{"id":388,"date":"2026-05-05T04:43:07","date_gmt":"2026-05-05T04:43:07","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-on-kiem-tra-giua-ki-2-toan-12-nam-2024-2025-truong-thpt-nguyen-huu-cau-tp-hcm\/"},"modified":"2026-05-05T07:15:51","modified_gmt":"2026-05-05T07:15:51","slug":"de-on-kiem-tra-giua-ki-2-toan-12-nam-2024-2025-truong-thpt-nguyen-huu-cau-tp-hcm","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-on-kiem-tra-giua-ki-2-toan-12-nam-2024-2025-truong-thpt-nguyen-huu-cau-tp-hcm\/","title":{"rendered":"\u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM"},"content":{"rendered":"<p><strong>\u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM <\/strong>l\u00e0 t\u00e0i li\u1ec7u \u0111\u1eafc l\u1ef1c gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 c\u00e1c ki\u1ebfn th\u1ee9c quan tr\u1ecdng trong ch\u01b0\u01a1ng 4 &amp; 5, bao g\u1ed3m Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n v\u00e0 \u1ee9ng d\u1ee5ng, T\u1ecda \u0111\u1ed9 Oxyz: ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng, kho\u1ea3ng c\u00e1ch li\u00ean quan \u0111\u1ebfn m\u1eb7t ph\u1eb3ng. C\u00e1c b\u1ea1n h\u1ecdc sinh l\u1edbp 12 kh\u00f4ng n\u00ean b\u1ecf qua b\u1ed9 \u0111\u1ec1 v\u1edbi \u0111a d\u1ea1ng c\u00e1c b\u00e0i t\u1eadp \u0111i k\u00e8m l\u1eddi gi\u1ea3i r\u00f5 r\u00e0ng, d\u1ec5 hi\u1ec3u v\u00e0 d\u1ec5 \u00f4n t\u1eadp. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a> kh\u00e1m ph\u00e1 ngay c\u1ea5u tr\u00fac \u0111\u1ec1 qua n\u1ed9i dung d\u01b0\u1edbi \u0111\u00e2y!<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 c\u1ee7a tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac m\u1edbi v\u1edbi 3 \u0111\u1ec1 thi k\u00e8m b\u1ed9 \u0111\u00e1p \u00e1n chi ti\u1ebft. \u0110\u1ec1 thi g\u1ed3m 3 ph\u1ea7n ch\u00ednh, trong \u0111\u00f3 c\u00f3 12 c\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn, 03 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai v\u00e0 05 c\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn. Th\u1eddi gian l\u00e0m b\u00e0i l\u00e0 75 ph\u00fat, gi\u00fap h\u1ecdc sinh l\u00e0m quen v\u1edbi k\u1ef9 n\u0103ng gi\u1ea3i <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-giua-ki-2-toan-12\/\" target=\"_blank\" rel=\"noopener\">\u0111\u1ec1 thi gi\u1eefa k\u00ec 2 to\u00e1n 12<\/a> tr\u01b0\u1edbc k\u1ef3 thi. C\u00f9ng t\u00ecm hi\u1ec3u chi ti\u1ebft t\u1eebng ph\u1ea7n trong \u0111\u1ec1 \u00f4n t\u1eadp ngay sau \u0111\u00e2y:<\/p>\n<p><span><strong>Ph\u1ea7n I \u2013 c\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (03 \u0111i\u1ec3m)<\/strong><\/span><\/p>\n<p>C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 l\u00e0m quen v\u1edbi c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c tr\u00edch trong \u0111\u1ec1 nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 5:<\/strong> M\u1eb7t ph\u1eb3ng \u0111i qua \u0111i\u1ec3m  M(0;-1;2)  v\u00e0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn  n\u20d7 = (1;2;-3)  c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n<p>A.  x + 2y &#8211; 3z &#8211; 8 = 0 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  x + 2y &#8211; 3z + 8 = 0 .<\/p>\n<p>C.  x + 2y &#8211; 3z &#8211; 4 = 0 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  x + 2y + 3z &#8211; 4 = 0 .<\/p>\n<p><strong>C\u00e2u 6:<\/strong> Trong kh\u00f4ng gian  Oxyz , cho ba \u0111i\u1ec3m  A(2;0;0) ,  B(0;-3;0) ,  C(0;0;1) . M\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng  (ABC)  l\u00e0:<\/p>\n<p>A. n\u20d7 = (2;-3;1) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  n\u20d7 = (3;-2;6) .<\/p>\n<p>C.  n\u20d7 = (2;3;1) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  n\u20d7 = (2;-3;-1) .<\/p>\n<p><span><strong>Ph\u1ea7n II \u2013 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4,5 \u0111i\u1ec3m)<\/strong><\/span><\/p>\n<p>\u0110\u1ec3 chi\u1ebfm tr\u1ecdng 4,5 \u0111i\u1ec3m c\u1ee7a ph\u1ea7n n\u00e0y, c\u00e1c b\u1ea1n h\u1ecdc sinh n\u00ean b\u1eaft tay v\u00e0o gi\u1ea3i ngay c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 1<\/strong>: Cho h\u00e0m s\u1ed1 f(x) = 2cos x v\u00e0 g(x) = 2sin\u00b2 x\/2. C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00e2y \u0111\u00fang hay sai?