{"id":362,"date":"2026-05-05T04:41:42","date_gmt":"2026-05-05T04:41:42","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-kiem-tra-giua-ky-2-toan-11-ket-noi-tri-thuc-nam-hoc-2024-2025\/"},"modified":"2026-05-05T07:14:26","modified_gmt":"2026-05-05T07:14:26","slug":"bo-de-kiem-tra-giua-ky-2-toan-11-ket-noi-tri-thuc-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-ket-noi-tri-thuc-nam-hoc-2024-2025\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 k\u1ebft n\u1ed1i tri th\u1ee9c n\u0103m h\u1ecdc 2024 \u2013 2025"},"content":{"rendered":"<p>\u00d4n t\u1eadp gi\u1eefa k\u1ef3 2 m\u00f4n To\u00e1n 11 K\u1ebft n\u1ed1i tri th\u1ee9c d\u1ec5 d\u00e0ng h\u01a1n v\u1edbi <strong>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 K\u1ebft n\u1ed1i tri th\u1ee9c n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> c\u1ee7a \u0111\u1ed9i ng\u0169 To\u00e1n T\u1eeb T\u00e2m bi\u00ean so\u1ea1n. 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 l\u00e0m quen v\u1edbi d\u1ea1ng \u0111\u1ec1 thi chu\u1ea9n. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>Tailieuonthi<\/strong><\/a> kh\u00e1m ph\u00e1 xem b\u1ed9 t\u00e0i li\u1ec7u n\u00e0y c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 k\u1ebft n\u1ed1i tri th\u1ee9c 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 k\u1ebft n\u1ed1i tri th\u1ee9c n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> n\u1eb1m trong b\u1ed9 \u0111\u1ec1 thi gi\u1eefa k\u00ec 2 to\u00e1n 11 bao g\u1ed3m 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 d\u00e0nh cho h\u1ecdc sinh l\u1edbp 11, \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo ch\u01b0\u01a1ng tr\u00ecnh K\u1ebft n\u1ed1i tri th\u1ee9c v\u1edbi cu\u1ed9c s\u1ed1ng. M\u1ed7i \u0111\u1ec1 g\u1ed3m 4 ph\u1ea7n ch\u00ednh, t\u1ed5ng c\u1ed9ng 21 c\u00e2u h\u1ecfi, v\u1edbi \u0111i\u1ec3m s\u1ed1 ph\u00e2n b\u1ed5 nh\u01b0 sau:<\/p>\n<p><strong>Ph\u1ea7n A. G\u1ed3m 12 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m (03 \u0111i\u1ec3m).<\/strong><\/p>\n<p>M\u1ed7i c\u00e2u c\u00f3 4 ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (A, B, C, D). N\u1ed9i dung bao g\u1ed3m: h\u00e0m s\u1ed1 m\u0169 v\u00e0 logarit, th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p, kh\u1ed1i l\u0103ng tr\u1ee5, ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u0169, logarit, h\u00ecnh h\u1ecdc kh\u00f4ng gian. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0111\u1ec1<\/p>\n<p><strong>C\u00e2u 1.<\/strong> V\u1edbi  a  l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd,  \u221a[3]a\u00b2  b\u1eb1ng: A.  a^1\/6 . B.  a\u2076 . C.  a^2\/3 . D.  a^3\/2 <\/p>\n<p><strong>C\u00e2u 2.<\/strong> T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1  y = (x-1)^5\/3  l\u00e0: A.  mathbbR setminus 1 . B.  mathbbR . C.  (1;+\u221e) . D.  (-1;+\u221e) <\/p>\n<p><strong>Ph\u1ea7n B. G\u1ed3m 2 C\u00e2u h\u1ecfi \u0111\u00fang\/sai (02 \u0111i\u1ec3m).<\/strong><\/p>\n<p>M\u1ed7i c\u00e2u c\u00f3 4 ph\u00e1t bi\u1ec3u, y\u00eau c\u1ea7u h\u1ecdc sinh \u0111\u00e1nh d\u1ea5u \u0110\u00fang ho\u1eb7c Sai. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0111\u1ec1<\/p>\n<p><strong>C\u00e2u 13.<\/strong> Cho ph\u01b0\u01a1ng tr\u00ecnh:  9^x &#8211; 13.6^x + 4^x+1 = 0 . X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<br \/>\n(a) N\u1ebfu \u0111\u1eb7t  (3\/2)^x = t  th\u00ec ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho tr\u1edf th\u00e0nh:  9t\u00b2 &#8211; 13t + 4 = 0<br \/>\n(b) Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 hai nghi\u1ec7m, trong \u0111\u00f3 c\u00f3 m\u1ed9t nghi\u1ec7m nguy\u00ean \u00e2m.<br \/>\n(c) T\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho b\u1eb1ng 0.<br \/>\n(d) Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 hai nghi\u1ec7m v\u00e0 \u0111\u1ec1u l\u00e0 nghi\u1ec7m nguy\u00ean d\u01b0\u01a1ng.<\/p>\n<p><strong>C\u00e2u 14.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABC  c\u00f3 \u0111\u00e1y  ABC  l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh  a . Bi\u1ebft  SA = a\u221a2  v\u00e0  SA  vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y. G\u1ecdi  M  l\u00e0 trung \u0111i\u1ec3m c\u1ee7a  BC  v\u00e0  H  l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a  A  l\u00ean  SM . X\u00e9t c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<br \/>\n(a) \u0110\u01b0\u1eddng th\u1eb3ng  AH  vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng  (SBC) .<br \/>\n(b) \u0110\u01b0\u1eddng th\u1eb3ng  SH  l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng  SA  l\u00ean m\u1eb7t ph\u1eb3ng  (SBC) .<br \/>\n(c) \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng  AH  b\u1eb1ng  6a\/11 .<br \/>\n(d) Cosin g\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng  SA  v\u00e0 m\u1eb7t ph\u1eb3ng  (SBC)  b\u1eb1ng  (\u221a11)\/(33) .