ᠶᠢᠰᠤᠳᠤᠭᠡᠷ ᠪᠥᠯᠥᠭ ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠪᠠ ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠪᠥᠯᠥᠭ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 1） .pdf

ᠶᠢᠰᠤ ᠳᠤᠭᠡᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢᠴ ᠠᠭᠠᠯ ᠲᠠ 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.ᠬᠡ ᠷᠪᠡ 𝑎 𝑏 ᠪ ᠣᠯ ᠳᠣ ᠣᠷᠠᠬ ᠢ ᠲᠡ ᠩᠴᠡᠳᠭᠡᠯ ᠪᠣᠰᠤ ᠳᠤ ᠪᠠᠶᠢᠭ ᠤᠯᠤᠭᠳᠠᠬᠤ ᠨᠢ ( ) A. 𝑎𝑚 𝑏𝑚 B. 𝑎 + 𝑚 = 𝑏+ 𝑚 C. 𝑎𝑚 2= 𝑏𝑚 2 D. 𝑚 − 𝑎 2( 3𝑥 + 5) ᠶᠢᠨ ᠰᠦ᠋ ᠭᠡᠷᠬᠦ ᠪᠣᠰᠤ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ ᠠᠨ ᠬᠠᠷ ᠢᠭᠤ ᠶᠢ ᠨ ᠪᠣᠳᠠᠭ ᠠᠯᠢ ᠲᠣᠭ ᠠ ᠨᠢ ( ) A. 0 ᠪᠠᠢᠨ ᠠ B. 1 ᠪᠠᠢᠨ ᠠ C. 2 ᠪᠠᠢᠨ ᠠ D. 3 ᠪᠠᠢᠨ ᠠ 5. ᠬᠡᠷᠪᠡ 𝑥 ᠤᠨ ᠲᠤ ᠬᠠᠢ ᠲᠡᠭᠰᠢᠳ ᠭᠡᠯ 𝑥 − 2= 4𝑚 + 3 ᠶᠢᠨ ᠬᠠᠷᠢᠭ ᠤ ᠨ ᠢ ᠰᠦ᠋ᠭᠡᠷ ᠬᠦ ᠲᠣᠭ ᠠ ᠪᠣ ᠯᠪᠠᠯ ᠂ 𝑚 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠠᠪᠬᠤ ᠬᠡ ᠪᠴᠢᠶ ᠡ ᠨᠢ ( ) A. 𝑚 − 54 B. 𝑚 54 D. 𝑚 9 ᠶᠢᠨ ᠬᠠᠷᠢᠭ ᠤ ᠨᠢ ︵ ︶ A. 𝑥 −4 B. 𝑥 3 C. 𝑥 −3 7.ᠲ ᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠣᠰᠤ 13 ( 𝑥− 𝑚) 2− 𝑚 ᠶᠢᠨ ᠬᠠᠷᠢᠭ ᠤ ᠴᠤᠭᠯ ᠠᠷᠠᠯ ᠨᠢ 𝑥 2 ᠲᠡᠭᠡᠪ ᠡᠯ 𝑚 ᠶᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨᠢ ︵ ︶ A. 4 B. 2 C. 32 D. 12 8. ᠨᠢᠭᠡ ᠦ ᠯᠦ ᠮᠡ ᠳᠡᠭᠳᠡᠭ ᠴᠢᠲᠡᠢ ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷ ᠭᠡ ᠶᠢᠨ ᠲᠡᠩ ᠴᠡᠳᠭᠡᠯ ᠪᠣᠰᠤ ᠪᠣᠯᠬᠤ ᠨᠢ ( ) A. 𝑚𝑥 + 2 0 B. (2 𝑥− 1) − (2 𝑥+ 3) 1 D. 2𝑥 2− (2 𝑥 2 − 3𝑥 )+ 5𝑥 − 4≤ 1 9. ᠨᠢᠭᠡᠨ ᠤᠷ ᠲᠤ ᠳᠦ᠋ᠷᠪ ᠡᠯᠵᠢᠨ ᠪᠡᠶ ᠡ ᠬᠡ ᠯᠪᠡᠷ ᠢᠲᠡᠢ ᠰᠠᠪ ᠠ ᠶᠢᠨ ᠤᠷᠲᠤ ᠨᠢ 3cm ᠦᠷᠭᠡᠨ ᠨᠢ 2cm ᠥᠨᠳᠦ ᠷ ᠨᠢ 5cm ᠪᠣᠯᠤᠨ ᠠ᠂ ᠰᠠᠪ ᠠᠨ ᠳᠡᠬᠢ ᠤᠭ ᠤᠨ ᠪᠠᠢᠭᠰᠠᠨ ᠤᠰᠤ ᠨ ᠤ ᠦᠨᠳ ᠦᠷ ᠨᠢ 2cm ᠂ ᠣᠳᠣ ᠲᠡ ᠭᠦᠨ ᠳᠦ ᠦᠷᠭᠦᠯ ᠵᠢᠯᠡᠨ ᠤᠰ ᠤ ᠣ ᠷᠤᠭᠤᠯ ᠤᠨ ᠠ ᠃ V ᠪᠠᠷ ᠰᠢᠨ ᠡ ᠣ ᠷᠤᠭᠤᠯ ᠤᠭᠰ ᠠᠨ ᠤᠰᠤ ᠨ ᠤ ᠡᠵᠡᠯ ᠡᠭᠦᠨ ᠢ ᠢᠯ ᠡᠷᠬᠡᠢᠯ ᠡᠵᠦ ᠂ V ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠠᠪᠬ ᠤ ᠬᠡᠪ ᠴᠢᠶ ᠡ ᠨᠢ ( ) A. 𝑉 ≤ 18 B. 𝑉 3 ᠶᠢᠨ ᠬ ᠠᠷᠢᠭ ᠤ ᠴᠤᠭᠯ ᠠᠷᠠᠯ ᠨᠢ ( ) A. 𝑥 ≤ −2 B. 𝑥 4 0 1 2 3 4 –1 –4 –3 –2 –1 0 1 –5 0 1 2 3 –1 1 2 3 4 5 0 C. − 2≤ 𝑥 6 ᠪᠠ 2 𝑥− 1 b ᠪ ᠣᠯ᠂ 𝑎𝑐 2 ( ) 𝑏 𝑐 2 ᠲᠣᠭ ᠠᠨ ᠤ ᠬᠡ ᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠲᠡ ᠩᠴᠡᠳᠭᠡᠯ ᠪᠣᠰᠤ ᠶᠢ ᠨ ᠬᠠᠷ ᠢᠭᠤ ᠭᠡᠨ ᠡ᠃ 16. ᠰᠣ ᠶᠤᠯᠲᠤ ᠭᠡᠷ ᠡᠴᠡ ᠪ ᠡᠨ ᠰ ᠤᠷᠭᠠᠭ ᠤᠯᠢ ᠳᠤ ᠬᠦᠷᠬ ᠦ ᠵᠠ ᠮ ᠤᠨ ᠤᠷᠲᠤ ᠨᠢ 2 40 0m ᠪᠣᠯᠤᠨ ᠠ ᠂ ᠲᠡᠷᠡ ᠥᠷᠯᠦ ᠭᠡ 8 ᠴᠠᠭ ᠲᠤ ᠭᠡᠷ ᠡᠴᠡ ᠪᠡ ᠨ ᠭᠠᠷ ᠴᠤ᠂ 8 ᠴᠠ ᠭ 30 ᠮᠢ ᠨᠦ᠋ᠲ ᠡᠴᠡ 8 ᠴᠠ ᠭ 4 0 ᠮᠢᠨᠦ᠋ ᠲ ᠦ ᠨ ᠬᠣᠭᠤᠷ ᠤᠨᠳᠤ ᠰᠤᠷᠭ ᠠᠭᠤᠯ ᠢ ᠳᠠᠭ ᠠᠨ ᠬᠦ ᠷᠦᠨ ᠡ᠃ ᠬᠡᠷᠪᠡ 𝑥 ᠪᠡᠷ ᠲᠡ ᠭᠦᠨ ᠦ ᠬᠤᠷᠳᠤᠴᠠ (ᠨᠢ ᠭᠡᠴᠢ᠄ m/ min ) ᠶᠢ ᠢᠯ ᠡᠷᠭᠡᠢᠯ ᠡᠪᠡᠯ᠂ 𝑥 ᠦᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠᠪᠬᠤ ᠬᠡᠪ ᠴᠢᠶ ᠡ ᠨᠢ ( ) ᠭᠤᠷᠪ ᠠ᠂ ᠪᠣᠳᠣᠵ ᠤ ᠬᠠᠷ ᠢᠭᠤᠯ ᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ ︵ ᠨᠠᠢᠲᠡ 66 ᠬᠤᠪᠢ ︶ 17. (8 ᠬᠤᠪᠢ ) ᠲᠡ ᠩᠴᠡᠳᠭᠡᠯ ᠪᠣ ᠰᠤ 1− 𝑥3 ≤ 1− 2𝑥7 ᠶᠢ ᠪᠣᠳᠤᠭᠠᠳ ᠂ ᠪᠠᠰᠠ ᠲᠡ ᠭᠦᠨ ᠦ ᠬᠠᠷᠢᠭ ᠤ ᠴᠤᠭᠯ ᠠᠷᠠᠯ ᠢ ᠲᠣᠭ ᠠᠨ ᠤ ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠳᠡ ᠭᠡᠷ ᠡ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡ ᠃ 18. ( 8 ᠬᠤᠪᠢ ) ᠲᠡᠩ ᠴᠡᠳᠭᠡᠯ ᠪᠣᠰ ᠤ ᠶᠢ ᠨ ᠪᠦᠯᠦ ᠭ { 5 𝑥− 1 3( 𝑥+ 1) 12 𝑥 − 1≤ 7− 32 𝑥 ᠢ ᠪᠣᠳᠣ ᠃ 19. (8 ᠬᠤᠪᠢ ) ᠲᠡ ᠭᠰᠢᠳᠭᠡᠯ ᠦᠨ ᠪᠦᠯᠦ ᠭ { 3𝑥 + 2𝑦 = 𝑎+ 1 2𝑥 + 𝑦= 𝑎− 1 ᠦᠭ ᠭᠦᠭᠳᠡᠵᠡᠢ᠂ 𝑎 ᠨᠢ ᠶᠠᠮᠠᠷ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠦᠶ ᠡᠰ 𝑥 𝑦 ᠪ ᠣᠯᠬᠤ ᠪᠣᠢ ︖ 20. ( 8 ᠬᠤᠪᠢ ) 𝑥 ᠨᠢ ᠠᠯᠢ ᠠᠯᠢ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ ᠠᠨ ᠬᠡ ᠮᠵᠢᠭ ᠳᠡᠯ ᠠᠪᠬ ᠤ ᠦ ᠶᠡᠰ1 ≤ 2𝑥 − 3 8 ᠨᠢ ᠪᠠᠢᠭ ᠤᠯᠤᠭᠳᠠ ᠬᠤ ᠪ ᠣᠢ ︖ 21. (10 ᠬᠤᠪᠢ ) ᠨᠢ ᠭᠡᠨ ᠬᠣᠶ ᠠᠷ ᠣ ᠷᠤᠨᠲᠤ ᠲᠣᠭ ᠠ ᠪ ᠠᠶᠢᠨ ᠠ ᠂ ᠲᠡᠭᠦᠨ ᠦ ᠠ ᠷᠪᠠ ᠶᠢᠨ ᠣᠷᠣᠨ ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠲᠣᠭ ᠠ ᠨᠢ ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠣᠷ ᠣᠨ ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠲᠣᠭ ᠠ ᠠᠴ ᠠ 2 ᠶᠡᠬᠡ ᠂ ᠡᠨ ᠡ ᠬᠣ ᠶᠠᠷ ᠣᠷᠤᠨᠲᠤ ᠲᠣᠭ ᠠ ᠨᠢ 30 ᠡᠴᠡ 50 ᠶᠢᠨ ᠬᠣᠭᠤᠷ ᠤᠨᠳᠤ ᠪᠠᠶᠢᠨ ᠠ ᠃ ᠲᠠ ᠡᠨᠡ ᠬᠣᠶ ᠠᠷ ᠣ ᠷᠤᠨᠲᠤ ᠲᠣᠭ ᠠ ᠶᠢ ᠶᠠᠮᠠᠷ ᠲᠣᠭ ᠠ ᠪᠣᠯᠬᠤ ᠶᠢ ᠮᠡ ᠳᠡᠨ ᠡ ᠤ ᠤ ︖ 22. (12 ᠬᠤᠪ ᠢ) ᠰᠡᠷᠭᠦᠯ ᠡᠩ ᠦ ᠨ ᠭᠡᠷ ᠦᠨ ᠰᠠᠷ ᠠ ᠪ ᠦᠷᠢ ᠶᠢ ᠨ ᠤᠰᠤ ᠨ ᠤ ᠰᠦ᠋ᠢᠳᠭᠡᠯ ᠨᠢ 15 ᠲᠦ᠋ᠭ ᠦᠷᠢᠭ ᠡᠴᠡ ᠪᠠᠭ ᠠ ᠦᠭᠡᠢ ᠂ ᠲᠦ᠋ ᠭᠡᠭᠡᠭᠦᠷ ᠤᠰ ᠤᠨ ᠤ ᠺᠣᠮᠫ ᠠᠨᠢ ᠶᠢᠨ ᠰᠦ᠋ᠢ ᠳᠭᠡᠯ ᠬᠤᠷᠢᠶᠠ ᠬᠤ ᠪᠠᠷᠢᠮᠵᠢᠶ ᠠ ᠨᠢ ᠳᠣᠣᠷ ᠠᠬᠢ ᠮᠡᠲᠦ ᠄ ᠬᠡ ᠷᠪᠡ ᠡᠷᠦᠬ ᠡ ᠪᠦᠷᠢ ᠶᠢᠨ ᠰᠠᠷ ᠠ ᠪᠦᠷᠢ ᠬᠡᠷᠡᠭᠯᠡᠬ ᠦ ᠤᠰᠤ ᠨᠢ 5 m 3 ᠡᠴᠡ ᠬᠡᠲᠦ ᠷᠡᠬᠦ ᠦᠭᠡᠢ ᠪᠣᠯ m 3 ᠪᠦᠷᠢ ᠡᠴᠡ 1.8 ᠲᠦ᠋ᠭ ᠦᠷᠢᠭ ᠬᠤᠷᠢᠶᠠᠨ ᠠ ᠂ ᠬᠡᠷᠪᠡ ᠡᠷᠦᠬ ᠡ ᠪ ᠦᠷᠢ ᠶᠢ ᠨ ᠰ ᠠᠷ ᠠ ᠪᠦᠷᠢ ᠬᠡᠷᠡᠭᠯᠡᠬ ᠦ ᠤᠰᠤ ᠨᠢ5 m 3 ᠡᠴᠡ ᠬᠡᠲᠦ ᠷᠡᠪᠡᠯ ᠂ ᠬᠡ ᠲᠦᠷᠡᠭᠰ ᠡᠨ ᠬᠡᠰᠡᠭ ᠦᠨ m 3 ᠪᠦᠷᠢ ᠡᠴᠡ 2 ᠲ ᠦ᠋ᠭᠦᠷᠢ ᠭ ᠬᠤᠷᠢᠶᠠᠨ ᠠ ᠃ ᠰᠡᠷᠭᠦᠯ ᠡᠩ ᠦ ᠨ ᠭᠡᠷ ᠦᠨ ᠰᠠᠷ ᠠ ᠪᠦᠷᠢ ᠬᠡᠷᠡᠭᠯᠡᠬ ᠦ ᠤᠰᠤ ᠨ ᠤ ᠬᠡᠮᠵᠢᠶ ᠡ ᠨᠢ ᠠᠳᠠᠭ ᠲᠠ ᠭᠠᠨ ᠬᠡᠳᠦ ᠢ ᠪᠣᠢ ︖ 23 .