua file b\u00ean d\u01b0\u1edbi.<\/p>\n