{"id":562,"date":"2026-05-05T04:52:18","date_gmt":"2026-05-05T04:52:18","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-khao-sat-chat-luong-toan-12-nam-hoc-2024-2025-truong-thpt-chuyen-ha-long-quang-ninh-lan-1\/"},"modified":"2026-05-05T07:26:01","modified_gmt":"2026-05-05T07:26:01","slug":"de-khao-sat-chat-luong-toan-12-nam-hoc-2024-2025-truong-thpt-chuyen-ha-long-quang-ninh-lan-1","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-khao-sat-chat-luong-toan-12-nam-hoc-2024-2025-truong-thpt-chuyen-ha-long-quang-ninh-lan-1\/","title":{"rendered":"\u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Chuy\u00ean H\u1ea1 Long Qu\u1ea3ng Ninh L\u1ea7n 1"},"content":{"rendered":"

\u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Chuy\u00ean H\u1ea1 Long Qu\u1ea3ng Ninh<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n nh\u1eb1m \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c c\u1ee7a c\u00e1c b\u1ea1n h\u1ecdc sinh 12. Qua \u0111\u00f3, gi\u00e1o vi\u00ean bi\u1ebft \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c v\u00e0 \u0111\u01b0a ra quy tr\u00ecnh gi\u1ea3ng d\u1ea1y v\u00e0 \u00f4n t\u1eadp ph\u00f9 h\u1ee3p nh\u1ea5t v\u1edbi c\u00e1c b\u1ea1n. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u qua n\u1ed9i dung c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y nh\u00e9!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Chuy\u00ean H\u1ea1 Long Qu\u1ea3ng Ninh<\/strong><\/h2>\n

N\u1ed9i dung \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Chuy\u00ean H\u1ea1 Long Qu\u1ea3ng Ninh<\/strong> c\u00f3 c\u1ea5u tr\u00fac chu\u1ea9n c\u1ee7a b\u1ed9 GD &DT. \u0110\u1ec1 thi g\u1ed3m 22 c\u00e2u h\u1ecfi v\u1edbi 3 d\u1ea1ng tr\u1eafc nghi\u1ec7m l\u1ef1a ch\u1ecdn ph\u01b0\u01a1ng \u00e1n, tr\u1eafc nghi\u1ec7m \u0111\u00fang sai, tr\u1ea3 l\u1eddi ng\u1eafn. N\u1ed9i dung c\u00e2u h\u1ecfi ph\u00e2n b\u1ed5 \u0111\u1ec1u v\u00e0 b\u00e1m s\u00e1t theo ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n 12 t\u1eeb \u0111\u1ea1i s\u1ed1 \u0111\u1ebfn h\u00ecnh h\u1ecdc kh\u00f4ng gian. Ma tr\u1eadn chi ti\u1ebft \u0110\u1ec1 Kh\u1ea3o S\u00e1t Ch\u1ea5t L\u01b0\u1ee3ng To\u00e1n 12 nh\u01b0 sau:<\/p>\n

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

H\u1ecdc sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12. M\u1ed7i c\u00e2u, c\u00e1c b\u1ea1n ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn trong c\u00e1c \u0111\u00e1p \u00e1n A, B, C, D. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = (ax + b)\/(cx + d) (c \u2260 0, ad – bc \u2260 0) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0:<\/p>\n

\"\"<\/p>\n

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

C\u00e2u 2.<\/strong> Cho m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m:<\/p>\n

beginarray|c|c|c|c|c|c|c| hline Nh\u00f3m & [4;6) & [6;8) & [8;10) & [10;12) & [12;14) & [14;16) hline T\u1ea7n s\u1ed1 & 3 & 5 & 8 & 9 & 6 & 4 hline endarray<\/p>\n

T\u00ednh s\u1ed1 trung b\u00ecnh c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c):<\/p>\n

A. 10,3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 10,4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. 10,5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 10,2 <\/p>\n

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

Trong m\u1ed7i \u00fd a), b), c), d), \u1edf m\u1ed7i c\u00e2u h\u1ecfi, h\u1ecdc sinh ch\u1ecdn gi\u00e1 tr\u1ecb \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i c\u00e2u.<\/p>\n

