{"id":324,"date":"2026-05-05T04:39:39","date_gmt":"2026-05-05T04:39:39","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-tham-khao-giua-hoc-ki-2-toan-12-nam-2024-2025-so-gddt-thanh-hoa\/"},"modified":"2026-05-05T07:12:21","modified_gmt":"2026-05-05T07:12:21","slug":"bo-de-tham-khao-giua-hoc-ki-2-toan-12-nam-2024-2025-so-gddt-thanh-hoa","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-tham-khao-giua-hoc-ki-2-toan-12-nam-2024-2025-so-gddt-thanh-hoa\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&#038;\u0110T Thanh H\u00f3a"},"content":{"rendered":"<p><strong>B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong> l\u00e0 t\u00e0i li\u1ec7u quan tr\u1ecdng gi\u00fap h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi ch\u00ednh th\u1ee9c. \u0110\u1ec1 thi bao qu\u00e1t c\u00e1c d\u1ea1ng b\u00e0i t\u1eeb \u0111\u1ea1i s\u1ed1, gi\u1ea3i t\u00edch \u0111\u1ebfn h\u00ecnh h\u1ecdc v\u00e0 x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea, b\u00e1m s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa HK2 v\u00e0 THPT Qu\u1ed1c gia. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i Li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u chi ti\u1ebft v\u1ec1 t\u00e0i li\u1ec7u qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 c\u00f3 s\u1ef1 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi gi\u1eefa h\u1ecdc k\u1ef3 2 nh\u00e9!<\/p>\n<h2>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/h2>\n<p><strong>B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong> t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp m\u00f4n To\u00e1n t\u1eeb d\u1ec5 \u0111\u1ebfn n\u00e2ng cao. M\u1ed7i \u0111\u1ec1 \u0111\u1ec1u chu\u1ea9n c\u1ea5u tr\u00fac v\u00e0 c\u00f3 t\u1ea5t c\u1ea3 4 ph\u1ea7n nh\u01b0 sau:<\/p>\n<p><strong>PH\u1ea6N 1 \u2013 C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M<\/strong><\/p>\n<p>T\u1ed5ng h\u1ee3p to\u00e0n b\u1ed9 c\u00e1c ki\u1ebfn th\u1ee9c li\u00ean quan \u0111\u1ebfn \u0111\u1ea1o h\u00e0m v\u00e0 nguy\u00ean h\u00e0m, t\u00edch ph\u00e2n v\u00e0 \u1ee9ng d\u1ee5ng, h\u00ecnh h\u1ecdc, x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea, ph\u01b0\u01a1ng tr\u00ecnh m\u0169, h\u00e0m s\u1ed1 v\u00e0 \u0111\u1ed3 th\u1ecb,\u2026 chia \u0111\u1ec1u 12 c\u00e2u tr\u1eafc nghi\u1ec7m. M\u1ed9t s\u1ed1 v\u00ed d\u1ee5 c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 1:<\/strong> H\u00e0m s\u1ed1 n\u00e0o trong c\u00e1c h\u00e0m s\u1ed1 sau \u0111\u00e2y l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  y = e^x ?<\/p>\n<p>A. y = 1\/x.] [B. y = e^x.] [C. y = e^-x.] [D. y = ln x.<\/p>\n<p><strong>C\u00e2u 2:<\/strong> H\u1ecd nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) = 3x\u00b2 + 2x + 5  l\u00e0:<\/p>\n<p>A. x\u00b3 + x\u00b2 + 5.] [B. x\u00b3 + x + C.] [C. x\u00b3 + x\u00b2 + 5x + C.] [D. x\u00b3 + x\u00b2 + C.<\/p>\n<p><strong>PH\u1ea6N 2 \u2013 C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M \u0110\u00daNG\/ SAI<\/strong><\/p>\n<p>C\u00f3 2 c\u00e2u, m\u1ed7i c\u00e2u c\u00f3 4 \u0111\u00e1p \u00e1n h\u1ecdc sinh ch\u1ecdn \u0111\u00fang ho\u1eb7c sai. Sau \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tham kh\u1ea3o:<\/p>\n<p><strong>C\u00e2u 1<\/strong>. Cho h\u00e0m s\u1ed1  f(x) = 4x\u00b3 &#8211; 2x . Bi\u1ebft  F(x)  l\u00e0 nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) .