{"id":1002,"date":"2026-05-05T06:11:26","date_gmt":"2026-05-05T06:11:26","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-thi-cuoi-ki-2-toan-12\/"},"modified":"2026-05-05T07:52:37","modified_gmt":"2026-05-05T07:52:37","slug":"bo-de-thi-cuoi-ki-2-toan-12","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-thi-cuoi-ki-2-toan-12\/","title":{"rendered":"B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n"},"content":{"rendered":"<p>Ch\u1eb7ng \u0111\u01b0\u1eddng chinh ph\u1ee5c \u0111i\u1ec3m 8, 9 m\u00f4n to\u00e1n trong k\u00ec thi cu\u1ed1i k\u00ec 2 lu\u00f4n l\u00e0 th\u1eed th\u00e1ch l\u1edbn nh\u1ea5t, b\u1edfi \u0111\u00e2y l\u00e0 l\u00fac ki\u1ebfn th\u1ee9c v\u1ec1 Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n, H\u00ecnh h\u1ecdc Oxyz v\u00e0 X\u00e1c su\u1ea5t th\u1ed1ng k\u00ea d\u1ed3n n\u00e9n, d\u1ec5 g\u00e2y nh\u1ea7m l\u1eabn. \u0110\u00f3 ch\u00ednh l\u00e0 l\u00fd do <strong>B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 12<\/strong> ra \u0111\u1eddi, gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng chuy\u00ean \u0111\u1ec1 m\u1ed9t c\u00e1ch khoa h\u1ecdc v\u00e0 t\u1ef1 tin l\u00e0m ch\u1ee7 nh\u1eefng c\u00e2u h\u1ecfi \u201c\u0103n \u0111i\u1ec3m\u201d trong \u0111\u1ec1 thi. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>Tailieuonthi Edu<\/strong><\/a> t\u00ecm hi\u1ec3u b\u1ed9 t\u00e0i li\u1ec7u \u0111\u1eb7c bi\u1ec7t n\u00e0y ngay sau \u0111\u00e2y.<\/p>\n<h2><strong>\u01afu \u0111i\u1ec3m c\u1ee7a B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n<\/strong><\/h2>\n<p>B\u1ed9 \u0111\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n k\u1ef9 l\u01b0\u1ee1ng nh\u1eb1m mang l\u1ea1i hi\u1ec7u qu\u1ea3 t\u1ed1i \u0111a cho h\u1ecdc sinh trong giai \u0111o\u1ea1n \u00f4n t\u1eadp cu\u1ed1i c\u00f9ng:<\/p>\n<ul>\n<li><strong>Ph\u1ea1m vi \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i:<\/strong> T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 \u201cD\u00d9NG CHUNG 3 LO\u1ea0I S\u00c1CH\u201d (C\u1ea3 ba b\u1ed9 s\u00e1ch gi\u00e1o khoa m\u1edbi), \u0111\u1ea3m b\u1ea3o t\u00ednh bao qu\u00e1t v\u00e0 ph\u00f9 h\u1ee3p v\u1edbi m\u1ecdi h\u1ecdc sinh tr\u00ean c\u1ea3 n\u01b0\u1edbc.<\/li>\n<li><strong>C\u1ea5u tr\u00fac \u0111\u1ec1 thi chu\u1ea9n h\u00f3a:<\/strong> M\u1ed7i \u0111\u1ec1 thi \u0111\u1ec1u tu\u00e2n th\u1ee7 ch\u1eb7t ch\u1ebd c\u1ea5u tr\u00fac ki\u1ec3m tra cu\u1ed1i k\u1ef3, bao g\u1ed3m \u0111\u1ea7y \u0111\u1ee7 c\u00e1c ph\u1ea7n: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn, C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai, v\u00e0 C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn.<\/li>\n<li><strong>T\u1eadp trung v\u00e0o c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng \u0111i\u1ec3m:<\/strong> N\u1ed9i dung \u0111\u1ec1 bao ph\u1ee7 to\u00e0n di\u1ec7n 3 chuy\u00ean \u0111\u1ec1 ch\u00ednh c\u1ee7a h\u1ecdc k\u1ef3 II l\u00e0: Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n v\u00e0 \u1ee8ng d\u1ee5ng, H\u00ecnh h\u1ecdc Oxyz v\u00e0 X\u00e1c su\u1ea5t th\u1ed1ng k\u00ea.