{"id":368,"date":"2026-05-05T04:42:02","date_gmt":"2026-05-05T04:42:02","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/on-tap-giua-ki-2-toan-11-nam-2024-2025-truong-thpt-tran-phu-ha-noi\/"},"modified":"2026-05-05T07:14:46","modified_gmt":"2026-05-05T07:14:46","slug":"on-tap-giua-ki-2-toan-11-nam-2024-2025-truong-thpt-tran-phu-ha-noi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/on-tap-giua-ki-2-toan-11-nam-2024-2025-truong-thpt-tran-phu-ha-noi\/","title":{"rendered":"\u00d4n t\u1eadp gi\u1eefa k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i"},"content":{"rendered":"

B\u1ed9 t\u00e0i li\u1ec7u \u00d4n t\u1eadp gi\u1eefa k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n k\u1ef9 l\u01b0\u1ee1ng, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc, gi\u00fap h\u1ecdc sinh h\u1ec7 th\u1ed1ng h\u00f3a ki\u1ebfn th\u1ee9c v\u00e0 l\u00e0m quen v\u1edbi c\u00e1c d\u1ea1ng b\u00e0i thi chu\u1ea9n. T\u00e0i li\u1ec7u bao g\u1ed3m c\u1ea3 ph\u1ea7n tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn, ph\u1ee7 r\u1ed9ng c\u00e1c chuy\u00ean \u0111\u1ec1. H\u00e3y c\u00f9ng tailieuonthi<\/strong><\/a> kh\u00e1m ph\u00e1 ngay \u0111\u1ec3 chu\u1ea9n b\u1ecb th\u1eadt t\u1ed1t cho k\u1ef3 ki\u1ec3m tra gi\u1eefa k\u1ef3 nh\u00e9!<\/p>\n

N\u1ed9i dung \u00d4n t\u1eadp gi\u1eefa k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong><\/h2>\n

T\u00e0i li\u1ec7u \u00d4n t\u1eadp gi\u1eefa k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong>, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc v\u00e0 c\u1ea5u tr\u00fac \u0111\u1ec1 to\u00e1n gi\u1eefa k\u00ec 2 l\u1edbp 11. N\u1ed9i dung bao g\u1ed3m 2 chuy\u00ean \u0111\u1ec1, m\u1ed7i chuy\u00ean \u0111\u1ec1 g\u1ed3m 3 ph\u1ea7n ch\u00ednh:<\/p>\n

Chuy\u00ean \u0111\u1ec1 1: H\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 l\u00f4garit<\/strong><\/p>\n

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  • Ph\u1ea7n 1: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n ch\u1ecdn (50 c\u00e2u), m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 sau<\/strong><\/li>\n<\/ul>\n

    C\u00e2u 1.<\/strong> Cho a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng, m, n t\u00f9y \u00fd. Ph\u00e1t bi\u1ec3u n\u00e0o sau \u0111\u00e2y l\u00e0 ph\u00e1t bi\u1ec3u sai? A. a^m + a\u207f = a^m+n . B. (a^m)\/(b\u207f) = ( a\/b )^m . C. (a^m)\/(a\u207f) = a^m-n . D. (a^m)\u207f = a^m \u00b7 n .<\/p>\n

    C\u00e2u 2.<\/strong> Cho x, y l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng v\u00e0 m, n l\u00e0 hai s\u1ed1 th\u1ef1c t\u00f9y \u00fd. \u0110\u1eb3ng th\u1ee9c n\u00e0o sau \u0111\u00e2y l\u00e0 sai? A. x^m \u00b7 x\u207f = x^m+n . B. (x^m)\u207f = x^m \u00b7 n . C. (x \u00b7 y)\u207f = x\u207f \u00b7 y\u207f . D. (x^m)\u207f = x^m\u207f .<\/p>\n

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    • Ph\u1ea7n 2: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (5 c\u00e2u),\u00a0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 sau<\/strong><\/li>\n<\/ul>\n

      C\u00e2u 1.<\/strong> Cho bi\u1ec3u th\u1ee9c: A = log\u2082 x\u00b2 + log_1\/2 x\u00b3 + log\u2084 x.\n<\/p>\n

      C\u00e2u 2.<\/strong> Bi\u1ebft a > 0, a \u2260 1 . C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

        \n
      • Ph\u1ea7n 3: B\u00e0i t\u1eadp t\u1ef1 lu\u1eadn (20 b\u00e0i),\u00a0 m\u1ed9t s\u1ed1 b\u00e0i minh h\u1ecda nh\u01b0 sau<\/strong><\/li>\n<\/ul>\n