<\/p>\n<p>a)  F'(x) = f(x) .<\/p>\n<p>b)  f(x)  l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  g(x) = 12x\u00b2 &#8211; 2 .<\/p>\n<p>c) Nguy\u00ean h\u00e0m  F(x)  c\u1ee7a h\u00e0m s\u1ed1  f(x)  th\u1ecfa m\u00e3n  F(0) = 1  l\u00e0  F(x) = 4x\u2074 &#8211; 2x\u00b2 + 1.\n<\/p>\n<p>d) T\u00edch ph\u00e2n int\u2080\u00b9 f(x)dx = 1.\n<\/p>\n<p><strong>C\u00e2u 2<\/strong>. Trong kh\u00f4ng gian  Oxyz , cho hai m\u1eb7t ph\u1eb3ng  (P): x &#8211; 2y + 3z + 1 = 0, (Q): 2x &#8211; 4y + 6z + 1 = 0.\n<\/p>\n<p>a) C\u00e1c vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a hai m\u1eb7t ph\u1eb3ng  (P)  v\u00e0  (Q)  c\u00f9ng ph\u01b0\u01a1ng.<\/p>\n<p>b) Hai m\u1eb7t ph\u1eb3ng  (P)  v\u00e0  (Q)  \u0111\u1ec1u \u0111i qua \u0111i\u1ec3m  M(1;1;2) .<\/p>\n<p>c) Kho\u1ea3ng c\u00e1ch gi\u1eefa hai m\u1eb7t ph\u1eb3ng b\u1eb1ng (\u221a14)\/(14).\n<\/p>\n<p>d) G\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng  (P), (Q)  b\u1eb1ng  60^\u00b0 .<\/p>\n<p><strong>PH\u1ea6N 3 \u2013 TR\u1ea2 L\u1edcI C\u00c2U H\u1eceI NG\u1eaeN<\/strong><\/p>\n<p>Ph\u1ea7n n\u00e0y c\u00f3 4 c\u00e2u y\u00eau c\u1ea7u h\u1ecdc sinh t\u1ef1 tr\u1ea3 l\u1eddi \u0111\u00e1p \u00e1n theo d\u1ea1ng \u0111\u1ec1 y\u00eau c\u1ea7u. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong b\u1ed9 \u0111\u1ec1:<\/p>\n<p>(*) Trong kh\u00f4ng gian Oxyz , ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua M (2;3; 1), song song v\u1edbi tr\u1ee5c Ox v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (Q): x + 2y -3z +1= 0 c\u00f3 d\u1ea1ng ax+by +cz -7 =0 . T\u00ednh a+b+c<\/p>\n<p>(*) M\u1ed9t vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn th\u1eb3ng \u0111\u1ee9ng l\u00ean t\u1eeb m\u1eb7t \u0111\u1ea5t. Gi\u1ea3 s\u1eed t\u1ea1i th\u1eddi \u0111i\u1ec3m t gi\u00e2y (coi t=0 l\u00e0 th\u1eddi \u0111i\u1ec3m vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn l\u00ean). V\u1eadn t\u1ed1c c\u1ee7a vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c:<br \/>\nv(t)=160\u22129.8t(m\/s). H\u00e3y t\u00ecm \u0111\u1ed9 cao c\u1ef1c \u0111\u1ea1i m\u00e0 vi\u00ean \u0111\u1ea1n \u0111\u1ea1t \u0111\u01b0\u1ee3c, l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb.<\/p>\n<p><strong>PH\u1ea6N 4 \u2013 C\u00c2U H\u1eceI T\u1ef0 LU\u1eacN<\/strong><\/p>\n<p>\u1ede ph\u1ea7n n\u00e0y, h\u1ecdc sinh n\u00ean tr\u00ecnh b\u00e0y b\u00e0i gi\u1ea3i m\u1ed9t c\u00e1ch chi ti\u1ebft, c\u00f3 l\u1eadp lu\u1eadn ch\u1eb7t ch\u1ebd s\u1ebd \u0111\u01b0\u1ee3c \u0111i\u1ec3m t\u1ed1i \u0111a nh\u1ea5t.