{"id":466,"date":"2026-05-05T04:47:18","date_gmt":"2026-05-05T04:47:18","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-van-giang-hung-yen\/"},"modified":"2026-05-05T07:20:20","modified_gmt":"2026-05-05T07:20:20","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-van-giang-hung-yen","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-van-giang-hung-yen\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u0103n Giang H\u01b0ng Y\u00ean"},"content":{"rendered":"<p>T\u1eadp <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u0103n Giang H\u01b0ng Y\u00ean<\/strong> l\u00e0 ch\u00eca kh\u00f3a \u0111\u1eafc l\u1ef1c h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n h\u1ecdc sinh 12 trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1 m\u00f4n To\u00e1n. N\u1ed9i dung \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n kh\u00e1 chi ti\u1ebft c\u00e1c ki\u1ebfn th\u1ee9c c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc c\u1ea5p 3. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 \u0111\u1ec1 thi qua n\u1ed9i dung sau \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 V\u0103n Giang H\u01b0ng Y\u00ean<\/strong><\/h2>\n<p>N\u1ed9i dung<strong> \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u0103n Giang H\u01b0ng Y\u00ean<\/strong> c\u00f3 c\u1ea5u tr\u00fac chu\u1ea9n \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p c\u1ee7a b\u1ed9 Gi\u00e1o d\u1ee5c. \u0110\u01b0\u1ee3c chia th\u00e0nh 3 ph\u1ea7n v\u00e0 c\u00f3 k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft c\u1ee7a m\u1ed7i ph\u1ea7n gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp v\u00e0 r\u00fat kinh nghi\u1ec7m cho \u0111\u1ec1 thi ch\u00ednh th\u1ee9c. N\u1ed9i dung chi ti\u1ebft c\u1ee7a \u0111\u1ec1 thi th\u1eed to\u00e1n thpt nh\u01b0 sau:<\/p>\n<p><strong>PH\u1ea6N I. C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M NHI\u1ec0U PH\u01af\u01a0NG \u00c1N<\/strong><\/p>\n<p>\u0110\u1ed1i v\u1edbi ph\u1ea7n 1, c\u00e1c c\u00e2u h\u1ecfi s\u1ebd c\u00f3 4 \u0111\u00e1p \u00e1n A, B, C, D, c\u00e1c b\u1ea1n h\u1ecdc sinh ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn 1 \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c. H\u00e3y xem qua c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n<p>C\u00e2u 1: Cho c\u1ea5p s\u1ed1 c\u1ed9ng  (u_n)  c\u00f3  u\u2081 = -2  v\u00e0 c\u00f4ng sai  d = 3 . T\u00ecm s\u1ed1 h\u1ea1ng  u\u2081\u2080 .<\/p>\n<p>A.  u\u2081\u2080 = -2 \u00b7 3\u2079 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  u\u2081\u2080 = 25 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  u\u2081\u2080 = -29 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  u\u2081\u2080 = 28 <\/p>\n<p>C\u00e2u 2: \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = (x &#8211; 1)\/(x + 2)  l\u00e0<\/p>\n<p>A.  x = 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  x = -1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  x = -2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  x = 2 <\/p>\n<p><strong>PH\u1ea6N II. C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M \u0110\u00daNG SAI<\/strong><\/p>\n<p>C\u00f3 t\u1ea5t c\u1ea3 4 c\u00e2u h\u1ecfi, m\u1ed7i c\u00e2u s\u1ebd g\u1ed3m 4 \u0111\u00e1p \u00e1n, c\u00e1c b\u1ea1n h\u1ecdc sinh ch\u1ec9 c\u1ea7n ch\u1ecdn ph\u01b0\u01a1ng \u00e1n \u0111\u00fang h\u1ecdc sai cho m\u1ed7i c\u00e2u tr\u1ea3 l\u1eddi nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 3:<\/strong> Cho h\u00e0m s\u1ed1  y = (x\u00b2 + 2x &#8211; 1)\/(x &#8211; 1)  c\u00f3 \u0111\u1ed3 th\u1ecb  (C) .<\/p>\n<p>a) H\u00e0m s\u1ed1 c\u00f3 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<br \/>\nb) \u0110\u1ed3 th\u1ecb  (C)  c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh  x = 1 .<br \/>\nc) H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng  (0; 2) .<br \/>\nd)  M  l\u00e0 \u0111i\u1ec3m b\u1ea5t k\u1ef3 thu\u1ed9c \u0111\u1ed3 th\u1ecb  (C) . T\u00edch kho\u1ea3ng c\u00e1ch t\u1eeb  M  \u0111\u1ebfn ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb  (C)  b\u1eb1ng  \u221a2 .<\/p>\n<p>C\u00e2u 4: M\u1ed9t ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng theo ph\u01b0\u01a1ng tr\u00ecnh  s(t) = t\u00b3 &#8211; 3t\u00b2 + 8t + 1 , trong \u0111\u00f3  t  t\u00ednh b\u1eb1ng gi\u00e2y v\u00e0  s(t)  t\u00ednh b\u1eb1ng m\u00e9t.