{"id":326,"date":"2026-05-05T04:39:45","date_gmt":"2026-05-05T04:39:45","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-on-tap-giua-hoc-ki-2-toan-12-nam-2024-2025-truong-thpt-viet-duc-ha-noi\/"},"modified":"2026-05-05T07:12:28","modified_gmt":"2026-05-05T07:12:28","slug":"de-on-tap-giua-hoc-ki-2-toan-12-nam-2024-2025-truong-thpt-viet-duc-ha-noi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-on-tap-giua-hoc-ki-2-toan-12-nam-2024-2025-truong-thpt-viet-duc-ha-noi\/","title":{"rendered":"\u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i"},"content":{"rendered":"<p><strong>\u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/strong> l\u00e0 t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp thu\u1ed9c ch\u01b0\u01a1ng 4 &amp; 5 To\u00e1n 12 t\u1eadp 2 theo format m\u1edbi nh\u1ea5t. T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c c\u00e1c th\u1ea7y c\u00f4 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i bi\u00ean so\u1ea1n chi ti\u1ebft, gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3. C\u00f9ng <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i Li\u1ec7u \u00d4n Thi<\/a> <\/strong>xem qua c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi qua b\u00e0i vi\u1ebft sau \u0111\u00e2y nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/strong> c\u00f3 3 \u0111\u1ec1 \u00f4n t\u1eadp, bao g\u1ed3m 2 ch\u1ee7 \u0111\u1ec1 ch\u00ednh: <strong>Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n<\/strong> v\u00e0 <strong>Ph\u01b0\u01a1ng ph\u00e1p t\u1ecda \u0111\u1ed9 trong kh\u00f4ng gian<\/strong>. To\u00e0n b\u1ed9 \u0111\u1ec1 thi \u0111\u01b0\u1ee3c chia th\u00e0nh 3 d\u1ea1ng b\u00e0i t\u1eadp v\u00e0 ph\u00e2n b\u1ed5 \u0111\u1ec1u trong t\u1eebng \u0111\u1ec1.<\/p>\n<p><span><strong>D\u1ea1ng 1: C\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 12 c\u00e2u )<\/strong><\/span><\/p>\n<p>N\u1ed9i dung c\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3i d\u00e0i t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12, tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi trong \u0111\u1ec1 nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 4<\/strong>:T\u00ednh t\u00edch ph\u00e2n  I = int\u2080^\u03c0\/2 sin (\u03c0\/4 &#8211; x ) dx.\n<\/p>\n<p>A.  I = \u03c0\/4 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  I = 0 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  I = 1 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  I = -1 .<\/p>\n<p><strong>C\u00e2u 5<\/strong>: Cho  int\u2080\u00b9 f(x)dx = 2  v\u00e0  int\u2080\u00b9 g(x)dx = 5 , khi \u0111\u00f3  I = int\u2080\u00b9 [f(x) &#8211; 2g(x)]dx  c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng<\/p>\n<p>A.  I = -3 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  I = 12 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  I = -8 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  I = 8 .<\/p>\n<p><strong>C\u00e2u 6<\/strong>: Cho h\u00e0m s\u1ed1  y = f(x)  c\u00f3 \u0111\u1ea1o h\u00e0m li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n  [0;2]  v\u00e0  f(0) &#8211; f(2) = 2 . T\u00ednh  int\u2080\u00b2 f'(x)dx.\n<\/p>\n<p>A.  -2 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  2 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  4 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  -4 .<\/p>\n<p><span><strong>D\u1ea1ng 2: C\u00e2u h\u1ecfi d\u1ea1ng \u0111\u00fang sai ( 4 c\u00e2u )<\/strong><\/span><\/p>\n<p>Ch\u1ee7 y\u1ebfu c\u00e1c c\u00e2u h\u1ecfi xoay quanh ki\u1ebfn th\u1ee9c v\u1ec1 h\u00ecnh h\u1ecdc kh\u00f4ng gian, c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. H\u1ecdc sinh ch\u1ec9 c\u1ea7n \u0111\u1ecdc \u0111\u1ec1 v\u00e0 tr\u1ea3 l\u1eddi \u0111\u00e1p \u00e1n theo gi\u00e1 tr\u1ecb \u0111\u00fang ho\u1eb7c sai. D\u1ea1ng c\u00e2u h\u1ecfi l\u00e0:<\/p>\n<p><strong>C\u00e2u 15<\/strong>: Trong kh\u00f4ng gian  Oxyz , cho \u0111i\u1ec3m  M(2;-1;4)  v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng  (P): 3x &#8211; 2y + z + 1 = 0.