{"id":512,"date":"2026-05-05T04:49:42","date_gmt":"2026-05-05T04:49:42","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ngo-gia-tu-vinh-phuc\/"},"modified":"2026-05-05T07:23:02","modified_gmt":"2026-05-05T07:23:02","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ngo-gia-tu-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-ngo-gia-tu-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 Ng\u00f4 Gia T\u1ef1 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 Ng\u00f4 Gia T\u1ef1 V\u0129nh Ph\u00fac<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n nh\u1eb1m h\u1ed7 tr\u1ee3 h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3, chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 thi ch\u00ednh th\u1ee9c. \u0110\u1ec1 thi b\u00e1m s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o, bao g\u1ed3m c\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn v\u1edbi n\u1ed9i dung \u0111a d\u1ea1ng, t\u1eeb ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m b\u00e0i v\u00e0 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c. T\u1ea3i ngay b\u1ed9 \u0111\u1ec1 qua b\u00e0i vi\u1ebft c\u1ee7a <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> \u0111\u1ec3 luy\u1ec7n t\u1eadp 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 Ng\u00f4 Gia T\u1ef1 V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n<p><span><strong>Th\u00f4ng tin chung:<\/strong><\/span><\/p>\n<ul>\n<li><strong>M\u00f4n:<\/strong> To\u00e1n<\/li>\n<li><strong>Th\u1eddi gian l\u00e0m b\u00e0i:<\/strong> 90 ph\u00fat<\/li>\n<li><strong>H\u00ecnh th\u1ee9c:<\/strong> Tr\u1eafc nghi\u1ec7m kh\u00e1ch quan (22 c\u00e2u)<\/li>\n<\/ul>\n<p><strong><span>M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi ti\u00eau bi\u1ec3u:<\/span><\/strong><\/p>\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> Cho h\u00e0m s\u1ed1  f(x)  c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau:<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-2638 size-full\" decoding=\"async\" height=\"152\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ngo-gia-tu-vinh-phuc1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ngo-gia-tu-vinh-phuc1.jpg 620w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-ngo-gia-tu-vinh-phuc1-300x74.jpg 300w\" width=\"620\"\/><\/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.  (-3; 3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (-3; 0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  (0; 3) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  (-\u221e; -3) <\/p>\n<p><strong>C\u00e2u 2.<\/strong> X\u00e1c \u0111\u1ecbnh s\u1ed1 h\u1ea1ng \u0111\u1ea7u  u\u2081  v\u00e0 c\u00f4ng sai  d  c\u1ee7a c\u1ea5p s\u1ed1 c\u1ed9ng  (u_n)  c\u00f3  u\u2089 = 5u\u2082  v\u00e0  u\u2081\u2083 = 2u\u2086 + 5 .<\/p>\n<p>A.  u\u2081 = 3, ; d = 4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  u\u2081 = 3, ; d = 5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  u\u2081 = 4, ; d = 5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  u\u2081 = 4, ; d = 3 <\/p>\n<p><span><strong>Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 13.<\/strong> Cho h\u00e0m s\u1ed1  y = x\u00b3 &#8211; 3x + 2 . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00e2y l\u00e0 \u0111\u00fang hay sai?<\/p>\n<p>a) H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng  (-1; 1) .<\/p>\n<p>b) H\u00e0m s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u b\u1eb1ng 1.<\/p>\n<p>c)  minlimits_[-1;0] y + maxlimits_[0;1] y = 4 .<\/p>\n<p>d) Ph\u01b0\u01a1ng tr\u00ecnh  x\u00b3 &#8211; 3x + 2 = m  c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t khi  a &lt; m &lt; b , khi \u0111\u00f3  a + b = 3 .<\/p>\n<p><strong>C\u00e2u 14.<\/strong> Trong kh\u00f4ng gian  Oxyz , cho \u0111\u01b0\u1eddng th\u1eb3ng  D: x\/-1 = (y + 3)\/(2) = (z &#8211; 2)\/(3)  v\u00e0 m\u1eb7t ph\u1eb3ng  (P): x + 2y &#8211; z + 2025 = 0 . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00e2y l\u00e0 \u0111\u00fang hay sai?