{"id":2396,"date":"2025-08-04T11:18:06","date_gmt":"2025-08-04T04:18:06","guid":{"rendered":"https:\/\/navi.edu.vn\/blog\/?p=2396"},"modified":"2025-08-04T11:18:06","modified_gmt":"2025-08-04T04:18:06","slug":"luu-y-noi-dung-kien-thuc-quan-trong-toan-8-chuong-trinh-moi","status":"publish","type":"post","link":"https:\/\/navi.edu.vn\/blog\/luu-y-noi-dung-kien-thuc-quan-trong-toan-8-chuong-trinh-moi\/","title":{"rendered":"L\u01b0u \u00fd n\u1ed9i dung ki\u1ebfn th\u1ee9c quan tr\u1ecdng To\u00e1n 8 (Ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi)"},"content":{"rendered":"

Ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 8 ti\u1ebfp t\u1ee5c m\u1edf r\u1ed9ng v\u00e0 n\u00e2ng cao t\u1eeb n\u1ec1n t\u1ea3ng c\u1ee7a l\u1edbp 7, b\u1eaft \u0111\u1ea7u xu\u1ea5t hi\u1ec7n nh\u1eefng ph\u1ea7n ki\u1ebfn th\u1ee9c n\u1eb7ng v\u00e0 kh\u00f3.\u00a0N\u1ebfu h\u1ecdc sinh \u0111\u00e3 n\u1eafm ch\u1eafc c\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m l\u1edbp 7 th\u00ec vi\u1ec7c ti\u1ebfp c\u1eadn ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 8 s\u1ebd thu\u1eadn l\u1ee3i h\u01a1n r\u1ea5t nhi\u1ec1u. Tr\u01b0\u1edbc th\u1ec1m n\u0103m h\u1ecdc m\u1edbi, h\u1ecdc sinh c\u1ea7n l\u01b0u \u00fd m\u1ed9t s\u1ed1 \u0111i\u1ec3m c\u1ed1t l\u00f5i.<\/strong><\/p>\n

1. Ph\u1ea7n \u0110\u1ea1i s\u1ed1 To\u00e1n 8<\/strong><\/h2>\n

H\u1ecdc k\u1ef3 I<\/strong><\/h3>\n

To\u00e1n l\u1edbp 8 h\u1ecdc k\u1ef3 I t\u1eadp trung v\u00e0o hai ch\u1ee7 \u0111\u1ec1 c\u1ed1t l\u00f5i:<\/p>\n

    \n
  • H\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/li>\n
  • Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed<\/li>\n<\/ul>\n

    \u0110\u00e2y l\u00e0 n\u1ec1n m\u00f3ng \u0111\u1ec3 x\u1eed l\u00fd c\u00e1c d\u1ea1ng b\u00e0i quan tr\u1ecdng nh\u01b0: Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai, B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, B\u1ea5t \u0111\u1eb3ng th\u1ee9c… Y\u00eau c\u1ea7u h\u1ecdc sinh:<\/p>\n

      \n
    • N\u1eafm v\u1eefng 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c th\u01b0\u1eddng d\u00f9ng<\/li>\n
    • Th\u00e0nh th\u1ea1o c\u00e1c ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed: \u0111\u1eb7t nh\u00e2n t\u1eed chung, d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c, nh\u00f3m h\u1ea1ng t\u1eed\u2026<\/li>\n
    • Ngo\u00e0i ra, h\u1ecdc sinh kh\u00e1 – gi\u1ecfi c\u00f3 th\u1ec3 m\u1edf r\u1ed9ng t\u00ecm hi\u1ec3u m\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p m\u1edf r\u1ed9ng nh\u01b0:\n
        \n
      • H\u1ec7 s\u1ed1 b\u1ea5t \u0111\u1ecbnh<\/li>\n
      • \u0110\u1eb7t \u1ea9n ph\u1ee5<\/li>\n
      • Gi\u00e1 tr\u1ecb ri\u00eang<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

        Ngo\u00e0i ra, h\u1ecdc sinh c\u1ea7n luy\u1ec7n t\u1eadp th\u01b0\u1eddng xuy\u00ean d\u1ea1ng b\u00e0i nh\u00e2n \u2013 chia \u0111a th\u1ee9c, ch\u1ee7 y\u1ebfu r\u00e8n k\u1ef9 n\u0103ng t\u00ednh to\u00e1n c\u1ea9n th\u1eadn, tr\u00e1nh sai s\u00f3t do nh\u1ea7m l\u1eabn d\u1ea5u ho\u1eb7c sai th\u1ee9 t\u1ef1.<\/p>\n

