{"id":1014,"date":"2026-05-05T06:12:12","date_gmt":"2026-05-05T06:12:12","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-thi-cuoi-ki-2-toan-11\/"},"modified":"2026-05-05T07:53:18","modified_gmt":"2026-05-05T07:53:18","slug":"bo-de-thi-cuoi-ki-2-toan-11","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-thi-cuoi-ki-2-toan-11\/","title":{"rendered":"B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 11 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n"},"content":{"rendered":"<p>Trong giai \u0111o\u1ea1n n\u01b0\u1edbc r\u00fat c\u1ee7a n\u0103m h\u1ecdc l\u1edbp 11, vi\u1ec7c chu\u1ea9n b\u1ecb cho k\u1ef3 thi cu\u1ed1i k\u1ef3 kh\u00f4ng ch\u1ec9 l\u00e0 \u00f4n l\u1ea1i ki\u1ebfn th\u1ee9c m\u00e0 c\u00f2n l\u00e0 th\u1eed th\u00e1ch k\u1ef9 n\u0103ng v\u1eadn d\u1ee5ng to\u00e1n h\u1ecdc linh ho\u1ea1t. Nhi\u1ec1u h\u1ecdc sinh c\u1ea3m th\u1ea5y b\u1ed1i r\u1ed1i khi ph\u1ea3i gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, \u0111\u1eb7c bi\u1ec7t l\u00e0 c\u00e1c chuy\u00ean \u0111\u1ec1 nh\u01b0 H\u00e0m s\u1ed1, \u0110\u1ea1o h\u00e0m hay L\u0169y th\u1eeba \u2013 Logarit. <strong>B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 11<\/strong> s\u1ebd gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng h\u00f3a ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m, luy\u1ec7n t\u1eadp theo m\u1ee9c \u0111\u1ed9 t\u1eeb d\u1ec5 \u0111\u1ebfn kh\u00f3, v\u00e0 t\u1ef1 tin x\u1eed l\u00fd c\u00e1c d\u1ea1ng b\u00e0i \u0103n \u0111i\u1ec3m. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>Tailieuonthi<\/strong><\/a> kh\u00e1m ph\u00e1 nh\u1eefng \u0111i\u1ec3m n\u1ed5i b\u1eadt c\u1ee7a b\u1ed9 t\u00e0i li\u1ec7u n\u00e0y ngay sau \u0111\u00e2y.<\/p>\n<h2><strong>B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 11 c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t?<\/strong><\/h2>\n<p>B\u1ed9 \u0111\u1ec1 thi \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng v\u1eeba l\u00e0 c\u00f4ng c\u1ee5 luy\u1ec7n t\u1eadp, v\u1eeba l\u00e0 l\u1ed9 tr\u00ecnh \u00f4n thi khoa h\u1ecdc, gi\u00fap h\u1ecdc sinh t\u1ed1i \u01b0u h\u00f3a th\u1eddi gian v\u00e0 c\u00f4ng s\u1ee9c:<\/p>\n<ul>\n<li><strong>B\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi:<\/strong> N\u1ed9i dung \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n chu\u1ea9n x\u00e1c theo 3 s\u00e1ch gi\u00e1o khoa To\u00e1n 11: Ch\u00e2n Tr\u1eddi S\u00e1ng T\u1ea1o, K\u1ebft N\u1ed1i Tri Th\u1ee9c v\u00e0 C\u00e1nh Di\u1ec1u.<\/li>\n<li><strong>C\u1ea5u tr\u00fac \u0111a d\u1ea1ng:<\/strong> \u0110\u1ec1 thi g\u1ed3m 4 ph\u1ea7n r\u00f5 r\u00e0ng (Tr\u1eafc nghi\u1ec7m 4 ph\u01b0\u01a1ng \u00e1n, Tr\u1eafc nghi\u1ec7m \u0110\u00fang\/Sai, Tr\u1ea3 l\u1eddi ng\u1eafn v\u00e0 T\u1ef1 lu\u1eadn), m\u00f4 ph\u1ecfng \u0111\u1ea7y \u0111\u1ee7 c\u00e1c h\u00ecnh th\u1ee9c ki\u1ec3m tra hi\u1ec7n h\u00e0nh \u0111\u1ec3 h\u1ecdc sinh l\u00e0m quen v\u1edbi m\u1ecdi d\u1ea1ng \u0111\u1ec1.<\/li>\n<li><strong>\u0110\u1ed9 kh\u00f3 ph\u00e2n c\u1ea5p r\u00f5 r\u00e0ng:<\/strong> C\u00e1c c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf t\u1eeb m\u1ee9c \u0111\u1ed9 Nh\u1eadn bi\u1ebft (t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh c\u01a1 b\u1ea3n) \u0111\u1ebfn Th\u00f4ng hi\u1ec3u, V\u1eadn d\u1ee5ng v\u00e0 V\u1eadn d\u1ee5ng cao (t\u00ednh x\u00e1c su\u1ea5t, t\u00ednh th\u1ec3 t\u00edch, b\u00e0i to\u00e1n l\u00e3i su\u1ea5t).