{"id":472,"date":"2026-05-05T04:47:36","date_gmt":"2026-05-05T04:47:36","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-vinh-yen-vinh-phuc\/"},"modified":"2026-05-05T07:20:40","modified_gmt":"2026-05-05T07:20:40","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-vinh-yen-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-vinh-yen-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 V\u0129nh Y\u00ean 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 V\u0129nh Y\u00ean V\u0129nh Ph\u00fac<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac m\u1edbi nh\u1ea5t c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. B\u00e0i thi g\u1ed3m nhi\u1ec1u d\u1ea1ng c\u00e2u h\u1ecfi \u0111a d\u1ea1ng t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh SGK v\u00e0 chu\u1ea9n \u0111\u1ea7u ra c\u1ee7a 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 Mi\u1ec5n Ph\u00ed<\/strong><\/a> kh\u00e1m ph\u00e1 chi ti\u1ebft v\u1ec1 \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 V\u0129nh Y\u00ean V\u0129nh Ph\u00fac<\/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 V\u0129nh Y\u00ean V\u0129nh Ph\u00fac<\/strong> c\u00f3 c\u1ea5u tr\u00fac 22 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed5 h\u1ee3p l\u00fd gi\u1eefa c\u00e1c m\u1ea3ng ki\u1ebfn th\u1ee9c \u0110\u1ea1i s\u1ed1, Gi\u1ea3i t\u00edch v\u00e0 H\u00ecnh h\u1ecdc kh\u00f4ng gian, \u0111\u1ed3ng th\u1eddi bao qu\u00e1t \u0111\u1ea7y \u0111\u1ee7 c\u00e1c m\u1ee9c \u0111\u1ed9 t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao.<\/p>\n<p><strong>PH\u1ea6N I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1  y = f(x)  c\u00f3 \u0111\u1ea1o h\u00e0m  f'(x) = x\u00b3, forall x in mathbbR . H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n<p>A.  (-\u221e; +\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (-\u221e; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  (0; +\u221e) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  (-\u221e; 0) <\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho h\u00e0m  y = -x\u00b3 + 6x\u00b2 &#8211; 9x + 4 . M\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y l\u00e0 sai?<\/p>\n<p>A. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i  x = 1, y_CT = 0 <br \/>\nB. H\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<br \/>\nC. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i  x = 3, y_CD = 4 <br \/>\nD. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i  x = 1, y_CT = 2 <\/p>\n<p><strong>PH\u1ea6N II: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1  y = f(x) = (ax\u00b2 + bx + c)\/(dx + e)  c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean sau.<\/p>\n<p>a) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng  (-\u221e; -1)  v\u00e0  (3; +\u221e) .<br \/>\nb) Gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 l\u00e0  y = 3 .<br \/>\nc) Ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh  y = mx + n  khi \u0111\u00f3  m &gt; 0 .<br \/>\nd) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 \u00e2m.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n<p>a)  int cos x dx = sin x + C <br \/>\nb)  I = int\u2081^e ( 1\/x &#8211; (1)\/(x\u00b2) ) dx = 1 <br \/>\nc) Bi\u1ebft  int\u2083\u2075 (x\u00b2 + x + 1)\/(x) dx = a + ln b\/3 , v\u1edbi  a, b  l\u00e0 c\u00e1c s\u1ed1 nguy\u00ean. Khi \u0111\u00f3,  S = a &#8211; 2b = 0 .<br \/>\nd) Di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb hai h\u00e0m s\u1ed1  y = x\u00b2 + 1 ,  y = 1  v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng  x = 1  b\u1eb1ng  4\/3 .<\/p>\n<p><strong>PH\u1ea6N III: C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> G\u1ecdi  S  l\u00e0 t\u1eadp t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 th\u1ef1c  m  sao cho gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1  y = | 1\/4x\u2074 &#8211; 14x\u00b2 + 48x + m &#8211; 30 | <br \/>\ntr\u00ean \u0111o\u1ea1n  [0; 2]  kh\u00f4ng v\u01b0\u1ee3t qu\u00e1  30 . T\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a  S  b\u1eb1ng?<\/p>\n<p><strong>C\u00e2u 2.<\/strong> \u00d4ng An mu\u1ed1n l\u00e0m c\u1eeda r\u00e0o s\u1eaft c\u00f3 h\u00ecnh d\u1ea1ng v\u00e0 k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd b\u00ean, bi\u1ebft \u0111\u01b0\u1eddng cong ph\u00eda tr\u00ean l\u00e0 m\u1ed9t Parabol. Gi\u00e1  1(m\u00b2)  c\u1ee7a r\u00e0o s\u1eaft l\u00e0 700 ngh\u00ecn \u0111\u1ed3ng. H\u1ecfi \u00f4ng An ph\u1ea3i tr\u1ea3 bao nhi\u00eau ti\u1ec1n \u0111\u1ec3 l\u00e0m c\u00e1i c\u1eeda s\u1eaft nh\u01b0 v\u1eady (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb).<\/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 V\u0129nh Y\u00ean V\u0129nh Ph\u00fac<\/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 V\u0129nh Y\u00ean V\u0129nh Ph\u00fac<\/strong> v\u00f4 c\u00f9ng h\u1eefu \u00edch gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m b\u00e0i, t\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c v\u00e0 ph\u00e1t hi\u1ec7n nh\u1eefng \u0111i\u1ec3m y\u1ebfu c\u1ea7n kh\u1eafc ph\u1ee5c, v\u00ec v\u1eady c\u00e1c em h\u00e3y t\u1ea3i ngay file PDF <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<\/a> v\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft b\u00ean d\u01b0\u1edbi \u0111\u1ec3 b\u1eaft \u0111\u1ea7u \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3 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\/1uolSg_6-C20GgnUT1IGgYJ1Nk4lOWJDQ\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1uolSg_6-C20GgnUT1IGgYJ1Nk4lOWJDQ\/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\/1uolSg_6-C20GgnUT1IGgYJ1Nk4lOWJDQ\/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 V\u0129nh Y\u00ean 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 V\u0129nh Y\u00ean V\u0129nh Ph\u00fac \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac m\u1edbi nh\u1ea5t c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. B\u00e0i thi g\u1ed3m nhi\u1ec1u d\u1ea1ng c\u00e2u h\u1ecfi \u0111a d\u1ea1ng t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh SGK v\u00e0 chu\u1ea9n \u0111\u1ea7u [&#8230;]\n","protected":false},"author":1,"featured_media":1671,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-472","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\/472","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=472"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/472\/revisions"}],"predecessor-version":[{"id":1672,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/472\/revisions\/1672"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1671"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}