{"id":506,"date":"2026-05-05T04:49:23","date_gmt":"2026-05-05T04:49:23","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-lien-bao-vinh-phuc\/"},"modified":"2026-05-05T07:22:40","modified_gmt":"2026-05-05T07:22:40","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-lien-bao-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-lien-bao-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 Li\u00ean B\u1ea3o 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 Li\u00ean B\u1ea3o V\u0129nh Ph\u00fac<\/strong> l\u00e0 m\u1ed9t t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n quan tr\u1ecdng, gi\u00fap h\u1ecdc sinh chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi ch\u00ednh th\u1ee9c. \u0110\u1ec1 thi c\u00f3 c\u1ea5u tr\u00fac r\u00f5 r\u00e0ng, bao g\u1ed3m c\u00e1c d\u1ea1ng b\u00e0i t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, nh\u1eb1m ki\u1ec3m tra to\u00e0n di\u1ec7n n\u0103ng l\u1ef1c t\u01b0 duy to\u00e1n h\u1ecdc v\u00e0 kh\u1ea3 n\u0103ng v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u00e0o th\u1ef1c t\u1ebf c\u1ee7a h\u1ecdc sinh. C\u00f9ng T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed<\/strong><\/a> t\u00ecm hi\u1ec3u chi ti\u1ebft 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 Li\u00ean B\u1ea3o 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 Li\u00ean B\u1ea3o V\u0129nh Ph\u00fac<\/strong> g\u1ed3m 4 trang v\u1edbi t\u1ed5ng c\u1ed9ng 22 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m, c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft \u0111\u1ec3 h\u1ecdc sinh d\u1ec5 d\u00e0ng \u0111\u1ed1i chi\u1ebfu v\u00e0 t\u1ef1 \u0111\u00e1nh gi\u00e1 k\u1ebft qu\u1ea3. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi ti\u00eau bi\u1ec3u \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i theo t\u1eebng d\u1ea1ng b\u00e0i quen thu\u1ed9c trong \u0111\u1ec1 thi chu\u1ea9n c\u1ee7a B\u1ed9 GD&\u0110T.<\/p>\n

Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn\u00a0<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = (2)\/(x – 1) l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng<\/p>\n

A. x = 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. y = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. x = 0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. y = 0 <\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m nh\u01b0 h\u00ecnh d\u01b0\u1edbi. S\u1ed1 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 y = f(x) l\u00e0<\/p>\n

beginarray|c|cccccc| hline x & -\u221e & & -3 & & 1 & & 3 & & +\u221e hline f'(x) & & – & 0 & + & 0 & – & 0 & + & hline endarray<\/p>\n

A. 3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. 1<\/p>\n

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

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = 1\/8(x\u00b3 – 3x\u00b2 – 9x – 5) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (C) .<\/p>\n

a) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

b) \u0110i\u1ec3m \u0111\u1ed1i x\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb c\u00f3 t\u1ecda \u0111\u1ed9 l\u00e0 (1; -2) .<\/p>\n

c) Tr\u00ean \u0111o\u1ea1n [4; 8] th\u00ec gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u1ea1i x = 4 .<\/p>\n

d) Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c nh\u1ecf nh\u1ea5t c\u1ee7a \u0111\u1ed3 th\u1ecb (C) \u0111i qua \u0111i\u1ec3m A(0; -7\/3 ) .<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t v\u01b0\u1eddn \u01b0\u01a1m c\u00e2y c\u1ea3nh b\u00e1n m\u1ed9t c\u00e2y sau 6 n\u0103m tr\u1ed3ng v\u00e0 u\u1ed1n t\u1ea1o d\u00e1ng. T\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a c\u00e2y \u0111\u00f3 trong su\u1ed1t 6 n\u0103m \u0111\u01b0\u1ee3c t\u00ednh x\u1ea5p x\u1ec9 b\u1edfi c\u00f4ng th\u1ee9c h'(t) = 1,5t + 5 , trong \u0111\u00f3 h(t) (cm) l\u00e0 chi\u1ec1u cao c\u1ee7a c\u00e2y sau t (n\u0103m). C\u00e2y con khi \u0111\u01b0\u1ee3c tr\u1ed3ng cao 12 cm. X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n

a) h(t) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 h'(t) = 1,5t + 5 <\/p>\n

b) h(t) = 3\/4t\u00b2 + 5t + C v\u1edbi C l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1.<\/p>\n

c) Chi\u1ec1u cao c\u1ee7a c\u00e2y \u0111\u00f3 kh\u00f4ng \u0111\u1ed5i trong 6 n\u0103m \u0111\u01b0\u1ee3c tr\u1ed3ng.<\/p>\n

d) Chi\u1ec1u cao c\u1ee7a c\u00e2y \u0111\u00f3 khi \u0111\u01b0\u1ee3c b\u00e1n l\u00e0 70 cm.<\/p>\n

