{"id":366,"date":"2026-05-05T04:41:56","date_gmt":"2026-05-05T04:41:56","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-kiem-tra-giua-ky-2-toan-11-chan-troi-sang-tao-nam-hoc-2024-2025\/"},"modified":"2026-05-05T07:14:40","modified_gmt":"2026-05-05T07:14:40","slug":"bo-de-kiem-tra-giua-ky-2-toan-11-chan-troi-sang-tao-nam-hoc-2024-2025","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-kiem-tra-giua-ky-2-toan-11-chan-troi-sang-tao-nam-hoc-2024-2025\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025"},"content":{"rendered":"<p><strong>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 Ch\u00e2n Tr\u1eddi S\u00e1ng T\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> c\u1ee7a \u0111\u1ed9i ng\u0169 <strong>To\u00e1n T\u1eeb T\u00e2m<\/strong> mang \u0111\u1ebfn c\u01a1 h\u1ed9i r\u00e8n luy\u1ec7n to\u00e0n di\u1ec7n cho h\u1ecdc sinh l\u1edbp 11. V\u1edbi n\u1ed9i dung b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh, t\u00e0i li\u1ec7u gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u00e0 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi gi\u1eefa k\u1ef3 2. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> kh\u00e1m ph\u00e1 ngay t\u00e0i li\u1ec7u h\u1eefu \u00edch n\u00e0y nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p><strong>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong>\u00a0bao g\u1ed3m 10 b\u1ed9 \u0111\u1ec1 thi theo ch\u01b0\u01a1ng tr\u00ecnh Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o.\u00a0M\u1ed7i \u0111\u1ec1 ki\u1ec3m tra \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf g\u1ed3m 21 c\u00e2u h\u1ecfi, v\u1edbi 4 ph\u1ea7n ch\u00ednh:<\/p>\n<p><strong>Ph\u1ea7n A G\u1ed3m 12 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m (3 \u0111i\u1ec3m)<\/strong> v\u1ec1 c\u00e1c ch\u1ee7 \u0111\u1ec1 \u0111\u1ea1i s\u1ed1, logarit, ph\u01b0\u01a1ng tr\u00ecnh, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, h\u00ecnh h\u1ecdc kh\u00f4ng gian. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi nh\u01b0 sau<\/p>\n<p><strong>C\u00e2u 1.<\/strong> V\u1edbi  a  l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd,  \u221a[4]a\u2075  b\u1eb1ng: A.  5\/4 a\u2074 . B.  4\/5 a\u2075 . C.  a\u00b2\u2070 . D.  5\/2 a\u00b2 <\/p>\n<p><strong>C\u00e2u 2.<\/strong> H\u00e0m s\u1ed1  y = (x-1)^1\/3  c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0: A.  [1; +\u221e) . B.  (1; +\u221e) . C.  (-\u221e; +\u221e) . D.  (-\u221e;1) cup (1;+\u221e) <\/p>\n<p><strong>Ph\u1ea7n B G\u1ed3m 2 C\u00e2u h\u1ecfi \u0111\u00fang\/sai (2 \u0111i\u1ec3m):<\/strong> Y\u00eau c\u1ea7u h\u1ecdc sinh x\u00e1c \u0111\u1ecbnh t\u00ednh \u0111\u00fang\/sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 to\u00e1n h\u1ecdc v\u1ec1 h\u00ecnh h\u1ecdc kh\u00f4ng gian, logarit, c\u1ea5p s\u1ed1 nh\u00e2n. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 13.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABC  c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c vu\u00f4ng c\u00e2n t\u1ea1i  B ,  SA perp (ABC) ,  AB = BC = a ,  SA = a\u221a3 .<\/p>\n<p><strong>C\u00e2u 14.<\/strong> Gi\u1ea3 s\u1eed  A, B  l\u00e0 hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t tr\u00ean \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1  y = log\u2083 (5x &#8211; 3)  sao cho  A  l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n  OB .<\/p>\n<p><strong>Ph\u1ea7n C G\u1ed3m 4 C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn (2 \u0111i\u1ec3m):<\/strong> C\u00e1c b\u00e0i to\u00e1n y\u00eau c\u1ea7u \u0111i\u1ec1n \u0111\u00e1p s\u1ed1 ng\u1eafn g\u1ecdn, c\u00f3 th\u1ec3 li\u00ean quan \u0111\u1ebfn ph\u01b0\u01a1ng tr\u00ecnh, h\u00ecnh h\u1ecdc kh\u00f4ng gian, v\u00e0 to\u00e1n \u1ee9ng d\u1ee5ng. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 15.