{"id":578,"date":"2026-05-05T04:53:06","date_gmt":"2026-05-05T04:53:06","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-quang-binh\/"},"modified":"2026-05-05T07:27:01","modified_gmt":"2026-05-05T07:27:01","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-quang-binh","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-quang-binh\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &#038; \u0110T Qu\u1ea3ng B\u00ecnh"},"content":{"rendered":"<p><a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a> g\u1eedi \u0111\u1ebfn th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Qu\u1ea3ng B\u00ecnh<\/strong>. L\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ec1 thi \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 cao v\u00e0 ch\u1ecdn l\u00e0m t\u00e0i li\u1ec7u trong qu\u00e1 tr\u00ecnh \u00f4n luy\u1ec7n thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n. C\u1ea5u tr\u00fac \u0111\u1ec1 thi b\u00e1m s\u00e1t v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc v\u00e0 \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9, gi\u00fap c\u00e1c b\u1ea1n l\u00e0m quen v\u1edbi <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\">\u0111\u1ec1 thi <span>to\u00e1n thpt qu\u1ed1c gia<\/span><\/a>, n\u00e2ng cao c\u00e1c k\u1ef9 n\u0103ng l\u00e0m b\u00e0i v\u00e0 t\u00ecm ra \u0111\u01b0\u1ee3c chi\u1ebfn thu\u1eadt cho m\u00ecnh. H\u00e3y c\u00f9ng ch\u00fang t\u00f4i t\u00ecm hi\u1ec3u xem n\u1ed9i dung 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 Qu\u1ea3ng B\u00ecnh<\/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 Qu\u1ea3ng B\u00ecnh<\/strong> g\u1ed3m 22 c\u00e2u h\u1ecfi v\u1edbi h\u00ecnh th\u1ee9c tr\u1eafc nghi\u1ec7m v\u00e0 c\u00f3 90 ph\u00fat \u0111\u1ec3 ho\u00e0n th\u00e0nh, ph\u00f9 h\u1ee3p v\u1edbi \u0111\u1ecbnh d\u1ea1ng \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p THPT ch\u00ednh th\u1ee9c \u0111\u00e3 quy \u0111\u1ecbnh. N\u1ed9i dung c\u1ee7a \u0111\u1ec1 xoay quanh c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1: H\u00e0m s\u1ed1 v\u00e0 \u0111\u1ed3 th\u1ecb, M\u0169 \u2013 logarit, Nguy\u00ean h\u00e0m \u2013 t\u00edch ph\u00e2n \u2013 \u1ee9ng d\u1ee5ng, S\u1ed1 ph\u1ee9c, H\u00ecnh h\u1ecdc kh\u00f4ng gian, T\u1ecda \u0111\u1ed9 Oxyz. Ngo\u00e0i ra, \u1edf cu\u1ed1i \u0111\u1ec1, \u0111\u00e3 c\u00f3 s\u1eb5n \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch tr\u00ecnh b\u00e0y \u2013 gi\u1ea3i \u0111\u00e1p t\u1eebng c\u00e2u v\u00f4 c\u00f9ng chi ti\u1ebft v\u00e0 d\u1ec5 hi\u1ec3u.<\/p>\n<p><strong>Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/p>\n<p>Th\u00ed sinh ho\u00e0n th\u00e0nh 12 c\u00e2u h\u1ecfi, m\u1ed7i c\u00e2u ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn m\u1ed9t ph\u01b0\u01a1ng \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t, tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi sau:<\/p>\n<p><strong>C\u00e2u 1:<\/strong> \u0110i\u1ec3m ki\u1ec3m tra 15 ph\u00fat c\u1ee7a l\u1edbp 12A \u0111\u01b0\u1ee3c cho b\u1edfi b\u1ea3ng sau:<\/p>\n<p>beginarray|c|c|c|c|c|c|c|c| hline \u0110i\u1ec3m &amp; [3;4) &amp; [4;5) &amp; [5;6) &amp; [6;7) &amp; [7;8) &amp; [8;9) &amp; [9;10] hline S\u1ed1 h\u1ecdc sinh &amp; 3 &amp; 8 &amp; 7 &amp; 12 &amp; 7 &amp; 1 &amp; 1 hline endarray<\/p>\n<p>T\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 nh\u1ea5t c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m tr\u00ean (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m) l\u00e0:<\/p>\n<p>A. 2,10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. 4,84\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 2,09\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 6,94<\/p>\n<p>C\u00e2u 2: Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh  log\u2082 x = 3  l\u00e0:<\/p>\n<p>A.  x = 3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  x = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  x = 3\u00b2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  x = 2\u00b3 <\/p>\n<p><strong>C\u00e2u 3:<\/strong> Trong kh\u00f4ng gian  Oxyz , cho hai vect\u01a1  a\u20d7 = (1; -2; 1)  v\u00e0  b\u20d7 = (2; -4; -2) . Khi \u0111\u00f3  a\u20d7 \u00b7 b\u20d7  b\u1eb1ng:<\/p>\n<p>A. 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. -8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. -12<\/p>\n<p><strong>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n<p>M\u1ed7i c\u00e2u s\u1ebd c\u00f3 4 \u00fd a), b), c), d). Th\u00ed sinh ch\u1ec9 c\u1ea7n ghi gi\u00e1 tr\u1ecb \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i c\u00e2u.