{"id":364,"date":"2026-05-05T04:41:49","date_gmt":"2026-05-05T04:41:49","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-kiem-tra-giua-ky-2-toan-11-canh-dieu-nam-hoc-2024-2025\/"},"modified":"2026-05-05T07:14:33","modified_gmt":"2026-05-05T07:14:33","slug":"bo-de-kiem-tra-giua-ky-2-toan-11-canh-dieu-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-canh-dieu-nam-hoc-2024-2025\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 C\u00e1nh Di\u1ec1u 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 C\u00e1nh Di\u1ec1u n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> c\u1ee7a \u0111\u1ed9i ng\u0169 To\u00e1n T\u1eeb T\u00e2m l\u00e0 t\u00e0i li\u1ec7u luy\u1ec7n t\u1eadp to\u00e0n di\u1ec7n d\u00e0nh cho h\u1ecdc sinh l\u1edbp 11. V\u1edbi h\u1ec7 th\u1ed1ng c\u00e2u h\u1ecfi \u0111a d\u1ea1ng t\u1eeb tr\u1eafc nghi\u1ec7m \u0111\u1ebfn t\u1ef1 lu\u1eadn, \u0111\u00e2y ch\u00ednh l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch \u0111\u1ec3 c\u00e1c b\u1ea1n t\u1ef1 tin chinh ph\u1ee5c k\u1ef3 thi. H\u00e3y 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 b\u1ed9 t\u00e0i li\u1ec7u 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 C\u00e1nh Di\u1ec1u n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p><strong>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 m\u00f4n To\u00e1n l\u1edbp 11 C\u00e1nh Di\u1ec1u n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> bao g\u1ed3m 10 \u0111\u1ec1 ki\u1ec3m tra. M\u1ed7i \u0111\u1ec1 g\u1ed3m 21 c\u00e2u v\u00e0 \u0111\u01b0\u1ee3c chia th\u00e0nh c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u1ea5u tr\u00fac \u0111\u1ec1 v\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng c\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p c\u1ee7a \u0111\u1ec1 <strong>ki\u1ec3m tra to\u00e1n l\u1edbp 11 gi\u1eefa h\u1ecdc k\u00ec 2<\/strong><\/p>\n<p><strong>Ph\u1ea7n A. C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m (3 \u0111i\u1ec3m):<\/strong> Kho\u1ea3ng 12 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m v\u1ec1 c\u00e1c ch\u1ee7 \u0111\u1ec1 nh\u01b0 l\u0169y th\u1eeba, logarit, h\u00ecnh h\u1ecdc kh\u00f4ng gian, t\u1ed5 h\u1ee3p x\u00e1c su\u1ea5t\u2026 M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 d\u01b0\u1edbi \u0111\u00e2y<\/p>\n<p><strong>C\u00e2u 1.<\/strong> V\u1edbi  a  l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, gi\u00e1 tr\u1ecb c\u1ee7a  \u221a[4]a\u2075  b\u1eb1ng:  A. a^5\/4 B. a^4\/5 C. a\u00b2\u2070 D. a^5\/2\n<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho  a &gt; 0  th\u1ecfa m\u00e3n  log a = 7 . Gi\u00e1 tr\u1ecb c\u1ee7a  log(100a)  b\u1eb1ng:  A. 9 B. 700 C. 14 D. 7\n<\/p>\n<p><strong>Ph\u1ea7n B. C\u00e2u h\u1ecfi \u0111\u00fang\/sai (2 \u0111i\u1ec3m):<\/strong> H\u1ecdc sinh c\u1ea7n x\u00e1c \u0111\u1ecbnh c\u00e1c m\u1ec7nh \u0111\u1ec1 \u0111\u00fang ho\u1eb7c sai. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0111\u1ec1 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> Kh\u1ea3o s\u00e1t th\u1eddi gian t\u1eadp th\u1ec3 d\u1ee5c trong ng\u00e0y c\u1ee7a m\u1ed9t s\u1ed1 h\u1ecdc sinh kh\u1ed1i 11 thu \u0111\u01b0\u1ee3c m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m sau<\/p>\n<p>(a) T\u1ed5ng s\u1ed1 h\u1ecdc sinh \u0111\u01b0\u1ee3c kh\u1ea3o s\u00e1t l\u00e0  42  h\u1ecdc sinh.<\/p>\n<p>(b) Gi\u00e1 tr\u1ecb \u0111\u1ea1i di\u1ec7n c\u1ee7a nh\u00f3m  [20;40]  l\u00e0  25 .<\/p>\n<p>(c) S\u1ed1 trung b\u00ecnh c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u tr\u00ean thu\u1ed9c nh\u00f3m  [0;20] .