{"id":416,"date":"2026-05-05T04:44:36","date_gmt":"2026-05-05T04:44:36","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-kiem-tra-giua-hoc-ki-2-toan-11-nam-2024-2025-truong-thpt-hung-vuong-tp-hcm\/"},"modified":"2026-05-05T07:17:22","modified_gmt":"2026-05-05T07:17:22","slug":"de-kiem-tra-giua-hoc-ki-2-toan-11-nam-2024-2025-truong-thpt-hung-vuong-tp-hcm","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-kiem-tra-giua-hoc-ki-2-toan-11-nam-2024-2025-truong-thpt-hung-vuong-tp-hcm\/","title":{"rendered":"\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00f9ng V\u01b0\u01a1ng TP HCM"},"content":{"rendered":"

\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00f9ng V\u01b0\u01a1ng TP HCM<\/strong> l\u00e0 t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p nh\u1eefng ki\u1ebfn th\u1ee9c quan tr\u1ecdng v\u1ec1 c\u1ea5p s\u1ed1 c\u1ed9ng, c\u1ea5p s\u1ed1 nh\u00e2n, gi\u1edbi h\u1ea1n d\u00e3y s\u1ed1 v\u00e0 \u0111\u1ea1o h\u00e0m. C\u00f9ng c\u1ea5u tr\u00fac \u0111\u1ec1 thi v\u1edbi c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp \u0111\u01b0\u1ee3c ph\u00e2n theo t\u1eebng m\u1ee9c \u0111\u1ed9 t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao, gi\u00fap h\u1ecdc sinh l\u1edbp 11 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i t\u1eadp v\u00e0 c\u1ee7ng c\u1ed1 n\u1ec1n t\u1ea3ng ki\u1ebfn th\u1ee9c m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3. \u0110\u1ec3 n\u1eafm v\u1eefng n\u1ed9i dung c\u1ee7a \u0111\u1ec1 ki\u1ec3m tra n\u00e0y, h\u00e3y c\u00f9ng \u00d4n Thi<\/strong><\/a> xem qua nh\u1eefng \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t c\u1ee7a t\u1eadp \u0111\u1ec1 ngay sau \u0111\u00e2y!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00f9ng V\u01b0\u01a1ng TP HCM<\/span><\/strong><\/h2>\n

\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00f9ng V\u01b0\u01a1ng TP HCM <\/strong>\u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u1ea5p \u0111\u1ed9 t\u01b0 duy t\u1eeb nh\u1eadn bi\u1ebft \u2013 th\u00f4ng hi\u1ec3u \u2013 v\u1eadn d\u1ee5ng \u2013 v\u1eadn d\u1ee5ng cao. \u0110\u00e2y l\u00e0 c\u00f4ng c\u1ee5 h\u1eefu \u00edch gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c, ph\u00e1t tri\u1ec3n t\u01b0 duy logic v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/p>\n

Th\u1eddi gian l\u00e0m b\u00e0i:<\/strong> 60 ph\u00fat<\/p>\n

C\u1ea5u tr\u00fac \u0111\u1ec1 ki\u1ec3m tra:<\/strong><\/p>\n

PH\u1ea6N 1: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (3 \u0111i\u1ec3m) \u2013 6 c\u00e2u<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00ecnh ch\u00f3p $S.ABCD$ c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng, $SA$ vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng \u0111\u00e1y. M\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y \u0111\u00fang?<\/p>\n

A. $BA \\perp (SAC).$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $BA \\perp (SCD).$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. $BA \\perp (SBC).$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $BA \\perp (SAD).$<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00ecnh ch\u00f3p $S.ABCD$ c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt, c\u1ea1nh $SA$ vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y. G\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng $SD$ v\u00e0 $BC$ b\u1eb1ng g\u00f3c n\u00e0o sau \u0111\u00e2y?<\/p>\n

