{"id":2859,"date":"2026-10-30T17:04:30","date_gmt":"2026-10-30T10:04:30","guid":{"rendered":"https:\/\/navi.edu.vn\/blog\/?p=2859"},"modified":"2026-10-30T17:04:30","modified_gmt":"2026-10-30T10:04:30","slug":"de-cuong-on-tap-giua-ki-1-toan-10","status":"publish","type":"post","link":"https:\/\/navi.edu.vn\/blog\/de-cuong-on-tap-giua-ki-1-toan-10\/","title":{"rendered":"\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 (2026-2027) &#038; \u0110\u1ec1 thi m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n"},"content":{"rendered":"<div class=\"naviedu-intro-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p>B\u01b0\u1edbc v\u00e0o l\u1edbp 10, h\u1ecdc sinh ch\u00ednh th\u1ee9c b\u01b0\u1edbc v\u00e0o b\u1eadc THPT, chuy\u1ec3n d\u1ecbch t\u1eeb t\u01b0 duy t\u00ednh to\u00e1n quen thu\u1ed9c sang t\u01b0 duy logic tr\u1eebu t\u01b0\u1ee3ng nh\u01b0 m\u1ec7nh \u0111\u1ec1 v\u00e0 t\u1eadp h\u1ee3p. \u0110\u1ed3ng th\u1eddi, c\u00e1c em ph\u1ea3i l\u00e0m quen v\u1edbi \u0111\u1ecbnh d\u1ea1ng \u0111\u1ec1 ki\u1ec3m tra m\u1edbi g\u1ed3m c\u00e2u h\u1ecfi \u0111\u00fang\/sai v\u00e0 tr\u1ea3 l\u1eddi ng\u1eafn. S\u1ef1 \u0111\u1ed5i m\u1edbi n\u00e0y d\u1ec5 t\u1ea1o ra \u00e1p l\u1ef1c v\u00e0 khi\u1ebfn h\u1ecdc sinh l\u00fang t\u00fang. Hi\u1ec3u \u0111\u01b0\u1ee3c nh\u1eefng kh\u00f3 kh\u0103n \u0111\u00f3, NaviEdu x\u00e2y d\u1ef1ng tr\u1ecdn b\u1ed9 <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 to\u00e1n 10<\/strong> chu\u1ea9n h\u00f3a: h\u1ec7 th\u1ed1ng to\u00e0n b\u1ed9 l\u00fd thuy\u1ebft c\u1ed1t l\u00f5i, ph\u00e2n lo\u1ea1i ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i chi ti\u1ebft, l\u1ecbch \u00f4n t\u1eadp 7 ng\u00e0y khoa h\u1ecdc k\u00e8m \u0111\u1ec1 thi m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n gi\u00fap h\u1ecdc sinh t\u1ef1 tin b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1.<\/p>\n<\/div>\n<figure style=\"margin: 24px 0; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2860\" style=\"max-width: 100%; height: auto; border-radius: 10px;\" src=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-tom-tat.png\" alt=\"\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 \u2013 t\u00f3m t\u1eaft ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m\" width=\"1200\" height=\"760\" srcset=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-tom-tat.png 1200w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-tom-tat-300x190.png 300w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-tom-tat-1024x649.png 1024w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-tom-tat-768x486.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><figcaption style=\"font-size: 14px; color: #718096; margin-top: 8px;\">S\u01a1 \u0111\u1ed3 t\u00f3m t\u1eaft \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 (2026\u20132027)<\/figcaption><\/figure>\n<div class=\"naviedu-toc\" style=\"background: #f7fafc; border: 1px solid #e2e8f0; border-radius: 8px; padding: 16px 22px; margin: 24px 0;\">\n<p style=\"margin: 0 0 8px 0; font-weight: bold; color: #0056b3; font-size: 17px;\">M\u1ee5c l\u1ee5c \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10<\/p>\n<ul style=\"margin: 0; padding-left: 22px; line-height: 1.9;\">\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-1-cau-truc-de-thi-giua-ki-1-toan-10-theo-dinh-dang-moi\">C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 10 theo \u0111\u1ecbnh d\u1ea1ng m\u1edbi<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-2-phan-i-menh-de-va-tap-hop\">Ph\u1ea7n I: M\u1ec7nh \u0110\u1ec1 v\u00e0 T\u1eadp H\u1ee3p<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-3-menh-de-toan-hoc\">M\u1ec7nh \u0111\u1ec1 to\u00e1n h\u1ecdc<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-4-menh-de-phu-dinh\">M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-5-menh-de-keo-theo-menh-de-dao\">M\u1ec7nh \u0111\u1ec1 k\u00e9o theo, m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-6-menh-de-chua-bien\">M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-7-tap-hop-va-cac-phep-toan-tren-tap-hop\">T\u1eadp h\u1ee3p v\u00e0 c\u00e1c ph\u00e9p to\u00e1n tr\u00ean t\u1eadp h\u1ee3p<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-8-cac-tap-hop-so\">C\u00e1c t\u1eadp h\u1ee3p s\u1ed1<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-9-phan-ii-bat-phuong-trinh-va-he-bat-phuong-trinh-bac-nhat-hai\">Ph\u1ea7n II: B\u1ea5t Ph\u01b0\u01a1ng Tr\u00ecnh v\u00e0 H\u1ec7 B\u1ea5t Ph\u01b0\u01a1ng Tr\u00ecnh B\u1eadc Nh\u1ea5t Hai \u1ea8n<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-10-bat-phuong-trinh-bac-nhat-hai-an\">B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-11-he-bat-phuong-trinh-bac-nhat-hai-an\">H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-12-phan-iii-he-thuc-luong-trong-tam-giac\">Ph\u1ea7n III: H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng Trong Tam Gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-13-gia-tri-luong-giac-cua-mot-goc-tu-0-den-180\">Gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-14-dinh-li-cosin-dinh-li-sin\">\u0110\u1ecbnh l\u00ed c\u00f4sin, \u0111\u1ecbnh l\u00ed sin<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-15-giai-tam-giac\">Gi\u1ea3i tam gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-16-he-thuc-luong-trong-tam-giac\">H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-17-phan-iv-lich-on-tap-7-ngay-de-thi-mau\">Ph\u1ea7n IV: L\u1ecbch \u00d4n T\u1eadp 7 Ng\u00e0y &amp; \u0110\u1ec1 Thi M\u1eabu<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-18-lich-on-tap-giua-ki-1-toan-10-trong-7-ngay-giup-but-pha-diem\">L\u1ecbch \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 trong 7 ng\u00e0y gi\u00fap b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-19-tai-de-cuong-on-tap-giua-ki-1-toan-10-va-de-thi-mau-pdf-co-d\">T\u1ea3i \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 v\u00e0 \u0111\u1ec1 thi m\u1eabu (PDF c\u00f3 \u0111\u00e1p \u00e1n)<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-20-loi-ket\">L\u1eddi k\u1ebft<\/a><\/li>\n<\/ul>\n<\/div>\n<p><!-- B\u1eaeT \u0110\u1ea6U: C\u1ea4U TR\u00daC \u0110\u1ec0 THI GI\u1eeeA K\u00cc 1 TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<h2 id=\"muc-1-cau-truc-de-thi-giua-ki-1-toan-10-theo-dinh-dang-moi\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 30px; font-size: 22px;\">C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 10 theo \u0111\u1ecbnh d\u1ea1ng m\u1edbi<\/h2>\n<figure id=\"attachment_2908\" aria-describedby=\"caption-attachment-2908\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2908\" src=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-1-300x188.png\" alt=\"T\u00ecm hi\u1ec3u v\u1ec1 c\u1ea5u tr\u00fac ma tr\u1eadn \u0111\u1ec1 thi gi\u1eefa k\u1ef3 1 To\u00e1n 10\" width=\"800\" height=\"500\" srcset=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-1-300x188.png 300w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-1-1024x640.png 1024w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-1-768x480.png 768w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-1-1536x961.png 1536w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-10-1.png 1586w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-2908\" class=\"wp-caption-text\">T\u00ecm hi\u1ec3u v\u1ec1 c\u1ea5u tr\u00fac ma tr\u1eadn \u0111\u1ec1 thi gi\u1eefa k\u1ef3 1 To\u00e1n 10<\/figcaption><\/figure>\n<p>H\u1ecdc sinh c\u1ea5p THPT \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 theo <a href=\"https:\/\/luatvietnam.vn\/giao-duc\/thong-tu-22-2021-tt-bgddt-207846-d1.html\" target=\"_blank\" rel=\"noopener\">Th\u00f4ng t\u01b0 22\/2021\/TT-BGD\u0110T<\/a>. T\u1eeb n\u0103m h\u1ecdc 2024\u20132025 v\u00e0 \u00e1p d\u1ee5ng cho c\u00e1c n\u0103m ti\u1ebfp theo, \u0111\u1ec1 ki\u1ec3m tra \u0111\u1ecbnh k\u00ec m\u00f4n To\u00e1n THPT \u00e1p d\u1ee5ng \u0111\u1ecbnh d\u1ea1ng m\u1edbi g\u1ed3m 4 ph\u1ea7n nh\u1eb1m \u0111\u00e1nh gi\u00e1 to\u00e0n di\u1ec7n n\u0103ng l\u1ef1c t\u01b0 duy, kh\u1ea3 n\u0103ng l\u1eadp lu\u1eadn v\u00e0 v\u1eadn d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a h\u1ecdc sinh.<\/p>\n<p>V\u00ec ma tr\u1eadn v\u00e0 \u0111\u1ec1 ki\u1ec3m tra ch\u00ednh th\u1ee9c do S\u1edf Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o ho\u1eb7c t\u1eebng tr\u01b0\u1eddng THPT x\u00e2y d\u1ef1ng, c\u1ea5u tr\u00fac d\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1eabu tham kh\u1ea3o ph\u1ed5 bi\u1ebfn nh\u1ea5t v\u1edbi t\u1ed5ng th\u1eddi gian l\u00e0m b\u00e0i l\u00e0 <strong>90 ph\u00fat<\/strong>:<\/p>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Ph\u1ea7n I \u2013 Tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn (3,0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 12 c\u00e2u h\u1ecfi (m\u1ed7i c\u00e2u 0,25 \u0111i\u1ec3m), y\u00eau c\u1ea7u h\u1ecdc sinh ch\u1ecdn 1 ph\u01b0\u01a1ng \u00e1n \u0111\u00fang duy nh\u1ea5t trong 4 l\u1ef1a ch\u1ecdn, ki\u1ec3m tra nhanh ki\u1ebfn th\u1ee9c nh\u1eadn bi\u1ebft v\u00e0 th\u00f4ng hi\u1ec3u c\u01a1 b\u1ea3n v\u1ec1 m\u1ec7nh \u0111\u1ec1, t\u1eadp h\u1ee3p, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c.<\/li>\n<li><strong>Ph\u1ea7n II \u2013 Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (2,0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 2 c\u00e2u h\u1ecfi l\u1edbn, m\u1ed7i c\u00e2u c\u00f3 4 \u00fd a, b, c, d (t\u1ed1i \u0111a 1 \u0111i\u1ec3m\/c\u00e2u). C\u00e1ch ch\u1ea5m \u0111i\u1ec3m l\u0169y ti\u1ebfn theo s\u1ed1 \u00fd l\u00e0m \u0111\u00fang trong m\u1ed7i c\u00e2u: \u0111\u00fang 1 \u00fd \u0111\u1ea1t 0,1 \u0111i\u1ec3m; \u0111\u00fang 2 \u00fd \u0111\u1ea1t 0,25 \u0111i\u1ec3m; \u0111\u00fang 3 \u00fd \u0111\u1ea1t 0,5 \u0111i\u1ec3m; \u0111\u00fang c\u1ea3 4 \u00fd \u0111\u1ea1t tr\u1ecdn v\u1eb9n 1,0 \u0111i\u1ec3m. Ph\u1ea7n n\u00e0y ki\u1ec3m tra t\u01b0 duy logic \u0111a chi\u1ec1u v\u00e0 b\u1ea3n ch\u1ea5t chuy\u00ean s\u00e2u.