ᠠᠩᠬᠠ ᠬᠤᠶᠡᠷ ᠤᠨ ᠲᠤᠤᠷᠠᠳᠤ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠡᠴᠦᠰ ᠤᠨ ᠰᠢᠯᠭᠠᠯᠳᠠ 初二下学期期末考试题.pdf
ᠠᠩᠬᠠ ᠬᠤᠶᠡ ᠷ ᠦᠨ ᠲᠣᠭ ᠠᠨ ᠤ ᠤᠬ ᠠᠭᠠᠨ ᠤ ᠬᠤᠭᠤ ᠴᠠᠭ ᠠᠨ ᠡ ᠴᠦᠰ ᠤ᠋ᠨ ᠰᠢᠯ ᠭᠠᠯᠳᠠ ᠨᠢᠭᠡ ᠂ ᠰᠤᠨᠭᠭᠤᠬᠤ ᠰᠡᠳᠤ ᠪ᠄ ᠵᠥᠪ ᠰᠣᠩᠭᠤᠭᠳᠠᠬᠤᠨ ᠤ ᠬᠠᠷᠠ ᠭᠠᠯᠵᠠ ᠭᠰᠠᠨ ᠳ᠋ᠤᠭᠠ ᠷ ᠢ ᠬᠦᠰ ᠦᠨᠦᠭ ᠳᠤ ᠳ᠋ᠤ ᠲᠠᠭᠯᠠ ᠄ ︵ ᠰᠡᠳᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤ ᠪᠢ᠂ ᠨᠡᠢᠳᠠ 3 0ᠬᠤ ᠪᠢ ︶ ⒈ ᠲᠤᠤᠷᠠᠬᠢ ᠨᠥᠬᠦᠴ ᠡᠯ ᠨᠢ ᠵ ᠢᠰᠢᠭᠦᠯᠵᠢᠨ ᠪᠣᠯᠬᠤ ᠵ ᠢ ᠮᠠᠭᠠᠳᠯᠠᠵᠤ ᠲᠡᠢ ᠯᠬᠦ ᠦᠭᠡᠢ ᠨᠢ ︵ ︶ A. ᠬᠤᠶ ᠠᠷ ᠬᠣᠣᠰ ᠡᠰᠡᠷᠭᠦ ᠲᠠ ᠯᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠵᠡᠷᠭᠡᠴ ᠡᠭᠡ ᠪᠣᠯᠬᠤ ᠲᠦᠷᠪᠡᠯᠵᠢ ᠨ B. ᠨᠢᠭᠡ ᠬ ᠣᠣᠰ ᠡᠰᠡᠷ ᠭᠦ ᠲᠠᠯᠠ ᠨᠢ ᠵᠡ ᠷᠭᠡᠴ ᠡᠭᠡ ᠪᠥᠭᠡᠳ ᠲᠠᠨᠭ ᠴᠡᠭᠦᠤ ᠪᠣᠯᠬᠤ ᠲ ᠦᠷᠪᠡᠯᠵᠢ ᠨ C. ᠨᠢᠭᠡ ᠬ ᠣᠣᠰ ᠡᠰᠡᠷ ᠭᠦ ᠲᠠ ᠯᠠ ᠨ ᠢ ᠵᠡᠷᠭᠡᠴ ᠡᠭᠡ᠂ ᠨᠥᠭᠥᠭᠡ ᠨᠢᠭᠡ ᠬᠣᠣᠰ ᠡᠰᠡᠷᠭᠦ ᠲᠠ ᠯᠠ ᠨᠢ ᠲᠡᠨᠭ ᠴᠡᠭᠦᠤ ᠪᠣᠯᠬᠤ ᠲᠦᠷᠪᠡᠯᠵᠢ ᠨ D. ᠬᠤᠶ ᠠᠷ ᠬᠣᠣᠰ ᠡᠰᠡᠷᠭᠦ ᠲᠠ ᠯᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠲᠡᠨᠭ ᠴᠡᠭᠦᠤ ᠪᠣᠯ ᠬᠤ ᠲᠦᠷᠪᠡᠯᠵᠢ ᠨ ⒉ ᠵ ᠢᠷᠤᠭ ᠮ ᠡᠳᠤ ᠄ ᠵᠢ ᠰᠢᠭᠦᠯᠵᠢ ᠨABCD ᠳ᠋ᠤ ᠲᠠᠰ ᠢᠭᠤᠪᠴᠢ AC ,BD ᠨᠢ ᠴ ᠡᠭ O ᠳ᠋ᠤ ᠤᠭᠳᠤᠯ ᠤᠯᠴᠠᠬᠤ ᠪᠥ ᠭᠡᠳ AD = 8 , BD = 12 ,AC = 6 ᠪᠤᠯ ∆OBC ᠶᠢᠨ ᠬᠦᠷᠢ ᠶᠠᠨ ᠤ ᠤ ᠷᠳᠤ ᠨᠢ ︵ ︶ A . 26 B. 20 C . 17 D . 13 ⒊ ᠥᠭᠭᠦᠭᠳᠡᠭᠰ ᠡᠨ ᠨᠢ ᠨᠢᠭᠡᠳᠤᠭᠡ ᠷ ᠵ ᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠨᠭᠺᠼ 𝑦 = 𝑘𝑥 + 𝑏 ᠳ᠋ᠤ 𝑦 ᠨᠢ 𝑥 ᠤ᠋ᠨ ᠨᠡᠮᠡᠭᠳᠡᠬᠦ ᠵᠢ ᠲᠠᠭᠠᠯᠳ ᠤᠨ ᠬᠣᠷᠤᠭᠳ ᠠᠬᠤ ᠪᠥᠭᠡᠳ 𝑘𝑏 3 B. 𝑥 −3 C. 𝑥 ≥ −3 D. 