\"\"<\/p>\n

A. $\\widehat{SDA}$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $\\widehat{SAC}$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. $\\widehat{SBC}$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. $\\widehat{SAD}$<\/p>\n

PH\u1ea6N 2: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (2 \u0111i\u1ec3m) \u2013 2 c\u00e2u (m\u1ed7i c\u00e2u 4 \u00fd)<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) = 3^x .<\/p>\n

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

a) H\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 mathbbR v\u00e0 t\u1eadp gi\u00e1 tr\u1ecb l\u00e0 (0; +\u221e) .
\nb) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng y = 9 t\u1ea1i \u0111i\u1ec3m c\u00f3 ho\u00e0nh \u0111\u1ed9 b\u1eb1ng 3.
\nc) H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean mathbbR .
\nd) G\u1ecdi M, m l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 f(x) tr\u00ean [-1;5] . Khi \u0111\u00f3: M – 3m = 242 .<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.A\u2019B\u2019C\u2019D\u2019 .<\/p>\n

\"\"<\/p>\n

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

a) BC perp DD\u2019 .
\nb) AC perp B\u2019D\u2019 .
\nc) (A\u2019B, AC) = 45^\u00b0 .
\nd) G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 BC . Khi \u0111\u00f3: MN perp (BDD\u2019B\u2019) .<\/p>\n

PH\u1ea6N 3: C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (2 \u0111i\u1ec3m) \u2013 4 c\u00e2u\u00a0<\/strong><\/p>\n

C\u00e2u 1.<\/strong> \u0110\u1eb7t log\u2082 2 = a , log\u2083 7 = b . Bi\u1ec3u th\u1ecb log\u2081\u2082 21 theo a v\u00e0 b , ta \u0111\u01b0\u1ee3c: $log_{12} 21 = \\frac{m + b}{1 + n a}$ v\u1edbi m, n l\u00e0 c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean. T\u00ednh m + n .<\/p>\n

C\u00e2u 2.<\/strong> Bi\u1ebft r\u1eb1ng 10^\u03b1 = 3 v\u00e0 10^\u03b2 = 5 . H\u00e3y t\u00ednh 10^\u03b1 \u00b7 \u03b2 .<\/p>\n

PH\u1ea6N 4: T\u1ef1 lu\u1eadn (3 \u0111i\u1ec3m) \u2013\u00a0 2 c\u00e2u\u00a0<\/strong><\/p>\n

C\u00e2u 1. (1 \u0111i\u1ec3m)<\/strong> Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $log_2 (x \u2013 1) + \\log_2 (x + 1) = 3$.<\/p>\n

C\u00e2u 2. (2 \u0111i\u1ec3m)<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 SA perp (ABCD) .<\/p>\n

a) (1 \u0111i\u1ec3m) Ch\u1ee9ng minh r\u1eb1ng: BD perp SC .
\nb) (1 \u0111i\u1ec3m) G\u1ecdi H, K l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a \u0111i\u1ec3m A tr\u00ean c\u00e1c c\u1ea1nh SB, SD . Ch\u1ee9ng minh r\u1eb1ng: HK perp (SAC) .<\/p>\n

T\u1ea3i \u0110\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00f9ng V\u01b0\u01a1ng TP HCM<\/span><\/strong><\/h2>\n

\u0110\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT H\u00f9ng V\u01b0\u01a1ng TP HCM<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n t\u1eadp kh\u00f4ng th\u1ec3 b\u1ecf qua d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh, gi\u00fap c\u00e1c em h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i v\u00e0 n\u00e2ng cao t\u01b0 duy to\u00e1n h\u1ecdc. T\u1ea3i ngay \u0111\u1ec1 to\u00e1n gi\u1eefa k\u00ec 2 l\u1edbp 11 \u0111\u1ea7y \u0111\u1ee7 qua \u0111\u01b0\u1eddng link sau \u0111\u1ec3 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 v\u00e0 s\u1eb5n s\u00e0ng b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1!<\/p>\n