        B\u00e0i 1:<\/strong> T\u00ednh a) (1\/5)\u207b\u00b2 ; b) 4^3\/2 ; c) (1\/8)^2\/3 ; d) (1\/16)^-0.75 .<\/p>\n

        B\u00e0i 2:<\/strong> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh
        \na) 27^2\/3 + 81^0.75 – 25^0.5 ; b) 4^2 – 3\u221a7 \u00b7 8^2\u221a7 .<\/p>\n

        Chuy\u00ean \u0111\u1ec1 2: Quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian<\/strong><\/p>\n

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        • Ph\u1ea7n 1: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n ch\u1ecdn (29 c\u00e2u), m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 d\u01b0\u1edbi \u0111\u00e2y<\/strong><\/li>\n<\/ul>\n

          C\u00e2u 1.<\/strong> Trong kh\u00f4ng gian, cho \u0111\u01b0\u1eddng th\u1eb3ng d v\u00e0 \u0111i\u1ec3m O . Qua O c\u00f3 bao nhi\u00eau \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng d A. 3. B. v\u00f4 s\u1ed1. C. 1.\u00a0D. 2.<\/p>\n

          C\u00e2u 2.<\/strong> Trong kh\u00f4ng gian cho tr\u01b0\u1edbc \u0111i\u1ec3m M v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0394 . C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua M v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi \u0394 th\u00ec:
          \nA. Vu\u00f4ng g\u00f3c v\u1edbi nhau.
          \nB. Song song v\u1edbi nhau.
          \nC. C\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi m\u1ed9t m\u1eb7t ph\u1eb3ng.
          \nD. C\u00f9ng thu\u1ed9c m\u1ed9t m\u1eb7t ph\u1eb3ng.<\/p>\n

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          • Ph\u1ea7n 2: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u), m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 d\u01b0\u1edbi \u0111\u00e2y<\/strong><\/li>\n<\/ul>\n

            C\u00e2u 1.<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 SA vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng \u0111\u00e1y. G\u1ecdi H, K theo th\u1ee9 t\u1ef1 l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a A tr\u00ean c\u00e1c c\u1ea1nh SB, SD .<\/p>\n

            C\u00e2u 2.<\/strong> Cho t\u1ee9 di\u1ec7n OABC c\u00f3 OA, OB, OC \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c v\u1edbi nhau. G\u1ecdi OK l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c OBC v\u00e0 OH l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c OAK .<\/p>\n

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            • Ph\u1ea7n 3: B\u00e0i t\u1eadp t\u1ef1 lu\u1eadn (14 b\u00e0i), m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda nh\u01b0 d\u01b0\u1edbi \u0111\u00e2y<\/strong><\/li>\n<\/ul>\n

              B\u00e0i 1.<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh, tam gi\u00e1c SAD l\u00e0 tam gi\u00e1c \u0111\u1ec1u v\u00e0 M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AD . T\u00ednh g\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng BC v\u00e0 SA ; BC v\u00e0 SM .<\/p>\n

              B\u00e0i 2.<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng t\u00e2m O v\u00e0 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u b\u1eb1ng a . G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u00e1c c\u1ea1nh SA, AB .<\/p>\n

              a) T\u00ednh g\u00f3c gi\u1eefa c\u00e1c c\u1eb7p \u0111\u01b0\u1eddng th\u1eb3ng sau: MN v\u00e0 SD ; MO v\u00e0 SB .<\/p>\n

              b) T\u00ednh tang c\u1ee7a g\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng SN v\u00e0 BC .<\/p>\n

              T\u1ea3i \u00d4n t\u1eadp gi\u1eefa k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong><\/h2>\n

              V\u1edbi n\u1ed9i dung b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 th\u1ed1ng b\u00e0i t\u1eadp \u0111a d\u1ea1ng, \u00d4n t\u1eadp gi\u1eefa k\u00ec 2 To\u00e1n 11 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Tr\u1ea7n Ph\u00fa H\u00e0 N\u1ed9i<\/strong> l\u00e0 t\u00e0i li\u1ec7u kh\u00f4ng th\u1ec3 b\u1ecf qua gi\u00fap h\u1ecdc sinh n\u00e2ng cao ki\u1ebfn th\u1ee9c, l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n. H\u00e3y nhanh tay t\u1ea3i ngay t\u00e0i li\u1ec7u theo \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y<\/p>\n