𝑥 ≤ −3 ⒎ᠬᠠᠪ ᠳᠠᠭᠠ ᠢ ᠶᠢ ᠨ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴᠦᠭᠳᠤ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ ᠤ᠋ᠨ ᠰᠢ ᠰᠲ᠋ᠧᠮ 𝑥𝑜𝑦 ᠳ᠋ᠤ ᠴᠡᠭ A( −4 ,0 ) ᠪᠠ B ᠪᠤᠢ᠃ ᠴ ᠡᠭ B ᠨᠢ ᠰᠢᠯᠤᠭᠤᠨ 𝑦= 𝑥+ 2 ᠲᠡᠭᠡᠷ ᠠ ᠤ ᠷᠤᠰᠢ ᠬᠤ ᠪᠥᠭᠡᠳ A, B ᠬᠤᠶ ᠠᠷ ᠴ ᠡᠭ ᠦᠨ ᠬᠣᠭᠤᠷᠤᠨᠳ ᠤᠬᠢ ᠵᠠᠢ ᠵ ᠢ ᠬᠠᠮᠤᠭ ᠤᠬᠤᠷ ᠪᠣᠯᠭᠠᠬ ᠤ ᠬᠡᠪᠡᠯ ᠴᠡᠭ B ᠤ᠋ᠨ ᠪᠠᠢᠷᠢ ᠰᠢᠯ ᠨᠢ ︵ ︶ A. (− 2 , −2 ) B. ( −2 ,2 ) C. ( −3 ,− 1) D. ( −3 ,− 2) ⒏ ᠠ ᠩᠬᠠ ᠬᠤᠶ ᠠᠷ ᠤ᠋ᠨ ᠰᠤᠷ ᠤᠭᠴ ᠢ ᠶᠢ ᠨ ᠭᠤᠷᠪᠠᠨ ᠬᠡᠯᠡᠨ ᠤ ᠶᠠᠷᠢ ᠶᠠ ᠢ ᠯᠡᠳᠭᠡᠯ ᠦ ᠨ ᠮᠦ ᠷᠤᠢ ᠴᠡᠭᠡᠨ ᠳ᠋ ᠤ11 ᠬᠢᠨᠠ ᠭᠴᠢ ᠬᠤᠪᠢ ᠣᠯᠭᠤᠵᠤ᠂ ᠮᠥ ᠷᠦᠢ ᠴᠡᠭᠡᠨ ᠦ ᠡᠴᠦᠰ ᠲᠤ ᠬᠠᠮᠤᠭ ᠥᠨᠳ ᠦᠷ ᠪᠠ ᠬᠠᠮᠤᠭ ᠲᠤᠤᠷᠠ ᠬᠤᠪᠢ ᠵᠢ ᠬᠠᠰ ᠤᠨ ᠬᠠᠶ ᠠᠵᠤ ᠳ᠋ᠦᠩ ᠢ ᠨᠡᠢᠳᠡᠯᠡ ᠨᠡ᠂ ᠡᠭᠦᠨ ᠳ᠋ ᠤ ᠬᠤᠪᠢᠷᠠᠯᠳᠠ ᠭᠠᠷᠬᠤ ᠦᠭᠡ ᠢ ᠬᠡᠮᠵᠢᠭᠳ ᠡᠬᠦᠨ ᠨ ᠢ ︵ ︶ A. ᠲᠤᠮᠳ ᠠᠴᠢ ᠲᠣᠭᠠ B. ᠰᠠᠷᠨᠢ ᠴᠠ C. ᠲᠤᠮᠳ ᠠ ᠪᠠᠢᠷᠢ ᠶᠢᠨ ᠲᠣᠭᠠ D. ᠮᠣᠳ᠋ ⒐ ᠲᠤᠤᠷᠠᠬᠢ ᠭᠤᠷᠪᠠᠨ ᠪᠦᠯ ᠦᠭ ᠲᠣᠭᠠ ᠨᠢᠭᠡ ᠪᠦᠷᠢ ᠪᠠᠷ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ ᠪᠦᠳ ᠤᠭᠡᠪᠡᠯ ᠲᠡᠭᠰ ᠢ ᠦ ᠨᠴᠦᠭᠳ ᠤ ᠭ ᠤᠷᠪᠠᠯᠵᠢ ᠨ ᠪᠦᠷᠢ ᠯᠳᠦᠭᠦ ᠯᠵᠤ ᠲᠡᠢ ᠯᠬᠦ ᠨ ᠢ( ) A. 1 ,3 ,3 B. 3 , 4 , 5 C. 5 ,6 ,7 D. 2 ,4 ,5 ⒑𝑥 ᠤ᠋ᠨ ᠲᠤᠬᠠᠢ ᠨᠢᠭᠡ ᠦᠯᠤ ᠮᠡᠳᠡ ᠭᠳᠡᠭᠴ ᠢᠲᠡᠢ ᠬᠣᠶ ᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰ ᠢᠳᠭᠡᠯ 𝑥 2 + 2𝑥 − 𝑎= 0 ᠲᠤ ᠲᠡᠨᠭ ᠴᠡᠭᠦᠤ ᠬᠤᠶ ᠠᠷ ᠪᠤᠳᠠᠳᠤ ᠲᠣᠭᠠᠨ ᠢ ᠵᠠᠭᠤᠷ ᠲᠠᠢ᠂ ᠲᠡᠭᠡᠪᠡ ᠯ 𝑎 ᠶᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨᠢ ︵ ︶ A. 1 B. −1 C. 14 D. − 14 ᠬᠤᠶ ᠡᠷ᠂ ᠬ ᠠᠭᠠᠯᠳ ᠠ ᠲᠠᠭᠯᠠᠬᠤ ᠰᠡᠳᠤ ᠪ᠄ ︵ ᠰᠡᠳᠤ ᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨᠡᠢᠲ ᠡ 30 ᠬᠤᠪᠢ ︶ ⒒ ᠹᠦᠨᠭᠺᠼ y= 2𝑥 + 𝑚 − 1 ᠨᠢ ᠰᠢᠭᠤᠳ ᠬᠠᠷᠢ ᠴᠠᠯᠳ ᠤ ᠹᠦᠨᠭᠺᠼ ᠪᠤᠯ 𝑚 ᠨᠢ __ __ __ __ . ⒓ ᠴ ᠡᠭ𝑃 1 (− 3, 𝑦1 ),𝑃 2 (2 ,𝑦 2 ) ᠨᠢ ᠰᠢᠯᠤᠭᠤᠨ 𝑦 = −2 𝑥+ 1 ᠲᠡᠭᠡᠷ ᠠ ᠤᠷᠤᠰᠢ ᠬᠤ ᠬᠤᠶ ᠠᠷ ᠴᠡᠭ ᠪᠤᠯ 𝑦1 ___ 𝑦2 . ( ᠶ ᠡᠬᠡ ᠪᠠᠭᠠ ᠶᠢᠨ ᠲᠡᠮᠳ ᠡᠭ ᠢ ᠲᠠᠭᠯᠠ ) ⒔ ᠨᠢᠭᠡᠳᠤᠭᠡ ᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠨᠭᠺᠼ 𝑦 = −5 𝑥+ 3 ᠶᠢᠨ ᠲᠠᠭᠠᠷᠢ ᠬᠤ ᠮᠥᠴ ᠡ ᠨᠢ __ __ __ _. ⒕ ᠲᠡᠭᠴᠡ ᠭᠦᠤ ᠲᠠᠯᠠᠳ ᠤ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ABC ᠶᠢᠨ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ ᠤ ᠷᠳᠤ ᠨᠢ 4𝑐𝑚 ᠪᠤᠯ ᠲᠠᠬᠦᠨ ᠦ ᠦᠨ ᠳᠤᠷ ᠨᠢ ___ __ __ . ⒖ ᠷᠣᠮᠪ ᠤ᠋ᠨ ᠬᠤᠶ ᠠᠷ ᠲᠠᠰ ᠢᠭᠤᠪᠴᠢ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ 6 𝑐𝑚 ᠪᠠ 8𝑐𝑚 ᠪᠤᠯ ᠲᠡᠭᠦᠨ ᠦ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠤ ᠷᠳᠤ ᠨᠢ __ ___ __ ___ . ⒗ ᠬᠤᠶ ᠠᠷ ᠡ ᠭᠴᠡ ᠲᠠᠯᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ 6 ᠪᠠ 8 ᠪᠣᠯᠬᠤ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴᠦᠭᠳᠤ ᠭᠤᠷᠪᠠᠯᠵᠢ ᠨ ᠤ ᠵᠢᠰᠢ ᠭᠦᠤ ᠲᠠᠯᠠ ᠲᠡᠭᠡᠷᠡ ᠬᠢ ᠲ ᠤᠮᠳᠠ ᠱᠤᠭᠤᠮ ᠤ᠋ᠨ ᠤᠷᠳᠤ ᠨᠢ__ __ __ ___ . ⒘ ᠬᠡᠷ ᠪᠡ 5− √3 ᠶ ᠢᠨ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭᠠᠨ ᠤ ᠬᠡᠰᠡᠭ ᠨᠢ 𝑎, ᠪᠤᠳᠠᠷᠬᠠᠢ ᠶᠢᠨ ᠬᠡᠰᠡᠭ ᠨᠢ b ᠪᠤᠯ 𝑎 − 2𝑏 ᠶᠢ ᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨᠢ __ __ __ _. ⒙ ᠬᠡᠷ ᠪᠡ( 𝑘− 2) 𝑥 | 𝑘| − 2𝑥 + 1= 0 ᠨᠢ ᠨ ᠢᠭᠡ ᠦ ᠯᠤ ᠮ ᠡᠳᠡᠭᠳᠡ ᠭᠴᠢᠲᠡᠢ ᠬᠣᠶ ᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠪᠤᠯ 𝑘= ___ ___ . ⒚ ᠨᠢᠭᠡᠨ ᠰᠤᠷᠤ ᠭᠴᠢ ᠲᠠ ᠯᠠ ᠶ ᠢᠨ ᠤᠷᠳᠤ ᠨᠢ 2 ᠪᠣᠯᠬᠤ ᠲᠡᠨᠭ ᠴᠡᠭᠦᠤ ᠲᠠᠯᠠ ᠳᠤ ᠭᠤ ᠷᠪᠠᠯᠵᠢ ᠨ ᠬᠡᠯ ᠪᠡᠷᠢ ᠳᠠᠢ ᠪᠠᠢᠭᠰ ᠠᠨ ᠳ᠋ᠤ ᠰᠤᠮᠤ ᠬᠠᠷᠪᠤᠵᠤ ᠨᠠᠭᠠᠳᠪᠠ ᠂ ᠵᠢ ᠷᠤᠭ ᠮ ᠡᠳᠤ ᠄ E ,F ,D ᠪᠤᠯ ᠭᠤᠷᠪᠠᠨ ᠲᠠ ᠯᠠ ᠶ ᠢᠨ ᠲᠤᠮᠳ ᠠ ᠴᠡᠭ ᠪᠤᠯ ᠰᠡᠭᠦ ᠳᠡᠷ ᠲᠠᠢ ᠬᠡᠰᠡᠭ ᠲᠤ ᠲᠤᠰ ᠬᠤ ᠶᠢᠨ ᠲᠣᠬᠢ ᠶᠠᠯᠳ ᠤᠮᠵᠢ ᠨᠢ __ __ __ ___ _. E F D ⒛ᠨᠢᠭᠡᠨ ᠴᠥᠭᠦᠷᠦᠮ ᠳ᠋ ᠤ ᠡ ᠳᠤᠢ ᠲᠡᠳ ᠤᠢ ᠵᠢᠭᠠᠰᠤ ᠪᠤᠢ᠂ ᠵᠢᠭᠠᠰᠤ ᠴᠢᠨ ᠠᠴᠠ ᠵᠢᠭᠠᠰᠤ ᠨ ᠤ ᠲᠣᠭᠠ ᠵᠢ ᠪᠠᠷᠤᠭᠴᠠᠭᠠᠯᠠᠬᠤ ᠤ᠋ᠨ ᠲᠥ ᠯᠦᠭᠡ 50 ᠵ ᠢᠭᠠᠰᠤ ᠨ ᠳ᠋ᠤ ᠲᠡᠮᠳ ᠡᠭ ᠲᠠᠯᠪᠢᠨ ᠴᠥᠭᠦᠷᠦᠮ ᠳ᠋ ᠤ ᠬᠢᠵᠤ ᠲᠠᠬᠢ ᠨ40 ᠵᠢᠭᠠᠰᠤ ᠰᠦ ᠬᠦᠨ ᠣᠯᠤᠭᠰ ᠠᠨ ᠪᠥᠭᠡᠳ ᠲᠡᠭᠦᠨ ᠦ ᠲᠤᠳ ᠤᠷᠠ 20 ᠵᠢᠭᠠ ᠰᠤ ᠨᠢ ᠲᠠᠮᠳ ᠡᠭ ᠲᠠᠢ ᠵᠢᠭᠠᠰᠤ ᠪᠠᠢᠯᠠ᠂ ᠲᠡᠭᠡᠪᠡ ᠯ ᠴ ᠥᠭᠦᠷᠦᠮ ᠳ᠋ ᠤ ᠪᠠᠷᠤᠭ __ __ __ _ ᠵ ᠢᠭᠠᠰ ᠤ ᠪᠠᠢ ᠨᠠ ᠬᠡᠵᠤ ᠪᠠᠷᠤᠭᠴᠠᠭ ᠠᠯᠠᠪᠠ ᠃ ᠭᠤᠷ ᠪᠠ᠂ ᠪᠣᠳᠤ ᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠳᠤ ᠪ ︵ 90 ᠬᠤ ᠪᠢ ︶ 21 . ( 14 ᠬᠤᠪᠢ )ᠵᠢᠷᠤᠭ ᠮ ᠡᠳᠤ ᠄ P ᠪᠤᠯ ᠲᠡᠭᠰ ᠢ ᠲᠦᠷ ᠪᠡᠯᠵᠢ ᠨABCD ᠶᠢᠨ ᠲᠤᠳ ᠤᠷᠠᠬᠢ ᠨ ᠢᠭᠡᠨ ᠴ ᠡᠭ ᠂ ∠ PAD = ∠P DA = 15 0. ᠪᠠᠳᠤᠯᠠ᠄ ∆P BC ᠪᠤᠯ ᠵᠥ ᠪ ᠭ ᠤᠷᠪᠠᠯᠵᠢ ᠨ᠃ 22 . ( 14 ᠬᠤᠪᠢ) ᠨᠢᠭᠡᠳᠤᠭᠡ ᠷ ᠵ ᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠨᠭᠺᠼ 𝑦 = 𝑘𝑥 + 𝑏 ᠨᠢ ᠴᠡᠭ A( −2 ,− 1) ,𝐵 (1 ,3 ) ᠵᠢ ᠲᠠᠭᠠᠷᠢ ᠨᠠ᠂ ᠪᠠᠰᠠ 𝑥 ᠲᠡᠨᠭ ᠬᠡᠯᠢᠭ ᠲᠠᠢ ᠴᠡᠭ C ᠳ᠋ᠤ᠂ 𝑦 ᠲᠡᠨᠭ ᠬᠡᠯᠢᠭ ᠲᠠᠢ ᠴᠡᠭ D ᠳ᠋ᠤ ᠤᠭᠳᠤᠯ ᠤᠯᠴᠠᠨᠠ᠃ (1) ᠡᠨᠡᠬᠦ ᠨᠢᠭᠡᠳᠤᠭᠡ ᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠨᠭ ᠺᠼ ᠦ ᠨ ᠠᠨᠠᠯᠢ ᠰ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ ᠢ ᠤᠯ ᠃ (2) ∆A OB ᠶᠢ ᠨ ᠲᠠᠯᠠ ᠪᠠᠢ ᠵᠢ ᠤᠯ ᠃ 23 . ︵15 ᠬᠤᠪᠢ ︶ᠪᠤᠳᠤ᠄ (1) ( 12 ) −1 + (3 .14 − 𝜋) 0+ √( −3 ) 2 + 1 √2 +1 . (2) ᠥᠭᠭᠦᠭᠳᠡᠭᠰ ᠡᠨ𝑥 = 1+ √3 ,𝑦 = 1− √3 ᠪᠤᠯ ᠠᠯ ᠭᠸᠪ ᠷᠠ ᠶ ᠢᠨ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ 𝑥 2 − 𝑥𝑦 + 𝑦 2 ᠶᠢ ᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠤᠯ ᠃ (3) ᠪᠤᠳᠠᠳᠤ ᠲᠣᠭᠠ 𝑎 ,𝑏 ᠶ ᠢᠨ ᠲᠣᠭᠠᠨ ᠲ ᠡᠨᠭᠬᠡᠯᠢ ᠭ ᠲᠡ ᠭᠡᠷᠡ ᠬᠢ ᠪᠠᠢᠷᠢ ᠨᠢ ᠲᠤᠤᠷᠠ ᠬᠢ ᠮᠠᠳᠤ ᠪᠤᠯ ᠬᠢ ᠯᠪᠠᠷᠴᠢᠯᠠ: √ (𝑎 − 1) 2− √ (𝑎 − 𝑏) 2. 24 . ︵15 ᠬᠤᠪᠢ ︶ᠲᠠᠷᠠᠭ ᠠᠬᠢ ᠲᠡᠭᠰᠢ ᠳᠭᠡᠯ ᠢ ᠪᠤᠳᠤ ᠄ (1) 3 𝑥 2 + 8𝑥 − 3= 0 . (2) 𝑥 2+ 2√ 3𝑥 + 3= 0. (3) 4( 𝑥− 3) 2+ 𝑥( 𝑥− 3) = 0 25 . ︵16 ᠬᠤᠪᠢ ︶ᠨᠢᠭᠡᠨ ᠵ ᠢᠮᠢᠰ ᠦᠨ ᠬ ᠤᠳᠠᠯ ᠳᠤᠭᠠ ᠠ᠂ ᠡ ᠬᠤᠶ ᠠᠷ ᠡᠭᠦ ᠯᠳᠡᠷ ᠦᠨ ᠵ ᠢᠮᠢᠰ ᠢ ᠨᠡᠢᠳᠡ 140 kg ᠣ ᠷᠤᠭᠤᠯᠬᠤ ᠪᠠᠷ ᠪᠠᠢ ᠨᠠ᠃ ᠬᠤᠶ ᠠᠷ ᠡᠭᠦ ᠯᠳᠡᠷ ᠦᠨ ᠵ ᠢᠮᠢᠰ ᠤ᠋ᠨ ᠣ ᠷᠤᠭᠤᠯᠬᠤ ᠦᠨᠡ ᠂ ᠪᠣᠷᠤᠯᠠᠭᠤᠯᠬ ᠤ ᠦᠨᠡ ᠨᠢ ᠲᠠᠷᠠᠭᠠᠬᠢ ᠬᠦᠰᠦᠨ ᠦᠭᠲ ᠦ ᠮ ᠡᠳᠤ ᠄ D A B C P 𝒚 𝑥 𝑂 D C 𝑎 𝑏 −2 −1 1 0 2 (1) ᠬᠡᠷᠪᠡ ᠲᠤᠰ ᠬᠤᠳ ᠠᠯᠳᠤᠭᠠ ᠪᠠᠷᠠᠭᠠ ᠣᠷᠤᠭᠤᠯᠬᠤ ᠵᠣᠭᠤᠰ ᠢᠶᠠᠨ 100 0 ᠲᠥᠭᠦ ᠷᠢᠭ ᠭᠡᠵᠤ ᠲᠤᠭᠳ ᠠᠭᠠᠪᠠᠯ᠂ ᠲᠤᠰ ᠬᠤᠶ ᠠᠷ ᠡ ᠭᠦᠯᠳᠡᠷ ᠦᠨ ᠵᠢᠮᠢ ᠰ ᠢ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳᠤᠢ ᠺᠢᠯᠣᠭ ᠷᠠᠮ ᠣᠷᠤᠭᠤᠯᠬᠤ ᠪᠤᠢ ︖ (2) ᠬᠡᠷᠪᠡ ᠲᠤᠰ ᠬᠤᠳ ᠠᠯᠳᠤ ᠭᠠ ᠡ ᠡᠭᠦᠯᠳᠡ ᠷ ᠦᠨ ᠵᠢᠮᠢ ᠰ ᠢ ᠣ ᠷᠤᠭᠤᠯᠬᠤ ᠬᠡᠮᠵᠢᠶᠡ ᠵᠢ ᠠ ᠡᠭᠦᠯᠳᠡ ᠷ ᠦᠨ ᠵᠢᠮᠢ ᠰ ᠤ᠋ᠨ ᠣ ᠷᠤᠭᠤᠯᠬᠤ ᠬᠡᠮᠵᠢᠶ ᠡᠨ ᠦ 3 ᠲᠠᠬᠢ ᠨ ᠠ ᠴᠠ ᠲᠠᠪᠠᠭᠤᠯᠬᠤ ᠦ ᠭᠡᠢ ᠭᠡᠪᠡ ᠯ᠂ ᠶᠠᠭᠠᠬᠢ ᠵᠤ ᠪᠠᠷᠠᠭᠠ ᠤᠷᠤᠭᠤᠯᠪᠠᠯ ᠵᠢᠮᠢ ᠰ ᠤ᠋ᠨ ᠬᠤᠳ ᠠᠯᠳᠤᠭᠠ ᠡᠨᠡ ᠪᠦᠯᠦᠭ ᠵᠢᠮᠢ ᠰ ᠢ ᠪᠣᠷᠤᠯᠠᠭᠤᠯᠵᠤ ᠪᠠᠷᠠᠭᠠᠬ ᠤ ᠦᠶ ᠡᠰ ᠬᠠᠮᠤᠭ ᠤ᠋ ᠨ ᠶ ᠠᠬᠡ ᠠᠰᠢ ᠭ ᠤᠯᠬᠤ ᠪᠤᠢ︖ ᠡᠨᠡ ᠦᠶ ᠡᠰ ᠦᠨ ᠠᠰᠢ ᠭ ᠬᠤᠨᠵᠢ ᠪᠦᠷᠢ ᠨ ᠢ ᠬᠡ ᠳᠤᠢ ᠪᠤᠢ︖ 26. (16 ᠬᠤᠪᠢ ) ︽ᠰᠤᠷᠭᠠᠭ ᠤᠯᠢ ᠶᠢᠨ ᠬᠦᠷ ᠢᠶᠡᠨ ᠦ ᠠᠮᠤᠷ ᠲᠦᠪᠰᠢ ᠨ ︾ ᠨᠢ ᠪᠦᠬᠦ ᠨᠡᠢ ᠭᠡᠮ ᠦᠨ ᠠᠩᠬᠠᠷᠤᠯ ᠪᠣᠯ ᠤᠨᠠ᠃ ᠮᠠᠨ ᠤ ᠬᠤᠳ ᠠ ᠶᠢ ᠨ ᠨᠢᠭᠡ ᠲᠤᠮᠳ ᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ᠂ ᠬᠡᠰᠡᠭ ᠰᠤᠷᠤᠭᠴ ᠢ ᠶᠢ ᠨ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠶᠢᠨ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠠᠮᠤᠷ ᠲᠦᠪᠰᠢ ᠨ ᠦ ᠲᠤᠬᠠᠢ ᠮᠡᠳᠡ ᠯᠭᠡ ᠵᠢ ᠮ ᠡᠳᠡᠵᠤ ᠪᠠᠢᠭᠠ ᠬᠡᠮᠵᠢᠶᠡ ᠵᠢ ᠪᠠᠢᠴᠠᠭᠠᠬᠤ ᠶᠢᠨ ᠲᠥᠯᠦᠭᠡ᠂ ᠲᠠᠰ ᠢᠷᠠᠮ ᠢᠶᠠᠷ ᠶᠠᠨᠭᠵᠤ ᠰᠤᠭᠤᠯᠤᠨ ᠪᠠᠢᠴᠠᠭᠠᠬᠤ ᠠᠷᠭᠠ ᠵᠢ ᠬᠡᠷᠡᠭᠯ ᠡᠵᠤ᠂ ᠣᠯᠤᠭᠰᠠ ᠨ ᠰᠤᠷᠠ ᠭ ᠵ ᠠᠨᠭᠭᠢ ᠵᠢ ᠪᠦᠷᠢ ᠳᠭᠡᠨ ᠲᠠᠷᠠᠭᠠᠬᠢ ᠬᠤᠶ ᠠᠷ ᠵ ᠦᠢᠯ ᠦ ᠨ ᠪᠦᠷᠢ ᠨ ᠪᠤᠰᠤ ᠪᠦᠷᠢ ᠳᠭᠡᠯ ᠦᠨ ᠵᠢᠷᠤᠭ ᠪᠣᠯᠭᠠᠨ ᠵᠢᠷᠤᠵᠠᠢ᠃ ᠪᠦᠷᠢ ᠳᠭᠡᠯ ᠦᠨ ᠵᠢᠷᠤᠭ ᠲᠤ ᠬᠠᠩᠭᠠ ᠭᠰᠠᠨ ᠰᠤᠷᠠ ᠭ ᠵ ᠠᠨᠭᠭᠢ ᠵᠢ ᠦᠨᠳ ᠦᠰᠦᠯᠡ ᠨ ᠲᠠᠷᠠᠭᠠᠬᠢ ᠠᠰᠠᠭᠤ ᠯᠳᠠ ᠵ ᠢ ᠪᠣᠳᠤ ᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯ ︔ (1) ᠪᠠᠢᠴᠠᠭᠠᠭᠰᠠᠨ ᠰᠤᠷᠤᠭ ᠴᠢ ᠶ ᠢᠨ ᠲᠣᠭ ᠠ ᠨᠢ ( ) ᠬᠦᠮᠤᠨ᠂ ᠲᠡᠪᠢ ᠭᠦᠷ ᠬᠡᠯᠪᠡᠷᠢ ᠳᠤ ᠪᠦᠷᠢ ᠳᠭᠡᠯ ᠦᠨ ᠵᠢᠷᠤᠭ ᠲᠤ ︽ ᠦᠨᠳ ᠦᠰᠤᠨ ᠳ᠋ᠡᠭᠡᠨ ᠮᠡᠳᠡ ᠵᠤ ᠪᠠᠢᠬᠤ ︾ ᠬᠡᠰᠡᠭ ᠲᠠ ᠢ ᠬᠠᠷᠠ ᠭᠠᠯᠵᠠᠭᠰ ᠠᠨ ᠲᠡᠪᠢ ᠬᠦᠷ ᠬᠡᠯᠪᠡᠷᠢᠳ ᠤ ᠶᠢ ᠨ ᠲᠥᠪ ᠥᠨ ᠴᠦᠭ ᠨᠢ( ) ᠭᠷᠠᠳ ᠦᠰ᠃ (2) ᠰᠠᠪᠠᠭᠠᠨ ᠪᠦᠷᠢ ᠳᠭᠡ ᠯ ᠦᠨ ᠵ ᠢᠷᠤᠭ ᠢ ᠨᠦᠬᠦᠵᠤ ᠪᠦᠳ ᠦᠨ ᠪᠣᠯ ᠭᠠ᠃ (3) ᠬᠡᠷ ᠪᠡ ᠲᠤᠰ ᠰᠤᠷᠭᠠᠭ ᠤᠯᠢ 90 0 ᠰᠤᠷᠤᠭ ᠴᠢ ᠪᠠᠢ ᠪᠠᠯ᠂ ᠲᠡᠭᠡᠷᠡ ᠬᠢ ᠪᠠᠢ ᠴᠠᠭᠠᠭᠰ ᠠᠨ ᠦᠷᠡ ᠳ᠋ᠦᠩ ᠢ ᠦᠨᠳ ᠦᠰᠦᠯᠡ ᠨ ᠲᠤᠰ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠶᠢᠨ ᠰᠤᠷᠤᠭᠴ ᠢ ᠳ᠋ᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠶᠢᠨ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠠ ᠮᠤᠷ ᠲᠦᠪᠰᠢ ᠨ ᠦ ᠮᠡᠳᠡ ᠯᠭᠡ ᠵᠢ ︽ ᠮᠡᠳᠡ ᠵᠤ ᠪᠠᠢᠬᠤ ︾ ᠪᠠ ︽ ᠦᠨᠳ ᠤᠰᠤᠨ ᠳ᠋ᠡᠭᠡᠨ ᠮᠡᠳᠡ ᠵᠤ ᠪᠠᠢᠬᠤ ︾ ᠬᠡᠮᠵᠢᠶ ᠡᠨ ᠳ᠋ᠤ ᠬᠦᠷᠦᠭ ᠰᠡᠨ ᠶᠡᠷᠦᠨᠭ ᠬᠡᠢ ᠬᠦᠮᠤᠨ ᠤ ᠲᠣᠭᠠ ᠵ ᠢ ᠤᠯ ᠃ (4)ᠬᠡ ᠷᠪᠡ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠶᠢᠨ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠠ ᠮᠤᠷ ᠲᠦᠪᠰᠢ ᠨ ᠦ ᠮᠡᠳᠡ ᠯᠭᠡ ᠵᠢ ︽ ᠮᠡᠳᠡ ᠵᠤ ᠪᠠᠢᠬᠤ ︾ ᠬᠡᠮᠵᠢᠶ ᠡᠨ ᠳ᠋ᠤ ᠬᠦᠷᠦᠭᠰ ᠡᠨ 3 ᠡᠮᠡᠭᠲ ᠡᠢ ᠰᠤᠷᠤᠭᠴ ᠢ ᠪᠠ 2 ᠡᠷᠡᠭᠳ ᠠᠢ ᠰᠤᠷᠤ ᠭᠴᠢ ᠶᠢᠨ ᠲᠤᠮᠳ ᠠ ᠡᠴ ᠡ ᠲᠠᠰ ᠢᠷᠠᠮ ᠢᠶᠠᠷ 2 ᠰᠤᠷᠤᠭᠴ ᠢ ᠵ ᠢ ᠰᠣᠩᠭ ᠤᠨ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠶᠢᠨ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠠ ᠮᠤᠷ ᠲᠦᠪᠰᠢ ᠨ ᠦ ᠲᠤᠬᠠᠢ ᠮᠡᠳᠡ ᠯᠭᠡ ᠶᠢᠨ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳ᠋ᠤ ᠣᠷᠤᠯᠴᠠ ᠭᠤᠯᠬᠤ ᠭᠡᠪᠡ ᠯ᠂ ᠮ ᠣᠳᠤᠯ ᠵᠢᠨ ᠵ ᠢᠷᠤᠭ ᠪᠤ ᠶᠤ ᠬᠦᠰᠦ ᠨᠦᠭᠵᠢ ᠭᠦᠯᠬᠦ ᠠᠷ ᠭᠠ ᠪᠠ ᠷ ᠶᠠᠭ ᠰᠠᠢᠬᠠᠨ 1 ᠡᠮᠡᠭᠳᠠᠢ ᠰᠤᠷᠤᠭ ᠴᠢ ᠪᠠ 1 ᠡᠷᠡᠭᠳᠠᠢ ᠰᠤᠷᠤᠭᠴᠢ ᠰᠣᠩᠭᠤ ᠭᠳᠠᠬᠤ ᠲᠣᠬᠢ ᠶᠠᠯᠳ ᠤᠮᠵᠢ ᠵ ᠢ ᠤᠯ ᠃ ᠠ ᠡᠭᠦ ᠯᠳᠡᠷ ᠡ ᠡᠭᠦ ᠯᠳᠡᠷ ᠣᠷᠤᠭᠤᠯᠬᠤ ᠦ ᠨᠡ(ᠲ ᠥᠭᠦᠷᠢᠭ /𝑘𝑔 ) 5 9 ᠪᠣᠷᠤᠯᠠᠭᠤᠯᠬᠤ ᠦ ᠨᠡ(ᠲ ᠥᠭᠦᠷᠢᠭ /𝑘𝑔 ) 8 13 ------ --- --- ---- --- ----- ------ --- --- ---- --- ----- ------ --- --- ---- --- ----- ------ --- --- ---- --- ----- ------ --- --- ---- - ᠰᠡᠳᠤᠪ ᠰᠤᠨᠭᠭᠤᠬᠤ 1 2 3 4 5 6 7 8 9 10 ᠬᠠᠷᠢᠭᠤᠯᠳᠠ ᠬᠠᠷᠢ ᠭᠤᠯᠳᠠ ᠶᠢᠨ ᠬᠠᠭᠤ ᠳᠠᠰᠤ ᠠᠨᠭᠭᠢ᠄ ᠨᠡᠷᠡ ᠄ ᠨᠢᠭᠡ ᠂ ᠰᠣᠩᠭᠤᠬ ᠤ ᠰᠡᠳᠣᠪ (3×10 = 30) ᠬᠤᠶᠠᠷ᠂ ᠬᠠᠭᠠᠯ ᠳᠠ ᠲᠠᠭᠯᠠ ᠬᠤ ᠰᠡᠳᠤᠪ (3×10 = 30) 11________； 12 ________； 13________； 14________； 15________； 16________； 17________； 18_________； 19________； 20________； ᠭᠤᠷᠪᠠ᠂ ᠪᠣᠳᠤᠵᠤ ᠬᠠᠷᠢᠭᠤᠯᠬ ᠤ ᠰᠡᠳᠤᠪ (90 ᠬᠤᠪᠢ ) 22. ------------------------------------------------------------------------------------------------------------------------------------------------- 21 ᠨᠡᠢᠲᠡ 14 ᠬᠤᠪᠢ ︵14 ᠬᠤᠪᠢ ︶ D A B C P 𝒚 𝑥 𝑂 D C ------ --- --- ---- --- ----- ------ --- --- ---- --- ----- ------ --- --- ---- --- ----- ------ --- --- ---- --- ----- ------ --- --- ---- - ᠬᠠᠷᠢ ᠭᠤᠯᠳ ᠠ ------------------------------------------------------------------------------------------------------------------------------------------------- 25. ----------------------------------------------------------------------------------------------------------------------------------------------------- 26. ︵15 ᠬᠤ ᠪᠢ ︶ ︵ 16 ᠬᠤ ᠪᠢ ︶ 23. 24. ︵ 15 ᠬᠤ ᠪᠢ ︶ ︵ 16 ᠬᠤ ᠪᠢ ︶ (1) (12)−1 + (3.14 − 𝜋)0 + √(−3)2 + 1√2+1 . (2) 𝑥 = 1+√3 ,𝑦 = 1−√3 ,𝑥2 −𝑥𝑦 +𝑦2 ᠤ᠋ᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠯ ᠢ ᠤᠯ (3) √(𝑎 −1)2 − √(𝑎 −𝑏)2. (1) 3𝑥2 +8𝑥 −3 = 0 . (2) 𝑥2 +2√3𝑥 +3 = 0. (3)4(𝑥 −3)2 +𝑥(𝑥 − 3) = 0
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