{"id":328,"date":"2026-05-05T04:39:52","date_gmt":"2026-05-05T04:39:52","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-kiem-tra-giua-hoc-ky-2-mon-toan-12-nam-hoc-2024-2025\/"},"modified":"2026-05-05T07:12:35","modified_gmt":"2026-05-05T07:12:35","slug":"bo-de-kiem-tra-giua-hoc-ky-2-mon-toan-12-nam-hoc-2024-2025","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-kiem-tra-giua-hoc-ky-2-mon-toan-12-nam-hoc-2024-2025\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025"},"content":{"rendered":"<p><strong>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> l\u00e0 t\u1eadp t\u00e0i li\u1ec7u g\u1ed3m 38 trang \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u1edfi t\u00e1c gi\u1ea3 To\u00e1n T\u1eeb T\u00e2m. N\u1ed9i dung b\u00e1m s\u00e1t v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 12, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng, t\u01b0 duy gi\u1ea3i \u0111\u1ec1 t\u1ed1t. H\u00e3y c\u00f9ng <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i Li\u1ec7u \u00d4n Thi<\/a> <\/strong>t\u00ecm hi\u1ec3u 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 h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p><strong>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> c\u00f3 t\u1ea5t c\u1ea3 10 \u0111\u1ec1 \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac \u0111\u1ecbnh d\u1ea1ng tr\u1eafc nghi\u1ec7m m\u1edbi nh\u1ea5t, v\u1edbi n\u1ed9i dung g\u1ed3m 04 ph\u1ea7n nh\u01b0 sau:<\/p>\n<p><span><strong>Ph\u1ea7n A \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 3 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tham kh\u1ea3o sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 4.<\/strong> X\u00e1c \u0111\u1ecbnh t\u00e2m  I  v\u00e0 b\u00e1n k\u00ednh  R  c\u1ee7a m\u1eb7t c\u1ea7u  (S) :  (x &#8211; 1)\u00b2 + (y &#8211; 4)\u00b2 + (z + 2)\u00b2 = 9.\n<\/p>\n<p>A.  I(1;4;-2), R = 3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  I(-1;-4;2), R = 3 <\/p>\n<p>C.  I(1;4;-2), R = 9 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  I(-1;-4;2), R = 9 <\/p>\n<p><strong>C\u00e2u 5.<\/strong> Qu\u00e3ng \u0111\u01b0\u1eddng v\u1eadt c\u00f3 v\u1eadn t\u1ed1c  v(t) = 3t\u00b2 + 5  (m\/s) t\u1eeb  t = 4  \u0111\u1ebfn  t = 10  l\u00e0:<\/p>\n<p>A. 669 m\u00a0 \u00a0 \u00a0 \u00a0 B. 696 m\u00a0 \u00a0 \u00a0 \u00a0 C. 699 m\u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 966 m<\/p>\n<p><strong>C\u00e2u 6<\/strong>. Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng  (P): x + y + z &#8211; 1 = 0  l\u00e0:<\/p>\n<p>A.  (-1;1;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (1;-1;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  (1;1;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  (1;1;-1) <\/p>\n<p><span><strong>Ph\u1ea7n B \u2013 C\u00e2u h\u1ecfi \u0111\u00fang sai ( 2 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>Trong kh\u00f4ng gian  Oxyz , cho \u0111i\u1ec3m  I(1;2;3)  v\u00e0 m\u1eb7t ph\u1eb3ng  (\u03b1): 2x + 2y &#8211; z + 6 = 0 . X\u00e9t c\u00e1c m\u1ec7nh \u0111\u1ec1:<\/p>\n<p>(a)  I notin (\u03b1) .<\/p>\n<p>(b)  d(I, \u03b1) = 3 .<\/p>\n<p>(c) M\u1eb7t c\u1ea7u t\u00e2m  I , b\u00e1n k\u00ednh  R = 5 , c\u1eaft  \u03b1  theo \u0111\u01b0\u1eddng tr\u00f2n b\u00e1n k\u00ednh  r = 4 .<\/p>\n<p>(d) N\u1ebfu \u0111\u01b0\u1eddng th\u1eb3ng trong  \u03b1  c\u1eaft m\u1eb7t c\u1ea7u theo d\u00e2y cung  AB , th\u00ec di\u1ec7n t\u00edch  triangle IAB  l\u1edbn nh\u1ea5t khi  tan \u03c6 = (\u221a14)\/(6) .