(12 ᠬᠤᠪᠢ) ᠰ ᠤᠷᠤᠭᠴᠢᠳ ᠢ ᠵᠣᠷ ᠢᠭᠵᠢᠭ ᠤᠯᠤᠨ ᠪᠡᠶ ᠡ ᠶᠢᠨ ᠲᠠᠮᠢᠷ ᠤᠨ ᠬᠦᠳᠡ ᠯᠭᠡᠭᠡᠨ ᠳᠦ ᠣᠷᠣᠯ ᠴᠠᠭᠤ ᠯᠬᠤ ᠶᠢ ᠨ ᠲ ᠥᠯᠥ ᠭᠡ᠂ ᠰᠤᠷᠭ ᠠᠭᠤᠯ ᠢ ᠠᠴᠠ1 60 0 ᠲ ᠥᠬᠥ ᠷᠢᠭ ᠡᠴᠡ ᠬᠡᠳᠤᠷᠡ ᠬᠦ ᠦᠭᠡᠢ ᠪᠡᠯᠡ ᠮᠥᠩᠬ ᠦ ᠭᠠᠷᠭ ᠠᠵᠤ᠂ ᠨᠢᠭᠡ ᠪᠥᠯᠥ ᠭ ᠰ ᠠᠭᠰᠤᠨ ᠪᠥᠮ ᠪᠥᠭᠡ ᠪᠠ ᠠ ᠯᠠᠭᠠᠳᠠ ᠬᠤ ᠪ ᠥᠮᠪᠥᠭᠡ ᠬᠤᠳᠠᠯ ᠳᠤᠨ ᠠᠪᠬ ᠤ ᠪᠠᠷ ᠲᠥᠯᠥᠪᠯᠡᠪ ᠡ᠂ ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ ᠰᠠᠭᠰᠤᠨ ᠪᠥ ᠮᠪᠥᠭᠡ ᠪᠠ ᠠᠯ ᠠᠭᠠᠳᠠ ᠬᠤ ᠪᠥ ᠮᠪᠥᠭᠡ ᠶᠢᠨ ᠨᠢᠭ ᠡᠴᠢ ᠦᠨ ᠡ ᠶᠢᠨ ᠬᠠᠷ ᠢᠴᠠᠯ ᠨᠢ 3: 2᠂ ᠨᠢᠭᠡᠴᠢ ᠦᠨ ᠡ ᠶᠢᠨ ᠨᠠᠢᠯ ᠡᠪᠤᠷᠢ ᠨᠢ 80 ᠲᠥᠬᠥ ᠷᠢᠭ᠃ (1) ᠰᠠᠭᠰᠤ ᠨ ᠪ ᠥᠮᠪᠥᠭᠡ ᠪᠠ ᠠᠯᠠᠭ ᠠᠳᠠᠬ ᠤ ᠪᠥ ᠮᠪᠥᠭᠡ ᠶᠢᠨ ᠨᠢᠭᠡ ᠴᠢ ᠦᠨ ᠡ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳᠤᠢ ᠲᠥᠬᠥ ᠷᠢᠭ ᠪᠣᠢ︖ (2) ᠬᠡᠷ ᠪᠡ ᠬᠤᠳᠠᠯᠳᠤ ᠨ ᠠ ᠪᠬᠤ ᠰᠠᠭᠰ ᠤᠨ ᠪᠥᠮᠪᠥᠭᠡ ᠪᠠ ᠠᠯ ᠠᠭᠠᠳᠠ ᠬᠤ ᠪᠥᠮᠪᠥᠭᠡ ᠶᠢᠨ ᠶᠡᠷᠤᠩᠬᠡᠢ ᠲᠣᠭ ᠠ ᠨᠢ 36 ᠪᠥ ᠭᠡᠳ ᠬᠤᠳᠠᠯ ᠳᠤᠨ ᠠᠪᠤᠭᠰ ᠠᠨ ᠰ ᠠᠭᠰᠤ ᠨ ᠪ ᠥᠮᠪᠥᠭᠡ ᠶᠢᠨ ᠲᠣᠭ ᠠ ᠨᠢ 25 ᠡᠴᠡ ᠢᠯ ᠡᠬᠦᠦ ᠪᠠᠢᠬ ᠤ ᠬᠡᠷᠡᠭᠳᠡᠢ ᠭᠡᠵ ᠤ ᠱᠠᠭᠠ ᠷᠳᠠᠪ ᠠᠯ᠂ ᠬᠡᠳᠤᠨ ᠵᠦ᠋ᠢᠯ ᠦ ᠨ ᠬᠤᠳᠠ ᠯᠳᠤᠨ ᠠᠪ ᠬᠤ ᠲᠥ ᠰᠥᠯ ᠪᠠᠢᠬᠤ ᠪᠣᠢ︖