{"id":520,"date":"2026-05-05T04:50:07","date_gmt":"2026-05-05T04:50:07","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc\/"},"modified":"2026-05-05T07:23:27","modified_gmt":"2026-05-05T07:23:27","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-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-quang-ha-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 Quang H\u00e0 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 Quang H\u00e0 V\u0129nh Ph\u00fac<\/strong>\u00a0 g\u1ed3m 22 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m v\u1edbi c\u00e1c m\u1ee9c \u0111\u1ed9 t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao, gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp to\u00e0n di\u1ec7n v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi ch\u00ednh th\u1ee9c. H\u00f4m nay, c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> t\u1ea3i ngay \u0111\u1ec1 v\u1ec1 \u0111\u1ec3 luy\u1ec7n t\u1eadp.<\/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 Quang H\u00e0 V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<h3><strong>T\u1ed5ng quan<\/strong><\/h3>\n<ul>\n<li>Th\u1eddi gian l\u00e0m b\u00e0i: 90 ph\u00fat<\/li>\n<li>T\u1ed5ng s\u1ed1 c\u00e2u h\u1ecfi: 22 c\u00e2u (12 c\u00e2u ph\u1ea7n I + 4 c\u00e2u ph\u1ea7n II + 6 c\u00e2u ph\u1ea7n III)<\/li>\n<li>H\u00ecnh th\u1ee9c: Tr\u1eafc nghi\u1ec7m kh\u00e1ch quan v\u00e0 b\u00e0i to\u00e1n th\u1ef1c t\u1ebf<\/li>\n<\/ul>\n<h3><strong>Ph\u00e2n b\u1ed1 theo m\u1ee9c \u0111\u1ed9 nh\u1eadn th\u1ee9c<\/strong><\/h3>\n<ul>\n<li>Nh\u1eadn bi\u1ebft: 35% (c\u01a1 b\u1ea3n, nh\u1eadn di\u1ec7n ki\u1ebfn th\u1ee9c)<\/li>\n<li>Th\u00f4ng hi\u1ec3u: 27,5% (hi\u1ec3u b\u1ea3n ch\u1ea5t v\u1ea5n \u0111\u1ec1)<\/li>\n<li>V\u1eadn d\u1ee5ng th\u1ea5p: 22,5% (\u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c v\u00e0o t\u00ecnh hu\u1ed1ng \u0111\u01a1n gi\u1ea3n)<\/li>\n<li>V\u1eadn d\u1ee5ng cao: 15% (\u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c v\u00e0o t\u00ecnh hu\u1ed1ng ph\u1ee9c t\u1ea1p)<\/li>\n<\/ul>\n<h3><strong>N\u1ed9i dung ki\u1ebfn th\u1ee9c \u0111\u01b0\u1ee3c ki\u1ec3m tra<\/strong><\/h3>\n<p><span><strong>Ph\u1ea7n I (12 c\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n)<\/strong><\/span><\/p>\n<p class=\"whitespace-pre-wrap break-words\"><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 $y = f(x)$ c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd sau:<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"size-full wp-image-2675 aligncenter\" decoding=\"async\" height=\"205\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-a.jpg\" width=\"262\"\/><\/p>\n<p class=\"whitespace-pre-wrap break-words\">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 \u00a0 \u00a0 \u00a0 B. $(1;2)$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. $(-1;0)$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. $(-1;1)$<\/p>\n<p class=\"whitespace-pre-wrap break-words\"><strong>C\u00e2u 2.<\/strong> Cho h\u00e0m $f(x)$ c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau:<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-2674 size-full\" decoding=\"async\" height=\"253\" sizes=\"auto, (max-width: 631px) 100vw, 631px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-2.