ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠲ ᠦᠷᠪ ᠡᠳᠦᠭ ᠡᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1ᠲ ᠤᠤᠷᠠᠬ ᠢ ᠪᠤ ᠳᠤᠯᠭ ᠠ ᠳᠤ ᠵᠦ᠋ᠪ ᠪᠤᠯ ᠬᠤ ᠨ ᠢ\s A\s𝑚\s𝑛 2 𝑚 2 𝑛 2 B\s𝑚𝑛\s3\s𝑚 3𝑛 3 C\s𝑚 3 2 𝑚 5 D 𝑚 ∙�

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠳ ᠦᠷᠪ ᠡᠳᠦᠭ ᠡᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1 ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠪᠣ ᠳᠣᠯᠭ ᠠ ᠳᠤ ᠳᠦ᠋ ᠩ ᠨ ᠢ 𝑎 5 ᠪ ᠣᠯᠬᠤ ᠨᠢ\s A 𝑎 10 𝑎 2 B 𝑎 2 3 C − 𝑎 5 D 𝑎 3∙ 𝑎 2 2 ᠳᠠᠷᠠᠭᠠᠬ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠲ ᠠᠪᠤᠳ ᠤᠭᠠᠷ ᠪᠥ ᠯᠥᠭ ᠦᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1ᠲ ᠠᠷᠠᠭᠠ ᠬᠢ ᠪ ᠣᠲᠠᠷᠬ ᠠᠢ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ ᠳ ᠦ 𝑥\s−2 ᠦᠶ ᠡᠰ ᠤᠳ ᠬ ᠠ ᠲ ᠠᠢ ᠨᠢ\s A 𝑥 −2𝑥2 B 𝑥 2𝑥−2 C 𝑥 2 |𝑥 |− 2 D 𝑥− 2 𝑥

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠲ ᠠᠪᠤᠳ᠋ ᠤᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃\sᠰᠡᠲᠤ ᠪ ᠪᠦᠷ ᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨᠠᠢ ᠲᠡ 30 ᠬᠤ ᠪᠢ 1ᠢᠯ ᠡᠷᠬᠡᠶ ᠢᠯᠡᠯ 𝑥𝑥1 , 𝑥3 , 𝑎𝜋 , 𝑥 2𝑥 ᠳ᠋ᠦ ᠂ ᠪᠤᠳ᠋ ᠠᠷᠬᠠᠢ ᠢᠯᠡᠷᠬ ᠡᠶᠢᠯᠡᠯ ᠦᠨ ᠪ ᠤᠳ᠋ᠠᠭᠠᠯ ᠢ ᠲᠤ ᠭ ᠠ ᠨᠢ\s A 1 B 2 C 3 D 4 2

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠭᠤ ᠷᠪᠠᠳ ᠤᠭᠠᠷ ᠪᠥ ᠯᠥᠭ ᠦᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1 ᠲᠠᠷᠠᠭᠠ ᠬᠢ ᠲ ᠠᠪᠤᠨ ᠦᠨᠴ ᠦᠭᠳᠦ AB CD E ᠪ ᠤᠯ ᠵᠦ᠋ᠪ ᠲᠠᠪ ᠤᠨ ᠦᠨᠴ ᠦᠭᠳᠦ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠡᠳ ᠡᠭᠡᠷ ᠵᠢᠷᠤᠭ ᠲᠦ᠋ ᠷᠰᠦ ᠲ ᠤᠳᠤᠷ ᠠ ᠡ ᠴᠡ ᠲᠡᠩ ᠭᠡᠯᠢᠭ ᠲᠤ ᠲ ᠡᠭᠰᠢ ᠭ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠭᠤ ᠷᠪᠠᠳ ᠤᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1 ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠭ ᠠᠷ ᠤ ᠳᠠᠰᠤ ᠨ ᠤ ᠨᠢᠭᠤ ᠴᠠ ᠨᠣᠮᠧᠷ ᠢ ᠲᠠ ᠢᠯᠬᠤ ᠵᠢᠷᠤᠭ ᠤᠳ ᠲᠤ ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠲᠦ ᠲᠡᠭᠰ ᠢ ᠬᠡᠮᠳ ᠤ ᠵᠢ ᠷᠤᠭ ᠪᠤᠯᠬᠤ ᠨᠢ\s 2 ᠬᠠᠪᠳ ᠠᠭᠠᠢ ᠶᠢᠨ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠬᠤ ᠶᠠᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃\sᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ\s1 ᠵᠢᠷᠤ ᠭ 1 ᠮᠡᠳ ᠦ᠂ ᠥᠭ ᠭᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ ∆AB C≌ ∆D EF , AC\s22 , CF\s4 ᠪᠣᠯ CD ᠶ᠋ᠢᠨ ᠤᠷᠳ ᠤ ᠨᠢ ᠄\s A 22 B 18 C 16 D 4 2 ᠵᠢᠷᠤᠭ 2

