{"id":952,"date":"2026-05-05T06:08:44","date_gmt":"2026-05-05T06:08:44","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-thi-cuoi-ki-1-toan-12\/"},"modified":"2026-05-05T07:49:49","modified_gmt":"2026-05-05T07:49:49","slug":"bo-de-thi-cuoi-ki-1-toan-12","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-thi-cuoi-ki-1-toan-12\/","title":{"rendered":"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"},"content":{"rendered":"<p>B\u1ea1n \u0111ang b\u01b0\u1edbc v\u00e0o giai \u0111o\u1ea1n n\u01b0\u1edbc r\u00fat c\u1ee7a l\u1edbp 12 v\u00e0 c\u1ea3m th\u1ea5y \u00e1p l\u1ef1c khi ph\u1ea3i \u00f4n t\u1eadp m\u1ed9t kh\u1ed1i l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c kh\u1ed5ng l\u1ed3. \u0110\u1eb7c bi\u1ec7t l\u00e0 ph\u1ea7n \u0111\u1ea1i s\u1ed1 \u2013 h\u00ecnh h\u1ecdc \u2013 x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 12? <strong>B\u1ed9 \u0110\u1ec1 Thi B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12<\/strong>\u00a0ch\u00ednh l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u gi\u00fap b\u1ea1n gi\u1ea3i tr\u00fang \u201cn\u1ed7i lo\u201d \u0111\u00f3. T\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p \u0111\u1ec1 th\u1ef1c h\u00e0nh theo \u0111\u00fang chu\u1ea9n 3 b\u1ed9 s\u00e1ch gi\u00e1o khoa, c\u00f3 ph\u00e2n lo\u1ea1i \u0111\u1ed9 kh\u00f3, c\u00f3 \u0111\u00e1p \u00e1n r\u00f5 r\u00e0ng, b\u00e1m s\u00e1t c\u00e1ch ra \u0111\u1ec1 th\u1ef1c t\u1ebf c\u1ee7a tr\u01b0\u1eddng v\u00e0 \u0111\u1ecbnh h\u01b0\u1edbng thi THPT Qu\u1ed1c Gia. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> xem b\u1ed9 t\u00e0i li\u1ec7u n\u00e0y h\u1ed7 tr\u1ee3 b\u1ea1n \u201cch\u1ed1t ki\u1ebfn th\u1ee9c\u201d cu\u1ed1i k\u1ef3 nh\u01b0 th\u1ebf n\u00e0o nh\u00e9!<\/p>\n<h2><strong>T\u1ea1i sao n\u00ean s\u1edf h\u1eefu B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12<\/strong><\/h2>\n<p><strong>B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12<\/strong> l\u00e0 m\u1ed9t trong nh\u1eefng t\u00e0i li\u1ec7u \u00f4n thi cu\u1ed1i k\u1ef3 1 To\u00e1n 12 ch\u1ea5t l\u01b0\u1ee3ng nh\u1ea5t hi\u1ec7n nay nh\u1edd v\u00e0o nh\u1eefng \u01b0u \u0111i\u1ec3m n\u1ed5i tr\u1ed9i, b\u00e1m s\u00e1t \u0111\u1ecbnh h\u01b0\u1edbng ki\u1ec3m tra \u0111\u00e1nh gi\u00e1 m\u1edbi:<\/p>\n<ul>\n<li>Ph\u00e2n b\u1ed5 chuy\u00ean \u0111\u1ec1 \u0111a d\u1ea1ng nh\u01b0 H\u00e0m s\u1ed1, Kh\u1ed1i \u0111a di\u1ec7n, L\u0169y th\u1eeba \u2013 Logarit, T\u00edch ph\u00e2n,\u2026 t\u1ea1o th\u00e0nh h\u1ec7 th\u1ed1ng ki\u1ebfn th\u1ee9c to\u00e0n di\u1ec7n.<\/li>\n<li>B\u00e0i t\u1eadp \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i theo m\u1ee9c \u0111\u1ed9 r\u00e8n luy\u1ec7n t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, bao g\u1ed3m Nh\u1eadn bi\u1ebft, Th\u00f4ng hi\u1ec3u, V\u1eadn d\u1ee5ng v\u00e0 V\u1eadn d\u1ee5ng cao, gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng theo d\u00f5i ti\u1ebfn tr\u00ecnh h\u1ecdc t\u1eadp.<\/li>\n<li>N\u1ed9i dung \u0111\u1ec1 thi th\u1ec3 hi\u1ec7n r\u00f5 c\u1ea5u tr\u00fac \u0111\u1ec1 hi\u1ec7n \u0111\u1ea1i, t\u1eadp trung ph\u00e1t tri\u1ec3n n\u0103ng l\u1ef1c ph\u00e2n t\u00edch v\u00e0 t\u01b0 duy logic.<\/li>\n<li>\u0110\u00e1p \u00e1n chi ti\u1ebft, k\u00e8m theo h\u01b0\u1edbng d\u1eabn gi\u1ea3i t\u1eebng b\u01b0\u1edbc, gi\u00fap h\u1ecdc sinh hi\u1ec3u b\u1ea3n ch\u1ea5t b\u00e0i to\u00e1n thay v\u00ec h\u1ecdc v\u1eb9t.