{"id":570,"date":"2026-05-05T04:52:42","date_gmt":"2026-05-05T04:52:42","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc\/"},"modified":"2026-05-05T07:26:32","modified_gmt":"2026-05-05T07:26:32","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc","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-xuan-hoa-vinh-phuc\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac"},"content":{"rendered":"<p><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac <\/strong>\u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng b\u00e1m s\u00e1t c\u1ea5u tr\u00fac v\u00e0 \u0111\u1ecbnh h\u01b0\u1edbng c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c &amp; \u0110\u00e0o t\u1ea1o, bao qu\u00e1t \u0111\u1ea7y \u0111\u1ee7 c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n THPT, t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. Trong b\u00e0i vi\u1ebft n\u00e0y, <strong>T\u00e0i Li\u1ec7u <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\">\u00d4n Thi<\/a><\/strong> s\u1ebd c\u00f9ng b\u1ea1n l\u00e0m r\u00f5 \u0111\u1ec1 thi n\u00e0y.<\/p>\n<h2><strong>N\u1ed9i dung <span data-sheets-root=\"1\">\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<p>D\u1ef1a tr\u00ean c\u1ea5u tr\u00fac chung c\u1ee7a c\u00e1c <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\">\u0111\u1ec1 thi thpt to\u00e1n<\/a> t\u1ea1i V\u0129nh Ph\u00fac n\u0103m 2024\u20132025, <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac<\/strong>\u00a0bao g\u1ed3m c\u00e1c ph\u1ea7n ch\u00ednh sau:<\/p>\n<p><span><strong>Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1  y = f(x)  c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 H\u00ecnh 1.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"size-medium wp-image-2929 aligncenter\" decoding=\"async\" height=\"286\" 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-xuan-hoa-vinh-phuc-1-300x286.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-1-300x286.jpg 300w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-1.jpg 360w\" width=\"300\"\/><\/p>\n<p>H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o trong c\u00e1c kho\u1ea3ng sau \u0111\u00e2y?<\/p>\n<p>A.  (0;1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (1;2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  (-1;0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  (-1;1) <\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho h\u00e0m s\u1ed1  y = f(x)  c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 H\u00ecnh 2.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"size-medium wp-image-2928 aligncenter\" decoding=\"async\" height=\"280\" 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-xuan-hoa-vinh-phuc-2-300x280.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-2-300x280.jpg 300w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-2.jpg 362w\" width=\"300\"\/><\/p>\n<p>\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang l\u00e0:<\/p>\n<p>A.  x = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  x = -2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  y = 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  y = -2 <\/p>\n<p><span><strong>Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u, m\u1ed7i c\u00e2u g\u1ed3m 4 \u00fd nh\u1ecf)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> Trong kh\u00f4ng gian t\u1ecda \u0111\u1ed9  Oxyz , cho \u0111\u01b0\u1eddng th\u1eb3ng  \u0394: (x &#8211; 2)\/(5) = (y &#8211; 1)\/(12) = (z &#8211; 6)\/(-13)  v\u00e0 m\u1eb7t ph\u1eb3ng  (P): x &#8211; 2y &#8211; 2z &#8211; 2025 = 0 .<\/p>\n<p>a) Vecto c\u00f3 t\u1ecda \u0111\u1ed9  (2;1;6)  l\u00e0 m\u1ed9t vecto ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a  \u0394 .<\/p>\n<p>b) Vecto c\u00f3 t\u1ecda \u0111\u1ed9  (1;2;-2)  l\u00e0 m\u1ed9t vecto ph\u00e1p tuy\u1ebfn c\u1ee7a  (P) .<\/p>\n<p>c) Cosin c\u1ee7a g\u00f3c gi\u1eefa hai vecto  u\u20d7 = (5;12;-13)  v\u00e0  n\u20d7 = (1;-2;-2)  b\u1eb1ng  (7)\/(39\u221a2) .<\/p>\n<p>d) G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng  \u0394  v\u00e0 m\u1eb7t ph\u1eb3ng  (P)  (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb c\u1ee7a \u0111\u1ed9) b\u1eb1ng  83^\u00b0 .<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho h\u00e0m s\u1ed1  y = x + 4\/x .<\/p>\n<p>a) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0  y\u2019 = 1 &#8211; (4)\/(x\u00b2) .<\/p>\n<p>b) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho nh\u1eadn gi\u00e1 tr\u1ecb \u00e2m tr\u00ean c\u00e1c kho\u1ea3ng  (-2;0) cup (0;2)  v\u00e0 nh\u1eadn gi\u00e1 tr\u1ecb d\u01b0\u01a1ng tr\u00ean c\u00e1c kho\u1ea3ng  (-\u221e;-2) cup (2;+\u221e) .<\/p>\n<p>c) B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0:<\/p>\n<p><img alt=\"\" class=\"aligncenter wp-image-2932 size-full\" decoding=\"async\" height=\"227\" loading=\"lazy\" sizes=\"auto, (max-width: 663px) 100vw, 663px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-5.