{"id":458,"date":"2026-05-05T04:46:52","date_gmt":"2026-05-05T04:46:52","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-tran-phu-vinh-phuc\/"},"modified":"2026-05-05T07:19:51","modified_gmt":"2026-05-05T07:19:51","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-tran-phu-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-tran-phu-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 Tr\u1ea7n Ph\u00fa 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 Tr\u1ea7n Ph\u00fa V\u0129nh Ph\u00fac<\/strong> r\u1ea5t h\u1eefu \u00edch cho h\u1ecdc sinh l\u1edbp 12 trong giai \u0111o\u1ea1n n\u01b0\u1edbc r\u00fat chu\u1ea9n b\u1ecb cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT s\u1eafp t\u1edbi. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng theo \u0111\u00fang \u0111\u1ecbnh h\u01b0\u1edbng ra \u0111\u1ec1 c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o, bao ph\u1ee7 c\u00e1c d\u1ea1ng b\u00e0i tr\u1ecdng t\u00e2m v\u00e0 m\u1ee9c \u0111\u1ed9 ph\u00e2n h\u00f3a r\u00f5 r\u00e0ng. H\u00f4m n\u00e0y, c\u00f9ng t\u00ecm hi\u1ec3u k\u1ef9 h\u01a1n v\u1ec1 \u0111\u1ec1 thi n\u00e0y v\u1edbi Tailieuonthi<\/strong><\/a>.<\/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 Tr\u1ea7n Ph\u00fa V\u0129nh Ph\u00fac <\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa V\u0129nh Ph\u00fac<\/strong> <\/span> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n c\u00f4ng phu, b\u00e1m s\u00e1t theo c\u1ea5u tr\u00fac \u0111\u1ec1 tham kh\u1ea3o m\u1edbi nh\u1ea5t c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 g\u1ed3m 4 trang, v\u1edbi 50 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111a d\u1ea1ng v\u1ec1 n\u1ed9i dung, tr\u1ea3i \u0111\u1ec1u c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 12 nh\u01b0: h\u00e0m s\u1ed1, m\u0169 \u2013 logarit, nguy\u00ean h\u00e0m \u2013 t\u00edch ph\u00e2n, s\u1ed1 ph\u1ee9c, h\u00ecnh h\u1ecdc kh\u00f4ng gian, x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea,\u2026<\/p>\n

PH\u1ea6N I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> \u0110\u01b0\u1eddng cong cho trong h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o trong c\u00e1c h\u00e0m s\u1ed1 d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n

\"\"<\/p>\n

A. y = -x\u00b3 + 2x – 1 \u00a0 \u00a0 B. y = -x\u00b3 + 3x + 1 \u00a0 \u00a0 C. y = 2x\u00b3 – 6x + 1 \u00a0 \u00a0 D. y = x\u00b3 – 3x + 1 <\/p>\n

C\u00e2u 2.<\/strong> Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh sin x = 1\/2 l\u00e0:<\/p>\n

A. x = \u03c0\/3 + k2\u03c0 \u00a0 \u00a0 B. x = 5\u03c0\/6 + k\u03c0 \u00a0 \u00a0 C. x = k\u03c0 \u00a0 \u00a0 D. x = \u03c0\/6 + k2\u03c0 <\/p>\n

PH\u1ea6N II: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = (2x + 1)\/(x – 1) <\/p>\n

a) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 y\u2019 = (-3)\/((x – 1)\u00b2) <\/p>\n

b) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho nh\u1eadn gi\u00e1 tr\u1ecb \u00e2m v\u1edbi m\u1ecdi x ne 1 <\/p>\n

c) B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0:<\/p>\n

\"\"<\/p>\n

d) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho nh\u01b0 sau.<\/p>\n

\"\"<\/p>\n

C\u00e2u 2.<\/strong> Trong kh\u00f4ng gian Oxyz , cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 S(0; 0; 3,5) , ABCD l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt v\u1edbi A(0; 0; 0) , B(4; 0; 0) , D(0; 10; 0) <\/p>\n

\"\"<\/p>\n

a) T\u1ecda \u0111\u1ed9 \u0111i\u1ec3m C(4; 10; 0) <\/p>\n

b) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng (SBD) l\u00e0 x\/4 + y\/10 + z\/3,5 = 1 <\/p>\n

c) T\u1ecda \u0111\u1ed9 c\u1ee7a vect\u01a1 SC\u20d7 l\u00e0 (4; 10; -3,5) <\/p>\n

d) G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng SC v\u00e0 m\u1eb7t ph\u1eb3ng (SBD) (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb c\u1ee7a \u0111\u1ed9) l\u00e0 20^\u00b0 <\/p>\n

PH\u1ea6N III: C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> M\u1ed9t v\u1eadn \u0111\u1ed9ng vi\u00ean th\u1ec3 thao hai m\u00f4n ph\u1ed1i h\u1ee3p luy\u1ec7n t\u1eadp v\u1edbi m\u1ed9t b\u1ec3 b\u01a1i h\u00ecnh ch\u1eef nh\u1eadt r\u1ed9ng 800 m , d\u00e0i 400 m .<\/p>\n

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V\u1eadn \u0111\u1ed9ng vi\u00ean ch\u1ea1y ph\u1ed1i h\u1ee3p v\u1edbi b\u01a1i nh\u01b0 sau: Xu\u1ea5t ph\u00e1t t\u1eeb \u0111i\u1ec3m A , ch\u1ea1y \u0111\u1ebfn \u0111i\u1ec3m X v\u00e0 b\u01a1i t\u1eeb \u0111i\u1ec3m X \u0111\u1ebfn \u0111i\u1ec3m C (H\u00ecnh 4). H\u1ecfi n\u00ean ch\u1ecdn \u0111i\u1ec3m X c\u00e1ch A g\u1ea7n b\u1eb1ng bao nhi\u00eau m\u00e9t \u0111\u1ec3 v\u1eadn \u0111\u1ed9ng vi\u00ean \u0111\u1ebfn C nhanh nh\u1ea5t (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb)? Bi\u1ebft r\u1eb1ng v\u1eadn t\u1ed1c ch\u1ea1y l\u00e0 30 km\/h , v\u1eadn t\u1ed1c b\u01a1i l\u00e0 6 km\/h .<\/p>\n

C\u00e2u 2.<\/strong> B\u1ea1n H\u1ea3i nh\u1eadn thi\u1ebft k\u1ebf logo h\u00ecnh con m\u1eaft (ph\u1ea7n \u0111\u01b0\u1ee3c t\u00f4 \u0111\u1eadm) cho m\u1ed9t c\u01a1 s\u1edf y t\u1ebf: Logo l\u00e0 h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi hai parabol y = f(x) v\u00e0 y = g(x) nh\u01b0 H\u00ecnh 7 (\u0111\u01a1n v\u1ecb tr\u00ean m\u1ed7i tr\u1ee5c to\u1ea1 \u0111\u1ed9 l\u00e0 decim\u00e9t). B\u1ea1n H\u1ea3i c\u1ea7n t\u00ednh di\u1ec7n t\u00edch c\u1ee7a logo \u0111\u1ec3 b\u00e1o gi\u00e1 cho c\u01a1 s\u1edf y t\u1ebf \u0111\u00f3 tr\u01b0\u1edbc khi k\u00ed h\u1ee3p \u0111\u1ed3ng. Di\u1ec7n t\u00edch c\u1ee7a logo l\u00e0 bao nhi\u00eau decim\u00e9t vu\u00f4ng (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi)?<\/p>\n

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T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa V\u0129nh Ph\u00fac <\/strong><\/h2>\n

V\u1edbi c\u1ea5u tr\u00fac h\u1ee3p l\u00fd, n\u1ed9i dung b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh v\u00e0 \u0111\u1ed9 kh\u00f3 ph\u00f9 h\u1ee3p, \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa V\u0129nh Ph\u00fac<\/strong> <\/span> l\u00e0 t\u00e0i li\u1ec7u luy\u1ec7n t\u1eadp hi\u1ec7u qu\u1ea3 gi\u00fap h\u1ecdc sinh t\u1ef1 tin chinh ph\u1ee5c k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT 2025. Qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c em h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i file \u0111\u1ec1 thi th\u1eed to\u00e1n<\/a> k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft \u1edf ph\u00eda d\u01b0\u1edbi \u0111\u1ec3 tham kh\u1ea3o v\u00e0 \u00f4n luy\u1ec7n.<\/p>\n