ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ ᠤ ᠳᠣᠯᠣᠳᠤᠭᠠᠷ ᠣᠨ ᠤ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠪᠦᠯᠦᠭ ᠤᠨ ᠰᠤᠷᠢᠯᠳᠠ ᠰᠢᠯᠭᠠᠯᠳᠠ .pdf
ᠠᠩᠭᠢ᠄ ᠨᠡᠷ ᠡ᠄ ᠰᠤᠷᠢᠯᠳᠠ ᠰᠢᠯᠭᠠᠯᠳᠠ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬᠤ ᠰᠡᠳᠤᠪ ︵ᠪᠠᠭᠠ ᠰᠡᠳ ᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤ ᠪᠢ᠂ ᠨ᠊ ᠢᠳ ᠡ 30 ᠬᠤ ᠪᠢ︶ 1. − 1,0 ,2, 1 ᠡᠨᠡ ᠲᠦᠷ ᠪᠠᠨ ᠲᠣᠭᠠ ᠨ᠊ ᠲᠤ᠂ ᠡ ᠶᠡᠷᠭᠦ ᠲᠤᠭᠠ ᠪᠢᠰᠢ ᠪᠦ ᠭᠡᠳ ᠰ᠊ ᠥᠭᠡᠷ ᠭᠦ ᠲᠤᠭᠠ ᠴᠤ ᠪᠢᠰᠢ ᠨᠢ ︵︶ A. 2 B. 0 C. −1 D. 1 2. − 17 ᠶ᠊ ᠶᠢᠨ ᠲᠣᠩᠭᠤᠷᠠᠭᠤ ᠲ᠊ ᠣᠭᠠ ᠨᠢ A. 17 B. 7 C. − 17 D. −7 3. 12 ᠶᠢᠨ ᠡᠰᠡᠷᠭᠦ ᠲᠣᠭᠠᠨ ᠤ ᠲᠣᠩᠭᠤᠷᠠᠭᠤ ᠲ᠊ ᠣᠭᠠ ᠨᠢ A. −2 B. 12 C. 2 D. − 12 4.| −2020 | ᠶ᠊ ᠶᠢᠨ ᠡᠰᠡᠷ ᠭᠦ ᠲᠤᠭᠠ ᠨᠢ A. − 12020 B.2020 C. −2020 D. 12020 5.0 ,− 3, |− 10 |,0 .01 ᠲᠠᠬᠢ ᠬᠠᠮᠤᠭ ᠤᠨ ᠪᠠᠭᠠ ᠲᠤᠭᠠ ᠪᠣᠯᠬᠤ ᠨᠢ A. 0 B.− 3 C. |− 10 | D. 0.01 6. ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩ ᠭᠡᠯᠢᠭ ᠲᠡᠭᠡ ᠷᠡᠬᠢ −2 ᠢ ᠢᠯ ᠡᠷᠬᠡᠢᠯᠡᠭᠰ ᠠ ᠴᠡᠭ ᠡᠴ ᠡ 6 ᠨᠢᠭᠡ ᠴᠢ ᠤᠷᠳᠤ ᠵᠠᠢ ᠲᠠ ᠢ ᠴᠡᠭ ᠦᠨ ᠢᠯ ᠡᠷᠬᠡᠢᠯᠡ ᠬᠦ ᠲᠣ ᠭᠠ ᠨᠢ A. 4 ᠪᠠ − 8 B.4 ᠪᠠ − 6 C. −8 ᠪᠠ 2 D. −6 ᠪᠠ 2 7. ᠵ᠊ ᠡᠭᠦᠨᠰᠢ ᠴᠢᠭᠯᠡ ᠯ᠊ ᠢ ᠡᠶᠡᠷᠭᠦ ᠬᠡᠵ ᠤ ᠲᠤᠭᠳ ᠠᠭᠠᠪᠠᠯ᠂ ᠨᠢᠭᠡ ᠬᠦ ᠮᠤᠨ + 10m ᠶᠠᠪᠤᠵᠤ ᠲᠠᠬᠢ ᠭᠠᠳ −8 m ᠶᠠᠪᠤᠭᠰᠠᠨ ᠪᠤᠯ ᠪᠤ ᠳᠠᠳ ᠠᠢ ᠶ᠊ ᠠᠪᠤᠭᠰᠠᠨ ᠨᠢ A. ᠵᠡᠭᠦᠨᠰᠢ 2m ᠶᠠᠪᠤᠵᠠᠢ B. ᠪᠠᠷᠠᠭᠤᠨᠰ ᠢ 2m ᠶᠠᠪᠤᠵᠠᠢ C. ᠵᠡᠭᠦᠨᠰᠢ 18m ᠶᠠᠪᠤᠵᠠᠢ D. ᠪᠠᠷᠠᠭᠤᠨᠰ ᠢ 2m ᠶᠠᠪᠤᠵᠠᠢ 8. ᠲ᠊ ᠤᠤᠷᠠᠬᠢ ᠬᠡ ᠯᠡᠯᠭᠡ ᠠᠴᠠ ᠵ᠊ ᠥᠪ ᠪᠤ ᠯᠬᠤ ᠨᠢ A. ᠡᠶᠡᠷᠭᠦ ᠲᠤᠭᠠ ᠪᠢᠰᠢ ᠲᠤᠭᠠ ᠨᠢ ᠯ᠊ ᠠᠪᠳ ᠠᠢ ᠰ᠊ ᠥᠭᠡᠷᠭᠦ ᠲᠣ ᠭᠠ᠂ ᠰᠥᠭᠡᠷ ᠭᠦ ᠲᠤᠭᠠ ᠪᠢᠰᠢ ᠲᠤᠭᠠ ᠨᠢ ᠯ᠊ ᠠᠪᠳ ᠠᠢ ᠡᠶᠡᠷ ᠭᠦ ᠲᠣ ᠭᠠ᠃ B. ᠲᠠᠮᠳ ᠡᠭ ᠨᠢ ᠣᠨᠳᠣᠣ ᠬᠤᠶ ᠠᠷ ᠲᠤᠭᠠ ᠨᠢ ᠬᠠᠷᠢ ᠯᠴᠠᠨ ᠡᠰᠡᠷ ᠭᠦ ᠲᠤᠭᠠ᠃ C. ᠨᠢ ᠭᠡᠨ ᠲᠣᠭᠠᠨ ᠤ ᠬᠠᠷᠢ ᠴᠠᠯᠠᠰ ᠢᠭᠦᠢ ᠬᠡᠮᠵᠢᠭᠳ ᠡᠯ ᠨᠢ ᠬᠡᠳᠤᠢ ᠶᠡᠭᠡ ᠪᠤᠯ ᠲᠡᠭᠦ ᠨ᠊ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩ ᠭᠡᠯᠢᠭ ᠲᠡᠭᠡᠷ ᠠ ᠢᠯᠡᠷ ᠬᠡᠢᠯᠡ ᠬᠦ ᠴ᠊ ᠡᠭ ᠨᠢ ᠡᠬᠢᠨ ᠦ ᠴᠡᠭ ᠠᠴᠠ ᠬᠡ ᠳᠤᠢ ᠬᠤᠯ ᠠ᠃ D. ᠬᠡᠷᠪᠡ 𝑎 𝑏 ᠪᠣᠯ 𝑎 ᠶᠢᠨ ᠲᠣᠩᠭᠤᠷᠠᠭᠤ ᠲᠤᠭᠠ ᠨᠢ 𝑏 ᠶᠢᠨ ᠲᠣᠩᠭᠤᠷᠠᠭᠤ ᠲ᠊ ᠣᠭᠠ ᠠᠴᠠ ᠪᠠ ᠭᠠ᠃ 9. ᠲᠤᠤᠷᠠᠬᠢ ᠬᠡᠯᠡᠯᠭᠡ ᠠᠴᠠ ᠪᠤᠷᠤ ᠭᠤ ᠪᠣᠯᠬᠤ ᠨᠢ A. −3 .14 