<\/li>\n<li><strong>Ph\u1ea7n III \u2013 Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (2,0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 4 c\u00e2u h\u1ecfi (m\u1ed7i c\u00e2u 0,5 \u0111i\u1ec3m), y\u00eau c\u1ea7u h\u1ecdc sinh t\u1ef1 t\u00ednh to\u00e1n v\u00e0 \u0111i\u1ec1n k\u1ebft qu\u1ea3 ch\u00ednh x\u00e1c v\u00e0o phi\u1ebfu tr\u1ea3 l\u1eddi m\u00e0 kh\u00f4ng c\u00f3 c\u00e1c ph\u01b0\u01a1ng \u00e1n s\u1eb5n c\u00f3.<\/li>\n<li><strong>Ph\u1ea7n IV \u2013 T\u1ef1 lu\u1eadn (3,0 \u0111i\u1ec3m):<\/strong> G\u1ed3m c\u00e1c b\u00e0i to\u00e1n t\u1ef1 lu\u1eadn \u0111\u00f2i h\u1ecfi k\u1ef9 n\u0103ng l\u1eadp lu\u1eadn ch\u1eb7t ch\u1ebd, tr\u00ecnh b\u00e0y c\u00e1c b\u01b0\u1edbc gi\u1ea3i chi ti\u1ebft \u0111\u1ed1i v\u1edbi chuy\u00ean \u0111\u1ec1 h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n, \u1ee9ng d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng v\u00e0o tam gi\u00e1c v\u00e0 c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf.<\/li>\n<\/ul>\n<h3 style=\"color: #2b6cb0; font-size: 18px; margin-top: 22px;\">B\u1ea3ng ma tr\u1eadn tham kh\u1ea3o ph\u00e2n b\u1ed5 n\u1ed9i dung v\u00e0 h\u00ecnh th\u1ee9c<\/h3>\n<div style=\"overflow-x: auto; margin: 15px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<colgroup>\n<col style=\"width: 25%;\" \/>\n<col style=\"width: 15%;\" \/>\n<col style=\"width: 15%;\" \/>\n<col style=\"width: 15%;\" \/>\n<col style=\"width: 15%;\" \/>\n<col style=\"width: 15%;\" \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3;\">Ch\u1ee7 \u0111\u1ec1<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">Nhi\u1ec1u l\u1ef1a ch\u1ecdn<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">\u0110\u00fang \/ Sai<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">Tr\u1ea3 l\u1eddi ng\u1eafn<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">T\u1ef1 lu\u1eadn<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">T\u1ed5ng \u0111i\u1ec3m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">M\u1ec7nh \u0111\u1ec1 \u2013 T\u1eadp h\u1ee3p<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,25 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">3,25 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, h\u1ec7 BPT b\u1eadc nh\u1ea5t hai \u1ea9n<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">2,25 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">4,5 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr style=\"background-color: #f7fafc; font-weight: bold;\">\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3;\">T\u1ed4NG \u0110I\u1ec2M<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">3,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">2,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">2,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">3,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; color: #c53030;\">10,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P L\u01afU \u00dd --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin-top: 25px;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u01b0u \u00fd quan tr\u1ecdng cho h\u1ecdc sinh:<\/strong> C\u1ea5u tr\u00fac \u0111\u1ec1 thi c\u00f3 th\u1ec3 c\u00f3 nh\u1eefng \u0111i\u1ec1u ch\u1ec9nh nh\u1ecf ph\u1ee5 thu\u1ed9c v\u00e0o y\u00eau c\u1ea7u ki\u1ec3m tra c\u1ee7a t\u1eebng tr\u01b0\u1eddng THPT ho\u1eb7c S\u1edf Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o \u0111\u1ecba ph\u01b0\u01a1ng. Do \u0111\u00f3, c\u00e1c em h\u1ecdc sinh n\u00ean tham kh\u1ea3o k\u1ef9 \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp do gi\u00e1o vi\u00ean b\u1ed9 m\u00f4n t\u1ea1i tr\u01b0\u1eddng ph\u00e1t ra \u0111\u1ec3 n\u1eafm ch\u00ednh x\u00e1c ph\u1ea1m vi ki\u1ebfn th\u1ee9c v\u00e0 d\u1ea1ng b\u00e0i tr\u1ecdng t\u00e2m.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: C\u1ea4U TR\u00daC \u0110\u1ec0 THI GI\u1eeeA K\u00cc 1 TO\u00c1N 10 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N I - M\u1ec6NH \u0110\u1ec0 V\u00c0 T\u1eacP H\u1ee2P TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N I --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-2-phan-i-menh-de-va-tap-hop\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n I: M\u1ec7nh \u0110\u1ec1 v\u00e0 T\u1eadp H\u1ee3p<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: M\u1ec6NH \u0110\u1ec0 TO\u00c1N H\u1eccC --><\/p>\n<p style=\"margin: 0 0 16px 0;\">M\u1ec7nh \u0111\u1ec1 v\u00e0 t\u1eadp h\u1ee3p l\u00e0 ch\u01b0\u01a1ng m\u1edf \u0111\u1ea7u c\u1ee7a <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10<\/strong>, r\u1ea5t hay xu\u1ea5t hi\u1ec7n \u1edf d\u1ea1ng c\u00e2u \u0111\u00fang\/sai. N\u1eafm ch\u1eafc \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00e1ch l\u1eadp m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh s\u1ebd gi\u00fap con l\u1ea5y tr\u1ecdn \u0111i\u1ec3m ph\u1ea7n n\u00e0y.<\/p>\n<h2 id=\"muc-3-menh-de-toan-hoc\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">M\u1ec7nh \u0111\u1ec1 to\u00e1n h\u1ecdc<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Kh\u00e1i ni\u1ec7m v\u00e0 nh\u1eadn di\u1ec7n m\u1ec7nh \u0111\u1ec1<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a:<\/strong> M\u1ec7nh \u0111\u1ec1 to\u00e1n h\u1ecdc (ho\u1eb7c g\u1ecdi t\u1eaft l\u00e0 m\u1ec7nh \u0111\u1ec1) l\u00e0 m\u1ed9t <strong>c\u00e2u kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang ho\u1eb7c m\u1ed9t c\u00e2u kh\u1eb3ng \u0111\u1ecbnh sai<\/strong>. M\u1ed9t c\u00e2u kh\u00f4ng th\u1ec3 v\u1eeba \u0111\u00fang l\u1ea1i v\u1eeba sai.<\/li>\n<li><strong>C\u00e1c c\u00e2u kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1:<\/strong> C\u00e1c c\u00e2u nghi v\u1ea5n (c\u00e2u h\u1ecfi), c\u00e2u c\u1ea3m th\u00e1n, c\u00e2u c\u1ea7u khi\u1ebfn ho\u1eb7c c\u00e1c c\u00e2u ch\u1ee9a bi\u1ebfn s\u1ed1 m\u00e0 ch\u01b0a x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c t\u00ednh \u0111\u00fang sai (m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn).<\/li>\n<li><strong>T\u00ednh \u0111\u00fang sai:<\/strong> M\u1ed7i m\u1ec7nh \u0111\u1ec1 ph\u1ea3i ho\u1eb7c \u0111\u00fang ho\u1eb7c sai. C\u00e1c m\u1ec7nh \u0111\u1ec1 \u0111\u00fang th\u01b0\u1eddng \u0111\u01b0\u1ee3c kh\u1eb3ng \u0111\u1ecbnh b\u1eb1ng ch\u1ee9ng minh to\u00e1n h\u1ecdc, c\u00f2n m\u1ec7nh \u0111\u1ec1 sai th\u01b0\u1eddng \u0111\u01b0\u1ee3c b\u00e1c b\u1ecf b\u1eb1ng m\u1ed9t ph\u1ea3n v\u00ed d\u1ee5.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 m\u1ec7nh \u0111\u1ec1:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn c\u00e1c c\u00e2u c\u1ea3m th\u00e1n, c\u00e2u h\u1ecfi (v\u00ed d\u1ee5: &#8220;H\u00f4m nay tr\u1eddi \u0111\u1eb9p qu\u00e1 nh\u1ec9?&#8221;) ho\u1eb7c c\u00e2u ch\u1ee9a bi\u1ebfn s\u1ed1 ch\u01b0a r\u00f5 r\u00e0ng (v\u00ed d\u1ee5: &#8220;x + 2 &gt; 5&#8221;) l\u00e0 m\u1ec7nh \u0111\u1ec1. H\u1ecdc sinh c\u1ea7n nh\u1edb c\u00e2u ch\u1ee9a bi\u1ebfn ch\u01b0a r\u00f5 gi\u00e1 tr\u1ecb c\u1ee7a x th\u00ec ch\u01b0a th\u1ec3 kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang sai n\u00ean ch\u01b0a ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU (D\u1ea0NG \u0110\u00daNG\/SAI A, B, C, D) --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Trong c\u00e1c ph\u00e1t bi\u1ec3u sau, ph\u00e1t bi\u1ec3u n\u00e0o l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang, ph\u00e1t bi\u1ec3u n\u00e0o l\u00e0 m\u1ec7nh \u0111\u1ec1 sai?<br \/>\na) S\u1ed1 2026 l\u00e0 m\u1ed9t s\u1ed1 chia h\u1ebft cho 2.<br \/>\nb) Tam gi\u00e1c c\u00f3 ba g\u00f3c b\u1eb1ng nhau th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c \u0111\u1ec1u.<br \/>\nc) B\u1ea1n c\u00f3 th\u00edch h\u1ecdc m\u00f4n To\u00e1n kh\u00f4ng?<br \/>\nd) Ph\u01b0\u01a1ng tr\u00ecnh x b\u00ecnh ph\u01b0\u01a1ng c\u1ed9ng 1 b\u1eb1ng 0 c\u00f3 nghi\u1ec7m th\u1ef1c.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 <strong>\u00dd a:<\/strong> S\u1ed1 2026 c\u00f3 t\u1eadn c\u00f9ng l\u00e0 6 n\u00ean chia h\u1ebft cho 2. \u0110\u00e2y l\u00e0 <strong>m\u1ec7nh \u0111\u1ec1 \u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd b:<\/strong> Theo \u0111\u1ecbnh ngh\u0129a h\u00ecnh h\u1ecdc, tam gi\u00e1c c\u00f3 3 g\u00f3c b\u1eb1ng nhau (60 \u0111\u1ed9) ch\u00ednh l\u00e0 tam gi\u00e1c \u0111\u1ec1u.<\/p>\n<p style=\"margin: 0;\">\u0110\u00e2y l\u00e0 <strong>m\u1ec7nh \u0111\u1ec1 \u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd c:<\/strong> \u0110\u00e2y l\u00e0 c\u00e2u h\u1ecfi (c\u00e2u nghi v\u1ea5n), kh\u00f4ng ph\u1ea3i c\u00e2u kh\u1eb3ng \u0111\u1ecbnh t\u00ednh \u0111\u00fang sai n\u00ean <strong>kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1<\/strong>.<br \/>\n\u2022 <strong>\u00dd d:<\/strong> Ph\u01b0\u01a1ng tr\u00ecnh x b\u00ecnh ph\u01b0\u01a1ng c\u1ed9ng 1 b\u1eb1ng 0 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng x b\u00ecnh ph\u01b0\u01a1ng b\u1eb1ng -1 (v\u00f4 nghi\u1ec7m tr\u00ean t\u1eadp s\u1ed1 th\u1ef1c). Do \u0111\u00f3 \u0111\u00e2y l\u00e0 <strong>m\u1ec7nh \u0111\u1ec1 sai<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: M\u1ec6NH \u0110\u1ec0 PH\u1ee6 \u0110\u1ecaNH --><\/p>\n<h2 id=\"muc-4-menh-de-phu-dinh\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Quy t\u1eafc l\u1eadp v\u00e0 t\u00ednh ch\u1ea5t m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>K\u00fd hi\u1ec7u:<\/strong> Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 P \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 ngang tr\u00ean \u0111\u1ea7u P (ho\u1eb7c g\u1ea1ch ph\u1ee7 \u0111\u1ecbnh).<\/li>\n<li><strong>T\u00ednh ch\u1ea5t:<\/strong> N\u1ebfu P \u0111\u00fang th\u00ec ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P l\u00e0 sai; n\u1ebfu P sai th\u00ec ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P l\u00e0 \u0111\u00fang.<\/li>\n<li><strong>Quy t\u1eafc ph\u1ee7 \u0111\u1ecbnh bi\u1ec3u th\u1ee9c to\u00e1n h\u1ecdc:<\/strong>\n<ul>\n<li>Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a d\u1ea5u l\u1edbn h\u01a1n (&gt;) l\u00e0 nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng (\u2264).