{"id":516,"date":"2026-05-05T04:49:55","date_gmt":"2026-05-05T04:49:55","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-thai-hoc-vinh-phuc\/"},"modified":"2026-05-05T07:23:14","modified_gmt":"2026-05-05T07:23:14","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-thai-hoc-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-nguyen-thai-hoc-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 Nguy\u1ec5n Th\u00e1i H\u1ecdc 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 Nguy\u1ec5n Th\u00e1i H\u1ecdc V\u0129nh Ph\u00fac<\/strong> c\u00f3 c\u1ea5u tr\u00fac b\u00e1m s\u00e1t \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 g\u1ed3m 22 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m kh\u00e1ch quan, ki\u1ec3m tra to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c l\u1edbp 12, \u0111\u1ed3ng th\u1eddi c\u00f3 th\u00eam m\u1ed9t s\u1ed1 c\u00e2u v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c l\u1edbp 10 v\u00e0 11 \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 t\u01b0 duy logic, kh\u1ea3 n\u0103ng v\u1eadn d\u1ee5ng linh ho\u1ea1t c\u1ee7a h\u1ecdc sinh. C\u00f9ng Tailieuonthi<\/strong><\/a> t\u1ea3i ngay \u0111\u1ec1 thi \u0111\u1ec3 tham kh\u1ea3o.<\/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 Nguy\u1ec5n Th\u00e1i H\u1ecdc V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

V\u1edbi c\u1ea5u tr\u00fac b\u00e1m s\u00e1t \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 GD&\u0110T, \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Th\u00e1i H\u1ecdc V\u0129nh Ph\u00fac<\/strong> kh\u00f4ng ch\u1ec9 ki\u1ec3m tra ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m m\u00e0 c\u00f2n r\u00e8n luy\u1ec7n kh\u1ea3 n\u0103ng t\u01b0 duy logic th\u00f4ng qua nhi\u1ec1u d\u1ea1ng b\u00e0i ti\u00eau bi\u1ec3u nh\u01b0 sau:<\/p>\n

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

C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau:<\/p>\n

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n

A. (-1; +\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. (1; +\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (-1; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. (-\u221e; 1) <\/p>\n

C\u00e2u 2:<\/strong> \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n

\"\"<\/p>\n

A. y = (2x – 1)\/(x – 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. y = x\u00b3 – 3x – 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. y = -x\u00b3 + 3x\u00b2 + 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. y = (x + 1)\/(x – 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 = x + 4\/x .<\/p>\n

a) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 y\u2019 = 1 – (4)\/(x\u00b2) .<\/p>\n

b) H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (-2; 0) cup (0; 2) . H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; -2) cup (2; +\u221e) .<\/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 \u1edf h\u00ecnh v\u1ebd.<\/p>\n

\"\"<\/p>\n

C\u00e2u 2:<\/strong> Cho h\u00ecnh (H) gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u01b0\u1eddng y = 2\/x , y = 0 , x = 1 , x = 4 .<\/p>\n

a) Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh (H) \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi c\u00f4ng th\u1ee9c S = intlimits\u2081\u2074 2\/x dx (S l\u00e0 di\u1ec7n t\u00edch h\u00ecnh (H)).<\/p>\n

b) Di\u1ec7n t\u00edch h\u00ecnh (H) b\u1eb1ng 4\u221a2 .<\/p>\n

c) Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u00f2n xoay khi quay h\u00ecnh (H) xung quanh tr\u1ee5c ho\u00e0nh b\u1eb1ng 2\u03c0 .<\/p>\n

d) G\u1ecdi x = k l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng chia h\u00ecnh (H) th\u00e0nh 2 ph\u1ea7n c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau, khi \u0111\u00f3 k = 1 .<\/p>\n

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

C\u00e2u 1:<\/strong> Cho h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABC.A\u2019B\u2019C\u2019 c\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh b\u1eb1ng a = \u221a21 . G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a CC\u2019 (tham kh\u1ea3o h\u00ecnh b\u00ean). Kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (A\u2019BC) b\u1eb1ng<\/p>\n

\"\"<\/p>\n

C\u00e2u 2:<\/strong> Ta coi n\u0103m l\u1ea5y 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 s\u1ed1 theo bi\u1ebfn t \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c S = A e^rt , trong \u0111\u00f3 A l\u00e0 d\u00e2n s\u1ed1 c\u1ee7a 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\u00e0ng n\u0103m. Bi\u1ebft r\u1eb1ng d\u00e2n s\u1ed1 Vi\u1ec7t Nam n\u0103m 2021 \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\u00e0ng n\u0103m c\u1ee7a Vi\u1ec7t Nam l\u00e0 r = 0,93% . Gi\u1ea3 s\u1eed t\u1ec9 l\u1ec7 t\u0103ng d\u00e2n s\u1ed1 h\u00e0ng n\u0103m l\u00e0 nh\u01b0 nhau t\u00ednh t\u1eeb n\u0103m 2021. 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

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Th\u00e1i H\u1ecdc 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 Nguy\u1ec5n Th\u00e1i H\u1ecdc V\u0129nh Ph\u00fac<\/strong> ph\u00f9 h\u1ee3p \u0111\u1ec3 h\u1ecdc sinh l\u1edbp 12 luy\u1ec7n t\u1eadp, \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c hi\u1ec7n t\u1ea1i v\u00e0 b\u1ed5 sung k\u1ecbp th\u1eddi nh\u1eefng m\u1ea3ng ki\u1ebfn th\u1ee9c c\u00f2n thi\u1ebfu s\u00f3t. H\u00e3y t\u1ea3i v\u1ec1 v\u00e0 l\u00e0m th\u1eed \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n<\/a> \u0111\u1ec3 chu\u1ea9n b\u1ecb th\u1eadt t\u1ed1t cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p s\u1eafp t\u1edbi!<\/p>\n