{"id":376,"date":"2026-05-05T04:42:30","date_gmt":"2026-05-05T04:42:30","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-khao-sat-chat-luong-thang-2-toan-12-co-dap-an-va-loi-giai\/"},"modified":"2026-05-05T07:15:12","modified_gmt":"2026-05-05T07:15:12","slug":"bo-de-khao-sat-chat-luong-thang-2-toan-12-co-dap-an-va-loi-giai","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-khao-sat-chat-luong-thang-2-toan-12-co-dap-an-va-loi-giai\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i"},"content":{"rendered":"<p><strong>B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i <\/strong>l\u00e0 t\u00e0i li\u1ec7u quan tr\u1ecdng gi\u00fap h\u1ecdc sinh l\u1edbp 12 r\u00e8n luy\u1ec7n, n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i \u0111\u1ec3 \u0111\u1ea1t k\u1ebft qu\u1ea3 cao trong k\u1ef3 kh\u1ea3o s\u00e1t ch\u00ednh th\u1ee9c. \u0110\u01b0\u1ee3c bi\u00ean so\u1ea1n k\u1ef9 l\u01b0\u1ee1ng b\u1edfi c\u00e1c th\u1ea7y c\u00f4 trong nh\u00f3m<strong> Di\u1ec5n \u0110\u00e0n Gi\u00e1o Vi\u00ean To\u00e1n<\/strong>, b\u1ed9 \u0111\u1ec1 n\u00e0y gi\u00fap b\u1ea1n ph\u00e1t tri\u1ec3n t\u01b0 duy, l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi v\u00e0 \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3. T\u00ecm hi\u1ec3u th\u00eam b\u1ed9 t\u00e0i li\u1ec7u n\u00e0y qua 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> nh\u00e9.<\/p>\n<h2><strong>N\u1ed9i dung B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i<\/strong><\/h2>\n<p><strong>B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i<\/strong> g\u1ed3m 95 trang. C\u00e1c \u0111\u1ec1 thi \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac 30% tr\u1eafc nghi\u1ec7m v\u1edbi b\u1ed1n ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u), 40% tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 c\u00e2u) v\u00e0 30% tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u). V\u1edbi th\u1eddi gian l\u00e0m b\u00e0i 90 ph\u00fat, b\u1ed9 \u0111\u1ec1 gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n t\u01b0 duy logic, ph\u1ea3n x\u1ea1 nhanh v\u00e0 l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1.<\/p>\n<p><span><strong>Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m (12 c\u00e2u)<\/strong><\/span><\/p>\n<p>M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 \u0111\u1ec3 c\u00e1c b\u1ea1n h\u1ecdc sinh l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac nh\u01b0 sau:<\/p>\n<p><strong>C\u00e2u 4:<\/strong> Cho c\u1ea5p s\u1ed1 nh\u00e2n  (u_n)  c\u00f3  u\u2081 = 2 ,  u\u2082 = 6 , gi\u00e1 tr\u1ecb  u\u2085  l\u00e0:<\/p>\n<p>A.  27 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  54 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  81 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  162 <\/p>\n<p><strong>C\u00e2u 5:<\/strong> Trong cu\u1ed9c thi c\u00f3 10 th\u00ed sinh tham gia, s\u1ed1 c\u00e1ch trao m\u1ed9t gi\u1ea3i nh\u1ea5t, m\u1ed9t gi\u1ea3i nh\u00ec v\u00e0 m\u1ed9t gi\u1ea3i ba l\u00e0:<\/p>\n<p>A.  10\u00b3 \u00a0 \u00a0 \u00a0 \u00a0 B.  3.10 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.  A\u2081\u2080\u00b3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.  C\u2081\u2080\u00b3 <\/p>\n<p><span><strong>Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 c\u00e2u)<\/strong><\/span><\/p>\n<p>\u1ede ph\u1ea7n n\u00e0y b\u1ea1n s\u1ebd ch\u1ecdn ra m\u1ec7nh \u0111\u1ec1 \u0111\u00fang \/ sai cho m\u1ed7i c\u00e2u tr\u1ea3 l\u1eddi, h\u00e3y tham kh\u1ea3o qua c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n<p><strong>C\u00e2u 3:<\/strong> Cho m\u1ed9t c\u1ea5p s\u1ed1 nh\u00e2n  (u_n)  c\u00f3 s\u1ed1 h\u1ea1ng \u0111\u1ea7u b\u1eb1ng  -7 , s\u1ed1 h\u1ea1ng th\u1ee9 hai b\u1eb1ng  14  v\u00e0 s\u1ed1 h\u1ea1ng cu\u1ed1i b\u1eb1ng  14336 .<\/p>\n<p>a) C\u00f4ng b\u1ed9i c\u1ee7a c\u1ea5p s\u1ed1 nh\u00e2n b\u1eb1ng bao nhi\u00eau?<\/p>\n<p>b) 224 l\u00e0 s\u1ed1 h\u1ea1ng th\u1ee9 n\u0103m c\u1ee7a c\u1ea5p s\u1ed1 nh\u00e2n \u0111\u00e3 cho. \u0110\u00fang hay sai?<\/p>\n<p>c) C\u1ea5p s\u1ed1 nh\u00e2n \u0111\u00e3 cho c\u00f3 bao nhi\u00eau s\u1ed1 h\u1ea1ng?<\/p>\n<p>d) T\u00ednh t\u1ed5ng  u\u2081 + u\u2083 + u\u2085 + u\u2087 + u\u2089  b\u1eb1ng bao nhi\u00eau?