{"id":332,"date":"2026-05-05T04:40:05","date_gmt":"2026-05-05T04:40:05","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-chon-hoc-sinh-gioi-cap-tinh-toan-12-nam-2024-2025-so-gddt-phu-tho\/"},"modified":"2026-05-05T07:12:47","modified_gmt":"2026-05-05T07:12:47","slug":"de-thi-chon-hoc-sinh-gioi-cap-tinh-toan-12-nam-2024-2025-so-gddt-phu-tho","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-chon-hoc-sinh-gioi-cap-tinh-toan-12-nam-2024-2025-so-gddt-phu-tho\/","title":{"rendered":"\u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&#038;\u0110T Ph\u00fa Th\u1ecd"},"content":{"rendered":"<p><strong>\u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/strong> l\u00e0 t\u1eadp t\u00e0i li\u1ec7u d\u00e0nh cho h\u1ecdc sinh 12 r\u00e8n luy\u1ec7n, \u0111\u1ec3 chu\u1ea9n b\u1ecb k\u1ef3 thi ch\u1ecdn l\u1ecdc h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh m\u00f4n To\u00e1n. \u0110\u1ec3 nhanh ch\u00f3ng s\u1edf h\u1eefu \u0111\u01b0\u1ee3c t\u1eadp t\u00e0i li\u1ec7u n\u00e0y, h\u00e3y tham kh\u1ea3o b\u00e0i vi\u1ebft sau \u0111\u00e2y c\u00f9ng <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i Li\u1ec7u \u00d4n Thi<\/a><\/strong>.<\/p>\n<h2><strong>N\u1ed9i dung \u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/strong><\/h2>\n<p><strong>\u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/strong> c\u00f3 t\u1ea5t c\u1ea3 39 c\u00e2u tr\u1eafc nghi\u1ec7m v\u00e0 l\u00e0m b\u00e0i trong th\u1eddi gian 180 ph\u00fat, c\u00f3 c\u1ea5u tr\u00fac nh\u01b0 sau:<\/p>\n<p><span><strong>Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 8 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>Ph\u1ea7n n\u00e0y s\u1ebd t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 32, h\u1ecdc sinh ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang cho m\u1ed7i c\u00e2u. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tham kh\u1ea3o sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 6.<\/strong> Nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = 2024 sin (\u03c0 + x) + (2025)\/(cos\u00b2 x) l\u00e0<\/p>\n<p>A.  2024cos x + 2025tan x + C \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  -2024cos x + 2025tan x + C <\/p>\n<p>C.  -2024sin x &#8211; 2025tan x + C \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  2024sin x &#8211; 2025cot x + C <\/p>\n<p><strong>C\u00e2u 7.<\/strong> Trong m\u1eb7t ph\u1eb3ng  Oxy , cho \u0111\u01b0\u1eddng th\u1eb3ng  d: 2x &#8211; y + 1 = 0  v\u00e0 hai \u0111i\u1ec3m  A(-1;2), B(4;0) . G\u1ecdi  C  tr\u00ean tr\u1ee5c  Oy  sao cho tr\u1ecdng t\u00e2m  triangle ABC  thu\u1ed9c  d . Chu vi  triangle ABC  (l\u00e0m tr\u00f2n) b\u1eb1ng<\/p>\n<p>A. 19\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. 18\u00a0 \u00a0 \u00a0 \u00a0 C. 20\u00a0 \u00a0 \u00a0 \u00a0D. 17<\/p>\n<p><span><strong>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi \u0111\u00fang sai ( 2 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>C\u00f3 2 c\u00e2u, trong m\u1ed7i \u00fd a), b), c), d) c\u1ee7a m\u1ed7i c\u00e2u b\u1ea1n ch\u1ecdn gi\u00e1 tr\u1ecb \u0111\u00fang ho\u1eb7c sai. M\u1ed9t s\u1ed1 d\u1ea1ng c\u00e2u h\u1ecfi trong \u0111\u1ec1 thi.