{"id":456,"date":"2026-05-05T04:46:46","date_gmt":"2026-05-05T04:46:46","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-binh-xuyen-vinh-phuc\/"},"modified":"2026-05-05T07:19:43","modified_gmt":"2026-05-05T07:19:43","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-binh-xuyen-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-binh-xuyen-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 B\u00ecnh Xuy\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 B\u00ecnh Xuy\u00ean V\u0129nh Ph\u00fac<\/strong> l\u00e0 t\u00e0i li\u1ec7u tham kh\u1ea3o h\u1eefu \u00edch d\u00e0nh cho c\u00e1c em h\u1ecdc sinh l\u1edbp 12 \u0111ang trong giai \u0111o\u1ea1n \u00f4n luy\u1ec7n chu\u1ea9n b\u1ecb cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t c\u1ea5u tr\u00fac v\u00e0 m\u1ee9c \u0111\u1ed9 c\u1ee7a \u0111\u1ec1 thi ch\u00ednh th\u1ee9c do B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o c\u00f4ng b\u1ed1, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n, c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 l\u00e0m quen v\u1edbi \u00e1p l\u1ef1c th\u1eddi gian trong ph\u00f2ng thi. H\u00e3y 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 \u0111\u1ec1 thi 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 B\u00ecnh Xuy\u00ean V\u0129nh Ph\u00fac<\/strong><\/h2>\n<p>\u0110\u1ec1 thi c\u00f3 t\u1ed5ng s\u1ed1 4 trang, v\u1edbi th\u1eddi l\u01b0\u1ee3ng l\u00e0m b\u00e0i l\u00e0 90 ph\u00fat. \u0110\u1ec1 thi g\u1ed3m 3 ph\u1ea7n ch\u00ednh sau \u0111\u00e2y:<\/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> T\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh  2^x\u00b2 + 2x = 8^2 &#8211; x  b\u1eb1ng<br \/>\nA.  -5  \u00a0 \u00a0 \u00a0 B.  -6  \u00a0 \u00a0 \u00a0 C.  5  \u00a0 \u00a0 \u00a0 D.  6 <\/p>\n<p><strong>C\u00e2u 2.<\/strong> Trong m\u1ed9t c\u0103n ph\u00f2ng c\u00f3 25 ng\u01b0\u1eddi h\u1ecd Nguy\u1ec5n v\u00e0 14 ng\u01b0\u1eddi h\u1ecd L\u00ea, ch\u1ecdn ng\u1eabu nhi\u00ean hai ng\u01b0\u1eddi trong ph\u00f2ng. X\u00e1c su\u1ea5t \u0111\u1ec3 hai ng\u01b0\u1eddi \u0111\u01b0\u1ee3c ch\u1ecdn c\u00f3 c\u00f9ng h\u1ecd b\u1eb1ng<br \/>\nA.  27\/741  \u00a0 \u00a0 \u00a0 B.  7\/57  \u00a0 \u00a0 \u00a0 C.  100\/247  \u00a0 \u00a0 \u00a0 D.  391\/741 <\/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> H\u00ecnh ch\u00f3p  S.ABCD  c\u00f3 \u0111\u00e1y  ABCD  l\u00e0 h\u00ecnh vu\u00f4ng t\u00e2m  O , c\u1ea1nh  a ,  SA perp (ABCD) ,  SB = a\u221a2 .<\/p>\n<p>a)  BC perp SB <\/p>\n<p>b) M\u1eb7t ph\u1eb3ng  (a)  qua  O  v\u00e0 song song v\u1edbi  SA  v\u00e0  AB . C\u00e1c giao tuy\u1ebfn c\u1ee7a  (a)  v\u1edbi c\u00e1c m\u1eb7t c\u1ee7a h\u00ecnh ch\u00f3p  S.ABCD  t\u1ea1o th\u00e0nh m\u1ed9t h\u00ecnh thang vu\u00f4ng.<\/p>\n<p>c) Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i ch\u00f3p  S.ABCD  b\u1eb1ng  (a\u00b3 \u221a3)\/(3) <\/p>\n<p>d) G\u00f3c gi\u1eefa  SC  v\u00e0 m\u1eb7t ph\u1eb3ng  (SAB)  b\u1eb1ng  \u03b1  th\u00ec  tan \u03b1 = \u221a2 <\/p>\n<p><strong>C\u00e2u 2.<\/strong> B\u1ea1n An v\u00e0 b\u1ea1n Binh l\u00e0m th\u00ed nghi\u1ec7m tr\u1ed3ng c\u00e2y. M\u1ed7i b\u1ea1n tr\u1ed3ng 40 c\u00e2y c\u1ea7n t\u00e2y trong c\u1ed1c, ph\u1ea7n g\u1ed1c c\u1ee7a c\u00e1c c\u00e2y khi b\u1eaft \u0111\u1ea7u tr\u1ed3ng \u0111\u1ec1u d\u00e0i  4 cm . B\u1ea3ng 1 v\u00e0 B\u1ea3ng 2 l\u1ea7n l\u01b0\u1ee3t bi\u1ec3u di\u1ec5n m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m v\u1ec1 s\u1ed1 li\u1ec7u th\u1ed1ng k\u00ea chi\u1ec1u cao c\u1ee7a c\u00e1c c\u00e2y (\u0111\u01a1n v\u1ecb: centim\u00e9t) m\u00e0 b\u1ea1n An v\u00e0 b\u1ea1n Binh tr\u1ed3ng sau 5 tu\u1ea7n.<\/p>\n<p>beginarray|c|c| hline Nh\u00f3m &amp; T\u1ea7n s\u1ed1 hline [20,25) &amp; 2 [25,30) &amp; 16 [30,35) &amp; 20 [35,40) &amp; 2 hline n = 40 &amp; endarray B\u1ea3ng 1 beginarray|c|c| hline Nh\u00f3m &amp; T\u1ea7n s\u1ed1 hline [20,25) &amp; 5 [25,30) &amp; 9 [30,35) &amp; 25 [35,40) &amp; 1 hline n = 40 &amp; endarray B\u1ea3ng 2<\/p>\n<p>a) Chi\u1ec1u cao trung b\u00ecnh c\u1ee7a c\u00e1c c\u00e2y do hai b\u1ea1n An v\u00e0 Binh tr\u1ed3ng kh\u00f4ng b\u1eb1ng nhau.