2019 ᠣᠨ ᠤ ᠪᠠᠢᠭᠠᠯᠢ ᠶᠢᠨ ᠰᠢᠨᠵᠢᠯᠡᠭᠡᠨ ᠤ ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ ᠤ ᠤᠯᠤᠰ ᠤᠨ ᠰᠢᠯᠭᠠᠯᠲᠠ ᠶᠢᠨ ᠰᠡᠳᠤᠪ .docx

20 19 ᠣᠨ ᠤ ᠡᠩ ᠤ ᠨ ᠳᠡ ᠭᠡᠳᠤ ᠵᠡᠷ ᠭᠡ ᠶ ᠢᠨ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠶᠢᠨ ᠰ ᠤᠷᠤᠭᠴ ᠢ ᠡᠯᠰ ᠡᠬᠦ ᠪᠦ ᠬᠦ ᠤᠯᠤᠰ ᠤᠨ ᠨᠢᠭᠡ ᠲᠦᠯᠲ ᠠᠢ ᠰᠢ ᠯᠭᠠᠯᠲ ᠠ ᠪᠠᠢᠭᠠ ᠯᠢ ᠶᠢᠨ ᠰ ᠢᠨᠵᠢᠯᠡ ᠭᠡᠨ ᠤ ᠲᠣᠭ ᠠᠨ ᠤ ᠤᠬ ᠠᠭᠠᠨ ᠨᠢᠭᠡ᠂ ᠰᠣᠩᠭᠤᠬᠤ ᠰᠡᠳᠤᠪ ︵ ᠲᠤᠰ ᠶᠡᠬᠡ ᠰᠡᠳᠤᠪ ᠲᠤ ᠨᠡᠢᠲᠡ 12 ᠪᠠ ᠭ ᠠ ᠰᠡᠳᠤᠪ ᠲᠠᠢ᠂ ᠪᠠ ᠭ ᠠ ᠰᠡᠳᠤᠪ ᠪᠦᠷᠢ 5 ᠬᠤᠪ ᠢ᠂ ᠨᠡᠢᠲ ᠡ60 ᠬᠤ ᠪᠢ᠃ ᠪᠠᠭ ᠠ ᠰ ᠡᠳᠤᠪ ᠪᠦᠷᠢ ᠳ ᠤ ᠥᠭᠭ ᠦᠭᠳᠡ ᠭᠰᠡᠨ ᠳᠥᠷ ᠪᠡᠨ ᠰᠣᠩᠭᠤᠭ ᠳᠠᠬᠤᠨ ᠤ ᠳᠣᠳ ᠤᠷ ᠠ ᠵᠥᠪ ᠬᠡᠨ ᠨᠢᠭᠡ ᠰᠣᠩᠭᠤᠭᠳ ᠠᠬᠤᠨ ᠨᠢ ᠰ ᠡᠳᠤᠪ ᠤᠨ ᠱᠠᠭᠠ ᠷᠳᠠᠯᠭ ᠠ ᠳᠤ ᠨᠡᠢᠴᠡ ᠨ ᠡ᠃ ︶ 1.ᠴᠤᠭᠯᠠᠷᠠᠯ A = *𝑥 |𝑥 2− 5𝑥 + 6 0+ ,𝐵 = *𝑥 |𝑥 − 1 𝑏 ᠪᠣᠯ ᠂ A. ln (𝑎 − 𝑏) 0 B. 3 𝑎 3 𝑏 C. 𝑎 3− 𝑏 3 0 D. |𝑎 | |𝑏| 7.