<\/p>\n<p><strong>C\u00e2u 1.<\/strong> M\u1ed9t s\u1ee3i d\u00e2y kim lo\u1ea1i d\u00e0i 6 (cm). Ng\u01b0\u1eddi ta c\u1eaft s\u1ee3i d\u00e2y \u0111\u00f3 th\u00e0nh hai \u0111o\u1ea1n. \u0110o\u1ea1n c\u00f3 \u0111\u1ed9 d\u00e0i  x  (cm) \u0111\u01b0\u1ee3c u\u1ed1n th\u00e0nh \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 \u0111o\u1ea1n c\u00f2n l\u1ea1i \u0111\u01b0\u1ee3c u\u1ed1n th\u00e0nh h\u00ecnh vu\u00f4ng  (0 &lt; x &lt; 6) .<\/p>\n<p>a) B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n l\u00e0: r = x\/\u03c0\n<\/p>\n<p>b) Di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng l\u00e0: ( (6 &#8211; x)\/(4) )\u00b2\n<\/p>\n<p>c) T\u1ed5ng di\u1ec7n t\u00edch hai h\u00ecnh l\u00e0: ((4 + \u03c0)x\u00b2 &#8211; 12\u03c0 x + 36\u03c0)\/(16\u03c0)\n<\/p>\n<p>d) Khi  x = (6\u03c0)\/(2 + \u03c0) , th\u00ec h\u00ecnh vu\u00f4ng v\u00e0 h\u00ecnh tr\u00f2n t\u01b0\u01a1ng \u1ee9ng c\u00f3 t\u1ed5ng di\u1ec7n t\u00edch nh\u1ecf nh\u1ea5t.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1  f(x) = sin 2x &#8211; x <\/p>\n<p>a)  int_-\u03c0\/2^\u03c0\/2 f(x) dx = -\u03c0\/2\n<\/p>\n<p>b) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0: f'(x) = cos 2x &#8211; 1\n<\/p>\n<p>c) Ph\u01b0\u01a1ng tr\u00ecnh  f'(x) = 0  c\u00f3 hai nghi\u1ec7m tr\u00ean \u0111o\u1ea1n  [ -\u03c0\/2, \u03c0\/2 ]  l\u00e0: x = -\u03c0\/6 v\u00e0 x = \u03c0\/6\n<\/p>\n<p>d) Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1  y = f(x)  tr\u00ean \u0111o\u1ea1n  [ -\u03c0\/2, \u03c0\/2 ]  l\u00e0: -\u03c0\/2\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>Tr\u00edch m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi hay trong \u0111\u1ec1 nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1:<\/strong> M\u1ed9t m\u00e1y bay kh\u00f4ng ng\u01b0\u1eddi l\u00e1i bay l\u00ean t\u1ea1i m\u1ed9t \u0111i\u1ec3m. Sau m\u1ed9t th\u1eddi gian bay, m\u00e1y bay c\u00e1ch \u0111i\u1ec3m xu\u1ea5t ph\u00e1t v\u1ec1 ph\u00eda B\u1eafc  50 (km)  v\u00e0 v\u1ec1 ph\u00eda T\u00e2y  20 (km) , \u0111\u1ed3ng th\u1eddi c\u00e1ch m\u1eb7t \u0111\u1ea5t  1 (km) . L\u00fac \u0111\u00f3 m\u00e1y bay c\u00e1ch v\u1ecb tr\u00ed t\u1ea1i \u0111i\u1ec3m xu\u1ea5t ph\u00e1t c\u1ee7a n\u00f3 l\u00e0  a (km) , gi\u00e1 tr\u1ecb c\u1ee7a  a  l\u00e0 bao nhi\u00eau? (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u  S.ABCD , c\u00f3 c\u1ea1nh \u0111\u00e1y b\u1eb1ng  2 , c\u1ea1nh b\u00ean b\u1eb1ng  2\u221a2 . T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng  AB  v\u00e0  SD  (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/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 Qu\u1ea3ng B\u00ecnh<\/strong><\/h2>\n<p>Th\u1eed s\u1ee9c v\u1edbi <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Qu\u1ea3ng B\u00ecnh<\/strong> s\u1ebd gi\u00fap c\u00e1c b\u1ea1n \u0111\u00e1nh gi\u00e1 \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c c\u1ee7a b\u1ea3n th\u00e2n v\u00e0 chu\u1ea9n b\u1ecb k\u1ebf ho\u1ea1ch \u00f4n luy\u1ec7n m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 nh\u1ea5t. T\u1ea3i ngay v\u00e0 \u00f4n t\u1eadp \u0111\u1ec1 thi qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1TM7FbOmO_CR_gqTXDvAFPB4QztivKIfD\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1TM7FbOmO_CR_gqTXDvAFPB4QztivKIfD\/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\/1TM7FbOmO_CR_gqTXDvAFPB4QztivKIfD\/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 Qu\u1ea3ng B\u00ecnh<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u00e0i li\u1ec7u \u00d4n Thi g\u1eedi \u0111\u1ebfn th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD &amp; \u0110T Qu\u1ea3ng B\u00ecnh. L\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ec1 thi \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 cao v\u00e0 ch\u1ecdn l\u00e0m t\u00e0i li\u1ec7u trong qu\u00e1 tr\u00ecnh \u00f4n luy\u1ec7n thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n. C\u1ea5u [&#8230;]\n","protected":false},"author":1,"featured_media":1777,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-578","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\/578","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=578"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/578\/revisions"}],"predecessor-version":[{"id":1778,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/578\/revisions\/1778"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1777"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}