C\u00e2u 1.<\/strong> M\u1ed9t x\u01b0\u1edfng s\u1ea3n xu\u1ea5t th\u1ef1c ph\u1ea9m g\u1ed3m 3 k\u0129 s\u01b0 ch\u1ebf bi\u1ebfn th\u1ef1c ph\u1ea9m, 3 k\u0129 thu\u1eadt vi\u00ean v\u00e0 12 c\u00f4ng nh\u00e2n. \u0110\u1ec3 \u0111\u1ea3m b\u1ea3o s\u1ea3n xu\u1ea5t th\u1ef1c ph\u1ea9m ch\u1ed1ng d\u1ecbch Covid-19, x\u01b0\u1edfng c\u1ea7n chia th\u00e0nh 3 ca s\u1ea3n xu\u1ea5t theo th\u1eddi gian li\u00ean ti\u1ebfp nhau sao cho m\u1ed7i ca c\u00f3 6 ng\u01b0\u1eddi.<\/p>\n

a) S\u1ed1 c\u00e1ch ph\u00e2n chia lao \u0111\u1ed9ng v\u00e0o 3 ca s\u1ea3n xu\u1ea5t l\u00e0: C\u2081\u2088\u2076 \u00b7 C\u2081\u2082\u2076\n<\/p>\n

b) S\u1ed1 c\u00e1ch ph\u00e2n l\u1ecbch lao \u0111\u1ed9ng v\u00e0o 3 ca s\u1ea3n xu\u1ea5t sao cho ca \u0111\u1ea7u ti\u00ean g\u1ed3m to\u00e0n c\u00f4ng nh\u00e2n l\u00e0: C\u2081\u2082\u2076 \u00b7 C\u2086\u2076\n<\/p>\n

c) S\u1ed1 c\u00e1ch ph\u00e2n l\u1ecbch lao \u0111\u1ed9ng v\u00e0o 3 ca s\u1ea3n xu\u1ea5t sao cho m\u1ed7i ca c\u00f3 \u0111\u00fang 1 k\u0129 s\u01b0 v\u00e0 \u0111\u00fang 1 k\u0129 thu\u1eadt vi\u00ean l\u00e0: C\u2083\u00b9 \u00b7 C\u2082\u00b9 \u00b7 C\u2081\u00b9 \u00b7 C\u2083\u00b9 \u00b7 C\u2082\u00b9 \u00b7 C\u2081\u00b9\n<\/p>\n

d) X\u00e1c su\u1ea5t sao cho m\u1ed7i ca c\u00f3 \u0111\u00fang 1 k\u0129 thu\u1eadt vi\u00ean, 1 k\u0129 s\u01b0 ch\u1ebf bi\u1ebfn th\u1ef1c ph\u1ea9m l\u00e0: 225\/3094\n<\/p>\n

C\u00e2u 2.<\/strong> Gi\u00e1 \u0111\u00f3ng c\u1eeda c\u1ee7a m\u1ed9t c\u1ed5 phi\u1ebfu l\u00e0 gi\u00e1 c\u1ee7a c\u1ed5 phi\u1ebfu \u0111\u00f3 cu\u1ed1i m\u1ed9t phi\u00ean giao d\u1ecbch. B\u1ea3ng sau th\u1ed1ng k\u00ea gi\u00e1 \u0111\u00f3ng c\u1eeda (\u0111\u01a1n v\u1ecb: ngh\u00ecn \u0111\u1ed3ng) c\u1ee7a hai m\u00e3 c\u1ed5 phi\u1ebfu (A) v\u00e0 (B) trong 50 ng\u00e0y giao d\u1ecbch li\u00ean ti\u1ebfp:<\/p>\n

beginarray|c|c|c|c|c|c| hline Gi\u00e1 \u0111\u00f3ng c\u1eeda & [18;20) & [20;22) & [22;24) & [24;26) & [26;28) hline C\u1ed5 phi\u1ebfu A & 8 & 9 & 12 & 10 & 11 hline C\u1ed5 phi\u1ebfu B & 16 & 4 & 3 & 6 & 21 hline endarray<\/p>\n

a) X\u00e9t m\u1eabu s\u1ed1 li\u1ec7u c\u1ee7a c\u1ed5 phi\u1ebfu (A), ta c\u00f3 s\u1ed1 trung b\u00ecnh l\u00e0: barX_A = 23,28\n<\/p>\n

b) X\u00e9t m\u1eabu s\u1ed1 li\u1ec7u c\u1ee7a c\u1ed5 phi\u1ebfu (A), ta c\u00f3 ph\u01b0\u01a1ng sai c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m l\u00e0: S_A\u00b2 = 7,5216\n<\/p>\n