<\/p>\n<p><strong>C\u00e2u 33:<\/strong> Cho h\u00ecnh ch\u00f3p  S.ABCD  c\u00f3  SA = \u221a5 , c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i b\u1eb1ng  \u221a3 .<\/p>\n<p>G\u1ecdi  M  l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh  BC ,  O  l\u00e0 giao \u0111i\u1ec3m c\u1ee7a  AC  v\u00e0  BD .<\/p>\n<p>a) Ch\u1ee9ng minh  (SAC) perp (SBD) .<\/p>\n<p>b) Th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p  S.CDM  b\u1eb1ng  (\u221a15)\/(4) .<\/p>\n<p>c) G\u1ecdi  \u03b1  l\u00e0 g\u00f3c nh\u1ecb di\u1ec7n  [B; SC; D] . Gi\u00e1 tr\u1ecb  sin \u03b1  b\u1eb1ng  (4\u221a5)\/(3) .<\/p>\n<p>d) Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng  CD  v\u00e0  SM  b\u1eb1ng  (3\u221a345)\/(23) .<\/p>\n<p><span><strong>Ph\u1ea7n 3 \u2013 T\u1ef1 lu\u1eadn ( 10 \u0111i\u1ec3m )<\/strong><\/span><\/p>\n<p>C\u00f3 t\u1ea5t c\u1ea3 5 c\u00e2u t\u1ef1 lu\u1eadn, h\u1ecdc sinh c\u1ea7n \u0111\u1ecdc k\u0129 \u0111\u1ec1, t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn \u0111\u1ec3 tr\u1ea3 l\u1eddi<\/p>\n<p><strong>(*) Tr\u00edch \u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/strong><\/p>\n<p><strong>C\u00e2u 3 (3,0 \u0111i\u1ec3m).<\/strong><\/p>\n<p>1) Cho h\u00ecnh ch\u00f3p  S.ABCD  c\u00f3 \u0111\u00e1y  ABCD  l\u00e0 h\u00ecnh thang vu\u00f4ng t\u1ea1i  A  v\u00e0  B ,  AD = 2AB = 2BC ,  CD = 2\u221a2 . H\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a  S  tr\u00ean m\u1eb7t \u0111\u00e1y l\u00e0 trung \u0111i\u1ec3m  M  c\u1ee7a c\u1ea1nh  CD . T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb tr\u1ecdng t\u00e2m  G  c\u1ee7a tam gi\u00e1c  SAD  \u0111\u1ebfn m\u1eb7t ph\u1eb3ng  (SBM) .<\/p>\n<p>2) Cho kh\u1ed1i l\u0103ng tr\u1ee5  ABC.A\u2019B\u2019C\u2019 , kho\u1ea3ng c\u00e1ch t\u1eeb  C  \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng  BB\u2019  b\u1eb1ng  2\u221a2 ,<br \/>\nkho\u1ea3ng c\u00e1ch t\u1eeb  A  \u0111\u1ebfn c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng  BB\u2019  v\u00e0  CC\u2019  l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng  \u221a3  v\u00e0  \u221a5 .<br \/>\nH\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a  A  l\u00ean m\u1eb7t ph\u1eb3ng  (A\u2019B\u2019C\u2019)  l\u00e0 trung \u0111i\u1ec3m  H  c\u1ee7a  B\u2019C\u2019  v\u00e0  A\u2019H = 2 . T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u00e3 cho.<\/p>\n<p><strong>C\u00e2u 4 (1,0 \u0111i\u1ec3m).<\/strong><\/p>\n<p>Cho m\u1eabu s\u1ed1 li\u1ec7u c\u00f3 b\u1ea3ng s\u1ed1 li\u1ec7u sau:\\[\\begin{array}{|c|c|c|c|c|c|}\\hline \\text{Gi\u00e1 tr\u1ecb} &amp; x \u2013 y &amp; 2x + y &amp; 4x + 2y &amp; 5x + 3y &amp; 17x \u2013 2y \\\\<br \/>\n\\hline\\text{T\u1ea7n s\u1ed1} &amp; 14 &amp; 3x + 2y &amp; x + 3y &amp; 5x \u2013 y &amp; 8 \\\\\\hline\\end{array} \\] V\u1edbi  x, y  l\u00e0 c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean. Bi\u1ebft m\u1eabu s\u1ed1 li\u1ec7u th\u1ed1ng k\u00ea \u0111\u00e3 cho c\u00f3 m\u1ed7i l\u00e0 ba gi\u00e1 tr\u1ecb kh\u00e1c nhau.T\u00ednh ph\u01b0\u01a1ng sai c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u \u0111\u00e3 cho (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c).