<\/p>\n<p><span><strong>Ph\u1ea7n C \u2013 C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn ( 2 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>H\u1ecdc sinh ph\u1ea3i \u0111\u1ecdc k\u0129 \u0111\u1ec1 v\u00e0 tr\u1ea3 l\u1eddi c\u00e1c c\u00e2u h\u1ecfi sau b\u1eb1ng d\u1ea1ng tr\u1ea3 l\u1eddi ng\u1eafn:<\/p>\n<p><strong>C\u00e2u 17<\/strong>. Trong kh\u00f4ng gian  Oxyz , cho hai m\u1eb7t ph\u1eb3ng  (P): x + 4y &#8211; 2z &#8211; 6 = 0, (Q): x &#8211; 2y + 4z &#8211; 6 = 0.<br \/>\nM\u1eb7t ph\u1eb3ng  (\u03b1)  ch\u1ee9a giao tuy\u1ebfn c\u1ee7a  (P), (Q)  v\u00e0 c\u1eaft c\u00e1c tr\u1ee5c t\u1ecda \u0111\u1ed9 t\u1ea1i c\u00e1c \u0111i\u1ec3m  A, B, C  sao cho h\u00ecnh ch\u00f3p  O.ABC  l\u00e0 h\u00ecnh ch\u00f3p \u0111\u1ec1u. Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng  (\u03b1)  c\u00f3 d\u1ea1ng:  x + my + nz + p = 0. T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a  T = m &#8211; 3n &#8211; 5p.\n<\/p>\n<p><span><strong>Ph\u1ea7n D \u2013 C\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn ( 3 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>C\u00f3 3 c\u00e2u h\u1ecfi v\u1edbi d\u1ea1ng tr\u1ea3 l\u1eddi t\u1ef1 lu\u1eadn, h\u1ecdc sinh t\u1ef1 l\u1eadp lu\u1eadn v\u00e0 \u0111\u01b0a ra ph\u01b0\u01a1ng \u00e1n cu\u1ed1i c\u00f9ng. B\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi d\u1ea1ng t\u01b0\u01a1ng t\u1ef1 sau:<\/p>\n<p><strong>C\u00e2u 19.<\/strong> Trong kh\u00f4ng gian  Oxyz , cho \u0111i\u1ec3m  M(3;1;-2)  v\u00e0 m\u1eb7t ph\u1eb3ng  (P): 3x + 5y &#8211; z + 1 = 0. Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua  M  v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi  (P) .<\/p>\n<p><strong>C\u00e2u 20.<\/strong> Bi\u1ebft r\u1eb1ng  int\u2083\u2074 (3x+2)\/(x\u00b2 &#8211; 3x + 2) dx = mln 3 + nln 2, v\u1edbi m, n in mathbbZ. Gi\u00e1 tr\u1ecb c\u1ee7a  m + n + 2025  b\u1eb1ng bao nhi\u00eau?<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p>\u0110\u1ec3 gi\u00fap c\u00e1c b\u1ea1n h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c m\u1ed9t l\u1ea7n n\u1eefa v\u00e0 l\u00e0m quen v\u1edbi c\u00e1c d\u1ea1ng \u0111\u1ec1 c\u00f3 trong b\u00e0i. T\u1ea3i ngay <strong>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y. \u0110\u1eebng qu\u00ean luy\u1ec7n t\u1eadp m\u1ed7i ng\u00e0y th\u1eadt k\u1ef9 \u0111\u1ec3 \u0111\u1ea1t k\u1ebft qu\u1ea3 t\u1ed1t nh\u1ea5t!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1NYLbOpwiXFnzNkPMj5Iix_XPSw6ewF5F\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1NYLbOpwiXFnzNkPMj5Iix_XPSw6ewF5F\/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><strong><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1NYLbOpwiXFnzNkPMj5Iix_XPSw6ewF5F\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 To\u00e1n T\u1eeb T\u00e2m<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 l\u00e0 t\u1eadp t\u00e0i li\u1ec7u g\u1ed3m 38 trang \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u1edfi t\u00e1c gi\u1ea3 To\u00e1n T\u1eeb T\u00e2m. N\u1ed9i dung b\u00e1m s\u00e1t v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 12, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng, t\u01b0 duy gi\u1ea3i \u0111\u1ec1 t\u1ed1t. H\u00e3y c\u00f9ng [&#8230;]\n","protected":false},"author":1,"featured_media":1527,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[71,61],"class_list":["post-328","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\/328","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=328"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/328\/revisions"}],"predecessor-version":[{"id":1528,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/328\/revisions\/1528"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1527"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}