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠬᠣᠶᠠ ᠳᠤᠭ ᠠᠷ ᠪᠥ ᠯᠥᠭ ᠦᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃\sᠰᠡᠲᠤ ᠪ ᠪᠦᠷ ᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ 1 ᠵᠢᠷᠤᠭ 1 ᠮᠡᠳ ᠤ᠂ ∆A CB ≌ ∆A ′CB ′, ∠BC B ′\s32 0 ᠂ ᠲᠡᠭᠡᠪᠡᠯ ∠A CA ′\s\sA 30 0 B 32 0 C 35 0 D 45 0 2 ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠬᠡᠯ ᠡ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠨᠢ ᠭᠡᠳᠤ ᠭᠡᠷ ᠪ ᠥᠯᠥ ᠭ ᠦᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1ᠭ ᠤᠷᠪᠠ ᠨ ᠭ ᠡᠷᠴᠢ ᠮ 𝑎 , B , C ᠶᠢᠨ ᠤᠷ ᠳᠤ ᠨ ᠢ ᠴ ᠦ᠋ᠮ ᠪᠦᠬ ᠦᠯᠢ ᠲᠤᠭ ᠠ ᠪᠤ ᠯᠤᠨ ᠠ᠂ 𝑎 3 , B 5 ᠲ ᠡᠭᠡᠪᠡᠯ 𝑎 , B , C ᠪᠡᠷ ᠲᠠᠯ ᠠ ᠪᠤᠯ ᠭᠠᠭᠰᠠᠨ ᠭ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠨ ᠢᠭᠡᠳ ᠤᠭᠡᠷ ᠪ ᠥᠯᠥ ᠭ ᠦᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1ᠲ ᠠᠷᠠᠭᠠ ᠬᠢ ᠡ ᠯ ᠡ ᠪᠦᠯᠦᠭ ᠲᠣᠭᠠᠨ ᠡᠴᠡ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠭ ᠤᠷᠪᠠ ᠨ ᠲ ᠠᠯ ᠠ ᠶᠢ ᠪ ᠦᠷᠢ ᠯᠳᠦᠭ ᠦᠯᠵᠦ ᠲᠡᠢ ᠯᠬᠦ ᠨᠢ᠄\s A 1 , 1 , 2 B 1 , 2 , 4 C 2