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

C\u00e2u 1.<\/strong> Ta coi n\u0103m l\u1ea5y l\u00e0m m\u1ed1c \u0111\u1ec3 t\u00ednh d\u00e2n s\u1ed1 c\u1ee7a m\u1ed9t v\u00f9ng (ho\u1eb7c m\u1ed9t qu\u1ed1c gia) l\u00e0 n\u0103m 0 . Khi \u0111\u00f3, d\u00e2n s\u1ed1 c\u1ee7a qu\u1ed1c gia \u0111\u00f3 \u1edf n\u0103m th\u1ee9 t l\u00e0 h\u00e0m theo bi\u1ebfn t \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c: S = Ae^rt , trong \u0111\u00f3, A d\u00e2n s\u1ed1 c\u1ee7a m\u1ed9t v\u00f9ng (ho\u1eb7c qu\u1ed1c gia) \u0111\u00f3 \u1edf n\u0103m 0 , v\u00e0 r l\u00e0 t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u1eb1ng n\u0103m. Bi\u1ebft r\u1eb1ng d\u00e2n s\u1ed1 Vi\u1ec7t Nam n\u0103m 2025 \u01b0\u1edbc t\u00ednh l\u00e0 98 564 407 ng\u01b0\u1eddi v\u00e0 t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u1eb1ng n\u0103m l\u00e0 r = 0,93% . Gi\u1ea3 s\u1eed t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u1eb1ng n\u0103m l\u00e0 nh\u01b0 nhau t\u00ednh t\u1eeb n\u0103m 2025 . H\u1ecfi t\u1eeb n\u0103m n\u00e0o tr\u1edf \u0111i, d\u00e2n s\u1ed1 n\u01b0\u1edbc ta v\u01b0\u1ee3t 120 tri\u1ec7u ng\u01b0\u1eddi?<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t ng\u01b0\u1eddi n\u00f4ng d\u00e2n c\u00f3 15 000 000 \u0111\u1ed3ng \u0111\u1ec3 l\u00e0m m\u1ed9t h\u00e0ng r\u00e0o h\u00ecnh ch\u1eef E d\u1ecdc theo m\u1ed9t con s\u00f4ng bao quanh hai khu \u0111\u1ea5t tr\u1ed3ng rau c\u00f3 d\u1ea1ng hai h\u00ecnh ch\u1eef nh\u1eadt b\u1eb1ng nhau (H\u00ecnh v\u1ebd). \u0110\u1ed1i v\u1edbi m\u1eb7t h\u00e0ng r\u00e0o song song v\u1edbi b\u1edd s\u00f4ng th\u00ec chi ph\u00ed nguy\u00ean v\u1eadt li\u1ec7u l\u00e0 60 000 \u0111\u1ed3ng\/m\u00e9t, c\u00f2n \u0111\u1ed1i v\u1edbi ba m\u1eb7t h\u00e0ng r\u00e0o song song nhau th\u00ec chi ph\u00ed nguy\u00ean v\u1eadt li\u1ec7u l\u00e0 50 000 \u0111\u1ed3ng\/m\u00e9t, m\u1eb7t gi\u00e1p v\u1edbi b\u1edd s\u00f4ng kh\u00f4ng ph\u1ea3i r\u00e0o. T\u00ecm di\u1ec7n t\u00edch l\u1edbn nh\u1ea5t c\u1ee7a hai khu \u0111\u1ea5t thu \u0111\u01b0\u1ee3c sau khi l\u00e0m h\u00e0ng r\u00e0o.<\/p>\n

\"\"<\/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 Li\u00ean B\u1ea3o V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u00e2y l\u00e0 \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n<\/a> luy\u1ec7n t\u1eadp h\u1eefu \u00edch gi\u00fap h\u1ecdc sinh r\u00e8n k\u1ef9 n\u0103ng gi\u1ea3i \u0111\u1ec1, l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac v\u00e0 \u0111\u1ed9 kh\u00f3 c\u1ee7a \u0111\u1ec1 thi ch\u00ednh th\u1ee9c. H\u00e3y t\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Li\u00ean B\u1ea3o V\u0129nh Ph\u00fac<\/strong> \u0111\u1ec3 t\u1ef1 luy\u1ec7n t\u1eadp, c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u00e0 n\u00e2ng cao t\u1ed1c \u0111\u1ed9 l\u00e0m b\u00e0i cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p s\u1eafp t\u1edbi.<\/p>\n