{"id":538,"date":"2026-05-05T04:51:03","date_gmt":"2026-05-05T04:51:03","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-cum-chuong-my-thanh-oai-ha-noi\/"},"modified":"2026-05-05T07:24:31","modified_gmt":"2026-05-05T07:24:31","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-cum-chuong-my-thanh-oai-ha-noi","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-cum-chuong-my-thanh-oai-ha-noi\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT C\u1ee5m Ch\u01b0\u01a1ng M\u1ef9 \u2013 Thanh Oai H\u00e0 N\u1ed9i"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT C\u1ee5m Ch\u01b0\u01a1ng M\u1ef9 \u2013 Thanh Oai H\u00e0 N\u1ed9i<\/strong> l\u00e0 t\u00e0i li\u1ec7u quan tr\u1ecdng d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh cu\u1ed1i c\u1ea5p 3, \u00f4n t\u1eadp chu\u1ea9n b\u1ecb chinh ph\u1ee5c k\u00ec thi quan tr\u1ecdng. T\u00e0i li\u1ec7u n\u00e0y \u0111\u01b0\u1ee3c chia th\u00e0nh 2 ph\u1ea7n: \u0110\u1ec1 thi v\u00e0 \u0111\u00e1p \u00e1n k\u00e8m c\u00e1ch gi\u1ea3i chi ti\u1ebft. C\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 n\u1ed9i dung c\u1ee7a \u0111\u1ec1 thi n\u00e0y nh\u00e9!<\/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 C\u1ee5m Ch\u01b0\u01a1ng M\u1ef9 \u2013 Thanh Oai H\u00e0 N\u1ed9i<\/strong><\/h2>\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 C\u1ee5m Ch\u01b0\u01a1ng M\u1ef9 \u2013 Thanh Oai H\u00e0 N\u1ed9i<\/strong> \u0111\u01b0\u1ee3c th\u1ea7y c\u00f4 bi\u00ean so\u1ea1n chi ti\u1ebft v\u00e0 khoa h\u1ecdc. Ph\u00e2n b\u1ed5 \u0111\u00fang theo ma tr\u1eadn \u0111\u1ec1 v\u00e0 \u0111i\u1ec3m c\u1ee7a b\u1ed9 GD &\u0110T. \u0110\u1ec1 thi th\u1eed to\u00e1n thpt<\/a> n\u00e0y c\u00f3 t\u1ea5t c\u1ea3 22 c\u00e2u v\u00e0 th\u00ed sinh c\u00f3 th\u1eddi gian 90 ph\u00fat \u0111\u1ec3 l\u00e0m b\u00e0i. Chi ti\u1ebft n\u1ed9i dung c\u1ee7a \u0111\u1ec1 thi c\u00f3 d\u1ea1ng nh\u01b0 sau:<\/p>\n

PH\u1ea6N 1 \u2013 C\u00c2U TR\u1eaeC NGHI\u1ec6M NHI\u1ec0U PH\u01af\u01a0NG \u00c1N L\u1ef0A CH\u1eccN<\/strong><\/p>\n

Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12. M\u1ed7i c\u00e2u h\u1ecfi th\u00ed sinh ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n duy nh\u1ea5t. V\u00ed d\u1ee5 c\u00e1c c\u00e2u sau:<\/p>\n

C\u00e2u 1:<\/strong> B\u1ea1n Chi r\u1ea5t th\u00edch nh\u1ea3y hi\u1ec7n \u0111\u1ea1i. Th\u1eddi gian t\u1eadp nh\u1ea3y m\u1ed7i ng\u00e0y trong th\u1eddi gian g\u1ea7n \u0111\u00e2y c\u1ee7a b\u1ea1n Chi \u0111\u01b0\u1ee3c th\u1ed1ng k\u00ea l\u1ea1i \u1edf b\u1ea3ng sau:<\/p>\n

\"\"<\/p>\n

T\u00ecm ph\u01b0\u01a1ng sai c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m tr\u00ean.<\/p>\n

A. 31,75\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 31,25\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 32,25\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 32<\/p>\n

C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, cho hai \u0111i\u1ec3m A(2; -1; -1), B(-3; 2; -2) . T\u1ecda \u0111\u1ed9 c\u1ee7a vector AB\u20d7 l\u00e0:<\/p>\n

A. (5; -3; -1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. (5; -3; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (-5; 1; -1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. (-5; 3; -1) <\/p>\n