α ᠪᠠ β ᠶ ᠢ ᠬᠤ ᠶᠠᠷ ᠬᠠᠪᠲ ᠠᠭᠠᠢ ᠭᠡᠵᠦ ᠵᠢᠱ ᠢᠪᠡᠯ ᠂ α ∥β ᠪᠣᠯᠬ ᠤ ᠶᠢᠨ ᠭ ᠦᠢᠴᠡᠳ ᠴᠢᠬ ᠤᠯᠠ ᠨᠥᠬᠦᠴᠡᠯ ᠨ ᠢ A. α ᠳᠡᠭᠡ ᠷ ᠡ ᠬᠢᠵᠠ ᠭᠠᠷᠭᠦᠢ ᠣᠯᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠣᠷ ᠤᠰᠢᠵᠤ ᠂ β ᠲᠠᠢ ᠵᠡᠷᠭᠡ ᠴᠡᠭᠡ ᠪᠣᠯᠤᠨ ᠠ᠃ B. α ᠳᠡᠭᠡ ᠷ ᠡ ᠣᠭᠲᠤᠯ ᠤᠯᠴᠠ ᠭᠰᠠᠨ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭ ᠤᠨ ᠣᠷᠤᠰ ᠢᠵᠤ᠂ β ᠲᠠᠢ ᠵᠡᠷᠭᠡ ᠴᠡᠭᠡ ᠪᠣᠯᠤᠨ ᠠ᠃ C. α ,β ᠨᠢ ᠢᠵ ᠢᠯ ᠨ ᠢᠭᠡᠨ ᠰᠢᠯᠤᠭ ᠤᠨ ᠲ ᠠᠢ ᠵᠡᠷᠭᠡ ᠴᠡᠭᠡ ᠪᠣᠯᠤᠨ ᠠ᠃ D. α ,β ᠨᠢ ᠢᠵ ᠢᠯ ᠨ ᠢᠭᠡᠨ ᠬᠠᠪ ᠲᠠᠭᠠ ᠢ ᠳᠤ ᠡᠭᠴᠡ ᠪᠣᠯᠤᠨ ᠠ᠃ 8. ᠬᠠᠶᠠᠯᠲ ᠠ ᠶᠢᠨ ᠱᠤᠭᠤᠮ y 2 = 2𝑝𝑥 (𝑝 0) ᠤᠨ ᠲᠥᠪ ᠯᠡᠷᠡᠯ ᠨᠢ ᠵᠤᠤᠪ ᠠᠩ ᠲᠣᠭᠤᠷᠢᠭ 𝑥 23𝑝 + 𝑦 2𝑝 = 1( 𝑝 0) ᠶᠢᠨ ᠨᠢᠭᠡ ᠲᠥᠪ ᠯᠡᠷᠡᠯ ᠤᠨ ᠴᠡᠭ ᠪᠣᠯᠤᠨ ᠠ᠂ ᠲᠡᠭᠡ ᠪᠡᠯ 𝑝= A. 2 B. 3 C. 4 D. 8 9.ᠳᠣᠣᠷᠠᠬᠢ ᠹᠦᠩᠺ ᠼ ᠲ ᠤ 𝜋2 ᠪᠡᠷ ᠦ ᠶ ᠡ ᠪᠣᠯᠭ ᠠᠭᠰᠠᠨ ᠪᠥᠭᠡ ᠳ ᠲ ᠠᠰᠤᠯᠭ ᠠ ( 𝜋4 , 𝜋2 ) ᠳᠤ ᠨᠢᠭᠡ ᠬᠥᠭᠲ ᠦ ᠢᠶᠡ ᠷ ᠨᠡ ᠮᠡᠭᠳᠡ ᠬᠦ ᠨᠢ A. 𝑓( 𝑥) = |co s2 𝑥| B. 𝑓( 𝑥) = |sin2 𝑥| C. 