ᠨᠢ ᠰᠥᠭᠡᠷ ᠭᠦ ᠲᠤᠭᠠ᠂ ᠪᠤᠳᠠᠷ ᠬᠠᠢ ᠲᠤᠭᠠ᠂ ᠶᠤᠰᠤᠳ ᠠᠢ ᠲᠤᠭᠠ B. 0 ᠨᠢ ᠡᠶᠡᠷᠭᠦ ᠲᠣ ᠭᠠ ᠪᠢᠰ ᠢ ᠮᠦ ᠷᠳᠡᠭᠡᠨ ᠰ᠊ ᠥᠭᠡᠷ ᠭᠦ ᠲᠤᠭᠠ ᠪᠢᠰᠢ᠂ ᠭᠡᠪᠡ ᠴᠤ ᠪᠦᠬᠦᠯᠢ ᠲᠣ ᠭᠠ ᠮᠥ ᠨ᠊᠃ C. − 2000 ᠨᠢ ᠰᠥᠭᠡᠷᠭᠦ ᠲᠣ ᠭᠠ᠂ ᠪᠦ ᠬᠦᠯᠢ ᠲᠤᠭᠠ᠂ ᠭᠡᠪᠡᠴ ᠤ ᠶᠤᠰᠤᠳ ᠠᠢ ᠲᠤᠭᠠ ᠪᠢᠰᠢ᠃ D. 0 ᠨᠢ ᠡ ᠶᠡᠷᠭᠦ ᠲᠤᠭᠠ ᠪᠢᠰᠢ᠃ 10 . ᠲᠤᠤᠷᠠᠬᠢ ᠡᠯᠡ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ ᠲᠤ᠂ 𝑎 ᠨᠢ ᠯ᠊ ᠠᠪᠳ ᠠᠢ ᠡᠶᠡᠷ ᠭᠦ ᠲᠤᠭᠠ ᠪᠣᠯᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠢᠯᠡᠯ ᠨᠢ ①|𝑎 |= 𝑎 ②|𝑎 | −𝑎 ③|𝑎 |≥ −𝑎 ④ |𝑎 |𝑎 = 1 A. 4 B.3 C. 2 D. 1 ᠬᠤᠶ ᠠᠷ᠂ ᠬ᠊ ᠣᠭᠤᠰᠤ ᠨ᠊ ᠲᠤ ᠲᠠᠭᠯᠠ ᠬᠤ ᠰᠡᠳᠤᠪ ︵ᠪᠠᠭᠠ ᠰᠡᠳ ᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠡᠢᠳᠡ 30 ᠬᠤᠪᠢ︶ 11. ᠲᠠᠷᠠᠭᠠᠬᠢ ᠡᠯᠡ ᠲᠤᠭᠠ − 6, +2 .25 ,0, |− 0.1 |,| 0|, − 13 ᠲᠤᠳ ᠤᠷᠠ᠂ ᠢ ᠡᠷᠭᠦ ᠪᠤ ᠰᠤ ᠲᠤᠭᠠ ᠪᠣᠯᠬᠤ ᠨᠢ __ __ __ __ __ . 12 . ᠶᠤᠰᠤᠳ ᠠᠢ ᠲᠣᠭᠠ ᠨ᠊ ᠲᠤ ᠲᠣᠩᠭᠤᠷᠠᠭᠤ ᠲᠤᠭᠠ ᠨᠢ ᠥᠪᠡᠷ ᠦᠨ ᠲ᠊ ᠤᠰ ᠪᠡᠶᠡ ᠪᠣᠯᠬᠤ ᠲᠤᠭᠠ ᠨᠢ __ __ __ ___ . 13. ᠶᠤᠰᠤ ᠲᠠᠢ ᠲᠣᠭᠠᠨ ᠲᠠᠬᠢ ᠬᠠᠮᠤᠭ ᠤ ᠨ᠊ ᠪᠠᠭᠠ ᠡᠶᠡᠷ ᠭᠦ ᠪᠦᠬᠦ ᠯᠢ ᠲᠤᠭᠠ ᠨᠢ __ ___ ___ . 