2018 ᠣᠨ ᠤ ᠰᠢᠯᠢᠩᠬᠤᠲᠠ᠂ ᠠᠯᠠᠱᠠ᠂ ᠪᠣᠭᠤᠲᠤ ᠬᠤᠲᠠ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ ᠤ ᠳᠤᠮᠳᠠᠳᠤ ᠰᠢᠯᠭᠠᠯᠲᠠ ᠶᠢᠨ ᠰᠡᠲᠤᠪ

20 18 ᠣᠨ ᠤ ᠠᠩᠬ ᠠ ᠳ ᠣᠮᠳᠠᠳ ᠤ ᠢᠢ ᠨ ᠰᠤᠷᠭᠠᠭᠤ ᠯᠢ ᠳᠠᠪᠰ ᠢᠬᠤ ᠰᠢ ᠯᠭᠠᠯᠲ ᠠ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠳᠦᠪ ᠃ (ᠲᠤᠰ ᠰᠡᠳᠦᠪ 12 ᠪᠠᠭ ᠠ ᠰ ᠡᠳᠦᠪ ᠲᠠᠢ ᠂ ᠰᠡᠳ ᠦᠪ ᠪᠦ ᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨᠡᠶ ᠢᠲᠡ 36 ᠬᠤᠪᠢ ᠃ ᠰ ᠡᠳᠦᠪ ᠪᠦᠷᠢ ᠳ᠋ᠥ ᠵᠦᠪᠬ ᠡᠨ ᠨ ᠢᠭᠡ ᠵᠥᠪ ᠬᠠᠷᠢᠭ ᠤᠯᠲᠠ ᠲᠠᠢ ) 1. − √4 − |− 3| ᠢ ᠪᠤᠳᠤᠭᠠ ᠳ ᠣ ᠯᠬᠤ ᠨᠢ ( ) A. −1 B. − 5 C. 1 D. 5 2. ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ᠠᠳᠠᠯ ᠢᠬᠠᠨ ᠬᠡᠳᠦ ᠨ ᠵᠢ ᠵᠢᠭ ᠲᠡ ᠭᠰᠢ ᠳᠦᠷᠪ ᠡᠯᠵᠢᠨ ᠪᠡᠶ ᠡ ᠪ ᠠᠷ ᠦᠷᠦ ᠵᠤ ᠪᠦᠲ ᠦᠭᠡᠭᠰ ᠡᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠳᠡᠭᠡᠷ ᠡ ᠬᠠᠷ ᠠᠭᠠᠨ ᠤ ᠵᠢᠷᠤᠭ ᠪᠣᠯᠣᠨ ᠠ᠂ ᠡᠭᠦᠨ ᠳ᠋ᠥ ᠵᠢᠵᠢᠭ ᠲᠡᠭ ᠰᠢ ᠳ ᠦᠷᠪᠡ ᠯᠵᠢᠨ ᠲᠤᠳᠤᠷ ᠠᠬᠢ ᠨᠢ ᠡᠨ ᠡ ᠪ ᠠᠶᠢᠷᠢ ᠳ᠋ᠥ ᠬᠢ ᠵᠢᠵᠢᠭ ᠲᠡ ᠭᠰᠢ ᠳᠦᠷ ᠪᠡᠯᠵ ᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠪᠤᠳᠠᠭ ᠠᠯᠢ ᠲᠣᠭ ᠠ ᠢᠢ ᠢᠯᠡᠳᠭ ᠡᠨ ᠡ ᠂ ᠲᠡ ᠭᠡᠪᠡᠯ ᠡᠨᠡ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠣᠣ ᠯ ᠬᠠᠷ ᠠᠭᠠᠨ ᠤ ᠵᠢᠷ ᠤᠭ ᠨᠢ ( ) A. B. C. D. 3. ᠹᠦᠩᠺᠼᠢ y= 1 √𝑥 −1 ᠢᠢᠨ ᠬᠤᠪᠢᠰ ᠬᠤᠨ 𝑥 ᠦ ᠨ ᠬᠡ ᠮᠵᠢᠭᠳᠡᠯ ᠠ ᠪᠬᠤ ᠬᠡᠪ ᠴᠢᠶ ᠡ ᠨᠢ ( ) A. 𝑥 ≠ 1 B. 𝑥 0 C. 𝑥≥ 1 D. 𝑥 1 4. ᠳᠠᠷᠠᠭ ᠠᠬᠢ ᠶᠠᠪᠤᠳᠠᠯ ᠳᠤᠲᠤᠷᠠ ᠬᠢ ᠪ ᠣᠯᠣᠯᠴᠠ ᠭᠠᠭᠦᠢ ᠶ ᠠᠪᠤᠳᠠᠯ ᠪᠣᠯ ᠬᠤ ᠨᠢ ( ) A. ᠨᠢᠭᠡᠨ ᠲᠤᠭ ᠠᠨ ᠤ ᠬᠠᠷ ᠢᠴᠠᠯ ᠠᠰᠢᠭᠦᠢ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨᠢ 0 ᠡᠴᠡ ᠶᠡᠬᠡ ᠪᠣᠯᠬᠤ B. ᠨᠢᠭᠡᠨ ᠲᠤᠭ ᠠᠨ ᠤ ᠡᠰᠡᠷ ᠭᠦ ᠲᠣᠭ ᠠ ᠨᠢ ᠲᠡᠭᠦᠨ ᠤ ᠲᠤᠰ ᠪᠡᠶ ᠡ ᠲᠠ ᠢ ᠲᠡ ᠩᠴᠡᠬᠦ C. ᠳᠤᠷ ᠠ ᠢᠢᠨ ᠲᠠᠪᠤᠨ ᠦᠨᠴ ᠦᠭᠲᠦ ᠢ ᠢᠨ ᠭᠠᠳᠠ ᠭᠠᠳᠤ ᠦᠨᠴ ᠦᠭ ᠦ ᠨ ᠨᠡ ᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠢ 5 40 ° ᠪ ᠣᠯᠬᠤ D. ᠤᠷ ᠲᠤ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ 3 , 4 , 6 ᠪᠣᠯᠬᠤ ᠭᠤ ᠷᠪᠠᠨ ᠬᠡᠷᠴᠢ ᠮ ᠢᠢᠡᠷ ᠨᠢᠭᠡ ᠨ ᠭᠤᠷᠪ ᠠᠯᠵᠢ ᠨ ᠢ ᠬᠦᠷᠢᠶ ᠡᠯᠡᠨ ᠪᠦᠲ ᠦᠭᠡᠬᠦ 5. ᠬᠡᠷᠪᠡ 2𝑥 𝑎+ 1y ᠬᠢᠭᠡᠳ 