<\/p>\n<p><strong>C\u00e2u 5 (1,5 \u0111i\u1ec3m).<\/strong><br \/>\nTrong m\u1ed9t tr\u00f2 ch\u01a1i b\u1eafn bia, c\u00f3 9 t\u1ea5m bia \u0111\u01b0\u1ee3c \u0111\u00e1nh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 9. B\u1ea1n Nam c\u00f3 8 t\u1ea5m bia \u0111\u01b0\u1ee3c \u0111\u00e1nh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 8, m\u1ed7i b\u1ea1n ch\u1ecdn ra ba t\u1ea5m bia r\u1ed3i s\u1eafp x\u1ebfp ch\u00fang theo th\u1ee9 t\u1ef1 gi\u1ea3m d\u1ea7n \u0111\u1ec3 t\u1ea1o m\u1ed9t s\u1ed1 g\u1ed3m ba ch\u1eef s\u1ed1. Ng\u01b0\u1eddi th\u1eafng l\u00e0 ng\u01b0\u1eddi c\u00f3 s\u1ed1 l\u1edbn h\u01a1n.T\u00ednh x\u00e1c su\u1ea5t \u0111\u1ec3 Vi\u1ec7t th\u1eafng Nam.<\/p>\n<h2><strong>T\u1ea3i \u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/strong><\/h2>\n<p><strong> <iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1ptmdTByYt5SzGcE7TXz443QhMfo-m9GN\/preview\" width=\"640\"><\/iframe><\/p>\n<p><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1ptmdTByYt5SzGcE7TXz443QhMfo-m9GN\/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> <\/strong><\/p>\n<p><strong>\u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/strong> l\u00e0 ch\u00eca kh\u00f3a gi\u00fap c\u00e1c b\u1ea1n chu\u1ea9n b\u1ecb tinh th\u1ea7n c\u0169ng nh\u01b0 k\u1ef9 n\u0103ng th\u1eadt t\u1ed1t cho k\u1ef3 thi h\u1ecdc sinh gi\u1ecfi. H\u00e3y t\u1ea3i ngay \u0111\u1ec1 thi qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y v\u00e0 chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t.<\/p>\n<p><strong><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1ptmdTByYt5SzGcE7TXz443QhMfo-m9GN\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 thi ch\u1ecdn h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Ph\u00fa Th\u1ecd l\u00e0 t\u1eadp t\u00e0i li\u1ec7u d\u00e0nh cho h\u1ecdc sinh 12 r\u00e8n luy\u1ec7n, \u0111\u1ec3 chu\u1ea9n b\u1ecb k\u1ef3 thi ch\u1ecdn l\u1ecdc h\u1ecdc sinh gi\u1ecfi c\u1ea5p t\u1ec9nh m\u00f4n To\u00e1n. \u0110\u1ec3 nhanh ch\u00f3ng s\u1edf h\u1eefu \u0111\u01b0\u1ee3c t\u1eadp t\u00e0i li\u1ec7u n\u00e0y, h\u00e3y tham [&#8230;]\n","protected":false},"author":1,"featured_media":1531,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-332","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tong-hop","tag-tong-hop"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/332","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=332"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/332\/revisions"}],"predecessor-version":[{"id":1532,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/332\/revisions\/1532"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1531"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}