<\/li>\n<li><strong>Bao ph\u1ee7 to\u00e0n di\u1ec7n:<\/strong> \u0110\u1ec1 thi bao g\u1ed3m c\u00e1c chuy\u00ean \u0111\u1ec1 quan tr\u1ecdng nh\u1ea5t nh\u01b0 H\u00e0m s\u1ed1 \u2013 \u0110\u1ea1o h\u00e0m, Ph\u01b0\u01a1ng tr\u00ecnh M\u0169 \u2013 Logarit, H\u00ecnh h\u1ecdc kh\u00f4ng gian (G\u00f3c, Kho\u1ea3ng c\u00e1ch, Th\u1ec3 t\u00edch) v\u00e0 X\u00e1c su\u1ea5t \u2013 Th\u1ed1ng k\u00ea (bi\u1ebfn c\u1ed1 xung kh\u1eafc, bi\u1ebfn c\u1ed1 \u0111\u1ed9c l\u1eadp).<\/li>\n<\/ul>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 11<\/strong><\/h2>\n<p>N\u1ed9i dung <a href=\"https:\/\/tailieuonthi.edu.vn\/lop-11\/toan-11\/\" rel=\"noopener\" target=\"_blank\"><strong>t\u00e0i li\u1ec7u to\u00e1n 11<\/strong><\/a> \u0111\u01b0\u1ee3c t\u1ed5 ch\u1ee9c theo ph\u01b0\u01a1ng ph\u00e1p \u201ct\u1eeb t\u1ed5ng qu\u00e1t \u0111\u1ebfn c\u1ee5 th\u1ec3\u201d, gi\u00fap h\u1ecdc sinh v\u1eeba n\u1eafm v\u1eefng khung ki\u1ebfn th\u1ee9c t\u1ed5ng quan, v\u1eeba \u0111\u00e0o s\u00e2u v\u00e0o chi ti\u1ebft t\u1eebng d\u1ea1ng b\u00e0i.<\/p>\n<h3><strong>Ph\u1ea7n \u0111\u1ec1 b\u00e0i<\/strong><\/h3>\n<p>B\u1ed9 \u0111\u1ec1 \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng theo h\u01b0\u1edbng t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, chia th\u00e0nh c\u00e1c chuy\u00ean \u0111\u1ec1 ch\u1ee7 \u0111\u1ea1o, gi\u00fap h\u1ecdc sinh luy\u1ec7n t\u1eadp to\u00e0n di\u1ec7n:<\/p>\n<ul>\n<li><strong>H\u00e0m s\u1ed1:<\/strong> B\u00e0i t\u1eadp t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ed3 th\u1ecb \u0111\u1ebfn gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, \u00e1p d\u1ee5ng t\u00ednh ch\u1ea5t h\u00e0m s\u1ed1 \u0111\u1ec3 ph\u00e2n t\u00edch v\u00e0 ch\u1ee9ng minh.<\/li>\n<li><strong>Kh\u1ed1i \u0111a di\u1ec7n:<\/strong> Luy\u1ec7n c\u00e1c d\u1ea1ng b\u00e0i t\u00ednh th\u1ec3 t\u00edch, di\u1ec7n t\u00edch, x\u00e1c \u0111\u1ecbnh quan h\u1ec7 h\u00ecnh h\u1ecdc trong kh\u00f4ng gian.<\/li>\n<li><strong>L\u0169y th\u1eeba \u2013 Logarit:<\/strong> B\u00e0i t\u1eadp \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c, r\u00e8n k\u1ef9 n\u0103ng bi\u1ebfn \u0111\u1ed5i, gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n t\u1ed5ng h\u1ee3p.<\/li>\n<li><strong>T\u00edch ph\u00e2n v\u00e0 \u1ee9ng d\u1ee5ng:<\/strong> Ph\u00e1t tri\u1ec3n k\u1ef9 n\u0103ng t\u00ednh to\u00e1n v\u00e0 \u00e1p d\u1ee5ng v\u00e0o c\u00e1c t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf, \u0111\u1eb7c bi\u1ec7t l\u00e0 c\u00e1c b\u00e0i to\u00e1n li\u00ean quan di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch.<\/li>\n<\/ul>\n<p>M\u1ed7i chuy\u00ean \u0111\u1ec1 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp t\u1eeb b\u00e0i \u0111\u01a1n gi\u1ea3n \u2013 m\u1ee9c nh\u1eadn bi\u1ebft, \u0111\u1ebfn b\u00e0i t\u1ed5ng h\u1ee3p \u2013 v\u1eadn d\u1ee5ng cao, gi\u00fap h\u1ecdc sinh v\u1eeba \u00f4n t\u1eadp v\u1eeba n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n th\u1ef1c t\u1ebf.<\/p>\n<h3><strong>Ph\u1ea7n \u0111\u00e1p \u00e1n<\/strong><\/h3>\n<p>M\u1ed7i b\u00e0i t\u1eadp trong b\u1ed9 \u0111\u1ec1 \u0111\u1ec1u \u0111i k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft, gi\u1ea3i th\u00edch t\u1eebng b\u01b0\u1edbc gi\u1ea3i, gi\u00fap h\u1ecdc sinh n\u1eafm r\u00f5 ph\u01b0\u01a1ng ph\u00e1p, tr\u00e1nh nh\u1ea7m l\u1eabn v\u00e0 ph\u00e1t tri\u1ec3n t\u01b0 duy logic. M\u1ed9t s\u1ed1 b\u00e0i t\u1eadp \u0111\u01b0\u1ee3c minh h\u1ecda b\u1eb1ng h\u00ecnh v\u1ebd, s\u01a1 \u0111\u1ed3, ho\u1eb7c v\u00ed d\u1ee5 th\u1ef1c t\u1ebf, t\u0103ng t\u00ednh tr\u1ef1c quan v\u00e0 d\u1ec5 \u00e1p d\u1ee5ng.