𝑥 2y 𝑏− 1 ᠨᠢ ᠢᠵᠢᠯ ᠲᠦᠷ ᠦᠯ ᠦ ᠨ ᠭᠡᠰᠢᠭ ᠦᠨ ᠪᠣᠯᠪᠠ ᠯ 𝑎𝑏 ᠦᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨᠢ ( ) A. 12 B. 32 C. 1 D. 3 6. ᠨᠢᠭᠡ ᠪᠦᠯᠦᠭ ᠳ᠋ᠠᠶᠢᠲ᠋ᠠ 1,3,4 ,4,4 ,5,5 ,6 ᠢᠢᠨ ᠮᠤᠳ᠋ ᠪᠠ ᠰᠠᠷᠨᠢᠴᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ( ) A. 4 , 1 B. 4 , 2 C. 5 , 1 D. 5 , 2 7. ᠵᠢᠷᠤᠭ 2 ᠮᠡ ᠲᠦ ∆AB C ᠳ᠋ᠥ ᠂ AB = 2 , BC = 4 , ∠AB C= 30° ᠂ ᠴᠡ ᠭ B ᠪᠠᠷ ᠲᠤᠭ ᠤᠷᠢᠭ ᠦᠨ ᠲᠥᠪ ᠪᠣᠯᠭ ᠠᠵᠤ ᠂ AB ᠢᠢᠨ ᠤᠷᠲᠤ ᠪᠠᠷ ᠷᠠᠳᠢᠣᠰ ᠪᠣᠯ ᠭᠠᠨ ᠨᠤᠮ ᠤ ᠵᠢ ᠷᠤᠪᠠᠯ ᠂ BC ᠲᠠ ᠢ ᠴᠡ ᠭ D ᠳ᠋ᠥ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠵᠢᠷ ᠤᠭ ᠳ᠋ᠡᠬᠢ ᠰᠡᠭᠦ ᠳᠡᠷ ᠲᠠᠢ ᠬᠡᠰᠡᠭ ᠦᠨ ᠲᠠᠯ ᠠᠪᠠᠢ ᠨᠢ ( ) A. 2 − 𝜋3 B. 2− 𝜋6 C. 4− 𝜋3 D . 4 − 𝜋6 8. ᠵᠢᠷᠤᠭ 3 ᠮᠡᠲᠦ ∆AB C ᠳ᠋ᠥ AB = AC , ∆ ADE ᠢᠢᠨ ᠤᠷᠤᠢ ᠢᠢᠨ ᠴᠡᠭ D , E ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ BC , AC ᠳᠡ ᠭᠡᠷ ᠡ ᠤᠷᠤᠰ ᠢᠬᠤ ᠪᠦᠭᠡᠳ ∠D AE = 90° , AD = AE ᠬᠡ ᠷᠪᠡ ∠C + ∠B AC = 145° ᠪᠣᠯ ∠ED C ᠢᠢᠨ ᠭᠷᠠᠳᠦᠰ ᠦ ᠨ ᠲᠣᠭ ᠠ ᠨᠢ ( ) 2 2 1 DB A C CB A D E A. 17 .5° B. 12 .5° C. 12° D . 10° 9. 𝑥 ᠦ ᠨ ᠲᠤᠬ ᠠᠢ ᠨᠢᠭᠡ ᠦ ᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭ ᠴᠢᠲᠡᠢ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡᠷᠭᠡ ᠢᠢᠨ ᠲᠡᠭᠰᠢ ᠳᠭᠡᠯ 𝑥 2 + 2𝑥 + 𝑚 − 2= 0 ᠲᠦ ᠬᠤᠶ ᠠᠷ ᠪ ᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠᠨ ᠤ ᠢᠵ ᠠᠭᠤᠷ ᠲᠠᠢ ᠭᠡᠵᠤ ᠦᠭ ᠭᠦᠭᠳᠡᠪ ᠡ᠂ 𝑚 ᠨᠢ ᠡᠶᠡᠷ ᠬᠦ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ ᠠ ᠪᠦᠭᠡᠳ ᠡᠨᠡ ᠬᠦ ᠲᠡ ᠭᠰᠢᠳ ᠭᠡᠯ ᠦ ᠨ ᠢ ᠵᠠᠭᠤᠷ ᠨᠢ ᠴᠦᠮ ᠪᠦᠬᠦ ᠯᠢ ᠲᠣᠭ ᠠ ᠪᠣᠯ ᠤᠨ ᠠ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠨᠦᠬᠦᠴᠡ ᠯ ᠳ᠋ᠥ ᠲᠣᠬᠢᠷ ᠠᠬᠤ ᠪᠤᠢ ᠪᠦᠬᠦᠢ ᠡᠶ ᠡᠷᠬᠦ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ ᠠ 𝑚 ᠶᠢᠨ ᠨᠡᠶᠢᠯᠡ ᠪᠦᠷᠢ ᠨᠢ ( ) A. 6 B. 5 C. 4 D . 3 10. ᠳᠠᠷ ᠠᠭᠠᠬ ᠢ ᠦᠭ ᠦᠯᠡᠯ ᠦ ᠭᠭᠦᠭᠳᠡ ᠵᠡᠢ᠄ ① ᠬᠡᠷ ᠪᠡ 𝑎 3 b 3 ᠪᠣ ᠯᠪᠠᠯ ᠂ 𝑎 2 b 2 ② ᠬᠡᠷᠪᠡ ᠴᠡᠭ A (𝑥 1 ,𝑦 1 ) ᠪᠠ ᠴᠡᠭ B (𝑥 2 ,𝑦 2 ) ᠨᠢ ᠬᠤᠶ ᠠᠳᠤᠭ ᠠᠷ ᠵᠡ ᠷᠭᠡ ᠢᠢᠨ ᠹᠦᠩᠺᠼ 𝑦= 𝑥 2 − 2𝑥 − 1 ᠦ ᠨ ᠵᠢᠷ ᠤᠮᠠᠭ ᠦᠨ ᠳᠡᠭᠡᠷ ᠡ ᠤᠷ ᠤᠰᠢᠬ ᠤ ᠪ ᠦᠭᠡᠳ 𝑥 1 y2 −2 ③ 𝑎 ,𝑏 ,𝑐 ᠪᠣᠯ ᠢ ᠵᠢᠯ ᠨᠢᠭᠡᠨ ᠬᠠᠪ ᠲᠠᠭᠠᠢ ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠰᠢᠯᠤᠭᠤ ᠨ ᠪ ᠦᠭᠡᠳ 𝑎 ∥𝑏 , b⊥ c ᠪᠣᠯᠪᠠ ᠯ 𝑎 ∥𝑐 ④ ᠬᠦ ᠷᠢᠶᠡᠨ ᠤ ᠤᠷᠲᠤ ᠨᠢ ᠲᠡᠩ ᠴᠡᠭᠦᠤ ᠪᠣᠯᠬᠤ ᠪᠤᠢ ᠪᠦᠬᠦ ᠢ ᠠ ᠳᠠᠯᠢ ᠬᠠ ᠵᠠᠭᠤᠳᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠲᠦ ᠭᠤᠷᠪ ᠠᠯᠵᠢ ᠨ ᠪ ᠦᠷᠢ ᠨ ᠲᠡ ᠩᠴᠡᠭᠦᠤ ᠃ ᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠲᠤᠲᠤᠷ ᠠᠬᠢ ᠵᠢᠩᠬ ᠢᠨᠢ ᠦᠭ ᠦᠯᠡᠯ ᠦᠨ ᠪᠣᠳᠠᠭ ᠠᠯᠢ ᠲᠣᠭ ᠠ ᠨᠢ ( ) A. 4 B. 3 C. 2 D. 1 11. ᠵᠢᠷ ᠤᠭ 4 ᠮᠡ ᠲᠦ ᠂ ᠬᠠᠪ ᠲᠠᠭᠠᠢ ᠢᠢᠨ ᠲᠡᠭ ᠰᠢ ᠦᠨᠴᠦᠭᠲᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦ ᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠳ᠋ᠥ ᠰᠢᠯ ᠤᠭᠤᠨ 𝑙1 :y = − √24 𝑥+ 1 ᠨᠢ x ᠲᠡᠨᠬ ᠡᠯᠢᠭ ᠲᠠ ᠢ A , B ᠬᠤᠶ ᠠᠷ ᠴᠡᠭ ᠲᠦ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ ᠂ ᠰᠢᠯᠤᠭᠤᠨ 𝑙2 : y= 𝑘𝑥 (𝑘 ≠ 0) ᠬᠢᠭᠡᠳ ᠰᠢᠯ ᠤᠭᠤᠨ 𝑙1 ᠨᠢ ᠨᠢ ᠭᠡᠳᠦᠭᠡᠷ ᠮᠦᠴᠡ ᠳ᠋ᠥ C ᠴᠡᠭ ᠲᠦ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠ ᠨ ᠠ᠂ ᠬᠡᠷ ᠪᠡ ∠B OC = ∠B CO ᠪᠣᠯ 𝑘 ᠢᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨᠢ ( ) A. √ 2 3 B. √2 2 C. √2 D . 2 √2 12. ᠵᠢᠷ ᠤᠭ 5 ᠮᠡᠲᠦ ᠂ ᠳᠦᠷᠪ ᠡᠯᠵᠢᠨ A BC D ᠳ᠋ᠥ BD ᠨᠢ ∠AB C ᠢᠢ ᠲᠠᠯᠠᠠ ᠯᠨ ᠬᠤᠪᠢᠶ ᠠᠨ ᠠ ᠂ ∠B AD = ∠B DC = 90° , E ᠨᠢ BC ᠢᠢᠨ ᠳᠣᠮᠳᠠ ᠴᠡᠭ ᠂ AE ᠪᠠ BD ᠨᠢ ᠴᠡᠭ F ᠳ᠋ᠥ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠ ᠨ ᠠ᠃ ᠬᠡᠷᠪᠡ BC = 4 , ∠CB D = 30° ᠪᠣᠯ ᠪᠠᠯ DF ᠦᠨ ᠤᠷᠲᠤ ᠨᠢ ( ) A. 25 √ 3 B. 23 √ 3 C. 34 √ 3 D . 45 √ 3 ᠬᠤᠶ ᠠᠷ ᠂ ᠬᠠᠭᠠ ᠯᠲᠠ ᠲᠠᠭ ᠯᠠᠬᠤ ᠰᠡᠳ ᠦᠪ᠃ (ᠰ ᠡᠳᠦᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨᠡᠶ ᠢᠲᠡ 24 ᠬᠤᠪᠢ ) 13. ᠬᠡᠷ ᠪᠡ 𝑎 − 3𝑏 = 2,3 𝑎− 𝑏= 6ᠪᠣᠯ 𝑏− 𝑎 ᠦ ᠨ ᠬᠡ ᠮᠵᠢᠭ ᠳᠡᠯ ᠨ ᠢ ( )᠃ 14. ᠲᠡ ᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠢᠢᠨ ᠪᠦᠯᠦ ᠭ { 2𝑥 + 7 