<\/p>\n<p>a)  int f(x)dx = 2sin x + C. <\/p>\n<p>b)  int g(x)dx = -cos x + C. <\/p>\n<p>c)  int [f(x) + g(x)]dx = x + sin x + C. <\/p>\n<p>d)  int (f(x))\/(g(x)-1) dx = 2x + C  (bi\u1ebft  x  th\u1ecfa m\u00e3n  g(x) \u2260 1 ).<\/p>\n<p><strong>C\u00e2u 3:<\/strong> Trong kh\u00f4ng gian  Oxyz , cho \u0111i\u1ec3m  A(2;-3;4)  v\u00e0 m\u1eb7t ph\u1eb3ng  (P): -x + 2y + z = 0 . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00e2y \u0111\u00fang hay sai?<\/p>\n<p>a)  (P)  c\u00f3 m\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0  n\u20d7_P = (-1;2;0) .<\/p>\n<p>b) Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m  A  \u0111\u1ebfn m\u1eb7t ph\u1eb3ng  (P)  b\u1eb1ng  2\u221a2 .<\/p>\n<p>c) N\u1ebfu c\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng  AM parallel (P)  th\u00ec  AM \u00b7 n\u20d7_P = 0 .<\/p>\n<p>d) \u0110\u01b0\u1eddng th\u1eb3ng  d  \u0111i qua  A , c\u1eaft tr\u1ee5c  Ox  v\u00e0 song song v\u1edbi  (P)  c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0: x-2\/2 = y+3\/3 = z-4\/-4.\n<\/p>\n<p><span><strong>Ph\u1ea7n III \u2013 c\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (2,5 \u0111i\u1ec3m)<\/strong><\/span><\/p>\n<p>\u0110\u1ec3 l\u00e0m t\u1ed1t c\u00e1c 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 h\u1ecdc k\u00ec 2 to\u00e1n 12<\/a>, b\u1ea1n n\u00ean th\u1eed tham kh\u1ea3o gi\u1ea3i m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi d\u1ea1ng tr\u1ea3 l\u1eddi ng\u1eafn sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho h\u00e0m s\u1ed1  f(x) . Bi\u1ebft  f(0) = 4  v\u00e0  f'(x) = 2sin\u00b2 x + 1, forall x in mathbbR . Bi\u1ebft intlimits\u2080^\u03c0 f(x) dx = (\u03c0\u00b2 + a\u03c0 + b)\/(16), (a, b in mathbbZ), t\u00ednh  a + b .<\/p>\n<p><strong>C\u00e2u 3:<\/strong> G\u1ecdi  F(x)  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) = e^x\u00b2 &#8211; 12x (x\u2074 &#8211; 4x\u00b2) . Bi\u1ebft h\u00e0m s\u1ed1  F(x)  \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng  (a; +\u221e) , gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a  a  b\u1eb1ng bao nhi\u00eau?<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM<\/strong><\/h2>\n<p>\u0110\u1ec3 n\u00e2ng cao t\u01b0 duy logic, l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi, c\u00e1c b\u1ea1n h\u1ecdc sinh h\u00e3y t\u1ea3i ngay <strong>\u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM<\/strong> qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y. N\u1ebfu b\u1ea1n ch\u0103m ch\u1ec9 \u00f4n t\u1eadp s\u1ebd gi\u00fap b\u1ea1n t\u1ef1 tin chinh ph\u1ee5c m\u00f4n To\u00e1n v\u1edbi \u0111i\u1ec3m s\u1ed1 9+ trong k\u1ef3 thi s\u1eafp t\u1edbi \u0111\u1ea5y!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1PdpoxPG_4l6bQssiA7j7JD2FtpQuJ1Wz\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1PdpoxPG_4l6bQssiA7j7JD2FtpQuJ1Wz\/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\/1PdpoxPG_4l6bQssiA7j7JD2FtpQuJ1Wz\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 \u00f4n ki\u1ec3m tra gi\u1eefa k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n H\u1eefu C\u1ea7u \u2013 TP HCM l\u00e0 t\u00e0i li\u1ec7u \u0111\u1eafc l\u1ef1c gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 c\u00e1c ki\u1ebfn th\u1ee9c quan tr\u1ecdng trong ch\u01b0\u01a1ng 4 &amp; 5, bao g\u1ed3m Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n v\u00e0 \u1ee9ng d\u1ee5ng, T\u1ecda \u0111\u1ed9 [&#8230;]\n","protected":false},"author":1,"featured_media":1587,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-388","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\/388","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=388"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/388\/revisions"}],"predecessor-version":[{"id":1588,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/388\/revisions\/1588"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1587"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}