<\/p>\n<p>a) G\u1ecdi  u\u20d7  v\u00e0  n\u20d7  l\u1ea7n l\u01b0\u1ee3t l\u00e0 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng v\u00e0 vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a  D  v\u00e0  (P) . Khi \u0111\u00f3  u\u20d7 \u00b7 n\u20d7 = 0 .<\/p>\n<p>b) Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng  (Q)  \u0111i qua  A(1; -2; 3)  v\u00e0 song song v\u1edbi m\u1eb7t ph\u1eb3ng  (P)  l\u00e0  (Q): x + 2y &#8211; z &#8211; 6 = 0 .<\/p>\n<p>c) \u0110\u01b0\u1eddng th\u1eb3ng  D\u2019  vu\u00f4ng g\u00f3c v\u1edbi  D  v\u00e0 song song v\u1edbi m\u1eb7t ph\u1eb3ng  (Oxy)  c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0  u\u20d7\u2082 = (3; -3; 2) .<\/p>\n<p>d) \u0110\u01b0\u1eddng th\u1eb3ng  d\u2082  vu\u00f4ng g\u00f3c v\u1edbi  (P) , t\u1ea1o v\u1edbi  (Q): x + my &#8211; 3 = 0  m\u1ed9t g\u00f3c  30^\u00b0 . Khi \u0111\u00f3 t\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a tham s\u1ed1  m  b\u1eb1ng  -16\/5 .<\/p>\n<p><strong><span>Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/span><\/strong><\/p>\n<p><strong>C\u00e2u 17.<\/strong> Ta x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1  a, b, c  \u0111\u1ec3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = x\u00b3 + ax\u00b2 + bx + c  \u0111i qua \u0111i\u1ec3m  (1; 0)  v\u00e0 c\u00f3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb  (-2; 0) . T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c  T = a\u00b2 + b\u00b2 + c\u00b2 .<\/p>\n<p><strong>C\u00e2u 18.<\/strong> M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng d\u1ecdc theo m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng sao cho v\u1eadn t\u1ed1c c\u1ee7a n\u00f3 t\u1ea1i th\u1eddi \u0111i\u1ec3m  t  (gi\u00e2y) l\u00e0  v(t) = t\u00b2 &#8211; t &#8211; 6  (m\u00e9t\/gi\u00e2y). Qu\u00e3ng \u0111\u01b0\u1eddng (m\u00e9t) v\u1eadt \u0111i \u0111\u01b0\u1ee3c trong kho\u1ea3ng th\u1eddi gian  1 \u2264 t \u2264 4  b\u1eb1ng (l\u00e0m tr\u00f2n t\u1edbi h\u00e0ng ph\u1ea7n m\u01b0\u1eddi)<\/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 Ng\u00f4 Gia T\u1ef1 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 Ng\u00f4 Gia T\u1ef1 V\u0129nh Ph\u00fac<\/strong> cung c\u1ea5p l\u1eddi gi\u1ea3i chi ti\u1ebft cho t\u1eebng c\u00e2u h\u1ecfi, gi\u00fap h\u1ecdc sinh hi\u1ec3u r\u00f5 c\u00e1ch t\u00ednh to\u00e1n v\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i b\u00e0i. \u0110\u00e2y l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch \u0111\u1ec3 t\u1ef1 \u00f4n luy\u1ec7n v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT. T\u1ea3i ngay <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 thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a> qua file b\u00ean d\u01b0\u1edbi.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1SiJP85AaJ6qEyEE_YuhGYtvlzF2l9EBt\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1SiJP85AaJ6qEyEE_YuhGYtvlzF2l9EBt\/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\/1SiJP85AaJ6qEyEE_YuhGYtvlzF2l9EBt\/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 Ng\u00f4 Gia T\u1ef1 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 Ng\u00f4 Gia T\u1ef1 V\u0129nh Ph\u00fac \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n nh\u1eb1m h\u1ed7 tr\u1ee3 h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3, chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 thi ch\u00ednh th\u1ee9c. \u0110\u1ec1 thi b\u00e1m s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o [&#8230;]\n","protected":false},"author":1,"featured_media":1711,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-512","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\/512","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=512"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/512\/revisions"}],"predecessor-version":[{"id":1712,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/512\/revisions\/1712"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1711"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}