<\/p>\n<p>a) V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m t\u1ea1i th\u1eddi \u0111i\u1ec3m  t = 3 (s)  b\u1eb1ng  8 m\/s .<br \/>\nb) T\u1ea1i th\u1eddi \u0111i\u1ec3m m\u00e0 ch\u1ea5t \u0111i\u1ec3m di chuy\u1ec3n \u0111\u01b0\u1ee3c 13 m, v\u1eadn t\u1ed1c khi \u0111\u00f3 b\u1eb1ng  8 m\/s .<br \/>\nc) V\u1eadn t\u1ed1c nh\u1ecf nh\u1ea5t c\u1ee7a ch\u1ea5t \u0111i\u1ec3m l\u00e0  5 m\/s .<br \/>\nd) Gia t\u1ed1c t\u1ea1i th\u1eddi \u0111i\u1ec3m ch\u1ea5t \u0111i\u1ec3m \u0111\u1ea1t v\u1eadn t\u1ed1c nh\u1ecf nh\u1ea5t b\u1eb1ng  2 m\/s\u00b2 .<\/p>\n<p><strong>PH\u1ea6N III. C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M TR\u1ea2 L\u1edcI NG\u1eaeN<\/strong><\/p>\n<p>Tr\u00edch m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn trong \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u0103n Giang H\u01b0ng Y\u00ean:<\/p>\n<p>C\u00e2u 5: Trong h\u1ed9p c\u00f3 14 s\u1ea3n ph\u1ea9m, trong \u0111\u00f3 c\u00f3 8 s\u1ea3n ph\u1ea9m lo\u1ea1i I v\u00e0 6 s\u1ea3n ph\u1ea9m lo\u1ea1i II. Ch\u1ecdn ng\u1eabu nhi\u00ean \u0111\u1ed3ng th\u1eddi 3 s\u1ea3n ph\u1ea9m trong h\u1ed9p. G\u1ecdi  X  l\u00e0 s\u1ed1 s\u1ea3n ph\u1ea9m lo\u1ea1i I trong 3 s\u1ea3n ph\u1ea9m \u0111\u01b0\u1ee3c ch\u1ecdn ra.T\u00ednh k\u1ef3 v\u1ecdng c\u1ee7a bi\u1ebfn ng\u1eabu nhi\u00ean r\u1eddi r\u1ea1c  X  (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m).<\/p>\n<p>C\u00e2u 6: C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1  m  thu\u1ed9c  [-2024; 2024]  \u0111\u1ec3 h\u00e0m s\u1ed1 y = (sin x + m)\/(sin x &#8211; 1) ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng  ( \u03c0\/2, \u03c0 ) ?<\/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 V\u0103n Giang H\u01b0ng Y\u00ean<\/strong><\/h2>\n<p>\u0110\u1ec3 s\u1eb5n s\u00e0ng chinh ph\u1ee5c m\u00f4n To\u00e1n v\u1edbi k\u1ebft qu\u1ea3 cao trong k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT b\u1eb1ng c\u00e1ch 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 V\u0103n Giang H\u01b0ng Y\u00ean<\/strong> qua \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 \u00f4n t\u1eadp. T\u00e0i li\u1ec7u <a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\"><span data-sheets-root=\"1\">\u0111\u1ec1 thi th\u1eed to\u00e1n thpt <\/span><\/a>n\u00e0y s\u1ebd gi\u00fap c\u00e1c b\u1ea1n h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3, n\u00e2ng cao s\u1ef1 t\u1ef1 tin v\u00e0 t\u00edch l\u0169y kinh nghi\u1ec7m qu\u00fd b\u00e1u cho k\u1ef3 thi ch\u00ednh th\u1ee9c s\u1eafp t\u1edbi.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1JuIUKuxhucxN--WLN_LQDJPOqAn7O-b2\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1JuIUKuxhucxN--WLN_LQDJPOqAn7O-b2\/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\/1JuIUKuxhucxN--WLN_LQDJPOqAn7O-b2\/view\" rel=\"nofollow noopener\" target=\"_blank\"><strong>T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u0103n Giang H\u01b0ng Y\u00ean <\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u1eadp \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT V\u0103n Giang H\u01b0ng Y\u00ean l\u00e0 ch\u00eca kh\u00f3a \u0111\u1eafc l\u1ef1c h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n h\u1ecdc sinh 12 trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1 m\u00f4n To\u00e1n. N\u1ed9i dung \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n kh\u00e1 chi ti\u1ebft c\u00e1c ki\u1ebfn th\u1ee9c c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc [&#8230;]\n","protected":false},"author":1,"featured_media":1665,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-466","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\/466","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=466"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/466\/revisions"}],"predecessor-version":[{"id":1666,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/466\/revisions\/1666"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1665"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=466"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=466"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}