{"id":498,"date":"2026-05-05T04:48:59","date_gmt":"2026-05-05T04:48:59","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-vinh-nghe-an\/"},"modified":"2026-05-05T07:22:12","modified_gmt":"2026-05-05T07:22:12","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-vinh-nghe-an","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-chuyen-vinh-nghe-an\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Chuy\u00ean Vinh Ngh\u1ec7 An"},"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 Chuy\u00ean Vinh Ngh\u1ec7 An<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n tr\u01b0\u1edbc k\u00ec thi d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh 12. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf b\u00e1m s\u00e1t \u0111\u1ecbnh h\u01b0\u1edbng c\u1ee7a B\u1ed9 GD &amp; \u0110T, xen k\u1ebd gi\u1eefa h\u1ec7 th\u1ed1ng c\u00e2u h\u1ecfi c\u01a1 b\u1ea3n v\u00e0 n\u00e2ng cao, gi\u00fap h\u1ecdc sinh kh\u00f4ng ch\u1ec9 \u00f4n t\u1eadp ki\u1ebfn th\u1ee9c v\u1eefng ch\u1eafc m\u00e0 c\u00f2n n\u00e2ng cao k\u1ef9 n\u0103ng v\u00e0 ph\u1ea3n x\u1ea1 trong qu\u00e1 tr\u00ecnh l\u00e0m \u0111\u1ec1. H\u00e3y c\u00f9ng t\u00ecm hi\u1ec3u n\u1ed9i dung c\u1ee7a \u0111\u1ec1 thi v\u1edbi <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a> qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y.<\/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 Chuy\u00ean Vinh Ngh\u1ec7 An<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Chuy\u00ean Vinh Ngh\u1ec7 An<\/strong> tuy\u1ec3n t\u1eadp c\u00e1c c\u00e2u h\u1ecfi v\u1edbi c\u00e1c d\u1ea1ng tr\u1eafc nghi\u1ec7m, c\u00e2u h\u1ecfi \u0111\u00fang sai, tr\u1ea3 l\u1eddi ng\u1eafn. \u0110\u1ec3 chinh ph\u1ee5c <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 thpt qu\u1ed1c gia m\u00f4n to\u00e1n<\/a> c\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea7n n\u1eafm v\u1eefng ma tr\u1eadn \u0111\u1ec1 thi nh\u01b0 sau:<\/p>\n<p><span><strong>Ph\u1ea7n 1 \u2013 Tr\u1eafc nghi\u1ec7m 4 ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn ( 12 c\u00e2u )<\/strong><\/span><\/p>\n<p>Th\u00ed sinh c\u1ea7n \u0111\u1ecdc k\u0129 \u0111\u1ec1 v\u00e0 4 \u0111\u00e1p \u00e1n, sau \u0111\u00f3 ch\u1ecdn ra ph\u01b0\u01a1ng \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi:<\/p>\n<p><strong>C\u00e2u 1<\/strong>: Cho h\u00e0m s\u1ed1  y = (ax\u00b2 + bx + c)\/(mx + n) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean. Ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0:<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"alignnone size-full wp-image-2560 aligncenter\" decoding=\"async\" height=\"207\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-vinh-nghe-an-1.png\" width=\"270\"\/><\/p>\n<p>A.  y = -x + 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  y = x &#8211; 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  y = -x &#8211; 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  y = x + 1 <\/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  a . G\u00f3c nh\u1ecb di\u1ec7n t\u1ea1o b\u1edfi m\u1eb7t b\u00ean v\u00e0 m\u1eb7t \u0111\u00e1y c\u1ee7a h\u00ecnh ch\u00f3p c\u00f3 s\u1ed1 \u0111o b\u1eb1ng  45^\u00b0 . Th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p  S.ABCD  l\u00e0:<\/p>\n<p>A.  