ᠠᠷᠪᠠ ᠶᠢᠰᠤᠳᠤᠭᠡᠷ ᠪᠦᠯᠦᠭ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠩᠺᠼ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 1） .pdf

ᠠᠷᠪ ᠠ ᠶᠢ ᠰᠦᠳ ᠦᠭᠡᠷ ᠤ ᠦᠯᠦ ᠬ᠋᠊ ᠦᠨ ᠪᠠᠭ ᠠ ᠰᠣᠷᠢ ᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮ᠊ ᠢᠨᠦ᠋ᠲ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ︶ ᠨᠢᠭᠡ᠂ ᠰ᠊ ᠤᠩᠭᠤ ᠬᠤ ᠰ᠊ ᠡᠲᠤᠪ᠃ ︵ᠰᠡᠲ ᠤᠪ ᠤ ᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨ᠊ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ︶ 1. ᠹᠦᠩ ᠺᠼ y= √𝑥 +1 𝑥− 1 ᠤ ᠬᠤ ᠪᠢᠰᠬᠤᠨ 𝑥 ᠦᠨ ᠬᠡᠮᠵ ᠢᠭᠳᠡᠯ ᠠᠪᠬᠤ ᠬᠡᠪᠴᠢ ᠶ᠊ ᠡ ᠨ᠊ ᠢ ︵︶ A. 𝑥 −2 ᠪᠦᠭᠡᠳ 𝑥 ≠ 1 B. 𝑥 ≥ 2 ᠤ ᠦᠭᠡᠳ 𝑥≠ 1 C. 𝑥 ≥ −2 ᠪᠦᠭᠡᠳ 𝑥 ≠ 1 D. 𝑥 ≠ 1 2. ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠩ ᠺᠼ y= −𝑥 + 2 ᠦᠨ ᠵᠢᠷᠤᠮᠠᠭ ᠨᠢ ︵︶ ᠳᠠᠭᠠᠷᠢ ᠨ᠊ ᠠ᠃ A. ᠨᠢᠭᠡ᠂ ᠬᠣ ᠶᠠᠷ᠂ ᠭᠤ ᠷᠪᠠᠳ ᠤᠭᠠᠷ ᠮᠦ᠋ᠴ ᠡ B. ᠨᠢᠭᠡ᠂ ᠬᠣ ᠶᠠᠷ᠂ ᠳᠦ᠋ ᠷᠪᠡᠳ ᠦᠭᠡᠷ ᠮ᠊ ᠦᠴᠡ C. ᠨᠢᠭᠡ᠂ ᠭᠤ ᠷᠪᠠ᠂ ᠳᠦ᠋ ᠷᠪᠡᠳ ᠦᠭᠡᠷ ᠮ᠊ ᠦᠴᠡ D. ᠬᠣ ᠶᠠᠷ᠂ ᠭᠤ ᠷᠪᠠ᠂ ᠳᠦ᠋ ᠷᠪᠡᠳ ᠦᠭᠡᠷ ᠮ᠊ ᠦᠴᠡ 3. ᠳᠣᠣ ᠷᠠᠬᠢ ᠵᠢᠷᠤᠮᠠᠭ ᠲᠤ᠂ y ᠨᠢ 𝑥 ᠦᠨ ᠹᠦᠩ ᠺᠼ ᠪᠣᠯᠬᠤ ᠪᠤᠳᠠᠭᠠᠯ ᠢ ᠲ᠊ ᠣᠭ ᠠ ᠨᠢ ︵︶ A. 1 B. 2 C. 3 D. 4 4. ᠵᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ᠨᠢᠭᠡᠳ ᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢ ᠨ᠊ ᠹ᠊ ᠦᠩᠺ ᠼ᠊ y= ︵𝑚 − 1︶ 𝑥− 3 ᠶᠢᠨ ᠵᠢᠷᠤᠮᠠ ᠬ᠋᠊ ᠨ᠊ ᠢ ᠲ᠊ ᠤᠰ ᠲᠤᠰ 𝑥 ᠲᠡᠩ ᠬᠡᠯᠢᠭ y ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠦᠨ ᠰᠥᠭᠡᠷᠬ ᠦ ᠬᠠᠭᠠᠰ ᠲᠡ ᠩᠬᠡᠯ ᠢᠭ A᠂ B ᠴᠡᠭ ᠲᠤ ᠣᠭᠲᠣᠯ ᠣᠯᠴᠠᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ 𝑚 ᠶᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠ ᠪᠬᠤ ᠬᠡᠪᠴ ᠢᠶ ᠡ ᠨ᠊ ᠢ ︵︶ A. 𝑚 1 B. 𝑚 0 D. 𝑚 0 5. ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦ ᠩᠺᠼ y = k𝑥 + b ︵k≠ 0︶ ᠨᠢ ︵2 ,− 1︶᠂ ︵−3 ,4︶ ᠴᠡᠭ ᠢ ᠳᠠᠭᠠᠷᠢ ᠨ᠊ ᠠ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠲᠡᠭ ᠦᠨ ᠦ ᠵᠢᠷᠤᠮᠠᠭ ᠨᠢ ︵︶ ᠮᠦ᠋ᠴ ᠡ ᠶᠢ ᠳᠠᠭᠠᠷ ᠢᠬᠤ ᠦᠭᠡᠢ᠃ A. ᠨᠢᠭᠡᠳ ᠤᠭᠡᠷ B. ᠬᠣ ᠶᠠᠳᠤ ᠭᠠᠷ C. ᠭᠤ ᠷᠪᠠᠳ ᠤᠭᠠᠷ D. ᠲᠤ ᠷᠪᠡᠳ ᠤᠭᠡᠷ 6. ᠬᠡᠷᠪᠡ ᠤᠷᠪᠠ ᠭᠤ ᠬᠠᠷᠢ ᠴᠠᠯᠲ ᠤ ᠹ᠊ ᠦᠩᠺ ᠼ᠊ ᠨᠢ ᠴᠡᠭ ︵−1 ,2︶ ᠢ ᠳᠠᠭᠠᠷ ᠶᠢᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠡᠨᠡ ᠵᠢᠷᠤᠮᠠ ᠬ᠋᠊ ᠨ᠊ ᠢ ᠯᠠᠪ ᠲᠠᠢ ︵︶ ᠴ᠊ ᠡᠭ ᠢ ᠳᠠᠭᠠ ᠷᠢᠨ ᠠ᠃ A. ︵1 ,2︶ B. ︵− 1, −2︶ C. ︵2 ,− 1︶ D. ︵1 ,− 2︶ 7. ᠬᠡᠷᠪᠡ ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠩ ᠺᠼ y= ︵2 − 𝑚︶ 𝑥− 2 ᠶ᠊ ᠶᠢᠨ ᠹᠦᠩ ᠺᠼ ᠦᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨᠢ y ᠨᠢ 𝑥 ᠦᠨ ᠨᠡᠮᠡᠭ ᠳᠡᠬᠦ ᠶᠢ ᠳ᠋᠊ ᠠᠭᠠᠯ ᠳᠤᠨ ᠨᠡᠮᠡᠭ ᠳᠡᠪᠡᠯ᠂ 𝑚 ᠦᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠᠪᠬᠤ ᠬᠡᠪᠴ ᠢᠶ ᠡ ᠨᠢ ︵︶ A. 𝑚 0 B. 𝑚 2 D. 𝑚 ᠶᠢ ᠰᠤᠩ ᠭᠤᠵᠤ ᠲᠠᠭᠯ ᠠ︶᠃ 12. ᠴᠡᠭ P ︵𝑎, b︶ ᠨᠢ ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠩ ᠺᠼ y= 4𝑥 + 3 ᠶ᠊ ᠶᠢᠨ ᠵᠢᠷᠤᠮᠠᠭ ᠳᠡᠭᠡ ᠷ᠊ ᠡ ᠤ ᠠᠢᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ 4𝑎 − b− 2= __ ____ 13. ᠵᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ᠰᠢᠯᠤ ᠭᠤᠨ 𝑦= 𝑘𝑥 + 𝑏 ᠨᠢ ︵2,1︶᠂ ︵− 1, −2︶ ᠴ᠊ ᠡᠭ ᠢ ᠳᠠᠭᠠ ᠷᠢᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠲ᠊ ᠡᠩᠴ ᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ 12 𝑥 𝑘𝑥 + 𝑏 −2 ᠤᠨ ᠬᠠᠷᠢ ᠭᠤ ᠴ᠊ ᠤᠭᠯᠠᠷᠠᠯ ᠨᠢ __ _____ 14. ᠰᠢ ᠯᠤᠭᠤ ᠨ᠊ y = 2𝑥 − 1 ᠶ᠊ ᠢ y ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠳᠠᠭᠠᠤ 3 ᠨ᠊ ᠢᠭᠡᠴ ᠢ ᠵᠡᠷᠭᠡᠴ ᠡᠭᠡ ᠰᠢᠯᠵᠢ ᠭᠦᠯᠦᠨ ᠡ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠵ᠊ ᠡᠷᠭᠡᠴ ᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠳᠠᠷᠠᠭᠠ ᠬᠢ ᠰᠢᠯᠤ ᠭᠤᠨ ᠪᠠ y ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠦᠨ ᠣᠭᠲᠣᠯ ᠣᠯᠴᠠᠯ ᠤᠨ ᠴ᠊ ᠡᠭ ᠦᠨ ᠪᠠ ᠢᠷᠢ ᠰᠢᠯ ᠨ᠊ ᠢ ____ ____ 15. ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠩ ᠺᠼ 𝑦 = ︵2 𝑚 − 6︶ 𝑥+ 𝑚 ᠲᠤ᠂ y ᠨᠢ 𝑥 ᠦᠨ ᠨᠡᠮᠡᠭ ᠳᠡᠬᠦ ᠶᠢ ᠳᠠ ᠭᠠᠯᠳ ᠤᠨ ᠬᠣ ᠷᠣᠭᠳ ᠠᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ 𝑚 ᠦᠨ ᠬ᠊ ᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠠ ᠪᠬᠤ ᠬᠡᠪᠴᠢ ᠶ᠊ ᠡ ᠨ᠊ ᠢ _______ 16. ᠹᠦᠩ ᠺᠼ 𝑦1 = 𝑘1 𝑥 ᠦᠨ ᠵᠢᠷᠤᠮᠠᠭ ᠨᠢ ᠴᠡᠭ P ︵2,3︶ ᠢ ᠳᠠᠭᠠᠷ ᠶᠢᠨ ᠠ᠂ ᠮᠦ᠋ ᠷᠲᠡᠭᠡᠨ ᠹᠦᠩ ᠺᠼ 𝑦2 = 𝑘2 𝑥 ᠦᠨ ᠵᠢᠷᠤᠮᠠᠭ ᠲ᠊ ᠠᠢ y ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠦᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠡᠭᠰ ᠢ ᠬ᠊ ᠡᠮᠲᠦ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠲᠡᠳ ᠡᠭᠡᠷ ᠦᠨ ᠠ ᠨᠠᠯᠢᠰ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ 𝑦1 = ___ ___ ___᠂ 𝑦 2 = ___ ___ ___ __ 17. ᠬᠡᠷᠪᠡ ᠹᠦ ᠩᠺᠼ y = 𝑥− 2 ᠪᠠ y = −2 𝑥+ 4 ᠶᠢᠨ ᠶᠢ ᠷᠤᠮᠠᠭ ᠤᠨ ᠣᠭᠲᠣᠯ ᠣᠯᠴᠠᠯ ᠤᠨ ᠴᠡᠭ ᠤᠨ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ᠊ ᠨ᠊ ᠢ ︵2,0︶᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠬᠣ ᠶᠠᠷ ᠥᠯ ᠦ ᠮ᠊ ᠡᠳᠡᠭᠳ ᠡᠭᠴᠢ ᠲᠠᠢ ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠲᠡᠭ ᠰᠢᠳ ᠬᠡᠯ ᠦᠨ ᠪᠥᠯᠥᠭ { 𝑥− 𝑦= 2 2𝑥 + 𝑦= 4 ᠶ᠊ ᠶᠢᠨ ᠬ᠊ ᠠᠷᠢᠭᠤ ᠨᠢ ____ 18. ᠰᠢ ᠯᠤᠭᠤ ᠨ᠊ 𝑦 1 = 𝑥᠂ 𝑦 2 = 13 𝑥 + 1᠂ 𝑦 3 = − 45 𝑥 + 5 ᠶᠢᠨ ᠶᠢ ᠷᠤᠮᠠᠭ ᠨᠢ ᠵᠢᠷᠤ ᠬ᠋᠊ ᠮ᠊ ᠡᠲᠦ᠂ ᠬᠡᠷᠪᠡ 𝑥 ᠨᠢ ᠶᠠᠮᠠᠷ ᠪᠠ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠᠪᠤ ᠭᠰᠠᠨ ᠴᠤ᠂ y ᠨᠢ ᠬ᠊ ᠡᠵᠢᠶ ᠡᠳᠡ 𝑦 1᠂ 𝑦2᠂ 𝑦 3 ᠶᠢ ᠨ᠊ ᠬ᠊ ᠠᠮᠤᠭ ᠪᠠᠭ ᠠ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠠ ᠪᠤᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ y ᠶᠢᠨ ᠬᠠᠮᠤ ᠬ᠋᠊ ᠶᠠᠬ ᠡ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨ᠊ ᠢ ____ _ ᠭᠤᠷᠪᠠ᠂ ᠪᠣᠳ ᠣᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠲᠤ ᠪ᠊᠃ ︵ᠨᠠᠢ ᠲᠡ 66 ᠬᠤ ᠪᠢ︶ 19. ︵6 ᠬᠤ ᠪᠢ︶ ᠳᠣ ᠣᠷᠠᠬ ᠢ ᠬᠡᠮᠵ ᠢᠭᠳᠡᠯ ᠢ ᠥᠨᠳ ᠥᠰᠥᠯ ᠡᠵᠤ᠂ ᠹᠦ ᠩᠺᠼ ᠦᠨ ᠢᠯᠡᠷᠬ ᠢᠯᠡ ᠯ᠊ ᠢ ᠣᠯ᠃ ︵1︶ 𝑦 ᠪᠠ 𝑥 ᠨ᠊ ᠢ ᠰᠢ ᠭᠤᠳ ᠬᠠᠷᠢ ᠴᠠᠯᠳ ᠤ ᠹᠦᠩ ᠺᠼ ᠪᠥᠭᠡ ᠳ᠋᠊ 𝑥= 9 ᠥᠶ ᠡᠰ᠂ 𝑦= 16 ︵2︶ 𝑦 = 𝑘𝑥 + 𝑏 ᠶ᠊ ᠶᠢᠨ ᠵ᠊ ᠢᠷᠤᠮᠠ ᠬ᠋᠊ ᠨ᠊ ᠢ ᠴᠡ ᠬ᠋᠊ ︵3,2︶᠂ ︵− 2,1︶ ᠢ ᠳᠠᠭᠠᠷ ᠶᠢᠨ ᠠ᠃ 20. ︵8 ᠬ᠊ ᠤᠪᠢ︶ ᠰ᠊ ᠢᠯᠤᠭᠤ ᠨ᠊ 𝑦= 2𝑥 + 3 ᠪᠠ ᠰᠢ ᠯᠤᠭᠤ ᠨ᠊ 𝑦= −2 𝑥− 1 ᠥᠭ ᠭᠥᠭᠳ ᠡᠵᠡᠢ᠃ ︵1︶ ᠬᠣ ᠶᠠᠷ ᠰᠢᠯᠤ ᠭᠤᠨ ᠪᠠ y ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠦᠨ ᠣᠭᠲᠣᠯ ᠣᠯᠴᠠᠯ ᠤᠨ ᠴᠡᠭ A, B ᠦᠨ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ᠊ ᠢ ᠣᠯ᠃ ︵2︶ ᠬᠣ ᠶᠠᠷ ᠰᠢᠯᠤ ᠭᠤᠨ ᠤ ᠣ ᠭᠲᠣᠯ ᠣᠯᠴᠠᠯ ᠦᠨ ᠴ᠊ ᠡᠭ C ᠶᠢᠨ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ᠊ ᠢ ᠣ ᠯ᠊᠂ ︵3︶ ∆AB C ᠶ᠊ ᠶᠢᠨ ᠲ᠊ ᠠᠯᠠᠪᠠ ᠢ ᠶᠢ ᠣ ᠯ᠊᠃ 21. ︵1 0 ᠬ᠊ ᠤᠪᠢ︶ ᠰ᠊ ᠦᠯᠵᠢ ᠶᠡᠨ ᠦ ᠴ᠊ ᠠᠭ ᠦ ᠶ᠊ ᠡ ᠢᠷᠡᠵ ᠦ᠂ ᠠᠢ ᠯ᠊ ᠪᠤ ᠯᠭᠠᠨ ᠭᠡᠷ ᠲᠡᠭᠡ ᠨ᠊ ᠰ᠊ ᠦᠯᠵᠢ ᠶ᠊ ᠡ ᠵᠠᠯᠭᠠᠬᠤ ᠪᠣᠯᠵᠠᠢ᠂ ᠰ᠊ ᠦᠯᠵᠢ ᠶᠡᠨ ᠦ ᠲ᠊ ᠣᠪᠴᠢ ᠶ᠊ ᠠ ᠬ᠊ ᠣᠶᠠᠷ ᠵᠦ᠋ᠢ ᠯ᠊ ᠦᠨ ᠰ᠊ ᠦᠢᠳ ᠬᠡᠯ ᠬᠤ ᠷᠢᠶᠠᠬᠤ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠲ᠊ ᠣᠭᠲᠠᠭ ᠠᠵᠠᠢ᠂ ᠬᠡᠷᠡᠭᠯ ᠡᠭᠴᠢ ᠳ᠋᠊ ᠲᠤᠷ ᠠ ᠶᠢ ᠨ᠊ ᠨ᠊ ᠢᠭᠡ ᠶᠢ ᠰ᠊ ᠤᠩᠭᠤ ᠵᠤ ᠤ ᠣᠯᠤᠨ ᠠ᠂ A᠄ ᠴᠠᠭ ᠢᠶᠠᠷ ᠬᠢᠵᠠ ᠭᠠᠷᠯ ᠠᠬᠤ᠄ 0. 05 ᠲᠤ ᠭᠥᠷᠢ ᠬ᠋᠊ / ᠮ᠊ ᠢᠨᠦ᠋ᠲ᠂ B᠄ ᠰ᠊ ᠠᠷ ᠠ ᠶᠢᠨ ᠲᠣᠭᠲ ᠠᠭᠠᠯ᠄ 54 ᠲᠤ ᠭᠥᠷᠢ ᠬ᠋᠊ / ᠰᠠᠷ ᠠ ︵ ᠨᠢ ᠭᠡ ᠰᠠᠭᠤ ᠳᠠᠯ ᠳᠢᠶᠡᠩ ᠬᠤᠸᠠ ᠪᠠᠷ ᠰᠦ᠋ᠯ ᠵᠢᠶ ᠡ ᠣᠷᠣᠭᠤ ᠯᠬᠤ ᠪᠠᠷ ᠬᠢᠵᠠᠭᠠ ᠷᠯᠠᠨ ᠠ︶ ᠡᠭ ᠦᠨ ᠡ ᠴᠡ ᠭᠠᠳ ᠠᠨ ᠠ B ᠵᠦ᠋ ᠢᠯ ᠦᠨ ᠰᠦ᠋ᠯ ᠵᠢᠶᠡᠨ ᠲᠤ ᠭᠠᠷᠬᠤ ᠬᠡᠯᠪᠡᠷᠢ ᠠᠴᠠ ᠬ᠊ ᠠᠷᠢᠯᠴ ᠠᠭᠠᠨ ᠤ ᠰ᠊ ᠦᠢᠳ ᠬᠡᠯ 0.02 ᠲᠤ ᠭᠥᠷᠢ ᠬ᠋᠊ / ᠮᠢᠨᠦ᠋ ᠲ᠊ ᠬᠤ ᠷᠢᠶᠠᠵᠤ ᠠᠪᠤ ᠨ᠊ ᠠ ︵1︶ ᠨᠢᠭᠡ ᠬᠡᠷ ᠡᠭᠯᠡᠭᠴᠢ ᠨᠢᠭᠡ ᠰᠠᠷ ᠠ ᠶᠢ ᠨ᠊ ᠰ᠊ ᠦᠯᠵᠢ ᠶᠡᠨ ᠲᠤ ᠭᠠᠷᠤᠭ ᠰᠠᠨ ᠴᠠ ᠬ᠋᠊ ᠨ᠊ ᠢ 𝑥 ᠴᠠᠭ᠂ ᠬ᠊ ᠣᠶᠠᠷ ᠵᠦ᠋ᠢ ᠯ᠊ ᠦᠨ ᠰᠦ᠋ᠢ ᠲᠬᠡᠯ ᠬᠤᠷᠢ ᠶᠠᠬᠤ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢᠨ ᠰᠦ᠋ᠢ ᠲᠬᠡᠯ ᠨᠢ ᠲ᠊ ᠤᠰᠪᠦ ᠷᠢ 𝑦 1 ︵ ᠲᠤ ᠭᠥᠷᠢ ᠬ᠋᠊︶᠂ 