<\/li>\n<\/ul>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n<\/strong><\/h2>\n<p>B\u1ed9 t\u00e0i li\u1ec7u n\u00e0y \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng theo h\u01b0\u1edbng ti\u1ebfp c\u1eadn n\u0103ng l\u1ef1c, b\u00e1m s\u00e1t \u0111\u1ecbnh h\u01b0\u1edbng ra \u0111\u1ec1 thi THPT Qu\u1ed1c Gia, gi\u00fap h\u1ecdc sinh luy\u1ec7n t\u1eadp c\u00f3 h\u1ec7 th\u1ed1ng v\u00e0 hi\u1ec7u qu\u1ea3.<\/p>\n<h3><strong>Ph\u1ea7n \u0111\u1ec1 b\u00e0i<\/strong><\/h3>\n<p>C\u00e1c \u0111\u1ec1 thi \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed5 h\u1ee3p l\u00fd, bao g\u1ed3m c\u00e1c c\u00e2u h\u1ecfi t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, b\u00e1m s\u00e1t c\u1ea5u tr\u00fac 4 m\u1ee9c \u0111\u1ed9 nh\u1eadn th\u1ee9c (Nh\u1eadn bi\u1ebft, Th\u00f4ng hi\u1ec3u, V\u1eadn d\u1ee5ng, V\u1eadn d\u1ee5ng cao).<\/p>\n<ul>\n<li><strong>Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n v\u00e0 \u1ee9ng d\u1ee5ng:<\/strong> \u00d4n t\u1eadp c\u00e1c c\u00f4ng th\u1ee9c nguy\u00ean h\u00e0m c\u01a1 b\u1ea3n, t\u00ednh ch\u1ea5t t\u00edch ph\u00e2n, v\u00e0 \u0111\u1eb7c bi\u1ec7t l\u00e0 \u1ee9ng d\u1ee5ng t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay.<\/li>\n<li><strong>H\u00ecnh h\u1ecdc Oxyz:<\/strong> \u0110a d\u1ea1ng h\u00f3a c\u00e1c d\u1ea1ng b\u00e0i v\u1ec1 vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u, x\u00e1c \u0111\u1ecbnh c\u00e1c y\u1ebfu t\u1ed1 c\u01a1 b\u1ea3n (vector ph\u00e1p tuy\u1ebfn, vector ch\u1ec9 ph\u01b0\u01a1ng), v\u00e0 x\u1eed l\u00fd c\u00e1c b\u00e0i to\u00e1n g\u00f3c, kho\u1ea3ng c\u00e1ch ph\u1ee9c t\u1ea1p.<\/li>\n<li><strong>X\u00e1c su\u1ea5t th\u1ed1ng k\u00ea:<\/strong> T\u1eadp trung v\u00e0o c\u00e1c b\u00e0i to\u00e1n t\u00ednh x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n, c\u00f4ng th\u1ee9c x\u00e1c su\u1ea5t to\u00e0n ph\u1ea7n, bao g\u1ed3m c\u1ea3 c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf (v\u00ed d\u1ee5: x\u00e1c su\u1ea5t trong ch\u1ea9n \u0111o\u00e1n y h\u1ecdc, b\u00e0i to\u00e1n kinh t\u1ebf).<\/li>\n<\/ul>\n<p>B\u1ed9 \u0111\u1ec1 \u0111\u1eb7c bi\u1ec7t ch\u00fa tr\u1ecdng \u0111\u1ebfn c\u00e1c c\u00e2u h\u1ecfi v\u1eadn d\u1ee5ng cao g\u1eafn li\u1ec1n v\u1edbi th\u1ef1c ti\u1ec5n, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n t\u01b0 duy \u1ee9ng d\u1ee5ng.<\/p>\n<h3><strong>Ph\u1ea7n \u0111\u00e1p \u00e1n<\/strong><\/h3>\n<p>T\u00e0i li\u1ec7u \u0111i k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft, c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc, gi\u00fap h\u1ecdc sinh kh\u00f4ng ch\u1ec9 bi\u1ebft \u0111\u00e1p \u00e1n m\u00e0 c\u00f2n hi\u1ec3u r\u00f5 c\u00e1ch t\u01b0 duy v\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i t\u1eebng d\u1ea1ng b\u00e0i.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter size-full wp-image-5541\" decoding=\"async\" height=\"1131\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-1.jpg 800w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-1-212x300.jpg 212w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-1-724x1024.jpg 724w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-1-768x1086.jpg 768w\" width=\"800\"\/> <img loading=\"lazy\" alt=\"\" class=\"aligncenter size-full wp-image-5540\" decoding=\"async\" height=\"1131\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-2.