{"id":400,"date":"2026-05-05T04:43:48","date_gmt":"2026-05-05T04:43:48","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-giua-ky-2-toan-12-nam-2024-2025-truong-thpt-nguyen-tat-thanh-tp-hcm\/"},"modified":"2026-05-05T07:16:31","modified_gmt":"2026-05-05T07:16:31","slug":"de-giua-ky-2-toan-12-nam-2024-2025-truong-thpt-nguyen-tat-thanh-tp-hcm","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-giua-ky-2-toan-12-nam-2024-2025-truong-thpt-nguyen-tat-thanh-tp-hcm\/","title":{"rendered":"\u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM"},"content":{"rendered":"<p>Tuy\u1ec3n t\u1eadp 02 <strong>\u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM\u00a0<\/strong>m\u1edbi nh\u1ea5t s\u1ebd l\u00e0 ngu\u1ed3n t\u00e0i li\u1ec7u qu\u00fd gi\u00e1 gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c tr\u01b0\u1edbc k\u1ef3 thi s\u1eafp t\u1edbi. \u0110\u1eebng b\u1ecf l\u1ee1 c\u01a1 h\u1ed9i chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao v\u1edbi b\u1ed9 \u0111\u1ec1 n\u00e0y, c\u00f9ng t\u00ecm hi\u1ec3u qua n\u1ed9i dung v\u00e0 <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">\u00d4n Thi<\/a><\/strong> ngay nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM<\/strong> bao g\u1ed3m 2 \u0111\u1ec1 thi \u00f4n t\u1eadp, c\u00f9ng \u0111a d\u1ea1ng c\u00e1c c\u00e2u h\u1ecfi ki\u1ebfn th\u1ee9c to\u00e1n 12 t\u1eeb tr\u1eafc nghi\u1ec7m \u0111\u1ebfn t\u1ef1 lu\u1eadn \u0111\u01b0\u1ee3c h\u1ec7 th\u1ed1ng theo 3 ph\u1ea7n. C\u00e1c th\u00ed sinh c\u00f3 th\u1eddi gian 60 ph\u00fat \u0111\u1ec3 ho\u00e0n th\u00e0nh 18 c\u00e2u h\u1ecfi trong m\u1ed7i \u0111\u1ec1 chi ti\u1ebft nh\u01b0 sau:<\/p>\n<p><strong><span>Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 3 \u0111i\u1ec3m)<\/span><\/strong><\/p>\n<p>C\u00f9ng l\u00e0m quen c\u00e1c d\u1ea1ng to\u00e1n c\u01a1 b\u1ea3n trong <strong><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> <\/strong>qua m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c tr\u00edch trong <strong>\u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM<\/strong><\/p>\n<p><strong>C\u00e2u 1:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9  Oxyz , cho hai \u0111i\u1ec3m  A(4;0;1)  v\u00e0  B(-2;2;3) . M\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng  AB  nh\u1eadn vecto n\u00e0o sau \u0111\u00e2y l\u00e0 vecto ph\u00e1p tuy\u1ebfn?<\/p>\n<p>beginarrayll A. mathbfn = (-6;2;4) &amp; B. mathbfn = (3;-1;-1) C. mathbfn = (6;-2;2) &amp; D. mathbfn = (3;-1;1) endarray<\/p>\n<p><strong>C\u00e2u 2:<\/strong> H\u1ecd nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) = 3e^x + 2x  l\u00e0<\/p>\n<p>beginarrayllA. F(x) = 3e^x + 2 + C. &amp; B. F(x) = 3e^x + 2x\u00b2 + C. C. F(x) = 3e^x + x\u00b2 + C. &amp; D. F(x) = 3 (e^x+1)\/(x+1) + 2 + C. endarray<\/p>\n<p><strong><span>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi \u0111\u00fang\/ sai ( 4 \u0111i\u1ec3m)<\/span><\/strong><\/p>\n<p>G\u1ed3m c\u00f3 4 c\u00e2u, m\u1ed7i c\u00e2u c\u00f3 4 ph\u01b0\u01a1ng \u00e1n a), b), c), d), th\u00ed sinh c\u1ea7n ch\u1ecdn ph\u01b0\u01a1ng th\u1ee9c \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i \u0111\u00e1p \u00e1n. M\u1ed9t s\u1ed1 v\u00ed d\u1ee5 sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1  f(x) = x\u00b3 &#8211; 3x\u00b2 + 2x &#8211; 1  v\u00e0  F(x) = int f(x)dx . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n<p>a)  F'(x) = x\u00b3 &#8211; 3x\u00b2 + 2x &#8211; 1 .<\/p>\n<p>b) H\u00e0m s\u1ed1  y = 1\/4x\u2074 &#8211; x\u00b3 + x\u00b2 &#8211; x  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) .<\/p>\n<p>c)  F(x) = 1\/4x\u2074 &#8211; x\u00b3 + x\u00b2 &#8211; x .<\/p>\n<p>d) Bi\u1ebft  F(x)  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a  f(x)  th\u1ecfa  F(0) = 1 . Khi \u0111\u00f3  F(1) = 5\/4 .<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian  Oxyz  v\u1edbi ba vector \u0111\u01a1n v\u1ecb  mathbfi, mathbfj, mathbfk , cho  A(1;1;2) ,  B(2;-1;0) ,  mathbfu = (1;-2;-1) . X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau?<\/p>\n<p>a)  [mathbfi, mathbfj] = mathbfk .