<\/p>\n<p><strong>*** Tr\u00edch d\u1eabn m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi c\u1ee7a B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong><\/p>\n<p>(*) Khu v\u1ef1c trung t\u00e2m m\u1ed9t qu\u1ea3ng tr\u01b0\u1eddng c\u00f3 d\u1ea1ng h\u00ecnh tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AB b\u1eb1ng 10m. Ng\u01b0\u1eddi ta trang tr\u00ed khu v\u1ef1c n\u00e0y b\u1eb1ng hai \u0111\u01b0\u1eddng Parabol \u0111\u1ed1i x\u1ee9ng nhau qua AB. N\u1eb1m trong h\u00ecnh tr\u00f2n, \u0111i qua c\u00e1c \u0111i\u1ec3m A, B v\u00e0 c\u00f3 \u0111\u1ec9nh c\u00e1ch m\u00e9p h\u00ecnh tr\u00f2n 1m. Ph\u1ea7n gi\u1edbi h\u1ea1n b\u1edfi 2 parabol \u0111\u01b0\u1ee3c tr\u1ed3ng hoa v\u1edbi chi ph\u00ed 200 ngh\u00ecn \u0111\u1ed3ng 1 m\u00e9t vu\u00f4ng. Ph\u1ea7n c\u00f2n l\u1ea1i \u0111\u01b0\u1ee3c l\u00e1t g\u1ed1m s\u1ee9 v\u1edbi chi ph\u00ed 800 ngh\u00ecn \u0111\u1ed3ng 1 m\u00e9t vu\u00f4ng. T\u00ednh t\u1ed5ng chi ph\u00ed \u0111\u1ec3 ho\u00e0n th\u00e0nh khu v\u1ef1c n\u00e0y.<\/p>\n<p>(*) Trong m\u1eb7t ph\u1eb3ng OXYZ cho \u0111i\u1ec3m M(1;4;9). G\u1ecdi (P) l\u00e0 m\u1eb7t ph\u1eb3ng \u0111i qua M v\u00e0 c\u1eaft ba tia Ox;Oy;Oz t\u1ea1i c\u00e1c \u0111i\u1ec3m A,B,C( kh\u00e1c O) sao cho OA+OB+OC \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t. T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb g\u1ed1c t\u1ecda \u0111\u1ed9 O \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (P).<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong><\/h2>\n<p>\u0110\u1ec3 b\u1eaft \u0111\u1ea7u l\u00e0m quen v\u00e0 chu\u1ea9n b\u1ecb t\u1ed1t cho k\u1ef3 thi gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n.<strong> B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/strong> s\u1ebd l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u b\u1ed5 \u00edch gi\u00fap b\u1ea1n \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 cao trong k\u1ef3 thi s\u1eafp t\u1edbi. T\u1ea3i ngay b\u1ed9 \u0111\u1ec1 theo \u0111\u01b0\u1eddng link d\u01b0\u1edbi \u0111\u00e2y v\u00e0 luy\u1ec7n t\u1eadp h\u1eb1ng ng\u00e0y nh\u00e9.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1Q6CglaSzFr30UY4ZwwXFwk0woqoPymQE\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1Q6CglaSzFr30UY4ZwwXFwk0woqoPymQE\/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><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1Q6CglaSzFr30UY4ZwwXFwk0woqoPymQE\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 \u0111\u1ec1 tham kh\u1ea3o gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 12 n\u0103m 2024 \u2013 2025 s\u1edf GD&amp;\u0110T Thanh H\u00f3a l\u00e0 t\u00e0i li\u1ec7u quan tr\u1ecdng gi\u00fap h\u1ecdc sinh l\u1edbp 12 \u00f4n t\u1eadp v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi ch\u00ednh th\u1ee9c. \u0110\u1ec1 thi bao qu\u00e1t c\u00e1c d\u1ea1ng b\u00e0i t\u1eeb \u0111\u1ea1i s\u1ed1, gi\u1ea3i t\u00edch \u0111\u1ebfn h\u00ecnh h\u1ecdc [&#8230;]\n","protected":false},"author":1,"featured_media":1523,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-324","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\/324","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=324"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/324\/revisions"}],"predecessor-version":[{"id":1524,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/324\/revisions\/1524"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1523"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=324"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=324"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}