<\/li>\n<li>Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a d\u1ea5u b\u1eb1ng (=) l\u00e0 kh\u00e1c (\u2260).<\/li>\n<li>Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a ph\u00e1t bi\u1ec3u &#8220;M\u1ecdi&#8221; (v\u1edbi m\u1ecdi) l\u00e0 &#8220;C\u00f3 \u00edt nh\u1ea5t m\u1ed9t&#8221; (t\u1ed3n t\u1ea1i).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi l\u1eadp m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean \u0111\u1ed5i d\u1ea5u b\u1ea5t \u0111\u1eb3ng th\u1ee9c (v\u00ed d\u1ee5 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a l\u1edbn h\u01a1n (&gt;) l\u1ea1i vi\u1ebft th\u00e0nh nh\u1ecf h\u01a1n (&lt;) thay v\u00ec nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng (\u2264)). Ho\u1eb7c khi ph\u1ee7 \u0111\u1ecbnh m\u1ec7nh \u0111\u1ec1 c\u00f3 ch\u1ee9a l\u01b0\u1ee3ng t\u1eeb m\u1ecdi, h\u1ecdc sinh qu\u00ean chuy\u1ec3n th\u00e0nh t\u1ed3n t\u1ea1i.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU (D\u1ea0NG \u0110\u00daNG\/SAI A, B, C, D) --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho m\u1ec7nh \u0111\u1ec1 P: &#8220;S\u1ed1 2025 chia h\u1ebft cho 3&#8221;. X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c ph\u00e1t bi\u1ec3u sau:<br \/>\na) M\u1ec7nh \u0111\u1ec1 P l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai.<br \/>\nb) M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P l\u00e0: &#8220;S\u1ed1 2025 kh\u00f4ng chia h\u1ebft cho 3&#8221;.<br \/>\nc) M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<br \/>\nd) T\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a 2025 b\u1eb1ng 9 n\u00ean 2025 chia h\u1ebft cho 9, suy ra P \u0111\u00fang.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 <strong>\u00dd a:<\/strong> S\u1ed1 2025 c\u00f3 t\u1ed5ng ch\u1eef s\u1ed1 b\u1eb1ng 9 n\u00ean chia h\u1ebft cho 3. Do \u0111\u00f3 P l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang, ph\u00e1t bi\u1ec3u n\u00e0y <strong>sai<\/strong>.<br \/>\n\u2022 <strong>\u00dd b:<\/strong> Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a &#8220;chia h\u1ebft cho 3&#8221; l\u00e0 &#8220;kh\u00f4ng chia h\u1ebft cho 3&#8221;.<\/p>\n<p style=\"margin: 0;\">Ph\u00e1t bi\u1ec3u n\u00e0y <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd c:<\/strong> V\u00ec P \u0111\u00fang n\u00ean m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1 sai. Ph\u00e1t bi\u1ec3u n\u00e0y <strong>sai<\/strong>.<br \/>\n\u2022 <strong>\u00dd d:<\/strong> Gi\u1ea3i th\u00edch logic t\u1ed5ng ch\u1eef s\u1ed1 2+0+2+5=9 chia h\u1ebft cho 9 n\u00ean chia h\u1ebft cho 3, P \u0111\u00fang. Ph\u00e1t bi\u1ec3u n\u00e0y <strong>\u0111\u00fang<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 3: M\u1ec6NH \u0110\u1ec0 K\u00c9O THEO, M\u1ec6NH \u0110\u1ec0 \u0110\u1ea2O --><\/p>\n<h2 id=\"muc-5-menh-de-keo-theo-menh-de-dao\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">M\u1ec7nh \u0111\u1ec1 k\u00e9o theo, m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t t\u01b0\u01a1ng \u0111\u01b0\u01a1ng<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>M\u1ec7nh \u0111\u1ec1 k\u00e9o theo:<\/strong> M\u1ec7nh \u0111\u1ec1 &#8220;N\u1ebfu P th\u00ec Q&#8221; \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 P \u21d2 Q. M\u1ec7nh \u0111\u1ec1 n\u00e0y ch\u1ec9 <strong>sai khi P \u0111\u00fang v\u00e0 Q sai<\/strong>, c\u00e1c tr\u01b0\u1eddng h\u1ee3p c\u00f2n l\u1ea1i \u0111\u1ec1u \u0111\u00fang.<\/li>\n<li><strong>\u0110i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7:<\/strong> Trong m\u1ec7nh \u0111\u1ec1 P \u21d2 Q, ta c\u00f2n n\u00f3i P l\u00e0 <em>\u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7<\/em> \u0111\u1ec3 c\u00f3 Q, ho\u1eb7c Q l\u00e0 <em>\u0111i\u1ec1u ki\u1ec7n c\u1ea7n<\/em> \u0111\u1ec3 c\u00f3 P.<\/li>\n<li><strong>M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o:<\/strong> M\u1ec7nh \u0111\u1ec1 Q \u21d2 P \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o c\u1ee7a m\u1ec7nh \u0111\u1ec1 P \u21d2 Q. M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o kh\u00f4ng nh\u1ea5t thi\u1ebft ph\u1ea3i \u0111\u00fang c\u00f9ng m\u1ec7nh \u0111\u1ec1 thu\u1eadn.<\/li>\n<li><strong>M\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng:<\/strong> N\u1ebfu c\u1ea3 hai m\u1ec7nh \u0111\u1ec1 P \u21d2 Q v\u00e0 Q \u21d2 P \u0111\u1ec1u \u0111\u00fang, ta c\u00f3 m\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng k\u00fd hi\u1ec7u P \u21d4 Q (\u0111\u1ecdc l\u00e0 &#8220;P t\u01b0\u01a1ng \u0111\u01b0\u01a1ng Q&#8221; ho\u1eb7c &#8220;P l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7 \u0111\u1ec3 c\u00f3 Q&#8221;).<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 m\u1ec7nh \u0111\u1ec1 k\u00e9o theo:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn chi\u1ec1u suy ra gi\u1eefa \u0111i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7; ho\u1eb7c ng\u1ed9 nh\u1eadn r\u1eb1ng n\u1ebfu m\u1ec7nh \u0111\u1ec1 thu\u1eadn P \u21d2 Q \u0111\u00fang th\u00ec m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o Q \u21d2 P c\u0169ng m\u1eb7c nhi\u00ean \u0111\u00fang.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU (D\u1ea0NG \u0110\u00daNG\/SAI A, B, C, D) --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1 k\u00e9o theo v\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC. X\u00e9t m\u1ec7nh \u0111\u1ec1 P: &#8220;Tam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60 \u0111\u1ed9&#8221; v\u00e0 Q: &#8220;Tam gi\u00e1c ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u&#8221;. \u0110\u00e1nh gi\u00e1 t\u00ednh \u0111\u00fang sai c\u00e1c ph\u00e1t bi\u1ec3u:<br \/>\na) M\u1ec7nh \u0111\u1ec1 P \u21d2 Q l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<br \/>\nb) M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o c\u1ee7a P \u21d2 Q l\u00e0: &#8220;N\u1ebfu tam gi\u00e1c ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u th\u00ec tam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60 \u0111\u1ed9&#8221;.<br \/>\nc) M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<br \/>\nd) P l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 c\u00f3 Q.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 <strong>\u00dd a:<\/strong> Tam gi\u00e1c c\u00f3 hai g\u00f3c b\u1eb1ng 60 \u0111\u1ed9 th\u00ec g\u00f3c th\u1ee9 ba b\u1eb1ng 60 \u0111\u1ed9, suy ra 3 g\u00f3c b\u1eb1ng nhau n\u00ean l\u00e0 tam gi\u00e1c \u0111\u1ec1u. M\u1ec7nh \u0111\u1ec1 thu\u1eadn <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd b:<\/strong> Ph\u00e1t bi\u1ec3u \u0111\u1ea3o \u0111\u1ed5i v\u1ecb tr\u00ed gi\u1ea3 thi\u1ebft v\u00e0 k\u1ebft lu\u1eadn, ph\u00e1t bi\u1ec3u n\u00e0y <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd c:<\/strong> Tam gi\u00e1c \u0111\u1ec1u th\u00ec ch\u1eafc ch\u1eafn c\u00f3 3 g\u00f3c b\u1eb1ng 60 \u0111\u1ed9 (n\u00ean c\u00f3 \u00edt nh\u1ea5t hai g\u00f3c b\u1eb1ng 60 \u0111\u1ed9).<\/p>\n<p style=\"margin: 0;\">M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd d:<\/strong> P \u21d2 Q \u0111\u00fang n\u00ean P l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 c\u00f3 Q, c\u00f2n Q m\u1edbi l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 c\u00f3 P. Ph\u00e1t bi\u1ec3u n\u00e0y <strong>sai<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 4: M\u1ec6NH \u0110\u1ec0 CH\u1ee8A BI\u1ebeN --><\/p>\n<h2 id=\"muc-6-menh-de-chua-bien\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">K\u00fd hi\u1ec7u l\u01b0\u1ee3ng t\u1eeb v\u00e0 quy t\u1eafc ph\u1ee7 \u0111\u1ecbnh l\u01b0\u1ee3ng t\u1eeb<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn P(x) l\u00e0 c\u00e2u kh\u1eb3ng \u0111\u1ecbnh ch\u1ee9a bi\u1ebfn nh\u1eadn gi\u00e1 tr\u1ecb trong t\u1eadp h\u1ee3p X, khi thay x b\u1eb1ng m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3 ta \u0111\u01b0\u1ee3c m\u1ed9t m\u1ec7nh \u0111\u1ec1.<\/li>\n<li><strong>K\u00fd hi\u1ec7u l\u01b0\u1ee3ng t\u1eeb:<\/strong>\n<ul>\n<li>K\u00fd hi\u1ec7u \u2200 (\u0111\u1ecdc l\u00e0 &#8220;v\u1edbi m\u1ecdi&#8221;): &#8220;V\u1edbi m\u1ecdi x thu\u1ed9c X \u0111\u1ec3 P(x) \u0111\u00fang&#8221;.<\/li>\n<li>K\u00fd hi\u1ec7u \u2203 (\u0111\u1ecdc l\u00e0 &#8220;t\u1ed3n t\u1ea1i&#8221; ho\u1eb7c &#8220;c\u00f3 \u00edt nh\u1ea5t m\u1ed9t&#8221;): &#8220;T\u1ed3n t\u1ea1i x thu\u1ed9c X \u0111\u1ec3 P(x) \u0111\u00fang&#8221;.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Quy t\u1eafc ph\u1ee7 \u0111\u1ecbnh m\u1ec7nh \u0111\u1ec1 ch\u1ee9a l\u01b0\u1ee3ng t\u1eeb:<\/strong>\n<ul>\n<li>Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 &#8220;\u2200x \u2208 X, P(x)&#8221; l\u00e0 m\u1ec7nh \u0111\u1ec1 &#8220;\u2203x \u2208 X, ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P(x)&#8221;.<\/li>\n<li>Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 &#8220;\u2203x \u2208 X, P(x)&#8221; l\u00e0 m\u1ec7nh \u0111\u1ec1 &#8220;\u2200x \u2208 X, ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P(x)&#8221;.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi ph\u1ee7 \u0111\u1ecbnh m\u1ec7nh \u0111\u1ec1 ch\u1ee9a l\u01b0\u1ee3ng t\u1eeb:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean \u0111\u1ea3o chi\u1ec1u k\u00fd hi\u1ec7u l\u01b0\u1ee3ng t\u1eeb (\u2200 th\u00e0nh \u2203 ho\u1eb7c ng\u01b0\u1ee3c l\u1ea1i) khi th\u1ef1c hi\u1ec7n ph\u00e9p l\u1ea5y m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh, d\u1eabn \u0111\u1ebfn sai b\u1ea3n ch\u1ea5t logic to\u00e1n h\u1ecdc.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU (D\u1ea0NG \u0110\u00daNG\/SAI A, B, C, D) --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1 ch\u1ee9a l\u01b0\u1ee3ng t\u1eeb v\u00e0 ph\u1ee7 \u0111\u1ecbnh<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn: P: &#8220;M\u1ecdi s\u1ed1 th\u1ef1c x \u0111\u1ec1u th\u1ecfa m\u00e3n x b\u00ecnh ph\u01b0\u01a1ng l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0&#8221;. X\u00e9t t\u00ednh \u0111\u00fang sai c\u00e1c ph\u00e1t bi\u1ec3u:<br \/>\na) K\u00fd hi\u1ec7u m\u1ec7nh \u0111\u1ec1 P theo chu\u1ea9n to\u00e1n h\u1ecdc l\u00e0: \u2200x \u2208 R, x b\u00ecnh ph\u01b0\u01a1ng \u2265 0.