V = (a\u00b3)\/(2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  V = (a\u00b3)\/(6) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  V = (a\u00b3)\/(3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  V = (a\u00b3)\/(4) <\/p>\n<p><span><strong>Ph\u1ea7n 2 \u2013 Tr\u1eafc nghi\u1ec7m ch\u1ecdn \u0111\u00fang sai ( 4 c\u00e2u )<\/strong><\/span><\/p>\n<p>C\u00f3 t\u1ea5t c\u1ea3 4 c\u00e2u trong m\u1ed7i \u0111\u1ec1 thi, th\u00ed sinh ch\u1ec9 c\u1ea7n ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i \u0111\u00e1p \u00e1n.<\/p>\n<p><strong>C\u00e2u 1<\/strong>: Trong h\u1ec7 t\u1ecda \u0111\u1ed9  Oxyz , cho c\u00e1c \u0111i\u1ec3m  A(5;3;4), B(1;2;1), C(8;-3;2) . G\u1ecdi  D(a;b;c)  l\u00e0 ch\u00e2n \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong k\u1ec1 t\u1eeb \u0111\u1ec9nh  A  c\u1ee7a tam gi\u00e1c  ABC .<\/p>\n<p>a) Tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c  ABC  c\u00f3 t\u1ecda \u0111\u1ed9  G(14\/3, 2\/3, 7\/3 ) .<\/p>\n<p>b)  BC = 5\u221a2 .<\/p>\n<p>c) Tam gi\u00e1c  ABC  l\u00e0 tam gi\u00e1c vu\u00f4ng.<\/p>\n<p>d) Gi\u00e1 tr\u1ecb  a + 2b + 3c  l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean.<\/p>\n<p><strong>C\u00e2u 2<\/strong>: Cho h\u00e0m s\u1ed1  f(x) = log\u2082(x+4) <\/p>\n<p>a) T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho ch\u1ee9a \u0111\u00fang 4 s\u1ed1 nguy\u00ean \u00e2m.<\/p>\n<p>b) Ph\u01b0\u01a1ng tr\u00ecnh  f(x) = log\u2082(x\u00b2 + 2x &#8211; 16)  c\u00f3 nghi\u1ec7m duy nh\u1ea5t  x = 4 .<\/p>\n<p>c) H\u00e0m s\u1ed1  g(x) = -x\u00b2 + f(x) ln 1024  \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i  x = 1 .<\/p>\n<p>d) \u0110\u01b0\u1eddng th\u1eb3ng  y = x &#8211; 1  c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = f(x)  t\u1ea1i duy nh\u1ea5t m\u1ed9t \u0111i\u1ec3m.<\/p>\n<p><span><strong>Ph\u1ea7n 3 \u2013 Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn ( 6 c\u00e2u )<\/strong><\/span><\/p>\n<p>Xem qua c\u00e1c v\u00ed d\u1ee5 c\u00e2u h\u1ecfi c\u1ee7a ph\u1ea7n 3<\/p>\n<p><strong>C\u00e2u 1<\/strong>: \u1ede m\u1ed9t v\u1ecbnh bi\u1ec3n, ngo\u00e0i kh\u01a1i xa c\u00f3 m\u1ed9t h\u00f2n \u0111\u1ea3o nh\u1ecf. Ng\u01b0\u1eddi ta ti\u1ebfn h\u00e0nh l\u1ea5n bi\u1ec3n \u0111\u1ec3 x\u00e2y d\u1ef1ng khu \u0111\u00f4 th\u1ecb v\u00e0 l\u00e0m m\u1ed9t tuy\u1ebfn c\u00e1p treo n\u1ed1i khu \u0111\u00f4 th\u1ecb v\u1edbi h\u00f2n \u0111\u1ea3o \u0111\u1ec3 ph\u00e1t tri\u1ec3n du l\u1ecbch. X\u00e9t trong h\u1ec7 t\u1ecda \u0111\u1ed9  Oxy  v\u1edbi \u0111\u01a1n v\u1ecb t\u01b0\u01a1ng \u1ee9ng 1km c\u00f3 h\u00f2n \u0111\u1ea3o \u1edf  O , th\u00ec \u0111\u01b0\u1eddng bao c\u1ee7a ph\u1ea7n \u0111\u1ea5t l\u1ea5n bi\u1ec3n c\u00f3 d\u1ea1ng l\u00e0 m\u1ed9t ph\u1ea7n c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = (-x\u00b2 + 1)\/(x) Gi\u1ea3 s\u1eed tuy\u1ebfn c\u00e1p treo \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf n\u1ed1i \u0111\u1ea3o v\u1edbi \u0111\u01b0\u1eddng bao c\u1ee7a khu \u0111\u00f4 th\u1ecb v\u1edbi \u0111\u1ed9 d\u00e0i ng\u1eafn nh\u1ea5t. \u0110\u1ed9 d\u00e0i c\u1ee7a tuy\u1ebfn c\u00e1p treo l\u00e0 bao nhi\u00eau km (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi)?