{"id":344,"date":"2026-05-05T04:40:41","date_gmt":"2026-05-05T04:40:41","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-cuong-hoc-ki-2-toan-11-nam-2024-2025-truong-thpt-yen-hoa-ha-noi\/"},"modified":"2026-05-05T07:13:25","modified_gmt":"2026-05-05T07:13:25","slug":"de-cuong-hoc-ki-2-toan-11-nam-2024-2025-truong-thpt-yen-hoa-ha-noi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-cuong-hoc-ki-2-toan-11-nam-2024-2025-truong-thpt-yen-hoa-ha-noi\/","title":{"rendered":"\u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i"},"content":{"rendered":"<p>C\u00e1c b\u1ea1n h\u1ecdc sinh 11 chu\u1ea9n b\u1ecb cho k\u1ef3 thi h\u1ecdc k\u00ec 2 kh\u00f4ng th\u1ec3 b\u1ecf qua <strong>\u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i<\/strong>. T\u1eadp t\u00e0i li\u1ec7u h\u1ec7 th\u1ed1ng to\u00e0n b\u1ed9 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 To\u00e1n \u0110\u1ea1i s\u1ed1 &amp; H\u00ecnh h\u1ecdc 11. C\u00f9ng v\u1edbi \u0111\u00f3 l\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp t\u1eeb tr\u1eafc nghi\u1ec7m \u0111\u1ebfn t\u1ef1 lu\u1eadn chi ti\u1ebft c\u00e1c ph\u1ea7n gi\u00fap c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng ghi nh\u1edb, \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3. C\u00f9ng <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i li\u1ec7u \u00d4n Thi <\/a><\/strong>t\u00ecm hi\u1ec3u qua t\u1eadp t\u00e0i li\u1ec7u n\u00e0y nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p>Ma tr\u1eadn ki\u1ebfn th\u1ee9c c\u1ee7a<strong> \u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i<\/strong> bao g\u1ed3m nh\u1eefng n\u1ed9i dung sau, c\u00e1c b\u1ea1n h\u1ecdc sinh 11 n\u00ean n\u1eafm v\u1eefng v\u00e0 r\u00e8n luy\u1ec7n t\u01b0 duy nh\u1ea1y b\u00e9n khi \u00f4n t\u1eadp nh\u00e9!<\/p>\n<p><span><strong>C\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/strong><\/span><\/p>\n<p><span><strong>A- \u0110\u1ea1i s\u1ed1<\/strong><\/span><\/p>\n<p><strong>Ch\u01b0\u01a1ng VI: H\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 Logarit<\/strong><\/p>\n<p>\u2013 L\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 th\u1ef1c<\/p>\n<p>\u2013 Logarit<\/p>\n<p>\u2013 H\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 Logarit<\/p>\n<p>\u2013 Ph\u01b0\u01a1ng tr\u00ecnh, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u0169 v\u00e0 Logarit<\/p>\n<p><strong>Ch\u01b0\u01a1ng VIII: C\u00e1c quy t\u1eafc t\u00ednh x\u00e1c su\u1ea5t.<\/strong><\/p>\n<p>\u2013 Bi\u1ebfn c\u1ed1 h\u1ee3p, bi\u1ebfn c\u1ed1 giao. Bi\u1ebfn c\u1ed1 \u0111\u1ed9c l\u1eadp.<\/p>\n<p>\u2013 C\u00f4ng th\u1ee9c c\u1ed9ng x\u00e1c su\u1ea5t.<\/p>\n<p>\u2013 C\u00f4ng th\u1ee9c nh\u00e2n x\u00e1c su\u1ea5t cho hai bi\u1ebfn c\u1ed1 \u0111\u1ed9c l\u1eadp.<\/p>\n<p><strong>Ch\u01b0\u01a1ng IX: \u0110\u1ea1o h\u00e0m.<\/strong><\/p>\n<p>\u2013 \u0110\u1ea1o h\u00e0m.<\/p>\n<p>\u2013 C\u00e1c quy t\u1eafc t\u00ednh \u0111\u1ea1o h\u00e0m.<\/p>\n<p>\u2013 \u0110\u1ea1o h\u00e0m c\u1ea5p hai.<\/p>\n<p><span><strong>B \u2013 H\u00ecnh h\u1ecdc<\/strong><\/span><\/p>\n<p><strong>Ch\u01b0\u01a1ng VII: Quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian.<\/strong><\/p>\n<p>\u2013 Hai \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c.<\/p>\n<p>\u2013 \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng.<\/p>\n<p>\u2013 Ph\u00e9p chi\u1ebfu vu\u00f4ng g\u00f3c. G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng.<\/p>\n<p>\u2013 Hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c.<\/p>\n<p>\u2013 Kho\u1ea3ng c\u00e1ch.<\/p>\n<p>\u2013 Th\u1ec3 t\u00edch.<\/p>\n<p><span><strong>Luy\u1ec7n t\u1eadp<\/strong><\/span><\/p>\n<p><strong>Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m kh\u00e1ch quan<\/strong><\/p>\n<p>\u2013 D\u1ea1ng 1: C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m kh\u00e1ch quan nhi\u1ec1u l\u1ef1a ch\u1ecdn<\/p>\n<p>\u2013 D\u1ea1ng 2: C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m kh\u00e1ch quan \u0111\u00fang \u2013 sai<\/p>\n<p>\u2013 D\u1ea1ng 3: C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m kh\u00e1ch quan tr\u1ea3 l\u1eddi ng\u1eafn<\/p>\n<p><strong>Ph\u1ea7n II: T\u1ef1 lu\u1eadn<\/strong><\/p>\n<p><strong>(***) Tr\u00edch m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i nh\u01b0 sau:<\/strong><\/p>\n<p><strong>C\u00e2u 38.