{"id":556,"date":"2026-05-05T04:51:59","date_gmt":"2026-05-05T04:51:59","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-phu-tho\/"},"modified":"2026-05-05T07:25:41","modified_gmt":"2026-05-05T07:25:41","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-phu-tho","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-phu-tho\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &#038; \u0110T Ph\u00fa Th\u1ecd"},"content":{"rendered":"<p><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd<\/strong> l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch gi\u00fap c\u00e1c b\u1ea1n 12 l\u00e0m quen c\u00e1c d\u1ea1ng \u0111\u1ec1 thi th\u1eed \u0111\u1ec3 n\u1eafm v\u1eefng c\u1ea5u tr\u00fac \u0111\u1ec1, r\u00e8n luy\u1ec7n t\u01b0 duy v\u00e0 k\u1ef9 n\u0103ng gi\u1ea3i \u0111\u1ec1 hi\u1ec7u qu\u1ea3 nh\u1ea5t. \u0110\u1ec1 thi ph\u00e2n b\u1ed5 to\u00e0n b\u1ed9 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m To\u00e1n 12 t\u1eeb \u0111\u1ea1i s\u1ed1 \u0111\u1ebfn h\u00ecnh h\u1ecdc gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u qua n\u1ed9i dung \u0111\u1ec1 thi c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t 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 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd<\/strong> \u0111\u01b0\u1ee3c t\u1ed5ng h\u1ee3p b\u00e1m s\u00e1t nh\u1ea5t v\u1edbi c\u1ea5u tr\u00fac v\u00e0 \u0111\u1ecbnh d\u1ea1ng c\u1ee7a \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p THPT 2025 v\u1edbi th\u1eddi gian l\u00e0m b\u00e0i 90 ph\u00fat. Gi\u00fap c\u00e1c b\u1ea1n ph\u00e1t hi\u1ec7n v\u00e0 kh\u1eafc ph\u1ee5c nh\u1eefng l\u1ed7 h\u1ed5ng ki\u1ebfn th\u1ee9c c\u1ee7a m\u00ecnh v\u00e0 chu\u1ea9n b\u1ecb l\u1ed9 tr\u00ecnh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 nh\u1ea5t.<br \/>\nC\u1ea5u tr\u00fac c\u1ee7a m\u1ed9t <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\">\u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n<\/a> c\u00f3 ma tr\u1eadn c\u00e2u h\u1ecfi nh\u01b0 sau:<\/p>\n<p><strong>Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n<\/strong><\/p>\n<p>Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12, ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n cho m\u1ed7i c\u00e2u h\u1ecfi. Xem qua c\u00e1c c\u00e2u h\u1ecfi d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 1<\/strong>. Cho c\u1ea5p s\u1ed1 c\u1ed9ng  (u_n)  c\u00f3 s\u1ed1 h\u1ea1ng \u0111\u1ea7u  u\u2081 = 3 , c\u00f4ng sai  d = 2 . S\u1ed1 h\u1ea1ng th\u1ee9  5  c\u1ee7a  (u_n)  b\u1eb1ng<br \/>\n\\[<br \/>\nA.\u00a0 14 \\quad \\text{B. } 5 \\quad \\text{C. } 6 \\quad \\text{D. } 11<br \/>\n\\]\n<\/p>\n<p><strong>C\u00e2u 2<\/strong>. T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh log_1\/2(x+1) &gt; -1  l\u00e0<br \/>\n\\[<br \/>\nA.\u00a0 (-\\infty; 1) \\quad \\text{B. } (-1;1) \\quad \\text{C. } (1; +\\infty) \\quad \\text{D. } (0;3)<br \/>\n\\]\n<\/p>\n<p><strong>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n<p>Trong m\u1ed7i \u00fd a), b), c), d), th\u00ed sinh ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i \u0111\u00e1p \u00e1n. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1  f(x) = ln x &#8211; x\/2 <\/p>\n<p>a) T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 D = (0; +\u221e)\n<\/p>\n<p>b) f(1) = -1\/2; f(e) = -e\/2\n<\/p>\n<p>c) Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh  f'(x) = 0  tr\u00ean \u0111o\u1ea1n  [1; e]  l\u00e0 x = 2\n<\/p>\n<p>d) Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1  f(x)  tr\u00ean \u0111o\u1ea1n  [1; e]  b\u1eb1ng -1\/2\n<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1  f(x) = (x\u00b2 + 5x &#8211; 7)\/(x) <\/p>\n<p>a) int f(x) dx = (x\u00b2)\/(2) + 5x &#8211; 7 ln x + C\n<\/p>\n<p>b) H\u00e0m s\u1ed1  f(x)  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 g(x) = (x\u00b2 + 7)\/(x\u00b2)\n<\/p>\n<p>c) Bi\u1ebft int\u208b\u2082\u00b9 f(x) dx = m\/n + m ln n, m, n in mathbbZ, m\/n l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n. T\u1ed5ng  m + 2025n = 4057 <\/p>\n<p>d) G\u1ecdi  G(x)  l\u00e0 nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) , th\u1ecfa m\u00e3n G(1) = 4 v\u00e0 G(3) + G(-9) = 20\n<\/p>\n<p><strong>Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n<p>\u0110\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c \u0111i\u1ec3m t\u1ed1i \u0111a \u1edf ph\u1ea7n 3, c\u00e1c b\u1ea1n tham kh\u1ea3o v\u00e0 gi\u1ea3i ngay c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u1ec3 l\u00e0m quen v\u1edbi d\u1ea1ng n\u00e0y nh\u00e9:<\/p>\n<p><strong>C\u00e2u 1<\/strong>. Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u  S.ABCD , c\u00f3  O  l\u00e0 giao \u0111i\u1ec3m c\u1ee7a  AC  v\u00e0  BD . Bi\u1ebft SO = AB = 2.<br \/>\nGi\u00e1 tr\u1ecb  sin  c\u1ee7a g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng  SA  v\u00e0 m\u1eb7t ph\u1eb3ng  (SBC)  b\u1eb1ng bao nhi\u00eau? (K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)<\/p>\n<p><strong>C\u00e2u 2<\/strong>. C\u00f3 bao nhi\u00eau s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 b\u1ed1n ch\u1eef s\u1ed1 m\u00e0 t\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng  7 ?<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd<\/strong><\/h2>\n<p>H\u00e3y t\u1ea3i ngay <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd<\/strong> k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch gi\u1ea3i chi ti\u1ebft \u1edf cu\u1ed1i b\u00e0i. C\u00e1c b\u1ea1n h\u00e3y luy\u1ec7n t\u1eadp th\u01b0\u1eddng xuy\u00ean v\u1edbi nhi\u1ec1u \u0111\u1ec1 thi th\u1eed kh\u00e1c nhau \u0111\u1ec3 n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i \u0111\u1ec1 v\u00e0 \u00f4n t\u1eadp v\u1eefng ki\u1ebfn th\u1ee9c \u0111\u1ec3 chu\u1ea9n b\u1ecb cho k\u00ec thi s\u1eafp t\u1edbi.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1g9EMsCuw7MvYiroga1cAOzKElq7MNp47\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1g9EMsCuw7MvYiroga1cAOzKElq7MNp47\/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\/1g9EMsCuw7MvYiroga1cAOzKElq7MNp47\/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 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Ph\u00fa Th\u1ecd l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch gi\u00fap c\u00e1c b\u1ea1n 12 l\u00e0m quen c\u00e1c d\u1ea1ng \u0111\u1ec1 thi th\u1eed \u0111\u1ec3 n\u1eafm v\u1eefng c\u1ea5u tr\u00fac \u0111\u1ec1, r\u00e8n luy\u1ec7n t\u01b0 duy v\u00e0 k\u1ef9 n\u0103ng gi\u1ea3i \u0111\u1ec1 hi\u1ec7u qu\u1ea3 nh\u1ea5t. \u0110\u1ec1 thi ph\u00e2n b\u1ed5 [&#8230;]\n","protected":false},"author":1,"featured_media":1755,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-556","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\/556","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=556"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/556\/revisions"}],"predecessor-version":[{"id":1756,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/556\/revisions\/1756"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1755"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}