ᠠᠷᠪᠠᠨ ᠵᠢᠷᠭᠤᠳᠤᠭᠠᠷ ᠪᠦᠯᠦᠭ ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠯ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 1） .pdf

ᠠᠷᠪᠠ ᠨ᠊ ᠵᠢᠷᠭᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠊᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ᠊ ᠤᠪᠢ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ᠃ ︵ᠰᠡᠲᠤᠪ ᠪᠦ ᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤᠪᠢ︶ 1. ᠳᠠ ᠷᠠᠭᠠᠬ ᠢ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠳᠤ᠂ ᠯᠠᠪᠲᠠ ᠢ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠤᠨ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠪᠤᠯᠬ ᠤ ᠨᠢ ︵︶ A. √𝑥 + 2 B. √ 𝑥 C. √ 𝑥 2 + 1 D. √ 𝑥 2 − 2 2. ᠲᠤᠤᠷᠠ ᠬᠢ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢ ᠵᠠᠭᠤᠷ ᠤᠨ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠳᠤ᠂ ᠬᠠᠮᠤᠭ ᠤᠨ ᠬᠢᠯᠪᠡ ᠷ᠊ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡ ᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠤᠨ ᠢᠯ ᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠪᠤᠯ ᠬᠤ ᠨᠢ ︵︶ A. √10 B. √3 𝑎 2 C. √8 D. √ 12 3. 4 ᠶᠢᠨ ᠲᠤᠭ ᠠ ᠪᠣᠳᠤᠯ ᠬ᠋᠊ ᠠ ᠶᠢᠨ ᠺᠦᠸᠠ ᠳ᠋᠊ ᠢ ᠵᠠᠭᠤᠷ ᠨᠢ ︵︶ A. ± 2 B. − 2 C. 2 D. √5 4. ᠳᠠᠷ ᠠᠭᠠᠬ ᠢ ᠡᠯ ᠠ ᠤ ᠦᠯᠦ ᠬ᠋᠊ ᠬᠤ ᠶᠠᠳᠤᠭ ᠠᠷ ᠵᠡ ᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠤᠨ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠳᠤ᠂ ᠢᠵᠢᠯ ᠲᠦ᠋ᠷᠤᠯ ᠦᠨ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡ ᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠦ ᠨ᠊ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠪᠤᠯᠬ ᠤ ᠨᠢ ︵︶ A. √3 ᠪᠠ √18 B. √3 ᠪᠠ √ 13 C. √𝑎 2b ᠪᠠ √𝑎 b 2 D. √𝑎 + 1 ᠪᠠ √𝑎 − 1 5. ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ √ ︵𝑚 +1︶ ︵𝑚 −1︶ ᠶᠢ ᠤᠳᠭ ᠠ ᠲᠠᠢ ᠪᠠᠢᠯ ᠭᠠᠭ᠋ᠤ ᠭᠡᠪᠡᠯ᠂ 𝑚 ᠦᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠᠪᠬ ᠤ ᠬᠡᠪᠴᠢᠶ ᠡ ᠨᠢ ︵︶ A. 𝑚 −1 B. 𝑚 −1 ᠪᠥᠭᠡᠳ 𝑚 ≠ 1 C. 𝑚 ≥ −1 D. 𝑚 ≥ −1 ᠪᠥᠭᠡᠳ 𝑚 ≠ 1 6. ᠥᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ √ ︵𝑎 − 3︶ 2= 3− 𝑎᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ︵︶ A. 𝑎≥ 3 B. 𝑎 ≤ 3 C. 𝑎 3 D. 𝑎 3 7. √8 − √2 ︵√ 2+ 2︶ ᠶᠢ ᠬ᠊ ᠢᠯᠪᠡ ᠷᠴᠢᠯ ᠡᠪᠠᠯ ᠳ᠋ᠦ᠋ᠩ ᠨᠢ ︵︶ A. −2 B. √ 2− 2 C. 2 D. 2√ 2− 2 8. ᠳᠠ ᠷᠠᠭᠠᠬ ᠢ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠳᠤ ᠪᠠᠢᠭ ᠤᠯᠤᠭᠳᠡᠬᠤ ᠨᠢ ︵︶ A. √ ︵− 3︶ 2= −3 B. − √3 .6 = −0 .6 C. √ 𝑥 2 + 𝑦 2 = 𝑥+ 𝑦 D. − √16 = −4 9. ᠥᠭ ᠭᠦᠭᠳᠡᠭ ᠰᠡᠨ ᠨᠢ √ 𝑎+ 2+ |b − 1| = 0 ᠲᠡ ᠭᠡᠪᠡᠯ ︵𝑎 + b︶ 2016 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨᠢ ︵︶ A. −1 B. 1 C. 20 16 D. −2016 10. ᠴᠡᠭ 𝑃 ᠶᠢᠨ ᠲᠤᠭ ᠠᠨ ᠤ ᠲᠡᠨ ᠭᠭᠡᠯᠢᠭ ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠪᠠᠢᠷ ᠢ ᠨᠢ ᠵᠢᠷ ᠤᠭ 1 ᠮᠡ ᠲᠤ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠴᠡᠭ 𝑝 ᠨᠢ ᠪᠠᠷᠤᠭ ︵︶ ᠶᠢ ᠢᠯ ᠡᠷᠬᠡᠢᠯ ᠠ ᠡ᠃ A. −√ 7 B. − √3 C. −3 .2 D. −√ 10 ᠬᠤᠶ ᠠᠷ᠂ ᠬᠠᠭ ᠠᠯᠲᠠ ᠳᠤ ᠲᠠ ᠭᠯᠠᠬᠤ ᠰᠡᠲᠤᠪ᠃ ︵ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠ ᠢᠲᠡ 30 ᠬᠤᠪᠢ︶ 11. ᠥᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ √ 20n ᠨᠢ ᠪᠦᠬᠦᠯᠢ ᠲᠤᠭ ᠠ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠨᠥᠬᠦᠴᠡ ᠯ᠊ ᠢ ᠬᠠᠩᠭ ᠠᠬᠤ ︵1︶ ᠬᠠᠮᠤᠭ ᠤᠨ ᠪᠠᠭ ᠠ ᠪᠦᠬᠦᠯᠢ ᠲᠤᠭ ᠠ 𝑛 ᠨᠢ __ __ __ __᠃ 12. ᠬᠡ ᠷᠪᠡ 𝑥− 𝑦= √2 + 1, 𝑥𝑦 = √2 ᠪᠤᠯ᠂ ᠠᠯᠭᠧᠪ ᠷᠠ ᠶᠢᠨ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ ︵𝑥 − 1︶ ︵𝑦 + 1︶ ᠶᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨᠢ __ __ __ __ _᠃ 13. √3 ᠶᠢᠨ ᠲᠤᠩᠭᠤᠷ ᠠᠭᠤ ᠲᠤᠭ ᠠ ᠨᠢ __ __ __ __᠃ 14. ᠶᠡᠭᠡ ᠪᠠ ᠬ᠋᠊ ᠠ ᠶᠢ ᠠᠳᠠ ᠯᠢᠳᠭ ᠠ᠄ 2√ 2 _ __ __ __ √6 15. ᠬᠡᠷ ᠪᠡ 1 √2 𝑥− 1 ᠶᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠤᠭ ᠠᠨ ᠤ ᠬᠡᠪᠴᠢᠶ ᠠ ᠳ᠋᠊ ᠦ ᠤᠳᠭ ᠠ ᠲᠠᠢ ᠪᠠᠢᠯᠭᠠᠬᠤ ᠭᠡᠪᠡᠯ᠂ 𝑥 ᠦ ᠨ᠊ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠠᠪᠬ ᠤ ᠬᠡᠪ ᠴᠢᠶ ᠡ ᠨᠢ __ __ __ __᠃ 16. ᠵᠢᠷ ᠤᠭ 2 ᠮᠡ ᠲᠤ᠂ ᠲᠤᠭ ᠠᠨ ᠤ ᠲᠡᠩᠭᠡᠯᠢᠭ ᠳᠡᠭᠡᠷ ᠡ᠂ A , B ᠬᠤᠶ ᠠᠷ ᠴᠡ ᠬ᠋᠊ ᠦᠨ ᠬᠤᠭᠤᠷ ᠣᠨᠳᠤ ᠪᠦᠬᠦ ᠯᠢ ᠲᠤᠭ ᠠ ᠶᠢ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠬᠦ ᠴᠡ ᠬ᠋᠊ ᠨᠡ ᠢᠲᠠ __ __ __ ᠪᠠᠢ ᠨ᠊ ᠠ᠃ 17. ᠬᠣ ᠶᠠᠷ ᠬᠠᠮᠤᠭ ᠤᠨ ᠭᠢᠯᠪᠡ ᠷ᠊ ᠬᠤᠶ ᠠᠳᠤᠭᠠ ᠷ᠊ ᠵᠡ ᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠤᠨ ᠢᠯ ᠡᠷᠬᠡᠢᠯ ᠡᠯ √ 2𝑎 + 1 ᠪᠠ √ 7− 𝑎 ᠨᠢ ᠢ ᠵᠢᠯᠢ ᠲᠥᠷᠦᠯ ᠦᠨ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡ ᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠤᠨ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠤ ᠤᠯ᠂ 𝑎 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨᠢ __ __ __ _᠃ 18. 𝑥 ≤ 0 ᠦ ᠶᠡᠰ᠂ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ | 1− 𝑥| − √𝑥 2 ᠢ ᠬᠢ ᠯᠪᠠᠷ ᠴᠢᠯᠠᠪ ᠠᠯ᠂ ᠳ᠋ᠦ᠋ᠩ ᠨᠢ __ __ __᠃ 19. 𝑎 , 𝑏 ,𝑐 ᠨᠢ ∆AB C ᠶᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠲᠠᠯ ᠠ ᠪᠣᠯᠤ ᠨ᠊ ᠠ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ √ ︵𝑎− 𝑏+ 𝑐︶ 2 +| 𝑐− 𝑎− 𝑏| = __ __ __ __ _᠃ 20 . ᠲᠤᠷ ᠠ ᠶᠢᠨ ᠬᠣ ᠶᠠᠷ ᠲᠠᠨᠭ ᠴᠡᠭᠦᠦ ᠪᠤᠰᠤ ᠪᠣᠳᠠᠲᠤ ᠲᠤᠭ ᠠ 𝑎 ,𝑏 ᠳᠤ᠂ ᠳᠣᠣᠷ ᠠᠬᠢ ᠪᠣᠳᠤᠯ ᠬ᠋᠊ ᠠ ᠶᠢᠨ ᠲᠦ᠋ᠷᠢᠮ ᠲᠣᠭᠲᠠᠭ ᠠᠪᠠ᠄ 𝑎 ※𝑏 = √𝑎 +𝑏 𝑎− 𝑏᠂ ᠲᠡ ᠭᠡᠪᠡᠯ 12 ※4 =᠃ ᠭᠤᠷᠪ ᠠ᠂ ᠪᠣᠳᠣᠵ ᠤ ᠬᠠᠷ ᠢᠭᠤᠯ ᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ ︵ᠨᠠᠢᠲᠡ 60 ᠬᠤᠪᠢ︶ 21 . ︵2 0 ᠬᠤᠪᠢ︶ ᠪᠣᠳᠤ᠄ ︵1︶ 2 √18 − √32 + √ 18 ︵2︶ |1 − √3 |+ ︵√ 3︶ 0− √12 ︵3︶ √ 3 ︵2− √3︶ − √27 + ︵− 13︶ −1 ︵4︶ √ 8− ︵4 √3 − 3√ 6︶ ÷ 2√ 3 ︵2︶ 22. ︵12 ᠬᠤᠪᠢ︶ ᠥᠭ ᠭᠦᠭᠳᠡ ᠭᠰᠡᠨ ᠨᠢ᠄ 𝑥= √3 + 1 , 𝑦 = √3 − 1 ᠲᠡ ᠭᠡᠪᠡᠯ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ 𝑥 2− 𝑦 2 ᠦᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠤᠯ᠃ 23. ︵14 ᠬᠤᠪᠢ︶ ᠤᠷ ᠢᠳᠠᠪᠠ ᠷ᠊ ᠬᠢᠯ ᠪᠡᠷᠴᠢᠯ ᠠᠵᠤ ᠳᠠᠷᠠᠭ ᠠ ᠨᠢ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠨᠢ ᠤᠯ᠄ 𝑥+ 1𝑥 ÷ ︵𝑥 − 1+ 𝑥 22𝑥︶᠂ ᠡᠭᠦᠨ ᠳᠤ 𝑥= √2 + 1 24 . ︵14 ᠬ᠊ ᠤᠪᠢ︶ ᠥᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ᠄ 𝑦= √𝑥 − 2+ √2 − 𝑥− 3, ᠲᠡᠭᠡᠪ ᠡᠯ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ︵𝑥 + 𝑦︶ 4 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠤᠯ᠃