3( 𝑥+ 1) 23 𝑥 − 3𝑥 +46 ≤ 23 ᠦᠨ ᠰᠦᠬ ᠡᠷᠬᠦ ᠪᠦᠬᠦᠯ ᠢ ᠲᠣᠭ ᠠᠨ ᠤ ᠬᠠᠷ ᠢᠭᠤ ᠨ ᠢ ( ) 15. ᠳᠦ ᠷᠪᠡᠨ ᠲᠣᠭ ᠠ －2,− 1,1 ,2 ᠡᠴᠠ ᠲᠠᠰᠢᠷᠠ ᠮ ᠢᠢᠠᠷ ᠬᠤᠶ ᠠᠷ ᠲᠣᠭ ᠠ ᠠ ᠪᠴᠤ ᠬᠠᠷ ᠢᠯᠴᠠ ᠨ ᠦᠷᠡ ᠵᠢᠭᠦᠯ ᠦᠨ ᠡ ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠦᠷᠡ ᠵᠢᠪᠦᠷ ᠢ ᠨ ᠢ －4 ᠡᠴᠡ ᠶᠡᠬᠡ 2 ᠡᠴᠡ ᠪᠠᠭ ᠠ ᠪᠣᠯᠬ ᠤ ᠲᠤᠬ ᠢᠶᠠᠯᠳᠤᠮᠵ ᠢ ᠨ ᠢ ( ) 16. ᠬᠢᠯᠪᠠ ᠷᠴᠢᠯ ᠠ ᠄ 𝑥 2 −4 𝑥+ 4 𝑥 2 +2 𝑥 ÷ ( 4𝑥+2 − 1) =( ) ᠃ 17. ᠵᠢᠷ ᠤᠭ 6 ᠮᠡ ᠲᠦ AB ᠪᠣᠯ ⨀O ᠦᠨ ᠳ᠋ᠢᠶᠠᠮ ᠧᠲ᠋ᠷ ᠂ ᠴᠡᠭ C ᠨ ᠢ ⨀O ᠳᠡ ᠭᠡᠷ ᠡ ᠤᠷ ᠤᠰᠢᠨ ᠠ ᠂ x y L 2 L 1 A B C O F A D B CE ᠴᠡᠭ C ᠢ ᠢ ᠳᠠᠭ ᠠᠷᠢᠭᠰᠠᠨ ᠰᠢᠬ ᠠᠭᠴ ᠢ ᠰᠢᠯᠤᠭᠤᠨ ᠬᠢᠭᠡᠳ BA ᠦᠨ ᠦᠷᠭᠦᠯ ᠵᠢᠯᠡᠯ ᠱᠤᠭᠤᠮ ᠨ ᠢ ᠴᠡᠭ D ᠳ᠋ᠥ ᠤᠭᠲᠤ ᠯᠤᠯᠴᠠᠨ ᠠ᠂ ᠴᠡᠭ E ᠨ ᠢ BĈ ᠳᠡ ᠭᠡᠷ ᠡ ᠤᠷᠤ ᠰᠢᠨ ᠠ᠂ ( ᠴᠡ ᠭ B,C ᠲᠠ ᠢ ᠳᠠ ᠪᠬᠤᠴᠠᠬ ᠤ ᠦ ᠭᠡ ᠢ) ᠂ BE , CE ᠢ ᠢ ᠬᠣᠯ ᠪᠤᠨ ᠠ ᠃ ᠬᠡᠷᠪᠡ ∠D = 40° ᠪᠣᠯ ∠B EC = ( ) 18. ᠵᠢᠷ ᠤᠭ 7 ᠮᠡᠲᠦ᠂ ᠵᠢᠰᠢᠭᠦᠯᠵᠢ ᠨ A BC D ᠳ᠋ᠥ AC ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠲᠠᠰᠢᠭᠤᠪ ᠴ ᠢ᠂ EF //BC ᠪᠦᠭᠡᠳ EF ᠨ ᠢ AB ᠲᠠ ᠢ ᠴᠡᠭ E ᠳ᠋ᠥ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠵ ᠤ ᠂ AC ᠲᠠ ᠢ ᠴᠡᠭ F ᠳ᠋ᠥ ᠤᠭᠲ ᠤᠯᠤᠯ ᠴᠠᠨ ᠠ ᠂ 3AE = 2EB , DF ᠢ ᠢ ᠬᠣᠯ ᠪᠤᠨ ᠠ ᠂ ᠬᠡᠷᠪᠡ SΔ AEF = 1 ᠪᠣᠯ SΔ ADF ᠦᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨ ᠢ ( ) 19. ᠲᠡᠭ ᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠦ AB CD ᠶᠢᠨ ᠬᠤᠶ ᠠᠷ ᠲᠠ ᠰᠢᠭᠤᠪ ᠴ ᠢ ᠢᠢᠨ ᠤᠭᠲᠤ ᠯᠤᠯᠴᠠᠯ ᠴᠡᠭ O ᠢᠢᠡᠷ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠡᠬ ᠢᠨ ᠤ ᠴᠡ ᠭ ᠪ ᠣᠯᠭᠠᠨ ᠬᠤ ᠶᠠᠷ ᠲᠠᠯ ᠠ ᠲᠠ ᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠴᠢᠭᠯᠡᠯ ᠢᠢᠡᠷ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠲᠡᠩᠬ ᠡᠯᠢᠭ ᠪᠣᠯ ᠭᠠᠵᠤ ᠵᠢᠷ ᠤᠭ 8 ᠮᠡᠲᠦ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴᠦ ᠭᠲᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧ ᠮ ᠪᠠᠶᠢᠭ ᠤᠯᠤᠨ ᠠ ᠃ BE ⊥ AC , ᠡᠭ ᠴᠡ ᠢᠢᠨ ᠰᠠᠭ ᠤᠷ ᠢ ᠨ ᠢ E ᠂ ᠬᠡ ᠷᠪᠡ ᠬᠣᠣ ᠰ ᠮᠤᠷ ᠤ ᠢ ᠱᠤᠭᠤ ᠮ y = 32x ( x 0) ᠨ ᠢ ᠴᠡ ᠭ D ᠢ ᠢ ᠳᠠᠭ ᠠᠷᠢᠪᠠ ᠯ OB ᠂ BE ᠦᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠨ ᠢ ( ) 20. ᠵᠢᠷ ᠤᠭ 9 ᠮᠡᠲᠦ᠂ Rt ∆A CB ᠳ᠋ᠥ ∠A CB = 90° , AC = BC , D ᠨ ᠢ AB ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠨᠢᠭᠡᠨ ᠬᠦᠳᠡᠯ ᠬᠦ ᠴᠡ ᠭ ( ᠴᠡᠭ A , B ᠲᠠ ᠢ ᠳᠠᠪᠬᠤᠴ ᠠᠬᠤ ᠦᠭᠡ ᠢ ) ᠂ CD ᠢ ᠢ ᠬᠣᠯ ᠪᠤᠭᠠᠳ ᠴᠡᠭ C ᠢ ᠢ ᠲᠤᠭ ᠤᠷᠢᠭ ᠤᠯᠤᠨ ᠴᠠᠭ ᠦᠨ ᠵᠡᠭᠦᠤ ᠢᠢᠨ ᠳᠠᠭ ᠠᠤ 90° ᠡᠷ ᠭᠢᠭᠦᠯ ᠵᠦ CE ᠳ᠋ᠥ ᠬᠦᠷᠭᠡᠨ ᠡ᠂ DE ᠢ ᠢ ᠬᠣᠯᠪᠤᠪᠠ ᠯ AC ᠲᠠ ᠢ F ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ ᠂ AE ᠢ ᠢ ᠬᠤᠯ ᠪᠤᠨ ᠠ ᠃ ᠳᠠ ᠷᠠᠭᠠᠬ ᠢ ᠳ᠋ᠦ ᠩᠨᠡᠯ ᠲᠡ ᠢᠢ ᠨ ᠵᠥ ᠪ ᠨ ᠢ ( )᠃ ︵ᠪᠤ ᠢ ᠪᠦᠬᠦ ᠢ ᠵᠥᠪ ᠳ᠋ᠦ ᠩᠨᠡᠯ ᠲᠡ ᠢᠢᠨ ᠵᠥᠪ ᠳ᠋ᠤᠭᠠᠷ ᠯᠠᠯ ᠢ ᠲᠠ ᠭᠯᠠ ) ① ∆AEC ≅ ∆B CD ② ᠬᠡᠷᠪᠡ ∠B CD = 25° ᠪᠣᠯ ᠬᠡᠷᠪᠡ ∠AED = 65° ③ DE 2= 2CF .CA ④ ᠬᠡᠷ ᠪᠡ A B=3 √2 , A D= 2BD ᠪᠣᠯ A F= 53 ᠭᠤᠷᠪ ᠠ ᠂ ᠪ ᠣᠳᠤᠵ ᠤ ᠬᠠᠷ ᠢᠭᠤᠯ ᠬᠤ ᠰᠡ ᠳᠦᠪ ᠃ ( ᠨᠡ ᠶᠢᠲᠡ 60 ᠬᠤᠪᠢ ) 21. ( 8 ᠬᠤᠪᠢ ) ᠨᠢ ᠭᠡᠨ ᠺᠣᠮᠫ ᠠᠨᠢ ᠬᠤᠶ ᠠᠷ ᠠ ᠵᠢᠯᠲᠠᠨ ᠡᠯᠰᠡᠬᠦ ᠭᠡᠵ ᠤ ᠪᠠᠶᠢᠨ ᠠ ᠃ ᠠ ᠂ ᠢ ᠣ ᠳᠦᠷᠪ ᠡᠨ ᠰᠢᠯᠭ ᠠᠯᠲᠠ ᠳ᠋ᠥ ᠤᠷ ᠤᠯᠴᠠᠭᠴᠢ ᠢᠢ ᠨ ᠪ ᠢᠷ ᠦᠨ ᠰᠢᠯᠭ ᠠᠯᠲᠠ ᠪᠠ ᠨᠢᠭᠤᠷ ᠦᠨ ᠰᠢᠯᠭ ᠠᠯᠲᠠ ᠳ᠋ᠥ ᠬ ᠤᠪᠢ ᠣᠯᠭ ᠤᠨ ᠠ ᠃ ᠡᠯ ᠡ ᠲᠦᠷᠦᠯ ᠦᠨ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ ᠢ ᠢ ᠴᠦ ᠮ ᠵᠠ ᠭᠤᠨ ᠬᠤᠪ ᠢ ᠢᠢᠨ ᠳᠦᠷ ᠢᠮ ᠢᠢᠡᠷ ᠲᠡ ᠮᠳᠡᠭᠯᠡᠨ ᠡ᠂ ᠳᠠᠷᠠᠭ ᠠ ᠨ ᠢ ᠪᠢᠷ ᠦ ᠨ ᠰᠢᠯᠭ ᠠᠯᠲᠠ ᠨ ᠢ 60% ᠡᠵᠡᠯ ᠡᠵᠤ᠂ ᠨᠢᠭᠤᠷ ᠦ ᠨ ᠰ ᠢᠯᠭᠠᠯᠲ ᠠ ᠨ ᠢ 40% ᠡᠵᠡᠯ ᠡᠬᠦ ᠬᠠᠷ ᠢᠴᠠᠯ ᠢᠢᠠᠷ ᠣᠷ ᠣᠯᠴᠠᠭ ᠰᠠᠳ ᠦ ᠨ ᠶᠡᠷᠦ ᠩᠬᠡ ᠢ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ ( ᠵᠠ ᠭᠤᠨ ᠬᠤᠪᠢ ᠢᠢᠨ ᠳᠦᠷᠢᠮ ) ᠢ ᠢ ᠪᠣᠳᠤᠨ ᠠ ᠃ ᠲᠡᠳᠡᠨ ᠤ ᠡᠯ ᠡ ᠵᠤᠶᠢᠯ ᠦᠨ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ ᠨ ᠢ ᠳᠤᠤᠷ ᠠᠬᠢ ᠬᠦᠰ ᠦᠨᠦᠭ ᠲᠦ ᠳ᠋ ᠥ ᠦᠵ ᠡᠭᠦᠯᠦ ᠭᠰᠡᠨ ᠮᠡᠲᠦ ᠄ (1) ᠡᠨᠡ ᠳᠦᠷᠪ ᠡᠨ ᠣ ᠷᠣᠯᠴᠠᠭᠴ ᠢ ᠢᠢᠨ ᠨᠢᠭᠤᠷ ᠦᠨ ᠰᠢᠯᠭ ᠠᠯᠲᠠ ᠢᠢᠨ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ ᠢᠢᠨ ᠳᠣᠮ ᠳᠠ ᠪᠠᠶᠢᠷ ᠢ ᠢᠢᠨ ᠲᠣᠭ ᠠ ᠢ ᠢ ᠰᠢᠭ ᠤᠳ ᠪᠢᠴᠢ ᠵᠦ ᠭᠠ ᠷᠭ ᠠ ᠃ O A B D C E CB DA E F y xO E A B C D F D