{"id":338,"date":"2026-05-05T04:40:22","date_gmt":"2026-05-05T04:40:22","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-tham-khao-giua-hoc-ki-2-toan-11-nam-2024-2025-so-gddt-thanh-hoa\/"},"modified":"2026-05-05T07:13:06","modified_gmt":"2026-05-05T07:13:06","slug":"bo-de-tham-khao-giua-hoc-ki-2-toan-11-nam-2024-2025-so-gddt-thanh-hoa","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-tham-khao-giua-hoc-ki-2-toan-11-nam-2024-2025-so-gddt-thanh-hoa\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&#038;\u0110T Thanh H\u00f3a"},"content":{"rendered":"<p>\u0110\u1ec3 chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 thi gi\u1eefa To\u00e1n HK2, c\u00e1c b\u1ea1n h\u1ecdc sinh 11 c\u00f3 th\u1ec3 tham kh\u1ea3o qua <strong>B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong>. \u0110\u00e2y l\u00e0 t\u1eadp t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p c\u00e1c \u0111\u1ec1 thi c\u1ee7a s\u1edf GD&amp;\u0110T Thanh H\u00f3a c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft. Gi\u00fap c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp, h\u1ec7 th\u1ed1ng ki\u1ebfn th\u1ee9c m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 v\u00e0 \u0111\u1ea1t k\u1ebft qu\u1ea3 cao. Xem qua t\u00e0i li\u1ec7u v\u00e0 <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">\u00d4n thi<\/a> <\/strong>qua b\u00e0i vi\u1ebft sau \u0111\u00e2y nh\u00e9!<\/p>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong><\/h2>\n<p><strong>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong> v\u1edbi nhi\u1ec1u d\u1ea1ng \u0111\u1ec1 \u00f4n t\u1eadp, gi\u00fap \u0111\u00e1nh gi\u00e1 \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c c\u1ee7a h\u1ecdc sinh. Bao g\u1ed3m c\u00e1c b\u00e0i t\u1eadp v\u1ec1 ki\u1ebfn th\u1ee9c ch\u01b0\u01a1ng 6 &amp; 7 To\u00e1n 11 v\u1edbi n\u1ed9i dung g\u1ed3m 04 ph\u1ea7n nh\u01b0 sau:<\/p>\n<p><strong><span>Ch\u01b0\u01a1ng VI. H\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 Logarit<\/span><\/strong><\/p>\n<p>+ L\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 th\u1ef1c.<br \/>\n+ L\u00f4garit.<br \/>\n+ H\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 logarit.<br \/>\n+ Ph\u01b0\u01a1ng tr\u00ecnh, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u0169 v\u00e0 logarit.<\/p>\n<p><span><strong>Ch\u01b0\u01a1ng VII. Quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian<\/strong><\/span><\/p>\n<p>+ Hai \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c.<br \/>\n+ \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng.<br \/>\n+ Ph\u00e9p chi\u1ebfu vu\u00f4ng g\u00f3c. G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng.<br \/>\n+ Hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c.<br \/>\n+ Kho\u1ea3ng c\u00e1ch.<br \/>\n+ Th\u1ec3 t\u00edch.<\/p>\n<p><span><strong>Ph\u1ea7n I. C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn.<\/strong><\/span><\/p>\n<p>C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn. M\u1ed7i c\u00e2u h\u1ecfi h\u1ecdc sinh ch\u1ec9 ch\u1ecdn m\u1ed9t ph\u01b0\u01a1ng<br \/>\n\u00e1n. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi m\u1eabu c\u00f3 d\u1ea1ng nh\u01b0:<\/p>\n<p><strong>C\u00e2u 3<\/strong>. Cho c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng  a, b, c  v\u1edbi  a  v\u00e0  b  kh\u00e1c 1. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang?<\/p>\n<p>A.  log_a b\u00b2 \u00b7 log_b c = log_a c. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  log_a b\u00b2 \u00b7 log_b c = 1\/4 log_a c. <\/p>\n<p>C.  log_a b\u00b2 \u00b7 log_b c = 4 log_a c. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  log_a b\u00b2 \u00b7 log_b c = 2 log_a c. <\/p>\n<p><strong>C\u00e2u 4.<\/strong> T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 y = log\u2082 (x &#8211; 1) l\u00e0<\/p>\n<p>A.  (2; +\u221e) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (-\u221e; +\u221e) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  (1; +\u221e) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  (-\u221e; 1) .<\/p>\n<p><strong>C\u00e2u 5.<\/strong> Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3^2x+1 = 3^2-x l\u00e0<\/p>\n<p>A.  x = 1\/3 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  x = 0 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  x = -1 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  x = 1 .<\/p>\n<p><span><strong>Ph\u1ea7n II. C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai.<\/strong><\/span><\/p>\n<p>Th\u00ed sinh tr\u1ea3 l\u1eddi c\u00e2u 1, c\u00e2u 2. Trong m\u1ed7i \u00fd a), b), c), d) \u1edf m\u1ed7i c\u00e2u, th\u00ed sinh ch\u1ecdn \u0111\u00fang ho\u1eb7c sai.<\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho ph\u01b0\u01a1ng tr\u00ecnh log\u2083 ( x\u00b2 + 4x ) + log_1\/3 ( 2x + 3 ) = 0. (1)\n<\/p>\n<p>a) Ph\u01b0\u01a1ng tr\u00ecnh logarit c\u01a1 b\u1ea3n  log_a x = b  (v\u1edbi  0 &lt; a \u2260 1 ) c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 x = a^b.