<\/p>\n<p><strong>Ph\u1ea7n C. G\u1ed3m 4 C\u00e2u h\u1ecfi \u0111i\u1ec1n \u0111\u00e1p s\u1ed1 ng\u1eafn (02 \u0111i\u1ec3m).<\/strong><\/p>\n<p>N\u1ed9i dung bao g\u1ed3m: t\u00ednh to\u00e1n logarit, t\u00ecm nghi\u1ec7m b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, \u1ee9ng d\u1ee5ng to\u00e1n h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf (b\u00e0i to\u00e1n l\u00e3i su\u1ea5t ng\u00e2n h\u00e0ng, d\u00e2n s\u1ed1\u2026). D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0111\u1ec1<\/p>\n<p><strong>C\u00e2u 15.<\/strong> Cho hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng  a  v\u00e0  b  th\u1ecfa m\u00e3n:  log\u2082 (ab) = 4  v\u1edbi  b &gt; 1 &gt; a &gt; 0 . H\u1ecfi gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c:  log\u2088 (ab\u00b2)  t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng bao nhi\u00eau?<\/p>\n<p><strong>C\u00e2u 16.<\/strong> T\u00ednh t\u1ed5ng c\u00e1c gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1  m  thu\u1ed9c \u0111o\u1ea1n  [0;5]  \u0111\u1ec3 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh:  log\u2082 (5^x -1) \u2264 m  c\u00f3 nghi\u1ec7m  x \u2265 1 .<\/p>\n<p><strong>Ph\u1ea7n D. G\u1ed3m 3 C\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn (03 \u0111i\u1ec3m).<\/strong><\/p>\n<p>N\u1ed9i dung bao g\u1ed3m: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh logarit, t\u00ednh th\u1ec3 t\u00edch h\u00ecnh h\u1ecdc kh\u00f4ng gian, b\u00e0i to\u00e1n th\u1ef1c t\u1ebf li\u00ean quan \u0111\u1ebfn m\u00f4 h\u00ecnh t\u0103ng tr\u01b0\u1edfng. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0111\u1ec1<\/p>\n<p><strong>C\u00e2u 20.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABCD  c\u00f3 \u0111\u00e1y  ABCD  l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt,  AB = 1, AD = 2\u221a3 . C\u1ea1nh b\u00ean  SA  vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y, bi\u1ebft tam gi\u00e1c  SAD  c\u00f3 di\u1ec7n t\u00edch  S = 3 . T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb  C  \u0111\u1ebfn m\u1eb7t ph\u1eb3ng  (SBD) .<\/p>\n<p><strong>C\u00e2u 21.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABCD  c\u00f3 \u0111\u00e1y  ABCD  l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt,  AB = 1, AD = \u221a3 , tam gi\u00e1c  SAB  c\u00e2n t\u1ea1i  S  v\u00e0 n\u1eb1m trong m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y. Kho\u1ea3ng c\u00e1ch gi\u1eefa  AB  v\u00e0  SC  b\u1eb1ng  3\/2 . T\u00ednh th\u1ec3 t\u00edch  V  c\u1ee7a kh\u1ed1i ch\u00f3p  S.ABCD  (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 k\u1ebft n\u1ed1i tri th\u1ee9c 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 K\u1ebft n\u1ed1i tri th\u1ee9c n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> kh\u00f4ng ch\u1ec9 gi\u00fap b\u1ea1n l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi m\u00e0 c\u00f2n r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i nhanh ch\u00f3ng, ch\u00ednh x\u00e1c. T\u00e0i li\u1ec7u n\u00e0y s\u1ebd l\u00e0 b\u00ed k\u00edp gi\u00fap b\u1ea1n chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao. H\u00e3y t\u1ea3i ngay t\u00e0i li\u1ec7u theo \u0111\u01b0\u1eddng d\u1eabn b\u00ean d\u01b0\u1edbi \u0111\u1ec3 c\u00f3 trong tay b\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ch\u1ea5t l\u01b0\u1ee3ng nh\u1ea5t!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1jmEOZ_nVk2CPRQCkXSqRwt-vq0aHNlGU\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1jmEOZ_nVk2CPRQCkXSqRwt-vq0aHNlGU\/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\/1jmEOZ_nVk2CPRQCkXSqRwt-vq0aHNlGU\/view\" rel=\"noopener nofollow\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 K\u1ebft n\u1ed1i tri th\u1ee9c n\u0103m h\u1ecdc 2024 \u2013 2025<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00d4n t\u1eadp gi\u1eefa k\u1ef3 2 m\u00f4n To\u00e1n 11 K\u1ebft n\u1ed1i tri th\u1ee9c d\u1ec5 d\u00e0ng h\u01a1n v\u1edbi B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 K\u1ebft n\u1ed1i tri th\u1ee9c n\u0103m h\u1ecdc 2024 \u2013 2025 c\u1ee7a \u0111\u1ed9i ng\u0169 To\u00e1n T\u1eeb T\u00e2m bi\u00ean so\u1ea1n. 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 [&#8230;]\n","protected":false},"author":1,"featured_media":1561,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[71,61],"class_list":["post-362","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\/362","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=362"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/362\/revisions"}],"predecessor-version":[{"id":1562,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/362\/revisions\/1562"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1561"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}