{"id":478,"date":"2026-05-05T04:47:55","date_gmt":"2026-05-05T04:47:55","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ben-tre-vinh-phuc\/"},"modified":"2026-05-05T07:20:59","modified_gmt":"2026-05-05T07:20:59","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ben-tre-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-ben-tre-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 B\u1ebfn Tre 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 B\u1ebfn Tre V\u0129nh Ph\u00fac<\/strong> bao g\u1ed3m c\u00e1c ph\u1ea7n tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn, c\u00e2u h\u1ecfi \u0111\u00fang sai, v\u00e0 b\u00e0i to\u00e1n tr\u1ea3 l\u1eddi ng\u1eafn, t\u1eadp trung v\u00e0o c\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n THPT. C\u00f9ng Tailieuonthi<\/strong><\/a> t\u1ea3i ngay b\u1ed9 \u0111\u1ec1 v\u1ec1 luy\u1ec7n t\u1eadp \u0111\u1ec3 chu\u1ea9n b\u1ecb cho k\u1ef3 thi s\u1eafp t\u1edbi.<\/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 B\u1ebfn Tre 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 B\u1ebfn Tre V\u0129nh Ph\u00fac<\/strong> g\u1ed3m 12 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn, 4 c\u00e2u \u0111\u00fang sai, v\u00e0 6 b\u00e0i to\u00e1n tr\u1ea3 l\u1eddi ng\u1eafn, tr\u1ea3i d\u00e0i tr\u00ean 4 trang. \u0110\u1ec1 thi c\u00f3 k\u00e8m theo \u0111\u00e1p \u00e1n chi ti\u1ebft, gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng t\u1ef1 \u0111\u00e1nh gi\u00e1 k\u1ebft qu\u1ea3 v\u00e0 \u00f4n luy\u1ec7n.<\/p>\n

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

C\u00e2u 1.<\/strong> Cho c\u1ea5p s\u1ed1 nh\u00e2n (u_n) v\u1edbi u\u2081 = 1 v\u00e0 u\u2082 = 2 . C\u00f4ng b\u1ed9i c\u1ee7a c\u1ea5p s\u1ed1 nh\u00e2n \u0111\u00e3 cho l\u00e0<\/p>\n

A. q = 1\/2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. q = 2 \u00a0 \u00a0 \u00a0 \u00a0 C. q = -2 \u00a0 \u00a0 \u00a0 \u00a0 D. q = -1\/2 <\/p>\n

C\u00e2u 2.<\/strong> H\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y ngh\u1ecbch bi\u1ebfn tr\u00ean (-\u221e; +\u221e) ?<\/p>\n

A. y = ln x \u00a0 \u00a0 \u00a0 \u00a0 B. y = log_1\/7 x \u00a0 \u00a0 \u00a0 \u00a0 C. y = ( \u03c0\/6 )^x \u00a0 \u00a0 \u00a0 \u00a0 D. y = e^x <\/p>\n

Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ea1o h\u00e0m tr\u00ean mathbbR v\u00e0 h\u00e0m s\u1ed1 y = f'(x) l\u00e0 h\u00e0m s\u1ed1 b\u1eadc ba c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd. X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau:<\/p>\n

\"\"<\/p>\n

a) H\u00e0m s\u1ed1 y = f(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; -2) .<\/p>\n

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

c) f'(2) = 4 .<\/p>\n

d) H\u00e0m s\u1ed1 g(x) = f(x) – 1\/2x\u00b2 + x + 2024 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng ( 5\/2; 3\/2 ) .<\/p>\n

C\u00e2u 2.<\/strong> Trong m\u1eb7t ph\u1eb3ng v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxy , cho h\u00e0m s\u1ed1 y = f(x) = x\u00b2 – x – 6 c\u00f3 \u0111\u1ed3 th\u1ecb (C) .<\/p>\n

a) Th\u1ec3 t\u00edch c\u1ee7a v\u1eadt th\u1ec3 tr\u00f2n xoay \u0111\u01b0\u1ee3c sinh ra khi h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb (C) v\u00e0 tr\u1ee5c ho\u00e0nh Ox quay quanh Ox l\u00e0 V = \u03c0 int\u208b\u2082\u00b3 (x\u00b2 – x – 6)\u00b2 dx .<\/p>\n