        C\u1ea7n l\u00e0m t\u1ed1t c\u00e1c b\u00e0i t\u1eadp v\u1ec1 Ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1, \u0111\u00e2y c\u0169ng l\u00e0 1 d\u1ea1ng b\u00e0i kh\u00f4ng qu\u00e1 kh\u00f3, ch\u1ec9 c\u1ea7n ch\u1eafc ki\u1ebfn th\u1ee9c s\u00e1ch gi\u00e1o khoa v\u00e0 l\u00e0m th\u00eam 1 s\u1ed1 b\u00e0i \u1edf c\u00e1c s\u00e1ch tham kh\u1ea3o l\u00e0 c\u00f3 th\u1ec3 “chi\u1ebfn” t\u1ed1t. Kh\u00f4ng \u0111\u01b0\u1ee3c ch\u1ee7 quan ph\u1ea7n n\u00e0y v\u00ec \u0111\u00e2y ch\u00ednh l\u00e0 c\u00e1c b\u00e0i m\u1edf \u0111\u1ea7u cho d\u1ea1ng b\u00e0i R\u00fat g\u1ecdn \u1edf l\u1edbp 9, l\u00e0 1 trong nh\u1eefng d\u1ea1ng kh\u00f4ng th\u1ec3 thi\u1ebfu trong k\u00ec thi v\u00e0o l\u1edbp 10.<\/p>\n

        Ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1 l\u00e0 ch\u1ee7 \u0111\u1ec1 kh\u00f4ng qu\u00e1 kh\u00f3, ch\u1ec9 c\u1ea7n n\u1eafm ch\u1eafc ki\u1ebfn th\u1ee9c SGK v\u00e0 ch\u0103m ch\u1ec9 luy\u1ec7n m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp trong s\u00e1ch tham kh\u1ea3o l\u00e0 c\u00f3 th\u1ec3 x\u1eed l\u00fd t\u1ed1t. Tuy nhi\u00ean, \u0111\u00e2y l\u00e0 n\u1ed9i dung quan tr\u1ecdng, kh\u00f4ng th\u1ec3 ch\u1ee7 quan, m\u1edf \u0111\u1ea7u cho d\u1ea1ng b\u00e0i R\u00fat g\u1ecdn \u1edf l\u1edbp 9 – N\u1ed9i dung ch\u1eafc ch\u1eafn xu\u1ea5t hi\u1ec7n trong b\u00e0i thi tuy\u1ec3n sinh v\u00e0o l\u1edbp 10.<\/p>\n

        \"\"<\/p>\n

        H\u1ecdc k\u1ef3 II<\/strong><\/h3>\n

        H\u1ecdc sinh \u0111\u01b0\u1ee3c l\u00e0m quen v\u1edbi:<\/p>\n

          \n
        • \n

          X\u00e1c su\u1ea5t, ph\u01b0\u01a1ng tr\u00ecnh, c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh th\u01b0\u1eddng g\u1eb7p: Ki\u1ebfn th\u1ee9c ph\u1ea7n n\u00e0y trong SGK v\u00e0 b\u00e0i t\u1eadp kh\u00f4ng qu\u1ea3 kh\u00f3 v\u1edbi h\u1ecdc sinh, n\u1ebfu \u0111\u00e3 h\u1ecdc t\u1ed1t \u1edf HK1, h\u1ecdc sinh s\u1ebd kh\u00e1 d\u1ec5 th\u1edf khi b\u01b0\u1edbc sang HK2<\/p>\n<\/li>\n

        • \n

          Gi\u1ea3i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh – D\u1ea1ng b\u00e0i h\u1ecdc sinh t\u1eebng g\u1eb7p \u1edf l\u1edbp 6, 7: Th\u1ef1c ch\u1ea5t l\u00e0 d\u1ea1ng b\u00e0i gi\u1ea3i to\u00e1n c\u00f3 l\u1eddi v\u0103n, \u0111\u00e2y l\u00e0 d\u1ea1ng b\u00e0i t\u01b0\u01a1ng \u0111\u1ed1i d\u1ec5 nh\u01b0ng l\u1ea1i khi\u1ebfn nhi\u1ec1u h\u1ecdc sinh e d\u00e8 v\u00ec \u0111\u1ec1 b\u00e0i th\u01b0\u1eddng kh\u00e1 d\u00e0i, h\u1ecdc sinh c\u1ea7n ph\u00e2n t\u00edch k\u1ef9 l\u01b0\u1ee1ng t\u1eebng \u00fd, t\u1eebng c\u00e2u v\u00e0 n\u1eafm ch\u1eafc nh\u1eefng d\u1ea1ng b\u00e0i th\u01b0\u1eddng g\u1eb7p nh\u01b0: chuy\u1ec3n \u0111\u1ed9ng, c\u00f4ng vi\u1ec7c chung – ri\u00eang, v\u00f2i n\u01b0\u1edbc, n\u0103ng su\u1ea5t – th\u1eddi gian…<\/p>\n<\/li>\n<\/ul>\n

