ᠬᠤᠷᠢᠨ ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠪᠦᠯᠦᠭ ᠲᠤᠬᠢᠶᠠᠯᠳᠤᠮᠵᠢ ᠶᠢᠨ ᠠᠩᠬ᠎ᠠ ᠠᠯᠬᠤᠮ ᠤᠨ ᠮᠡᠳᠡᠯᠭᠡ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 2） .pdf

ᠬᠣᠷ ᠢᠨ ᠲᠠᠪᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢᠴ ᠠᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭ ᠤᠬᠤ ᠰᠡᠲᠤ ᠪ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ ︶ 1. ᠳᠣᠣᠷ ᠠᠬᠢ ᠡᠴᠠ ᠵᠠᠶᠢᠯᠠᠰ ᠢᠭᠦᠢ ᠶᠠᠪᠤᠳᠠ ᠯ ᠪᠣᠯ ᠬᠤ ᠨᠢ () A. ᠳᠤᠤᠷ ᠠ ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠯᠵᠢ ᠨ ᠢ ᠵᠢᠷᠤᠬ ᠤ ᠳ᠋ᠤ ᠲᠡᠭᠦᠨ ᠦ ᠳᠣᠲᠤᠭᠠ ᠳᠤ ᠦᠨᠴᠦᠭ ᠦᠨ ᠨᠡᠶᠢᠯᠡ ᠪᠦᠷᠢ ᠨᠢ 360° ᠪᠣᠯᠬᠤ ᠃ B. ᠨᠢᠭᠡ ᠤᠳᠠ ᠭ ᠠ ᠱᠣ᠋ ᠣᠷᠬ ᠢᠬᠤ ᠳ᠋ᠤ ᠂ ᠳᠡᠭᠡᠭᠰ ᠢ ᠬᠠᠨ ᠳᠤᠭ ᠰᠠᠨ ᠭᠠᠳᠠ ᠷᠭᠤ ᠢᠢᠨ ᠴᠡᠭ ᠦᠨ ᠲᠣᠭ ᠠ ᠨᠢ 6 ᠪ ᠣᠯᠬᠤ ᠃ C. ᠶᠡᠷᠦ ᠳ᠋ ᠦ ᠪᠡ ᠨ ᠂ ᠬᠠ ᠯᠠᠭᠠᠭ ᠠᠳ 100 ℃ ᠪᠣᠯ ᠬᠤ ᠦᠶ ᠡᠰ ᠂ ᠤ ᠰᠤ ᠪ ᠤᠴᠠᠯ ᠬᠤ ᠃ D. ᠬᠠᠷ ᠪᠤᠯᠭ ᠠ ᠢᠢᠨ ᠲᠠᠮᠢᠷ ᠴᠢᠨ ᠨᠢᠭᠡ ᠤᠳ ᠠᠭ ᠠ ᠬᠠᠷᠪᠤᠬ ᠤ ᠳ᠋ᠤ ᠫᠠᠢ ᠢᠢᠨ ᠲᠥᠪ ᠢ ᠣ ᠨᠤᠭᠠᠬᠤ ᠃ 2. ︽𝑎 ᠪᠣᠯ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ ᠂ |𝑎| ≥ 0 ︾ᠡᠨᠡ ᠶᠠᠪᠤᠳᠠᠯ ᠪᠣᠯ ( ) A. ᠵᠠᠶᠢᠯᠠᠰ ᠢᠭᠦᠢ ᠶᠠᠪᠤᠳᠠᠯ B. ᠮᠠᠭ ᠠᠳ ᠪᠤᠰᠤ ᠶ ᠠᠪᠤᠳᠠᠯ C. ᠪᠣᠯ ᠤᠯᠴᠠᠭ ᠠᠭᠦ ᠢ ᠶᠠᠪᠤᠳᠠᠯ D. ᠳᠠᠰᠢᠷᠠ ᠮ ᠦ ᠨ ᠶᠠᠪᠤ ᠳᠠᠯ 3. ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ ᠂ 4 × 4 ᠳᠡᠭᠰᠢ ᠳᠦ᠋ᠷ ᠪᠡᠯᠵ ᠢᠭᠡᠰᠦ ᠳ᠋ᠦ ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠨᠢᠭᠡᠨ ᠴᠠᠭᠠᠨ ᠦᠩᠭᠡᠲᠠᠢ ᠵᠢᠵᠢ ᠭ ᠳᠡᠭᠰᠢ ᠳᠦ᠋ᠷᠪ ᠡᠯᠵᠢᠨ ᠢ ᠰᠤᠩᠭᠤᠵ ᠤ ᠬᠠᠷᠠᠯᠠᠭ ᠤᠯᠤᠨ ᠠ ᠃ ᠵᠢᠷᠤᠭ ᠲᠠᠬᠢ ᠬᠠᠷ ᠠ ᠦᠩᠭᠡᠲᠠᠢ ᠵᠢᠷᠤᠭ ᠳᠦ᠋ᠷ ᠰᠦ ᠨᠢ ᠨᠢᠭᠡᠨ ᠲᠡᠩᠬᠡ ᠯᠢᠭ ᠲᠦ ᠳᠡᠭᠰᠢ ᠬᠡᠮᠲᠦ ᠵᠢᠷ ᠤᠭ ᠳᠦ᠋ᠷ ᠰᠦ ᠪ ᠣᠯᠬᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮ ᠵᠢ ᠨᠢ ( ) A. 16 B. 14 C. 13 D. 112 4. ᠳᠣᠣᠷ ᠠᠬᠢ ᠡᠴᠠ ᠳᠠᠰᠢᠷᠠ ᠮ ᠦᠨ ᠶ ᠠᠪᠤᠳᠠᠯ ᠪᠣᠯ ᠬᠤ ᠨᠢ ( ) ᠪᠠᠶᠢᠨ ᠠ ᠃ ① ᠲᠡ ᠮᠦᠷᠯᠢᠭ ᠵᠣᠭᠣᠰ ᠢ ᠳᠡᠭᠡᠭᠰ ᠢ ᠰ ᠢᠷᠲᠡᠭᠡᠳ ᠨᠢᠭ ᠤᠷ ᠲᠠ ᠯ ᠠ ᠨᠢ ᠳᠡ ᠭᠡᠭᠰ ᠢ ᠬᠠᠨ ᠳᠤᠬ ᠤ ᠃ ② ᠮᠠᠷᠭ ᠠᠰᠢ ᠢᠢᠨ ᠨᠠᠷᠠ ᠳᠣᠷ ᠣᠨ ᠠ ᠵᠦ᠋ᠭ ᠡᠴᠡ ᠮᠠᠨᠳᠤᠬᠤ ᠃ ③ ᠵᠦ᠋ ᠪ ᠲᠠ ᠪᠤᠨ ᠦᠨᠴ ᠦᠭᠲᠦ ᠢᠢᠨ ᠳᠣᠲᠤᠭᠠ ᠳᠤ ᠦᠨᠴᠦ ᠭ ᠦ ᠨ ᠨᠡ ᠶᠢᠯᠡᠪᠦᠷᠢ 560° A. 0 B. 1 C. 2 D. 3 5. ᠵᠢᠷᠤᠭ ᠮᠡ ᠲᠦ ᠂ ᠵᠢᠰᠢᠭᠦ ᠯᠵᠢᠨ ᠬᠡᠯ ᠪᠡᠷᠢᠲᠠᠢ ᠴᠠᠭᠠᠰᠤᠨ ᠢ ᠯᠲᠠᠰᠤ ᠳᠡᠭᠡᠷ ᠡ ᠳᠠᠰᠢᠷᠠ ᠮ ᠢᠢᠠᠷ ᠵᠡᠭᠦᠦ ᠪᠡᠷ ᠬᠠᠳ ᠬᠤᠨ ᠠ ᠂ ᠵᠡᠭᠦᠦ ᠢᠢᠨ ᠰᠡᠭᠦᠳᠡ ᠷ ᠲᠠ ᠢ ᠭᠡᠰᠡᠭ ᠢ ᠬᠠᠳ ᠬᠤᠬ ᠤ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨᠢ ( ) A. 13 B. 14 C. 15 D. 16 6. ᠨᠢᠭᠡᠨ ᠲᠤᠩᠭ ᠠᠯᠠᠭ ᠪᠤᠰ ᠤ ᠤᠭ ᠤᠲᠠᠨ ᠳ᠋ᠤ ᠦᠩᠭᠡ ᠡᠴᠡ ᠪᠤᠰᠤᠳ ᠨᠢ ᠴᠦ᠋ᠮ ᠠᠳᠠᠯᠢ ᠪᠣᠯᠬ ᠤ ᠰ ᠢᠷ ᠠ᠂ ᠴᠠᠭᠠᠨ ᠬᠣᠶ ᠠᠷ ᠥᠩᠭᠡ ᠢᠢᠨ ᠪᠦᠮᠪᠦᠭᠡ ᠨᠡᠶᠢᠲᠡ 50 ᠪᠤᠢ᠂ ᠮᠡᠷᠭᠡᠨ ᠣᠯᠠᠨ ᠤᠳᠠ ᠭᠠᠨ ᠤ ᠪᠦᠮᠪᠦᠭᠡ ᠲᠡᠮᠲᠡᠷ ᠢᠬᠦ ᠳᠤᠷ ᠰᠢᠯᠲᠠ ᠪᠠᠷ ᠳᠠᠮᠵᠢ ᠨ ᠰ ᠢᠷ ᠠ ᠪᠦᠮᠪᠦ ᠭᠡ ᠲᠡ ᠮᠲᠡᠷ ᠢᠵᠤ ᠣᠯᠬ ᠤ ᠳᠠ ᠪᠲᠠᠮᠵᠢ ᠨᠢ 0 .3 ᠣᠷᠴᠢᠮ ᠳᠣᠭᠲᠠᠪᠤᠷᠢ ᠵᠢᠵᠤ ᠪᠠᠶᠢᠬᠤ ᠢᠢ ᠣ ᠯᠵᠤ ᠮᠡ ᠳᠡᠪᠡ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠡᠨ ᠡ ᠤᠭ ᠤᠲᠠᠨ ᠳ᠋ᠤ ( ) ᠴᠠᠭ ᠠᠨ ᠪ ᠦᠮᠪᠦᠭᠡ ᠪᠤᠢ ᠃ A. 15 B. 20 C. 30 D. 35 7. A , B ᠬᠣ ᠶᠠᠷ ᠵᠢᠭᠳᠡ ᠪᠣᠯᠬᠤ ᠱᠣ ( ᠨᠢᠭ ᠤᠷ ᠳᠡ ᠭᠡᠷ ᠡ ᠨᠢ ᠲᠤᠰ ᠪᠦᠷᠢ 1, 2 , 3 , 4 , 5 , 6 ᠭᠡᠰᠡ ᠨ ᠲᠡ ᠮᠲᠡᠭ ᠲᠠ ᠢ ) ᠢᠢ ᠵᠡᠷᠭᠡ ᠪᠡᠷ ᠣᠷ ᠬᠢᠬᠤ ᠳ᠋ᠤ ᠂ ᠬᠣ ᠶᠠᠷ ᠱᠣ ᠢᠢᠨ ᠨᠢᠭᠤᠷ ᠲᠠᠯ ᠠ ᠨᠢ ᠳᠡ ᠭᠡᠭᠰ ᠢ ᠬᠠᠨᠳᠤᠬ ᠤ ᠲᠣᠭ ᠠ ᠨᠢ ᠲᠤᠰ ᠪᠦᠷᠢ 𝑥 , 𝑦 ᠡᠭᠦᠨ ᠢᠢᠡᠷ ᠴᠡᠭ P (𝑥 ,𝑦 ) ᠢᠢ ᠲᠣᠭᠲᠠᠭ ᠠᠨ ᠠ ᠂ ᠲᠡ ᠭᠡᠪᠡᠯ ᠴᠡᠭ P ᠨᠢ ᠬᠠ ᠶᠠᠯᠲ ᠠ ᠢᠢᠨ ᠱᠤᠭᠤᠮ y = −𝑥 2+ 3𝑥 ᠳᠡ ᠭᠡᠷ ᠡ ᠣᠷᠣᠰ ᠢᠬᠤ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨ ᠢ ( ) A. 118 B. 112 C. 19 D. 16 8. ᠲᠤᠩᠭᠠ ᠯᠠᠭ ᠪᠤᠰᠤ ᠤᠭ ᠤᠲᠠᠨ ᠳ᠋ᠤ 6 ᠴᠠ ᠭᠠᠨ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠠ 12 ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠲᠠᠢ᠂ ᠬᠡᠷ ᠪᠡ ︽ ᠳᠤᠷ ᠠ ᠢᠢᠨ 𝑛 ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠠᠪᠬᠤ ᠳ᠋ᠤ ᠂ ᠳᠣᠲᠤᠷ ᠠ ᠨᠢ ᠠᠳᠠᠭ ᠲᠦ ᠪᠠᠨ ᠨᠢᠭᠡ ᠴᠠᠭᠠᠨ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠠᠶᠢᠨ ᠠ ᠃ ︾ᠨᠢ ᠵᠠᠶᠢᠯᠠ ᠰᠢᠭᠦᠢ ᠶᠠᠪᠤᠳᠠ ᠯ ᠪᠣᠯ ᠂ 𝑛 = ( ) A. 6 B. 7 C. 13 D. 18 9. ᠬᠡᠷᠪᠡ A ᠪ ᠡᠷ ᠶᠠᠪᠤ ᠳᠠᠯ ︽ 𝑎 b ᠪᠣᠯ ᠂ 𝑎 + c b+ c ︾ ᠢ ᠲᠦ᠋ ᠯᠦᠭᠡᠯ ᠡᠵᠤ᠂ P( A) ᠪᠠᠷ ᠶᠠᠪᠤ ᠳᠠᠯ A ᠢᠢᠨ ᠡᠭᠦ ᠰᠬᠦ ᠳᠣᠬ ᠢᠶᠠᠯᠳ ᠤᠮᠵᠢ ᠢᠢ ᠲᠦ᠋ ᠯᠦᠭᠡ ᠯᠡᠪᠡᠯ ᠂ ᠳᠣ ᠣᠷᠠᠬ ᠢ ᠳ᠋ ᠦ᠋ᠩᠨᠡ ᠯᠲᠡ ᠡᠴᠡ ᠵᠦ᠋ ᠪ ᠪᠣᠯᠬ ᠤ ᠨᠢ ( ) A. P (𝐴 )= 1 B. P( 𝐴) = 0 C. 0 1 10. ᠰᠢᠪᠠ ᠭᠤᠨ ᠤ ᠥᠨᠳᠡ ᠭᠡ ᠨᠡᠪᠴᠢ ᠭᠰᠡᠨ ᠦ ᠰ ᠡᠭᠦᠯᠡᠷ ᠴᠣᠷ ᠪᠠᠭ ᠠ ᠨᠢ ᠡᠷ ᠡ ᠪᠣᠯᠤᠨ ᠡᠮ ᠡ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨᠢ ᠠᠳᠠ ᠯᠢ ᠂ ᠬᠡᠷ ᠪᠡ ᠭᠤ ᠷᠪᠠᠨ ᠰᠢᠪᠠ ᠭᠤᠨ ᠤ ᠥᠨᠳᠡ ᠭᠡ ᠨᠢ ᠪᠦᠷᠢ ᠮᠦᠰᠦ ᠨ ᠨᠡ ᠪᠴᠢᠪᠡᠯ ᠳᠣ ᠲᠣᠷ ᠠ ᠨᠢ ᠬᠣᠶ ᠠᠷ ᠨᠢ ᠡᠮ ᠡ ᠴᠣᠷ ᠪᠠᠭ ᠠ ᠪᠣᠯᠬᠤ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮ ᠵᠢ ᠨᠢ ( ) A. 16 B. 38 C. 58 D. 23 ᠬᠣᠶ ᠠᠷ᠂ ᠬᠠᠭ ᠠᠯᠲᠠ ᠳ᠋ᠤ ᠲᠠᠭ ᠯᠠᠬᠤ ᠰᠡᠲ ᠤᠪ᠃ ︵ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 4 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲ ᠡ 2 4 ᠬᠤᠪᠢ ︶ 11. ᠤᠷ ᠲᠤ ᠨᠢ 4c m , 5c m , 6c m ᠪᠣᠯᠬ ᠤ ᠭ ᠤᠷᠪᠠᠨ ᠮᠤᠳᠤᠨ ᠰᠢᠳᠠ ᠮ ᠢᠢᠠᠷ ᠭᠤᠷᠪ ᠠᠯᠵᠢ ᠨ ᠵᠦ᠋ᠢᠵ ᠤ ᠳᠡ ᠶᠢᠯᠬᠦ ᠶᠠᠪᠤ ᠳᠠᠯ ᠨᠢ ( ) ᠶᠠᠪᠤ ᠳᠠᠯ ᠃ 12. 