𝑦 2 ︵ ᠲᠤ ᠭᠥᠷᠢ ᠬ᠋᠊︶᠂ 𝑦1᠂ 𝑦 2 ᠪᠠ 𝑥 ᠦᠨ ᠲ᠊ ᠤᠬᠠᠢ ᠹᠦᠩ ᠺᠼ ᠦᠨ ᠠ ᠨᠠᠯᠢᠰ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ ᠢ ᠪᠢᠴ ᠢᠵᠤ ᠭᠠᠷᠭ ᠠ᠃ ︵2︶ ᠰᠦ᠋ ᠯᠵᠢᠶ ᠠ ᠳ᠋᠊ ᠦ ᠬ᠋᠊ ᠠᠷᠤᠭ ᠰᠠᠨ ᠴᠠᠭ ᠨᠢ ᠠᠳᠠᠯ ᠢᠬᠠᠨ ᠨᠦ᠋ ᠬᠦᠴᠡᠯ ᠳᠣᠣ ᠷ᠊ ᠠ᠂ ᠲᠠ ᠬᠡᠷᠡᠭᠯ ᠡᠭᠴᠢ ᠳ᠋᠊ ᠢ ᠬᠠᠪᠰ ᠤᠷᠴᠤ ᠠ ᠯᠢ ᠵᠦ᠋ᠢ ᠯ᠊ ᠦᠨ ᠠᠷᠭ ᠠ ᠪᠠ ᠷ᠊ ᠰ᠊ ᠦᠯᠵᠢ ᠶᠡᠨ ᠲᠤ ᠭᠠᠷᠪᠠ ᠯ᠊ ᠨ᠊ ᠡᠩ ᠵᠣᠭᠤ ᠰᠣᠨ ᠲᠤ ᠠᠷᠪᠢ ᠲᠠᠢ ᠶᠢ ᠲᠣᠳ ᠣᠷᠬᠠ ᠢᠯᠠ᠃ 22. ︵10 ᠬᠤᠪ ᠢ︶ ᠵᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ᠰᠢᠯᠤ ᠭᠤᠨ y = k𝑥 + 6 ᠨᠢ ᠲᠤᠰ ᠲ᠊ ᠤᠰ 𝑥 ᠲᠡᠩ ᠬᠡᠯᠢᠭ᠂ y ᠲᠡᠩ ᠬᠡᠯᠢᠭ ᠲᠠᠢ ᠴᠡᠭ E ᠪᠠ ᠴᠡᠭ F ᠲᠠᠢ ᠣᠭᠲᠣᠯ ᠣᠯᠴᠠᠨ ᠠ᠂ ᠴᠡᠭ E ᠶᠢᠨ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ᠊ ᠨᠢ ︵− 8,0︶᠂ ᠴ᠊ ᠡᠭ A ᠶᠢᠨ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ᠊ ᠨᠢ ︵0 ,3︶᠃ ︵1︶ k ᠶᠢᠨ ᠬ᠊ ᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠣ ᠯ᠊᠃ ︵2︶ ᠬᠡᠷᠪᠡ ᠴᠡᠭ P ︵𝑥, 𝑦︶ ᠨᠢ ᠬᠤᠶ ᠠᠳᠤᠭᠠᠷ ᠮᠦ᠋ᠴ ᠡ ᠶᠢ ᠨ᠊ ᠲ᠊ ᠣᠳᠤᠷᠠᠬ ᠢ ᠨᠢ ᠭᠡᠨ ᠬᠥᠳ ᠡᠯᠬᠦ ᠴᠡᠭ ᠭᠡᠪᠡᠯ᠂ p ᠴ᠊ ᠡᠭ ᠦᠨ ᠬᠥᠳ ᠡᠯᠬᠦ ᠶᠠᠪᠤᠴ ᠠ ᠲᠤ ᠮᠳᠠ᠂ ∆OP A ᠶ᠊ ᠶᠢᠨ ᠲ᠊ ᠠᠯᠠᠪᠠ ᠢ S ᠪᠠ 𝑥 ᠦᠨ ᠹᠦ ᠩᠺᠼ ᠦᠨ ᠢᠯᠡᠷᠬ ᠢᠯᠡᠯ ᠢ ᠲᠤᠷᠰ ᠢᠵᠤ ᠪᠢᠴᠢ ᠵᠤ ᠦᠵᠡ᠃ ᠪᠠ ᠰᠠ ᠬ᠊ ᠤᠪᠢᠰ ᠬᠤᠨ 𝑥 ᠦᠨ ᠬᠡᠮᠵ ᠢᠭᠳᠡᠯ ᠠ ᠪᠬᠤ ᠬᠡᠪᠴ ᠢᠶ ᠡ ᠶᠢ ᠪᠢᠴ ᠢᠵᠤ ᠭᠠᠷᠭ ᠠ᠃ ︵3︶ ᠰᠥ᠋ ᠪᠡᠭᠴᠢ ᠯᠡᠬᠦ᠄ ᠴᠡᠭ P ᠬᠥᠳ ᠡᠯᠭᠡᠭ ᠠ ᠬᠢᠭᠡᠳ ᠶᠠᠮᠠᠷ ᠪᠠᠢ ᠷᠢ ᠳ᠋᠊ ᠤ ᠬᠦᠷ ᠬᠦ ᠦᠶ ᠡᠰ᠂ ∆OP A ᠶᠢᠨ ᠲᠠᠯ ᠠᠪᠠᠢ ᠨ᠊ ᠢ 27 8 ᠤ ᠣᠯᠬᠤ ᠪᠣᠢ︖ ᠰᠢᠯ ᠲᠠᠭᠠᠨ ᠢ ᠬ᠊ ᠡᠯᠡᠵᠤ ᠦᠵᠡ᠃ 23. ︵1 0 ᠬ᠊ ᠤᠪᠢ︶ ᠠ ᠭᠠᠷ ᠦᠨ ᠳᠤᠯ ᠠᠭᠠᠴ ᠠ ᠨᠢ ᠪᠢᠳ ᠠᠨ ᠤ ᠠᠮᠢ ᠳᠤᠷᠠᠯ ᠲᠠᠢ ᠨᠢᠭᠲᠠ ᠬᠣ ᠯᠪᠣᠭᠳ ᠠᠯ ᠲ᠊ ᠠᠢ᠂ ᠲᠠ ᠳᠤᠯ ᠠᠭᠠᠴ ᠠ ᠶᠢ ᠨ᠊ ᠬ᠊ ᠡᠮᠵᠢᠭ ᠦᠷ ᠢ ᠨᠠᠷᠢ ᠨ᠊ ᠠ ᠵᠢᠭᠯ ᠠᠵᠤ ᠦᠵ ᠡᠪᠡ ᠦᠦ︖ ᠶᠢ ᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ᠨ᠊ ᠢᠭᠡᠨ ᠲᠤ ᠯᠠᠭᠠᠴ ᠠ ᠶᠢ ᠨ᠊ ᠬᠡᠮᠵᠢ ᠭᠦᠷ ᠦᠨ ᠲᠠᠢ ᠯᠪᠤᠷᠢ ᠵᠢᠷᠤᠭ᠂ ᠵᠩ ᠦᠨ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠬᠤ ᠪᠢᠶᠠᠷᠢ ᠨᠢ ℃ ᠪᠠᠷᠠᠭᠤᠨ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ᠊ ᠬ᠊ ᠤᠪᠢᠶ ᠠᠷᠢ ᠨᠢ ︵℉︶ ᠽ᠊ ᠧᠯᠰ ᠭᠷᠠ ᠳᠦ᠋ᠰ ᠢ 𝑥 ︵℃︶᠂ 𝑦 ︵℉︶ ᠬ᠋᠊ ᠡᠵᠤ ᠵᠢᠱᠢ ᠶ᠊ ᠡ᠂ ᠲᠡᠭᠡᠪᠡᠯ y ᠨᠢ 𝑥 ᠦᠨ ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠹᠦᠩ ᠺᠼ᠃ ︵1︶ ᠶᠢ ᠷᠤᠭ ᠳᠡᠭᠡ ᠷᠡᠬᠢ ᠲ᠊ ᠣᠭ ᠠ ᠪᠠ ᠷᠢᠮᠲ ᠠ ᠶᠢ ᠨᠠᠷᠢ ᠨ᠊ ᠠ ᠵᠢᠭᠯ ᠠᠵᠤ ᠦᠵᠡᠭᠡ ᠳ᠋᠊ y ᠪᠠ 𝑥 ᠦᠨ ᠹᠦᠩ ᠺᠼ ᠦᠨ ᠠ ᠨᠠᠯᠢᠰ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ ᠦᠨ ᠪᠢᠴ ᠢᠵᠤ ᠦᠵ ᠡ᠃ ︵2︶ ᠽᠧᠯ ᠰ᠊ ᠭᠷᠠᠳ ᠦᠰ ᠦᠨ ᠲᠤ ᠯᠠᠭᠠᠴ ᠠ ᠨ᠊ ᠢ ᠲ᠊ ᠡᠭ ᠡ ᠴᠡ ᠳᠣ ᠷᠤᠭᠰ ᠢ 15 ℃ ᠦᠶ ᠡᠰ᠂ ᠹᠠᠷᠧᠨ ᠾᠲ ᠤᠨ ᠳᠤᠯ ᠠᠭᠠᠨ ᠤ ᠬ᠊ ᠡᠮᠵᠢᠶ ᠡ ᠨ᠊ ᠢ ᠬᠡᠳ ᠤᠢ ᠤ ᠣᠢ︖ 24. ︵1 2 ᠬ᠊ ᠤᠪᠢ︶ ᠵ᠊ ᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ 𝑙 1 ᠪᠠ 𝑙2 ᠨᠢ ᠲᠣᠰ ᠲᠣ ᠰ᠊ ᠴ᠊ ᠠᠭᠠᠨ ᠳᠤᠩ ᠪᠠ ᠴᠠᠬᠢ ᠯᠭᠠᠨ ᠠᠷᠪᠢᠯ ᠠᠬᠤ ᠳᠤᠩ ᠦᠨ ᠰᠦ᠋ᠢ ᠲᠬᠡᠯ ᠪᠠ ᠭᠡᠷᠡᠯ ᠲᠦᠬᠦ ᠴᠠᠭ ᠤᠨ ᠲᠣᠬᠠᠢ ᠹᠦᠩ ᠺᠼ ᠦᠨ ᠬᠤᠯ ᠪᠣᠭᠳ ᠠᠯᠢᠯ ᠡᠷᠭᠡᠢ ᠯᠡᠯ ᠤ ᠨ᠊ ᠵᠢᠷᠤᠮᠠ ᠬ᠋᠊ ᠤ ᠣᠯᠤᠨ ᠠ᠂ ᠬᠤᠶ ᠠᠷ ᠵ᠊ ᠦᠢᠯ ᠦᠨ ᠳᠤᠩ ᠤᠨ ᠬᠡᠷᠡᠭ ᠯᠡᠵᠥ ᠲᠠᠢ ᠯᠬᠦ ᠴᠠᠭ ᠨᠢ ᠴᠥᠮ 2000 ᠴᠠᠭ ᠭᠡᠵᠤ᠂ ᠭᠡᠷᠡᠯ ᠲᠦᠬᠦ ᠮᠠᠶ ᠢᠭ ᠨᠢ ᠠᠳᠠᠯ ᠢᠬᠠᠨ ᠭᠡᠵᠤ ᠵᠢᠱᠢ ᠨ᠊ ᠡ᠃ ︵ᠰᠦ᠋ᠢ ᠲᠬᠡᠯ = ᠳᠤᠩ ᠦᠨ ᠬᠤᠳ ᠠᠯᠳᠤ ᠬᠤ ᠦᠨ ᠡ + ᠴᠠᠬᠢ ᠯᠭᠠᠨ ᠰᠦ᠋ ᠢᠳᠬ ᠡᠯ︶ ︵1︶ ᠶᠢ ᠷᠤᠮᠠᠭ ᠢ ᠥᠨ ᠳᠦᠰ ᠦᠯᠡᠨ 𝑙 