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-2.jpg 800w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-2-212x300.jpg 212w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-2-724x1024.jpg 724w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-ki-2-toan-12-2-768x1086.jpg 768w\" width=\"800\"\/><\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 2 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n<\/strong><\/h2>\n<p>\u0110\u1ec3 kh\u00f4ng b\u1ecf l\u1ee1 c\u01a1 h\u1ed9i l\u00e0m ch\u1ee7 c\u00e1c chuy\u00ean \u0111\u1ec1 kh\u00f3 nh\u1ea5t (T\u00edch ph\u00e2n, Oxyz, X\u00e1c su\u1ea5t) v\u00e0 ti\u1ebfn th\u1eb3ng \u0111\u1ebfn m\u1ee5c ti\u00eau \u0111i\u1ec3m 9+ trong k\u1ef3 thi cu\u1ed1i k\u00ec 2, b\u1ea1n h\u00e3y t\u1ea3i ngay b\u1ed9 <a href=\"https:\/\/tailieuonthi.edu.vn\/lop-12\/toan-12\/\" rel=\"noopener\" target=\"_blank\"><strong>t\u00e0i li\u1ec7u to\u00e1n 12<\/strong><\/a> n\u00e0y v\u1ec1 m\u00e1y v\u00e0 b\u1eaft \u0111\u1ea7u h\u00e0nh tr\u00ecnh \u00f4n luy\u1ec7n ngay h\u00f4m nay.<\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1puLaeyXq6TpRi8qgTsK5DmheMdNyRnWL\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0110\u1ec1 Ki\u1ec3m Tra Cu\u1ed1i K\u00ec 2 To\u00e1n 12 n\u0103m 2025 (D\u00f9ng chung 3 s\u00e1ch)<\/a><\/p>\n<p><strong>T\u00e0i li\u1ec7u li\u00ean quan: <\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/tailieuonthi.edu.vn\/bo-de-thi-giua-ki-1-toan-12\/\" rel=\"noopener\" target=\"_blank\">B\u1ed9 \u0110\u1ec1 Thi Gi\u1eefa K\u00ec 1 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n<\/a><\/li>\n<li><a href=\"https:\/\/tailieuonthi.edu.vn\/bo-de-thi-cuoi-ki-1-toan-12\/\" rel=\"noopener\" target=\"_blank\">B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n<\/a><\/li>\n<li><a href=\"https:\/\/tailieuonthi.edu.vn\/bo-de-thi-giua-ki-2-toan-12\/\" rel=\"noopener\" target=\"_blank\">B\u1ed9 \u0110\u1ec1 Thi Gi\u1eefa K\u00ec 2 To\u00e1n 12 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi c\u00f3 \u0111\u00e1p \u00e1n<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Ch\u1eb7ng \u0111\u01b0\u1eddng chinh ph\u1ee5c \u0111i\u1ec3m 8, 9 m\u00f4n to\u00e1n trong k\u00ec thi cu\u1ed1i k\u00ec 2 lu\u00f4n l\u00e0 th\u1eed th\u00e1ch l\u1edbn nh\u1ea5t, b\u1edfi \u0111\u00e2y l\u00e0 l\u00fac ki\u1ebfn th\u1ee9c v\u1ec1 Nguy\u00ean h\u00e0m \u2013 T\u00edch ph\u00e2n, H\u00ecnh h\u1ecdc Oxyz v\u00e0 X\u00e1c su\u1ea5t th\u1ed1ng k\u00ea d\u1ed3n n\u00e9n, d\u1ec5 g\u00e2y nh\u1ea7m l\u1eabn. \u0110\u00f3 ch\u00ednh l\u00e0 l\u00fd do B\u1ed9 \u0110\u1ec1 Thi [&#8230;]\n","protected":false},"author":1,"featured_media":2200,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[10],"class_list":["post-1002","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-toan-12","tag-toan-12"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/1002","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=1002"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/1002\/revisions"}],"predecessor-version":[{"id":2201,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/1002\/revisions\/2201"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2200"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=1002"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=1002"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=1002"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}