<\/li>\n<\/ul>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12<\/strong><\/h2>\n<p>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> \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng v\u1edbi c\u1ea5u tr\u00fac logic, t\u1eadp trung v\u00e0o c\u00e1c chuy\u00ean \u0111\u1ec1 c\u1ed1t l\u00f5i c\u1ee7a h\u1ecdc k\u1ef3 1 To\u00e1n 12, gi\u00fap h\u1ecdc sinh luy\u1ec7n t\u1eadp c\u00f3 h\u1ec7 th\u1ed1ng v\u00e0 hi\u1ec7u qu\u1ea3 cao. M\u1ed7i \u0111\u1ec1 thi bao g\u1ed3m kho\u1ea3ng 50 c\u00e2u tr\u1eafc nghi\u1ec7m, th\u1eddi gian 90 ph\u00fat, ph\u00f9 h\u1ee3p \u0111\u1ec3 ki\u1ec3m tra to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c.<\/p>\n<h3><strong>Ph\u1ea7n \u0111\u1ec1 b\u00e0i<\/strong><\/h3>\n<p>T\u00e0i li\u1ec7u t\u1eadp trung v\u00e0o c\u00e1c chuy\u00ean \u0111\u1ec1 c\u1ed1t l\u00f5i c\u1ee7a To\u00e1n 12 H\u1ecdc k\u1ef3 I, \u0111\u1ea3m b\u1ea3o ph\u1ee7 s\u00f3ng ki\u1ebfn th\u1ee9c to\u00e0n di\u1ec7n:<\/p>\n<ul>\n<li><strong>Chuy\u00ean \u0111\u1ec1 H\u00e0m s\u1ed1 v\u00e0 \u1ee8ng d\u1ee5ng \u0110\u1ea1o h\u00e0m:<\/strong> Bao g\u1ed3m c\u00e1c d\u1ea1ng b\u00e0i v\u1ec1 t\u00ednh \u0110\u1ed3ng bi\u1ebfn\/Ngh\u1ecbch bi\u1ebfn, Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t\/Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t, Ti\u1ec7m c\u1eadn v\u00e0 nh\u1eadn d\u1ea1ng \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (H\u00e0m b\u1eadc ba, H\u00e0m ph\u00e2n th\u1ee9c).<\/li>\n<li><strong>Chuy\u00ean \u0111\u1ec1 H\u00ecnh h\u1ecdc v\u00e0 T\u1ecda \u0111\u1ed9 trong kh\u00f4ng gian Oxyz:<\/strong> Luy\u1ec7n t\u1eadp c\u00e1c c\u00e2u h\u1ecfi v\u1ec1 Vector, T\u1ecda \u0111\u1ed9 \u0111i\u1ec3m\/vector, v\u00e0 c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00e1c y\u1ebfu t\u1ed1 H\u00ecnh h\u1ecdc.<\/li>\n<li><strong>Chuy\u00ean \u0111\u1ec1 Th\u1ed1ng k\u00ea v\u00e0 X\u00e1c su\u1ea5t:<\/strong> T\u00edch h\u1ee3p c\u00e1c c\u00e2u h\u1ecfi v\u1ec1 vi\u1ec7c x\u1eed l\u00fd m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m (t\u00ednh Kho\u1ea3ng bi\u1ebfn thi\u00ean, Kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb, Gi\u00e1 tr\u1ecb trung b\u00ecnh), ph\u1ea3n \u00e1nh \u0111\u00fang tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi.<\/li>\n<\/ul>\n<h3><strong>Ph\u1ea7n \u0111\u00e1p \u00e1n<\/strong><\/h3>\n<p>Ph\u1ea7n n\u00e0y cung c\u1ea5p l\u1eddi gi\u1ea3i chi ti\u1ebft t\u1eebng b\u01b0\u1edbc, gi\u00fap h\u1ecdc sinh t\u1ef1 h\u1ecdc hi\u1ec7u qu\u1ea3 v\u00e0 d\u1ec5 d\u00e0ng ki\u1ec3m tra l\u1ed7i sai v\u00e0 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c ngay l\u1eadp t\u1ee9c.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-5284\" decoding=\"async\" height=\"1118\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-hoc-ki-1-toan-12-nam-2025-dung-chung-3-sach-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-hoc-ki-1-toan-12-nam-2025-dung-chung-3-sach-1.jpg 606w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-hoc-ki-1-toan-12-nam-2025-dung-chung-3-sach-1-215x300.jpg 215w\" width=\"800\"\/> <img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-5283\" decoding=\"async\" height=\"1139\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-hoc-ki-1-toan-12-nam-2025-dung-chung-3-sach-2.