1 ᠪᠠ 𝑙 2 ᠤ ᠨ᠊ ᠹᠦ ᠩᠺᠼ ᠦᠨ ᠬᠤᠯ ᠪᠣᠭᠳ ᠠᠯ ᠤ ᠨ᠊ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ ᠢ ᠪᠢᠴᠢ ᠵᠤ ᠬ᠋᠊ ᠠᠷᠭ ᠠ᠃ ︵2︶ ᠭᠡᠷᠡᠯ ᠲᠦᠬᠦ ᠴᠠᠭ ᠨᠢ ᠬᠡᠳᠦᠢ ᠦᠶ ᠡᠰ᠂ ᠬᠤᠶ ᠠᠷ ᠵᠦ᠋ ᠢᠯ ᠦᠨ ᠳᠤᠩ ᠤᠨ ᠰᠦ᠋ᠢ ᠲᠬᠡᠯ ᠨᠢ ᠲ᠊ ᠡᠩᠴ ᠡᠬᠦ ᠤ ᠣᠢ︖ ︵3︶ ᠪᠠᠲ ᠤ 25 00 ᠴᠠᠭ ᠲᠤ ᠩ᠊ ᠬ᠋᠊ ᠡᠷᠡᠯᠲ ᠦᠭᠦᠯ ᠬᠦ ᠪᠠᠷ ᠲᠦ᠋ ᠯᠦᠪᠯ ᠡᠵᠡᠢ᠂ ᠲᠡᠷᠡ ᠨᠢᠭᠡ ᠴᠠᠭᠠᠨ ᠳᠤᠩ ᠪᠠ ᠨᠢᠭᠡ ᠴᠠᠬ ᠢᠯᠭᠠᠨ ᠠᠷᠪᠢᠯ ᠠᠬᠤ ᠳᠤᠩ ᠬ᠊ ᠤᠳᠠᠯ ᠳᠤᠨ ᠠᠪᠴᠠᠢ᠃ ᠲ᠊ ᠠ ᠲ᠊ ᠡᠭᠦᠨ ᠢ ᠬ᠊ ᠠᠪᠰᠤ ᠷᠴᠤ ᠵᠣᠭᠤ ᠰᠣᠨ ᠲᠤ ᠬᠠᠮᠤ ᠬ᠋᠊ ᠠᠷᠪᠢᠲ ᠠᠢ ᠳ᠋᠊ ᠸᠩ ᠬ᠊ ᠡᠷᠡᠭᠯ ᠡᠬᠦ ᠲ᠊ ᠦᠰᠦᠪ ᠢ ᠲ᠊ ᠥᠯᠥᠪᠯ ᠡᠵᠤ ᠦᠵᠡ᠃ 25. ︵1 0 ᠬ᠊ ᠤᠪᠢ︶ ᠨᠢ ᠭᠡᠨ ᠲᠤᠷᠰ ᠢᠯᠲᠠ ᠶᠢᠨ ᠲᠠᠷᠢ ᠶᠠᠨ ᠤ ᠡᠳ ᠦᠷ ᠤ ᠣᠯᠭᠠᠨ ᠤ ᠤ ᠰᠤ ᠬ᠊ ᠡᠷᠡᠭᠰ ᠡᠬᠦ ᠬ᠊ ᠡᠮᠵᠢᠶ ᠡ 𝑦 ︵kg︶ ᠪᠠ ᠤᠷᠭᠤ ᠬᠤ ᠴ᠊ ᠠᠭ 𝑥 ︵ᠡᠳ ᠦᠷ︶ ᠤᠨ ᠬᠣ ᠭᠤᠷᠣᠨᠳ ᠤᠬᠢ ᠬᠣ ᠯᠪᠣᠭᠳ ᠠᠯ ᠨ᠊ ᠢ ᠳᠠᠬ ᠢᠷ ᠱᠤ ᠭᠤᠮᠤ ᠨ᠊ ᠶᠢ ᠷᠤᠭ ᠮᠡᠲᠦ ᠡᠳᠡᠭᠡᠷ ᠲᠠᠷᠢ ᠮᠠᠯ ᠤ ᠨ᠊ ᠠ ᠷᠪᠠᠳ ᠤᠭᠠᠷ ᠡᠳ ᠦᠷ᠂ ᠭᠤᠴ ᠢᠳᠤᠭᠠᠷ ᠡᠳ ᠦᠷ ᠦᠨ ᠤᠰᠤ ᠬᠡᠷᠡᠭ ᠰᠡᠬᠦ ᠬᠡᠮᠵᠢ ᠶ᠊ ᠡ ᠨᠢ ᠲ᠊ ᠣᠰ ᠲᠣᠰ 2000 kg᠂ 3000 kg᠂ ᠲ᠊ ᠥᠴᠢ ᠳᠦᠭᠡᠷ ᠡᠳᠦᠷ ᠠᠴᠠ ᠬᠤᠢ ᠰᠢ ᠡᠳᠦᠷ ᠪᠣᠯᠭᠠᠨ ᠤ ᠤ ᠰᠤ ᠬᠡᠷᠡᠭ ᠰᠡᠬᠦ ᠬᠡᠮᠵᠢ ᠶ᠊ ᠡ ᠨ᠊ ᠢ ᠡᠮ ᠦᠨ ᠠ ᠡᠳ ᠦᠷ ᠡ ᠴᠡ ᠪᠠᠨ 200k g ᠨ᠊ ᠡᠮᠡᠭᠳ ᠠ ᠡ᠃ ︵1︶ 𝑥 ≤ 40 ᠪᠠ 𝑥≥ 40 ᠦᠶ ᠡᠰ ᠦᠨ 𝑦 ᠪᠠ 𝑥 ᠦᠨ ᠬᠤᠭᠤ ᠷᠣᠨᠳ ᠤᠬᠢ ᠬᠤᠯ ᠪᠣᠭᠳ ᠠᠯ ᠤ ᠨ᠊ ᠢᠯᠡᠷᠬ ᠢᠯᠡᠯ ᠢ ᠲ᠊ ᠣᠰ ᠲ᠊ ᠣᠰ ᠤ ᠢᠴᠢᠵᠦ ᠭᠠᠷᠭ ᠠ᠃ ︵2︶ ᠬᠡᠷᠪᠡ ᠡᠳᠡᠭᠡᠷ ᠲᠠᠷ ᠢᠮᠠᠯ ᠤᠨ ᠡ ᠳᠦᠷ ᠪᠣᠯᠭᠠᠨ ᠤ ᠤ ᠰᠤ ᠬ᠊ ᠡᠷᠡᠭᠰ ᠡᠬᠦ ᠬ᠊ ᠡᠮᠵᠢ ᠶ᠊ ᠡ ᠨ᠊ ᠢ ᠶᠠᠬ ᠡ ᠪᠤ ᠶᠤ ᠲ᠊ ᠡᠩᠴ ᠡᠭᠦᠦ 4000kg ᠦᠶ ᠡᠰ ᠬᠦᠮᠦᠨ ᠦ ᠬᠦᠴᠦ ᠪᠠᠷ ᠤᠰ ᠤᠯᠠᠬᠤ ᠴᠢᠬᠤᠯ ᠠᠲᠠᠢ᠂ ᠲᠡᠭᠡᠪᠡ ᠯ᠊ ᠠ ᠯᠢ ᠡ ᠳᠦᠷ ᠠᠴᠠ ᠡᠬᠢᠯ ᠡᠵᠦ ᠬᠦᠮᠦᠨ ᠦ ᠬᠦᠴᠦ ᠪᠠᠷ ᠤᠰᠤ ᠯᠠᠬᠤ ᠴᠢᠬᠤᠯ ᠠᠲᠠᠢ ᠤ ᠣᠢ︖