ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠩᠬ᠎ᠠ ᠬᠤᠶᠡ ᠷ ᠦᠨ ᠲᠣᠭ ᠠᠨ ᠤ ᠤᠬ ᠠᠭᠠᠨ ᠤ ᠬᠤᠭᠤ ᠴᠠᠭ ᠠᠨ ᠡ ᠴᠦᠰ ᠤ᠋ᠨ ᠰᠢᠯ ᠭᠠᠯᠳᠠ ᠨᠢᠭᠡ ᠂ ᠰᠤᠨᠭᠭᠤᠬᠤ ᠰᠡᠳᠤ ᠪ᠄ ᠵᠥᠪ ᠰᠣᠩᠭᠤᠭᠳᠠᠬᠤᠨ ᠤ ᠬᠠᠷᠠ ᠭᠠᠯᠵᠠ ᠭᠰᠠᠨ ᠳ᠋ᠤᠭᠠ ᠷ ᠢ ᠬᠦᠰ ᠦᠨᠦᠭ ᠳᠤ ᠳ᠋ᠤ ᠲᠠᠭᠯᠠ ᠄ ︵ ᠰᠡᠳᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤ ᠪᠢ᠂ ᠨᠡᠢᠳᠠ 3 0ᠬᠤ ᠪᠢ ︶ ⒈ ᠲᠤᠤᠷᠠᠬᠢ ᠨᠥᠬᠦᠴ ᠡᠯ ᠨᠢ ᠵ ᠢᠰᠢᠭᠦᠯᠵᠢᠨ ᠪᠣᠯᠬᠤ ᠵ ᠢ ᠮᠠᠭᠠᠳᠯᠠᠵᠤ ᠲᠡᠢ ᠯᠬᠦ ᠦᠭᠡᠢ ᠨᠢ ︵ ︶ A ᠬᠤᠶ ᠠᠷ ᠬᠣᠣᠰ ᠡᠰᠡᠷᠭᠦ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ︵ ︶ ⒈

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠣ ᠷᠢᠳᠤ ᠭᠠᠷ ᠪᠦᠯ ᠦᠭ ᠦ ᠨ᠊ ᠤ ᠠᠢᠴᠠ ᠭᠠᠯᠲ ᠠ 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 ᠨ᠊ ᠢᠭᠡ ᠤᠳ ᠠᠭᠠᠨ ᠤ ᠶᠠᠷ ᠢᠶᠠᠨ ᠤ ᠤᠷᠤ ᠯᠳᠤᠭᠠᠨ ᠳᠤᠮ ᠳᠠ᠂ ᠲᠠᠪ ᠤᠨ ᠬ᠊ ᠢᠨᠠᠭᠴ ᠢ ᠶᠢ ᠨ᠊ ᠪᠠ ᠲᠤ ᠳ᠋᠊ ᠤ ᠥᠭᠭ ᠥᠭᠰᠡᠨ ᠬᠤᠪᠢ ᠨᠢ ᠳᠣᠣ ᠷᠠᠬᠢ ᠮᠡᠲ ᠦ᠄ 90 , 8 5 , 90 , 80 , 95

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠤᠷᠢ ᠳᠤᠭ ᠠᠷ ᠪᠦ ᠯᠦᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭ ᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮ᠊ ᠢᠨᠦ᠋ᠲ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ︶ ᠨᠢᠭᠡ᠂ ᠬ᠊ ᠠᠷᠢᠭᠤ ᠯᠲᠠ ᠰ᠊ ᠣᠩᠭᠤ ᠬᠤ ᠰ᠊ ᠡᠳᠦᠪ᠃ ︵ᠪᠠᠭ ᠠ ᠰ᠊ ᠡᠳᠦᠪ ᠪᠦᠷ ᠢ 3 ᠬᠤ ᠪᠢ᠂ ᠨᠡᠢ ᠲᠡ 30 ᠬᠤ ᠪᠢ︶ 1 ᠨ᠊ ᠢᠭᠡ ᠪᠦᠯᠦᠭ ᠲᠤᠭ ᠠ ᠪᠠ ᠷᠢᠮᠲ ᠠ 4, 5 ,6 ,4 ,7 , 𝑥 , 5 ᠶᠢᠨ ᠲᠤ ᠮᠳᠠᠴ ᠢ ᠲ᠊ ᠣᠭ ᠠ ᠨᠢ 5 ᠪᠣᠯ᠂ ᠲ᠊ ᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠲᠤ ᠮᠳᠠ ᠪᠠ ᠢᠷᠢ ᠶᠢᠨ ᠲᠣ ᠬ᠋᠊ ᠠ 