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-2.jpg 631w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-2-300x120.jpg 300w\" width=\"631\"\/><\/p>\n<p class=\"whitespace-pre-wrap break-words\">Gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho b\u1eb1ng:<\/p>\n<p>A. $3$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. $-5$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. $0$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. $2$<\/p>\n<p><span><strong>Ph\u1ea7n II (4 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 $y = f(x)$ c\u00f3 \u0111\u1ea1o h\u00e0m tr\u00ean $\\mathbb{R}$ v\u00e0 h\u00e0m s\u1ed1 $y = f'(x)$ l\u00e0 h\u00e0m s\u1ed1 b\u1eadc ba c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd.<\/p>\n<p><img alt=\"\" class=\"size-medium wp-image-2673 aligncenter\" decoding=\"async\" height=\"274\" loading=\"lazy\" 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-quang-ha-vinh-phuc-3-300x274.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-3-300x274.jpg 300w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-3.jpg 363w\" width=\"300\"\/><\/p>\n<p>X\u00e9t t\u00ednh \u0111\u00fang ho\u1eb7c sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n<p>a) $f'(-1) &lt; 0$<br \/>\nb) H\u00e0m s\u1ed1 $y = f(x)$ c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb<br \/>\nc) $f'(2) = 4$<br \/>\nd) H\u00e0m s\u1ed1 $g(x) = f(x) \u2013 \\frac{1}{2}x^2 + x + 2024$ \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng $(-\\frac{5}{2}, -\\frac{3}{2})$<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Gi\u1ea3 s\u1eed m\u1ed9t h\u1ea1t chuy\u1ec3n \u0111\u1ed9ng tr\u00ean m\u1ed9t tr\u1ee5c th\u1eb3ng \u0111\u1ee9ng chi\u1ec1u d\u01b0\u01a1ng h\u01b0\u1edbng l\u00ean tr\u00ean sao cho t\u1ecda \u0111\u1ed9 c\u1ee7a h\u1ea1t (\u0111\u01a1n v\u1ecb: m\u00e9t) t\u1ea1i th\u1eddi \u0111i\u1ec3m t (gi\u00e2y) l\u00e0 $y = t^3 \u2013 12t + 3, t \\geq 0$.<\/p>\n<p>a) H\u00e0m gia t\u1ed1c c\u1ee7a v\u1eadt l\u00e0 $a(t) = y\u2019$<br \/>\nb) H\u00e0m v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt l\u00e0 $v(t) = 3t^2 \u2013 12$<br \/>\nc) T\u1ea1i th\u1eddi \u0111i\u1ec3m $t = 1$ th\u00ec h\u1ea1t \u0111ang chuy\u1ec3n \u0111\u1ed9ng l\u00ean tr\u00ean<br \/>\nd) Trong kho\u1ea3ng th\u1eddi gian $0 \\leq t \\leq 3$ th\u00ec qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 h\u1ea1t \u0111i \u0111\u01b0\u1ee3c l\u00e0 23m<\/p>\n<p><span><strong>Ph\u1ea7n III (6 c\u00e2u tr\u1eafc nghi\u1ec7m b\u00e0i to\u00e1n th\u1ef1c t\u1ebf)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> M\u1ed9t c\u00f4ng ty chuy\u00ean s\u1ea3n xu\u1ea5t d\u1ee5ng c\u1ee5 th\u1ec3 thao nh\u1eadn \u0111\u01b0\u1ee3c \u0111\u01a1n \u0111\u1eb7t h\u00e0ng s\u1ea3n xu\u1ea5t 8000 qu\u1ea3 b\u00f3ng r\u1ed5. C\u00f4ng ty c\u00f3 m\u1ed9t s\u1ed1 m\u00e1y m\u00f3c, m\u1ed7i m\u00e1y c\u00f3 kh\u1ea3 n\u0103ng s\u1ea3n xu\u1ea5t 30 b\u00f3ng r\u1ed5 trong m\u1ed9t gi\u1edd. Chi ph\u00ed thi\u1ebft l\u1eadp m\u1ed7i m\u00e1y l\u00e0 200 ngh\u00ecn \u0111\u1ed3ng. Sau khi thi\u1ebft l\u1eadp, qu\u00e1 tr\u00ecnh s\u1ea3n xu\u1ea5t s\u1ebd di\u1ec5n ra ho\u00e0n to\u00e0n t\u1ef1 \u0111\u1ed9ng v\u00e0 ch\u1ec9 c\u1ea7n c\u00f3 ng\u01b0\u1eddi gi\u00e1m s\u00e1t. Chi ph\u00ed tr\u1ea3 cho ng\u01b0\u1eddi gi\u00e1m s\u00e1t l\u00e0 192 ngh\u00ecn \u0111\u1ed3ng m\u1ed7i gi\u1edd. C\u00f4ng ty c\u1ea7n s\u1eed d\u1ee5ng bao nhi\u00eau m\u00e1y m\u00f3c \u0111\u1ec3 chi ph\u00ed ho\u1ea1t \u0111\u1ed9ng \u0111\u1ea1t m\u1ee9c th\u1ea5p nh\u1ea5t?