<br \/>\nb) Kho\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a c\u1ea3 hai m\u1eabu s\u1ed1 li\u1ec7u tr\u00ean l\u00e0  20 .<br \/>\nc) Kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u \u1edf B\u1ea3ng 1 l\u00e0  5,5 .<br \/>\nd) X\u00e9t theo ph\u01b0\u01a1ng sai th\u00ec chi\u1ec1u cao c\u1ee7a c\u00e1c c\u00e2y m\u00e0 b\u1ea1n Binh tr\u1ed3ng \u0111\u1ed3ng \u0111\u1ec1u h\u01a1n c\u00e1c c\u00e2y m\u00e0 b\u1ea1n An tr\u1ed3ng.<\/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> B\u00e1c An g\u1eedi ti\u1ebft ki\u1ec7m ng\u00e2n h\u00e0ng  100  tri\u1ec7u \u0111\u1ed3ng v\u1edbi k\u00ec h\u1ea1n  12  th\u00e1ng, l\u00e3i su\u1ea5t kh\u00f4ng \u0111\u1ed5i l\u00e0  6%  m\u1ed9t n\u0103m v\u00e0 theo h\u00ecnh th\u1ee9c l\u00e3i k\u1ef3 n\u00e0y \u0111\u01b0\u1ee3c nh\u1eadp v\u00e0o v\u1ed1n \u0111\u1ec3 t\u00ednh l\u00e3i cho k\u1ef3 li\u1ec1n sau. H\u1ecfi sau \u00edt nh\u1ea5t bao nhi\u00eau n\u0103m, t\u1ed5ng s\u1ed1 ti\u1ec1n v\u1ed1n l\u1eabn l\u00e3i b\u00e1c An thu \u0111\u01b0\u1ee3c l\u00e0 kh\u00f4ng d\u01b0\u1edbi  150  tri\u1ec7u \u0111\u1ed3ng?<\/p>\n<p><strong>C\u00e2u 2.<\/strong> M\u1ed9t b\u00ecnh \u0111\u1ef1ng  50  vi\u00ean bi k\u00edch th\u01b0\u1edbc, ch\u1ea5t li\u1ec7u nh\u01b0 nhau, trong \u0111\u00f3 c\u00f3  30  vi\u00ean bi xanh v\u00e0  20  vi\u00ean bi tr\u1eafng. L\u1ea5y ng\u1eabu nhi\u00ean ra m\u1ed9t vi\u00ean bi, r\u1ed3i l\u1ea1i l\u1ea5y ng\u1eabu nhi\u00ean ra m\u1ed9t vi\u00ean bi n\u1eefa. X\u00e1c su\u1ea5t \u0111\u1ec3 l\u1ea5y \u0111\u01b0\u1ee3c m\u1ed9t vi\u00ean bi xanh \u1edf l\u1ea7n th\u1ee9 nh\u1ea5t v\u00e0 m\u1ed9t vi\u00ean bi tr\u1eafng \u1edf l\u1ea7n th\u1ee9 hai l\u00e0  a\/b ,  (a; b in mathbbN^*, a\/b  l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n. T\u00ednh  a + b .<\/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 B\u00ecnh Xuy\u00ean V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<p>V\u1edbi n\u1ed9i dung b\u00e1m s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 thi ch\u00ednh th\u1ee9c, <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT B\u00ecnh Xuy\u00ean V\u0129nh Ph\u00fac<\/strong> s\u1ebd gi\u00fap h\u1ecdc sinh t\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c v\u00e0 h\u1ed7 tr\u1ee3 t\u1ed1t cho qu\u00e1 tr\u00ecnh \u00f4n thi. Qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c em h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i file <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> k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft \u1edf ph\u00eda d\u01b0\u1edbi \u0111\u1ec3 tham kh\u1ea3o v\u00e0 luy\u1ec7n t\u1eadp th\u00eam.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1h-92hxCDunGX9s0_fMtLsraw2fe0qh-V\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1h-92hxCDunGX9s0_fMtLsraw2fe0qh-V\/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\/1h-92hxCDunGX9s0_fMtLsraw2fe0qh-V\/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 B\u00ecnh Xuy\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 B\u00ecnh Xuy\u00ean V\u0129nh Ph\u00fac l\u00e0 t\u00e0i li\u1ec7u tham kh\u1ea3o h\u1eefu \u00edch d\u00e0nh cho c\u00e1c em h\u1ecdc sinh l\u1edbp 12 \u0111ang trong giai \u0111o\u1ea1n \u00f4n luy\u1ec7n chu\u1ea9n b\u1ecb cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi. \u0110\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t c\u1ea5u [&#8230;]\n","protected":false},"author":1,"featured_media":1655,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-456","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\/456","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=456"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/456\/revisions"}],"predecessor-version":[{"id":1656,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/456\/revisions\/1656"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1655"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=456"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=456"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}