<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"size-full wp-image-2561 aligncenter\" decoding=\"async\" height=\"215\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-vinh-nghe-an-2.png\" width=\"279\"\/><\/p>\n<p><strong>C\u00e2u 2<\/strong>: \u0110\u1ea7u n\u0103m m\u1edbi 2025, c\u00f4ng ty  A  v\u1eeba k\u00ed h\u1ee3p \u0111\u1ed3ng s\u1ea3n xu\u1ea5t v\u00e0 cung c\u1ea5p linh ki\u1ec7n theo \u0111\u01a1n \u0111\u1eb7t h\u00e0ng c\u1ee7a nh\u00e0 m\u00e1y  B . Theo h\u1ee3p \u0111\u1ed3ng, nh\u00e0 m\u00e1y  B  mua kh\u00f4ng qu\u00e1 1500 linh ki\u1ec7n. N\u1ebfu s\u1ed1 l\u01b0\u1ee3ng \u0111\u1eb7t h\u00e0ng l\u00e0  x  th\u00ec gi\u00e1 b\u00e1n m\u1ed7i linh ki\u1ec7n l\u00e0  P(x) = 40 000 &#8211; 0,01x\u00b2 (\u0111\u1ed3ng). Chi ph\u00ed \u0111\u1ec3 c\u00f4ng ty s\u1ea3n xu\u1ea5t  x  linh ki\u1ec7n l\u00e0  C(x) = 10 000 000 + 10 000x. H\u1ecfi c\u00f4ng ty  A  n\u00ean s\u1ea3n xu\u1ea5t v\u00e0 cung c\u1ea5p bao nhi\u00eau linh ki\u1ec7n cho nh\u00e0 m\u00e1y  B  \u0111\u1ec3 thu \u0111\u01b0\u1ee3c l\u1ee3i nhu\u1eadn l\u1edbn nh\u1ea5t?<\/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 Chuy\u00ean Vinh Ngh\u1ec7 An<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Chuy\u00ean Vinh Ngh\u1ec7 An<\/strong> s\u1ebd l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u h\u1eefu \u00edch d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea5p 3. H\u00e3y t\u1ea3i ngay b\u1ed9 \u0111\u1ec1 k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch gi\u1ea3i chi ti\u1ebft qua \u0111\u01b0\u1eddng link sau. V\u00e0 b\u1eaft \u0111\u1ea7u chu\u1ea9n b\u1ecb cho b\u1ea3n th\u00e2n m\u1ed9t l\u1ed9 tr\u00ecnh \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3 v\u00e0 v\u01b0\u1ee3t qua k\u00ec thi thpt m\u00f4n to\u00e1n ch\u00ednh th\u1ee9c nh\u00e9.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1zON4XJsM-grswuc9C0ztDDldx7pd4eHs\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1zON4XJsM-grswuc9C0ztDDldx7pd4eHs\/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\/1zON4XJsM-grswuc9C0ztDDldx7pd4eHs\/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 Chuy\u00ean Vinh Ngh\u1ec7 An<\/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 tr\u01b0\u1eddng THPT Chuy\u00ean Vinh Ngh\u1ec7 An l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n tr\u01b0\u1edbc k\u00ec thi d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh 12. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf b\u00e1m s\u00e1t \u0111\u1ecbnh h\u01b0\u1edbng c\u1ee7a B\u1ed9 GD &amp; \u0110T, xen k\u1ebd gi\u1eefa h\u1ec7 th\u1ed1ng c\u00e2u h\u1ecfi c\u01a1 b\u1ea3n [&#8230;]\n","protected":false},"author":1,"featured_media":1697,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-498","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\/498","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=498"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/498\/revisions"}],"predecessor-version":[{"id":1698,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/498\/revisions\/1698"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1697"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}