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪᠠ ᠨ᠊ ᠵᠢᠷᠭᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠢ ᠨᠦ᠋ᠲ᠂ ᠨᠠᠢᠲᠡ 02 1 ᠢᠪᠤᠬ︶ ᠨᠢᠭᠡ᠂ ᠰᠪᠩᠭᠪᠬ ᠤ ᠰᠡ ᠲᠪᠪ᠃ ︵ᠰᠡᠳ᠋ᠪᠪ ᠪᠦ ᠷᠢ 3 ᠢᠪᠤᠬ᠂ ᠨᠠᠢᠲᠡ 31 ᠢᠪ ᠤᠬ︶ 1 ᠢᠣᠶ ᠠᠳᠪᠭ ᠠᠷ ᠵᠡᠷᠭᠡ ᠢᠢᠨ ᠢᠵᠠᠭ ᠪᠷ ᠦᠨ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ √2 𝑥− 4 ᠢ ᠤᠳᠬ ᠠ ᠲᠠ ᠢ ᠪᠣᠯᠭ ᠠᠬᠤ 𝑥 ᠦ ᠨ᠊ ᠬᠡ ᠮᠵᠢᠭᠳᠡᠯ ᠠᠤᠬᠤ ᠬᠡ ᠪᠴᠢᠶ ᠡ ᠨᠢ ︵︶ A 𝑥 2 B 𝑥 2 C 𝑥≥ 2 D

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪᠠ ᠨ᠊ ᠵᠢᠷᠭᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲᠠ 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 ᠳᠠ ᠷᠠᠭᠠᠬ ᠢ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠳᠤ᠂ ᠯᠠᠪᠲᠠ ᠢ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭ ᠤᠷ ᠤᠨ ᠢ ᠯᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠪᠤᠯᠬ ᠤ ᠨᠢ ︵︶ A √𝑥\s2 B √ 𝑥 C √ 𝑥 2\s1 D √ 𝑥 2 − 2

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠳ᠋᠊ ᠣᠯᠣᠳ ᠤᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ᠊ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮ᠊ ᠢᠨᠦ᠋ᠲ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ︶ ᠨᠢᠭᠡ᠂ ᠰ᠊ ᠤᠩᠭᠤ ᠬᠤ ᠰ᠊ ᠡᠲᠤᠪ᠃ ︵ᠰᠡᠲᠤ ᠤ ᠪᠦᠷ ᠢ 3 ᠬᠤᠪᠢ᠂ ᠨ᠊ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ︶ 1 ∆AB C ᠲᠤ᠂᠂ ∠A\s12 ∠ B 13 ∠ C ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠲ᠊ ᠡᠭᠦᠨ ᠳ᠋᠊᠂ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠠᠯ ᠠᠳ ᠶᠢᠨ ᠬᠠᠷᠢ ᠴᠠᠯ ᠨ᠊ ᠢ ︵︶ A 1 ∶1 ∶√ 2 B 1 ∶√ 3∶ 2 C 1 ∶√ 2

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠᠨ ᠳ᠋᠊ ᠣᠯᠣᠳ ᠤᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ᠊ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ 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 ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠡ ᠯ᠊ ᠡ ᠪᠦᠯᠦᠭ ᠲᠤᠭ ᠠ ᠳ᠋᠊ ᠥ᠂ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠠᠯ ᠠ ᠶᠢᠨ ᠬᠤᠯ ᠪᠤᠭᠳ ᠠᠯ ᠢ ᠤ ᠦᠷᠢ ᠯᠳᠤᠭ ᠦᠯᠵᠤ ᠴᠢᠳ ᠠᠬᠤ ᠦᠭᠡᠢ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷᠪ ᠠ ᠨ᠊ ᠠᠢ ᠮᠠᠳ ᠤᠭᠠᠷ ᠪᠦᠯ ᠦᠭ ᠦ ᠨ᠊ ᠤ ᠠᠭ 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 ᠲᠦ᠋ ᠷᠪᠡᠯ ᠶᠢᠨ AB CD ᠨᠢ ᠵᠢᠰᠢ ᠭᠦᠯᠵ ᠶᠢᠨ ᠤ ᠤᠯᠬᠤ ᠶᠢ ᠮᠠᠭᠠᠳ ᠯᠡᠵᠤ ᠴᠢᠳ ᠡᠬᠤ ᠨᠢ ︵︶ A AB ∥ CD ,AD\sBC B ∠ A\s∠B , ∠ C ∠D C AB\sCD , AD

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠠᠷ ᠪᠠ ᠨᠠᠢ ᠮᠠᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠨᠢᠭᠡ ᠴᠢ ᠶᠢ ᠨ᠊ ᠪᠠᠢᠴᠠ ᠭᠠᠯᠲᠠ 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 ᠵᠢᠷᠤᠭ 1 ᠮᠡᠲᠦ᠂ ᠵᠢᠰᠢᠭ ᠦᠯᠵᠢ ᠨ᠊ AB CD ᠲᠤ᠂ ᠳᠣᠣᠷ ᠠᠬᠢ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ ᠠᠴᠠ ᠵᠥᠪ ᠪᠢᠰᠢ ᠮᠠᠭᠠᠳ ᠨᠢ︶ ︵A ∠1\s∠2 ＝18 0 B ∠2\s∠3 ＝18 0A

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 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 ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠹᠦ ᠩᠺᠼ ᠨᠤᠭᠤ ᠳ᠋᠊ ᠡ ᠴᠡ ᠬᠤᠪᠢ ᠰᠬᠤᠨ 𝑥 ᠦᠨ ᠬ᠋᠊ ᠡᠮᠵᠢᠭ ᠳ᠋ᠡᠯ ᠠᠪᠬᠤ ᠭᠡᠪᠴ ᠢᠶ ᠡ ᠨᠢ 𝑥 ≥ 2 ᠪᠤᠯᠬᠤ ᠨᠢ ︵︶ A 𝑦\s√4 − 𝑥 2 B 𝑦 1 √𝑥 −2

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 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