{"id":384,"date":"2026-05-05T04:42:55","date_gmt":"2026-05-05T04:42:55","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/05-de-thi-thu-giua-hoc-ki-2-mon-toan-12-nam-hoc-2024-2025-co-dap-an\/"},"modified":"2026-05-05T07:15:39","modified_gmt":"2026-05-05T07:15:39","slug":"05-de-thi-thu-giua-hoc-ki-2-mon-toan-12-nam-hoc-2024-2025-co-dap-an","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/05-de-thi-thu-giua-hoc-ki-2-mon-toan-12-nam-hoc-2024-2025-co-dap-an\/","title":{"rendered":"05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 c\u00f3 \u0111\u00e1p \u00e1n"},"content":{"rendered":"<p><strong>B\u1ed9 t\u00e0i li\u1ec7u 05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> \u0111\u01b0\u1ee3c th\u1ea7y gi\u00e1o <strong>Chu Ho\u00e0ng Minh<\/strong> t\u1ed5ng h\u1ee3p theo c\u1ea5u tr\u00fac \u0111\u1ec1 thi To\u00e1n m\u1edbi v\u1edbi 5 b\u1ed9 \u0111\u1ec1 kh\u00e1 chi ti\u1ebft. N\u1ed9i dung chi ti\u1ebft v\u00e0 b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc k\u00e8m \u0111\u00e1p \u00e1n \u0111\u1ea7y \u0111\u1ee7, ch\u1eafc h\u1eb3n b\u1ed9 t\u00e0i li\u1ec7u thi th\u1eed n\u00e0y v\u00f4 c\u00f9ng h\u1eefu \u00edch gi\u00fap h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3, n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i v\u00e0 t\u1ef1 tin tr\u01b0\u1edbc k\u1ef3 thi gi\u1eefa h\u1ecdc k\u00ec 2. C\u00f9ng <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">\u00d4n Thi<\/a><\/strong> t\u00ecm hi\u1ec3u n\u1ed9i dung c\u1ee7a 05 \u0111\u1ec1 n\u00e0y qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung 05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p><strong>N\u1ed9i dung 05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n ph\u00f9 h\u1ee3p v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi hi\u1ec7n h\u00e0nh, g\u1ed3m 12 c\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn + 04 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai + 06 c\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn, h\u1ecdc sinh l\u00e0m b\u00e0i trong th\u1eddi gian l\u00e0m b\u00e0i 90 ph\u00fat. C\u00f9ng xem qua n\u1ed9i dung c\u1ee7a 05 \u0111\u1ec1 thi th\u1eed n\u00e0y ngay sau \u0111\u00e2y nh\u00e9<\/p>\n<p><span><strong>Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m g\u1ed3m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/span><\/p>\n<p>\u2013 C\u00f3 12 c\u00e2u tr\u1eafc nghi\u1ec7m v\u1edbi 4 \u0111\u00e1p \u00e1n l\u1ef1a ch\u1ecdn, h\u1ecdc sinh n\u00ean n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m \u0111\u1ec3 l\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t nh\u00e9. C\u00f9ng xem qua c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp trong <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-giua-ki-2-toan-12\/\" target=\"_blank\" rel=\"noopener\">\u0111\u1ec1 thi gi\u1eefa k\u1ef3 2 to\u00e1n12<\/a> sau \u0111\u00e2y nh\u00e9!<\/p>\n<p><strong>C\u00e2u 1:<\/strong> H\u1ecd t\u1ea5t c\u1ea3 c\u00e1c nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = 2x + 4 l\u00e0<\/p>\n<p>A.  2x\u00b2 + 4x + C \u00a0 \u00a0 \u00a0B.  x\u00b2 + 4x + C \u00a0 \u00a0 \u00a0 C.  x\u00b2 + C \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  2x\u00b2 + C <\/p>\n<p><strong>C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9  Oxyz , cho m\u1eb7t ph\u1eb3ng  (P) : 2x &#8211; 4y + 6z &#8211; 9 = 0 . Vector n\u00e0o sau \u0111\u00e2y l\u00e0 vector ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng?<\/p>\n<p>A.  mathbfn = (2;6;9) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  mathbfn = (2;-4;9) <\/p>\n<p>C.  mathbfn = (1;2;3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  mathbfn = (1;-2;3) <\/p>\n<p><span><strong>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/span><\/p>\n<p>\u2013 C\u00e1c b\u1ea1n h\u1ecdc sinh 12 c\u00f3 th\u1ec3 b\u1eaft tay v\u00e0o th\u1eed s\u1ee9c ngay v\u1edbi d\u1ea1ng b\u00e0i t\u1eadp \u1edf ph\u1ea7n n\u00e0y sau \u0111\u00e2y nh\u00e9:<\/p>\n<p><strong>C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1  f(x), g(x)  li\u00ean t\u1ee5c tr\u00ean  mathbbR . X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau:<\/p>\n<p>a) N\u1ebfu int\u2081\u00b3 f(x)dx = 5 v\u00e0 int\u2081\u00b2 g(x)dx = -1\/2 th\u00ec int\u2081\u00b2 [f(x) &#8211; g(x)]dx = 11\/2.\n<\/p>\n<p>b) N\u1ebfu int\u2081\u00b3 [g(x) + 2x +3]dx = 10 th\u00ec int\u2081\u00b3 g(x)dx = 3.\n<\/p>\n<p>c) N\u1ebfu  f(x) = e^3x ,  F(0) = 1\/3  th\u00ec F(1\/3) = e.\n<\/p>\n<p>d) N\u1ebfu  f(x) = 2x +1 ,  g(x) = x  th\u00ec int\u2081\u2075 (f(x))\/(g(x))dx = a + b ln b. Khi \u0111\u00f3  a + 3b = 11 .<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9  Oxyz , cho ba \u0111i\u1ec3m  A(1;2;-2) ,  B(2;1;2) ,  C(3;-2;1) . X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau:<\/p>\n<p>a) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng  (P)  \u0111i qua ba \u0111i\u1ec3m  A,B,C  c\u00f3 m\u1ed9t vector ph\u00e1p tuy\u1ebfn l\u00e0 mathbfn = [AB\u20d7, AC\u20d7].\n<\/p>\n<p>b) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng  (P)  l\u00e0 13x + 5y &#8211; 2z + 27 = 0.\n<\/p>\n<p>c) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua \u0111i\u1ec3m  A(1;2;-2)  v\u00e0 nh\u1eadn  BC\u20d7  l\u00e0m vect\u01a1 ph\u00e1p tuy\u1ebfn c\u00f3 d\u1ea1ng: (x-1) &#8211; 3(y-2) -1(z+2) = 0.\n<\/p>\n<p>d) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua ba \u0111i\u1ec3m  E,F,K  l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a  A  l\u00ean tr\u1ee5c  Ox,Oy,Oz  c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x\/1 + y\/2 = z\/2.\n<\/p>\n<p><span><strong>Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n<p>M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi d\u1ea1ng tr\u1ea3 l\u1eddi ng\u1eafn trong \u0111\u1ec1 nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1:<\/strong> Ng\u01b0\u1eddi ta truy\u1ec1n nhi\u1ec7t cho m\u1ed9t b\u00ecnh nu\u00f4i c\u1ea5y vi sinh v\u1eadt t\u1eeb  1^\u00b0 C . T\u1ed1c \u0111\u1ed9 t\u0103ng nhi\u1ec7t \u0111\u1ed9 c\u1ee7a b\u00ecnh t\u1ea1i th\u1eddi \u0111i\u1ec3m  t  ph\u00fat  (0 \u2264 t \u2264 5)  \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1  f(t) = 3t\u00b2  ( ^\u00b0 C \/ph\u00fat). Bi\u1ebft r\u1eb1ng nhi\u1ec7t \u0111\u1ed9 c\u1ee7a b\u00ecnh \u0111o t\u1ea1i th\u1eddi \u0111i\u1ec3m  t  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(t) . T\u00ecm nhi\u1ec7t \u0111\u1ed9 c\u1ee7a b\u00ecnh t\u1ea1i th\u1eddi \u0111i\u1ec3m 3 ph\u00fat k\u1ec3 t\u1eeb khi truy\u1ec1n nhi\u1ec7t.