{"id":420,"date":"2026-05-05T04:44:49","date_gmt":"2026-05-05T04:44:49","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-cuong-giua-hoc-ky-2-toan-11-nam-2024-2025-truong-thpt-xuan-dinh-ha-noi\/"},"modified":"2026-05-05T07:17:34","modified_gmt":"2026-05-05T07:17:34","slug":"de-cuong-giua-hoc-ky-2-toan-11-nam-2024-2025-truong-thpt-xuan-dinh-ha-noi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-cuong-giua-hoc-ky-2-toan-11-nam-2024-2025-truong-thpt-xuan-dinh-ha-noi\/","title":{"rendered":"\u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i"},"content":{"rendered":"<p><strong>\u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/strong> l\u00e0 t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p nh\u1eefng chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 11. T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t n\u1ed9i dung ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc k\u1ef3 2, gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng, r\u00e8n luy\u1ec7n t\u01b0 duy logic v\u00e0 kh\u1ea3 n\u0103ng v\u1eadn d\u1ee5ng to\u00e1n h\u1ecdc v\u00e0o th\u1ef1c ti\u1ec5n. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>tailieuonthi<\/strong><\/a> kh\u00e1m ph\u00e1 ngay c\u00e1c d\u1ea1ng b\u00e0i trong \u0111\u1ec1 c\u01b0\u01a1ng n\u00e0y \u0111\u1ec3 s\u1eb5n s\u00e0ng chinh ph\u1ee5c b\u00e0i ki\u1ec3m tra gi\u1eefa k\u1ef3 nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/strong> \u0111\u01b0\u1ee3c chia th\u00e0nh ba ph\u1ea7n. Ph\u1ea7n A g\u1ed3m 81 c\u00e2u tr\u1eafc nghi\u1ec7m kh\u00e1ch quan v\u1edbi b\u1ed1n l\u1ef1a ch\u1ecdn A, B, C, D, bao ph\u1ee7 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c d\u1ea1ng b\u00e0i t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. Ph\u1ea7n B g\u1ed3m 36 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai, t\u1eadp trung ki\u1ec3m tra kh\u1ea3 n\u0103ng t\u01b0 duy logic v\u00e0 m\u1ee9c \u0111\u1ed9 hi\u1ec3u s\u00e2u l\u00fd thuy\u1ebft. Ph\u1ea7n C l\u00e0 13 b\u00e0i t\u1ef1 lu\u1eadn, y\u00eau c\u1ea7u h\u1ecdc sinh tr\u00ecnh b\u00e0y chi ti\u1ebft, gi\u1ea3i th\u00edch r\u00f5 r\u00e0ng. \u0110\u1ec1 c\u01b0\u01a1ng t\u1eadp trung v\u00e0o hai ch\u01b0\u01a1ng tr\u1ecdng t\u00e2m l\u00e0<\/p>\n<p>Ch\u01b0\u01a1ng VI \u2013 H\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 l\u00f4garit<\/p>\n<p>Ch\u01b0\u01a1ng VII \u2013 Quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian<\/p>\n<ul>\n<li>B\u00e0i 22: Hai \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c.<\/li>\n<li>B\u00e0i 23: \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng.<\/li>\n<li>B\u00e0i 24: Ph\u00e9p chi\u1ebfu vu\u00f4ng g\u00f3c. G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng.<\/li>\n<li>B\u00e0i 25: Hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c.<\/li>\n<\/ul>\n<p><strong>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u00edch t\u1eeb \u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/strong><\/p>\n<p><strong>C\u00e2u 1:<\/strong> V\u1edbi $a$ l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, $\\sqrt[3]{a^3}$ b\u1eb1ng: A. $a^6$\u00a0 \u00a0 B. $a^{\\frac{3}{2}}$\u00a0 \u00a0 C. $a^{\\frac{2}{3}}$\u00a0 \u00a0 D. $a^{\\frac{1}{6}}$<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho $a &gt; 0$, $m,n \\in \\mathbb{R}$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?<\/p>\n<p>A. $a^m + a^n = a^{m+n}$\u00a0 \u00a0 \u00a0 \u00a0B. $a^m \\cdot a^n = a^{m \u2013 n}$\u00a0 \u00a0 \u00a0 \u00a0C. $(a^n)^m = (a^m)^n$\u00a0 \u00a0 \u00a0 \u00a0D. $\\dfrac{a^m}{a^n} = a^{m \u2013 n}$<\/p>\n<p><strong>C\u00e2u 3:<\/strong> R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c $Q = b^{\\frac{5}{3}} \\div \\sqrt[3]{b}$ v\u1edbi $b &gt; 0$.<\/p>\n<p>A. $Q = b^{\\frac{4}{3}}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $Q = b^3$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. $Q = b^5$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $Q = b^2$<\/p>\n<p><strong>C\u00e2u 4:<\/strong> Cho $a$ l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng. Vi\u1ebft v\u00e0 r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c $a^{\\frac{3}{2024}} \\cdot \\sqrt[4]{a}$ d\u01b0\u1edbi d\u1ea1ng l\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 h\u1eefu t\u1ec9. T\u00ecm s\u1ed1 m\u0169 c\u1ee7a bi\u1ec3u th\u1ee9c r\u00fat g\u1ecdn \u0111\u00f3:<\/p>\n<p>A. $\\dfrac{2}{1005}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. $\\dfrac{1}{506}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. $\\dfrac{3}{2012}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. $\\dfrac{3}{2024^2}$<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/strong> kh\u00f4ng ch\u1ec9 l\u00e0 t\u00e0i li\u1ec7u h\u1ec7 th\u1ed1ng ki\u1ebfn th\u1ee9c quan tr\u1ecdng, m\u00e0 c\u00f2n gi\u00fap h\u1ecdc sinh l\u00e0m ch\u1ee7 c\u00e1c d\u1ea1ng b\u00e0i th\u01b0\u1eddng g\u1eb7p trong \u0111\u1ec1 ki\u1ec3m tra. V\u1edbi nhi\u1ec1u b\u00e0i t\u1eadp r\u00e8n luy\u1ec7n t\u01b0 duy logic, t\u00e0i li\u1ec7u to\u00e1n 11 n\u00e0y s\u1ebd h\u1ed7 tr\u1ee3 b\u1ea1n \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3 v\u00e0 t\u1ef1 tin b\u01b0\u1edbc v\u00e0o k\u1ef3 thi gi\u1eefa k\u1ef3. C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 click v\u00e0o \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 t\u1ea3i to\u00e0n b\u1ed9 \u0111\u1ec1 c\u01b0\u01a1ng:<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1uzpmTOnZdFtRrQ3VN2HKtrcWizf_RXLy\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1uzpmTOnZdFtRrQ3VN2HKtrcWizf_RXLy\/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\/1uzpmTOnZdFtRrQ3VN2HKtrcWizf_RXLy\/view\" rel=\"noopener nofollow\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 c\u01b0\u01a1ng gi\u1eefa h\u1ecdc k\u1ef3 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n \u0110\u1ec9nh H\u00e0 N\u1ed9i l\u00e0 t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p nh\u1eefng chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 11. T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t n\u1ed9i dung ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc k\u1ef3 2, gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c [&#8230;]\n","protected":false},"author":1,"featured_media":1619,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-420","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\/420","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=420"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/420\/revisions"}],"predecessor-version":[{"id":1620,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/420\/revisions\/1620"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1619"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}