{"id":96,"date":"2026-05-05T04:52:48","date_gmt":"2026-05-05T04:52:48","guid":{"rendered":"https:\/\/79.buffdemo.com\/?p=96"},"modified":"2026-05-05T07:26:39","modified_gmt":"2026-05-05T07:26:39","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-yen-lac-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-yen-lac-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 Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac"},"content":{"rendered":"<p>K\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT n\u0103m 2025 \u0111ang \u0111\u1ebfn g\u1ea7n v\u00e0 <strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n kh\u00f4ng th\u1ec3 thi\u1ebfu cho h\u1ecdc sinh l\u1edbp 12. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed<\/strong><\/a> \u201cgi\u1ea3i m\u00e3\u201d \u0111\u1ec1 thi trong b\u00e0i vi\u1ebft sau 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 Y\u00ean L\u1ea1c 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 Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac <\/strong>\u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t theo \u0111\u1ecbnh h\u01b0\u1edbng v\u00e0 c\u1ea5u tr\u00fac \u0111\u1ec1 tham kh\u1ea3o c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o, ph\u00f9 h\u1ee3p v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh GDPT 2018 m\u1edbi. N\u1ed9i dung <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> bao ph\u1ee7 to\u00e0n b\u1ed9 ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 12, \u0111\u1ed3ng th\u1eddi c\u00f3 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi li\u00ean h\u1ec7 ki\u1ebfn th\u1ee9c l\u1edbp 10 v\u00e0 11, t\u1eadp trung v\u00e0o c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m nh\u01b0:<\/p>\n<p><span><strong>Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> Cho  A  v\u00e0  B  l\u00e0 hai bi\u1ebfn c\u1ed1 \u0111\u1ed9c l\u1eadp, v\u1edbi  P(A) = 0,2024 ,  P(B) = 0,2025 . T\u00ednh  P(A|B) .<\/p>\n<p>A. 0,7976 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 0,7975 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 0,2025\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. 0,2024<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Ph\u01b0\u01a1ng tr\u00ecnh  2cos x &#8211; 1 = 0  c\u00f3 m\u1ed9t nghi\u1ec7m l\u00e0<\/p>\n<p>A.  x = \u03c0\/3  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  x = \u03c0\/4  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  x = \u03c0\/2  \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  x = \u03c0\/6 <\/p>\n<p><span><strong>Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u, m\u1ed7i c\u00e2u g\u1ed3m 4 \u00fd nh\u1ecf)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1  y = f(x) = (x\u00b2 + 3x)\/(x &#8211; 1) .<\/p>\n<p>a) H\u00e0m s\u1ed1  y = f(x)  \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng  (-\u221e; 1) .<\/p>\n<p>b) Gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1  y = f(x)  b\u1eb1ng  1 .<\/p>\n<p>c) H\u00e0m s\u1ed1  y = f(x)  c\u00f3  3  \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n<p>d) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean t\u1ea1o v\u1edbi 2 tr\u1ee5c to\u1ea1 \u0111\u1ed9 m\u1ed9t tam gi\u00e1c c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng  8 .<\/p>\n<p><strong>C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian  Oxyz , cho c\u00e1c \u0111i\u1ec3m  A(1; -3; 5), B(-3; 7; 1), C(5; -1; 17) .<\/p>\n<p>a) Vecto  AB\u20d7  c\u00f3 t\u1ecda \u0111\u1ed9 l\u00e0  (-2; 4; 6) .<\/p>\n<p>b) Ba \u0111i\u1ec3m  O, A, B  th\u1eb3ng h\u00e0ng.<\/p>\n<p>c) Tam gi\u00e1c  ABC  l\u00e0 tam gi\u00e1c t\u00f9.<\/p>\n<p>d) Kh\u00f4ng c\u00f3 \u0111i\u1ec3m  M  n\u00e0o thu\u1ed9c m\u1eb7t ph\u1eb3ng  (Oxz)  \u0111\u1ec3 tam gi\u00e1c  MBC  \u0111\u1ec1u.<\/p>\n<p><span><strong>Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1:<\/strong> L\u00e1t c\u1eaft ngang c\u1ee7a m\u1ed9t v\u00f9ng \u0111\u1ea5t \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh ho\u00e1 l\u00e0 m\u1ed9t ph\u1ea7n h\u00e0m s\u1ed1 b\u1eadc ba  y = f(x)  c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i tr\u00ean c\u00e1c tr\u1ee5c l\u00e0 kil\u00f4m\u00e9t). Bi\u1ebft kho\u1ea3ng c\u00e1ch hai b\u00ean ch\u00e2n \u0111\u1ed3i  OM = 2 (km) , \u0111\u1ed9 r\u1ed9ng c\u1ee7a h\u1ed3 n\u01b0\u1edbc  MN = 1 (km)  v\u00e0 ng\u1ecdn \u0111\u1ed3i cao  528 (m) . \u0110\u1ed9 s\u00e2u nh\u1ea5t c\u1ee7a h\u1ed3 n\u01b0\u1edbc l\u00e0 bao nhi\u00eau m\u00e9t (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb c\u1ee7a m\u00e9t)?<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-2947 size-full\" decoding=\"async\" height=\"296\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-yen-lac-vinh-phuc-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-yen-lac-vinh-phuc-1.jpg 492w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-yen-lac-vinh-phuc-1-300x180.jpg 300w\" width=\"492\"\/><\/p>\n<p><strong>C\u00e2u 2:<\/strong> \u0110\u1ec3 chu\u1ea9n b\u1ecb cho ho\u1ea1t \u0111\u1ed9ng c\u1eafm tr\u1ea1i, b\u1ea1n An t\u00ecm hi\u1ec3u c\u00e1c m\u1eabu l\u1ec1u c\u1eafm tr\u1ea1i c\u00f3 d\u1ea1ng kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u1ee9ng ng\u0169 gi\u00e1c v\u1edbi k\u00edch th\u01b0\u1edbc nh\u01b0 trong h\u00ecnh  a  v\u00e0 h\u00ecnh  b .<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-2946 size-full\" decoding=\"async\" height=\"227\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-yen-lac-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-yen-lac-vinh-phuc-2.jpg 611w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-yen-lac-vinh-phuc-2-300x111.jpg 300w\" width=\"611\"\/><\/p>\n<p>B\u1ea1n An mu\u1ed1n bi\u1ebft th\u1ec3 t\u00edch ch\u00eanh l\u1ec7ch c\u1ee7a hai l\u1ec1u n\u00ean th\u1ef1c hi\u1ec7n t\u00ednh  V\u2081 &#8211; V\u2082 , trong \u0111\u00f3  V\u2081, V\u2082  l\u1ea7n l\u01b0\u1ee3t l\u00e0 th\u1ec3 t\u00edch c\u1ee7a m\u1eabu l\u1ec1u c\u1eafm tr\u1ea1i \u1edf h\u00ecnh  a, b . Gi\u00e1 tr\u1ecb c\u1ee7a  V\u2081 &#8211; V\u2082  b\u1eb1ng bao nhi\u00eau decim\u00e9t kh\u1ed1i (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \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 Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<p><span data-sheets-root=\"1\"><strong>\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac<\/strong> <\/span>\u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 cao v\u1ec1 t\u00ednh c\u1eadp nh\u1eadt, s\u00e1t v\u1edbi \u0111\u1ec1 thi ch\u00ednh th\u1ee9c, ph\u00f9 h\u1ee3p cho vi\u1ec7c luy\u1ec7n t\u1eadp n\u01b0\u1edbc r\u00fat tr\u01b0\u1edbc k\u1ef3 thi th\u1eadt. C\u00f9ng t\u1ea3i ngay b\u1ed9 \u0111\u1ec1 \u0111\u1ec3 luy\u1ec7n t\u1eadp tr\u01b0\u1edbc k\u1ef3 thi.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1tDEPFvQulcT1zBOC0kcz1V5qI5hZuJ-_\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1tDEPFvQulcT1zBOC0kcz1V5qI5hZuJ-_\/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\/1tDEPFvQulcT1zBOC0kcz1V5qI5hZuJ-_\/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 Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>K\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT n\u0103m 2025 \u0111ang \u0111\u1ebfn g\u1ea7n v\u00e0 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Y\u00ean L\u1ea1c V\u0129nh Ph\u00fac l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n kh\u00f4ng th\u1ec3 thi\u1ebfu cho h\u1ecdc sinh l\u1edbp 12. C\u00f9ng T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed \u201cgi\u1ea3i m\u00e3\u201d \u0111\u1ec1 thi trong b\u00e0i vi\u1ebft sau nh\u00e9! [&#8230;]\n","protected":false},"author":1,"featured_media":1771,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-96","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\/96","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=96"}],"version-history":[{"count":2,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/96\/revisions"}],"predecessor-version":[{"id":1772,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/96\/revisions\/1772"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1771"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=96"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=96"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}