b) Di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb (C) v\u00e0 tr\u1ee5c ho\u00e0nh Ox l\u00e0 V = int\u208b\u2082\u00b3 (x\u00b2 – x – 6) dx .<\/p>\n

c) Gi\u1ea3 s\u1eed m\u1ed9t v\u1eadt M chuy\u1ec3n \u0111\u1ed9ng d\u1ecdc theo m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng sao cho v\u1eadn t\u1ed1c c\u1ee7a n\u00f3 t\u1ea1i th\u1eddi \u0111i\u1ec3m x (gi\u00e2y) l\u00e0 f(x) = x\u00b2 – x – 6 (m\/s) . Khi \u0111\u00f3, \u0111\u1ed9 d\u1ecbch chuy\u1ec3n c\u1ee7a v\u1eadt M trong kho\u1ea3ng th\u1eddi gian x in [1;4] l\u00e0 9\/2 .<\/p>\n

d) T\u1ed5ng qu\u00e3ng \u0111\u01b0\u1eddng c\u1ee7a v\u1eadt M \u1edf tr\u00ean \u0111i \u0111\u01b0\u1ee3c trong kho\u1ea3ng th\u1eddi gian x in [1;4] l\u00e0 61\/6 (m) .<\/p>\n

Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Tr\u1eadn b\u00f3ng \u0111\u00e1 giao h\u1eefu gi\u1eefa \u0111\u1ed9i tuy\u1ec3n Vi\u1ec7t Nam v\u00e0 Th\u00e1i Lan \u1edf s\u00e2n v\u1eadn \u0111\u1ed9ng M\u1ef9 \u0110\u00ecnh c\u00f3 s\u1ee9c ch\u1ee9a 55,000 kh\u00e1n gi\u1ea3. Ban t\u1ed5 ch\u1ee9c b\u00e1n v\u00e9 v\u1edbi gi\u00e1 m\u1ed7i v\u00e9 l\u00e0 100 ngh\u00ecn \u0111\u1ed3ng, s\u1ed1 kh\u00e1n gi\u1ea3 trung b\u00ecnh \u0111\u1ebfn s\u00e2n xem b\u00f3ng \u0111\u00e1 l\u00e0 27,000 ng\u01b0\u1eddi. Qua th\u0103m d\u00f2 d\u01b0 lu\u1eadn, ng\u01b0\u1eddi ta th\u1ea5y r\u1eb1ng m\u1ed7i khi gi\u00e1 v\u00e9 gi\u1ea3m th\u00eam 10 ngh\u00ecn \u0111\u1ed3ng, s\u1ebd c\u00f3 th\u00eam kho\u1ea3ng 3,000 kh\u00e1n gi\u1ea3. H\u1ecfi ban t\u1ed5 ch\u1ee9c n\u00ean \u0111\u1eb7t gi\u00e1 v\u00e9 l\u00e0 bao nhi\u00eau \u0111\u1ec3 doanh thu t\u1eeb ti\u1ec1n b\u00e1n v\u00e9 l\u00e0 l\u1edbn nh\u1ea5t v\u1edbi \u0111\u01a1n v\u1ecb t\u00ednh gi\u00e1 v\u00e9 l\u00e0 ngh\u00ecn \u0111\u1ed3ng?<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 tam gi\u00e1c SAB \u0111\u1ec1u n\u1eb1m trong m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y. Bi\u1ebft kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng SA v\u00e0 BD b\u1eb1ng \u221a21 . H\u00e3y cho bi\u1ebft c\u1ea1nh \u0111\u00e1y b\u1eb1ng 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 B\u1ebfn Tre V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed to\u00e1n<\/a> n\u00e0y s\u1ebd gi\u00fap h\u1ecdc sinh l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi ch\u00ednh th\u1ee9c, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n v\u00e0 t\u01b0 duy logic. H\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i file \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT B\u1ebfn Tre V\u0129nh Ph\u00fac<\/strong> \u0111\u1ec3 luy\u1ec7n t\u1eadp, n\u00e2ng cao ki\u1ebfn th\u1ee9c v\u00e0 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT s\u1eafp t\u1edbi.<\/p>\n