\n<\/p>\n<p>A. M\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng  (P)  l\u00e0  n\u20d7 = (3;-2;1) .<\/p>\n<p>B. Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng  (Q)  \u0111i qua \u0111i\u1ec3m  M  v\u00e0 song song v\u1edbi m\u1eb7t ph\u1eb3ng  (P) l\u00e0  3x &#8211; 2y + z &#8211; 12 = 0.\n<\/p>\n<p>C. M\u1eb7t ph\u1eb3ng  (P)  t\u1ea1o v\u1edbi m\u1eb7t ph\u1eb3ng  (Oxy)  m\u1ed9t g\u00f3c l\u1edbn h\u01a1n  50^\u00b0 .<\/p>\n<p>D. M\u1eb7t ph\u1eb3ng  (R)  song song v\u1edbi m\u1eb7t ph\u1eb3ng  (P)  v\u00e0 c\u00e1ch \u0111i\u1ec3m  N(1;-1;5)  m\u1ed9t kho\u1ea3ng b\u1eb1ng  (11)\/(\u221a14) c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0  3x &#8211; 2y + z + 12 = 0.\n<\/p>\n<p><span><strong>D\u1ea1ng 3: C\u00e2u h\u1ecfi d\u1ea1ng tr\u1ea3 l\u1eddi ng\u1eafn ( 6 c\u00e2u )<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 17<\/strong>: Bi\u1ebft  F(x) = ax\u00b3 + bx\u00b2 + cx  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = 3x\u00b2 + 2x &#8211; 6.  Khi \u0111\u00f3 gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c  P = a + b + c  c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng bao nhi\u00eau?<br \/>\n\u0110\u00e1p \u00e1n: \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.<\/p>\n<p><strong>C\u00e2u 18<\/strong>: Cho h\u00e0m s\u1ed1  y = f(x)  c\u00f3 \u0111\u1ea1o h\u00e0m li\u00ean t\u1ee5c tr\u00ean  [0;1] , th\u1ecfa m\u00e3n  (f'(x))\u00b2 + 4f(x) = 8x\u00b2 + 4, forall x in [0;1] v\u00e0  f(1) = 2 . Khi \u0111\u00f3 t\u00edch ph\u00e2n int\u2080\u00b9 f(x) dx = a\/b.  H\u00e3y t\u00ednh gi\u00e1 tr\u1ecb  a + b  (bi\u1ebft  a\/b  l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n).<br \/>\n\u0110\u00e1p \u00e1n: \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.<\/p>\n<p>Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0111\u1ec1 <strong>\u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/strong>. Qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o qua v\u00e0 luy\u1ec7n t\u1eadp ngay nh\u00e9!<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/18qCtqEaamT7aWNnr2LeyWmsIGPuE7NKJ\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/18qCtqEaamT7aWNnr2LeyWmsIGPuE7NKJ\/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>T\u1ea3i ngay <strong>\u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/strong> qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u00e0 l\u00e0m b\u00e0i hi\u1ec7u qu\u1ea3 nh\u1ea5t nh\u00e9. Ch\u00fac c\u00e1c b\u1ea1n h\u1ecdc sinh 12 \u00f4n t\u1eadp th\u1eadt t\u1ed1t v\u00e0 \u0111\u1ea1t \u0111\u01b0\u1ee3c th\u00e0nh t\u00edch cao trong k\u00ec thi s\u1eafp t\u1edbi.<\/p>\n<p><strong><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/18qCtqEaamT7aWNnr2LeyWmsIGPuE7NKJ\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i l\u00e0 t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp thu\u1ed9c ch\u01b0\u01a1ng 4 &amp; 5 To\u00e1n 12 t\u1eadp 2 theo format m\u1edbi nh\u1ea5t. T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c c\u00e1c th\u1ea7y c\u00f4 tr\u01b0\u1eddng THPT Vi\u1ec7t \u0110\u1ee9c H\u00e0 N\u1ed9i bi\u00ean so\u1ea1n [&#8230;]\n","protected":false},"author":1,"featured_media":1525,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-326","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\/326","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=326"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/326\/revisions"}],"predecessor-version":[{"id":1526,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/326\/revisions\/1526"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1525"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}