<br \/>\nb) M\u1ec7nh \u0111\u1ec1 P l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<br \/>\nc) M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P l\u00e0: \u2203x \u2208 R, x b\u00ecnh ph\u01b0\u01a1ng &lt; 0.<br \/>\nd) M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 <strong>\u00dd a:<\/strong> K\u00fd hi\u1ec7u to\u00e1n h\u1ecdc ph\u1ea3n \u00e1nh \u0111\u00fang ph\u00e1t bi\u1ec3u b\u1eb1ng l\u1eddi. Ph\u00e1t bi\u1ec3u n\u00e0y <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd b:<\/strong> B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ecdi s\u1ed1 th\u1ef1c lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 v\u1edbi m\u1ecdi x thu\u1ed9c R.<\/p>\n<p style=\"margin: 0;\">M\u1ec7nh \u0111\u1ec1 P <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd c:<\/strong> Ph\u1ee7 \u0111\u1ecbnh c\u1ee7a &#8220;v\u1edbi m\u1ecdi x, x b\u00ecnh ph\u01b0\u01a1ng \u2265 0&#8221; l\u00e0 &#8220;t\u1ed3n t\u1ea1i x sao cho x b\u00ecnh ph\u01b0\u01a1ng &lt; 0&#8221;. Ph\u00e1t bi\u1ec3u n\u00e0y <strong>\u0111\u00fang<\/strong>.<br \/>\n\u2022 <strong>\u00dd d:<\/strong> V\u00ec m\u1ec7nh \u0111\u1ec1 P ban \u0111\u1ea7u \u0111\u00fang, n\u00ean m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a n\u00f3 ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1 sai. Ph\u00e1t bi\u1ec3u n\u00e0y <strong>sai<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N I - M\u1ec6NH \u0110\u1ec0 V\u00c0 T\u1eacP H\u1ee2P TO\u00c1N 10 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N I (TI\u1ebeP THEO) TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- CH\u1ee6 \u0110\u1ec0 5: T\u1eacP H\u1ee2P V\u00c0 C\u00c1C PH\u00c9P TO\u00c1N TR\u00caN T\u1eacP H\u1ee2P --><\/p>\n<h2 id=\"muc-7-tap-hop-va-cac-phep-toan-tren-tap-hop\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">T\u1eadp h\u1ee3p v\u00e0 c\u00e1c ph\u00e9p to\u00e1n tr\u00ean t\u1eadp h\u1ee3p<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Kh\u00e1i ni\u1ec7m t\u1eadp con v\u00e0 c\u00e1c ph\u00e9p to\u00e1n t\u1eadp h\u1ee3p<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>T\u1eadp h\u1ee3p con:<\/strong> T\u1eadp h\u1ee3p A \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1eadp con c\u1ee7a t\u1eadp h\u1ee3p B (k\u00fd hi\u1ec7u A c B) n\u1ebfu m\u1ecdi ph\u1ea7n t\u1eed c\u1ee7a A \u0111\u1ec1u l\u00e0 ph\u1ea7n t\u1eed c\u1ee7a B. T\u1eadp r\u1ed7ng l\u00e0 t\u1eadp con c\u1ee7a m\u1ecdi t\u1eadp h\u1ee3p.<\/li>\n<li><strong>Hai t\u1eadp h\u1ee3p b\u1eb1ng nhau:<\/strong> A = B khi v\u00e0 ch\u1ec9 khi A c B v\u00e0 B c A.<\/li>\n<li><strong>Giao c\u1ee7a hai t\u1eadp h\u1ee3p:<\/strong> A giao B (A \u2229 B) l\u00e0 t\u1eadp h\u1ee3p g\u1ed3m c\u00e1c ph\u1ea7n t\u1eed v\u1eeba thu\u1ed9c A v\u1eeba thu\u1ed9c B.<\/li>\n<li><strong>H\u1ee3p c\u1ee7a hai t\u1eadp h\u1ee3p:<\/strong> A h\u1ee3p B (A \u222a B) l\u00e0 t\u1eadp h\u1ee3p g\u1ed3m c\u00e1c ph\u1ea7n t\u1eed thu\u1ed9c A ho\u1eb7c thu\u1ed9c B.<\/li>\n<li><strong>Hi\u1ec7u c\u1ee7a hai t\u1eadp h\u1ee3p:<\/strong> A hi\u1ec7u B (A \\ B) l\u00e0 t\u1eadp h\u1ee3p g\u1ed3m c\u00e1c ph\u1ea7n t\u1eed thu\u1ed9c A nh\u01b0ng kh\u00f4ng thu\u1ed9c B. Khi A l\u00e0 t\u1eadp con c\u1ee7a E, ph\u1ea7n b\u00f9 c\u1ee7a A trong E \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 ph\u1ea7n b\u00f9 CE c\u1ee7a A.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi l\u00e0m to\u00e1n v\u1ec1 t\u1eadp h\u1ee3p:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa d\u1ea5u giao (\u2229) v\u00e0 d\u1ea5u h\u1ee3p (\u222a), ho\u1eb7c vi\u1ebft nh\u1ea7m th\u1ee9 t\u1ef1 hi\u1ec7u t\u1eadp h\u1ee3p (l\u1ea5y ph\u1ea7n t\u1eed c\u1ee7a B tr\u1eeb cho A thay v\u00ec A tr\u1eeb cho B).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: C\u00e1c ph\u00e9p to\u00e1n tr\u00ean t\u1eadp h\u1eefu h\u1ea1n<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho hai t\u1eadp h\u1ee3p A = {1, 2, 3, 4, 5} v\u00e0 B = {3, 4, 5, 6, 7}. T\u00ecm A giao B, A h\u1ee3p B v\u00e0 A hi\u1ec7u B.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 <strong>Giao c\u1ee7a hai t\u1eadp h\u1ee3p:<\/strong> C\u00e1c ph\u1ea7n t\u1eed chung c\u1ee7a A v\u00e0 B l\u00e0 3, 4, 5. Suy ra <code>A \u2229 B = {3, 4, 5}<\/code>.<br \/>\n\u2022 <strong>H\u1ee3p c\u1ee7a hai t\u1eadp h\u1ee3p:<\/strong> L\u1ea5y t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n t\u1eed thu\u1ed9c A ho\u1eb7c B (kh\u00f4ng l\u1eb7p l\u1ea1i): <code>A \u222a B = {1, 2, 3, 4, 5, 6, 7}<\/code>.<br \/>\n\u2022 <strong>Hi\u1ec7u c\u1ee7a hai t\u1eadp h\u1ee3p:<\/strong> C\u00e1c ph\u1ea7n t\u1eed thu\u1ed9c A nh\u01b0ng kh\u00f4ng thu\u1ed9c B l\u00e0 1, 2. Suy ra <code>A \\ B = {1, 2}<\/code>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 6: C\u00c1C T\u1eacP H\u1ee2P S\u1ed0 --><\/p>\n<h2 id=\"muc-8-cac-tap-hop-so\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">C\u00e1c t\u1eadp h\u1ee3p s\u1ed1<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">H\u1ec7 th\u1ed1ng t\u1eadp s\u1ed1 v\u00e0 c\u00e1c kho\u1ea3ng, \u0111o\u1ea1n, n\u1eeda kho\u1ea3ng<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Quan h\u1ec7 bao h\u00e0m gi\u1eefa c\u00e1c t\u1eadp h\u1ee3p s\u1ed1:<\/strong> T\u1eadp s\u1ed1 t\u1ef1 nhi\u00ean N c t\u1eadp s\u1ed1 nguy\u00ean Z c t\u1eadp s\u1ed1 h\u1eefu t\u1ec9 Q c t\u1eadp s\u1ed1 th\u1ef1c R.<\/li>\n<li><strong>Kho\u1ea3ng, \u0111o\u1ea1n, n\u1eeda kho\u1ea3ng tr\u00ean tr\u1ee5c s\u1ed1 th\u1ef1c:<\/strong>\n<ul>\n<li>\u0110o\u1ea1n [a; b] g\u1ed3m c\u00e1c s\u1ed1 x th\u1ecfa m\u00e3n a \u2264 x \u2264 b.<\/li>\n<li>Kho\u1ea3ng (a; b) g\u1ed3m c\u00e1c s\u1ed1 x th\u1ecfa m\u00e3n a &lt; x &lt; b.<\/li>\n<li>N\u1eeda kho\u1ea3ng [a; b) g\u1ed3m c\u00e1c s\u1ed1 x th\u1ecfa m\u00e3n a \u2264 x &lt; b (v\u00e0 t\u01b0\u01a1ng t\u1ef1 cho kho\u1ea3ng (a; b]).<\/li>\n<\/ul>\n<\/li>\n<li><strong>Giao v\u00e0 h\u1ee3p c\u1ee7a hai kho\u1ea3ng:<\/strong> S\u1eed d\u1ee5ng tr\u1ee5c s\u1ed1 \u0111\u1ec3 bi\u1ec3u di\u1ec5n tr\u1ef1c quan v\u00e0 x\u00e1c \u0111\u1ecbnh ch\u00ednh x\u00e1c ph\u1ea7n giao ho\u1eb7c h\u1ee3p c\u1ee7a c\u00e1c kho\u1ea3ng s\u1ed1.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi thao t\u00e1c v\u1edbi kho\u1ea3ng s\u1ed1:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa ngo\u1eb7c tr\u00f2n (kh\u00f4ng l\u1ea5y \u0111\u1ea7u m\u00fat) v\u00e0 ngo\u1eb7c vu\u00f4ng (l\u1ea5y c\u1ea3 \u0111\u1ea7u m\u00fat) khi bi\u1ec3u di\u1ec5n giao, h\u1ee3p c\u1ee7a c\u00e1c kho\u1ea3ng, d\u1eabn \u0111\u1ebfn k\u1ebft qu\u1ea3 sai l\u1ec7ch \u1edf c\u00e1c \u0111i\u1ec3m bi\u00ean.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 giao c\u1ee7a hai t\u1eadp h\u1ee3p kh\u00e1c r\u1ed7ng<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho hai t\u1eadp h\u1ee3p A = [-1; 3) v\u00e0 B = [m; m + 3). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 A giao B kh\u00e1c r\u1ed7ng.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u0110\u1ec3 giao c\u1ee7a hai t\u1eadp h\u1ee3p A v\u00e0 B kh\u00e1c r\u1ed7ng, hai kho\u1ea3ng [ -1; 3 ) v\u00e0 [ m; m + 3 ) ph\u1ea3i c\u00f3 ph\u1ea7n t\u1eed chung.<br \/>\n\u2022 \u0110i\u1ec1u ki\u1ec7n \u0111\u1ec3 hai kho\u1ea3ng giao nhau kh\u00e1c r\u1ed7ng l\u00e0 \u0111\u1ea7u m\u00fat b\u00ean ph\u1ea3i c\u1ee7a kho\u1ea3ng n\u00e0y ph\u1ea3i l\u1edbn h\u01a1n \u0111\u1ea7u m\u00fat b\u00ean tr\u00e1i c\u1ee7a kho\u1ea3ng kia, \u0111\u1ed3ng th\u1eddi th\u1ecfa m\u00e3n:<br \/>\n<code>m &lt; 3<\/code> v\u00e0 <code>m + 3 &gt; -1<\/code>.<br \/>\n\u2022 Gi\u1ea3i h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c:<\/p>\n<p style=\"margin: 0;\"><code>-4 &lt; m &lt; 3<\/code>. V\u1eady gi\u00e1 tr\u1ecb m c\u1ea7n t\u00ecm l\u00e0 <strong>-4 &lt; m &lt; 3<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N I (TI\u1ebeP THEO) TO\u00c1N 10 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N II - B\u1ea4T PH\u01af\u01a0NG TR\u00ccNH V\u00c0 H\u1ec6 B\u1ea4T PH\u01af\u01a0NG TR\u00ccNH B\u1eacC NH\u1ea4T HAI \u1ea8N TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px; margin-top: 40px;\">\n<p><!-- BANNER PH\u1ea6N II --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-bottom: 30px;\">\n<h2 id=\"muc-9-phan-ii-bat-phuong-trinh-va-he-bat-phuong-trinh-bac-nhat-hai\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n II: B\u1ea5t Ph\u01b0\u01a1ng Tr\u00ecnh v\u00e0 H\u1ec7 B\u1ea5t Ph\u01b0\u01a1ng Tr\u00ecnh B\u1eadc Nh\u1ea5t Hai \u1ea8n<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: B\u1ea4T PH\u01af\u01a0NG TR\u00ccNH B\u1eacC NH\u1ea4T HAI \u1ea8N --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Ph\u1ea7n ti\u1ebfp theo c\u1ee7a \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 l\u00e0 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n, n\u01a1i th\u01b0\u1eddng c\u00f3 m\u1ed9t b\u00e0i to\u00e1n th\u1ef1c t\u1ebf t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t.<\/p>\n<h2 id=\"muc-10-bat-phuong-trinh-bac-nhat-hai-an\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">D\u1ea1ng t\u1ed5ng qu\u00e1t v\u00e0 ph\u01b0\u01a1ng ph\u00e1p bi\u1ec3u di\u1ec5n mi\u1ec1n nghi\u1ec7m<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a:<\/strong> B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n x, y c\u00f3 d\u1ea1ng t\u1ed5ng qu\u00e1t l\u00e0 <code>ax + by &lt; c<\/code> (ho\u1eb7c \u2264, &gt;, \u2265), trong \u0111\u00f3 a, b, c l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c v\u1edbi a v\u00e0 b kh\u00f4ng \u0111\u1ed3ng th\u1eddi b\u1eb1ng 0.<\/li>\n<li><strong>Nghi\u1ec7m:<\/strong> M\u1ed7i c\u1eb7p s\u1ed1 (x0; y0) sao cho khi thay v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c m\u1ed9t kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang g\u1ecdi l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3.<\/li>\n<li><strong>Quy t\u1eafc bi\u1ec3u di\u1ec5n mi\u1ec1n nghi\u1ec7m tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 (3 b\u01b0\u1edbc):<\/strong>\n<ol>\n<li>V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng delta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh <code>ax + by = c<\/code> tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy.<\/li>\n<li>Ch\u1ecdn m\u1ed9t \u0111i\u1ec3m M(x0; y0) kh\u00f4ng n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng delta (th\u01b0\u1eddng ch\u1ecdn \u0111i\u1ec3m g\u1ed1c t\u1ecda \u0111\u1ed9 O(0; 0) n\u1ebfu \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng \u0111i qua O).<\/li>\n<li>Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m M v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh. N\u1ebfu th\u1ecfa m\u00e3n, n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd delta ch\u1ee9a \u0111i\u1ec3m M l\u00e0 mi\u1ec1n nghi\u1ec7m; n\u1ebfu kh\u00f4ng th\u1ecfa m\u00e3n, ta g\u1ea1ch b\u1ecf n\u1eeda m\u1eb7t ph\u1eb3ng \u0111\u00f3.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi bi\u1ec3u di\u1ec5n mi\u1ec1n nghi\u1ec7m:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>V\u1ebd nh\u1ea7m \u0111\u01b0\u1eddng th\u1eb3ng bi\u00ean (v\u1ebd n\u00e9t li\u1ec1n khi b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea5u nghi\u00eam ng\u1eb7t nh\u01b0 &lt; ho\u1eb7c &gt;, ho\u1eb7c v\u1ebd n\u00e9t \u0111\u1ee9t khi c\u00f3 d\u1ea5u kh\u00f4ng nghi\u00eam ng\u1eb7t nh\u01b0 \u2264 ho\u1eb7c \u2265). \u0110\u01b0\u1eddng th\u1eb3ng bi\u00ean ch\u1ec9 v\u1ebd n\u00e9t li\u1ec1n khi c\u00f3 d\u1ea5u b\u1eb1ng.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Bi\u1ec3u di\u1ec5n mi\u1ec1n nghi\u1ec7m b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Bi\u1ec3u di\u1ec5n mi\u1ec1n nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh <code>2x + y &lt; 4<\/code> tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 B\u01b0\u1edbc 1: V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng d: <code>2x + y = 4<\/code> (\u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m (2; 0) v\u00e0 (0; 4)). V\u00ec b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a d\u1ea5u &lt; nghi\u00eam ng\u1eb7t n\u00ean ta v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng d b\u1eb1ng <strong>n\u00e9t \u0111\u1ee9t<\/strong>.<br \/>\n\u2022 B\u01b0\u1edbc 2: Ch\u1ecdn \u0111i\u1ec3m ki\u1ec3m tra l\u00e0 g\u1ed1c t\u1ecda \u0111\u1ed9 O(0; 0).<\/p>\n<p style=\"margin: 0;\">Thay x = 0, y = 0 v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: <code>2(0) + 0 &lt; 4<\/code> (kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang).<br \/>\n\u2022 B\u01b0\u1edbc 3: Do \u0111i\u1ec3m O th\u1ecfa m\u00e3n b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, n\u1eeda m\u1eb7t ph\u1eb3ng ch\u1ee9a \u0111i\u1ec3m O l\u00e0 mi\u1ec1n nghi\u1ec7m. Ta gi\u1eef l\u1ea1i n\u1eeda m\u1eb7t ph\u1eb3ng ch\u1ee9a g\u1ed1c t\u1ecda \u0111\u1ed9 v\u00e0 <strong>g\u1ea1ch b\u1ecf<\/strong> ph\u1ea7n c\u00f2n l\u1ea1i.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: H\u1ec6 B\u1ea4T PH\u01af\u01a0NG TR\u00ccNH B\u1eacC NH\u1ea4T HAI \u1ea8N --><\/p>\n<h2 id=\"muc-11-he-bat-phuong-trinh-bac-nhat-hai-an\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">T\u00ecm mi\u1ec1n nghi\u1ec7m v\u00e0 b\u00e0i to\u00e1n t\u1ed1i \u01b0u h\u00f3a th\u1ef1c t\u1ebf<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n g\u1ed3m hai hay nhi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n c\u00f3 chung c\u00e1c \u1ea9n s\u1ed1.<\/li>\n<li><strong>Mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7:<\/strong> L\u00e0 giao c\u1ee7a c\u00e1c mi\u1ec1n nghi\u1ec7m c\u1ee7a t\u1eebng b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh th\u00e0nh ph\u1ea7n trong h\u1ec7 tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9.<\/li>\n<li><strong>B\u00e0i to\u00e1n t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \/ nh\u1ecf nh\u1ea5t (Quy ho\u1ea1ch tuy\u1ebfn t\u00ednh):<\/strong> Bi\u1ec3u th\u1ee9c c\u1ea7n t\u1ed1i \u01b0u c\u00f3 d\u1ea1ng <code>F(x; y) = ax + by<\/code>. Mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 th\u01b0\u1eddng l\u00e0 m\u1ed9t mi\u1ec1n \u0111a gi\u00e1c. Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t c\u1ee7a F(x; y) tr\u00ean mi\u1ec1n \u0111a gi\u00e1c \u0111\u00f3 s\u1ebd \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u1ea1i m\u1ed9t trong c\u00e1c \u0111\u1ec9nh c\u1ee7a \u0111a gi\u00e1c.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi gi\u1ea3i b\u00e0i to\u00e1n t\u1ed1i \u01b0u:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean x\u00e1c \u0111\u1ecbnh \u0111\u00fang t\u1ecda \u0111\u1ed9 c\u00e1c \u0111\u1ec9nh c\u1ee7a mi\u1ec1n \u0111a gi\u00e1c giao nhau ho\u1eb7c qu\u00ean x\u00e9t c\u00e1c \u0111i\u1ec1u ki\u1ec7n r\u00e0ng bu\u1ed9c th\u1ef1c t\u1ebf c\u1ee7a b\u00e0i to\u00e1n (nh\u01b0 x \u2265 0, y \u2265 0).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: B\u00e0i to\u00e1n t\u1ed1i \u01b0u l\u1ee3i nhu\u1eadn s\u1ea3n xu\u1ea5t th\u1ef1c t\u1ebf<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> M\u1ed9t x\u01b0\u1edfng s\u1ea3n xu\u1ea5t hai lo\u1ea1i s\u1ea3n ph\u1ea9m l\u00e0 s\u1ea3n ph\u1ea9m A v\u00e0 s\u1ea3n ph\u1ea9m B. \u0110\u1ec3 s\u1ea3n xu\u1ea5t m\u1ed9t kg s\u1ea3n ph\u1ea9m A c\u1ea7n 2 gi\u1edd m\u00e1y v\u00e0 1 kg nguy\u00ean li\u1ec7u, l\u00e3i \u0111\u01b0\u1ee3c 40 ngh\u00ecn \u0111\u1ed3ng. \u0110\u1ec3 s\u1ea3n xu\u1ea5t m\u1ed9t kg s\u1ea3n ph\u1ea9m B c\u1ea7n 1 gi\u1edd m\u00e1y v\u00e0 3 kg nguy\u00ean li\u1ec7u, l\u00e3i \u0111\u01b0\u1ee3c 30 ngh\u00ecn \u0111\u1ed3ng. X\u01b0\u1edfng c\u00f3 t\u1ed1i \u0111a 10 gi\u1edd m\u00e1y v\u00e0 15 kg nguy\u00ean li\u1ec7u. H\u1ecfi x\u01b0\u1edfng c\u1ea7n s\u1ea3n xu\u1ea5t bao nhi\u00eau kg m\u1ed7i lo\u1ea1i \u0111\u1ec3 t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e3i thu \u0111\u01b0\u1ee3c l\u00e0 l\u1edbn nh\u1ea5t?<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 G\u1ecdi x l\u00e0 s\u1ed1 kg s\u1ea3n ph\u1ea9m A, y l\u00e0 s\u1ed1 kg s\u1ea3n ph\u1ea9m B s\u1ea3n xu\u1ea5t (\u0111i\u1ec1u ki\u1ec7n <code>x \u2265 0, y \u2265 0<\/code>).<br \/>\n\u2022 Theo \u0111\u1ec1 b\u00e0i ta c\u00f3 h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh r\u00e0ng bu\u1ed9c:<br \/>\n&#8211; Gi\u1edbi h\u1ea1n th\u1eddi gian m\u00e1y:<\/p>\n<p style=\"margin: 0;\"><code>2x + y \u2264 10<\/code><br \/>\n&#8211; Gi\u1edbi h\u1ea1n nguy\u00ean li\u1ec7u: <code>x + 3y \u2264 15<\/code><br \/>\n\u2022 T\u1ed5ng ti\u1ec1n l\u00e3i c\u1ea7n t\u1ed1i \u0111a h\u00f3a l\u00e0: <code>F(x; y) = 40x + 30y<\/code>.<br \/>\n\u2022 Bi\u1ec3u di\u1ec5n h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9, ta thu \u0111\u01b0\u1ee3c mi\u1ec1n \u0111a gi\u00e1c ch\u1ee9a c\u00e1c \u0111\u1ec9nh:<\/p>\n<p style=\"margin: 0;\">O(0; 0), A(0; 5), B(3; 4), C(5; 0).<br \/>\n\u2022 Thay t\u1ecda \u0111\u1ed9 c\u00e1c \u0111\u1ec9nh v\u00e0o bi\u1ec3u th\u1ee9c F(x; y):<br \/>\n&#8211; T\u1ea1i O(0; 0): F = 0.<br \/>\n&#8211; T\u1ea1i A(0; 5): F = 40(0) + 30(5) = 150.<br \/>\n&#8211; T\u1ea1i B(3; 4): F = 40(3) + 30(4) = 120 + 120 = 240.<br \/>\n&#8211; T\u1ea1i C(5; 0): F = 40(5) + 30(0) = 200.<br \/>\n\u2022 So s\u00e1nh c\u00e1c gi\u00e1 tr\u1ecb, F \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng 240 t\u1ea1i \u0111i\u1ec3m B(3; 4).<\/p>\n<p style=\"margin: 0;\">V\u1eady c\u1ea7n s\u1ea3n xu\u1ea5t <strong>3 kg s\u1ea3n ph\u1ea9m A v\u00e0 4 kg s\u1ea3n ph\u1ea9m B<\/strong> \u0111\u1ec3 thu l\u00e3i l\u1edbn nh\u1ea5t l\u00e0 240 ngh\u00ecn \u0111\u1ed3ng.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N II - B\u1ea4T PH\u01af\u01a0NG TR\u00ccNH V\u00c0 H\u1ec6 B\u1ea4T PH\u01af\u01a0NG TR\u00ccNH B\u1eacC NH\u1ea4T HAI \u1ea8N TO\u00c1N 10 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N III - H\u1ec6 TH\u1ee8C L\u01af\u1ee2NG TRONG TAM GI\u00c1C TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N III --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-12-phan-iii-he-thuc-luong-trong-tam-giac\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n III: H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng Trong Tam Gi\u00e1c<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: GI\u00c1 TR\u1eca L\u01af\u1ee2NG GI\u00c1C C\u1ee6A M\u1ed8T G\u00d3C T\u1eea 0 \u0110\u1ed8 \u0110\u1ebeN 180 \u0110\u1ed8 --><\/p>\n<p style=\"margin: 0 0 16px 0;\">H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c th\u01b0\u1eddng chi\u1ebfm nhi\u1ec1u \u0111i\u1ec3m nh\u1ea5t trong \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10, \u0111\u1eb7c bi\u1ec7t \u1edf ph\u1ea7n tr\u1ea3 l\u1eddi ng\u1eafn v\u00e0 t\u1ef1 lu\u1eadn. Con c\u1ea7n thu\u1ed9c b\u1ea3ng gi\u00e1 tr\u1ecb \u0111\u1eb7c bi\u1ec7t v\u00e0 bi\u1ebft ch\u1ecdn \u0111\u00fang \u0111\u1ecbnh l\u00ed.<\/p>\n<h2 id=\"muc-13-gia-tri-luong-giac-cua-mot-goc-tu-0-den-180\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a, d\u1ea5u v\u00e0 t\u00ednh ch\u1ea5t g\u00f3c b\u00f9<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a qua n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01a1n v\u1ecb:<\/strong> V\u1edbi m\u1ed7i g\u00f3c \u03b1 t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0, g\u1ecdi M(x0; y0) l\u00e0 \u0111i\u1ec3m tr\u00ean n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01a1n v\u1ecb sao cho g\u00f3c xOM = \u03b1. Khi \u0111\u00f3:<br \/>\n+ <code>sin \u03b1 = y0<\/code> (tung \u0111\u1ed9)<br \/>\n+ <code>cos \u03b1 = x0<\/code> (ho\u00e0nh \u0111\u1ed9)<br \/>\n+ <code>tan \u03b1 = sin \u03b1 \/ cos \u03b1<\/code> (v\u1edbi cos \u03b1 kh\u00e1c 0)<br \/>\n+ <code>cot \u03b1 = cos \u03b1 \/ sin \u03b1<\/code> (v\u1edbi sin \u03b1 kh\u00e1c 0)<\/li>\n<li><strong>D\u1ea5u c\u1ee7a gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c:<\/strong><br \/>\n+ V\u1edbi g\u00f3c nh\u1ecdn (0\u00b0 &lt; \u03b1 &lt; 90\u00b0): t\u1ea5t c\u1ea3 sin, cos, tan, cot \u0111\u1ec1u mang d\u1ea5u d\u01b0\u01a1ng (+).<br \/>\n+ V\u1edbi g\u00f3c t\u00f9 (90\u00b0 &lt; \u03b1 &lt; 180\u00b0): sin \u03b1 d\u01b0\u01a1ng (+), c\u00f2n cos \u03b1, tan \u03b1, cot \u03b1 mang d\u1ea5u \u00e2m (-).