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter size-full wp-image-5704\" decoding=\"async\" height=\"1131\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-1.jpg 800w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-1-212x300.jpg 212w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-1-724x1024.jpg 724w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-1-768x1086.jpg 768w\" width=\"800\"\/> <img loading=\"lazy\" alt=\"\" class=\"aligncenter size-full wp-image-5703\" decoding=\"async\" height=\"1131\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-2.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-2.jpg 800w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-2-212x300.jpg 212w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-2-724x1024.jpg 724w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/11\/bo-de-thi-cuoi-ki-2-toan-11-2-768x1086.jpg 768w\" width=\"800\"\/><\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 11<\/strong><\/h2>\n<p><strong>B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 11<\/strong> l\u00e0 h\u00e0nh trang kh\u00f4ng th\u1ec3 thi\u1ebfu gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng ki\u1ebfn th\u1ee9c, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m b\u00e0i d\u01b0\u1edbi \u00e1p l\u1ef1c th\u1eddi gian v\u00e0 s\u1eb5n s\u00e0ng b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1 trong k\u1ef3 thi s\u1eafp t\u1edbi. B\u1ea1n \u0111\u1ecdc c\u00f3 th\u1ec3 t\u1ea3i ngay b\u1ed9 t\u00e0i li\u1ec7u theo \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1N3zVqO0Errb93cXkIdCQIERV5DjFWc63\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec To\u00e1n 11 n\u0103m 2025 (Ch\u00e2n Tr\u1eddi S\u00e1ng T\u1ea1o)<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/19yzrXlo5w5_c-zxtsXNKzYRxRxC0lZ6q\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec To\u00e1n 11 n\u0103m 2025 (K\u1ebft N\u1ed1i Tri Th\u1ee9c)<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1GReRfYJl_ZDTN92aQbQWiggr5x0s7gEy\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec To\u00e1n 11 n\u0103m 2025 (C\u00e1nh Di\u1ec1u)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trong giai \u0111o\u1ea1n n\u01b0\u1edbc r\u00fat c\u1ee7a n\u0103m h\u1ecdc l\u1edbp 11, vi\u1ec7c chu\u1ea9n b\u1ecb cho k\u1ef3 thi cu\u1ed1i k\u1ef3 kh\u00f4ng ch\u1ec9 l\u00e0 \u00f4n l\u1ea1i ki\u1ebfn th\u1ee9c m\u00e0 c\u00f2n l\u00e0 th\u1eed th\u00e1ch k\u1ef9 n\u0103ng v\u1eadn d\u1ee5ng to\u00e1n h\u1ecdc linh ho\u1ea1t. Nhi\u1ec1u h\u1ecdc sinh c\u1ea3m th\u1ea5y b\u1ed1i r\u1ed1i khi ph\u1ea3i gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n t\u1eeb c\u01a1 b\u1ea3n [&#8230;]\n","protected":false},"author":1,"featured_media":2212,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[16],"class_list":["post-1014","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-toan-11","tag-toan-11"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/1014","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=1014"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/1014\/revisions"}],"predecessor-version":[{"id":2213,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/1014\/revisions\/2213"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2212"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=1014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=1014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=1014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}