<\/strong> C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1  m in (-2024; 2024)  \u0111\u1ec3 h\u00e0m s\u1ed1  y = \u221a[5]x\u00b2 &#8211; 2x &#8211; m + 1  c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 (\\mathbb{R} \\)?<\/p>\n<p><strong>C\u00e2u 16.<\/strong> T\u00ecm s\u1ed1 nghi\u1ec7m nguy\u00ean c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh:  log_2-\u221a5 (x-1) + log_2+\u221a5 (11 &#8211; 2x) \u2265 0.\n<\/p>\n<p><strong>Ph\u1ea7n D G\u1ed3m 3 C\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn (3 \u0111i\u1ec3m):<\/strong> C\u00e1c b\u00e0i to\u00e1n y\u00eau c\u1ea7u gi\u1ea3i chi ti\u1ebft, bao g\u1ed3m \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf nh\u01b0 t\u00ednh l\u00e3i su\u1ea5t ng\u00e2n h\u00e0ng, t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i d\u00e2n s\u1ed1, nhi\u1ec7t \u0111\u1ed9 v\u1eadt th\u1ec3 theo th\u1eddi gian. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi nh\u01b0 sau<\/p>\n<p><strong>C\u00e2u 20.<\/strong> Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng  ABCD.A\u2019B\u2019C\u2019D\u2019  c\u00f3 c\u1ea1nh b\u1eb1ng 4. T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng  AB\u2019  v\u00e0  CD\u2019 .<\/p>\n<p><strong>C\u00e2u 21.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABCD  c\u00f3 \u0111\u00e1y  ABCD  l\u00e0 h\u00ecnh vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng  a\u221a2  v\u00e0  SA  vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng  (ABCD) . G\u1ecdi  \u03b1  l\u00e0 g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng  (SBD)  v\u00e0  (ABCD) . Khi  tan \u03b1 = \u221a2 , h\u00e3y t\u00ednh g\u00f3c gi\u1eefa  (SAC)  v\u00e0  (SBC)  (\u0111\u01a1n v\u1ecb: \u0111\u1ed9).<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o l\u00e0 t\u00e0i li\u1ec7u <strong>\u0111\u1ec1 to\u00e1n gi\u1eefa k\u00ec 2 l\u1edbp 11<\/strong> kh\u00f4ng th\u1ec3 thi\u1ebfu gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp to\u00e0n di\u1ec7n, n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m b\u00e0i hi\u1ec7u qu\u1ea3. H\u00e3y b\u1ea5m v\u00e0o \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 t\u1ea3i tr\u1ecdn b\u1ed9 t\u00e0i li\u1ec7u nh\u00e9!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1DWEmjUHcctWrgnbTMzEeB8Hyp_UFEqgY\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1DWEmjUHcctWrgnbTMzEeB8Hyp_UFEqgY\/view\" rel=\"nofollow noopener\" target=\"_blank\">M\u1edf t\u00e0i li\u1ec7u n\u1ebfu khung xem tr\u01b0\u1edbc kh\u00f4ng hi\u1ec3n th\u1ecb<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1DWEmjUHcctWrgnbTMzEeB8Hyp_UFEqgY\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 Ch\u00e2n Tr\u1eddi S\u00e1ng T\u1ea1o n\u0103m h\u1ecdc 2024 \u2013 2025 c\u1ee7a \u0111\u1ed9i ng\u0169 To\u00e1n T\u1eeb T\u00e2m mang \u0111\u1ebfn c\u01a1 h\u1ed9i r\u00e8n luy\u1ec7n to\u00e0n di\u1ec7n cho h\u1ecdc sinh l\u1edbp 11. V\u1edbi n\u1ed9i dung b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh, t\u00e0i li\u1ec7u gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u00e0 chu\u1ea9n [&#8230;]\n","protected":false},"author":1,"featured_media":1565,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[71,61],"class_list":["post-366","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tong-hop","tag-toan-tu-tam","tag-tong-hop"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/366","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=366"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/366\/revisions"}],"predecessor-version":[{"id":1566,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/366\/revisions\/1566"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1565"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}