<\/li>\n<li><strong>T\u00ednh ch\u1ea5t g\u00f3c b\u00f9:<\/strong> Hai g\u00f3c b\u00f9 nhau (c\u00f3 t\u1ed5ng b\u1eb1ng 180\u00b0) th\u00ec c\u00f3 sin b\u1eb1ng nhau, c\u00f2n cos, tan, cot \u0111\u1ed1i nhau:\n<div style=\"background: #edf2f7; padding: 6px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">sin(180\u00b0 &#8211; \u03b1) = sin \u03b1<br \/>\ncos(180\u00b0 &#8211; \u03b1) = -cos \u03b1<br \/>\ntan(180\u00b0 &#8211; \u03b1) = -tan \u03b1 (v\u1edbi \u03b1 kh\u00e1c 90\u00b0)<br \/>\ncot(180\u00b0 &#8211; \u03b1) = -cot \u03b1 (v\u1edbi 0\u00b0 &lt; \u03b1 &lt; 180\u00b0)<\/div>\n<\/li>\n<\/ul>\n<p><!-- B\u1ea2NG GI\u00c1 TR\u1eca L\u01af\u1ee2NG GI\u00c1C \u0110\u1eb6C BI\u1ec6T --><\/p>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">B\u1ea3ng gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u00e1c g\u00f3c \u0111\u1eb7c bi\u1ec7t<\/h3>\n<div style=\"overflow-x: auto; margin: 15px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 14px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: center;\">\n<colgroup>\n<col style=\"width: 14%;\" \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0; color: #0056b3;\">G\u00f3c \u03b1<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">0\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">30\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">45\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">60\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">90\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">120\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">135\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">150\u00b0<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">180\u00b0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0; font-weight: bold;\">sin \u03b1<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">0<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u00bd<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a2 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a3 \/ 2<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a3 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a2 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u00bd<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0; font-weight: bold;\">cos \u03b1<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a3 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a2 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u00bd<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">0<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-\u00bd<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-\u221a2 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-\u221a3 \/ 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-1<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0; font-weight: bold;\">tan \u03b1<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">0<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a3 \/ 3<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">\u221a3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">Kh\u00f4ng x\u00e1c \u0111\u1ecbnh<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-\u221a3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">-\u221a3 \/ 3<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 8px; border: 1px solid #cbd5e0;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 l\u01b0\u1ee3ng gi\u00e1c g\u00f3c t\u00f9:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean m\u1ea5t d\u1ea5u tr\u1eeb (-) khi t\u00ednh cos, tan c\u1ee7a g\u00f3c t\u00f9 (v\u00ed d\u1ee5 ng\u1ed9 nh\u1eadn cos(120\u00b0) b\u1eb1ng 1\/2 thay v\u00ec \u0111\u00fang b\u1ea3n ch\u1ea5t l\u00e0 -1\/2).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: <code>A = sin(30\u00b0) + cos(120\u00b0) + tan(135\u00b0)<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Ta c\u00f3 c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1eb7c bi\u1ec7t:<br \/>\n&#8211; <code>sin(30\u00b0) = \u00bd<\/code>.<br \/>\n&#8211; <code>cos(120\u00b0) = -cos(180\u00b0 - 120\u00b0) = -cos(60\u00b0) = -\u00bd<\/code>.<br \/>\n&#8211; <code>tan(135\u00b0) = -tan(180\u00b0 - 135\u00b0) = -tan(45\u00b0) = -1<\/code>.<br \/>\n\u2022 Thay v\u00e0o bi\u1ec3u th\u1ee9c A: <code>A = \u00bd + (-\u00bd) + (-1) = <strong>-1<\/strong><\/code>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: \u0110\u1ecaNH L\u00cd C\u00d4SIN, \u0110\u1ecaNH L\u00cd SIN --><\/p>\n<h2 id=\"muc-14-dinh-li-cosin-dinh-li-sin\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">\u0110\u1ecbnh l\u00ed c\u00f4sin, \u0111\u1ecbnh l\u00ed sin<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u00f4ng th\u1ee9c v\u00e0 ph\u01b0\u01a1ng ph\u00e1p s\u1eed d\u1ee5ng<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh l\u00ed c\u00f4sin:<\/strong> Trong tam gi\u00e1c ABC v\u1edbi c\u00e1c c\u1ea1nh \u0111\u1ed1i di\u1ec7n l\u1ea7n l\u01b0\u1ee3t l\u00e0 a, b, c:\n<div style=\"background: #edf2f7; padding: 6px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">a<sup>2<\/sup> = b<sup>2<\/sup> + c<sup>2<\/sup> &#8211; 2bc \u00b7 cos A<br \/>\nb<sup>2<\/sup> = a<sup>2<\/sup> + c<sup>2<\/sup> &#8211; 2ac \u00b7 cos B<br \/>\nc<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup> &#8211; 2ab \u00b7 cos C<\/div>\n<p><em>H\u1ec7 qu\u1ea3 t\u00ednh g\u00f3c:<\/em> <code>cos A = (b<sup>2<\/sup> + c<sup>2<\/sup> - a<sup>2<\/sup>) : (2bc)<\/code>.<\/li>\n<li><strong>\u0110\u1ecbnh l\u00ed sin:<\/strong> Trong tam gi\u00e1c ABC v\u1edbi R l\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp:\n<div style=\"background: #edf2f7; padding: 6px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">a : sin A = b : sin B = c : sin C = 2R<\/div>\n<\/li>\n<li><strong>Khi n\u00e0o d\u00f9ng \u0111\u1ecbnh l\u00ed n\u00e0o?<\/strong><br \/>\n+ D\u00f9ng <strong>\u0111\u1ecbnh l\u00ed c\u00f4sin<\/strong> khi bi\u1ebft 3 c\u1ea1nh c\u1ee7a tam gi\u00e1c (\u0111\u1ec3 t\u00ednh g\u00f3c) ho\u1eb7c bi\u1ebft 2 c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa (\u0111\u1ec3 t\u00ednh c\u1ea1nh th\u1ee9 ba).<br \/>\n+ D\u00f9ng <strong>\u0111\u1ecbnh l\u00ed sin<\/strong> khi bi\u1ebft 1 c\u1ea1nh v\u00e0 2 g\u00f3c (\u0111\u1ec3 t\u00ednh c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i) ho\u1eb7c li\u00ean quan \u0111\u1ebfn b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp R.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00ed:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn d\u1ea5u tr\u1eeb th\u00e0nh d\u1ea5u c\u1ed9ng trong \u0111\u1ecbnh l\u00ed c\u00f4sin (vi\u1ebft th\u00e0nh + 2bc\u00b7cos A) ho\u1eb7c d\u00f9ng nh\u1ea7m c\u00f4ng th\u1ee9c \u0111\u1ecbnh l\u00ed sin khi b\u00e0i to\u00e1n ch\u1ec9 cho c\u00e1c c\u1ea1nh m\u00e0 kh\u00f4ng c\u00f3 g\u00f3c \u0111\u1ed1i di\u1ec7n.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh b\u1eb1ng \u0111\u1ecbnh l\u00ed c\u00f4sin<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC c\u00f3 b = 7 cm, c = 5 cm v\u00e0 g\u00f3c A b\u1eb1ng 60\u00b0. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh a.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed c\u00f4sin trong tam gi\u00e1c ABC:<br \/>\n<code>a<sup>2<\/sup> = b<sup>2<\/sup> + c<sup>2<\/sup> - 2bc \u00b7 cos A<\/code><br \/>\n\u2022 Thay s\u1ed1 v\u00e0o c\u00f4ng th\u1ee9c: <code>a<sup>2<\/sup> = 7<sup>2<\/sup> + 5<sup>2<\/sup> - 2 \u00b7 7 \u00b7 5 \u00b7 cos(60\u00b0)<\/code><br \/>\n<code>a<sup>2<\/sup> = 49 + 25 - 70 \u00b7 (\u00bd) = 74 - 35 = 39<\/code>.<br \/>\n\u2022 Suy ra <code>a = \u221a39 cm<\/code> (kho\u1ea3ng <code>6,24 cm<\/code>).<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 3: GI\u1ea2I TAM GI\u00c1C --><\/p>\n<h2 id=\"muc-15-giai-tam-giac\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Gi\u1ea3i tam gi\u00e1c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u00e1c b\u00e0i to\u00e1n gi\u1ea3i tam gi\u00e1c v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Gi\u1ea3i tam gi\u00e1c l\u00e0 g\u00ec?<\/strong> L\u00e0 \u0111i t\u00ednh t\u1ea5t c\u1ea3 c\u00e1c \u0111\u1ed9 d\u00e0i c\u1ea1nh v\u00e0 s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t tam gi\u00e1c khi bi\u1ebft m\u1ed9t s\u1ed1 y\u1ebfu t\u1ed1 cho tr\u01b0\u1edbc.<\/li>\n<li><strong>Ba b\u00e0i to\u00e1n gi\u1ea3i tam gi\u00e1c c\u01a1 b\u1ea3n:<\/strong><br \/>\n+ B\u00e0i to\u00e1n 1: Bi\u1ebft hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa (d\u00f9ng \u0111\u1ecbnh l\u00ed c\u00f4sin t\u00ednh c\u1ea1nh th\u1ee9 ba, sau \u0111\u00f3 d\u00f9ng \u0111\u1ecbnh l\u00ed sin ho\u1eb7c h\u1ec7 qu\u1ea3 c\u00f4sin t\u00ednh c\u00e1c g\u00f3c).<br \/>\n+ B\u00e0i to\u00e1n 2: Bi\u1ebft ba c\u1ea1nh (d\u00f9ng h\u1ec7 qu\u1ea3 \u0111\u1ecbnh l\u00ed c\u00f4sin t\u00ednh c\u1ea3 3 g\u00f3c).<br \/>\n+ B\u00e0i to\u00e1n 3: Bi\u1ebft m\u1ed9t c\u1ea1nh v\u00e0 hai g\u00f3c (d\u00f9ng t\u1ed5ng 3 g\u00f3c b\u1eb1ng 180\u00b0 t\u00ednh g\u00f3c c\u00f2n l\u1ea1i, sau \u0111\u00f3 d\u00f9ng \u0111\u1ecbnh l\u00ed sin t\u00ednh hai c\u1ea1nh kia).<\/li>\n<li><strong>\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf:<\/strong> Gi\u1ea3i tam gi\u00e1c gi\u00fap \u0111o \u0111\u1ea1c kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m kh\u00f4ng th\u1ec3 t\u1edbi tr\u1ef1c ti\u1ebfp (nh\u01b0 \u0111o chi\u1ec1u cao ng\u1ecdn th\u00e1p, kho\u1ea3ng c\u00e1ch gi\u1eefa hai b\u1edd s\u00f4ng, kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u1ea3o).<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi gi\u1ea3i tam gi\u00e1c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>L\u00e0m tr\u00f2n s\u1ed1 qu\u00e1 s\u1edbm \u1edf c\u00e1c b\u01b0\u1edbc trung gian, d\u1eabn \u0111\u1ebfn sai s\u1ed1 l\u1edbn \u1edf k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng c\u1ee7a b\u00e0i to\u00e1n th\u1ef1c t\u1ebf. Nguy\u00ean t\u1eafc l\u00e0 gi\u1eef nguy\u00ean gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c ho\u1eb7c l\u1ea5y nhi\u1ec1u ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n, ch\u1ec9 l\u00e0m tr\u00f2n \u1edf \u0111\u00e1p s\u1ed1 cu\u1ed1i c\u00f9ng.