B C A E ᠣᠷᠣᠯᠴ ᠠᠭᠴ ᠢ ᠠ ᠡ ᠢ ᠣ ᠪᠢᠷ ᠰᠢᠯᠭ ᠠᠯᠲᠠ ᠢᠢᠨ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ 90 84 𝑥 88 ᠨᠢᠭ ᠤᠷ ᠦᠨ ᠰ ᠢᠯᠭᠠᠯᠲ ᠠ ᠢᠢᠨ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ 88 92 90 86 (2) ᠣᠳᠤ ᠢ ᠢ ᠢᠨ ᠶᠡᠷ ᠦᠩᠬᠡ ᠢ ᠬᠢᠷ ᠢ ᠪᠦ ᠲᠦᠮᠵ ᠢ ᠨ ᠢ 87 .6 ᠬᠤᠪᠢ ᠪᠣᠯᠬ ᠤ ᠢ ᠢ ᠮᠡ ᠳᠡᠪᠡ ᠂ ᠬᠦᠰ ᠦᠨᠦᠭ ᠲᠦ ᠳ᠋ᠡᠬ ᠢ 𝑥 ᠢᠢᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠣ ᠯ ᠃ (3) ᠪᠤᠰ ᠤᠳ ᠭᠤᠷᠪ ᠠᠨ ᠬ ᠦᠮᠦ ᠨ ᠤ ᠶᠡᠷᠤᠩᠬᠡ ᠢ ᠬᠢᠷ ᠢ ᠪᠦᠲ ᠦᠮᠵ ᠢ ᠢ ᠢ ᠣᠯᠵ ᠤ ᠂ ᠨᠡᠷᠡᠰ ᠦᠨ ᠳ᠋ᠤᠭᠠᠷ ᠯᠠᠯ ᠢᠢᠠᠷ ᠨ ᠢ ᠡᠯᠰ ᠡᠬᠦ ᠡᠮ ᠦᠨ ᠡ ᠬᠤᠶ ᠠᠷ ᠨᠡ ᠷ ᠡ ᠢ ᠢ ᠲᠣᠭ ᠲᠠᠭ ᠠ ᠃ 22. ( 8 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ ᠂ ᠳᠦᠷᠪ ᠡᠯᠵᠢ ᠨ A BC D ᠳ᠋ᠥ AD //BC , ∠AB C= 90 ° , AB = AD , BD ᠢ ᠢ ᠬᠣᠯ ᠪᠤᠨ ᠠ ᠂ ᠴᠡ ᠭ E ᠨ ᠢ AB ᠳᠡ ᠭᠡᠷ ᠡ ᠤᠷᠤᠰ ᠢᠬᠤ ᠪᠦᠭᠡᠳ ∠B DE = 15 ° , DE = 4√ 3 , DC = 2√ 21 (1) BE ᠦᠨ ᠤᠷᠲᠤ ᠢ ᠢ ᠣ ᠯ ᠃ (2) ᠳᠦᠷᠪ ᠡᠯᠵᠢ ᠨ D EBC ᠢᠢᠨ ᠲᠠᠯ ᠠᠪᠠ ᠢ ᠢ ᠢ ᠣ ᠯ᠃ (※ ᠠᠩ ᠬᠠᠷ ᠄ ᠪᠣᠳᠤᠯ ᠭ ᠠ ᠢᠢᠨ ᠶᠠᠪᠤᠴ ᠠ ᠪ ᠠ ᠳ᠋ ᠦᠩ ᠳ᠋ᠥ ᠴᠦ ᠮ ᠢ ᠵᠠᠭᠤᠷ ᠦ ᠨ ᠲᠡ ᠮᠳᠡᠭ ᠢ ᠨ ᠢ ᠦᠯ ᠡᠳᠡᠭᠡ ) A D CB E 23. ( 10 ᠬᠤᠪᠢ ) ᠨᠢᠭᠡᠨ ᠳᠡᠯᠭᠡᠭᠦᠷ ᠲᠤᠭᠲᠠᠭᠰᠠᠨ ᠦ ᠨ ᠡ ᠪᠠᠷ ᠨᠢᠭᠡᠨ ᠲᠦ ᠷᠦᠯ ᠦ ᠨ ᠲᠠ ᠧᠠᠷ ᠢ ᠪᠦᠭᠡ ᠮ ᠢᠢᠡᠷ ᠣᠷ ᠣᠭᠤᠯ ᠪᠠ ᠂ 3 ᠳ᠋ᠤᠭᠠᠷ ᠰᠠᠷ ᠠ ᠳ᠋ᠥ ᠲᠤᠭᠲᠠᠭ ᠠᠭᠰᠠᠨ ᠦᠨ ᠡ ᠪ ᠠᠷ ᠬᠤᠳᠠ ᠯᠳᠤᠭᠰᠠᠨ ᠳ᠋ᠥ ᠂ ᠪᠣᠷᠤᠯ ᠠᠭᠤᠯᠲᠠ ᠢᠢᠨ ᠮᠦᠩᠭᠦ ᠨ ᠢ 24 00 ᠲᠦᠭ ᠦᠷᠢᠭ ᠪᠠᠶᠢᠪ ᠠ᠂ ᠪᠣᠷᠤᠯ ᠠᠭᠤᠯᠲᠠ ᠪᠠᠨ ᠨᠡᠮᠡᠭ ᠳᠡᠭᠦ ᠯᠵᠦ᠂ ᠬᠦᠮ ᠦᠷᠭᠡ ᠢ ᠢᠨ ᠬᠠᠳᠠ ᠭᠠᠯᠠᠮᠵ ᠢ ᠪᠠᠨ ᠪᠠᠭᠠᠰᠬ ᠠᠬᠤ ᠢᠢᠨ ᠲᠦ ᠯᠦᠭᠡ ᠂ 4 ᠳ᠋ᠦ ᠭᠡᠷ ᠰᠠᠷ ᠠ ᠳ᠋ᠥ ᠤᠭ ᠦ ᠨ ᠦ ᠨ ᠡ ᠢ ᠢ 9 ᠨᠤᠭ ᠤᠯᠵᠤ ᠬᠤᠳᠠ ᠯᠳᠤᠭᠰᠠᠨ ᠳ᠋ᠥ ᠪᠣᠷᠤᠯ ᠠᠯᠭᠤᠯ ᠲᠠ ᠢ ᠢᠨ ᠬᠡᠮᠵᠢ ᠶ ᠡ ᠨ ᠢ 30 ᠬᠠᠶᠢ ᠷᠴᠠᠭ ᠨᠡᠮᠡᠭ ᠳᠡᠵᠦ ᠂ ᠪᠣᠷᠤᠯ ᠠᠭᠤᠯ ᠲᠠ ᠢ ᠢᠨ ᠮᠦᠩ ᠭᠦ ᠨ ᠢ 8 40 ᠲᠦᠭ ᠦᠷᠢᠭ ᠨᠡᠮᠡᠭ ᠳᠡᠪᠡ ᠃ (1 ) ᠲᠤᠰ ᠳᠡᠯᠭᠡᠭᠦᠷ 3 ᠳ᠋ᠤᠭᠠᠷ ᠰᠠᠷ ᠠ ᠳ᠋ᠥ ᠡᠨᠡ ᠲᠦᠷᠦᠯ ᠦᠨ ᠲᠠᠧᠠᠷ ᠢ ᠬᠡᠳᠦ ᠢ ᠲᠦᠭ ᠦᠷᠢᠭ ᠢᠢᠡᠷ ᠬᠤᠳᠠᠯ ᠳᠤᠭᠰᠠ ᠨ ᠪᠤ ᠢ ︖ (2 ) ᠬᠡ ᠷᠪᠡ ᠲᠤᠰ ᠳᠡᠯᠭᠡᠭᠦᠷ 3 ᠳ᠋ᠤᠭᠠᠷ ᠰᠠᠷ ᠠ ᠳ᠋ᠥ ᠡᠨᠡ ᠲᠦ ᠷᠦᠯ ᠦᠨ ᠲᠠᠧᠠ ᠷ ᠢ ᠪᠤᠷᠤᠯ ᠠᠭᠤᠯ ᠤᠨ ᠣᠯᠤᠭᠰ ᠠᠨ ᠠ ᠰᠢᠭ ᠬᠤᠨᠵ ᠢᠪᠦᠷ ᠢ ᠨ ᠢ 9 00 ᠲᠦᠭ ᠦᠷᠢᠭ ᠪᠣᠯ ᠲᠤᠰ ᠳᠡᠯᠭᠡ ᠭᠦᠷ ᠦᠨ 4 ᠳ᠋ ᠦᠭᠡᠷ ᠰᠠᠷ ᠠ ᠳ᠋ᠥ ᠡᠨᠡ ᠲᠦᠷᠦᠯ ᠦᠨ ᠲᠠᠧᠠ ᠷ ᠢ ᠪᠤᠷᠤᠯ ᠠᠭᠤᠯᠤᠨ ᠣᠯᠤᠭᠰ ᠠᠨ ᠠ ᠰᠢᠭ ᠬᠤᠨᠵ ᠢᠪᠦᠷ ᠢ ᠨ ᠢ ᠬᠡᠳᠦ ᠢ ᠲᠦᠭ ᠦᠷᠢᠭ ᠪᠤ ᠢ ︖ 24. ︵10 ᠬᠤᠪᠢ ︶ ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ ᠂ Rt ∆A CB ᠳ᠋ᠥ ∠A CB = 90° ᠂ ᠴᠡ ᠭ A ᠪᠠᠷ ᠲᠤᠭ ᠤᠷᠢᠭ ᠦᠨ ᠲᠥᠪ ᠪᠣᠯ ᠭᠠᠨ AC ᠦᠨ ᠤᠷᠲᠤ ᠪᠠᠷ ᠷᠠᠳᠢᠣᠰ ᠪᠣᠯᠭ ᠠᠭᠰᠠᠨ ᠲᠤᠭᠤᠷ ᠢᠭ ᠨ ᠢ AB ᠲᠠ ᠢ ᠴᠡᠭ D ᠳ᠋ᠥ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠ ᠵᠤ BA ᠢᠢᠨ ᠦᠷᠭᠦᠯ ᠵᠢᠯᠡᠯ ᠱᠤᠭᠤᠮ ᠲᠠ ᠢ ᠴᠡ ᠭ E ᠳ᠋ᠥ ᠤᠭ ᠲᠤᠯᠤ ᠯᠴᠠᠨ ᠠ ᠂ CE , CD ᠢ ᠢ ᠬᠣᠯ ᠪᠤᠨ ᠠ ᠂ F ᠪᠣᠯ ⨀ A ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠨᠢᠭᠡᠨ ᠴᠡᠭ ᠂ ᠴᠡ ᠭ F ᠬᠢᠭᠡᠳ ᠴᠡᠭ C ᠨ ᠢ BE ᠢᠢᠨ ᠬᠤᠶ ᠠᠷ ᠲᠠ ᠯ ᠠ ᠳᠥ ᠤᠷᠤᠰ ᠢᠬᠤ ᠪᠦᠭᠡᠳ ∠F AB = ∠AB C ᠂ BF ᠢ ᠢ ᠬᠤᠯ ᠪᠤᠨ ᠠ ᠃ (1 ) ᠪᠠᠲᠤᠯ ᠠ᠄ ∠B CD = ∠B EC (2 ) ᠬᠡᠷᠪᠡ BC = 2 , BD = 1 ᠪᠣᠯ CE ᠦᠨ ᠤᠷᠲᠤ ᠵᠢᠴ ᠢ sin ∠AB F ᠦ ᠨ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠣ ᠯ ᠃ A D E CB F 25. ( 12 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ ᠂ ᠲᠡ ᠭᠰ ᠢ ᠦᠨᠴᠦᠭᠲᠦ ABC D ᠳ᠋ᠥ AB =3 , BC= 5 ᠪᠣᠯᠤᠨ ᠠ ᠂ E ᠪ ᠣᠯ A D ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠨᠢᠭᠡᠨ ᠬᠦᠳᠡᠯᠬᠦ ᠴᠡᠭ ᠃ (1) ᠵᠢᠷᠤᠭ ① ᠮᠡᠲᠦ ᠂ BD ᠶᠢ ᠬᠤᠯᠪᠤᠨ ᠠ ᠂ O ᠪᠣᠯ ᠲᠠᠰᠢᠭᠤᠪ ᠴ ᠢ BD ᠢᠢᠨ ᠳᠣᠮᠳᠠ ᠴᠡᠭ ᠂ OE ᠢ ᠢ ᠬᠤᠯᠪᠤᠨ ᠠ ᠃ OE = DE ᠦᠶ ᠡᠰ AE ᠦᠨ ᠤᠷᠲᠤ ᠢ ᠢ ᠣ ᠯ ᠃ (2) ᠵᠢᠷᠤᠭ ② ᠮᠡᠲᠦ ᠂ BE , EC ᠶᠢ ᠬᠤᠯ ᠪᠤᠵᠤ ᠂ ᠴᠡ ᠭ E ᠢ ᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ EF ⊥ EC ᠪᠠᠷ ᠪᠠᠶᠢᠭ ᠤᠯᠪᠠ ᠯ AB ᠲᠠ ᠢ ᠴᠡ ᠭ F ᠳ᠋ᠥ ᠤᠭᠲ ᠤᠯᠤᠯ ᠴᠠᠨ ᠠ ᠂ CF ᠢ ᠢ ᠬᠤᠯ ᠪᠤᠪᠠᠯ BE ᠲᠠ ᠢ ᠴᠡ ᠭ G ᠳ᠋ᠥ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ᠃ BF ᠨ ᠢ ∠AB C ᠢ ᠢ ᠲᠠ ᠯᠠᠯᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠬᠤ ᠦᠶ ᠡᠰ ᠂ BG ᠦᠨ ᠤᠷᠲᠤ ᠢ ᠢ ᠣ ᠯ ᠃ (3) ᠵᠢᠷ ᠤᠭ ③ ᠮᠡᠲᠦ ᠂ EC ᠶᠢ ᠬᠤ ᠯᠪᠤᠨ ᠠ᠂ ᠴᠡᠭ H ᠨ ᠢ CD ᠳᠡ ᠭᠡᠷ ᠡ ᠤᠷᠤᠰ ᠢᠨ ᠠ ᠂ ᠲᠡ ᠭᠰ ᠢ ᠦᠨᠴᠦ ᠭᠲᠦ AB CD ᠢ ᠢ ᠰᠢᠯᠤᠭᠤᠨ EH ᠢᠢᠨ ᠳᠠᠭ ᠠᠤ ᠨᠤᠭ ᠤᠯᠤᠭ ᠠᠳ ᠴᠡᠭ D