<\/p>\n<p>(d) C\u00f3  16  h\u1ecdc sinh t\u1eadp th\u1ec3 d\u1ee5c \u00edt nh\u1ea5t  1  gi\u1edd trong ng\u00e0y.<\/p>\n<p><strong>Ph\u1ea7n C. C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn (2 \u0111i\u1ec3m):<\/strong> D\u1ea1ng b\u00e0i t\u1eadp ng\u1eafn y\u00eau c\u1ea7u t\u00ednh to\u00e1n ho\u1eb7c \u0111i\u1ec1n \u0111\u00e1p \u00e1n. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 sau<\/p>\n<p><strong>C\u00e2u 15.<\/strong> Cho  a, b, c  l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c kh\u00e1c 0 th\u1ecfa m\u00e3n  4^a = 25^b = 10^c . T\u00ednh:  T = c\/a + c\/b\n<\/p>\n<p><strong>C\u00e2u 16.<\/strong> Hai x\u1ea1 th\u1ee7 c\u00f9ng b\u1eafn v\u00e0o bia m\u1ed9t c\u00e1ch \u0111\u1ed9c l\u1eadp v\u1edbi nhau. X\u00e1c su\u1ea5t b\u1eafn tr\u00fang bia c\u1ee7a x\u1ea1 th\u1ee7 th\u1ee9 nh\u1ea5t b\u1eb1ng  1\/2 , x\u00e1c su\u1ea5t b\u1eafn tr\u00fang bia c\u1ee7a x\u1ea1 th\u1ee7 th\u1ee9 hai b\u1eb1ng  1\/3 . T\u00ednh x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1: \u201cX\u1ea1 th\u1ee7 th\u1ee9 nh\u1ea5t b\u1eafn tr\u00fang bia, x\u1ea1 th\u1ee7 th\u1ee9 hai b\u1eafn tr\u1eadt bia\u201d. (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi)<\/p>\n<p><strong>Ph\u1ea7n D. C\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn (3 \u0111i\u1ec3m):<\/strong> C\u00e1c b\u00e0i to\u00e1n n\u00e2ng cao y\u00eau c\u1ea7u gi\u1ea3i chi ti\u1ebft. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda tr\u00edch t\u1eeb \u0111\u1ec1 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 C\u00e1nh Di\u1ec1u 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 C\u00e1nh Di\u1ec1u n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch gi\u00fap l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi v\u00e0 c\u1ea3i thi\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i t\u1eadp m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3. V\u1edbi h\u1ec7 th\u1ed1ng c\u00e2u h\u1ecfi \u0111a d\u1ea1ng t\u1eeb tr\u1eafc nghi\u1ec7m \u0111\u1ebfn t\u1ef1 lu\u1eadn, t\u00e0i li\u1ec7u n\u00e0y s\u1ebd gi\u00fap b\u1ea1n t\u1ef1 tin h\u01a1n tr\u01b0\u1edbc k\u1ef3 thi quan tr\u1ecdng. Click ngay v\u00e0o \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 t\u1ea3i to\u00e0n b\u1ed9 \u0111\u1ec1 thi!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1-EU_M7_WIJAnfrx7D-pSy2QBNavB7zGD\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1-EU_M7_WIJAnfrx7D-pSy2QBNavB7zGD\/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\/1-EU_M7_WIJAnfrx7D-pSy2QBNavB7zGD\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 11 C\u00e1nh Di\u1ec1u 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 C\u00e1nh Di\u1ec1u n\u0103m h\u1ecdc 2024 \u2013 2025 c\u1ee7a \u0111\u1ed9i ng\u0169 To\u00e1n T\u1eeb T\u00e2m l\u00e0 t\u00e0i li\u1ec7u luy\u1ec7n t\u1eadp to\u00e0n di\u1ec7n d\u00e0nh cho h\u1ecdc sinh l\u1edbp 11. V\u1edbi h\u1ec7 th\u1ed1ng c\u00e2u h\u1ecfi \u0111a d\u1ea1ng t\u1eeb tr\u1eafc nghi\u1ec7m \u0111\u1ebfn t\u1ef1 lu\u1eadn, \u0111\u00e2y ch\u00ednh l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch [&#8230;]\n","protected":false},"author":1,"featured_media":1563,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[71,61],"class_list":["post-364","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\/364","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=364"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/364\/revisions"}],"predecessor-version":[{"id":1564,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/364\/revisions\/1564"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1563"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}