          2. Ph\u1ea7n H\u00ecnh h\u1ecdc To\u00e1n 8<\/strong><\/h2>\n

          \u26a0\ufe0f L\u01b0u \u00fd quan tr\u1ecdng:<\/strong> N\u1ebfu h\u1ecdc sinh c\u00f2n y\u1ebfu ho\u1eb7c l\u01a1 m\u01a1 \u1edf ph\u1ea7n H\u00ecnh h\u1ecdc 7, vi\u1ec7c ti\u1ebfp c\u1eadn H\u00ecnh h\u1ecdc 8 s\u1ebd g\u1eb7p nhi\u1ec1u kh\u00f3 kh\u0103n.<\/p>\n

          H\u1ecdc k\u1ef3 I<\/strong><\/h3>\n
            \n
          • Ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m: T\u1ee9 gi\u00e1c, T\u00ednh ch\u1ea5t – Nh\u1eadn d\u1ea1ng c\u00e1c t\u1ee9 gi\u00e1c \u0111\u1eb7c bi\u1ec7t (h\u00ecnh b\u00ecnh h\u00e0nh, h\u00ecnh ch\u1eef nh\u1eadt, h\u00ecnh thoi, h\u00ecnh vu\u00f4ng), Di\u1ec7n t\u00edch \u0111\u1ec1u ch\u01b0a qu\u00e1 kh\u00f3, h\u1ecdc sinh c\u1ea7n thu\u1ed9c v\u00e0 hi\u1ec3u c\u00e1c ki\u1ebfn th\u1ee9c trong ch\u01b0\u01a1ng tr\u00ecnh SGK.<\/li>\n
          • Y\u00eau c\u1ea7u: Hi\u1ec3u v\u00e0 v\u1eadn d\u1ee5ng \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t song song, vu\u00f4ng g\u00f3c, tam gi\u00e1c b\u1eb1ng nhau (\u0111\u00e3 h\u1ecdc \u1edf l\u1edbp 7) \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n<\/li>\n<\/ul>\n

            H\u1ecdc k\u1ef3 II<\/strong><\/h3>\n
              \n
            • Ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m: Tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng, c\u00e1c h\u1ec7 qu\u1ea3 t\u1eeb \u0111\u1ecbnh l\u00fd Talet v\u00e0 c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a Tam gi\u00e1c. C\u00e1c b\u00e0i to\u00e1n n\u00e0y kh\u00f4ng qu\u00e1 kh\u00f3 v\u1edbi h\u1ecdc sinh n\u1ebfu c\u00e1c em \u0111\u00e3 h\u1ecdc t\u1ed1t ph\u1ea7n Tam gi\u00e1c b\u1eb1ng nhay \u1edf ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 7.<\/li>\n
            • Th\u00e1ch th\u1ee9c: T\u01b0\u01a1ng t\u1ef1 nh\u01b0 \u1edf l\u1edbp 7, h\u1ecdc sinh ph\u1ea7n l\u1edbn g\u1eb7p kh\u00f3 kh\u0103n \u1edf c\u00e1c b\u00e0i t\u1eadp c\u1ea7n v\u1ebd th\u00eam \u0111\u01b0\u1eddng ph\u1ee5. \u0110\u00e2y l\u00e0 c\u00e1c d\u1ea1ng b\u00e0i d\u00e0nh cho \u0111\u1ed1i t\u01b0\u1ee3ng HSG. N\u1ebfu c\u00e1c em \u0111\u00e3 n\u1eafm ch\u1eafc ph\u1ea7n n\u00e0y \u1edf H\u00ecnh h\u1ecdc 7 th\u00ec c\u0169ng kh\u00f4ng g\u1eb7p qu\u00e1 nhi\u1ec1u tr\u1ee3 ng\u1ea1i v\u1edbi c\u00e1c b\u00e0i to\u00e1n trong SGK.<\/li>\n
            • M\u1edf r\u1ed9ng – H\u00ecnh h\u1ecdc kh\u00f4ng gian: Nhi\u1ec1u h\u1ecdc sinh c\u1ea3m th\u1ea5y \u201ckh\u00f3\u201d do y\u1ebfu t\u1ed1 tr\u1ef1c quan m\u1edbi l\u1ea1, ch\u1ee9 th\u1ef1c ch\u1ea5t c\u00e1c b\u00e0i to\u00e1n thi\u00ean v\u1ec1 nh\u1eadn d\u1ea1ng v\u00e0 t\u01b0 duy h\u00ecnh \u1ea3nh, d\u1ec5 h\u01a1n so v\u1edbi c\u00e1c b\u00e0i to\u00e1n ch\u1ee9ng minh. L\u1eddi khuy\u00ean \u0111\u1ec3 c\u00e1c em x\u1eed l\u00fd t\u1ed1t b\u00e0i t\u1eadp n\u00e0y l\u00e0 ch\u0103m \u0111\u1ecdc s\u00e1ch, h\u00ecnh dung kh\u00f4ng gian qua h\u00ecnh v\u1ebd, luy\u1ec7n t\u1eadp nhi\u1ec1u l\u00e0 c\u00f3 th\u1ec3 v\u01b0\u1ee3t qua t\u00e2m l\u00fd e ng\u1ea1i ban \u0111\u1ea7u.<\/li>\n<\/ul>\n