𝑓( 𝑥) = co s | 𝑥| D. |𝑓 (𝑥 )= sin |𝑥| 10. α ∈ (0 , 𝜋2 ) ,2sin 2α = co s2 α+ 1ᠭᠡ ᠵᠦ ᠦᠭᠭ ᠦᠭᠳᠡ ᠵᠡᠢ᠂ ᠲᠡᠭ ᠡᠪᠡᠯ sin α= A. 15 B. √ 55 C. √ 33 D. 2 √55 11.F ᠶᠢ ᠬᠣᠣᠰ ᠮᠤᠷᠤᠢ ᠱᠤᠭᠤᠮ C: 𝑥 2𝑎 2 + 𝑦 2𝑏 2 = 1( 𝑎 0, 𝑏 0) ᠶᠢᠨ ᠪᠠᠷᠠᠭᠤᠨ ᠲᠥᠪ ᠯᠡᠷᠡᠯ ᠤᠨ ᠴᠡᠭ᠂ O ᠶᠢ ᠪᠠᠢᠷᠢᠰ ᠢᠯ ᠤᠨ ᠡᠬᠢᠨ ᠤ ᠴᠡᠭ ᠭᠡᠵᠦ ᠵᠢᠱ ᠢᠨ ᠡ᠃ OF ᠢᠶᠡᠷ ᠳᠢᠶᠠᠮ ᠧᠲ᠋ᠷ ᠪᠣᠯᠭ ᠠᠭᠰᠠᠨ ᠲᠣᠭᠤᠷᠢᠭ ᠨ ᠢ ᠲᠣᠭᠤᠷᠢᠭ 𝑥 2+ 𝑦 2 = 𝑎 2 ᠲᠠᠢ P, Q ᠬᠣᠶᠠᠷ ᠴᠡᠭ ᠲᠤ ᠣᠭᠲᠤᠯ ᠤᠯᠴᠠ ᠨ ᠠ᠃ |PQ |= |OF | ᠪᠣᠯ ᠂C ᠶᠢᠨ ᠵᠢᠭᠤᠳᠠ ᠮᠵᠢ ᠨᠢ A. √ 2 B. √3 C. 2 D. √5 12. ᠹᠦᠩᠺ ᠼ𝑓 (𝑥 ) ᠤ ᠨ ᠲᠣᠳ ᠤᠷᠬᠠ ᠢᠯᠠᠯᠲ ᠠ ᠶᠢᠨ ᠣᠷᠤᠨ ᠨᠢR ᠪᠥ ᠭᠡᠳ 𝑓( 𝑥+ 1) = 2𝑓 (𝑥 ) ᠢ ᠬᠠᠩᠭᠠᠨ ᠠ᠂ 𝑥∈ (0 ,1] ᠦᠶ ᠡᠰ𝑓 (𝑥 )= 𝑥( 𝑥− 1) ᠂ ᠬᠡᠷᠪ ᠡ ᠳᠤᠷ ᠠ ᠶᠢᠨ 𝑥 ∈ (− ∞, 𝑚] ᠳᠤ ᠴᠥᠮ 𝑓( 𝑥) ≥ − 89 ᠪᠠ ᠢᠭᠤᠯᠤᠭᠳ ᠠᠪᠠᠯ ᠂ 𝑚 ᠤᠨ ᠬᠡᠮᠵᠢᠭᠳᠡ ᠯ ᠠᠪᠬᠤ ᠬᠡᠪᠴᠢᠶ ᠡ ᠨᠢ A. ( −∞ , 94 ) B. (− ∞, 73 ) C. ( −∞ , 52 ) D. ( −∞ , 83 ) ᠬᠣᠶᠠᠷ ᠂ ᠬᠠᠭᠠᠯᠲ ᠠ ᠲᠠ ᠭᠯᠠᠬ ᠤ ᠰ ᠡᠳᠤᠪ ( ᠲᠤᠰ ᠶᠡᠬᠡ ᠰᠡᠳᠤᠪ ᠲᠤ ᠨᠡᠢᠲ ᠡ4 ᠪᠠᠭ ᠠ ᠰᠡ ᠳᠤᠪ ᠲᠠᠢ᠂ ᠪᠠᠭ ᠠ ᠰ ᠡᠳᠤᠪ ᠪᠦᠷᠢ 5 ᠬᠤ ᠪᠢ᠂ ᠨᠡᠢᠲᠡ 20 ᠬᠤ ᠪᠢ) 13. ᠮᠠᠨ ᠤ ᠤ ᠯᠤᠰ ᠤ ᠨ ᠥᠨ ᠳᠦᠷ ᠬᠤᠷ ᠳᠤᠴ ᠠ ᠶᠢᠨ ᠲᠡᠮᠦ ᠷ ᠵᠠᠮ ᠤᠨ ᠦᠢᠯᠡᠰ ᠦᠳᠲ ᠡᠷ ᠳᠦᠷ ᠭᠡᠨ ᠬᠥᠭᠵᠢᠵ ᠦ ᠪᠤᠢ᠃ ᠪᠦᠷᠢᠳᠭᠡ ᠯ ᠢ ᠦᠨ ᠳᠦᠰᠦᠯᠡᠪ ᠡᠯ᠂ ᠨᠢᠭᠡ ᠨ ᠥᠷ ᠲᠡᠭᠡ ᠪ ᠡᠷ ᠥᠩᠭ ᠡᠷᠡᠨ ᠵᠣᠭᠰᠤᠬ ᠤ ᠠᠳᠠ ᠯᠢ ᠪᠤᠰ ᠤ ᠳᠣᠭᠠᠷᠳᠤ ᠥᠨ ᠳᠦᠷ ᠬᠤᠷ ᠳᠤᠴ ᠠᠳᠤ ᠭᠠᠯᠲ ᠤ ᠲᠡ ᠷᠭᠡᠨ ᠤ ᠳᠣᠲᠤᠷ ᠠ᠂10 ᠶᠢᠨ ᠬᠢᠨᠢ ᠲᠣᠭ ᠲᠠᠭᠰᠠᠨ ᠴᠠᠭ ᠢᠶᠡ ᠷ ᠢᠶᠡᠨ ᠠᠶᠠᠯᠠᠬᠤ ᠨᠤᠷᠮ ᠠ ᠨᠢ 0.97 , 2 0 ᠶ ᠢᠨ ᠬᠢᠨᠢ ᠲᠣᠭ ᠲᠠᠭᠰᠠᠨ ᠴᠠᠭ ᠢᠶᠡᠷ ᠢᠶᠡᠨ ᠠᠶᠠᠯᠠᠬᠤ ᠨᠤᠷᠮ ᠠ ᠨᠢ 0.98 , 10 ᠶᠢᠨ ᠬᠢᠨᠢ ᠲᠣᠭ ᠲᠠᠭᠰ ᠠᠨ ᠴᠠᠭ ᠢᠶᠡᠷ ᠢᠶᠡᠨ ᠠᠶᠠᠯᠠᠬᠤ ᠨᠤᠷᠮ ᠠ ᠨᠢ 0.99 ᠪᠠᠢᠵᠠ ᠢ᠃ ᠲᠡᠭᠡ ᠪᠡᠯ ᠲᠤᠰ ᠥᠷ ᠲᠡᠭᠡ ᠪᠡ ᠷ ᠥᠩᠭ ᠡᠷᠡᠨ ᠵᠣᠭᠰᠤᠬ ᠤ ᠪᠤᠢ ᠪᠦᠬᠦᠢ ᠠᠳᠠ ᠯᠢ ᠪᠤᠰ ᠤ ᠳ ᠤᠭᠠᠷᠲ ᠤ ᠥᠨ ᠳᠦᠷ ᠬᠤᠷ ᠳᠤᠴ ᠠᠲᠤ ᠭᠠᠯᠲ ᠤ ᠲᠡ ᠷᠭᠡᠨ ᠤ ᠳᠤᠮᠳ ᠠᠴᠢ ᠲᠣᠭ ᠲᠠᠭᠰᠠᠨ ᠴᠠᠭ ᠢᠶᠡᠷ ᠢᠶᠡᠨ ᠠᠶᠠᠯᠠᠬᠤ ᠨᠤᠷ ᠮ ᠠ ᠶ ᠢᠨ ᠪᠠ ᠷᠤᠭᠴᠠᠭᠠ ᠯᠠᠯ ᠬᠡ ᠮᠵᠢᠭᠳᠡ ᠯ ᠨᠢ ( ) 14. 