{"id":494,"date":"2026-05-05T04:48:46","date_gmt":"2026-05-05T04:48:46","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-khao-sat-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-dong-dau-vinh-phuc\/"},"modified":"2026-05-05T07:21:59","modified_gmt":"2026-05-05T07:21:59","slug":"de-thi-khao-sat-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-dong-dau-vinh-phuc","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-khao-sat-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-dong-dau-vinh-phuc\/","title":{"rendered":"\u0110\u1ec1 thi kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed3ng \u0110\u1eadu V\u0129nh Ph\u00fac"},"content":{"rendered":"

\u0110\u1ec1 thi kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed3ng \u0110\u1eadu V\u0129nh Ph\u00fac<\/strong> bao g\u1ed3m c\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn, \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf nh\u1eb1m \u0111\u00e1nh gi\u00e1 to\u00e0n di\u1ec7n n\u0103ng l\u1ef1c h\u1ecdc sinh. \u0110\u1ec1 thi k\u00e9o d\u00e0i 90 ph\u00fat, kh\u00f4ng k\u1ec3 th\u1eddi gian giao \u0111\u1ec1, v\u1edbi c\u1ea5u tr\u00fac g\u1ed3m ba ph\u1ea7n: tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn, tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai, v\u00e0 tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn. C\u00f9ng Tailieuonthi<\/strong><\/a> kh\u00e1m ph\u00e1 \u0111\u1ec1 thi ng\u00e0y h\u00f4m nay.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed3ng \u0110\u1eadu V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed3ng \u0110\u1eadu V\u0129nh Ph\u00fac<\/strong> <\/span>bao g\u1ed3m 4 trang v\u1edbi t\u1ed5ng c\u1ed9ng 22 c\u00e2u h\u1ecfi chia th\u00e0nh 3 ph\u1ea7n: tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn (12 c\u00e2u), tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u), v\u00e0 tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u). \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng to\u00e1n 12<\/a> c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft, gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng \u0111\u1ed1i chi\u1ebfu v\u00e0 t\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c.<\/p>\n

Ph\u1ea7n I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n ch\u1ecdn<\/strong><\/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 y = f(x) c\u00f3 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u l\u00e0?<\/p>\n

A. x = -2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. x = 0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. x = -3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. y = -3 <\/p>\n

C\u00e2u 2:<\/strong> Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f(x) = x\u00b3 – 6x\u00b2 + 9x – 1 tr\u00ean n\u1eeda kho\u1ea3ng [-1; +\u221e) l\u00e0<\/p>\n

A. 17 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. -17 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. 1<\/p>\n

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

C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1 y = x\u00b3 – 3x + 1 . X\u00e9t t\u00ednh \u0111\u00fang ho\u1eb7c sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n

a) \u0110i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 x = 1 .<\/p>\n

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

c) Gi\u1ea3 s\u1eed h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb l\u00e0 x\u2081, x\u2082 . Khi \u0111\u00f3 gi\u00e1 tr\u1ecb x\u2081 \u00b7 x\u2082 = -1 .<\/p>\n

d) G\u1ecdi A, B l\u1ea7n l\u01b0\u1ee3t l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i v\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. Khi \u0111\u00f3, di\u1ec7n t\u00edch tam gi\u00e1c ABC l\u00e0 12 v\u1edbi C(-1; 2) .<\/p>\n

C\u00e2u 2:<\/strong> M\u1ed9t \u00f4 t\u00f4 chuy\u1ec3n \u0111\u1ed9ng nhanh d\u1ea7n \u0111\u1ec1u v\u1edbi v\u1eadn t\u1ed1c \u0111\u01b0\u1ee3c t\u00ednh theo th\u1eddi gian t b\u1eb1ng v(t) = 10t (m\/s) . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

a) Qu\u00e3ng \u0111\u01b0\u1eddng \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c trong kho\u1ea3ng th\u1eddi gian 5 gi\u00e2y \u0111\u1ea7u ti\u00ean l\u00e0 50 m .<\/p>\n

b) Gia t\u1ed1c chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a \u00f4 t\u00f4 l\u00e0 a = 10 (m\/s\u00b2) .<\/p>\n

c) Qu\u00e3ng \u0111\u01b0\u1eddng \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c trong kho\u1ea3ng th\u1eddi gian t\u1eeb 5 gi\u00e2y \u0111\u1ebfn 10 gi\u00e2y l\u00e0 375 m .<\/p>\n

d) Gi\u1ea3 s\u1eed \u00f4 t\u00f4 \u0111\u00f3 \u0111i \u0111\u01b0\u1ee3c 10 gi\u00e2y th\u00ec g\u1eb7p ch\u01b0\u1edbng ng\u1ea1i v\u1eadt v\u00e0 phanh g\u1ea5p, \u00f4 t\u00f4 ti\u1ebfp t\u1ee5c chuy\u1ec3n \u0111\u1ed9ng ch\u1eadm d\u1ea7n \u0111\u1ec1u v\u1edbi gia t\u1ed1c a = -40 (m\/s\u00b2) . Khi \u0111\u00f3, qu\u00e3ng \u0111\u01b0\u1eddng \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c t\u1eeb l\u00fac b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng \u0111\u1ebfn l\u00fac d\u1eebng h\u1eb3n l\u00e0 625 m .<\/p>\n

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

C\u00e2u 1: <\/strong>M\u1ed9t b\u00e1c t\u00e0i x\u1ebf th\u1ed1ng k\u00ea l\u1ea1i \u0111\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng (\u0111\u01a1n v\u1ecb: km) b\u00e1c \u0111\u00e3 l\u00e1i xe m\u1ed7i ng\u00e0y trong m\u1ed9t th\u00e1ng \u1edf b\u1ea3ng sau:<\/p>\n

\"\"<\/p>\n

T\u00ecm kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m tr\u00ean (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n

C\u00e2u 2: <\/strong>Cho kh\u1ed1i h\u1ed9p ch\u1eef nh\u1eadt ABCD.A\u2019B\u2019C\u2019D\u2019 c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh b\u1eb1ng 2 . G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 B\u2019C\u2019 . Bi\u1ebft r\u1eb1ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng MN v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng AA\u2019 b\u1eb1ng 30^\u00b0 . T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i h\u1ed9p ch\u1eef nh\u1eadt (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n

T\u1ea3i \u0110\u1ec1 thi kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed3ng \u0110\u1eadu V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed3ng \u0110\u1eadu V\u0129nh Ph\u00fac<\/strong> kh\u00f4ng ch\u1ec9 gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c m\u00e0 c\u00f2n r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n th\u1ef1c t\u1ebf. \u0110\u00e2y l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch \u0111\u1ec3 chu\u1ea9n b\u1ecb cho c\u00e1c k\u1ef3 thi quan tr\u1ecdng, khuy\u1ebfn kh\u00edch t\u1ea3i v\u1ec1 \u0111\u1ec3 luy\u1ec7n t\u1eadp th\u00eam.<\/p>\n