              \"\"<\/p>\n

              H\u00ecnh h\u1ecdc 8 kh\u00f4ng th\u1ef1c s\u1ef1 qu\u00e1 kh\u00f3 n\u1ebfu h\u1ecdc sinh c\u00f3 n\u1ec1n t\u1ea3ng v\u1eefng ch\u1eafc t\u1eeb ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 7 v\u00e0 bi\u1ebft c\u00e1ch h\u1ec7 th\u1ed1ng h\u00f3a ki\u1ebfn th\u1ee9c. T\u1eeb vi\u1ec7c hi\u1ec3u s\u00e2u c\u00e1c t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc c\u01a1 b\u1ea3n \u0111\u1ebfn l\u00e0m quen v\u1edbi h\u00ecnh h\u1ecdc kh\u00f4ng gian, \u0111i\u1ec1u quan tr\u1ecdng nh\u1ea5t v\u1eabn l\u00e0 gi\u1eef v\u1eefng t\u00e2m l\u00fd, \u0111\u1ecdc k\u1ef9 l\u00fd thuy\u1ebft, luy\u1ec7n t\u1eadp \u0111\u1ec1u \u0111\u1eb7n v\u00e0 kh\u00f4ng ng\u1ea1i th\u1eed th\u00e1ch. Ch\u00fac c\u00e1c em s\u1ebd c\u00f3 s\u1ef1 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t tr\u01b0\u1edbc khi b\u01b0\u1edbc v\u00e0o l\u1edbp 8 v\u00e0 \u0111\u1ea1t th\u00e0nh t\u00edch cao trong n\u0103m h\u1ecdc s\u1eafp t\u1edbi.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 8 ti\u1ebfp t\u1ee5c m\u1edf r\u1ed9ng v\u00e0 n\u00e2ng cao t\u1eeb n\u1ec1n t\u1ea3ng c\u1ee7a l\u1edbp 7, b\u1eaft \u0111\u1ea7u xu\u1ea5t hi\u1ec7n nh\u1eefng ph\u1ea7n ki\u1ebfn th\u1ee9c n\u1eb7ng v\u00e0 kh\u00f3.\u00a0N\u1ebfu h\u1ecdc sinh \u0111\u00e3 n\u1eafm ch\u1eafc c\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m l\u1edbp 7 th\u00ec vi\u1ec7c ti\u1ebfp c\u1eadn ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 8 s\u1ebd thu\u1eadn l\u1ee3i h\u01a1n r\u1ea5t nhi\u1ec1u. Tr\u01b0\u1edbc…<\/p>\n","protected":false},"author":2,"featured_media":2397,"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":[32],"_links":{"self":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2396"}],"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=2396"}],"version-history":[{"count":1,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2396\/revisions"}],"predecessor-version":[{"id":2400,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2396\/revisions\/2400"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media\/2397"}],"wp:attachment":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media?parent=2396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/categories?post=2396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/tags?post=2396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}