{"id":542,"date":"2026-05-05T04:51:15","date_gmt":"2026-05-05T04:51:15","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-dao-duy-tu-thanh-hoa\/"},"modified":"2026-05-05T07:24:47","modified_gmt":"2026-05-05T07:24:47","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-dao-duy-tu-thanh-hoa","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-dao-duy-tu-thanh-hoa\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a"},"content":{"rendered":"<p><a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a> g\u1eedi \u0111\u1ebfn qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a<\/strong>. Nh\u1eb1m h\u1ed7 tr\u1ee3 th\u1ea7y c\u00f4 chu\u1ea9n b\u1ecb t\u00e0i li\u1ec7u trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 luy\u1ec7n \u0111\u1ec1 cho c\u00e1c em h\u1ecdc sinh 12 chu\u1ea9n b\u1ecb cho k\u00ec thi quan tr\u1ecdng s\u1eafp t\u1edbi. H\u00e3y c\u00f9ng ch\u00fang t\u00f4i t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 n\u1ed9i dung qua b\u00e0i vi\u1ebft sau \u0111\u00e2y nh\u00e9.<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a<\/strong><\/h2>\n<p>N\u1ed9i dung <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u1edfi c\u00e1c th\u1ea7y c\u00f4 gi\u00e1o nhi\u1ec1u n\u0103m kinh nghi\u1ec7m c\u1ee7a s\u1edf GD&amp;\u0110T Thanh H\u00f3a. C\u00f9ng v\u1edbi \u0111\u00f3 l\u00e0 c\u00e1c ph\u01b0\u1eddng gi\u00e1p v\u00e0 c\u00e1ch gi\u1ea3i chi ti\u1ebft \u1edf cu\u1ed1i \u0111\u1ec1 thi, gi\u00fap c\u00e1c b\u1ea1n h\u1ecdc sinh d\u1ec5 d\u00e0ng \u00f4n t\u1eadp v\u00e0 s\u1eeda b\u00e0i.<\/p>\n<p><span><strong>Ph\u1ea7n 1 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/span><\/p>\n<p>M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 thi th\u1eed to\u00e1n thpt c\u00f3 d\u1ea1ng tr\u00ean nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1<\/strong>: Ph\u01b0\u01a1ng tr\u00ecnh  2sin x &#8211; \u221a3 = 0  c\u00f3 t\u1eadp nghi\u1ec7m l\u00e0:<\/p>\n<p>A.  \u03c0\/6 + k2\u03c0, k in mathbbZ <\/p>\n<p>B.  \u00b1 \u03c0\/3 + k2\u03c0, k in mathbbZ <\/p>\n<p>C.  \u03c0\/6 + k2\u03c0, 5\u03c0\/6 + k2\u03c0, k in mathbbZ <\/p>\n<p>D.  \u03c0\/3 + k2\u03c0, 2\u03c0\/3 + k2\u03c0, k in mathbbZ <\/p>\n<p><strong>C\u00e2u 2<\/strong>: T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh  log\u2082(x &#8211; 1) &lt; 3  l\u00e0:<\/p>\n<p>A.  (-\u221e; 10) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (1; 9) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  (1; 10) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  (-\u221e; 9) <\/p>\n<p><span><strong>Ph\u1ea7n 2 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<br \/>\n<\/strong><\/span><br \/>\nTh\u00ed sinh c\u1ea7n \u0111\u01b0a ra m\u1ec7nh \u0111\u1ec1 <strong>\u0110\u00daNG \/ SAI<\/strong> cho m\u1ed7i c\u00e2u tr\u1ea3 l\u1eddi c\u00f3 s\u1eb5n c\u1ee7a \u0111\u1ec1 thi. Xem v\u00e0 gi\u1ea3i ngay c\u00e1c c\u00e2u h\u1ecfi d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 1<\/strong>: Cho h\u00e0m s\u1ed1  y = (2x + 1)\/(x &#8211; 1)  c\u00f3 \u0111\u1ed3 th\u1ecb  (C) .<\/p>\n<p>a. \u0110\u1ed3 th\u1ecb  (C)  c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng  x = 1  v\u00e0 ti\u1ec7m c\u1eadn ngang  y = 1 .<\/p>\n<p>b. H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng x\u00e1c \u0111\u1ecbnh c\u1ee7a n\u00f3.<\/p>\n<p>c. C\u00f3 \u0111\u00fang 3 \u0111i\u1ec3m thu\u1ed9c \u0111\u1ed3 th\u1ecb  (C)  m\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a ch\u00fang l\u00e0 nh\u1eefng s\u1ed1 nguy\u00ean.<\/p>\n<p>d. G\u1ecdi  M  l\u00e0 \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u1ed3 th\u1ecb  (C)  v\u00e0  H, K  t\u01b0\u01a1ng \u1ee9ng l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a  M  tr\u00ean c\u00e1c tr\u1ee5c  Ox  v\u00e0  Oy . C\u00f3 2 \u0111i\u1ec3m  M  c\u00f3 ho\u00e0nh \u0111\u1ed9 d\u01b0\u01a1ng th\u1ecfa m\u00e3n t\u1ee9 gi\u00e1c  MHOK  c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng 2.<\/p>\n<p><strong>C\u00e2u 2<\/strong>: Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9  Oxyz , cho tam gi\u00e1c  ABC  v\u1edbi  A(4; 0; 2), B(1; -4; -2), C(2; 1; 1).\n<\/p>\n<p>a. T\u1ecda \u0111\u1ed9 tr\u1ecdng t\u00e2m tam gi\u00e1c  ABC  l\u00e0  G( 7\/3; -1; -1\/3 ).