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-5.jpg 663w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-5-300x103.jpg 300w\" width=\"663\"\/><\/p>\n<p>d) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho nh\u01b0 \u1edf h\u00ecnh 4.<\/p>\n<p><img alt=\"\" class=\"size-medium wp-image-2930 aligncenter\" decoding=\"async\" height=\"300\" loading=\"lazy\" sizes=\"auto, (max-width: 295px) 100vw, 295px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-3-295x300.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-3-295x300.jpg 295w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-3.jpg 390w\" width=\"295\"\/><\/p>\n<p><span><strong>Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> M\u1ed9t chi\u1ebfc b\u00e1t thu\u1ef7 tinh c\u00f3 b\u1ec1 d\u00e0y c\u1ee7a ph\u1ea7n xung quanh l\u00e0 m\u1ed9t kh\u1ed1i tr\u00f2n xoay, khi xoay h\u00ecnh ph\u1eb3ng  D  quanh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng  a  b\u1ea5t k\u1ef3 n\u00e0o \u0111\u00f3 m\u00e0 khi g\u1eafn h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9  Oxy  (\u0111\u01a1n v\u1ecb tr\u00ean tr\u1ee5c l\u00e0 decimet) v\u00e0o h\u00ecnh ph\u1eb3ng  D  t\u1ea1i m\u1ed9t v\u1ecb tr\u00ed th\u00edch h\u1ee3p, th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng  a  s\u1ebd tr\u00f9ng v\u1edbi tr\u1ee5c  Ox . Khi \u0111\u00f3 h\u00ecnh ph\u1eb3ng  D  \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = x + 1\/x ,  y = x  v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng  x = 1 ,  x = 4  (H\u00ecnh 4). Th\u1ec3 t\u00edch c\u1ee7a b\u1ec1 d\u00e0y chi\u1ebfc b\u00e1t thu\u1ef7 tinh \u0111\u00f3 b\u1eb1ng bao nhi\u00eau decimet kh\u1ed1i? (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n<p><img alt=\"\" class=\"size-medium wp-image-2933 aligncenter\" decoding=\"async\" height=\"300\" loading=\"lazy\" sizes=\"auto, (max-width: 281px) 100vw, 281px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-4-281x300.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-4-281x300.jpg 281w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-xuan-hoa-vinh-phuc-4.jpg 392w\" width=\"281\"\/><\/p>\n<p><strong>C\u00e2u 2:<\/strong> M\u1ed9t ng\u01b0\u1eddi g\u1eedi  60  tri\u1ec7u \u0111\u1ed3ng v\u00e0o ng\u00e2n h\u00e0ng v\u1edbi l\u00e3i su\u1ea5t  0,5%  \/th\u00e1ng. Bi\u1ebft r\u1eb1ng n\u1ebfu kh\u00f4ng r\u00fat ti\u1ec1n ra kh\u1ecfi ng\u00e2n h\u00e0ng th\u00ec c\u1ee9 sau m\u1ed7i th\u00e1ng, s\u1ed1 ti\u1ec1n l\u00e3i s\u1ebd \u0111\u01b0\u1ee3c nh\u1eadp v\u00e0o v\u1ed1n ban \u0111\u1ea7u (hay g\u1ecdi l\u00e0 l\u00e3i k\u00e9p). Gi\u1ea3 s\u1eed trong nhi\u1ec1u th\u00e1ng li\u00ean ti\u1ebfp k\u1ec3 t\u1eeb khi g\u1eedi ti\u1ec1n, ng\u01b0\u1eddi \u0111\u00f3 kh\u00f4ng r\u00fat ti\u1ec1n ra v\u00e0 l\u00e3i su\u1ea5t kh\u00f4ng thay \u0111\u1ed5i. H\u1ecfi t\u1eeb th\u00e1ng th\u1ee9 m\u1ea5y tr\u1edf \u0111i, ng\u01b0\u1eddi \u0111\u00f3 c\u00f3 h\u01a1n  66  tri\u1ec7u \u0111\u1ed3ng?<\/p>\n<h2><strong>T\u1ea3i <span data-sheets-root=\"1\">\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<p>\u0110\u1ec3 xem tr\u1ecdn b\u1ed9 \u0111\u1ec1 thi v\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft c\u1ee7a <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac<\/strong>, h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i file PDF b\u00ean d\u01b0\u1edbi.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1Gjjl-lqfJjaOymDg6ztyxtq4JpOHxdOz\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1Gjjl-lqfJjaOymDg6ztyxtq4JpOHxdOz\/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\/1Gjjl-lqfJjaOymDg6ztyxtq4JpOHxdOz\/view\" rel=\"noopener nofollow\" 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 Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Xu\u00e2n H\u00f2a V\u0129nh Ph\u00fac \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng b\u00e1m s\u00e1t c\u1ea5u tr\u00fac v\u00e0 \u0111\u1ecbnh h\u01b0\u1edbng c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c &amp; \u0110\u00e0o t\u1ea1o, bao qu\u00e1t \u0111\u1ea7y \u0111\u1ee7 c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n THPT, t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. Trong [&#8230;]\n","protected":false},"author":1,"featured_media":1769,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-570","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\/570","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=570"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/570\/revisions"}],"predecessor-version":[{"id":1770,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/570\/revisions\/1770"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1769"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}