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: B\u00e0i to\u00e1n th\u1ef1c t\u1ebf \u0111o kho\u1ea3ng c\u00e1ch<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> \u0110\u1ec3 \u0111o kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m A v\u00e0 B b\u1ecb ng\u0103n b\u1edfi m\u1ed9t h\u1ed3 n\u01b0\u1edbc, ng\u01b0\u1eddi ta ch\u1ecdn m\u1ed9t \u0111i\u1ec3m C \u1edf b\u1edd v\u00e0 \u0111o \u0111\u01b0\u1ee3c kho\u1ea3ng c\u00e1ch CA = 300 m, CB = 450 m v\u00e0 g\u00f3c ACB b\u1eb1ng 60\u00b0. T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m A v\u00e0 B (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb).<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 X\u00e9t tam gi\u00e1c ABC, ta c\u1ea7n t\u00ednh c\u1ea1nh AB (k\u00fd hi\u1ec7u l\u00e0 c) khi bi\u1ebft b = 450, a = 300 v\u00e0 g\u00f3c C = 60\u00b0.<br \/>\n\u2022 \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed c\u00f4sin:<\/p>\n<p style=\"margin: 0;\"><code>c<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup> - 2ab \u00b7 cos C<\/code><br \/>\n<code>c<sup>2<\/sup> = 300<sup>2<\/sup> + 450<sup>2<\/sup> - 2 \u00b7 300 \u00b7 450 \u00b7 cos(60\u00b0)<\/code><br \/>\n<code>c<sup>2<\/sup> = 90000 + 202500 - 270000 \u00b7 (\u00bd) = 292500 - 135000 = 157500<\/code>.<br \/>\n\u2022 Suy ra <code>c = \u221a157500 \u2248 396,86 m<\/code>.<br \/>\n\u2022 L\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb, kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m A v\u00e0 B l\u00e0 <strong>397 m\u00e9t<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 4: H\u1ec6 TH\u1ee8C L\u01af\u1ee2NG TRONG TAM GI\u00c1C --><\/p>\n<h2 id=\"muc-16-he-thuc-luong-trong-tam-giac\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch v\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>C\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c S:<\/strong>\n<div style=\"background: #edf2f7; padding: 8px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">S = \u00bd \u00b7 b \u00b7 c \u00b7 sin A = \u00bd \u00b7 a \u00b7 c \u00b7 sin B = \u00bd \u00b7 a \u00b7 b \u00b7 sin C<br \/>\nS = (a \u00b7 b \u00b7 c) : (4R) \u00a0\u00a0(v\u1edbi R l\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp)<br \/>\nS = p \u00b7 r \u00a0\u00a0(v\u1edbi p = (a + b + c) : 2 l\u00e0 n\u1eeda chu vi, r l\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp)<br \/>\nS = \u221a(p \u00b7 (p &#8211; a) \u00b7 (p &#8211; b) \u00b7 (p &#8211; c)) \u00a0\u00a0(C\u00f4ng th\u1ee9c Heron)<\/div>\n<\/li>\n<li><strong>C\u00f4ng th\u1ee9c t\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn:<\/strong> Trong tam gi\u00e1c ABC, \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh A (k\u00fd hi\u1ec7u l\u00e0 ma) t\u00ednh theo ba c\u1ea1nh a, b, c \u0111\u01b0\u1ee3c cho b\u1edfi:\n<div style=\"background: #edf2f7; padding: 6px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">m<sub>a<\/sub><sup>2<\/sup> = (2(b<sup>2<\/sup> + c<sup>2<\/sup>) &#8211; a<sup>2<\/sup>) : 4<\/div>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean h\u1ec7 s\u1ed1 \u00bd trong c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch (vi\u1ebft nh\u1ea7m th\u00e0nh S = bc sin A thay v\u00ec \u00bd bc sin A) ho\u1eb7c t\u00ednh sai n\u1eeda chu vi p khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c Heron.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c theo hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c ABC bi\u1ebft hai c\u1ea1nh b = 8 cm, c = 10 cm v\u00e0 g\u00f3c A b\u1eb1ng 30\u00b0.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch: <code>S = \u00bd \u00b7 b \u00b7 c \u00b7 sin A<\/code><br \/>\n\u2022 Thay s\u1ed1 v\u00e0o c\u00f4ng th\u1ee9c: <code>S = \u00bd \u00b7 8 \u00b7 10 \u00b7 sin(30\u00b0)<\/code><br \/>\n<code>S = 40 \u00b7 (\u00bd) = <strong>20 (centim\u00e9t vu\u00f4ng)<\/strong><\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>20 cm<sup>2<\/sup><\/strong>.<\/p>\n<\/div>\n<p><!-- L\u01afU \u00dd \/ INTERNAL LINK BOX --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin-top: 25px;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u1eddi khuy\u00ean t\u1eeb chuy\u00ean gia NaviEdu:<\/strong> H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c chi\u1ebfm t\u1ec9 tr\u1ecdng \u0111i\u1ec3m s\u1ed1 r\u1ea5t l\u1edbn trong b\u00e0i ki\u1ec3m tra gi\u1eefa k\u00ec 1 To\u00e1n 10 v\u00e0 l\u00e0 n\u1ec1n t\u1ea3ng cho c\u1ea3 ch\u01b0\u01a1ng tr\u00ecnh H\u00ecnh h\u1ecdc THPT. N\u1ebfu con \u0111ang c\u1ea3m th\u1ea5y h\u1ed5ng ki\u1ebfn th\u1ee9c ho\u1eb7c g\u1eb7p kh\u00f3 kh\u0103n khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c, ba m\u1eb9 h\u00e3y tham kh\u1ea3o ngay l\u1ed9 tr\u00ecnh <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/mat-goc-toan\/lop-10\">l\u1ea5y l\u1ea1i g\u1ed1c To\u00e1n 10<\/a> t\u1ea1i NaviEdu. \u0110\u1eebng ch\u1ee7 quan v\u1edbi c\u00e1c <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/blog\/mat-goc-toan-la-gi-7-dau-hieu-hong-kien-thuc\/\">d\u1ea5u hi\u1ec7u m\u1ea5t g\u1ed1c To\u00e1n<\/a> xu\u1ea5t hi\u1ec7n t\u1eeb s\u1edbm \u0111\u1ec3 gi\u00fap con v\u1eefng v\u00e0ng b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1!<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N III - H\u1ec6 TH\u1ee8C L\u01af\u1ee2NG TRONG TAM GI\u00c1C TO\u00c1N 10 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U PH\u1ea6N IV: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y & \u0110\u1ec0 THI M\u1eaaU TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N IV --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-17-phan-iv-lich-on-tap-7-ngay-de-thi-mau\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n IV: L\u1ecbch \u00d4n T\u1eadp 7 Ng\u00e0y &amp; \u0110\u1ec1 Thi M\u1eabu<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Khi \u0111\u00e3 \u0111i h\u1ebft c\u00e1c ch\u1ee7 \u0111\u1ec1 trong \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10, con c\u00f3 th\u1ec3 d\u00f9ng l\u1ecbch 7 ng\u00e0y d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c v\u00e0 luy\u1ec7n \u0111\u1ec1 \u0111\u1ecbnh d\u1ea1ng m\u1edbi tr\u01b0\u1edbc ng\u00e0y thi.<\/p>\n<h2 id=\"muc-18-lich-on-tap-giua-ki-1-toan-10-trong-7-ngay-giup-but-pha-diem\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u1ecbch \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 trong 7 ng\u00e0y gi\u00fap b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1<\/h2>\n<p>\u0110\u1ec3 gi\u00fap h\u1ecdc sinh THPT l\u00e0m ch\u1ee7 tr\u1ecdn v\u1eb9n kh\u1ed1i l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 th\u00edch \u1ee9ng ho\u00e0n h\u1ea3o v\u1edbi \u0111\u1ecbnh d\u1ea1ng \u0111\u1ec1 thi m\u1edbi, \u0111\u1ed9i ng\u0169 chuy\u00ean m\u00f4n t\u1ea1i NaviEdu x\u00e2y d\u1ef1ng th\u1eddi gian bi\u1ec3u n\u01b0\u1edbc r\u00fat trong 7 ng\u00e0y (m\u1ed7i ng\u00e0y t\u1eeb 60 \u2013 90 ph\u00fat \u00f4n t\u1eadp chuy\u00ean s\u00e2u):<\/p>\n<div style=\"overflow-x: auto; margin: 20px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<colgroup>\n<col style=\"width: 16%;\" \/>\n<col style=\"width: 48%;\" \/>\n<col style=\"width: 36%;\" \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 18%;\">Th\u1eddi gian<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 47%;\">N\u1ed9i dung \u00f4n<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 35%;\">M\u1ee5c ti\u00eau (60\u201390 ph\u00fat\/ng\u00e0y)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">M\u1ec7nh \u0111\u1ec1, ph\u1ee7 \u0111\u1ecbnh, k\u00e9o theo, m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">N\u1eafm ch\u1eafc b\u1ea3n ch\u1ea5t logic, x\u00e9t \u0111\u00fang sai c\u00e1c m\u1ec7nh \u0111\u1ec1 v\u00e0 th\u00e0nh th\u1ea1o quy t\u1eafc ph\u1ee7 \u0111\u1ecbnh l\u01b0\u1ee3ng t\u1eeb.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">T\u1eadp h\u1ee3p, ph\u00e9p to\u00e1n t\u1eadp h\u1ee3p, c\u00e1c t\u1eadp h\u1ee3p s\u1ed1.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Th\u00e0nh th\u1ea1o giao, h\u1ee3p, hi\u1ec7u t\u1eadp h\u1ee3p v\u00e0 k\u1ef9 n\u0103ng bi\u1ec3u di\u1ec5n c\u00e1c kho\u1ea3ng, \u0111o\u1ea1n, n\u1eeda kho\u1ea3ng tr\u00ean tr\u1ee5c s\u1ed1.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 BPT b\u1eadc nh\u1ea5t hai \u1ea9n, b\u00e0i to\u00e1n t\u1ed1i \u01b0u.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">R\u00e8n k\u1ef9 n\u0103ng bi\u1ec3u di\u1ec5n mi\u1ec1n nghi\u1ec7m ch\u00ednh x\u00e1c v\u00e0 gi\u1ea3i th\u00e0nh th\u1ea1o b\u00e0i to\u00e1n quy ho\u1ea1ch tuy\u1ebfn t\u00ednh th\u1ef1c t\u1ebf.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 4<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c 0\u00b0\u2013180\u00b0, \u0111\u1ecbnh l\u00ed c\u00f4sin, sin.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Ghi nh\u1edb gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c \u0111\u1eb7c bi\u1ec7t, t\u00ednh ch\u1ea5t g\u00f3c b\u00f9 v\u00e0 \u00e1p d\u1ee5ng linh ho\u1ea1t \u0111\u1ecbnh l\u00ed c\u00f4sin, sin.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 5<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Gi\u1ea3i tam gi\u00e1c, c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch, b\u00e0i to\u00e1n th\u1ef1c t\u1ebf.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Th\u00e0nh th\u1ea1o gi\u1ea3i tam gi\u00e1c v\u00e0 v\u1eadn d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch v\u00e0o c\u00e1c b\u00e0i to\u00e1n \u0111o \u0111\u1ea1c th\u1ef1c t\u1ebf.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 6<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u00e0m 2 \u0111\u1ec1 m\u1eabu \u0111\u1ecbnh d\u1ea1ng m\u1edbi, b\u1ea5m gi\u1edd 90 ph\u00fat.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u00e0m quen \u00e1p l\u1ef1c ph\u00f2ng thi th\u1eadt v\u1edbi c\u1ea5u tr\u00fac 4 ph\u1ea7n, t\u1ed1i \u01b0u h\u00f3a th\u1eddi gian ph\u00e2n b\u1ed5 t\u1eebng ph\u1ea7n.