<\/p>\n<p><strong>C\u00e2u 2:<\/strong> M\u1ed9t ng\u01b0\u1eddi \u0111ang l\u00e1i xe \u00f4 t\u00f4 v\u1edbi v\u1eadn t\u1ed1c  24  (m\/s) th\u00ec ng\u01b0\u1eddi l\u00e1i ph\u00e1t hi\u1ec7n ph\u00eda tr\u01b0\u1edbc c\u00f3 ch\u01b0\u1edbng ng\u1ea1i v\u1eadt n\u00ean c\u1ea7n gi\u1ea3m t\u1ed1c \u0111\u1ed9 c\u1ee7a xe. Sau khi \u0111\u1ea1p phanh, \u00f4 t\u00f4 chuy\u1ec3n \u0111\u1ed9ng ch\u1eadm d\u1ea7n \u0111\u1ec1u v\u1edbi v\u1eadn t\u1ed1c v(t) = -8t + 24 (m\/s),<br \/>\ntrong \u0111\u00f3  t  l\u00e0 th\u1eddi gian t\u00ednh b\u1eb1ng gi\u00e2y k\u1ec3 t\u1eeb l\u00fac \u0111\u1ea1p phanh. H\u1ecfi t\u1eeb l\u00fac \u0111\u1ea1p phanh \u0111\u1ebfn khi xe d\u1eebng h\u1eb3n, \u00f4 t\u00f4 di chuy\u1ec3n qu\u00e3ng \u0111\u01b0\u1eddng bao nhi\u00eau m\u00e9t?<\/p>\n<h2><strong>T\u1ea3i 05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p>Hy v\u1ecdng b\u1ed9 t\u00e0i li\u1ec7u tr\u00ean s\u1ebd gi\u00fap \u00edch cho c\u00e1c b\u1ea1n trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c cho k\u1ef3 thi s\u1eafp t\u1edbi. T\u1ea3i ngay <strong>05 \u0111\u1ec1 thi th\u1eed 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 d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 r\u00e8n luy\u1ec7n v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i ngay h\u00f4m nay!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1UEukulXDP1BGRtejy0bXnfhSs0ncEi2z\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1UEukulXDP1BGRtejy0bXnfhSs0ncEi2z\/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\/1UEukulXDP1BGRtejy0bXnfhSs0ncEi2z\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i 05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 c\u00f3 \u0111\u00e1p \u00e1n<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 t\u00e0i li\u1ec7u 05 \u0111\u1ec1 thi th\u1eed gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 12 n\u0103m h\u1ecdc 2024 \u2013 2025 \u0111\u01b0\u1ee3c th\u1ea7y gi\u00e1o Chu Ho\u00e0ng Minh t\u1ed5ng h\u1ee3p theo c\u1ea5u tr\u00fac \u0111\u1ec1 thi To\u00e1n m\u1edbi v\u1edbi 5 b\u1ed9 \u0111\u1ec1 kh\u00e1 chi ti\u1ebft. N\u1ed9i dung chi ti\u1ebft v\u00e0 b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc k\u00e8m \u0111\u00e1p \u00e1n \u0111\u1ea7y [&#8230;]\n","protected":false},"author":1,"featured_media":1583,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-384","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tong-hop","tag-tong-hop"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/384","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=384"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/384\/revisions"}],"predecessor-version":[{"id":1584,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/384\/revisions\/1584"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1583"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=384"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=384"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=384"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}