{"id":518,"date":"2026-05-05T04:50:01","date_gmt":"2026-05-05T04:50:01","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-thi-giang-vinh-phuc\/"},"modified":"2026-05-05T07:23:20","modified_gmt":"2026-05-05T07:23:20","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-thi-giang-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-thi-giang-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\u1ecb Giang 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\u1ecb Giang V\u0129nh Ph\u00fac<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n t\u1eadp s\u00e1t v\u1edbi \u0111\u1ecbnh h\u01b0\u1edbng ra \u0111\u1ec1 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, \u0111\u1ed9 kh\u00f3 \u0111\u01b0\u1ee3c ph\u00e2n t\u1ea7ng t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao, nh\u1eb1m \u0111\u00e1nh gi\u00e1 to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c v\u00e0 k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 c\u1ee7a h\u1ecdc sinh l\u1edbp 12. H\u00f4m nay, T\u00e0i Li\u1ec7u \u00d4n Thi<\/a><\/strong> s\u1ebd cung c\u1ea5p cho b\u1ea1n nh\u1eefng n\u1ed9i dung ch\u00ednh c\u1ee7a \u0111\u1ec1.<\/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\u1ecb Giang 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\u1ecb Giang V\u0129nh Ph\u00fac<\/strong> \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf b\u00e1m s\u00e1t c\u1ea5u tr\u00fac chu\u1ea9n c\u1ee7a B\u1ed9, \u0111\u1ed3ng th\u1eddi ph\u00e2n b\u1ed1 h\u1ee3p l\u00fd c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao nh\u01b0 c\u00e1c v\u00ed d\u1ee5 ti\u00eau bi\u1ec3u d\u01b0\u1edbi \u0111\u00e2y:<\/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 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean. H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o sau \u0111\u00e2y?<\/p>\n

\"\"<\/p>\n

A. (0; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. (-3; -2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (0; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. (1; 2) <\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean. \u0110i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0<\/p>\n

\"\"<\/p>\n

A. x = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. x = 0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. y = -2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. y = 2 <\/p>\n

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

C\u00e2u 1.<\/strong> Cho \u0111\u01b0\u1eddng th\u1eb3ng \u0394: (x + 2024)\/(2) = (y + 2025)\/(3) = (z + 2026)\/(6) v\u00e0 m\u1eb7t ph\u1eb3ng (P): x – 2y – 2z + 1 = 0 . G\u1ecdi \u03b1 l\u00e0 g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng \u0394 v\u00e0 m\u1eb7t ph\u1eb3ng (P) .<\/p>\n

a) Vector u\u20d7 = (2024; 2025; 2026) l\u00e0 m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng \u0394 .<\/p>\n

b) \u0110i\u1ec3m M = (-2024; -2025; -2026) l\u00e0 m\u1ed9t \u0111i\u1ec3m chung c\u1ee7a \u0394 v\u00e0 (P) .<\/p>\n

c) V\u1edbi u\u20d7, n\u20d7 l\u1ea7n l\u01b0\u1ee3t l\u00e0 m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng, vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0394 v\u00e0 (P) . Ta c\u00f3:
\n\\[
\n\\sin \\alpha = \\dfrac{|\\vec{u} \\cdot \\vec{n}|}{|\\vec{u}| \\cdot |\\vec{n}|}
\n\\]\n<\/p>\n

d) G\u00f3c \u03b1 \u2248 50^\u00b0 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb c\u1ee7a \u0111\u1ed9).<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = (x\u00b2 + 2x + 2)\/(x + 1) .<\/p>\n

a) H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ed3ng bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-\u221e; -2) v\u00e0 (0; +\u221e) .<\/p>\n

b) H\u00e0m s\u1ed1 \u0111\u00e3 cho kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\n

c) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = x + 1 .<\/p>\n

d) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 t\u00e2m \u0111\u1ed1i x\u1ee9ng l\u00e0 \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 (-1; 0) .<\/p>\n

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

C\u00e2u 1.<\/strong> M\u1ed9t logo \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf nh\u01b0 ph\u1ea7n g\u1ea1ch s\u1ecdc trong h\u00ecnh v\u1ebd b\u00ean. Logo tr\u00ean l\u00e0 h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi hai Parabol y = f(x), y = g(x) nh\u01b0 h\u00ecnh v\u1ebd (\u0111\u01a1n v\u1ecb tr\u00ean m\u1ed7i tr\u1ee5c l\u00e0 dm ). T\u00ednh di\u1ec7n t\u00edch c\u1ee7a logo tr\u00ean (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n

\"\"<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t ng\u01b0\u1eddi g\u1eedi 60 tri\u1ec7u \u0111\u1ed3ng v\u00e0o ng\u00e2n h\u00e0ng v\u1edbi l\u00e3i su\u1ea5t 0,5% m\u1ed9t th\u00e1ng. Bi\u1ebft r\u1eb1ng n\u1ebfu kh\u00f4ng r\u00fat ti\u1ec1n ra kh\u1ecfi ng\u00e2n h\u00e0ng th\u00ec c\u1ee9 sau m\u1ed7i th\u00e1ng, s\u1ed1 ti\u1ec1n l\u00e3i s\u1ebd \u0111\u01b0\u1ee3c nh\u1eadp v\u00e0o v\u1ed1n ban \u0111\u1ea7u (hay g\u1ecdi l\u00e0 l\u00e3i k\u00e9p). Gi\u1ea3 s\u1eed trong nhi\u1ec1u th\u00e1ng li\u00ean ti\u1ebfp k\u1ec3 t\u1eeb khi g\u1eedi ti\u1ec1n, ng\u01b0\u1eddi \u0111\u00f3 kh\u00f4ng r\u00fat ti\u1ec1n ra v\u00e0 l\u00e3i su\u1ea5t kh\u00f4ng thay \u0111\u1ed5i. H\u1ecfi t\u1eeb th\u00e1ng th\u1ee9 m\u1ea5y tr\u1edf \u0111i, s\u1ed1 ti\u1ec1n c\u1ea3 v\u1ed1n l\u1eabn l\u00e3i, ng\u01b0\u1eddi \u0111\u00f3 c\u00f3 h\u01a1n 66 tri\u1ec7u \u0111\u1ed3ng?<\/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\u1ecb Giang 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\u1ecb Giang V\u0129nh Ph\u00fac<\/strong> l\u00e0 m\u1ed9t t\u00e0i li\u1ec7u luy\u1ec7n \u0111\u1ec1 thi\u1ebft th\u1ef1c, gi\u00fap h\u1ecdc sinh \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c v\u00e0 c\u1ee7ng c\u1ed1 chi\u1ebfn l\u01b0\u1ee3c l\u00e0m b\u00e0i hi\u1ec7u qu\u1ea3. H\u00e3y t\u1ea3i file \u0111\u1ec1 thi th\u1eed to\u00e1n thpt<\/a> k\u00e8m \u0111\u00e1p \u00e1n \u0111\u1ec3 t\u1ef1 luy\u1ec7n t\u1eadp v\u00e0 s\u1eb5n s\u00e0ng chinh ph\u1ee5c k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT 2025!<\/p>\n