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-hoc-ki-1-toan-12-nam-2025-dung-chung-3-sach-2.jpg 602w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/10\/bo-de-thi-cuoi-hoc-ki-1-toan-12-nam-2025-dung-chung-3-sach-2-211x300.jpg 211w\" width=\"800\"\/><\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12 mi\u1ec5n ph\u00ed c\u00f3 \u0111\u00e1p \u00e1n<\/strong><\/h2>\n<p>T\u1ea3i ngay b\u1ed9 B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 To\u00e1n 12\u00a0\u0111\u1ec3 s\u1eb5n s\u00e0ng h\u00e0nh trang chinh ph\u1ee5c \u0111i\u1ec3m cao trong k\u1ef3 thi s\u1eafp t\u1edbi.<\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1g2x84hg07TcXGGWW_5ferljZiEHxCz3k\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i H\u1ecdc K\u00ec 1 To\u00e1n 12 n\u0103m 2025 (D\u00f9ng Chung 3 S\u00e1ch)<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1g-pOGQaRG3At86I8C7xMLNqKqObUDhr7\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i T\u1ed5ng H\u1ee3p \u0110\u1ec1 Cu\u1ed1i K\u00ec 1 To\u00e1n 12 C\u00e1c Tr\u01b0\u1eddng 2024 \u2013 2025 C\u00f3 \u0110\u00e1p \u00c1n<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1RQDJDMwSc1MJCv0Ucu9WOcR5RbRxvKAm\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 Ki\u1ec3m Tra Cu\u1ed1i K\u00ec 1 To\u00e1n 12 N\u0103m H\u1ecdc 25-26 C\u1ea5u Tr\u00fac 3-4-3 (Kh\u00f4ng T\u1ef1 Lu\u1eadn)<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/16NroKe9J1FwxLl_AJZM2ibDuxaxQj3rj\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 Ki\u1ec3m Tra Cu\u1ed1i K\u00ec 1 To\u00e1n 12 N\u0103m H\u1ecdc 25-26 C\u1ea5u Tr\u00fac 3-2-2-3 (C\u00f3 T\u1ef1 Lu\u1eadn)<\/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-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<li><a href=\"https:\/\/tailieuonthi.edu.vn\/bo-de-thi-cuoi-ki-2-toan-12\/\" rel=\"noopener\" target=\"_blank\">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<\/a><\/li>\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<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ea1n \u0111ang b\u01b0\u1edbc v\u00e0o giai \u0111o\u1ea1n n\u01b0\u1edbc r\u00fat c\u1ee7a l\u1edbp 12 v\u00e0 c\u1ea3m th\u1ea5y \u00e1p l\u1ef1c khi ph\u1ea3i \u00f4n t\u1eadp m\u1ed9t kh\u1ed1i l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c kh\u1ed5ng l\u1ed3. \u0110\u1eb7c bi\u1ec7t l\u00e0 ph\u1ea7n \u0111\u1ea1i s\u1ed1 \u2013 h\u00ecnh h\u1ecdc \u2013 x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 12? B\u1ed9 \u0110\u1ec1 Thi B\u1ed9 \u0110\u1ec1 Thi Cu\u1ed1i K\u00ec 1 [&#8230;]\n","protected":false},"author":1,"featured_media":2150,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[10],"class_list":["post-952","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\/952","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=952"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/952\/revisions"}],"predecessor-version":[{"id":2151,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/952\/revisions\/2151"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2150"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=952"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=952"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}