<\/strong> S\u1ed1 nghi\u1ec7m nguy\u00ean c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh  (\u221a10 &#8211; 3)^3-x\/x-1 &gt; (\u221a10 + 3)^x+1\/x+3 l\u00e0<\/p>\n<p>   A.  1 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0   B.  0 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0    C.  3 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0    D.  2 .<\/p>\n<p><strong>C\u00e2u 39.<\/strong> Ph\u01b0\u01a1ng tr\u00ecnh  3^x \u00b7 4^x+1 = (1)\/(3^x)  c\u00f3 hai nghi\u1ec7m  x\u2081, x\u2082 . T\u00ednh  T = x\u2081 x\u2082 + x\u2081 + x\u2082 .<\/p>\n<p>   A.  T = 2 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0    B.  T = -log\u2084 4 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0   C.  T = 1 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0    D.  T = -1 .<\/p>\n<p><strong>C\u00e2u 40.<\/strong> B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh  ln (2x\u00b2 + 3) &gt; ln (x\u00b2 + ax + 1)  nghi\u1ec7m \u0111\u00fang v\u1edbi m\u1ecdi  x  khi:<\/p>\n<p>   A.  -2\u221a2 &lt; a &lt; 2\u221a2 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0   B.  0 &lt; a &lt; 2\u221a2 .<\/p>\n<p>   C.  0 &lt; a &lt; 2 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0    D.  -2 &lt; a &lt; 2 .<\/p>\n<p><strong>C\u00e2u 41.<\/strong> Cho bi\u1ec3u th\u1ee9c  A = ((a\u221a5)\/(b\u2075-x))^(\u221a5x &#8211; 2)\/(b-1) v\u1edbi  a, b &gt; 0 . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n<p>a) Sau khi r\u00fat g\u1ecdn, th\u00ec bi\u1ec3u th\u1ee9c  A  ch\u1ec9 ch\u1ee9a bi\u1ebfn  b .<\/p>\n<p>b) V\u1edbi  a = 2, b = 1 + 5\u221a2  th\u00ec  A = 113\/3 .<\/p>\n<p>c) Khi  A = a^m \u00b7 b  th\u00ec  m + n = 3 + \u221a5 .<\/p>\n<p>d) Khi  A = a^-m \u00b7 b  th\u00ec  m &#8211; n = 2 + \u221a5 .<\/p>\n<p><strong>C\u00e2u 42.<\/strong> V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c d\u01b0\u01a1ng  a, b, x, y  v\u00e0  a, b  kh\u00e1c  1 . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n<p>a)  log_a x log_x = log_x x .<\/p>\n<p>b)  log_a (xy) = log_a x + log_a y .<\/p>\n<p>c)  log_a x\/y = log_a x &#8211; log_a y .<\/p>\n<p>d)  log_a 1\/x = (1)\/(log_a x) .<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p>T\u1ea3i ngay <strong>\u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i<\/strong> qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y. H\u00e3y b\u1eaft tay v\u00e0o \u00f4n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1 m\u1ed7i ng\u00e0y nh\u00e9. Ch\u00fac b\u1ea1n c\u00f3 m\u1ed9t k\u1ef3 thi th\u1eadt may m\u1eafn v\u00e0 \u0111\u1ea1t th\u00e0nh t\u00edch cao.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1HKPF8jyjLqXp9KH9lsAQalgg8wWCwzO_\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1HKPF8jyjLqXp9KH9lsAQalgg8wWCwzO_\/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><strong><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1HKPF8jyjLqXp9KH9lsAQalgg8wWCwzO_\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00e1c b\u1ea1n h\u1ecdc sinh 11 chu\u1ea9n b\u1ecb cho k\u1ef3 thi h\u1ecdc k\u00ec 2 kh\u00f4ng th\u1ec3 b\u1ecf qua \u0110\u1ec1 c\u01b0\u01a1ng h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean H\u00f2a H\u00e0 N\u1ed9i. T\u1eadp t\u00e0i li\u1ec7u h\u1ec7 th\u1ed1ng to\u00e0n b\u1ed9 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 To\u00e1n \u0110\u1ea1i s\u1ed1 &amp; H\u00ecnh h\u1ecdc 11. C\u00f9ng v\u1edbi \u0111\u00f3 [&#8230;]\n","protected":false},"author":1,"featured_media":1543,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-344","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\/344","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=344"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/344\/revisions"}],"predecessor-version":[{"id":1544,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/344\/revisions\/1544"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1543"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}