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠦᠮᠦᠨ ᠰᠤᠷᠯᠴᠠᠬᠤ ᠦᠭᠡᠢ ᠪᠤᠯ ᠤᠬᠠᠭ᠋ᠨ ᠭᠡᠢ ᠨᠠᠴᠤᠭ‌‍ᠨ ᠪᠠᠭᠠᠪᠨᠳᠢ 19 20 ᠳ᠋ᠤᠭᠡᠷ ᠵᠠᠭᠤᠨ ᠤ ᠲᠡᠭᠦᠰᠭᠡᠯ ᠳ᠋ᠤᠭᠠᠷ ᠵᠭᠤᠨ ᠤ ᠡᠬᠢ ᠪᠠᠷ ᠦᠪᠦᠷᠯᠡᠭᠴᠢ ᠳᠤ ᠠᠮᠢᠳᠤᠷᠠᠵᠤ᠂ ᠲᠤᠭ᠋ᠷᠪᠢᠵᠤ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠮᠤᠩᠭ᠋ᠯ ᠨᠠᠶᠢᠷᠭᠴᠢ ᠷ᠊᠂ ᠬᠡᠰᠢᠭᠪᠡᠲᠦ ︽ᠬᠠᠭ᠋ᠳ ‍ᠠᠷᠴᠰ ᠭᠡᠳᠡᠭ ᠲ᠊ ᠢᠵᠠᠤᠯᠭᠠᠭ᠎ᠠ ᠭ᠊ ‍ᠡ᠊᠂ ᠬᠠᠷ᠎ᠠ ‍ᠯᠭᠠᠢ ᠲᠬᠦ᠋ᠮᠦᠪᠬᠦ ᠨᠢᠭᠡ᠊ ᠠᠳᠠᠯᠪᠦ᠋ᠯᠦᠭᠡ︾ ‍ᠡᠮᠡᠰᠢᠯᠦᠭᠯᠡᠭᠰᠪᠤᠢ᠃ ︽ᠲᠡᠭᠷᠢ ᠪᠤᠬᠠᠬᠦ᠋ᠮᠦᠤ ᠲᠡᠭ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪᠠᠨ ᠴᠠᠭ᠋ᠪᠤᠶᠠᠨ ᠢ ᠡᠷᠬᠢᠮᠯᠡᠬᠦ ᠨᠢ ᠮᠣᠩᠭ᠍ᠯᠴᠳ ᠥᠪᠡᠷ ᠤᠨ ᠵᠠᠩ ᠩᠰᠢᠯ ᠵᠠᠨ ᠢᠮᠠᠭᠲᠠ ᠡᠷᠬᠢᠮᠯᠡᠨ ᠲᠡᠭᠡᠳᠦᠯᠡᠵᠦ ᠪᠡᠯᠭᠡ ᠲ᠊ ‍ᠡᠮᠪᠡᠷᠢᠯ ᠲᠠᠢ ᠪᠣᠯᠭᠠᠭᠰᠨ ᠢ ᠪᠠ᠊ ︽ᠮᠠᠭᠤ ᠶᠢᠨ ᠶᠰᠤ ᠪᠢᠰᠢ᠂ ‍ᠣᠯ ᠶᠣᠰᠤ︾ ᠬᠡᠮᠡ᠊ ᠡᠷᠭᠦᠮᠵᠢᠯᠡᠲ᠋ᠡᠭᠡᠳᠦᠯᠡᠵᠦ᠂ ᠲᠡᠭᠦ ᠢ ᠵᠥᠷᠢᠴᠡᠪᠡᠯ ᠮ᠊ ‍ᠣᠩᠭ ᢈ ᠵᠠᠨ ᠠᠯᠳᠠᠯ᠎ᠠ ᠭᠡᠵᠦ ᠵᠢᠮᠡᠯᠳ᠋ᠭ᠃ ᠡᠶᠢᠮᠦᠷᠬᠦᠦ ᠪᠡᠷᠮᠢᠴᠡ ᠰᠡᠳᠬᠢᠬᠦᠢ ᠲᠠ᠊ ᠠᠷᠠᠳ ᠲᠥᠮᠡᠨ᠂ ᠡᠨᠡ ᠬᠦ ᠰᠡᠳᠬᠢᠯᠭᠡᠨ ᠠ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 1 2 3\s\s\s\s 1 2 3\s6 5 2 1\s2 1 ︖︾︖ ︽ 1 － ︵1642\s1727︶ ︽︾ ︽︾ 2 － ︵1736\s1819︶ 3 － 4 － ︵551\s479︶ 1 2 3 １ ︵︶ ２ ︵︶ ︵︶ ３ ︵︶ ︵︶ ︵︶ ４ ︵︶ ⒌ ︵︶ ︵︶ ︵︶ ︵︶\s\s︾ ︽︖

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠵᠣᠳᠤᠭ .pdf ﹇ ᠳᠡᠯᠭᠡᠷᠡᠩᠭᠦᠢ ﹈

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠲᠡᠷᠯᠢᠭ ᠤᠨ ᠲᠠᠢᠯᠪᠤᠷᠢ ᠵᠢᠷᠤᠭ .pdf ﹇ ᠳᠡᠯᠭᠡᠷᠡᠩᠭᠦᠢ ﹈