𝑓( 𝑥) ᠨᠢ ᠰᠣᠨᠳ ᠤᠭᠤᠢ ᠹᠦᠩᠺ ᠼ ᠪᠣᠯᠬ ᠤ ᠪᠥᠭᠡ ᠳ𝑥 0) ᠨᠢ ᠮᠤᠷᠤᠢ ᠱᠤᠭᠤᠮ C: ρ= 4sin θᠳᠡ ᠭᠡᠷ ᠡ ᠣᠷᠤᠰ ᠢᠨ ᠠ᠂ ᠰᠢ ᠯᠤᠭᠤᠨ 𝑙 ᠨᠢ ᠴᠡᠭ A(4 ,0) ᠢ ᠳᠠᠭᠠᠷᠢᠬ ᠤ ᠪᠥᠭ ᠡᠳOM ᠳᠤ ᠡᠭᠴ ᠡ᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰ ᠠᠭᠤᠷ ᠢ ᠨᠢ P ᠪᠣᠯᠤᠨ ᠠ᠃ (1) θ 0 = 𝜋3 ᠦᠶ ᠡᠰ᠂ 𝜌0 ᠵᠢᠴᠢ 𝑙 ᠤ ᠨ ᠲᠦᠢᠯ ᠤᠨ ᠪ ᠠᠢᠷᠢᠰᠢᠯ ᠤᠨ ᠲᠡᠭᠰ ᠢᠳᠭᠡ ᠯ ᠢ ᠣᠯ᠃ (2) M ᠨᠢ ᠮᠤᠷᠤᠢ ᠱᠤᠭᠤᠮ C ᠳᠡᠭᠡ ᠷ ᠡ ᠬᠥᠳᠡ ᠯᠭᠡᠭᠡ ᠨ ᠬᠢ ᠬᠦ ᠪᠥᠭ ᠡᠳP ᠨᠢ ᠬᠡᠷᠴᠢᠮ OM ᠳᠡᠭᠡ ᠷ ᠡ ᠣᠷ ᠤᠰᠢᠬᠤ ᠦᠶ ᠡᠰ᠂ ᠴᠡᠭ P ᠶ ᠢᠨ ᠵᠢᠮ ᠤᠨ ᠲᠦᠢᠯ ᠤᠨ ᠪᠠᠢᠷᠢᠰᠢᠯ ᠤᠨ ᠲᠡᠭᠰ ᠢᠳᠭᠡ ᠯ ᠢ ᠣᠯ᠃ 23. ﹇ ᠰᠣᠩᠭᠤᠨ ᠰᠤᠷᠬ ᠤ 4 ︱ 5 ﹈ (10 ᠬᠤ ᠪᠢ) ᠹᠦᠩᠺ ᠼ 𝑓 (𝑥 )= |𝑥 − 𝑎| 𝑥+ |𝑥 − 2|( 𝑥− 𝑎) ᠭᠡᠵ ᠦ ᠦᠭᠭ ᠦᠭᠳᠡ ᠵᠡᠢ᠃ (1) 𝑎 = 1 ᠦᠶ ᠡᠰ᠂ ᠲᠡᠩᠴ ᠡᠳᠬᠡ ᠯ ᠪᠤᠰ ᠤ f (x) 0 ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠴᠤᠭᠯᠠᠷᠠᠯ ᠢ ᠣᠯ ᠃ (2) x ∈ (− ∞ ,1 )ᠦᠶ ᠡᠰ᠂ 𝑓( 𝑥) 0 ᠪᠣᠯ᠂ 𝑎 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠯ ᠠᠪᠬᠤ ᠬᠡᠪᠴᠢᠶ ᠡ ᠶᠢ ᠣᠯ᠃