{"id":480,"date":"2026-05-05T04:48:01","date_gmt":"2026-05-05T04:48:01","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-binh-son-vinh-phuc\/"},"modified":"2026-05-05T07:21:06","modified_gmt":"2026-05-05T07:21:06","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-binh-son-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-binh-son-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\u00ecnh S\u01a1n 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\u00ecnh S\u01a1n V\u0129nh Ph\u00fac <\/strong>\u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n s\u00e1t v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 thi nh\u1eb1m \u0111\u00e1nh gi\u00e1 to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c v\u00e0 k\u1ef9 n\u0103ng c\u1ee7a h\u1ecdc sinh l\u1edbp 12, \u0111\u1ed3ng th\u1eddi gi\u00fap c\u00e1c em l\u00e0m quen v\u1edbi m\u1ee9c \u0111\u1ed9 kh\u00f3 v\u00e0 d\u1ea1ng b\u00e0i c\u1ee7a k\u1ef3 thi ch\u00ednh th\u1ee9c. C\u00f9ng T\u00e0i Li\u1ec7u <\/strong>\u00d4n Thi<\/strong><\/a> t\u00ecm hi\u1ec3u v\u1ec1 \u0111\u1ec1 thi n\u00e0y.<\/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\u00ecnh S\u01a1n 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\u00ecnh S\u01a1n V\u0129nh Ph\u00fac <\/strong>bao g\u1ed3m 12 c\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn, 4 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai v\u00e0 6 b\u00e0i t\u1eadp t\u1ef1 lu\u1eadn. \u0110\u1ec1 thi c\u00f3 \u0111\u1ea7y \u0111\u1ee7 \u0111\u00e1p \u00e1n chi ti\u1ebft, gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng \u0111\u1ed1i chi\u1ebfu k\u1ebft qu\u1ea3 v\u00e0 hi\u1ec3u r\u00f5 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi ti\u00eau bi\u1ec3u theo t\u1eebng d\u1ea1ng:<\/p>\n

Ph\u1ea7n I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n ch\u1ecdn<\/strong><\/span><\/p>\n

C\u00e2u 1-12: C\u00e1c c\u00e2u h\u1ecfi \u0111a d\u1ea1ng v\u1ec1 h\u00e0m s\u1ed1, x\u00e1c su\u1ea5t, h\u00ecnh h\u1ecdc kh\u00f4ng gian, v\u00e0 c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf. V\u00ed d\u1ee5:<\/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 1<\/em>. \u0110i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0:<\/p>\n

\"\"<\/p>\n

A. x = -1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. x = 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. x = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. x = -4 <\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 H\u00ecnh 2<\/em>. \u0110\u01b0\u1eddng th\u1eb3ng n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho?<\/p>\n

\"\"<\/p>\n

A. x = 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. x = -1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. y = 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. y = -1 <\/p>\n

Ph\u1ea7n II: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/span><\/p>\n

C\u00e2u 1-4: \u0110\u00e1nh gi\u00e1 kh\u1ea3 n\u0103ng nh\u1eadn \u0111\u1ecbnh \u0111\u00fang sai v\u1edbi c\u00e1c m\u1ec7nh \u0111\u1ec1 li\u00ean quan \u0111\u1ebfn b\u1ea3ng bi\u1ebfn thi\u00ean, chuy\u1ec3n \u0111\u1ed9ng ch\u1eadm d\u1ea7n \u0111\u1ec1u, h\u00ecnh h\u1ecdc kh\u00f4ng gian v\u00e0 b\u00e0i to\u00e1n th\u1ef1c t\u1ebf v\u1ec1 x\u00e2y d\u1ef1ng b\u1ec3 ch\u1ee9a n\u01b0\u1edbc.<\/em><\/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