PH\u1ea6N 2 \u2013 TR\u1eaeC NGHI\u1ec6M \u0110\u00daNG SAI<\/strong><\/p>\n

Th\u00ed sinh tr\u1ea3 l\u1eddi 4 c\u00e2u h\u1ecfi, trong m\u1ed7i \u00fd a), b), c), d), \u1edf m\u1ed7i c\u00e2u, th\u00ed sinh ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0110\u00daNG\/SAI<\/strong>.<\/p>\n

C\u00e2u 1:<\/strong> M\u1ed9t h\u1ed9p \u0111\u1ef1ng 100 t\u1ea5m th\u1ebb \u0111\u00e1nh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 100. L\u1ea5y ng\u1eabu nhi\u00ean t\u1eeb h\u1ed9p ra ba th\u1ebb.<\/p>\n

a) X\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 A : \u201cL\u1ea5y \u0111\u01b0\u1ee3c ba th\u1ebb \u0111\u1ec1u ghi s\u1ed1 ch\u1eb5n\u201d l\u00e0 P(A) = 49\/198\n<\/p>\n

b) X\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 B : \u201cL\u1ea5y \u0111\u01b0\u1ee3c ba th\u1ebb trong \u0111\u00f3 ch\u1ec9 c\u00f3 \u0111\u00fang m\u1ed9t th\u1ebb ghi s\u1ed1 ch\u1eb5n\u201d l\u00e0 P(B) = 1\/3\n<\/p>\n

c) X\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 C : \u201cTr\u00ean c\u00e1c s\u1ed1 ghi tr\u00ean ba th\u1ebb l\u00e0 m\u1ed9t s\u1ed1 ch\u1eb5n\u201d l\u00e0 P(C) = 29\/33\n<\/p>\n

d) X\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 D : \u201cT\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a ba s\u1ed1 ghi tr\u00ean ba th\u1ebb l\u00e0 m\u1ed9t s\u1ed1 chia h\u1ebft cho 3\u201d l\u00e0 P(D) = 33\/100\n<\/p>\n

C\u00e2u 2:<\/strong> C\u00f3 hai c\u00e2y c\u1ed9t, m\u1ed9t c\u1ed9t cao 16 m v\u00e0 m\u1ed9t c\u1ed9t c\u00e2y cao 24 m \u0111\u1ee9ng c\u00e1ch nhau 30 m. Ch\u00fang \u0111\u01b0\u1ee3c gi\u1eef b\u1eb1ng hai s\u1ee3i d\u00e2y, g\u1eafn v\u00e0o m\u1ed9t c\u1ecdc duy nh\u1ea5t n\u1ed1i t\u1eeb m\u1eb7t \u0111\u1ea5t \u0111\u1ebfn \u0111\u1ec9nh m\u1ed7i c\u1ed9t. (Tham kh\u1ea3o h\u00ecnh v\u1ebd sau).<\/p>\n

\"\"<\/p>\n

G\u1ecdi x (m) l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb ch\u00e2n c\u1ed9t cao 16 m \u0111\u1ebfn c\u1ecdc (0 \u2264 x \u2264 30) . Khi \u0111\u00f3:<\/p>\n

a) Kho\u1ea3ng c\u00e1ch t\u1eeb ch\u00e2n c\u00e2y c\u1ed9t cao 24 m \u0111\u1ebfn c\u1ecdc l\u00e0 30 – x (m)\n<\/p>\n

b) Chi\u1ec1u d\u00e0i c\u1ee7a s\u1ee3i d\u00e2y n\u1ed1i t\u1eeb c\u1ecdc \u0111\u1ebfn \u0111\u1ec9nh c\u1ed9t cao 24 m l\u00e0 \u221a(30 – x)\u00b2 + 24\u00b2\n<\/p>\n

c) T\u1ed5ng chi\u1ec1u d\u00e0i c\u1ee7a hai s\u1ee3i d\u00e2y l\u00e0 \u221a256 + x\u00b2 + \u221a1476 – 60x + x\u00b2\n<\/p>\n

d) T\u1ed5ng chi\u1ec1u d\u00e0i c\u1ee7a hai s\u1ee3i d\u00e2y ng\u1eafn nh\u1ea5t b\u1eb1ng 51 m\n<\/p>\n

PH\u1ea6N 3 \u2013 TR\u1eaeC NGHI\u1ec6M TR\u1ea2 L\u1edcI NG\u1eaeN<\/strong><\/p>\n

