{"id":530,"date":"2026-05-05T04:50:38","date_gmt":"2026-05-05T04:50:38","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-tran-hung-dao-vinh-phu\/"},"modified":"2026-05-05T07:24:00","modified_gmt":"2026-05-05T07:24:00","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-tran-hung-dao-vinh-phu","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-tran-hung-dao-vinh-phu\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa"},"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 Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa <\/strong>ph\u00f9 h\u1ee3p v\u1edbi \u0111\u1ecbnh h\u01b0\u1edbng \u0111\u1ed5i m\u1edbi c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 thi c\u00f3 nhi\u1ec1u c\u00e2u h\u1ecfi th\u1ef1c ti\u1ec5n v\u00e0 \u1ee9ng d\u1ee5ng ki\u1ebfn th\u1ee9c to\u00e1n h\u1ecdc v\u00e0o gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 trong \u0111\u1eddi s\u1ed1ng, khoa h\u1ecdc v\u00e0 k\u1ef9 thu\u1eadt. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed<\/strong><\/a> tham kh\u1ea3o b\u1ed9 \u0111\u1ec1 trong b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y.<\/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 Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa<\/span><\/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 Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa <\/strong>ph\u00e2n lo\u1ea1i h\u1ecdc sinh theo n\u0103ng l\u1ef1c th\u00f4ng qua c\u00e1c b\u00e0i to\u00e1n \u0111a d\u1ea1ng t\u1eeb \u0111\u1ea1i s\u1ed1, gi\u1ea3i t\u00edch \u0111\u1ebfn h\u00ecnh h\u1ecdc v\u00e0 x\u00e1c su\u1ea5t. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi \u0111\u1eb7c tr\u01b0ng trong t\u1eebng ph\u1ea7n c\u1ee7a <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>.<\/p>\n<p><span><strong>Ph\u1ea7n I (3.0 \u0111i\u1ec3m): C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $\\log_3(x^2 \u2013 7) = 2$ l\u00e0:<\/p>\n<p>A. ${4}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. ${-4}$ \u00a0 \u00a0 \u00a0 \u00a0 C. ${-\\sqrt{15};\\sqrt{15}}$ \u00a0 \u00a0 \u00a0 \u00a0 D. ${-4;4}$<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho c\u1ea5p s\u1ed1 nh\u00e2n $(u_n)$ v\u1edbi $u_1 = 3; u_2 = 1$. C\u00f4ng b\u1ed9i c\u1ee7a c\u1ea5p s\u1ed1 nh\u00e2n \u0111\u00e3 cho b\u1eb1ng:<\/p>\n<p>A. $\\frac{1}{3}$ \u00a0 \u00a0 \u00a0 \u00a0 B. $-2$ \u00a0 \u00a0 \u00a0 \u00a0 C. $3$ \u00a0 \u00a0 \u00a0 \u00a0 D. $2$<\/p>\n<p><strong><span>Ph\u1ea7n II (4 \u0111i\u1ec3m): C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/span><\/strong><\/p>\n<p><strong>C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1 $y = -x^4 + 8x^2 + 2024$. Khi \u0111\u00f3:<\/p>\n<p>a) H\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u1ea1o h\u00e0m l\u00e0 $y\u2019 = -4x^3 \u2013 16x$<\/p>\n<p>b) H\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 $2$ \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i v\u00e0 $1$ \u0111i\u1ec3m c\u1ef1c ti\u1ec3u<\/p>\n<p>c) H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng $(2;+\\infty)$<\/p>\n<p>d) Gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean b\u1eb1ng $2024$<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Cho h\u00e0m s\u1ed1 $f(x) = x^2 \u2013 3x + 2$. Khi \u0111\u00f3:<\/p>\n<p>a) $\\int_0^1 f(x)dx = \\frac{5}{6}$<\/p>\n<p>b) $\\int \\frac{f(x)}{x}dx = \\frac{x^2}{2} \u2013 3x \u2013 2\\ln x + C \\ (\\forall x \\in (0;+\\infty))$<\/p>\n<p>c) Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay sinh ra b\u1edfi h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = f(x)$ v\u00e0 tr\u1ee5c ho\u00e0nh l\u00e0 $V = \\frac{\\pi}{30}$<\/p>\n<p>d) G\u1ecdi $d$ l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m $A(0;2); B(1;1)$. Di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = f(x)$, \u0111\u01b0\u1eddng th\u1eb3ng $d$ v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $x = 1; x = 4$ l\u00e0: $S = \\frac{20}{3}$<\/p>\n<p><span><strong>Ph\u1ea7n III (3 \u0111i\u1ec3m): C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> M\u1ed9t c\u00f4ng ty s\u1ea3n xu\u1ea5t d\u1ee5ng c\u1ee5 th\u1ec3 thao nh\u1eadn \u0111\u01b0\u1ee3c m\u1ed9t \u0111\u01a1n \u0111\u1eb7t h\u00e0ng s\u1ea3n xu\u1ea5t $8000$ qu\u1ea3 b\u00f3ng tennis. C\u00f4ng ty n\u00e0y s\u1edf h\u1eefu m\u1ed9t s\u1ed1 m\u00e1y m\u00f3c, m\u1ed7i m\u00e1y c\u00f3 th\u1ec3 s\u1ea3n xu\u1ea5t $30$ qu\u1ea3 b\u00f3ng trong m\u1ed9t gi\u1edd. Chi ph\u00ed thi\u1ebft l\u1eadp c\u00e1c m\u00e1y n\u00e0y l\u00e0 $200$ ngh\u00ecn \u0111\u1ed3ng cho m\u1ed7i m\u00e1y. Khi \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp, ho\u1ea1t \u0111\u1ed9ng s\u1ea3n xu\u1ea5t s\u1ebd ho\u00e0n to\u00e0n di\u1ec5n ra t\u1ef1 \u0111\u1ed9ng d\u01b0\u1edbi s\u1ef1 gi\u00e1m s\u00e1t c\u1ee7a ng\u01b0\u1eddi gi\u00e1m s\u00e1t. S\u1ed1 ti\u1ec1n ph\u1ea3i tr\u1ea3 cho ng\u01b0\u1eddi gi\u00e1m s\u00e1t l\u00e0 $192$ ngh\u00ecn \u0111\u1ed3ng m\u1ed9t gi\u1edd. S\u1ed1 m\u00e1y m\u00f3c c\u00f4ng ty n\u00ean s\u1eed d\u1ee5ng l\u00e0 bao nhi\u00eau \u0111\u1ec3 chi ph\u00ed ho\u1ea1t \u0111\u1ed9ng l\u00e0 th\u1ea5p nh\u1ea5t?<\/p>\n<p><strong>C\u00e2u 2:<\/strong> B\u1ed5 d\u1ecdc m\u1ed9t qu\u1ea3 d\u01b0a h\u1ea5u ta \u0111\u01b0\u1ee3c thi\u1ebft di\u1ec7n l\u00e0 h\u00ecnh elip c\u00f3 tr\u1ee5c l\u1edbn $29cm$, tr\u1ee5c nh\u1ecf $26 cm$. Bi\u1ebft c\u1ee9 $1000cm^3$ d\u01b0a h\u1ea5u s\u1ebd l\u00e0m \u0111\u01b0\u1ee3c c\u1ed1c sinh t\u1ed1 gi\u00e1 $20000$ \u0111\u1ed3ng. H\u1ecfi t\u1eeb qu\u1ea3 d\u01b0a h\u1ea5u tr\u00ean c\u00f3 th\u1ec3 thu \u0111\u01b0\u1ee3c bao nhi\u00eau ngh\u00ecn \u0111\u1ed3ng t\u1eeb vi\u1ec7c b\u00e1n n\u01b0\u1edbc sinh t\u1ed1 <em>(l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 h\u00e0ng \u0111\u01a1n v\u1ecb)<\/em>. Bi\u1ebft r\u1eb1ng b\u1ec1 d\u00e0y v\u1ecf d\u01b0a h\u1ea5u l\u00e0 $1 cm$.<\/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 Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa<\/span><\/strong><\/h2>\n<p>C\u00e1c em h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i b\u1ea3n \u0111\u1ea7y \u0111\u1ee7 c\u1ee7a <span data-sheets-root=\"1\"><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa<\/strong> <\/span>v\u00e0 \u0111\u00e1p \u00e1n \u0111\u1ec3 luy\u1ec7n t\u1eadp, chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT s\u1eafp t\u1edbi.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1wFoI5N_0bHKy4tbnrKJYA-cjPz73UPys\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1wFoI5N_0bHKy4tbnrKJYA-cjPz73UPys\/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\/1wFoI5N_0bHKy4tbnrKJYA-cjPz73UPys\/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 Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa<\/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 Tr\u1ea7n H\u01b0ng \u0110\u1ea1o V\u0129nh Ph\u00fa ph\u00f9 h\u1ee3p v\u1edbi \u0111\u1ecbnh h\u01b0\u1edbng \u0111\u1ed5i m\u1edbi c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 thi c\u00f3 nhi\u1ec1u c\u00e2u h\u1ecfi th\u1ef1c ti\u1ec5n v\u00e0 \u1ee9ng d\u1ee5ng ki\u1ebfn th\u1ee9c to\u00e1n h\u1ecdc v\u00e0o gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 trong \u0111\u1eddi [&#8230;]\n","protected":false},"author":1,"featured_media":1729,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-530","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\/530","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=530"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/530\/revisions"}],"predecessor-version":[{"id":1730,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/530\/revisions\/1730"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1729"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}