C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

a) f'(x) = 0 Leftrightarrow begincases x = -1 x = 1 endcases
\nb) \u0110i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 x = -1 .
\nc) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f(x) c\u1eaft tr\u1ee5c Ox t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t.
\nd) H\u00e0m s\u1ed1 y = f(2 – x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (1; 3) .<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t \u00f4 t\u00f4 \u0111ang ch\u1ea1y \u0111\u1ec1u v\u1edbi v\u1eadn t\u1ed1c x (m\/s) th\u00ec ng\u01b0\u1eddi l\u00e1i xe \u0111\u1ea1p phanh. T\u1eeb th\u1eddi \u0111i\u1ec3m \u0111\u00f3, \u00f4 t\u00f4 chuy\u1ec3n \u0111\u1ed9ng ch\u1eadm d\u1ea7n \u0111\u1ec1u v\u1edbi v\u1eadn t\u1ed1c thay \u0111\u1ed5i theo h\u00e0m s\u1ed1 v = -5t + 20 (m\/s) , trong \u0111\u00f3 t l\u00e0 th\u1eddi gian t\u00ednh b\u1eb1ng gi\u00e2y k\u1ec3 t\u1eeb l\u00fac \u0111\u1ea1p phanh.<\/p>\n

a) Khi xe d\u1eebng h\u1eb3n th\u00ec v\u1eadn t\u1ed1c b\u1eb1ng 0 (m\/s) .
\nb) Th\u1eddi gian t\u1eeb l\u00fac ng\u01b0\u1eddi l\u00e1i xe \u0111\u1ea1p phanh cho \u0111\u1ebfn khi xe d\u1eebng h\u1eb3n l\u00e0 5 s .
\nc) int (-5t + 20) dt = (-5t\u00b2)\/(2) + 20t + C .
\nd) Qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb l\u00fac \u0111\u1ea1p phanh cho \u0111\u1ebfn khi xe d\u1eebng h\u1eb3n l\u00e0 400 m .<\/p>\n

Ph\u1ea7n III: C\u00e2u tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n

C\u00e2u 1-6: C\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf y\u00eau c\u1ea7u t\u00ednh to\u00e1n ho\u1eb7c t\u1ed1i \u01b0u h\u00f3a. V\u00ed d\u1ee5:<\/em><\/p>\n

C\u00e2u 1.<\/strong> M\u1ed9t nh\u00e0 s\u1ea3n xu\u1ea5t mu\u1ed1n thi\u1ebft k\u1ebf m\u1ed9t chi\u1ebfc h\u1ed9p c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt kh\u00f4ng c\u00f3 n\u1eafp, c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t b\u1eb1ng 108 cm\u00b2 nh\u01b0 H\u00ecnh 1.17. T\u00ecm t\u1ec9 l\u1ec7 c\u00e1c k\u00edch th\u01b0\u1edbc c\u1ee7a chi\u1ebfc h\u1ed9p sao cho th\u1ec3 t\u00edch c\u1ee7a h\u1ed9p l\u00e0 l\u1edbn nh\u1ea5t?<\/p>\n

\"\"<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t kh\u00e1ch s\u1ea1n c\u00f3 50 ph\u00f2ng. Hi\u1ec7n t\u1ea1i m\u1ed7i ph\u00f2ng cho thu\u00ea v\u1edbi gi\u00e1 400 ngh\u00ecn \u0111\u1ed3ng m\u1ed9t ng\u00e0y th\u00ec to\u00e0n b\u1ed9 ph\u00f2ng \u0111\u01b0\u1ee3c thu\u00ea h\u1ebft. Bi\u1ebft r\u1eb1ng c\u1ee9 m\u1ed7i l\u1ea7n t\u0103ng gi\u00e1 th\u00eam 20 ngh\u00ecn \u0111\u1ed3ng m\u1ed9t ph\u00f2ng th\u00ec c\u00f3 th\u00eam 2 ph\u00f2ng tr\u1ed1ng. Gi\u00e1m \u0111\u1ed1c ph\u1ea3i ch\u1ecdn gi\u00e1 ph\u00f2ng m\u1edbi l\u00e0 bao nhi\u00eau \u0111\u1ec3 thu nh\u1eadp c\u1ee7a kh\u00e1ch s\u1ea1n trong ng\u00e0y l\u00e0 l\u1edbn nh\u1ea5t?<\/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\u00ecnh S\u01a1n 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\u00ecnh S\u01a1n V\u0129nh Ph\u00fac<\/strong> s\u1ebd<\/span>\u00a0gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n ki\u1ebfn th\u1ee9c v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i thi th\u1ef1c t\u1ebf. H\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i \u0111\u1ec1 thi th\u1eed to\u00e1n 12<\/a> v\u1ec1 \u0111\u1ec3 t\u1ef1 \u00f4n luy\u1ec7n v\u00e0 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi ch\u00ednh th\u1ee9c.<\/p>\n