14. 𝑎 ᠪᠠ 1 ᠨᠢ ᠬᠠᠷᠢ ᠯᠴᠠᠨ ᠡᠰ ᠡᠷᠭᠦ ᠲᠤᠭᠠ᠂ 𝑏 ᠪᠠ 𝑐 ᠨᠢ ᠬᠠᠷᠢ ᠯᠴᠠᠨ ᠲᠣᠩᠭᠤᠷᠠᠭᠤ ᠲᠤᠭᠠ᠂ |𝑑 |= 2 ᠬᠡᠵᠤ ᠦᠭ ᠭᠦᠭᠳᠡᠪᠡ᠂ ᠲᠡ ᠭᠡᠪᠡᠯ 12 𝑑 + 2𝑎 +2 100 𝑎𝑏 = __ ___ ___ _. 15. |𝑎| = 6, |𝑏| = 4 ᠪᠥᠭᠡᠳ 𝑎 𝑏 ᠬᠡᠵᠤ ᠥᠭᠭᠦᠭ ᠳᠡᠭᠰᠡᠨ ᠪᠤᠯ᠂ 𝑎+ 𝑏= __ __ __ __ ___ _. 16. ᠬᠡᠷᠪᠡ x ᠨᠢ − 1 ᠲᠠᠢ ᠲ᠊ ᠡᠩᠴᠡᠬᠦ ᠦᠭᠡᠢ ᠶ᠊ ᠤᠰᠤᠳ ᠠᠢ ᠲᠤᠭᠠ ᠪᠥᠭᠡ ᠳ᠋᠊ |𝑥| = 1 ᠪᠤᠯ᠂ 3 𝑥− 3= __ ___ __ __. 17 . 𝑎 ᠨᠢ 1 ᠡᠴ ᠡ ᠪᠠ ᠭᠠ ᠡᠶᠡᠷ ᠭᠦ ᠲᠤᠭᠠ ᠪᠤᠯ᠂ 𝑎 , 1𝑎 , −𝑎 ,− 1𝑎 ᠶᠢᠨ ᠶᠡᠭᠡ ᠪᠠᠭ ᠠ ᠶᠢ ᠨ᠊ ᠲᠠᠷᠠᠭᠠᠯᠠ ᠯ᠊ ᠨᠢ __ ___ __ ___ ___ __ _. 18. |𝑥 + 4| + |𝑦 − 3| = 0 ᠪᠣᠯ᠂ 𝑥 =__ ___ _. 𝑦= __ __ __ . 19. ᠬᠡᠷᠪᠡ |1 − 𝑎| = 𝑎− 1 ᠪᠣᠯ 𝑎 ᠶᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠠ ᠪᠬᠤ ᠬᠡᠪᠴ ᠢᠶᠡ ᠨᠢ __ __ __ __. 20. ᠲᠠᠷᠠᠭᠠᠬᠢ ᠲᠣᠭᠠᠨ ᠤ ᠵ᠊ ᠢᠭᠰᠠᠭᠠ ᠭᠳᠠᠭᠰ ᠠᠨ ᠵᠢᠮᠠ ᠶᠣᠰᠤ ᠶᠢ ᠦᠨᠳ ᠦᠰᠦᠯᠡᠨ ᠬᠤᠭᠤᠰ ᠤᠨ ᠲᠤ ᠲᠠᠭᠯᠠ᠂ −1 ,2, −3 ,4, −5 ᠁ ᠲᠠᠪᠢ ᠨ᠊ ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠲᠣ ᠭᠠ ᠨᠢ __ ___ ___ _. ᠭᠤᠷᠪᠠ᠂ ᠪᠣᠳᠤᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠳᠤᠪ ︵ᠨᠡᠢᠳ ᠡ 40 ᠬᠤᠪᠢ︶ 21 . ᠬᠡᠷᠪᠡ 6𝑥 ᠪᠠ − 3 ᠬᠠᠷᠢ ᠯᠴᠠᠨ ᠡ ᠰᠡᠷᠭᠦ ᠲᠤᠭᠠ ᠪᠤ ᠯ᠊ 𝑥 ᠤᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠣᠯ᠃ 22 . ᠲᠠᠷᠠᠭᠠᠬᠢ ᠡ ᠯᠡ ᠲᠣᠭᠠᠨ ᠤ ᠡ ᠰᠡᠷᠭᠦ ᠲᠤᠭᠠ ᠵ᠊ ᠢ ᠪᠢ ᠴᠢᠵᠤ᠂ ᠲᠠᠷᠠᠭᠠ ᠨᠢ ᠡᠨᠡ ᠠᠷ ᠪᠠᠨ ᠲᠤᠭ ᠠᠨ ᠤ ᠶᠡᠭᠡ ᠪᠠᠭᠠ ᠶᠢ ᠨᠢ ᠠᠳᠠᠯᠢ ᠲᠭᠠ᠃ −8 ,0. 2, −0 .5, π, − 25 23 . ᠪᠣᠳᠤ᠄ ︵1︶ |− 3| + |− 8| − |− 2| ︵2︶ |− 28 |÷ |− 7| × |− 12 | 24 . ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩ ᠭᠡᠯᠢᠭ ᠲᠡᠭᠡᠷ ᠠ ᠬ᠊ ᠤᠷᠪᠠᠨ ᠴᠡᠭ A, B, C ᠶᠢᠨ ᠪᠠᠢ ᠷᠢ ᠨᠢ ᠵ᠊ ᠢᠷᠤᠭ ᠳ᠋᠊ ᠤ ᠦᠵᠡᠭᠦᠯᠦᠭᠰ ᠠ ᠮᠡᠳᠤ᠄ ︵1︶ ᠴᠡᠭ B ᠨᠢ ᠪᠠᠷᠠᠭᠤᠨᠰ ᠢ 3 ᠨᠢᠭᠡᠴ ᠢ ᠰᠢᠯ ᠵᠢᠭᠰᠡ ᠨ᠊ ᠤ ᠰᠡᠭᠦ ᠯᠡᠷᠬᠢ ᠤᠯᠬᠤ ᠴᠡᠭ ᠦᠨ ᠢᠯ ᠡᠷᠬᠡᠢᠯᠡᠭᠰ ᠠ ᠲᠤᠭᠠ ᠨᠢ ᠬᠡᠳᠤᠢ ᠪᠤᠢ︖ ︵2︶ ᠴᠡᠭ C ᠶᠢ ᠵᠡᠭᠦᠨᠰᠢ 8 ᠨᠢᠭᠡᠴ ᠢ ᠰᠢᠯ ᠵᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠰᠡᠭᠦ ᠯᠡᠷ ᠲᠤᠭᠠ 𝑥1 ᠶᠢ ᠣᠯᠵᠤ᠂ ᠲᠠ ᠬᠢᠭᠠᠳ ᠪᠠᠷᠠᠭᠤᠨᠰ ᠢ 4 ᠨᠢᠭᠡ ᠴᠢ ᠤᠷᠳᠤ ᠰᠢᠯᠵᠢ ᠭᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠰᠡᠭᠦ ᠯᠡᠷ 