{"id":306,"date":"2026-05-05T04:38:39","date_gmt":"2026-05-05T04:38:39","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-10-de-kiem-tra-giua-hoc-ky-2-toan-12-gdpt-2018-nam-hoc-2024-2025-phan-nhat-linh\/"},"modified":"2026-05-05T07:11:22","modified_gmt":"2026-05-05T07:11:22","slug":"bo-10-de-kiem-tra-giua-hoc-ky-2-toan-12-gdpt-2018-nam-hoc-2024-2025-phan-nhat-linh","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-10-de-kiem-tra-giua-hoc-ky-2-toan-12-gdpt-2018-nam-hoc-2024-2025-phan-nhat-linh\/","title":{"rendered":"B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025 Phan Nh\u1eadt Linh"},"content":{"rendered":"<p><strong>B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u h\u1eefu \u00edch do th\u1ea7y Phan Nh\u1eadt Linh bi\u00ean so\u1ea1n. V\u1edbi c\u1ea5u tr\u00fac b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh d\u1ea1y m\u00f4n To\u00e1n m\u1edbi nh\u1ea5t n\u0103m 2024 \u2013 2025 gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng \u00f4n t\u1eadp ki\u1ebfn th\u1ee9c v\u00e0 r\u00e8n luy\u1ec7n m\u1ed7i ng\u00e0y. \u0110\u1ec3 nhanh ch\u00f3ng s\u1edf h\u1eefu b\u1ed9 \u0111\u1ec1 n\u00e0y, h\u00e3y tham kh\u1ea3o b\u00e0i vi\u1ebft sau c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\" title=\"T\u00e0i Li\u1ec7u \u00d4n Thi\">T\u00e0i Li\u1ec7u \u00d4n Thi<\/a>.<\/p>\n<h2><strong>N\u1ed9i dung B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p><strong>B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> t\u1ed5ng h\u1ee3p c\u00e1c b\u00e0i t\u1eadp d\u1ea1ng nguy\u00ean h\u00e0m, ph\u01b0\u01a1ng tr\u00ecnh t\u00edch ph\u00e2n, h\u00ecnh h\u1ecdc theo 3 ph\u1ea7n ch\u00ednh g\u1ed3m 12 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m, 4 c\u00e2u \u0111\u00fang sai,\u00a0 6 c\u00e2u tr\u1ea3 l\u1eddi ng\u1eafn v\u00e0 \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed5 nh\u01b0 sau:<\/p>\n<p><strong>Ph\u1ea7n 1 \u2013 thu\u1ed9c d\u1ea1ng c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 12 c\u00e2u )<\/strong><\/p>\n<p>M\u1ed7i c\u00e2u c\u00f3 t\u1ea5t c\u1ea3 4 \u0111\u00e1p \u00e1n ( A, B, C, D ), h\u1ecdc sinh l\u1ef1a ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n trong s\u1ed1 \u0111\u00f3. Sau \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong b\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025:<\/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) = x\u00b3  l\u00e0<\/p>\n<p>beginarraylltextbfA. &amp; 4x\u2074 + C. textbfB. &amp; 3x\u00b2 + C. textbfC. &amp; x\u2074 + C. textbfD. &amp; 1\/4x\u2074 + C.endarray<\/p>\n<p><strong>C\u00e2u 2<\/strong>: H\u1ecd t\u1ea5t c\u1ea3 c\u00e1c nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) = 2sin x  l\u00e0<\/p>\n<p>beginarraylltextbfA. &amp; int 2sin x dx = -2cos x + C. textbfB. &amp; int 2sin x dx = 2cos x + C. textbfC. &amp; int 2sin x dx = sin\u00b2 x + C. textbfD. &amp; int 2sin x dx = sin 2x + C.endarray<\/p>\n<p><strong>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai ( 4 c\u00e2u )<\/strong><\/p>\n<p>H\u1ecdc sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 4. m\u1ed7i c\u00e2u c\u00f3 4 \u0111\u00e1p \u00e1n v\u00e0 ch\u1ecdn gi\u00e1 tr\u1ecb \u0111\u00fang ho\u1eb7c sai<\/p>\n<p>M\u1ed9t s\u1ed1 v\u00ed d\u1ee5 v\u1ec1 d\u1ea1ng c\u00e2u h\u1ecfi n\u00e0y b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o qua:<\/p>\n<p><strong>C\u00e2u 1<\/strong>: M\u1ed9t vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn th\u1eb3ng \u0111\u1ee9ng l\u00ean t\u1eeb \u0111\u1ed9 cao 2m so v\u1edbi m\u1eb7t \u0111\u1ea5t (coi  t = 0  gi\u00e2y l\u00e0 th\u1eddi \u0111i\u1ec3m vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn l\u00ean), v\u1eadn t\u1ed1c c\u1ee7a vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c:  v(t) = 60 &#8211; 10t (m\/s)\n<\/p>\n<p>a) V\u1eadn t\u1ed1c c\u1ee7a vi\u00ean \u0111\u1ea1n t\u1ea1i th\u1eddi \u0111i\u1ec3m  t = 2  gi\u00e2y b\u1eb1ng  40  m\/s.<\/p>\n<p>b) \u0110\u1ed9 cao c\u1ee7a vi\u00ean \u0111\u1ea1n t\u1ea1i th\u1eddi \u0111i\u1ec3m  t  \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi c\u00f4ng th\u1ee9c:\\[<br \/>\nh(t) = 60t \u2013 5t^2.\\]\n<\/p>\n<p>c) \u0110\u1ed9 cao l\u1edbn nh\u1ea5t c\u1ee7a vi\u00ean \u0111\u1ea1n so v\u1edbi m\u1eb7t \u0111\u1ea5t l\u00e0  180 m.<\/p>\n<p>d) Vi\u00ean \u0111\u1ea1n \u0111\u1ea1t \u0111\u1ed9 cao l\u1edbn nh\u1ea5t sau  6  gi\u00e2y.