\n<\/p>\n<p>b) \u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (1) l\u00e0 begincasesx &lt; -4, x &gt; 0.endcases\n<\/p>\n<p>c) V\u1edbi \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh, ph\u01b0\u01a1ng tr\u00ecnh (1) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi log\u2083 ( (x\u00b2 + 4x)(2x+3) ) = 0.\n<\/p>\n<p>d) Ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai nghi\u1ec7m.<\/p>\n<p><span><strong>Ph\u1ea7n III. C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n<p>Tr\u00edch m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho  a  v\u00e0  b  l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n a\u2074 b = 16. T\u00ednh A = 4 log\u2082 a + log\u2082 b.\n<\/p>\n<p><strong>C\u00e2u 2.<\/strong> C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1  m  tr\u00ean  [-2024; 2025]  \u0111\u1ec3 h\u00e0m s\u1ed1 y = ln ( x\u00b2 &#8211; 2x &#8211; m + 1 ) c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0  mathbbR ?<\/p>\n<p><strong>C\u00e2u 3.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABC  c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh a = 4\u221a2 cm, c\u1ea1nh b\u00ean  SC vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y v\u00e0 SC = 2 cm. G\u1ecdi  M, N  l\u00e0 trung \u0111i\u1ec3m c\u1ee7a  AB  v\u00e0  BC . G\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng  SN  v\u00e0  CM  b\u1eb1ng bao nhi\u00eau \u0111\u1ed9?<\/p>\n<p><span><strong>Ph\u1ea7n IV. T\u1ef1 lu\u1eadn.<\/strong><\/span><\/p>\n<p>C\u00e1c b\u1ea1n h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o qua c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 19.<\/strong> C\u01b0\u1eddng \u0111\u1ed9 m\u1ed9t tr\u1eadn \u0111\u1ed9ng \u0111\u1ea5t  M  (\u0111\u1ed9 Richter) \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c M = log A &#8211; log A\u2080, v\u1edbi  A  l\u00e0 bi\u00ean \u0111\u1ed9 rung ch\u1ea5n t\u1ed1i \u0111a v\u00e0  A\u2080  l\u00e0 m\u1ed9t bi\u00ean \u0111\u1ed9 chu\u1ea9n (h\u1eb1ng s\u1ed1). \u0110\u1ea7u th\u1ebf k\u1ec9 20, m\u1ed9t tr\u1eadn \u0111\u1ed9ng \u0111\u1ea5t \u1edf San Francisco c\u00f3 c\u01b0\u1eddng \u0111\u1ed9 8 \u0111\u1ed9 Richter. Trong c\u00f9ng n\u0103m \u0111\u00f3, m\u1ed9t tr\u1eadn \u0111\u1ed9ng \u0111\u1ea5t kh\u00e1c \u1edf Nam M\u1ef9 c\u00f3 bi\u00ean \u0111\u1ed9 rung ch\u1ea5n m\u1ea1nh h\u01a1n g\u1ea5p 4 l\u1ea7n. H\u1ecfi c\u01b0\u1eddng \u0111\u1ed9 c\u1ee7a tr\u1eadn \u0111\u1ed9ng \u0111\u1ea5t \u1edf Nam M\u1ef9 l\u00e0 bao nhi\u00eau \u0111\u1ed9 Richter (k\u1ebft qu\u1ea3 \u0111\u01b0\u1ee3c l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c)?<\/p>\n<p><strong>C\u00e2u 20.<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABCD  c\u00f3 \u0111\u00e1y  ABCD  l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt v\u1edbi AB = a, AD = a\u221a3. C\u1ea1nh b\u00ean  SA  vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y v\u00e0 SA = a. T\u00ednh g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng  (SCD)  v\u00e0  (ABCD) .<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong><\/h2>\n<p>\u0110\u1ec3 n\u00e2ng cao kh\u1ea3 n\u0103ng t\u01b0 duy v\u00e0 k\u1ef9 n\u0103ng nh\u1ea1y b\u00e9n v\u1edbi \u0111\u1ec1 thi, t\u1ea3i ngay <strong>B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong> qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y. B\u1ea3n t\u00e0i li\u1ec7u n\u00e0y c\u00f3 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp \u0111i k\u00e8m l\u1eddi gi\u1ea3i v\u00f4 c\u00f9ng chi ti\u1ebft s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng chinh ph\u1ee5c \u0111\u1ec1 thi s\u1eafp t\u1edbi v\u1edbi \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1iFKlVaVEdDir8fA3uPBK8Oa41XbP9RhS\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1iFKlVaVEdDir8fA3uPBK8Oa41XbP9RhS\/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\/1iFKlVaVEdDir8fA3uPBK8Oa41XbP9RhS\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T<strong>\u1ea3i B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec3 chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 thi gi\u1eefa To\u00e1n HK2, c\u00e1c b\u1ea1n h\u1ecdc sinh 11 c\u00f3 th\u1ec3 tham kh\u1ea3o qua B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a. \u0110\u00e2y l\u00e0 t\u1eadp t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p c\u00e1c \u0111\u1ec1 thi c\u1ee7a s\u1edf GD&amp;\u0110T Thanh H\u00f3a c\u00f3 k\u00e8m [&#8230;]\n","protected":false},"author":1,"featured_media":1537,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-338","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\/338","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=338"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/338\/revisions"}],"predecessor-version":[{"id":1538,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/338\/revisions\/1538"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1537"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}