ᠤᠷᠳᠤᠰ ᠬᠤᠲᠠ ᠶᠢᠨ 2019 ᠣᠨ ᠤ ᠰᠤᠷᠤᠯᠭ᠎ᠠ ᠲᠡᠭᠦᠰᠴᠦ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠳᠠᠪᠰᠢᠬᠤ ᠰᠢᠯᠭᠠᠯᠲᠠ ᠶᠢᠨ ᠰᠡᠳᠦᠪ 2019鄂尔多斯市中考.docx

ᠨᠢᠭᠡ᠂ ᠬ᠋᠊ ᠠᠭᠴᠠ ᠬ᠊ ᠠᠷᠢᠭᠤᠯᠲᠠ ᠰᠤ ᠩᠭᠤᠬ ᠤ ᠰᠡᠲᠤᠪ᠃ ︵ ᠤ ᠠᠭ ᠠ ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬ᠊ ᠤᠪᠢ᠂ ᠨᠠ ᠢᠲᠡ 30 ᠬᠤᠪ ᠢ︶ 1. ᠶᠤᠰᠤᠲᠠᠢ ᠲᠤᠭ ᠠ − 13 ᠶᠢᠨ ᠡ ᠰᠡᠷᠬ ᠦ ᠲᠤᠭ ᠠ ᠨᠢ ︵︶ A. −3 B. − 13 C. 13 D. 3 2. ᠳᠠᠷᠠᠭᠠ ᠬᠢ ᠲᠤ ᠷᠪᠡᠨ ᠵᠢᠷ ᠤᠭ ᠲᠤ ᠷᠰᠤ ᠲᠤ᠂ ᠨᠤᠭ ᠤᠯᠬᠤ ᠪᠠᠷ ᠲᠠᠮᠵᠢ ᠨ᠊ ᠵᠢᠷ ᠤᠭ ᠲᠠᠬᠢ ᠭᠧᠣ ᠮᠧᠳ᠋ᠷ ᠢ ᠶᠢᠨ ᠪᠡᠶ ᠡ ᠶᠢ ᠬᠦᠷᠢᠶᠡᠯᠡ ᠨ᠊ ᠪᠦᠳᠥᠭᠡ ᠵᠤ ᠲ᠊ ᠠᠢᠯᠬᠦ ᠨᠢ ︵︶ A. B. C. D. 3. ᠵᠢᠬᠦ ᠷᠲᠡᠨ ᠦ ᠬᠢᠵᠢ ᠬ᠋᠊ ᠦᠨ ᠸᠢ ᠷᠦ᠋ᠰ ᠦ ᠨ᠊ ᠷ᠊ ᠠᠳᠢᠤᠰ ᠨᠢ ᠪᠠᠷᠤᠭ 0. 000 00 0 4 5m᠂ ᠲᠡᠭᠦ ᠨ᠊ ᠦ ᠳᠢᠶᠠᠮ ᠧᠳ᠋ᠷ ᠢ ᠰᠢᠨᠵᠢ ᠯᠡᠬᠦ ᠤᠬᠠᠭ ᠠᠨᠴᠢ ᠲᠤᠭ ᠠ ᠲ᠊ ᠡᠮᠳᠡᠭᠯ ᠡᠬᠦ ᠠ ᠷᠭ ᠠ ᠪᠠᠷ ᠢᠯᠡᠷ ᠭᠡᠢᠯᠡᠪ ᠡᠯ ︵︶ A. 0.9 × 10 −7 𝑚 B. 9 × 10 −7 𝑚 C. 9 × 10 −6 𝑚 D. 9 × 10 7𝑚 4. ᠵᠢᠷᠤᠭ ᠮᠡᠲᠤ᠂ ᠲᠡᠭᠰ ᠢ ᠲ᠊ ᠥᠷᠪ ᠡᠯᠵᠢᠨ AB CD ᠶᠢᠨ ᠭᠠᠳᠠᠨ ᠠ ᠲ᠊ ᠠᠯ ᠠ ᠲᠤ ᠲᠡᠩᠴ ᠡᠬᠦᠦ ᠲᠠᠯᠠᠳᠤ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊ AB E ᠶᠢ ᠪᠠᠢ ᠭᠤᠯᠤᠨ ᠠ᠂ ᠲᠡᠭᠡᠪᠡᠯ ∠B ED ᠨᠢ ︵︶ A . 15° B . 35° C. 45° D. 55° 5. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠪᠣᠳᠣᠯᠭ ᠠ ① √9 = ±3 ② 3𝑎 2− 2𝑎 = 𝑎 ③ ︵2 𝑎 2︶ 3 = 6𝑎 6④ 𝑎 8÷ 𝑎 4 = 𝑎 2 ⑤ √ −27 3 = −3 ᠡ ᠭᠦᠨ ᠦ ᠳᠣᠲᠣᠷ ᠠ ᠠᠴ ᠠ ᠲᠤᠷ ᠠ ᠶᠢᠨ ᠨᠢ ᠭᠡ ᠤ ᠣᠳᠣᠯᠭ ᠠ ᠶᠢ ᠰᠤᠭᠤᠯᠵᠤ ᠠᠪᠬᠤ ᠲᠤ᠂ ᠪᠣᠳᠣᠯᠭ ᠠ ᠶᠢᠨ ᠳᠦ᠋ᠩ ᠨᠢ ᠵᠥ ᠤ ᠪᠣᠯᠬᠤ ᠶᠢ ᠨ᠊ ᠲ᠊ ᠣᠬᠢᠶ ᠠᠯᠳᠤ ᠮᠵᠢ ᠨᠢ ︵︶ A. 15 B. 25 C. 35 D. 45 6. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠬᠦ ᠰᠥᠨᠥ ᠭᠳᠦ ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠠᠩ ᠬᠢ ᠶᠢ ᠨ᠊ 10 ᠰᠤ ᠷᠤᠭᠴ ᠢ ᠶᠢᠨ ᠳᠤᠮ ᠳᠠᠳᠤ ᠰᠢᠯᠭᠠ ᠯᠲᠠ ᠶᠢᠨ ᠲᠠᠮ ᠢᠷ ᠤᠨ ᠬᠢᠷᠢ ᠪᠦ ᠳᠦᠮᠵᠢ ᠶᠢ ᠨ᠊ ᠪᠦᠷᠢᠳᠭᠡᠯ ᠪᠣᠯᠣ ᠨ᠊ ᠠ᠄ ᠬᠡᠷᠪ ᠡ ᠬᠢᠷᠢ ᠪᠦ ᠳᠦᠮᠵᠢ ᠶᠢᠨ ᠳᠤᠮ ᠳᠠᠴᠢ ᠲᠤᠭ ᠠ ᠨᠢ 23᠂ ᠳᠤᠮ ᠳᠠ ᠪᠠᠢ ᠷᠢ ᠶᠢ ᠨ᠊ ᠲ᠊ ᠣᠭ ᠠ ᠨᠢ 𝑎᠂ ᠮᠣᠳ᠋ ᠨᠢ b ᠪᠣᠯ᠂ 𝑎 − 𝑏 ᠶᠢᠨ ᠬᠡᠮ ᠵᠢᠭᠳᠡᠯ ᠨᠢ ︵︶ A. −5 B. −2 .5 C. 2.5 D. 5 7. ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠵᠢᠰᠢᠬ ᠦᠯᠵᠢ ᠨ᠊ AB CD ᠲᠤ᠂ ∠B DC = 47 °42 ′᠂ ᠣᠣᠢ ᠭᠤᠷ ᠳᠢᠭ ᠢᠶ ᠠᠷ ᠶᠢ ᠷᠤᠭ ᠪᠠᠢ ᠭᠤᠯᠤᠭ ᠰᠠᠨ ᠣᠷ ᠣᠮ ᠢ ᠦᠨᠳᠤᠰ ᠤᠯᠡᠪ ᠡᠯ᠂ α ᠶᠢᠨ ᠭᠷ ᠠᠳᠦ᠋ᠰ ᠤ ᠨ᠊ ᠲ᠊ ᠣᠭ ᠠ ᠨᠢ ︵︶ A. 67 °2 9′ B. 67°9′ C. 66 °2 9′ D. 66°9′ 8. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠬᠡᠯᠡᠯᠭ ᠡ ᠡ ᠴᠡ ᠵᠥ ᠤ ᠪᠣᠯᠬᠤ ᠨᠢ ︵︶ ᠬᠢᠷᠢ ᠪᠦᠳᠦ ᠮᠵᠢ ︵ᠬᠤᠪ ᠢ︶ ᠬᠦᠮᠦᠨ ᠢ ᠲᠤᠭ ᠠ 30 2 𝑥20 𝑦15 1 A E C D B ᠤᠷᠳᠤ ᠰ᠊ ᠬᠤᠳᠠ ᠢᠢᠨ 20 19 ᠣᠨ ᠤ ᠠᠩᠬ ᠠ ᠲᠤ ᠮᠳᠠᠳᠤ ᠢᠢ ᠨ᠊ ᠰᠤᠷ ᠤᠯᠭ ᠠ ᠲᠡᠭ ᠦᠰᠴ ᠤ ᠰᠤᠷ ᠭᠠᠭ ᠤᠯᠢ ᠲᠠᠪᠰ ᠢᠬᠤ ᠰᠢᠯ ᠭᠠᠯᠳᠠ ᠢᠢᠨ ᠰᠡᠳᠤ ᠤ ① ᠹᠦᠩ ᠺᠼ y = √ 1 3𝑥 +1 ᠲᠤ ᠬᠤᠪ ᠢᠰᠬᠤᠨ 𝑥 ᠤᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠᠪ ᠬᠤ ᠬᠡᠪᠴ ᠢᠶ ᠡ ᠨᠢ 𝑥 ≥ − 13 ② ᠬᠡᠷᠪ ᠡ ᠠ ᠳᠠᠯᠢ ᠬᠠᠵᠠ ᠭᠤᠲᠤ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊ ᠤ ᠬᠤᠶ ᠠᠷ ᠲ᠊ ᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠨᠢ ᠲᠣᠰ ᠲᠣᠰ 3 ᠪᠠ 7 ᠪᠣᠯ᠂ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠳᠤᠭᠠᠷ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠨᠢ 3 ᠪᠤᠶ ᠤ 7 ᠤ ᠣᠯᠣᠨ ᠠ᠃ ③ ᠨᠢᠭᠡᠨ ᠵᠥ ᠤ ᠵᠢᠷ ᠭᠤᠭ ᠠᠨ ᠥᠨᠴ ᠥᠭᠳᠥ ᠶᠢ ᠨ᠊ ᠲ᠊ ᠣᠳᠣᠭᠠᠳᠤ ᠥᠨᠴ ᠥᠭ ᠦ ᠨ᠊ ᠨᠠ ᠢᠯᠡᠪᠤ ᠷᠢ ᠨᠢ ᠭᠠᠳᠠᠭᠠ ᠲᠤ ᠥ ᠨᠴᠥᠭ ᠦᠨ ᠨᠠᠢ ᠯᠡᠪᠤᠷ ᠢ ᠶᠢ ᠨ᠊ ᠲᠠᠬᠢᠨ ᠪᠣᠯᠣ ᠨ᠊ ᠠ᠃ ④ ︽ᠲ᠊ ᠣᠳᠣᠭᠠᠳᠤ ᠥᠷ ᠥᠭᠡᠯ ᠥᠨᠴ ᠥᠭ ᠨᠢ ᠬᠠᠷᠢ ᠯᠴᠠᠨ ᠨᠥ ᠬᠥᠪᠤᠷ ᠢ ᠥ ᠨᠴᠥᠭ ᠪᠣᠯᠣ ᠨ᠊ ᠠ︾ ᠭᠡᠬᠦ ᠦᠬᠦ ᠯᠡᠯ ᠨᠢ ᠵᠢᠩᠭ ᠬᠢᠨᠢ ᠦᠬᠦ ᠯᠡᠯ ᠪᠣᠯᠣ ᠨ᠊ ᠠ᠃ ⑤ 𝑥 ᠦ ᠨ᠊ ᠲᠤᠬᠠᠢ ᠨᠢᠭᠡ ᠥᠯ ᠥ ᠮᠡ ᠳᠡᠭᠳᠡᠭ ᠴᠢᠳᠡᠢ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡ ᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳ ᠭᠡᠯ 𝑥 2 − ︵𝑘 + 3︶ 𝑥+ 𝑘= 0 ᠲ᠊ ᠤ ᠲᠡ ᠩᠴᠡᠬᠦ ᠦ ᠪᠤᠰᠤ ᠬ᠊ ᠣᠶᠠᠷ ᠪᠣᠳᠠᠳᠤ ᠲᠣ ᠭᠠᠨ ᠢᠵᠠᠭ ᠤᠷ ᠲᠠ ᠢ᠃ A. ①②③ B. ①④ ⑤ C. ②④ D. ③⑤ 9. ᠵᠢᠷᠤᠭ ᠮᠡᠲᠤ᠂ ᠲᠡᠭᠰ ᠢ ᠥ ᠨᠴᠥᠭ ᠲᠤ 𝐴𝐵 𝐶𝐷 ᠪᠣᠯᠣ ᠨ᠊ ᠷ᠊ ᠤᠮᠪ 𝐸𝐹𝐺𝐻 ᠶᠢᠨ ᠲᠠᠰ ᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠴᠥᠮ ᠴᠡᠭ 𝑂 ᠲᠤ ᠣᠭ ᠳᠣᠯᠣᠯ ᠴᠠᠬᠤ ᠪᠥᠭᠡᠳ 𝐸𝐺 ∕∕ 𝐵𝐶᠂ ᠲ᠊ ᠡᠭᠰᠢ ᠥᠨᠴ ᠥᠭᠳᠥ ᠶᠢ ᠨᠤᠭ ᠤᠯᠵᠤ᠂ ᠴᠡᠭ 𝐶 ᠪᠣᠯᠣ ᠨ᠊ 𝑂 ᠴᠡᠭ ᠶᠢ ᠲᠠᠪᠬᠤᠴ ᠠᠭᠤᠯᠪ ᠠᠯ᠂ ᠨᠤᠭᠤᠯᠤᠭ ᠠᠰᠤ 𝑀𝑁 ᠨᠢ ᠴᠡᠭ 𝐺 ᠶᠢ ᠳᠠᠭᠠ ᠷᠢᠨ ᠠ᠃ ᠬᠡᠷᠪ ᠡ 𝐴𝐵 = √6 , 𝐸𝐹 = 2 , ∠ 𝐻 = 120 ° ᠤ ᠣᠯ 𝐷𝑁 ᠤ ᠤᠷ ᠲᠤ ᠨᠢ ︵︶ A. √6 −√ 3 B. √6 +√ 3 2 C. √32 D. 2√ 3− √6 10. ︽ᠢ ᠷᠤᠭᠡᠳᠤᠢ ᠵᠦ᠋ᠩ ᠴᠢᠷ ᠮᠠᠢ︾ ᠭᠡᠬᠦ ᠲᠧ ᠯᠧᠢ ᠰ᠊ ᠬᠤᠷᠢᠶ ᠠ ᠫᠷ ᠣᠭᠷᠠᠮ ᠲᠤ᠂ ᠬᠦᠰ ᠡᠯᠡᠩ ᠪᠠ ᠴᠡᠩᠭᠡᠯ ᠲᠤ ᠵᠢᠯᠣ ᠭᠤᠴ ᠢ ᠦᠭᠡᠢ ᠮᠠᠰᠢᠨ ᠲᠡ ᠷᠭᠡ ᠪᠠᠷ ᠪᠠᠷ ᠠᠭ ᠠ ᠲᠡᠭᠡᠭᠡᠪᠤᠷ ᠢᠯᠡᠨ ᠬᠦᠷᠭᠡᠬ ᠦ ᠲᠣ ᠭᠯᠠᠯᠳᠠ ᠭᠠᠷᠭ ᠠᠵᠠᠢ᠃ ᠬᠦ ᠰᠡᠯᠡᠩ ᠦᠨ ᠡᠵᠡᠮᠰᠢ ᠭᠰᠡᠨ ᠬᠤᠷᠳᠤᠨ ᠲᠡᠷᠭᠡ ᠪᠠ ᠴᠡᠩᠭᠡᠯ ᠲᠤ ᠶᠢᠨ ᠡᠵᠡᠮᠰᠢᠭ ᠰᠡᠨ ᠣᠳᠠᠭ ᠠᠨ ᠲᠡᠷᠭᠡ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ 𝐴 ,𝐵 ᠬᠤᠶ ᠠᠷ ᠭᠠᠵᠠᠷ ᠠᠴᠠ ᠵᠡᠷ ᠭᠡ ᠪᠠᠷ ᠭᠠ ᠷᠴᠤ᠂ ᠥᠭᠡᠳᠡ ᠥᠭᠡᠳᠡ ᠠᠴᠠ ᠪᠠᠨ ᠶᠠᠪᠤᠪᠠ᠃ ᠬᠤᠷᠳᠤᠨ ᠲᠡ ᠷᠭᠡ ᠨᠢ 𝐵 ᠭᠠᠵᠠᠷ ᠲᠤ ᠬᠦ ᠷᠦᠭᠡᠳ 3 𝑠 ᠵᠣᠭᠰ ᠣᠵᠤ ᠪᠠᠷᠠᠭ ᠠ ᠪᠠᠨ ᠪᠠᠭᠤᠯ ᠭᠠᠭᠰᠠᠨ ᠤ ᠳᠠᠷᠠᠭ ᠠ᠂ ᠤᠤᠯ ᠤᠨ ᠵᠠᠮ ᠢᠶᠠᠷ ᠢᠶᠡ ᠨ᠊ 𝐴 ᠭᠠᠵᠠᠷ ᠲᠤ ᠪᠤᠴᠠᠨ ᠠ᠃ ᠤᠳᠠ ᠭᠠᠨ ᠲᠡᠷᠭᠡ ᠨᠢ 𝐴 ᠭᠠᠵᠠᠷ ᠲᠤ ᠬᠦ ᠷᠦᠭᠡᠳ ᠠ ᠮᠠᠷᠠᠵᠠᠢ᠃ ᠳᠣᠣᠷ ᠠᠬᠢ ᠵᠢᠷᠤᠭ ᠪᠣᠯ ᠬᠤᠶ ᠠᠷ ᠲᠡ ᠭᠡᠨ ᠦ ᠬᠤᠭᠤᠷ ᠣᠨᠳᠤᠬ ᠢ ᠵᠠ ᠢ 𝑦 ︵ᠨᠢᠭᠡ ᠴᠢ :𝑚︶ ᠪᠠ ᠠᠶᠠᠯ ᠠᠭᠰᠠᠨ ᠬᠤᠭᠤ ᠴᠠᠭ ᠠ 𝑥 ︵ᠨᠢᠭᠡ ᠴᠢ᠄ 𝑠︶ ᠤᠨ ᠹᠦᠩᠺᠼ ᠦ ᠨ᠊ ᠵᠢᠷ ᠤᠮᠠᠭ ᠪᠣᠯᠣᠨ ᠠ᠃ ᠵᠢᠷᠤᠭ ᠲᠠᠬ ᠢ ᠮᠡ ᠳᠡᠭᠡ ᠵᠠᠩᠭᠢ ᠶᠢ ᠦᠨᠳᠤ ᠰᠤᠯᠡᠪ ᠡᠯ᠂ 𝑎 , 𝑏 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨᠢ ᠲᠤᠰ ᠲ᠊ ᠤᠰ ︵︶ A. 39,26 B. 39,26.4 C. 38,26 D . 