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 7<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Xem l\u1ea1i l\u1ed7i sai, \u0111\u1eb7c bi\u1ec7t c\u00e2u \u0111\u00fang\/sai v\u00e0 tr\u1ea3 l\u1eddi ng\u1eafn.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Kh\u1eafc ph\u1ee5c tri\u1ec7t \u0111\u1ec3 c\u00e1c b\u1eaby t\u01b0 duy \u1edf ph\u1ea7n \u0111\u00fang\/sai v\u00e0 r\u00e8n t\u00ednh c\u1ea9n th\u1eadn \u1edf ph\u1ea7n tr\u1ea3 l\u1eddi ng\u1eafn.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P G\u1ee2I \u00dd \/ BLOG LINK --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin: 20px 0;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u1eddi khuy\u00ean cho h\u1ecdc sinh THPT:<\/strong> Chuy\u1ec3n c\u1ea5p l\u00ean l\u1edbp 10 \u0111\u00f2i h\u1ecfi ph\u01b0\u01a1ng ph\u00e1p t\u1ef1 h\u1ecdc v\u00e0 t\u01b0 duy logic ho\u00e0n to\u00e0n m\u1edbi. Ba m\u1eb9 v\u00e0 h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam c\u00e1c ph\u01b0\u01a1ng ph\u00e1p <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/blog\/cach-hoc-toan-hieu-qua-thu-tu-hoc-chuan\/\">c\u00e1ch h\u1ecdc To\u00e1n hi\u1ec7u qu\u1ea3<\/a> \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a n\u0103ng l\u1ef1c ti\u1ebfp thu m\u1ed7i ng\u00e0y.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: T\u1ea2I \u0110\u1ec0 C\u01af\u01a0NG V\u00c0 \u0110\u1ec0 THI M\u1eaaU --><\/p>\n<h2 id=\"muc-19-tai-de-cuong-on-tap-giua-ki-1-toan-10-va-de-thi-mau-pdf-co-d\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">T\u1ea3i \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 v\u00e0 \u0111\u1ec1 thi m\u1eabu (PDF c\u00f3 \u0111\u00e1p \u00e1n)<\/h2>\n<p>Nh\u1eb1m gi\u00fap h\u1ecdc sinh l\u1edbp 10 c\u1ecd x\u00e1t v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 ki\u1ec3m tra \u0111\u1ecbnh k\u00ec theo \u0111\u1ecbnh d\u1ea1ng m\u1edbi nh\u1ea5t, \u0111\u1ed9i ng\u0169 gi\u00e1o vi\u00ean chuy\u00ean m\u00f4n t\u1ea1i NaviEdu \u0111\u00e3 bi\u00ean so\u1ea1n tr\u1ecdn b\u1ed9 t\u00e0i li\u1ec7u \u0111\u1ed9c quy\u1ec1n b\u00e1m s\u00e1t Th\u00f4ng t\u01b0 22:<\/p>\n<div style=\"background-color: #f7fafc; border: 1px solid #e2e8f0; border-radius: 8px; padding: 22px; margin: 20px 0;\">\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 0; margin-bottom: 12px;\">T\u00f3m t\u1eaft c\u1ea5u tr\u00fac b\u1ed9 \u0111\u1ec1 m\u1eabu NaviEdu theo \u0111\u1ecbnh d\u1ea1ng m\u1edbi:<\/h3>\n<ul style=\"padding-left: 20px; margin-bottom: 15px;\">\n<li><strong>Ph\u1ea7n I \u2013 Tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn (3.0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 12 c\u00e2u h\u1ecfi (m\u1ed7i c\u00e2u 0.25 \u0111i\u1ec3m), ki\u1ec3m tra nhanh nh\u1eadn bi\u1ebft v\u00e0 th\u00f4ng hi\u1ec3u to\u00e0n b\u1ed9 chuy\u00ean \u0111\u1ec1 gi\u1eefa k\u00ec 1.<\/li>\n<li><strong>Ph\u1ea7n II \u2013 Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (2.0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 2 c\u00e2u h\u1ecfi l\u1edbn d\u1ea1ng chu\u1ed7i \u00fd a, b, c, d (ch\u1ea5m \u0111i\u1ec3m l\u0169y ti\u1ebfn t\u1ed1i \u0111a 1 \u0111i\u1ec3m\/c\u00e2u), \u0111\u00e1nh gi\u00e1 s\u00e2u t\u01b0 duy logic \u0111a chi\u1ec1u.<\/li>\n<li><strong>Ph\u1ea7n III \u2013 Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (2.0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 4 c\u00e2u h\u1ecfi y\u00eau c\u1ea7u h\u1ecdc sinh t\u1ef1 t\u00ednh to\u00e1n v\u00e0 \u0111i\u1ec1n \u0111\u00e1p s\u1ed1 ch\u00ednh x\u00e1c, th\u1eed th\u00e1ch n\u0103ng l\u1ef1c t\u00ednh to\u00e1n th\u1ef1c t\u1ebf.<\/li>\n<li><strong>Ph\u1ea7n IV \u2013 T\u1ef1 lu\u1eadn (3.0 \u0111i\u1ec3m):<\/strong> G\u1ed3m c\u00e1c b\u00e0i to\u00e1n t\u1ef1 lu\u1eadn chuy\u00ean s\u00e2u v\u1ec1 h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n, \u1ee9ng d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng v\u00e0 gi\u1ea3i tam gi\u00e1c th\u1ef1c t\u1ebf.<\/li>\n<\/ul>\n<p style=\"margin-top: 15px; margin-bottom: 20px; color: #4a5568;\">To\u00e0n b\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m t\u00f3m t\u1eaft l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m, h\u1ec7 th\u1ed1ng b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n theo t\u1eebng chuy\u00ean \u0111\u1ec1 v\u00e0 03 \u0111\u1ec1 thi th\u1eed chu\u1ea9n format 90 ph\u00fat c\u00f3 k\u00e8m b\u1ea3ng \u0111\u00e1p \u00e1n, h\u01b0\u1edbng d\u1eabn gi\u1ea3i chi ti\u1ebft t\u1eebng b\u01b0\u1edbc gi\u00fap con t\u1ef1 h\u1ecdc hi\u1ec7u qu\u1ea3 t\u1ea1i nh\u00e0:<\/p>\n<div style=\"text-align: center; margin-top: 25px; padding-top: 18px; border-top: 1px dashed #cbd5e0;\"><a style=\"background-color: #d9534f; color: #ffffff; padding: 13px 30px; text-decoration: none; border-radius: 6px; font-weight: bold; font-size: 16px; display: inline-block; box-shadow: 0 2px 5px rgba(217,83,79,0.3);\" href=\"https:\/\/navi.edu.vn\/thu-vien\/danh-muc-tai-lieu\/lop-10\/\">\ud83d\udce5 T\u1ea2I TR\u1eccN B\u1ed8 \u0110\u1ec0 C\u01af\u01a0NG &amp; \u0110\u1ec0 M\u1eaaU TO\u00c1N 10 (PDF)<br \/>\n<\/a><\/p>\n<p style=\"margin-top: 12px; font-size: 14px; color: #4a5568;\">(T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt mi\u1ec5n ph\u00ed t\u1ea1i kho <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/thu-vien\/danh-muc-tai-lieu\/lop-10\/\">th\u01b0 vi\u1ec7n h\u1ecdc li\u1ec7u NaviEdu<\/a>)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC PH\u1ea6N IV: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y & \u0110\u1ec0 THI M\u1eaaU TO\u00c1N 10 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U K\u1ebeT B\u00c0I V\u00c0 KH\u1ed0I CTA WORDPRESS TO\u00c1N 10 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<h2 id=\"muc-20-loi-ket\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u1eddi k\u1ebft<\/h2>\n<p>B\u01b0\u1edbc sang c\u1ea5p THPT v\u1edbi nh\u1eefng \u0111\u00f2i h\u1ecfi kh\u1eaft khe v\u1ec1 t\u01b0 duy logic v\u00e0 h\u00ecnh th\u1ee9c ki\u1ec3m tra \u0111\u1ecbnh k\u00ec theo \u0111\u1ecbnh d\u1ea1ng m\u1edbi, vi\u1ec7c ch\u1ee7 \u0111\u1ed9ng \u00f4n t\u1eadp t\u1eeb s\u1edbm ch\u00ednh l\u00e0 ch\u00eca kh\u00f3a then ch\u1ed1t gi\u00fap c\u00e1c em h\u1ecdc sinh v\u1eefng v\u00e0ng v\u01b0\u1ee3t qua th\u1eed th\u00e1ch \u0111\u1ea7u \u0111\u1eddi. Hy v\u1ecdng r\u1eb1ng b\u1ed9 <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 to\u00e1n 10<\/strong> do \u0111\u1ed9i ng\u0169 chuy\u00ean m\u00f4n NaviEdu d\u00e0y c\u00f4ng bi\u00ean so\u1ea1n s\u1ebd l\u00e0 c\u1ea9m nang h\u1ed7 tr\u1ee3 \u0111\u1eafc l\u1ef1c, \u0111\u1ed3ng h\u00e0nh c\u00f9ng ba m\u1eb9 v\u00e0 c\u00e1c con trong su\u1ed1t ch\u1eb7ng \u0111\u01b0\u1eddng n\u01b0\u1edbc r\u00fat.<\/p>\n<p>H\u00e3y gi\u1eef v\u1eefng tinh th\u1ea7n t\u1ef1 tin, r\u00e8n luy\u1ec7n thu\u1ea7n th\u1ee5c c\u00e1c d\u1ea1ng b\u00e0i tr\u1ecdng t\u00e2m t\u1eeb \u0111\u1ea1i s\u1ed1 \u0111\u1ebfn h\u00ecnh h\u1ecdc \u0111\u1ec3 chu\u1ea9n b\u1ecb th\u1eadt chu \u0111\u00e1o cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi. Ch\u00fac c\u00e1c em b\u01b0\u1edbc v\u00e0o ph\u00f2ng thi v\u1edbi b\u1ea3n l\u0129nh v\u1eefng v\u00e0ng, ho\u00e0n th\u00e0nh xu\u1ea5t s\u1eafc b\u00e0i l\u00e0m v\u00e0 \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t!<\/p>\n<p><!-- KH\u1ed0I CTA WORDPRESS CHU\u1ea8N CHUY\u1ec2N \u0110\u1ed4I --><\/p>\n<div style=\"border: 2px dashed #0056b3; background-color: #f4f8ff; border-radius: 10px; padding: 25px; text-align: center; margin: 35px 0;\">\n<h3 style=\"color: #0056b3; margin-top: 0; font-size: 20px; font-weight: bold;\">B\u1ee9t Ph\u00e1 \u0110i\u1ec3m S\u1ed1 Gi\u1eefa K\u00ec 1 To\u00e1n 10 C\u00f9ng L\u1ed9 Tr\u00ecnh C\u00e1 Nh\u00e2n H\u00f3a T\u1ea1i NaviEdu!<\/h3>\n<p style=\"font-size: 16px; line-height: 1.6; color: #333333; margin-bottom: 20px; max-width: 750px; margin-left: auto; margin-right: auto;\">H\u1ecdc sinh v\u00e0 ba m\u1eb9 h\u00e3y \u0111\u01b0a con \u0111\u1ebfn c\u01a1 s\u1edf <strong>NaviEdu (33 LK6B M\u1ed7 Lao, L\u00e0ng Vi\u1ec7t Ki\u1ec1u Ch\u00e2u \u00c2u, H\u00e0 \u0110\u00f4ng)<\/strong> \u0111\u1ec3 tham gia l\u00e0m b\u00e0i \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c mi\u1ec5n ph\u00ed b\u1eb1ng Math AI v\u00e0 nh\u1eadn l\u1ed9 tr\u00ecnh h\u1ecdc &#8220;may \u0111o&#8221; ri\u00eang bi\u1ec7t cho ch\u00ednh m\u00ecnh ngay h\u00f4m nay!<\/p>\n<div><a style=\"background-color: #0056b3; color: #ffffff; padding: 13px 30px; text-decoration: none; border-radius: 6px; font-weight: bold; font-size: 16px; display: inline-block; box-shadow: 0 2px 4px rgba(0,86,179,0.2);\" href=\"https:\/\/navi.edu.vn\/giai-phap\/dang-ky-tu-van?utm_campaign=All.Blog._Organic.Dieuttm_Testtoan10.cta.2510_._.&amp;utm_medium=Dieuttm\" target=\"_blank\" rel=\"noopener\">L\u00c0M B\u00c0I \u0110\u00c1NH GI\u00c1 N\u0102NG L\u1ef0C MI\u1ec4N PH\u00cd<\/a><\/div>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC K\u1ebeT B\u00c0I V\u00c0 KH\u1ed0I CTA WORDPRESS TO\u00c1N 10 --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 10 (2026\u20132027): ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m, d\u1ea1ng b\u00e0i hay g\u1eb7p, \u0111\u1ec1 m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n, l\u1ecbch \u00f4n 7 ng\u00e0y v\u00e0 file PDF t\u1ea3i mi\u1ec5n ph\u00ed.<\/p>\n","protected":false},"author":2,"featured_media":2910,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2859"}],"collection":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/comments?post=2859"}],"version-history":[{"count":7,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2859\/revisions"}],"predecessor-version":[{"id":2909,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2859\/revisions\/2909"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media\/2910"}],"wp:attachment":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media?parent=2859"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/categories?post=2859"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/tags?post=2859"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}