{"id":510,"date":"2026-05-05T04:49:36","date_gmt":"2026-05-05T04:49:36","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-luong-tai-2-bac-ninh\/"},"modified":"2026-05-05T07:22:54","modified_gmt":"2026-05-05T07:22:54","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-luong-tai-2-bac-ninh","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-luong-tai-2-bac-ninh\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh"},"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 L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n ch\u1ea5t l\u01b0\u1ee3ng d\u00e0nh cho h\u1ecdc sinh l\u1edbp 12. C\u1ea5u tr\u00fac chia th\u00e0nh ba ph\u1ea7n r\u00f5 r\u00e0ng v\u00e0 c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft, h\u1ed7 tr\u1ee3 h\u1ecdc sinh t\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c v\u00e0 c\u1ea3i thi\u1ec7n k\u1ebft qu\u1ea3 h\u1ecdc t\u1eadp. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> t\u1ea3i v\u1ec1 luy\u1ec7n t\u1eadp ngay nh\u00e9!<\/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 L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh<\/span><\/strong><\/h2>\n<h3><strong>C\u1ea5u tr\u00fac \u0111\u1ec1 thi<\/strong><\/h3>\n<ul>\n<li>Th\u1eddi gian l\u00e0m b\u00e0i: 90 ph\u00fat.<\/li>\n<li>S\u1ed1 l\u01b0\u1ee3ng c\u00e2u h\u1ecfi: 50 c\u00e2u, g\u1ed3m:\n<ul>\n<li>Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u).<\/li>\n<li>Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u).<\/li>\n<li>Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><strong>M\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp ti\u00eau bi\u1ec3u<\/strong><\/h3>\n<p><span><strong>Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1. <\/strong>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i l\u0103ng tr\u1ee5 c\u00f3 di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0  B  v\u00e0 chi\u1ec1u cao  h  l\u00e0  V = 1\/3Bh .<\/p>\n<p>A.  V = 1\/3Bh  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  V = Bh  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  V = 2Bh  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  V = 3Bh <\/p>\n<p><strong>C\u00e2u 2. <\/strong>Cho h\u00e0m s\u1ed1  y = f(x)  li\u00ean t\u1ee5c tr\u00ean  mathbbR  c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u cho  f'(x)  nh\u01b0 h\u00ecnh v\u1ebd.<\/p>\n<p>beginarray|c|cccccc| hline x &amp; -\u221e &amp; &amp; -2 &amp; &amp; 0 &amp; &amp; 2 &amp; &amp; +\u221e hline f'(x) &amp; &amp; &#8211; &amp; 0 &amp; + &amp; 0 &amp; &#8211; &amp; 0 &amp; + &amp; hline endarray<\/p>\n<p>H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n<p>A.  (-\u221e; -2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  (0; 2)  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  (-2; 0)  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  (0; +\u221e) <\/p>\n<p><span><strong>Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 b\u1eadc ba  y = f(x)  c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"size-full wp-image-2605 aligncenter\" decoding=\"async\" height=\"290\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-luong-tai-2-bac-ninh-1.jpg\" width=\"295\"\/><\/p>\n<p>a) Gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho b\u1eb1ng  3 .<\/p>\n<p>b) Tr\u00ean kho\u1ea3ng  (0; +\u221e) , gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u1ea1i \u0111i\u1ec3m  x = -1 .<\/p>\n<p>c) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng  (0; 2) .<\/p>\n<p>d) Ph\u01b0\u01a1ng tr\u00ecnh  f(x) &#8211; 1 = 0  c\u00f3 \u0111\u00fang 3 nghi\u1ec7m.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1  y = (x\u00b2 + x + 7)\/(x &#8211; 1) .<\/p>\n<p>a) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n<p>b) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng  (-\u221e; -2) .<\/p>\n<p>c) \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng  y = x &#8211; 2 .<\/p>\n<p>d) Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean kho\u1ea3ng  (1; +\u221e)  b\u1eb1ng  9 .<\/p>\n<p><span><strong>Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1  y = -x\u00b3 + 6x\u00b2 + 12  c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong  (C) . \u0110i\u1ec3m  M(a; b)  l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a \u0111\u1ed3 th\u1ecb  (C) . Gi\u00e1 tr\u1ecb c\u1ee7a  2a + b  b\u1eb1ng bao nhi\u00eau?<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1  y = (2x &#8211; 4)\/(\u221ax\u00b2 &#8211; 4) . G\u1ecdi  a  l\u00e0 s\u1ed1 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0  b  l\u00e0 s\u1ed1 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho. Gi\u00e1 tr\u1ecb  20a &#8211; 10b\u00b2  b\u1eb1ng bao nhi\u00eau?<\/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 L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh<\/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 L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n ch\u1ea5t l\u01b0\u1ee3ng, gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c, ph\u00e1t tri\u1ec3n t\u01b0 duy logic v\u00e0 t\u1ef1 tin h\u01a1n khi b\u01b0\u1edbc v\u00e0o k\u1ef3 thi ch\u00ednh th\u1ee9c. H\u00e3y t\u1ea3i ngay 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 thpt<\/a> \u0111\u1ec3 b\u1eaft \u0111\u1ea7u luy\u1ec7n t\u1eadp v\u00e0 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1QvLFFu0eLznxqMU2U35rk-YEHuaYaUb_\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1QvLFFu0eLznxqMU2U35rk-YEHuaYaUb_\/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\/1QvLFFu0eLznxqMU2U35rk-YEHuaYaUb_\/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 L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh<\/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 L\u01b0\u01a1ng T\u00e0i 2 B\u1eafc Ninh l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n ch\u1ea5t l\u01b0\u1ee3ng d\u00e0nh cho h\u1ecdc sinh l\u1edbp 12. C\u1ea5u tr\u00fac chia th\u00e0nh ba ph\u1ea7n r\u00f5 r\u00e0ng v\u00e0 c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft, h\u1ed7 tr\u1ee3 h\u1ecdc sinh t\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c [&#8230;]\n","protected":false},"author":1,"featured_media":1709,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-510","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\/510","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=510"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/510\/revisions"}],"predecessor-version":[{"id":1710,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/510\/revisions\/1710"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1709"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}