<\/p>\n<p><strong>C\u00e2u 4:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9  Oxyz , cho m\u1eb7t ph\u1eb3ng  (P)  c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh  x &#8211; y &#8211; z &#8211; 3 = 0  v\u00e0 hai \u0111i\u1ec3m  A(1;-3;-4) ,  B(1;2;1) . Khi \u0111\u00f3:<\/p>\n<p>a) M\u1eb7t ph\u1eb3ng  (P)  c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn  n\u20d7 = (1;-1;-1) . \u0110\u00fang hay sai ?<\/p>\n<p>b) T\u00ednh  AB\u20d7 .<\/p>\n<p>c) Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m  A  \u0111\u1ebfn  (P)  l\u00e0  (5\u221a3)\/(3) .<\/p>\n<p>d) Cho \u0111i\u1ec3m  M  di \u0111\u1ed9ng tr\u00ean  (P) . Khi \u0111\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c  MA\u00b2 + 4MB\u00b2  b\u1eb1ng  56 .<\/p>\n<p><span><strong>Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 4:<\/strong> Trong 10 gi\u00e2y \u0111\u1ea7u ti\u00ean, m\u1ed9t ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng theo ph\u01b0\u01a1ng tr\u00ecnh s(t) = t\u00b3 &#8211; 12t\u00b2 + 5t + 1 , trong \u0111\u00f3 th\u1eddi gian  t  \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng gi\u00e2y, qu\u00e3ng \u0111\u01b0\u1eddng  s  t\u00ednh b\u1eb1ng m\u00e9t. H\u1ecfi sau kho\u1ea3ng th\u1eddi gian bao nhi\u00eau gi\u00e2y th\u00ec v\u1eadn t\u1ed1c t\u1ee9c th\u1eddi c\u1ee7a ch\u1ea5t \u0111i\u1ec3m b\u1eaft \u0111\u1ea7u t\u0103ng l\u00ean?<\/p>\n<p><strong>C\u00e2u 5:<\/strong> T\u1eeb m\u1ed9t t\u1ea5m b\u00eca m\u1ecfng h\u00ecnh vu\u00f4ng c\u1ea1nh  6dm , b\u1ea1n Hoa c\u1eaft b\u1ecf b\u1ed1n tam gi\u00e1c c\u00e2n b\u1eb1ng nhau c\u00f3 c\u1ea1nh \u0111\u00e1y l\u00e0 c\u1ea1nh c\u1ee7a h\u00ecnh vu\u00f4ng ban \u0111\u1ea7u v\u00e0 \u0111\u1ec9nh l\u00e0 \u0111\u1ec9nh c\u1ee7a m\u1ed9t h\u00ecnh vu\u00f4ng nh\u1ecf ph\u00eda trong r\u1ed3i g\u1ea5p l\u00ean, gh\u00e9p l\u1ea1i t\u1ea1o th\u00e0nh m\u1ed9t kh\u1ed1i ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u. Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i ch\u00f3p c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng bao nhi\u00eau decim\u00e9t kh\u1ed1i (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi)?<\/p>\n<h2><strong>T\u1ea3i B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i<\/strong><\/h2>\n<p>\u0110\u1ec3 chu\u1ea9n b\u1ecb t\u1ed1t cho \u0111\u1ee3t kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n s\u1eafp t\u1edbi c\u0169ng nh\u01b0 chu\u1ea9n b\u1ecb h\u00e0nh trang t\u1ed1t cho k\u1ef3 thi THPT Qu\u1ed1c gia. C\u00e1c b\u1ea1n h\u1ecdc sinh v\u00e0 th\u1ea7y c\u00f4 t\u1ea3i ngay <strong>B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i<\/strong> qua \u0111\u01b0\u1eddng link sau. V\u00e0 b\u1eaft tay ngay v\u00e0o qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp gi\u1ea3i \u0111\u1ec1 c\u00f3 k\u00e8m theo \u0111\u00e1p \u00e1n chi ti\u1ebft \u0111\u1ec3 \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 cao nh\u00e9.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1LtkCXXYmfC0Z18ggZ1HXfuZZwFBno3F1\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1LtkCXXYmfC0Z18ggZ1HXfuZZwFBno3F1\/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\/1LtkCXXYmfC0Z18ggZ1HXfuZZwFBno3F1\/view?usp=drive_link\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 \u0111\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng th\u00e1ng 2 To\u00e1n 12 c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i l\u00e0 t\u00e0i li\u1ec7u quan tr\u1ecdng gi\u00fap h\u1ecdc sinh l\u1edbp 12 r\u00e8n luy\u1ec7n, n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i \u0111\u1ec3 \u0111\u1ea1t k\u1ebft qu\u1ea3 cao trong k\u1ef3 kh\u1ea3o s\u00e1t ch\u00ednh th\u1ee9c. \u0110\u01b0\u1ee3c bi\u00ean so\u1ea1n k\u1ef9 l\u01b0\u1ee1ng b\u1edfi c\u00e1c th\u1ea7y c\u00f4 trong [&#8230;]\n","protected":false},"author":1,"featured_media":1575,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-376","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\/376","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=376"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/376\/revisions"}],"predecessor-version":[{"id":1576,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/376\/revisions\/1576"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1575"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=376"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}