\n<\/p>\n<p>b. \u0110i\u1ec3m  D  th\u1ecfa m\u00e3n  ABDC  l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh, khi \u0111\u00f3 t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m  D  l\u00e0  D(5; 5; 5).\n<\/p>\n<p>c. Tam gi\u00e1c  ABC  l\u00e0 tam gi\u00e1c t\u00f9.<\/p>\n<p>d. G\u1ecdi \u0111i\u1ec3m  E(a; b; c)  l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng  BC  v\u1edbi m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9  (Oxz) , khi \u0111\u00f3  2a\/c + b = 9\/2.\n<\/p>\n<p><span><strong>Ph\u1ea7n 3 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n<p>C\u00e1c b\u1ea1n tham kh\u1ea3o qua c\u00e1c c\u00e2u h\u1ecfi trong <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\">\u0111\u1ec1 thi th\u1eed to\u00e1n thpt<\/a> nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1<\/strong>: M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng theo quy lu\u1eadt  s = t\u00b3 &#8211; 18t\u00b2 , v\u1edbi  t  (gi\u00e2y) l\u00e0 kho\u1ea3ng th\u1eddi gian t\u00ednh t\u1eeb l\u00fac v\u1eadt b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng v\u00e0  s  (m\u00e9t) l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng v\u1eadt \u0111i \u0111\u01b0\u1ee3c trong th\u1eddi gian \u0111\u00f3. H\u1ecfi trong kho\u1ea3ng th\u1eddi gian 10 gi\u00e2y, k\u1ec3 t\u1eeb l\u00fac b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng, v\u1eadn t\u1ed1c l\u1edbn nh\u1ea5t c\u1ee7a v\u1eadt \u0111\u1ea1t \u0111\u01b0\u1ee3c b\u1eb1ng bao nhi\u00eau ( m\/s )?<\/p>\n<p><strong>C\u00e2u 2<\/strong>: Cho bi\u1ebft kim t\u1ef1 th\u00e1p Memphis t\u1ea1i bang Tennessee (M\u1ef9) c\u00f3 d\u1ea1ng h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u v\u1edbi chi\u1ec1u cao  98m  v\u00e0 c\u1ea1nh \u0111\u00e1y  180m . G\u1ecdi g\u00f3c nh\u1ecb di\u1ec7n t\u1ea1o b\u1edfi m\u1eb7t b\u00ean v\u00e0 m\u1eb7t \u0111\u00e1y l\u00e0  \u03b1 . T\u00ednh  tan\u03b1 . (L\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"alignnone size-medium wp-image-2785 aligncenter\" decoding=\"async\" height=\"168\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-dao-duy-tu-thanh-hoa-1-300x168.png\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-dao-duy-tu-thanh-hoa-1-300x168.png 300w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-dao-duy-tu-thanh-hoa-1.png 488w\" width=\"300\"\/><\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a<\/strong><\/h2>\n<p>\u0110\u1eebng b\u1ecf l\u1ee1 b\u1ed9 t\u00e0i li\u1ec7u b\u1ed5 \u00edch v\u00e0 quan tr\u1ecdng n\u00e0y, b\u1eb1ng c\u00e1ch t\u1ea3i ngay <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a<\/strong> qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y. Ch\u00fac b\u1ea1n \u0111\u1ea1t \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 cao trong k\u00ec thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n to\u00e1n.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1XMl6tsFdAVM8USuhBUqfr57BXY4wRFFV\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1XMl6tsFdAVM8USuhBUqfr57BXY4wRFFV\/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\/1XMl6tsFdAVM8USuhBUqfr57BXY4wRFFV\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u00e0i li\u1ec7u \u00d4n Thi g\u1eedi \u0111\u1ebfn qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u00e0o Duy T\u1eeb Thanh H\u00f3a. Nh\u1eb1m h\u1ed7 tr\u1ee3 th\u1ea7y c\u00f4 chu\u1ea9n b\u1ecb t\u00e0i li\u1ec7u trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 luy\u1ec7n \u0111\u1ec1 cho c\u00e1c em h\u1ecdc sinh 12 [&#8230;]\n","protected":false},"author":1,"featured_media":1741,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-542","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-de-thi-thu-thpt-mon-toan","tag-de-thi-thu-thpt-mon-toan"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/542","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=542"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/542\/revisions"}],"predecessor-version":[{"id":1742,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/542\/revisions\/1742"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1741"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}