{"id":514,"date":"2026-05-05T04:49:49","date_gmt":"2026-05-05T04:49:49","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-duy-thi-vinh-phuc\/"},"modified":"2026-05-05T07:23:08","modified_gmt":"2026-05-05T07:23:08","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-duy-thi-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-duy-thi-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 Duy Th\u00ec 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 Duy Th\u00ec V\u0129nh Ph\u00fac <\/strong>l\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ec1 m\u1eabu gi\u00fap h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp to\u00e0n di\u1ec7n, chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi ch\u00ednh th\u1ee9c. \u0110\u1ec1 thi bao g\u1ed3m c\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn, tr\u1ea3i r\u1ed9ng t\u1eeb ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m b\u00e0i v\u00e0 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m. C\u00f9ng T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed<\/strong><\/a> kh\u00e1m ph\u00e1 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 Nguy\u1ec5n Duy Th\u00ec 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 Duy Th\u00ec V\u0129nh Ph\u00fac <\/strong>c\u00f3 nhi\u1ec1u d\u1ea1ng b\u00e0i t\u1eadp phong ph\u00fa, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc v\u00e0 c\u1ea5u tr\u00fac \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi ti\u00eau bi\u1ec3u \u0111\u01b0\u1ee3c ph\u00e2n theo t\u1eebng d\u1ea1ng b\u00e0i:<\/p>\n

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

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12.<\/em><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd. H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o?<\/p>\n

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A. (-1; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. (-2; -1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (-1; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. (1; +\u221e) <\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) li\u00ean t\u1ee5c v\u00e0 c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean tr\u00ean \u0111o\u1ea1n [-1; 3] nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?<\/p>\n

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A. maxlimits_[-1;3] f(x) = f(0) \u00a0 \u00a0 \u00a0 \u00a0 B. maxlimits_[-1;3] f(x) = f(3) \u00a0 \u00a0 \u00a0 \u00a0 C. maxlimits_[-1;3] f(x) = f(2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. maxlimits_[-1;3] f(x) = f(-1) <\/p>\n

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

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 4.<\/em><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = -x + 2 – 1\/x+1 c\u00f3 \u0111\u1ed3 th\u1ecb (C) .<\/p>\n

a) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-2; -1) v\u00e0 (-1; 0) .<\/p>\n

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

c) \u0110\u1ed3 th\u1ecb (C) c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean \u0111i qua \u0111i\u1ec3m A(1; 2) .<\/p>\n

d) \u0110\u1ed3 th\u1ecb (C) c\u00f3 t\u00e2m \u0111\u1ed1i x\u1ee9ng l\u00e0 I(-1; 3) .<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = 2x + sin x v\u00e0 F(x) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a f(x) tr\u00ean mathbbR .<\/p>\n

a) F'(x) = 2x + sin x <\/p>\n

b) int f(x) dx = x\u00b2 + cos x + C <\/p>\n

c) intlimits\u2080^\u03c0\/2 f(x) dx = (\u03c0\u00b2)\/(4) – 1 <\/p>\n

d) Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ph\u1eb3ng (H) gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f(x) , \u0111\u01b0\u1eddng th\u1eb3ng x = 0 , \u0111\u01b0\u1eddng th\u1eb3ng x = \u03c0\/4 v\u00e0 tr\u1ee5c Ox b\u1eb1ng (\u03c0\u00b2)\/(16) – (\u221a2)\/(2) + 1 .<\/p>\n

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

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 6.<\/em><\/p>\n

C\u00e2u 1.<\/strong> T\u00ecm chi\u1ec1u d\u00e0i b\u00e9 nh\u1ea5t c\u1ee7a c\u00e1i thang \u0111\u1ec3 n\u00f3 c\u00f3 th\u1ec3 t\u1ef1a v\u00e0o t\u01b0\u1eddng v\u00e0 m\u1eb7t \u0111\u1ea5t, ngang qua c\u1ed9t \u0111\u1ee1 cao 4 m , song song v\u00e0 c\u00e1ch t\u01b0\u1eddng 0,5 m k\u1ec3 t\u1eeb g\u1ed1c c\u1ee7a c\u1ed9t \u0111\u1ee1 nh\u01b0 h\u00ecnh v\u1ebd (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n

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C\u00e2u 2.<\/strong> M\u1ed9t c\u00f4ng ty c\u00f3 \u00fd \u0111\u1ecbnh thi\u1ebft k\u1ebf m\u1ed9t logo h\u00ecnh vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i n\u1eeda \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng 4. Bi\u1ec3u t\u01b0\u1ee3ng 4 chi\u1ebfc l\u00e1 (\u0111\u01b0\u1ee3c t\u00f4 m\u00e0u) \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1edfi c\u00e1c \u0111\u01b0\u1eddng cong \u0111\u1ed1i x\u1ee9ng v\u1edbi nhau qua t\u00e2m c\u1ee7a h\u00ecnh vu\u00f4ng v\u00e0 qua c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o. M\u1ed9t trong s\u1ed1 c\u00e1c \u0111\u01b0\u1eddng cong \u1edf n\u1eeda b\u00ean ph\u1ea3i c\u1ee7a logo l\u00e0 m\u1ed9t ph\u1ea7n c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eadc ba d\u1ea1ng y = ax\u00b3 + bx\u00b2 – x v\u1edbi h\u1ec7 s\u1ed1 a < 0 . \u0110\u1ec3 k\u1ef7 ni\u1ec7m ng\u00e0y th\u00e0nh l\u1eadp m\u00f9ng 2 th\u00e1ng 3, c\u00f4ng ty thi\u1ebft k\u1ebf \u0111\u1ec3 t\u1ec9 s\u1ed1 di\u1ec7n t\u00edch \u0111\u01b0\u1ee3c t\u00f4 m\u00e0u so v\u1edbi ph\u1ea7n kh\u00f4ng \u0111\u01b0\u1ee3c t\u00f4 m\u00e0u b\u1eb1ng 2\/3 . T\u00ednh 20a + 20b ?<\/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 Nguy\u1ec5n Duy Th\u00ec V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n<\/a> n\u00e0y l\u00e0 t\u00e0i li\u1ec7u \u00f4n t\u1eadp h\u1eefu \u00edch 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\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c b\u1ea3n th\u00e2n. H\u00e3y 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 Duy Th\u00ec V\u0129nh Ph\u00fac <\/strong>\u0111\u1ec3 luy\u1ec7n t\u1eadp ngay h\u00f4m nay v\u00e0 chu\u1ea9n b\u1ecb th\u1eadt t\u1ed1t cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT!<\/p>\n