<\/p>\n<p>b)  [mathbfu, mathbfi] = (0;1;2) .<\/p>\n<p>c)  [AB\u20d7, mathbfu] = (6;1;0) .<\/p>\n<p>d)  [OA\u20d7, OB\u20d7] = (2;4;-3) .<\/p>\n<p><strong><span>Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn ( 3 \u0111i\u1ec3m )<\/span><\/strong><\/p>\n<p>Ph\u1ea7n n\u00e0y chi\u1ebfm r\u1ea5t nhi\u1ec1u th\u1eddi gian trong \u0111\u1ec1 thi, b\u1ea1n c\u1ea7n h\u1ecdc k\u0129 \u0111\u1ec1 v\u00e0 l\u1eadp lu\u1eadn gi\u1ea3i th\u00edch b\u00e1m s\u00e1t v\u1edbi c\u00e2u h\u1ecfi. H\u00e3y tham kh\u1ea3o v\u00e0 th\u1eed s\u1ee9c tr\u01b0\u1edbc v\u1edbi c\u00e1c c\u00e2u sau \u0111\u00e2y nh\u00e9:<\/p>\n<p><strong>C\u00e2u 3.<\/strong> Bi\u1ebft g\u00f3c quan s\u00e1t ngang c\u1ee7a m\u1ed9t camera l\u00e0  116^\u00b0 . Trong kh\u00f4ng gian  Oxyz , camera \u0111\u01b0\u1ee3c \u0111\u1eb7t t\u1ea1i \u0111i\u1ec3m  A(2;1;5)  v\u00e0 chi\u1ebfu th\u1eb3ng v\u1ec1 ph\u00eda m\u1eb7t ph\u1eb3ng  (P): 2x &#8211; y &#8211; 2z + 13 = 0  (nh\u01b0 h\u00ecnh minh h\u1ecda). H\u1ecfi v\u00f9ng quan s\u00e1t \u0111\u01b0\u1ee3c tr\u00ean m\u1eb7t ph\u1eb3ng  (P)  c\u1ee7a camera l\u00e0 h\u00ecnh tr\u00f2n c\u00f3 \u0111\u01b0\u1eddng k\u00ednh b\u1eb1ng bao nhi\u00eau? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n<p><strong>C\u00e2u 4. <\/strong>M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng trong 6 gi\u1edd v\u1edbi v\u1eadn t\u1ed1c  v(km\/h)  ph\u1ee5 thu\u1ed9c v\u00e0o th\u1eddi gian  t(h)  c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean d\u01b0\u1edbi. Trong kho\u1ea3ng th\u1eddi gian 2 gi\u1edd t\u1eeb khi b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng, \u0111\u1ed3 th\u1ecb l\u00e0 m\u1ed9t ph\u1ea7n \u0111\u01b0\u1eddng Parabol c\u00f3 \u0111\u1ec9nh  I(3;9)  v\u00e0 c\u00f3 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng song song v\u1edbi tr\u1ee5c tung. Kho\u1ea3ng th\u1eddi gian c\u00f2n l\u1ea1i, \u0111\u1ed3 th\u1ecb v\u1eadn t\u1ed1c l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c b\u1eb1ng  1\/4 . Qu\u00e3ng \u0111\u01b0\u1eddng  s  m\u00e0 v\u1eadt di chuy\u1ec3n \u0111\u01b0\u1ee3c trong 6 gi\u1edd l\u00e0 a\/b (a,b in mathbbZ) l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n. Khi \u0111\u00f3  a &#8211; b  b\u1eb1ng bao nhi\u00eau?<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM<\/strong> l\u00e0 t\u00e0i li\u1ec7u kh\u00f4ng th\u1ec3 b\u1ecf qua \u0111\u1ec3 h\u1ecdc sinh l\u1edbp 12 h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i. H\u00e3y t\u1eadn d\u1ee5ng ngay ngu\u1ed3n t\u00e0i li\u1ec7u ch\u1ea5t l\u01b0\u1ee3ng n\u00e0y \u0111\u1ec3 chu\u1ea9n b\u1ecb th\u1eadt t\u1ed1t cho k\u1ef3 thi. <strong>T\u1ea3i \u0111\u1ea7y \u0111\u1ee7 b\u1ed9 \u0111\u1ec1 qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y!<\/strong><\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1IRhSe6DcbPc1WZ7PInbqS54bmcbokZFZ\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1IRhSe6DcbPc1WZ7PInbqS54bmcbokZFZ\/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\/1IRhSe6DcbPc1WZ7PInbqS54bmcbokZFZ\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tuy\u1ec3n t\u1eadp 02 \u0110\u1ec1 gi\u1eefa k\u1ef3 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n T\u1ea5t Th\u00e0nh TP HCM\u00a0m\u1edbi nh\u1ea5t s\u1ebd l\u00e0 ngu\u1ed3n t\u00e0i li\u1ec7u qu\u00fd gi\u00e1 gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c tr\u01b0\u1edbc k\u1ef3 thi s\u1eafp t\u1edbi. \u0110\u1eebng b\u1ecf l\u1ee1 c\u01a1 h\u1ed9i chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao v\u1edbi b\u1ed9 \u0111\u1ec1 n\u00e0y, c\u00f9ng [&#8230;]\n","protected":false},"author":1,"featured_media":1599,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-400","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\/400","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=400"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/400\/revisions"}],"predecessor-version":[{"id":1600,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/400\/revisions\/1600"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1599"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}