C\u00f3 t\u1ea5t c\u1ea3 6 c\u00e2u h\u1ecfi, th\u00ed sinh c\u1ea7n \u0111\u1ecdc \u0111\u1ec1 v\u00e0 tr\u00ecnh b\u00e0y c\u00e1ch ng\u1eafn g\u1ecdn, m\u1ea1ch l\u1ea1c, v\u00e0 \u0111\u00fang tr\u1ecdng t\u00e2m. Tham kh\u1ea3o qua c\u00e1c v\u00ed d\u1ee5 sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1:<\/strong> Huy\u1ebft \u00e1p l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u1ec3 \u0111o \u0111\u1ed9 l\u1edbn c\u1ee7a l\u1ef1c t\u00e1c d\u1ee5ng l\u00ean th\u00e0nh m\u1ea1ch m\u00e1u. N\u00f3 \u0111\u01b0\u1ee3c \u0111o b\u1eb1ng 2 ch\u1ec9 s\u1ed1; huy\u1ebft \u00e1p t\u00e2m thu (l\u00e0 \u00e1p l\u1ef1c c\u1ee7a m\u00e1u l\u00ean \u0111\u1ed9ng m\u1ea1ch khi tim co b\u00f3p) v\u00e0 huy\u1ebft \u00e1p t\u00e2m tr\u01b0\u01a1ng (l\u00e0 \u00e1p l\u1ef1c c\u1ee7a m\u00e1u l\u00ean th\u00e0nh \u0111\u1ed9ng m\u1ea1ch khi tim gi\u00e3n ra). Huy\u1ebft \u00e1p kh\u00e1c nhau \u0111\u00e1ng k\u1ec3 gi\u1eefa ng\u01b0\u1eddi n\u00e0y v\u00e0 ng\u01b0\u1eddi kh\u00e1c, nh\u01b0ng huy\u1ebft \u00e1p ti\u00eau chu\u1ea9n l\u00e0 120\/80 , n\u00f3 c\u00f3 ngh\u0129a l\u00e0 huy\u1ebft \u00e1p t\u00e2m thu l\u00e0 120mmHg v\u00e0 huy\u1ebft \u00e1p t\u00e2m tr\u01b0\u01a1ng l\u00e0 80mmHg.<\/p>\n

Gi\u1ea3 s\u1eed r\u1eb1ng tr\u00e1i tim c\u1ee7a m\u1ed9t ng\u01b0\u1eddi \u0111\u1eadp 70 l\u1ea7n m\u1ed9t ph\u00fat, huy\u1ebft \u00e1p ri\u00eang P sau t gi\u00e2y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 b\u1eb1ng h\u00e0m s\u1ed1: P(t) = 100 + 20 sin( 7\u03c0\/3t ) Trong th\u1eddi gian t\u1eeb 0 gi\u00e2y \u0111\u1ebfn 1 gi\u00e2y, th\u1eddi \u0111i\u1ec3m t = a\/b ( a, b in mathbbN^*, a\/b t\u1ed1i gi\u1ea3n ) m\u00e0 t\u1ea1i \u0111\u00f3 huy\u1ebft \u00e1p b\u1eb1ng 80 mmHg. T\u00ednh: 2a – b\n<\/p>\n

C\u00e2u 2:<\/strong> Cho h\u00ecnh ch\u00f3p SABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh thoi t\u00e2m O , hai \u0111\u01b0\u1eddng ch\u00e9o: AC = 2a, BD = 2a\u221a3, SO perp (ABCD) . C\u1ea1nh b\u00ean: SD = 2a . G\u1ecdi \u03c6 l\u00e0 g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng SB v\u00e0 m\u1eb7t ph\u1eb3ng (SCD) . T\u00ednh: sin\u03c6 (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)\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 C\u1ee5m Ch\u01b0\u01a1ng M\u1ef9 \u2013 Thanh Oai H\u00e0 N\u1ed9i<\/strong><\/h2>\n

\u0110\u1ec3 chinh ph\u1ee5c v\u00e0 \u0111\u1ea1t s\u1ed1 \u0111i\u1ec3m cao trong th\u00ec thi thpt m\u00f4n To\u00e1n s\u1eafp t\u1edbi, c\u00e1c em h\u1ecdc sinh t\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT C\u1ee5m Ch\u01b0\u01a1ng M\u1ef9 \u2013 Thanh Oai H\u00e0 N\u1ed9i<\/strong> qua \u0111\u01b0\u1eddng d\u1eabn sau \u0111\u00e2y. \u0110\u00e2y ch\u00ednh l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u h\u1eefu \u00edch, h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng gi\u1ea3i \u0111\u1ec1 thi.<\/p>\n