{"id":340,"date":"2026-05-05T04:40:29","date_gmt":"2026-05-05T04:40:29","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/noi-dung-on-tap-giua-hoc-ki-2-toan-10-nam-2024-2025-truong-thpt-tran-phu-ha-noi\/"},"modified":"2026-05-05T07:13:12","modified_gmt":"2026-05-05T07:13:12","slug":"noi-dung-on-tap-giua-hoc-ki-2-toan-10-nam-2024-2025-truong-thpt-tran-phu-ha-noi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/noi-dung-on-tap-giua-hoc-ki-2-toan-10-nam-2024-2025-truong-thpt-tran-phu-ha-noi\/","title":{"rendered":"N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i"},"content":{"rendered":"<p><strong>N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong> l\u00e0 t\u1eadp t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p, h\u01b0\u1edbng d\u1eabn chi ti\u1ebft c\u00e1c ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m \u0111\u1ec3 chu\u1ea9n b\u1ecb cho ki\u1ec3m tra gi\u1eefa k\u1ef3 2 m\u00f4n To\u00e1n. B\u1ed9 \u0111\u1ec1 c\u01b0\u01a1ng n\u00e0y gi\u00fap h\u1ecdc sinh l\u1edbp 10\u00a0 h\u1ec7 th\u1ed1ng l\u1ea1i l\u00fd thuy\u1ebft, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i t\u1eadp v\u00e0 n\u1eafm v\u1eefng n\u1ed9i dung quan tr\u1ecdng theo ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc n\u0103m 2024 \u2013 2025. C\u00f9ng <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" target=\"_blank\" rel=\"noopener\">T\u00e0i Li\u1ec7u \u00d4n Thi<\/a><\/strong> t\u00ecm hi\u1ec3u n\u1ed9i dung c\u1ee7a t\u1eadp \u0111\u1ec1 c\u01b0\u01a1ng n\u00e0y qua b\u00e0i vi\u1ebft \u0111\u00e2y.<\/p>\n<h2><strong>N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p><strong>N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong> l\u00e0 t\u1eadp \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 ki\u1ebfn th\u1ee9c \u0110\u1ea1i s\u1ed1 t\u1ed5 h\u1ee3p, Ph\u01b0\u01a1ng ph\u00e1p t\u1ecda \u0111\u1ed9 trong m\u1eb7t ph\u1eb3ng. C\u1ea5u tr\u00fac c\u00e2u h\u1ecfi tr\u1ecdng t\u00e2m, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh gi\u00fap c\u00e1c b\u1ea1n t\u1ef1 tin h\u01a1n tr\u01b0\u1edbc k\u1ef3 thi. N\u1ed9i dung c\u1ee7a \u0111\u1ec1 \u00f4n t\u1eadp g\u1ed3m c\u00e1c 2 d\u1ea1ng ch\u00ednh v\u00e0 chia th\u00e0nh 3 ph\u1ea7n nh\u01b0 sau:<\/p>\n<p><span><strong>D\u1ea1ng 1: Ki\u1ebfn th\u1ee9c \u0110\u1ea1i s\u1ed1 t\u1ed5 h\u1ee3p ( 3 ph\u1ea7n )<\/strong><\/span><\/p>\n<p><span><strong>D\u1ea1ng 2 : C\u00e2u h\u1ecfi v\u1ec1 Ph\u01b0\u01a1ng ph\u00e1p trong t\u1ecda \u0111\u1ed9 m\u1eb7t ph\u1eb3ng ( 3 ph\u1ea7n )<\/strong><\/span><\/p>\n<p><span><strong>Ph\u1ea7n 1: C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 35 c\u00e2u )<\/strong><\/span><\/p>\n<p>\u2013 H\u1ecdc sinh l\u1ef1a ch\u1ecdn ph\u01b0\u01a1ng \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t trong 4 \u0111\u00e1p \u00e1n. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 nh\u01b0:<\/p>\n<p><strong>C\u00e2u 1.<\/strong> B\u1ea1n Lan c\u00f3 5 quy\u1ec3n s\u00e1ch To\u00e1n v\u00e0 6 quy\u1ec3n s\u00e1ch V\u0103n h\u1ecdc, c\u00e1c quy\u1ec3n s\u00e1ch l\u00e0 kh\u00e1c nhau. H\u1ecfi b\u1ea1n Lan c\u00f3 bao nhi\u00eau c\u00e1ch ch\u1ecdn m\u1ed9t quy\u1ec3n s\u00e1ch \u0111\u1ec3 \u0111\u1ecdc?<\/p>\n<p>textbfA. 6. textbfB. 5. textbfC. 30. textbfD. 11.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Cho 9 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t. H\u1ecfi l\u1eadp \u0111\u01b0\u1ee3c bao nhi\u00eau vect\u01a1 kh\u00e1c  0\u20d7 ?(Bi\u1ebft r\u1eb1ng hai \u0111\u1ea7u m\u00fat c\u1ee7a m\u1ed7i vect\u01a1 l\u00e0 2 trong 9 \u0111i\u1ec3m \u0111\u00e3 cho)<\/p>\n<p>textbfA. 9. textbfB. 72. textbfC. 36. textbfD. 17.<\/p>\n<p><strong>C\u00e2u 3.<\/strong> Cho hai \u0111i\u1ec3m  A(1;0)  v\u00e0  B(-3;3) . T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng  AB .<\/p>\n<p>textbfA. AB = \u221a13. textbfB. AB = 3\u221a2. textbfC. AB = 4. textbfD. AB = 5.<\/p>\n<p><strong><span>Ph\u1ea7n 2: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai ( 9 c\u00e2u )<\/span><\/strong><\/p>\n<p>\u2013 \u1ede ph\u1ea7n n\u00e0y, s\u1ebd c\u00f3 4 \u0111\u00e1p \u00e1n cho m\u1ed7i c\u00e2u h\u1ecfi, h\u1ecdc sinh l\u00e0m b\u00e0i theo c\u00e1ch ch\u1ecdn gi\u00e1 tr\u1ecb \u0111\u00fang ho\u1eb7c sai cho m\u1ed7i c\u00e2u tr\u1ea3 l\u1eddi. Tham kh\u1ea3o m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi m\u1eabu \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 ph\u1ea7n n\u00e0y nh\u00e9!