38,26.4 ᠬᠤᠶ ᠠᠷ᠂ ᠬᠤᠭᠤᠰᠤᠨ ᠲᠤ ᠲ᠊ ᠠᠭᠯᠠᠬᠤ ᠰᠡᠲᠤᠪ᠃ ︵ ᠤ ᠠᠭ ᠠ ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬ᠊ ᠤᠪᠢ᠂ ᠨᠠ ᠢᠲᠡ 18 ᠬᠤᠪ ᠢ︶ 11. ᠪᠣᠳ ᠣ᠃ ︵π + 1︶ 0+ |√ 3− 2| − ︵12︶ −2 = ︵︶ 12. ᠨᠢᠭᠡ ᠪᠥᠯᠥᠭ ᠲ᠊ ᠣᠭ ᠠ ᠪᠠᠷ ᠢᠮᠳᠠ −1,0,1, 2,3 ᠶᠢᠨ ᠰ᠊ ᠠᠷᠨᠢᠴ ᠡ ᠨᠢ ︵︶ 13. ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠤ᠂ ∆𝐴𝐵𝐶 ᠲᠤ᠂ 𝐴𝐵 = 𝐴𝐶 , 𝐴𝐵 ᠪᠠᠷ ᠳᠢᠶ ᠠᠮᠧᠳ᠋ᠷ ᠪᠤ ᠯᠭᠠᠭᠰᠠᠨ ⊙ O ᠨᠢ 𝐵𝐶 , 𝐴𝐶 ᠲᠠᠢ ᠲᠤᠰ ᠲᠤᠰ ᠴᠡᠭ 𝐷 , 𝐸 ᠲᠤ ᠣᠭᠳᠣ ᠯᠣᠯᠴᠠᠨ ᠠ᠃ 𝐷𝐸 ᠶᠢ ᠬᠤᠯᠪᠤ ᠵᠤ᠂ ᠴᠡᠭ 𝐷 ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ 𝐷𝐹 ⊥ 𝐴𝐶 ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠪᠠ ᠯ᠊᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ 𝐹᠃ ᠬᠡᠷᠪᠡ 𝐴𝐵 = 6 , ∠𝐶𝐷𝐹 = 15 ° ᠪᠣᠯ᠂ ᠰᠡᠭᠦᠳᠡ ᠷ᠊ ᠲᠠᠢ ᠭᠡᠰᠡᠭ ᠦᠨ ᠲᠠᠯᠠᠪ ᠠᠢ ᠨᠢ ︵︶᠃ E D' D C A O H G F MB 14. ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊ ᠤ ᠨᠢᠭᠡ ᠲᠠᠯ ᠠ ᠳ᠋᠊ ᠡᠭᠡᠷᠠᠬ ᠢ ᠳ᠋᠊ ᠤᠮᠲᠠ ᠱᠤᠭᠤᠮ ᠤᠨ ᠤᠷᠳᠤ ᠨᠢ ᠡᠨᠡ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠲᠠᠢ ᠤ ᠠᠨ ᠲᠡᠩᠴ ᠡᠬᠦᠦ ᠪᠣᠯ᠂ ᠡᠨᠡ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊ ᠢ ︽ᠰᠤᠨᠢᠷ ᠬᠠᠯᠲᠠᠢ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊︾ ᠭᠡᠨ ᠡ᠃ ᠬᠡᠷᠪ ᠡ 𝑅𝑡 ∆𝐴𝐵 𝐶 ᠨᠢ ︽ᠰᠤᠨᠢᠷ ᠬᠠᠯᠲᠠᠢ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊︾ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ᠂ ∠𝐴 = 90° ᠪᠣᠯ᠂ 𝑡 𝑎𝑛∠ 𝐴𝐵 𝐶 = ︵︶ 15. ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠤ᠂ ᠨᠢᠭᠡᠨ ᠲᠠᠬᠢᠷ ᠱᠤᠭᠤᠮ A 1 B 1 A 2 B 2 A 3 B 3 A 4 B 4 ᠁ ᠪᠣᠢ᠂ ᠲᠡᠷᠡ ᠨᠢ A 1 ︵0 ,0︶ ,B 1 ︵4 ,4︶ A 2 ︵8 ,0︶ ᠢ ᠲᠠᠭ ᠠᠷᠢᠵ ᠤ ᠪᠦᠳᠦ ᠭᠰᠡᠨ ᠲᠠᠬᠢᠷ ᠱᠤᠭᠤᠮ ᠢ ᠲᠡᠰ ᠳᠠᠷᠠᠭ ᠠᠯᠠᠨ 8,16 ,24 , ᠁ ᠨ᠊ ᠢᠭᠡᠴᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠵ ᠤ ᠣᠯᠵ ᠠᠢ᠃ ᠰᠢᠯᠤᠭᠤᠨ 𝑦= 𝑘𝑥 + 2 ᠤ ᠣᠯᠣᠨ ᠲᠤᠰ ᠲᠠᠬᠢᠷ ᠱᠤᠭ ᠤᠮ ᠨᠢ 2 𝑛 ︵𝑛≥ 1 ᠪᠥᠭᠡᠳ 𝑛 ᠨᠢ ᠪᠦ ᠬᠥᠯᠢ ᠲᠤᠭ ᠠ︶ ᠣᠭᠳᠣᠯ ᠣᠯᠴᠠᠯ ᠤᠨ ᠴᠡᠭ ᠲᠠᠢ ᠪᠣᠯ᠂ 𝑘 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨᠢ ︵︶ 16. ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠤ᠂ ᠲ᠊ ᠥᠪ ᠥᠨᠴᠥ ᠬ᠋᠊ ᠨᠢ 90 ° ᠪᠤ ᠯᠬᠤ ᠳᠡᠪᠢᠭᠦᠷ ᠬᠡᠯᠪᠡ ᠷᠢᠳᠤ 𝑂𝐴𝐵 ᠲᠤ᠂ 𝑂𝐵 = 2 , 𝑃 ᠨᠢ 𝐴𝐵̂ ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠲᠤᠷ ᠠ ᠶᠢᠨ ᠨᠢᠭᠡᠨ ᠴᠡ ᠬ᠋᠊᠂ ᠴᠡᠭ 𝑃 ᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ 𝑃𝐸 ⊥ 𝑂𝐵 ᠢᠶᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠪᠠ ᠯ᠊᠂ ᠡᠭ ᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ 𝐸᠃ 𝑀 ᠨᠢ ∆𝑂𝑃 𝐸 ᠶᠢᠨ ᠲᠣᠳᠣᠭᠠ ᠲᠤ ᠲᠥᠪ ᠬᠡᠵ ᠤ ᠵᠢᠱᠢᠪᠡᠯ᠂ ᠴᠡ ᠬ᠋᠊ 𝑃 ᠨᠢ ᠴᠡᠭ 𝐴 ᠠᠴᠠ ᠬᠦᠳᠡᠯ ᠭᠡᠭᠡᠨ ᠬᠢᠵᠤ ᠴᠡᠭ 𝐵 ᠬᠦᠷ ᠬᠦ ᠦ ᠶᠡᠰ᠂ ᠲᠣᠳᠣᠭᠠ ᠲᠤ ᠲᠥᠪ 𝑀 ᠶᠢᠨ ᠶᠠᠪᠤᠵ ᠤ ᠥ ᠩᠭᠡᠷ ᠡᠭᠰᠡᠨ ᠵᠠᠮ ᠤ ᠨ᠊ ᠤᠷ ᠲᠤ ᠨᠢ ︵︶ ᠭᠤᠷ ᠪᠠ᠂ ᠪᠣᠳ ᠣᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠲᠤᠪ᠃ ︵ᠨᠠ ᠢᠲᠡ 72 ᠬᠤᠪ ᠢ︶ 17. ︵ᠲ᠊ ᠤᠰ ᠪᠠᠭ ᠠ ᠰᠡᠲᠤᠪ ᠨᠠᠢ ᠲᠡ 8 ᠬ᠊ ᠤᠪᠢ︶ ︵1︶ ᠤᠷᠢᠳ ᠠᠪᠠᠷ ᠬᠢᠯᠪ ᠠᠷᠴᠢᠯ ᠠ᠄ 𝑥 2 −4 𝑥 2 −4 𝑥+ 4 + 𝑥𝑥 2−𝑥 ÷ 𝑥− 2 𝑥− 1 ᠳᠠᠷᠠᠭ ᠠ ᠨᠢ 𝑥 ᠲᠤ −1 ≤ 𝑥≤ 3 ᠬᠡᠪᠴ ᠢᠶᠡᠨ ᠳᠣᠲᠣᠷ ᠠ ᠠᠴ ᠠ ᠳ᠋᠊ ᠣᠬᠢᠷᠠ ᠮᠵᠢᠳᠠᠢ ᠨᠢᠭᠡ ᠪᠥᠬ ᠥᠯᠢ ᠲᠤᠭ ᠠ ᠶᠢ ᠰᠤᠩ ᠭᠤᠵᠤ᠂ ᠬᠡᠮ ᠵᠢᠭᠳᠡᠯ ᠢ ᠨᠢ ᠣᠯ᠃ ︵2︶ ᠲᠡ ᠩᠴᠡᠳ ᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢ ᠨ᠊ ᠪᠥᠯᠥ ᠬ᠋᠊ { − ︵2 𝑥+ 1︶ 2OA᠂ ᠴᠡᠭ C ᠨᠢ OB ᠳᠡᠭᠡᠷᠠᠬ ᠢ ᠨᠢᠭᠡᠨ ᠴᠡᠭ᠂ ∠CAD = 60° ᠪᠣᠯ᠂ OC ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠶᠢ ᠣᠯ᠃ 24. ︵ᠲᠤᠰ ᠪᠠᠭ ᠠ ᠰᠡᠲᠤᠪ ᠨᠠᠢ ᠲᠡ 12 ᠬᠤᠪ ᠢ︶ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠤ᠂ ᠬᠠᠶᠠᠯ ᠲᠠ ᠶᠢᠨ ᠱ᠊ ᠤᠭᠤᠮ 𝑦 = 𝑎𝑥 2+ 𝑏𝑥 − 2 ︵𝑎≠ 0︶ ᠨᠢ 𝑥 ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠲᠠᠢ 𝐴 ︵−3 ,0︶ , 𝐵 ︵1 ,0︶ ᠬᠤᠶ ᠠᠷ ᠴᠡᠭ ᠲᠤ ᠣᠭᠳᠣᠯ ᠣᠯᠴᠠ ᠵᠤ᠂ 𝑦 ᠲᠡ ᠩᠭᠡᠯ ᠢᠭ ᠲᠠᠢ ᠴᠡᠭ 𝐶 ᠲᠤ ᠣᠭᠳ ᠣᠯᠣᠯ ᠴᠠᠨ ᠠ᠃ ᠰᠢᠯᠤᠭᠤᠨ 𝑦 = −𝑥 ᠨᠢ ᠲᠤᠰ ᠬᠠᠶᠠ ᠯᠲᠠ ᠶᠢᠨ ᠱᠤᠭᠤ ᠮ᠊ ᠲ᠊ ᠠᠢ 𝐸 , 𝐹 ᠬᠤᠶ ᠠᠷ ᠴᠡ ᠬ᠋᠊ ᠲᠤ ᠣ ᠭᠳᠣᠯ ᠣᠯᠴᠠ ᠨ᠊ ᠠ᠃ ︵1︶ ᠬᠠᠶ ᠠᠯᠲᠠ ᠶᠢᠨ ᠱᠤ ᠭᠤᠮ ᠤᠨ ᠠᠨᠠᠯᠢᠰ ᠢᠯᠡᠷ ᠭᠡᠢᠯᠡᠯ ᠢ ᠣᠯ᠃ ︵2︶ 𝑃 ᠪᠣᠯ ᠰ᠊ ᠢᠯᠤᠭᠤᠨ 𝐸𝐹 ᠶᠢᠨ ᠳᠣᠣᠷ ᠠᠳᠤ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠬᠠᠶᠠᠯᠲᠠ ᠶᠢᠨ ᠱᠤᠭᠤᠮ ᠳ᠋᠊ ᠡᠭᠡᠷᠡ ᠬᠢ ᠨᠢᠭᠡ ᠨ᠊ ᠬᠦᠳᠡᠯᠬ ᠦ ᠴᠡᠭ᠂ 𝑃𝐻 ⊥ 𝐸𝐹 ᠢᠶᠡᠷ ᠪᠠᠢ ᠭᠤᠯᠪᠠᠯ᠂ ᠡᠭᠴ ᠡ ᠶᠢᠨ ᠰ᠊ ᠠᠭᠤᠷ ᠢ ᠨᠢ 𝐻 , 𝑃𝐻 ᠶᠢᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠶᠡᠭᠡ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠣ ᠯ᠊᠃ ︵3︶ ᠴᠡᠭ 𝐶 ᠢᠶ ᠡᠷ ᠲ᠊ ᠣᠭᠤᠷᠢ ᠬ᠋᠊ ᠤᠨ ᠲᠤ ᠤ ᠪᠣᠯᠭᠠᠵᠤ᠂ 1 ᠢᠶ ᠡᠷ ᠷ᠊ ᠠᠳᠢᠤᠰ ᠪᠣᠯᠭᠠᠨ ᠲᠣᠭᠤᠷᠢ ᠬ᠋᠊ ᠤ ᠠᠢᠭᠤᠯ ᠪᠠᠯ᠂ ⊙ C ᠳᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡᠨ ᠴᠡᠭ 𝑀 ᠣᠷᠣᠰ ᠢᠵᠤ᠂ ∆𝐵 𝐶𝑀 ᠶᠢ 𝐶𝑀 ᠪᠠᠷ ᠡᠭᠴ ᠡ ᠲᠠᠯ ᠠ ᠪᠠᠨ ᠪᠣᠯᠭᠠᠭ ᠰᠠᠨ ᠲ᠊ ᠡᠭᠰᠢ ᠥᠨᠴ ᠥᠭᠳᠥ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ᠊ ᠤ ᠣᠯᠭᠠᠵᠤ ᠲᠠᠢ ᠯᠤᠨ ᠡ ᠤᠤ︖ ᠬᠡᠷᠪ ᠡ ᠣ ᠷᠣᠰᠢᠪ ᠠᠯ 𝑀 ᠴᠡᠭ ᠦ ᠨ᠊ ᠤ ᠠᠢᠷᠢᠰ ᠢᠯ ᠢ ᠰᠢᠭᠤᠳ ᠪᠢᠴᠢᠵ ᠤ ᠬ᠋᠊ ᠠᠷᠭ ᠠ᠃ ᠬᠡᠷᠪ ᠡ ᠣ ᠷᠣᠰᠢᠬᠤ ᠦᠭᠡᠢ ᠪᠣᠯ ᠰᠢᠯᠲᠠᠭ ᠠᠨ ᠢ ᠨᠢ ᠲ᠊ ᠣᠳᠣᠷ ᠬᠠᠢ ᠯᠠ᠃ E F O B DA C ᠵᠢᠷ ᠤᠭ 1 FE O D A B C ᠵᠢᠷ ᠤᠭ 2 C O D B A ᠵᠢᠷ ᠤᠭ 3 ᠪᠡᠯᠡᠳ ᠭᠡᠯ ᠵᠢᠷᠤᠭ