26 ᠠᠩᠭᠢ ᠯᠢ ᠦᠰ ᠦᠭ ᠡᠴᠡ ᠳᠤᠷ ᠠ ᠢᠢᠨ 1 ᠢᠢ ᠰᠤᠭᠤᠯ ᠤᠨ ᠠᠪᠬ ᠤ ᠳ᠋ ᠤ C ᠪᠤᠶ ᠤ D ᠪᠣᠯ ᠬᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨᠢ ( ) 13. ᠨᠢᠭᠡ ᠵᠦ᠋ ᠢᠯ ᠦᠨ ᠲᠠᠧᠠ ᠷ ᠦ ᠨ ᠬᠢ ᠷᠢ ᠲᠡ ᠩᠴᠡᠬᠦ ᠦ ᠭᠡᠢ ᠲᠠ ᠧᠠᠷ ᠢᠯᠡᠷ ᠡᠬᠦ ᠳᠣ ᠬᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨᠢ 0. 05 ᠪᠣᠯ ᠂ ᠡᠨ ᠡ ᠵ ᠦ᠋ᠢᠯ ᠦᠨ ᠲᠠ ᠧᠠᠷ ᠡᠴᠠ ᠳᠤᠷ ᠠ ᠪ ᠠᠷ 6 00 ᠲᠠ ᠧᠠᠷ ᠰᠤᠭᠤ ᠯᠠᠨ ᠠᠪᠬᠤ ᠳ᠋ᠤ ᠡᠭᠦᠨ ᠦ ᠳᠣᠲᠤᠷ ᠠ ᠪᠠᠷᠤᠭ ( ) ᠬᠢᠷ ᠢ ᠲᠡ ᠩᠴᠡᠬᠦ ᠦᠭᠡ ᠢ ᠲᠠ ᠧᠠᠷ ᠪᠠ ᠶᠢᠨ ᠠ ᠃ 14. ᠶᠠᠪᠤ ᠳᠠᠯ A ᠡᠭᠦᠰᠬᠦ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵᠢ ᠨᠢ 14 . ᠶᠡᠬᠡ ᠬᠡᠮᠵᠢ ᠶᠡᠨ ᠦ ᠳᠠᠪᠲᠠ ᠭᠳᠠᠭᠰᠠᠨ ᠳᠤᠷ ᠰᠢᠯᠲᠠ ᠬᠢᠨ ᠡ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠂ 10 0 ᠤᠳᠠ ᠭᠠᠨ ᠤ ᠳᠤᠷ ᠰᠢᠯᠲᠠ ᠳ᠋ᠤ ᠶᠠᠪᠤᠳᠠᠯ A ᠳᠤᠮ ᠳᠠᠴᠢ ᠪᠠᠷ ( ) ᠤᠳᠠ ᠭ ᠠ ᠡᠭᠦᠰᠦ ᠨ ᠡ ᠃ 15 . − 1 , 3 , −2 ᠡᠨ ᠡ ᠭᠤᠷᠪ ᠠᠨ ᠲᠣᠭ ᠠ ᠳᠣᠲᠤᠷ ᠠ ᠡᠴᠠ ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠬᠣᠶ ᠠᠷ ᠲᠣᠭ ᠠ ᠢᠢ ᠰᠤᠩᠭᠤᠨ ᠦᠷᠡ ᠵᠢᠪᠦᠷᠢ ᠪᠡᠷ k ᠢᠢᠨ ᠬᠡᠮᠵ ᠢᠭᠳᠡᠯ ᠪᠣᠯᠭ ᠠᠪᠠᠯ ᠤᠷᠪᠠ ᠭᠤ ᠬᠠᠷᠢᠴᠠᠯ ᠲᠤ ᠹᠦᠩᠺᠽ y= 𝑘𝑥 ᠢᠢᠨ ᠵᠢᠷᠤᠮᠠᠭ ᠨᠢ ᠨᠢᠭᠡᠳᠦᠭᠡᠷ ᠂ ᠭᠤᠷᠪ ᠠᠳᠤᠭ ᠠᠷ ᠮᠦ᠋ᠴᠡ ᠳ᠋ᠦ ᠣᠷᠣᠰ ᠢᠬᠤ ᠳᠣᠬᠢᠶᠠ ᠯᠳᠤᠮᠵᠢ ᠨᠢ ( ) 16 . ᠳᠤᠭ ᠤᠶᠢᠯ ᠠᠩ ᠢᠢᠠᠷ ᠰᠤᠷᠤᠯ ᠴᠠᠬᠤ 4 ᠰ ᠤᠷᠤᠭᠴᠢ ᠰᠢᠷ ᠡᠭᠡᠨ ᠦ ᠬᠠ ᠵᠠᠭᠤ ᠳ᠋ᠤ ᠰ ᠠᠭᠤᠭᠠ ᠳ ᠠ ᠰᠠᠭᠤᠳᠠ ᠯ ᠢ ᠶᠠᠷᠢᠯ ᠴᠠᠨ ᠠ ᠃ ᠰᠤᠷᠤᠭᠴᠢ A ᠢᠢᠨ ᠰᠠᠭ ᠤᠳᠠᠯ ᠨ ᠢ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ ᠂ ᠰᠤᠷᠤᠭᠴ ᠢ B , C , D ᠳᠠ ᠰᠢᠷᠠ ᠮ ᠢᠢᠠᠷ ᠨᠦ᠋ᠭᠦ ᠭᠡ ᠭ ᠤᠷᠪᠠᠨ ᠰᠠᠭ ᠤᠳᠠᠯ ᠳ᠋ᠤ ᠰ ᠠᠭᠤᠨ ᠠ ᠃ ᠲᠡᠭᠡᠪ ᠡᠯ ᠰ ᠤᠷᠤᠭᠴ ᠢ C ᠢᠢᠨ 2 ᠨᠣᠮ ᠧᠷ ᠰ ᠠᠭᠤᠳᠠᠯ ᠳ᠋ᠤ ᠰᠠᠭ ᠤᠬᠤ ᠳᠣᠬᠢᠶᠠᠯ ᠳᠤᠮᠵ ᠢ ᠨᠢ ( ) ᠭᠤᠷᠪ ᠠ᠂ ᠪ ᠣᠳᠣᠵ ᠤ ᠬ ᠠᠷᠢᠭ ᠤᠯᠬᠤ ᠰᠡᠲ ᠤᠪ᠃ ( ᠨᠠ ᠢᠲᠡ 66 ᠬᠤᠪᠢ ) 17 . ( 10 ᠬᠤᠪᠢ ) ᠨᠢ ᠭᠡ ᠲᠤᠩᠭ ᠠᠯᠠᠭ ᠪᠤᠰᠤ ᠤᠭ ᠤᠲᠠᠨ ᠳ᠋ᠤ 5 ᠰ ᠢᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠂ 13 ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠂ 22 ᠤᠯ ᠠᠭᠠᠨ ᠪᠦᠮᠪᠦᠭᠡ ᠲᠠᠢ ᠂ ᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠵᠦ᠋ᠪᠬ ᠡᠨ ᠦᠩᠭᠡ ᠨᠢ ᠠᠳᠠᠯᠢ ᠪᠤᠰ ᠤ ᠃ (1 ) ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠨᠢ ᠭᠡ ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠲᠡᠮᠲᠡᠷ ᠢᠨ ᠠᠪᠬᠤ ᠳ᠋ᠤ ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠣᠯᠬᠤ ᠢᠢ ᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠢᠢ ᠣᠯ ᠃ ( 2) ᠤᠭ ᠤᠲᠠᠨ ᠡᠴᠠ ᠡᠳᠦᠢ ᠲᠡᠳᠦ ᠢ ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠭᠠᠷᠭ ᠠᠵᠤ ᠂ ᠢ ᠵᠢᠯᠢ ᠲᠣᠭ ᠠᠨ ᠤ ᠰᠢᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠬᠢᠵᠤ ᠵᠢᠭ ᠳᠡ ᠬᠣᠯ ᠢᠭᠰᠠᠨ ᠤ ᠰᠡ ᠭᠦᠯᠡᠷ ᠨᠢᠭᠡ ᠪᠦᠮᠪᠦᠭᠡ ᠲᠡᠮᠲᠡᠷ ᠢᠨ ᠠ ᠪᠤᠪᠠᠯ ᠰᠢᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠣᠯᠬᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳ ᠤᠮᠵᠢ ᠨᠢ 13 ᠡᠴᠡ ᠪᠠᠭ ᠠ ᠪᠤᠰᠤ ᠪᠣᠯ ᠂ ᠠ ᠳᠠᠭ ᠳᠠᠭ ᠠᠨ ᠬᠡ ᠳᠦᠨ ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠠᠪᠴᠤ ᠭᠠᠷᠭ ᠠᠬᠤ ᠪᠤᠢ ︖ 18 . ( 10 ᠬᠤᠪᠢ ) ᠪ ᠠᠲᠤ ᠂ ᠮᠡ ᠷᠭᠡᠨ ᠬᠣᠶ ᠠᠷ ᠱᠣ ᠣᠷ ᠬᠢᠬᠤ ᠳᠤᠷ ᠰᠢᠯᠲ ᠠ ᠬ ᠢᠵᠠᠢ ᠃ ᠲᠡᠳᠡ ᠬᠣ ᠶᠠᠷ ᠨᠡᠶᠢᠲᠡ 60 ᠤᠳᠠ ᠭ ᠠ ᠣᠷᠬ ᠢᠵᠤ ᠂ ᠳᠡᠭ ᠡᠭᠰᠢ ᠬᠠᠨ ᠳᠤᠭᠰᠠᠨ ᠲᠠᠯ ᠠ ᠳᠡ ᠭᠡᠷᠡᠬ ᠢ ᠲᠣ ᠭᠠᠨ ᠤ ᠢ ᠯᠡᠷᠡᠭᠰ ᠡᠨ ᠪ ᠠᠶᠢᠳ ᠠᠯ ᠢ ᠲᠡᠮᠲᠡᠭᠯᠡᠭᠰ ᠡᠨ ᠨᠢ ᠬᠦᠰᠦ ᠨᠦᠭᠲᠦ ᠮᠡᠲᠦ ᠄ (1 ) ᠳᠡ ᠭᠡᠭᠰᠢ ᠬᠠᠨ ᠳᠤᠭᠰᠠᠨ ᠲᠣᠭ ᠠ ᠨᠢ 6 ᠪᠣᠯᠬᠤ ᠢᠢᠨ ᠳᠠᠪᠲᠠ ᠮᠵᠢ ᠢᠢ ᠣᠯ ᠃ (2) ᠴᠣᠭᠲᠤ᠄ ︽ᠬᠡᠷᠪᠡ ᠱᠣ ᠢᠢ 60 0 ᠤᠳᠠ ᠭ ᠠ ᠣᠷᠬ ᠢᠪᠠᠯ ᠂ ᠳᠡᠭᠡᠭᠰ ᠢ ᠬᠠᠨ ᠳᠤᠭᠰᠠᠨ ᠲᠠ ᠯ ᠠ ᠳᠡᠭᠡᠷ ᠡ ᠨᠢ 6 ᠪᠣᠯᠬ ᠤ ᠪᠠᠶᠢᠳ ᠠᠯ ᠯᠠᠪᠲᠠ ᠢ 1 00 ᠤᠳᠠ ᠭ ᠠ ᠢᠯᠡᠷ ᠡᠨ ᠡ ᠃ ︾ ᠭᠡᠵ ᠠᠢ ᠃ ᠴᠣᠭᠲᠤ ᠢᠢᠨ ᠬᠡᠯᠡᠭ ᠰᠡᠨ ᠨᠢ ᠵᠦ᠋ᠪ ᠡᠰᠡᠬ ᠦ ᠢᠢ ᠮᠠᠭᠠᠳᠯ ᠠ ᠃ (3) ᠬᠡᠷᠪᠡ ᠪᠠᠲᠤ ᠂ ᠮᠡᠷᠭᠡᠨ ᠂ ᠴᠣᠭ ᠲᠤ ᠭᠤᠷᠪ ᠠ ᠲᠤᠰ ᠪᠦᠷᠢ ᠨᠢᠭᠡ ᠤᠳᠠ ᠭ ᠠ ᠱᠣ ᠣᠷ ᠬᠢᠪᠠᠯ ᠂ ᠳᠡᠭᠡᠭᠰ ᠢ ᠬᠠᠨ ᠳᠤᠭ ᠰᠠᠨ ᠲᠠᠯ ᠠ ᠳᠡ ᠭᠡᠷᠡᠬ ᠢ ᠲᠣᠭ ᠠᠨ ᠤ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠢ 7 ᠡᠴᠡ ᠪᠠᠭ ᠠ ᠪᠣᠯᠬᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳ ᠤᠮᠵᠢ ᠢᠢ ᠣᠯ ᠃ 19 . (1 2 ᠬᠤᠪᠢ ) ᠨᠢ ᠭᠡ ᠲᠤ ᠩᠭᠠᠯ ᠠᠭ ᠪ ᠤᠰᠤ ᠬᠠᠶᠢᠷ ᠴᠠᠭ ᠲᠦ ᠦᠩᠭ ᠡ ᠡᠴᠡ ᠪᠤᠰ ᠤᠳ ᠨᠢ ᠪᠦᠷ ᠠᠳᠠᠯᠢ ᠪᠣᠯᠬ ᠤ 7 ᠪᠦᠮᠪ ᠦᠭᠡ ᠢᠢ ᠰᠠᠪᠠᠯᠠᠵ ᠠᠢ ᠃ ᠡᠭᠦᠨ ᠳ᠋ᠦ 3 ᠴᠠᠭ ᠠᠨ ᠪ ᠦᠮᠪᠦᠭᠡ ᠂ 4 ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠣᠯᠤᠨ ᠠ ᠃ (1) ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠨᠢ ᠭᠡ ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠲᠡᠮᠲᠡᠷ ᠢᠨ ᠠᠪᠬᠤ ᠳ᠋ᠤ ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠣᠯᠬ ᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠢᠢ ᠣᠯ ᠃ (2) ᠬᠡᠷ ᠪᠡ ᠬᠠᠶᠢ ᠷᠴᠠᠭ ᠲᠦ ᠳᠠᠬᠢᠨ x ᠪᠤᠳᠠᠭ ᠠᠯᠢ ᠬᠠᠷ ᠠ ᠪᠦᠮᠪᠦ ᠭᠡ ᠬᠢᠪᠡ ᠯ ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠨᠢ ᠭᠡ ᠪᠦᠮᠪᠦᠭᠡ ᠢᠢ ᠲᠡᠮᠲᠡᠷ ᠢᠨ ᠠᠪᠬ ᠤ ᠳ᠋ ᠤ ᠴᠠ ᠭᠠᠨ ᠪᠦᠮᠪᠦᠭᠡ ᠪᠣᠯᠬ ᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨᠢ 14 ᠪᠣᠯᠤᠨ ᠠ ᠂ ᠠᠯᠭᠧᠪ ᠷᠠ ᠢᠢᠨ ᠢᠯ ᠡᠷᠬᠡᠶᠢᠯᠡᠯ 𝑥− 2 𝑥 2 −𝑥 ÷ (𝑥 + 1− 3𝑥−1 ) ᠢᠢᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠯ ᠢ ᠣ ᠯ ᠃ 20 . (1 0 ᠬ ᠤᠪᠢ ) ᠬᠠᠶᠢ ᠷᠴᠠᠭ ᠳᠣᠲ ᠤᠷ ᠠ 𝑥 ᠬᠠᠷ ᠠ ᠰᠢᠲᠠᠷ ᠠ ᠪᠠ 𝑦 ᠴᠠᠭᠠᠨ ᠰᠢᠲᠠᠷ ᠠ ᠪᠠᠶᠢᠨ ᠠ ᠂ ᠡᠳᠡᠭᠡᠷ ᠰᠢᠲᠠᠷ ᠠ ᠦᠩᠭᠡ ᠡᠴᠡ ᠪᠤᠰ ᠤᠳ ᠢᠯᠭᠠ ᠭ ᠠ ᠦᠭᠡᠢ ᠃ (1) ᠬᠠᠶᠢ ᠷᠴᠠᠭ ᠳᠣᠲ ᠣᠷ ᠠ ᠡᠴᠠ ᠨᠢᠭᠡ ᠰᠢᠲᠠᠷ ᠠ ᠢᠢ ᠳᠠᠰᠢᠷᠠ ᠮ ᠢᠢᠠᠷ ᠠᠪᠤ ᠨ ᠠ᠂ ᠬᠡᠷᠪᠡ ᠲᠡᠷᠡ ᠨᠢ ᠬᠠᠷ ᠠ ᠰᠢᠲᠠᠷ ᠠ ᠪ ᠣᠯᠬᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮ ᠵᠢ ᠨᠢ 38 ᠪᠣᠯ᠂ 𝑥 ᠪᠠ y ᠢᠢᠨ ᠬᠣ ᠯᠪᠤᠭᠳᠠᠯ ᠢ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠬᠦ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠢ ᠪ ᠢᠴᠢ ᠃ (2) ᠬᠡᠷᠪᠡ ᠬᠠᠶᠢ ᠷᠴᠠᠭ ᠳᠣᠲ ᠣᠷ ᠠ ᠳᠠᠬ ᠢᠭᠠᠳ 10 ᠬᠠᠷ ᠠ ᠰ ᠢᠲᠠᠷ ᠠ ᠬᠢᠪ ᠡᠯ ᠂ ᠬᠠᠷ ᠠ ᠰ ᠢᠲᠠᠷ ᠠ ᠢᠢ ᠣᠯᠬ ᠤ ᠢᠢᠨ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨᠢ 12 ᠪᠣᠯᠵᠤ ᠬᠤᠪᠢ ᠷᠠᠨ ᠠ ᠂ 𝑥 ᠪᠠ 𝑦 ᠢᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠣ ᠯ ᠃ ᠭᠠᠷᠤ ᠭᠰᠠᠳ ᠤᠳ ᠠᠭᠠᠨ ᠤ ᠲᠣᠭ ᠠ ᠳᠡᠭᠡᠭ ᠰᠢ ᠬᠠᠨᠳᠤᠵ ᠤ ᠢᠯᠡᠷ ᠡᠭᠰᠡᠨ ᠲᠣᠭ ᠠ ᠨᠢ 8 1 10 2 7 3 9 4 16 5 10 6 21 . (1 2 ᠬᠤᠪ ᠢ) ᠪᠦᠭᠡᠮ ᠢᠢᠡ ᠷ ᠪᠣᠷᠣᠯ ᠠᠭᠤᠯ ᠤᠭᠴᠢ ᠨᠢᠭᠡ ᠨ ᠬᠤᠪᠴᠠᠰᠤ ᠬᠢᠬᠦ ᠦᠢᠯ ᠡᠳᠪᠦᠷᠢ ᠡᠴᠡ 50 ᠪᠣᠭᠣᠳᠠᠯ L ᠨᠣᠮᠧᠷ ᠦᠨ ᠳᠣᠲᠣᠷ ᠴᠠᠮᠴᠠ ᠢᠢ ᠬᠤᠳᠠᠯ ᠳᠤᠨ ᠣᠷᠣᠭᠤᠯ ᠵᠠᠢ᠂ ᠪᠣᠭᠣᠳᠠᠯᠯᠠ ᠬᠤ ᠠ ᠵᠢᠯᠴ ᠢᠨ ᠤ ᠬᠠᠰᠢ ᠶᠠᠰᠢ ᠡᠴᠠ ᠪᠣᠯᠵ ᠤ ᠪᠣᠭᠣᠳᠠᠯ ᠳᠣᠲᠤᠷ ᠠ ᠨᠢ M ᠨᠣᠮ ᠧᠷ ᠦ ᠨ ᠳᠣᠲᠣᠷ ᠴᠠᠮᠴᠠ ᠬᠣᠯ ᠢᠯᠳᠤᠨ ᠣᠷᠣᠭᠰ ᠠᠨ ᠪᠠᠶᠢᠨ ᠠ ᠃ ᠪᠣᠭᠣᠳᠠᠯ ᠪᠦᠷᠢ ᠳ᠋ᠦ ᠬᠣᠯ ᠢᠯᠳᠤᠨ ᠣᠷ ᠣᠭᠰᠠᠨ M ᠨᠣᠮᠧᠷ ᠦᠨ ᠲᠣᠲᠣᠷ ᠴᠠᠮᠴᠠ ᠢᠢᠨ ᠲᠣᠭ ᠠ ᠨᠢ ᠬᠦᠰ ᠦᠨᠦᠭ ᠲᠦ ᠮᠡᠲᠦ ᠄ ᠨᠢᠭᠡᠨ ᠰᠤᠯᠠ ᠪᠠᠷ ᠬᠤᠳᠠᠯᠳᠤ ᠭᠴᠢ ᠡᠴᠠ 50 ᠪᠣᠭᠣᠳᠠᠯ ᠳᠣᠲᠣᠷ ᠠ ᠡᠴᠠ ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠨᠢᠭᠡ ᠪᠣᠭᠣᠳᠠᠯ ᠢ ᠰᠤᠩᠭᠤᠵ ᠠᠢ ᠂ ᠳᠠᠷᠠᠭ ᠠᠬᠢ ᠶᠠᠪᠤᠳᠠᠯ ᠦᠳ ᠦᠨ ᠳᠣᠬᠢᠶ ᠠᠯᠳᠤᠮᠵᠢ ᠢᠢ ᠣᠯ ᠄ (1) ᠪᠣᠭᠣᠳᠠᠯ ᠳ᠋ᠤ ᠨᠢ M ᠨᠣᠮᠧᠷ ᠦᠨ ᠳᠣᠲᠣᠷ ᠴᠠᠮ ᠴᠠ ᠬᠣᠯᠢᠯᠳᠤ ᠨ ᠣ ᠷᠣᠭᠰ ᠠᠨ ᠦᠭᠡᠢ ᠃ (2) ᠪᠣᠭᠣᠳᠠᠯ ᠳ᠋ᠤ ᠨᠢ ᠬᠣ ᠯᠢᠯᠳ ᠤᠨ ᠣᠷᠣᠭᠰ ᠠᠨ M ᠨᠣᠮ ᠧᠷ ᠦᠨ ᠳᠣᠲ ᠣᠷ ᠴᠠᠮ ᠴᠠ ᠢᠢᠨ ᠲᠣᠭ ᠠ ᠨᠢ 7 ᠡᠴᠡ ᠬᠡᠲᠦ ᠷᠡᠬᠦ ᠦᠭᠡᠢ ᠃ (3) ᠪᠣᠭᠣᠳᠠᠯ ᠳ᠋ᠤ ᠨᠢ ᠬ ᠣᠯᠢᠯ ᠳᠤᠨ ᠣᠷᠣᠭᠰ ᠠᠨ M ᠨᠣᠮ ᠧᠷ ᠦᠨ ᠳᠣᠲ ᠣᠷ ᠴᠠ ᠮᠴᠠ ᠢᠢᠨ ᠲᠣᠭ ᠠ ᠨᠢ 10 ᠡᠴᠡ ᠬᠡᠲᠦ ᠷᠡᠨ ᠡ ᠃ 22 . (1 2 ᠬᠤᠪᠢ ) ᠨᠢ ᠭᠡᠨ ᠰᠤᠷᠭ ᠠᠭᠤᠯ ᠢ ᠢᠢᠨ ᠶᠢᠰ ᠦᠳᠦᠭᠡᠷ ᠣᠨ ᠤ ᠰ ᠤᠷᠤᠭ ᠴᠢᠳ ᠲᠡᠭᠦᠰ ᠬᠦ ᠶᠣᠰ ᠣᠯᠠᠯ ᠶᠠᠪᠤᠭ ᠤᠯᠤᠨ ᠠ ᠂ ᠶᠢᠰᠦ ᠳᠦᠭᠡᠷ ᠣᠨ ᠤ ᠨᠢ ᠭᠡᠳᠦᠭᠡᠷ ᠠᠩᠭᠢ ᠡᠴᠠ 2 ᠨᠡ ᠷᠡᠰ ᠡᠷᠡᠭᠲᠡᠢ ᠰᠤᠷᠤᠭᠴᠢ ᠂ 1 ᠨᠡᠷ ᠡᠰ ᠡᠮ ᠡᠭᠲᠡᠢ ᠰᠤᠷᠤᠭᠴᠢ ᠢᠢ ᠲᠠᠨᠢᠯᠴ ᠠᠭᠤᠯ ᠵᠤ ᠂ ᠶᠢᠰᠦ ᠳᠦᠭᠡᠷ ᠣᠨ ᠤ ᠬᠣᠶ ᠠᠳᠤᠭ ᠠᠷ ᠠ ᠩᠭᠢ ᠡᠴᠠ 1 ᠨᠡᠷᠡᠰ ᠡᠷᠡᠭᠲᠡᠢ ᠰᠤᠷᠤᠭᠴᠢ᠂ 2 ᠨᠡ ᠷᠡᠰ ᠡᠮᠡᠭᠲᠡᠢ ᠰᠤᠷᠤᠭᠴᠢ ᠢᠢ ᠲᠠ ᠨᠢᠯᠴ ᠠᠭᠤᠯ ᠵᠤ ᠨᠡ ᠶᠢᠲᠡ 5 ᠬᠦᠮᠦ ᠨ ᠡᠴᠡ 2 ᠨᠡ ᠷᠡᠰ ᠢ ᠬᠦ ᠲᠦᠯᠦ ᠭᠴᠢ ᠪᠣᠯᠭ ᠠᠨ ᠠ ᠃ (1) ᠮᠤᠳ ᠤᠯᠵᠢᠨ ᠵᠢᠷᠤᠭ ᠪᠤᠶ ᠤ ᠬᠦ ᠰᠦᠨᠦᠭ ᠵᠢᠭᠦᠯ ᠬᠦ ᠠ ᠷᠭ ᠠ ᠪᠠᠷ ᠪᠤᠢ ᠪᠦᠬᠦᠢ ᠪᠣᠯᠤᠯ ᠴᠠᠭ ᠠ ᠢᠢ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠵ ᠤ ᠭᠠᠷᠭ ᠠ ᠃ (2) 2 ᠨᠡᠷ ᠡᠰ ᠬᠦ ᠲᠦᠯᠦ ᠭᠴᠢ ᠨᠢ ᠠ ᠳᠠᠯᠢ ᠪᠤᠰ ᠤ ᠠ ᠩᠭᠢ ᠡᠴᠠ ᠢᠷᠡᠬ ᠦ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮ ᠵᠢ ᠢᠢ ᠣᠯ ᠃ (3) 2 ᠨᠡᠷᠡᠰ ᠬᠦᠲ ᠦᠯᠦᠭ ᠴᠢ ᠨᠢ ᠶᠠᠭ ᠰᠠᠶ ᠢᠬᠠᠨ ᠨᠢᠭᠡ ᠡᠷᠡᠭᠲᠡᠢ ᠨᠢᠭᠡ ᠡᠮᠡᠭᠲᠡᠢ ᠪᠣᠯᠬᠤ ᠳᠣᠬ ᠢᠶᠠᠯᠳᠤᠮ ᠵᠢ ᠨᠢ ᠬᠡ ᠳᠦᠢ ᠪᠤᠢ ︖ M ᠨᠣᠮᠧᠷ ᠤᠨ ᠲᠣᠲ ᠣᠷ ᠠ ᠴᠠᠮᠴ ᠠᠨ ᠤ ᠲᠣᠭ ᠠ ᠪᠣ ᠭᠣᠳᠠ ᠯ ᠤᠨ ᠲᠣᠭ ᠠ 0 7 1 3 4 10 5 15 7 5 9 4 10 3 11 3