𝑥2 ᠢ ᠣᠯᠪᠠ᠂ 𝑥 1 , 𝑥2 ᠨᠢ ᠲᠤᠰ ᠪᠦᠷᠢ ᠬᠡᠳᠤᠢ ᠪᠤᠢ︖ ︵3︶ A ,B ,C ᠶᠢ ᠨ᠊ ᠲᠤᠳ ᠤᠷᠠᠬᠢ ᠬᠤᠶ ᠠᠷ ᠴ᠊ ᠡᠭ ᠢ ᠶᠠᠭᠠᠬᠢ ᠵᠤ ᠰᠢᠯᠵᠢ ᠭᠦᠯᠪᠡᠯ ᠭᠤᠷᠪᠠᠨ ᠴᠡᠭ ᠦᠨ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠭ ᠰᠡᠨ ᠲᠤᠭᠠ ᠨᠢ ᠠ ᠳᠠᠯᠢ ᠪᠣᠯᠬᠤ ᠪᠤᠢ︖ ᠬᠡᠳᠤᠨ ᠵ᠊ ᠦᠢᠯ ᠦ ᠨ᠊ ᠠᠷᠭᠠ ᠪᠠᠢ ᠬᠤ ᠪᠤᠢ︖ 25 . ᠨᠢᠭᠡᠨ ᠲᠤᠳ ᠤᠷᠭᠠ ᠶᠢᠨ ᠦᠢ ᠯᠡᠳᠪᠦᠷᠢ ᠶᠢᠨ ᠦᠢ ᠯᠡᠳᠪᠦᠷᠢ ᠯᠡᠭᠰ ᠠ ᠪᠤᠭᠤᠳᠠᠯᠳ ᠤ ᠲᠤᠳ ᠤᠷᠭ᠋ ᠠ ᠶ᠊ ᠶᠢᠨ ᠲᠤᠳ ᠤᠷᠠ ᠠᠴᠠ 20 ᠤ ᠭᠤᠳᠠ ᠰᠤᠭᠤᠯᠤᠨ ᠭᠠᠷᠭᠠᠵᠤ ᠶᠠᠩᠵᠤ ᠪᠣᠯᠭᠠᠨ᠂ ᠤᠭ ᠤᠳᠠ ᠪᠦᠷᠢ ᠶᠢᠨ ᠮᠠᠰ ᠨᠢ ᠪᠠᠷᠢ ᠮᠵᠢᠶᠠ ᠲᠤ ᠬᠦᠷᠬᠦ ᠡ ᠰᠡᠬᠦ ᠵ᠊ ᠢ ᠪᠠᠢ ᠴᠠᠭᠠᠨᠠ᠂ ᠬᠡᠳᠤᠷᠡᠭᠰ ᠠ ᠪᠤᠶᠤ ᠲᠤᠳ ᠠᠭᠰᠠ ᠨ᠊ ᠬᠡᠰᠡᠭ ᠢ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠡᠶᠡᠷᠭᠦ ᠪᠤᠶᠤ ᠰᠥ ᠭᠡᠷᠭᠦ ᠪᠠᠷ ᠲᠡᠮᠳ ᠡᠭᠯᠡᠪᠡ ᠯ᠊᠂ ᠬᠦᠰ ᠦᠨᠦᠭ ᠲᠤ ᠮᠡᠳᠤ᠄ ᠡᠨᠡ ᠪᠦᠯᠦᠭ ᠶᠠᠩᠵᠤ ᠶᠢᠨ ᠲᠤᠮᠳ ᠠᠴᠢ ᠮᠠᠰ ᠨᠢ ᠪᠠᠷᠢ ᠮᠵᠢᠶ ᠡ ᠮ᠊ ᠠᠰ ᠠᠴᠠ ᠢᠯᠡ ᠭᠦᠤ ᠤᠤ︖ ᠲᠤᠳ ᠠᠭᠤ ᠤᠤ︖ ᠬᠡᠳᠤᠢ ᠢᠯᠡᠭᠦᠤ ᠪᠤᠢ︖ ᠬᠡᠳᠤᠢ ᠲᠤᠳ ᠠᠭᠤ ᠪᠤᠢ︖ ᠬᠡᠷᠪᠡ ᠪᠠᠷᠢ ᠮᠵᠢᠶᠡ ᠮᠠᠰ ᠨᠢ 450 kg ᠪᠤᠯ᠂ ᠶᠠᠩᠵᠤ ᠶᠢᠨ ᠶᠡᠷᠤᠩ ᠬᠡᠢ ᠮ᠊ ᠠᠰ ᠨᠢ ᠬᠡ ᠳᠤᠢ ᠪᠤᠢ︖ −4 −3 −2 −1 0 3 2 1 4 𝐴 𝐵 𝐶
ᠮᠣᠩᠭᠣᠯ ᠳ᠋ᠣᠺ ᠤᠨ ᠬᠥᠮᠥᠷᠭᠡ