<\/p>\n<p><strong>C\u00e2u 2.<\/strong> M\u1ed9t chi\u1ebfc b\u00e1t th\u1ee7y 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\u00ec 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 $y = x + \\frac{1}{x}$, $y = x$ v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng $x = 1$, $x = 4$ (H\u00ecnh v\u1ebd). T\u00ednh th\u1ec3 t\u00edch c\u1ee7a b\u1ec1 d\u00e0y chi\u1ebfc b\u00e1t th\u1ee7y tinh \u0111\u00f3 (k\u1ebft qu\u1ea3 \u0111\u01b0\u1ee3c t\u00ednh theo decimet kh\u1ed1i v\u00e0 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t).<\/p>\n<p><img alt=\"\" class=\"size-medium wp-image-2676 aligncenter\" decoding=\"async\" height=\"300\" loading=\"lazy\" sizes=\"auto, (max-width: 266px) 100vw, 266px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-4-266x300.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-4-266x300.jpg 266w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-quang-ha-vinh-phuc-4.jpg 277w\" width=\"266\"\/><\/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 Quang H\u00e0 V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<p><a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\">\u0110\u1ec1 thi th\u1eed to\u00e1n 12<\/a> k\u00e8m theo \u0111\u00e1p \u00e1n v\u00e0 h\u01b0\u1edbng d\u1eabn gi\u1ea3i chi ti\u1ebft s\u1ebd l\u00e0 c\u00f4ng c\u1ee5 qu\u00fd gi\u00e1 gi\u00fap h\u1ecdc sinh t\u1ef1 luy\u1ec7n t\u1eadp, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 v\u00e0 chu\u1ea9n b\u1ecb t\u00e2m l\u00fd t\u1ed1t nh\u1ea5t cho k\u1ef3 thi ch\u00ednh th\u1ee9c. T\u1ea3i ngay <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Quang H\u00e0 V\u0129nh Ph\u00fac<\/strong> \u0111\u1ec3 tr\u1ea3i nghi\u1ec7m m\u1ed9t b\u00e0i ki\u1ec3m tra to\u00e0n di\u1ec7n v\u00e0 \u0111\u00e1nh gi\u00e1 ch\u00ednh x\u00e1c n\u0103ng l\u1ef1c to\u00e1n h\u1ecdc c\u1ee7a b\u1ea1n!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/18hIVn5v1bzbBRSh58fnVQLlL4oIRSxK0\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/18hIVn5v1bzbBRSh58fnVQLlL4oIRSxK0\/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\/18hIVn5v1bzbBRSh58fnVQLlL4oIRSxK0\/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 Quang H\u00e0 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 Quang H\u00e0 V\u0129nh Ph\u00fac\u00a0 g\u1ed3m 22 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m v\u1edbi c\u00e1c m\u1ee9c \u0111\u1ed9 t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao, gi\u00fap h\u1ecdc sinh \u00f4n t\u1eadp to\u00e0n di\u1ec7n v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi ch\u00ednh th\u1ee9c. H\u00f4m nay, c\u00f9ng T\u00e0i [&#8230;]\n","protected":false},"author":1,"featured_media":1719,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-520","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\/520","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=520"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/520\/revisions"}],"predecessor-version":[{"id":1720,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/520\/revisions\/1720"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1719"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=520"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=520"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}