<\/p>\n<p><strong>C\u00e2u 2<\/strong>: G\u1ecdi  (H)  l\u00e0 h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb hai h\u00e0m s\u1ed1:  f(x) = x\u00b2 &#8211; 2x + 2, g(x) = x + 2.\n<\/p>\n<p>a) Di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = g(x) , c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng  x = -1 ,  x = 1 , tr\u1ee5c  Ox  b\u1eb1ng  4 .<\/p>\n<p>b) Ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb hai h\u00e0m s\u1ed1  y = f(x)  v\u00e0  y = g(x)  l\u00e0  x = 0 ;  x = 3 .<\/p>\n<p>c) H\u00ecnh  (H)  c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng: 2\/3.\n<\/p>\n<p>d) Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay khi quay h\u00ecnh  (H)  quanh tr\u1ee5c  Ox  b\u1eb1ng: 117\/5.\n<\/p>\n<p><strong>Ph\u1ea7n 3 \u2013 D\u1ea1ng c\u00e2u t\u1ef1 lu\u1eadn tr\u1ea3 l\u1eddi ng\u1eafn ( 6 c\u00e2u )<\/strong><\/p>\n<p>H\u1ecdc sinh t\u1ef1 \u0111\u1ecdc \u0111\u1ec1 v\u00e0 t\u00ecm ra \u0111\u00e1p \u00e1n, vi\u1ebft c\u00e2u tr\u1ea3 l\u1eddi d\u01b0\u1edbi m\u1ed7i c\u00e2u. H\u00e3y xem qua c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi sau:<\/p>\n<p><strong>C\u00e2u 5<\/strong>: T\u1eeb m\u1eb7t n\u01b0\u1edbc trong m\u1ed9t b\u1ec3 n\u01b0\u1edbc, t\u1ea1i ba v\u1ecb tr\u00ed  A, B, C  \u0111\u00f4i m\u1ed9t c\u00e1ch nhau 2m, ng\u01b0\u1eddi ta th\u1ea3 d\u00e2y d\u1ecdi \u0111\u1ec3 qu\u1ea3 d\u1ecdi ch\u1ea1m \u0111\u00e1y b\u1ec3. Ph\u1ea7n d\u00e2y d\u1ecdi (th\u1eb3ng) n\u1eb1m trong n\u01b0\u1edbc t\u1ea1i ba v\u1ecb tr\u00ed \u0111\u00f3 l\u1ea7n l\u01b0\u1ee3t c\u00f3 \u0111\u1ed9 d\u00e0i 4m; 4,4m; 4,8m (Bi\u1ebft \u0111\u00e1y b\u1ec3 l\u00e0 ph\u1eb3ng). H\u1ecfi \u0111\u00e1y b\u1ec3 nghi\u00eang so v\u1edbi m\u1eb7t ph\u1eb3ng n\u1eb1m ngang m\u1ed9t g\u00f3c bao nhi\u00eau \u0111\u1ed9? Vi\u1ebft k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c.<\/p>\n<p><strong>C\u00e2u 6<\/strong>: M\u1ed9t v\u1eadt th\u1ec3 c\u00f3 k\u00edch th\u01b0\u1edbc v\u00e0 h\u00ecnh d\u00e1ng nh\u01b0 h\u00ecnh v\u1ebd minh h\u1ecda d\u01b0\u1edbi \u0111\u00e2y.\u00a0\u0110\u00e1y l\u00e0 h\u00ecnh elip c\u00f3 \u0111\u1ed9 d\u00e0i tr\u1ee5c l\u1edbn b\u1eb1ng  6  v\u00e0 \u0111\u1ed9 d\u00e0i tr\u1ee5c b\u00e9 b\u1eb1ng  4 .\u00a0Khi c\u1eaft v\u1eadt th\u1ec3 b\u1edfi m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi  Ox  ta \u0111\u01b0\u1ee3c thi\u1ebft di\u1ec7n l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u.\u00a0G\u1ecdi th\u1ec3 t\u00edch c\u1ee7a v\u1eadt th\u1ec3 l\u00e0  V . T\u00ednh  V\u00b2 .<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong><\/h2>\n<p>T\u1ea3i v\u00e0 chinh ph\u1ee5c ngay <strong>B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025<\/strong> theo \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 c\u00f3 \u0111\u01b0\u1ee3c \u0111i\u1ec3m s\u1ed1 t\u1ed1t nh\u1ea5t trong k\u1ef3 thi n\u00e0y nh\u00e9!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1FvrFmWMMq-WY8CeFJtB5vP3hMT8IwMSB\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1FvrFmWMMq-WY8CeFJtB5vP3hMT8IwMSB\/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><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1FvrFmWMMq-WY8CeFJtB5vP3hMT8IwMSB\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 10 \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 12 GDPT 2018 n\u0103m h\u1ecdc 2024 \u2013 2025 l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u h\u1eefu \u00edch do th\u1ea7y Phan Nh\u1eadt Linh bi\u00ean so\u1ea1n. V\u1edbi c\u1ea5u tr\u00fac b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh d\u1ea1y m\u00f4n To\u00e1n m\u1edbi nh\u1ea5t n\u0103m 2024 \u2013 2025 gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng \u00f4n t\u1eadp ki\u1ebfn [&#8230;]\n","protected":false},"author":1,"featured_media":1505,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[33,61],"class_list":["post-306","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tong-hop","tag-thay-phan-nhat-linh","tag-tong-hop"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/306","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=306"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/306\/revisions"}],"predecessor-version":[{"id":1506,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/306\/revisions\/1506"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1505"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}