c) X\u00e9t m\u1eabu s\u1ed1 li\u1ec7u c\u1ee7a c\u1ed5 phi\u1ebfu (B), ta c\u00f3 s\u1ed1 trung b\u00ecnh l\u00e0: barX_B = 23,48\n<\/p>\n

d) C\u1ed5 phi\u1ebfu (A) c\u00f3 m\u1ee9c bi\u1ebfn \u0111\u1ed9ng gi\u00e1 l\u1edbn c\u1ed5 phi\u1ebfu (B).<\/p>\n

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

G\u1ed3m 6 c\u00e2u h\u1ecfi c\u00f3 nhi\u1ec1u m\u1ee9c \u0111\u1ed9 t\u1eeb hi\u1ec3u bi\u1ebft \u2013 v\u1eadn d\u1ee5ng \u2013 v\u1eadn d\u1ee5ng cao. \u0110\u1ec3 chinh ph\u1ee5c \u0111i\u1ec3m t\u1ed1i \u0111a \u1edf ph\u1ea7n n\u00e0y h\u1ecdc sinh c\u1ea7n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u00e0 gi\u1ea3i th\u1eadt nhi\u1ec1u \u0111\u1ec1 thi kh\u00e1c nhau:<\/p>\n

C\u00e2u 1.<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz , cho tam gi\u00e1c ABC c\u00f3 A(1;2;-1), B(2;-1;3), C(-4;7;5). G\u1ecdi D(a;b;c) l\u00e0 \u0111i\u1ec3m th\u1ecfa m\u00e3n AD\u20d7 – AB\u20d7 – 2AC\u20d7 = 0\u20d7. T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a a + b + c .<\/p>\n

C\u00e2u 2.<\/strong>\u00a0H\u1ec7 th\u1ed1ng \u0111\u1ecbnh v\u1ecb To\u00e0n C\u1ea7u GPS hi\u1ec7n t\u1ea1i c\u00f3 24 v\u1ec7 tinh, m\u1ed7i v\u1ec7 tinh c\u00e1ch Tr\u00e1i \u0110\u1ea5t 20000 km, ta coi Tr\u00e1i \u0110\u1ea5t l\u00e0 kh\u1ed1i c\u1ea7u c\u00f3 b\u00e1n k\u00ednh R = 6 (ngh\u00ecn km). V\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz \u0111\u00e3 ch\u1ecdn, O l\u00e0 t\u00e2m Tr\u00e1i \u0110\u1ea5t v\u00e0 \u0111\u01a1n v\u1ecb tr\u00ean m\u1ed7i tr\u1ee5c l\u00e0 ngh\u00ecn km, hai v\u1ec7 tinh c\u00f3 t\u1ecda \u0111\u1ed9 A(26;0;0), B(0;26;0). X\u00e9t \u0111i\u1ec3m M(x;y;z) thu\u1ed9c b\u1ec1 m\u1eb7t Tr\u00e1i \u0110\u1ea5t. T\u00ednh gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a MA + MB theo \u0111\u01a1n v\u1ecb ngh\u00ecn km (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb).<\/p>\n

T\u1ea3i \u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Chuy\u00ean H\u1ea1 Long Qu\u1ea3ng Ninh<\/strong><\/h2>\n

\u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 Tr\u01b0\u1eddng THPT Chuy\u00ean H\u1ea1 Long Qu\u1ea3ng Ninh<\/strong> l\u00e0 t\u00e0i nguy\u00ean h\u1eefu \u00edch d\u00e0nh cho gi\u00e1o vi\u00ean v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1. \u0110\u1eb7c bi\u1ec7t, \u0111\u1ec1 thi \u0111\u00e3 k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch gi\u1ea3i chi ti\u1ebft \u1edf cu\u1ed1i, gi\u00fap c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng trong qu\u00e1 tr\u00ecnh l\u00e0m v\u00e0 s\u1eeda b\u00e0i. H\u00e3y t\u1ea3i \u0110\u1ec1 Kh\u1ea3o S\u00e1t Ch\u1ea5t L\u01b0\u1ee3ng To\u00e1n 12<\/a> qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y v\u00e0 luy\u1ec7n \u0111\u1ec1 ngay nh\u00e9!<\/p>\n