ᠢ ᠢ EC ᠳᠡᠭᠡᠷ ᠡᠬᠢ ᠨᠢᠭᠡᠨ ᠴᠡᠭ D ᠲᠦ ᠲᠤᠰᠬ ᠠᠨ ᠠ ᠂ ᠴᠡ ᠭ D ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ D N ⊥ AD ᠪᠠᠷ ᠪᠠᠶᠢᠭ ᠤᠯᠪᠠ ᠯ ᠡᠭ ᠴᠡ ᠢᠢᠨ ᠰᠠᠭ ᠤᠷ ᠢ ᠨ ᠢ N ᠪᠠᠶᠢᠵᠤ EH ᠲᠠ ᠢ ᠴᠡᠭ M ᠳ᠋ᠥ ᠤᠭᠲᠤ ᠯᠤᠯᠴᠠ ᠬᠤ ᠪ ᠦᠭᠡᠳ A E = 1 ᠪ ᠣᠯᠤᠨ ᠠ ᠃ ① S ∆E M S∆ EM N ᠤᠨ ᠬᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠢ ᠣ ᠯ ᠃ ② BE ᠶᠢ ᠬᠤᠯ ᠪᠤᠨ ᠠ ᠂ ∆ D MH ᠪᠠ ∆CB E ᠲᠦᠰ ᠲᠠ ᠢ ᠪᠣᠯᠤᠨ ᠠ ᠤᠤ ︖ ᠰᠢᠯᠲᠠᠭ ᠠᠨ ᠢ ᠨ ᠢ ᠲᠣᠳᠤᠷ ᠬᠠᠶᠢᠯ ᠠ᠃ O DA B C E G DA B F C E M N D B A C E H D' 26. (12 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ ᠂ ᠬᠠᠪ ᠲᠠᠭᠠ ᠢ ᠢᠢᠨ ᠲᠡᠭ ᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠦ ᠪᠠᠶ ᠢᠷᠢᠰᠢᠯ ᠦ ᠨ ᠰ ᠢᠰᠲ᠋ᠧ ᠮ ᠳ᠋ᠥ ᠂ ᠬᠠᠶᠠᠯ ᠲᠠ ᠢᠢᠨ ᠱᠤᠭᠤ ᠮ y = 12 𝑥 2+ 32 𝑥 − 2 ᠨ ᠢ 𝑥 ᠲᠡᠨᠬ ᠡᠯᠢᠭ ᠲᠠ ᠢ A , B ᠬᠤᠶ ᠠᠷ ᠴᠡ ᠭ ᠲᠦ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠ ᠵᠤ (ᠴᠡᠭ A ᠨ ᠢ ᠴᠡᠭ B ᠦᠨ ᠵᠡᠭᠦᠨ ᠲᠠᠯ ᠠ ᠳ᠋ᠥ ᠤᠷᠤ ᠰᠢᠨ ᠠ ) ᠂ y ᠲᠡ ᠨᠬᠡᠯᠢᠭ ᠲᠠ ᠢ C ᠴᠡᠭ ᠲᠦ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ ᠭᠡ ᠵᠤ ᠦᠭ ᠭᠦᠭᠳᠡᠵᠡ ᠢ᠃ ᠰᠢᠯᠤᠭᠤᠨ 𝑙 ᠨ ᠢ A ,C ᠬᠤᠶ ᠠᠷ ᠴᠡᠭ ᠢ ᠳᠠᠭ ᠠᠷᠢᠨ ᠠ᠂ BC ᠢ ᠢ ᠬᠤᠯ ᠪᠤᠨ ᠠ ᠃ (1) ᠰᠢᠯᠤᠭᠤᠨ 𝑙 ᠢᠢᠨ ᠠᠨᠠᠯ ᠢᠰ ᠢ ᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢ ᠣ ᠯ ᠃ (2) ᠬᠡᠷ ᠪᠡ ᠰᠢᠯᠤᠭᠤᠨ 𝑥 = 𝑚( 𝑚 0) ᠨ ᠢ ᠲᠤᠰ ᠬᠠᠶ ᠠᠯᠲᠠ ᠢ ᠢᠨ ᠱᠤᠭᠤ ᠮ ᠲᠠ ᠢ ᠭᠤᠷᠪ ᠠᠳᠤᠭ ᠠᠷ ᠮᠦᠴᠡ ᠢᠢᠨ ᠴᠡᠭ E ᠳ᠋ᠥ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠵ ᠤ᠂ ᠰᠢᠯᠤᠭᠤ ᠨ 𝑙 ᠲᠠ ᠢ ᠴᠡ ᠭ D ᠳ᠋ᠥ ᠤᠭᠲᠤᠯᠤᠴᠠᠪ ᠠᠯ᠂ OD ᠢ ᠢ ᠬᠤᠯ ᠪᠤᠭᠠᠳ ᠂ OD ⊥ AC ᠦᠶ ᠡᠰ ᠂ ᠬᠡᠷ ᠴᠢᠮ DE ᠦᠨ ᠤᠷᠲᠤ ᠢ ᠢ ᠣ ᠯ᠃ (3) ᠴᠡ ᠭ G (0, -1) ᠢ ᠢ ᠠᠪᠴᠤ ᠂ AG ᠢ ᠢ ᠬᠤᠯᠪᠤᠨ ᠠ ᠂ ᠨᠢᠭᠡᠳᠦᠭᠡᠷ ᠮᠦᠴᠡ ᠳ᠋ᠥ ᠬᠠᠶᠠ ᠯᠲᠠ ᠢ ᠢᠨ ᠱᠤᠭᠤᠮ ᠳᠡ ᠭᠡᠷ ᠡ ∠B AP = ∠B CD − ∠B AG ᠪᠣᠯ ᠭᠠᠬᠤ ᠴᠡ ᠭ P ᠤᠷ ᠤᠰᠢᠨ ᠠ ᠤᠤ ︖ ᠬᠡᠷᠪᠡ ᠤᠷᠤᠰ ᠢᠪᠠᠯ ᠴᠡᠭ P ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠣᠯᠵ ᠤ ᠥᠭ ᠃ ᠬᠡᠷᠪᠡ ᠤᠷᠤᠰ ᠢᠬᠤ ᠦᠭᠡ ᠢ ᠪᠣᠯ ᠰᠢᠯ ᠲᠠᠭᠠᠨ ᠢ ᠨ ᠢ ᠲᠤᠳᠤᠷ ᠬᠠᠶᠢᠯ ᠠ᠃ x y I B C A O