<\/p>\n<p><strong>C\u00e2u 3.<\/strong> Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9  Oxy , cho \u0111\u01b0\u1eddng th\u1eb3ng  \u0394: 3x + 4y &#8211; 2 = 0 .<br \/>\nX\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n<p>a) \u0110\u01b0\u1eddng th\u1eb3ng  \u0394  c\u1eaft tr\u1ee5c  Ox  t\u1ea1i \u0111i\u1ec3m  I ( 0; 1\/2 ) .<\/p>\n<p>b) \u0110\u01b0\u1eddng th\u1eb3ng  \u0394  \u0111i qua \u0111i\u1ec3m  M(2;-1) .<\/p>\n<p>c) Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua \u0111i\u1ec3m  A(1;1)  v\u00e0 song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng  \u0394  l\u00e0  3x + 4y &#8211; 7 = 0 .<\/p>\n<p>d) \u0110\u01b0\u1eddng th\u1eb3ng  \u0394  c\u00f3 m\u1ed9t vector ch\u1ec9 ph\u01b0\u01a1ng  u\u20d7 = (4;3) .<\/p>\n<p><span><strong>Ph\u1ea7n 3: T\u1ef1 lu\u1eadn ( 20 c\u00e2u )<\/strong><\/span><\/p>\n<p>\u2013 M\u1ed7i d\u1ea1ng s\u1ebd c\u00f3 20 c\u00e2u h\u1ecfi v\u1ec1 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a ph\u1ea7n \u0111\u00f3, h\u1ecdc sinh \u0111\u1ecdc \u0111\u1ec1 v\u00e0 tr\u1ea3 l\u1eddi theo d\u1ea1ng t\u1ef1 lu\u1eadn. M\u1ed7i ph\u1ea7n s\u1ebd c\u00f3 ma tr\u1eadn ch\u1ea5m \u0111i\u1ec3m kh\u00e1c nhau, h\u00e3y tham kh\u1ea3o m\u1eabu c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Trong m\u1eb7t ph\u1eb3ng, c\u00f3 bao nhi\u00eau h\u00ecnh ch\u1eef nh\u1eadt \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh t\u1eeb 6 \u0111\u01b0\u1eddng th\u1eb3ng song song v\u00e0 8 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi 6 \u0111\u01b0\u1eddng th\u1eb3ng song song \u0111\u00f3? (c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f4i m\u1ed9t ph\u00e2n bi\u1ec7t).<\/p>\n<p><strong>C\u00e2u 3.<\/strong> T\u00ednh g\u00f3c gi\u1eefa c\u00e1c c\u1eb7p \u0111\u01b0\u1eddng th\u1eb3ng sau:<br \/>\na)  \u0394\u2081: \u221a3x + y &#8211; 4 = 0  v\u00e0  \u0394\u2082: x + \u221a3y + 3 = 0 .<\/p>\n<p>b)  d\u2081: begincases x = -1 + 2t y = 3 + 4t endcases  v\u00e0  d\u2082: begincases x = 3 + 5s y = 1 &#8211; 3s endcases   (t, s l\u00e0 c\u00e1c tham s\u1ed1) .<\/p>\n<p><strong>C\u00e2u 4.<\/strong> Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9, cho tam gi\u00e1c  ABC  c\u00f3  A(1;0) ,  B(3;2)  v\u00e0  C(-2;-1) .<\/p>\n<p>a) T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao k\u1ebb t\u1eeb \u0111\u1ec9nh  A  c\u1ee7a tam gi\u00e1c  ABC .<\/p>\n<p>b) T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c  ABC .<\/p>\n<h2><strong>T\u1ea3i N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong><\/h2>\n<p>\u0110\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 t\u1ed1t trong k\u00ec thi s\u1eafp t\u1edbi, h\u00e3y t\u1ea3i ngay <strong>N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong> v\u00e0 r\u00e8n luy\u1ec7n m\u1ed7i ng\u00e0y nh\u00e9!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1VBnPIFcE79Yl36nrD1y-k635NfhiF5wG\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1VBnPIFcE79Yl36nrD1y-k635NfhiF5wG\/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\/1VBnPIFcE79Yl36nrD1y-k635NfhiF5wG\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>N\u1ed9i dung \u00f4n t\u1eadp gi\u1eefa h\u1ecdc k\u00ec 2 To\u00e1n 10 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i l\u00e0 t\u1eadp t\u00e0i li\u1ec7u t\u1ed5ng h\u1ee3p, h\u01b0\u1edbng d\u1eabn chi ti\u1ebft c\u00e1c ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m \u0111\u1ec3 chu\u1ea9n b\u1ecb cho ki\u1ec3m tra gi\u1eefa k\u1ef3 2 m\u00f4n To\u00e1n. B\u1ed9 \u0111\u1ec1 c\u01b0\u01a1ng n\u00e0y gi\u00fap h\u1ecdc sinh l\u1edbp 10\u00a0 [&#8230;]\n","protected":false},"author":1,"featured_media":1539,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-340","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\/340","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=340"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/340\/revisions"}],"predecessor-version":[{"id":1540,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/340\/revisions\/1540"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1539"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}