一元二次方程复习课教学设计.docx

ᠨᠢᠭᠡ ᠦᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠲᠠᠢ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠳᠠᠪᠳᠠᠯᠭ᠎ᠠ ᠶᠢᠨ ᠬᠢᠴᠢᠶᠡᠯ ᠺᠣᠨ᠋ᠰᠫᠧᠺᠲ
  ᠬᠢᠴᠢᠶᠡᠯᠯᠡᠭᠴᠢ᠄ ᠰᠠᠷᠠᠭᠤᠯ ᠠᠡᠭᠭᠢ᠄ ᠶᠢ᠍ᠰᠤ ᠶᠢᠨ ᠨᠢᠭᠡ
ᠵᠢᠭᠠᠨ ᠰᠤᠷᠭᠠᠬᠤ ᠬᠠᠷᠠᠯᠳᠠ᠄
ᠨᠢᠭᠡ᠄ ᠮᠡᠳᠡᠯᠭᠡ ᠪᠡ ᠮᠡᠷᠭᠡᠰᠢᠯ
1 ᠨᠢᠭᠡ ᠦᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠲᠠᠢ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠪᠤᠳᠤᠬᠤ ᠲᠦᠷᠪᠡᠨ ᠵᠤᠢᠯ ᠤᠨ ᠠᠷᠭ᠎ᠠ ᠶᠢ ᠡᠵᠡᠮᠰᠢᠨ᠎ᠡ᠃
2 ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠠᠳᠠᠯᠢ ᠪᠤᠰᠤ ᠣᠨᠴᠠᠯᠢᠭ ᠢ ᠦᠨᠳᠤᠰᠦᠯᠡᠨ᠂ ᠵᠣᠬᠢᠰᠲᠠᠢ ᠠᠷᠭ᠎ᠠ ᠶᠢ ᠰᠤᠡᠭᠭᠤᠨ ᠪᠤᠳᠤᠵᠦ ᠴᠢᠳᠠᠬᠤ᠃
ᠬᠤᠶᠠᠷ᠄ ᠶᠠᠪᠤᠴᠠ ᠪᠡ ᠠᠷᠭ᠎ᠠ
1 ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠪᠤᠳᠤᠬᠤ ᠲᠦᠷᠪᠡᠨ ᠵᠤᠢᠯ ᠤᠨ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠡᠵᠡᠮᠰᠢᠭᠰᠡᠨ ᠰᠠᠭᠤᠷᠢᠨ ᠲᠡᠭᠡᠷ᠎ᠠ᠂ ᠰᠠᠳᠤᠪ ᠪᠤᠳᠤᠬᠤ ᠠᠯᠬᠤᠮ ᠳᠠᠷᠠᠭ᠎ᠠ ᠲᠥᠬᠦᠮ ᠠᠪᠰᠠᠷᠬᠠᠨ ᠣᠨᠤᠪᠴᠢᠲᠠᠢ ᠪᠠᠢᠬᠤ᠃
2 ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠪᠤᠳᠤᠬᠤ ᠶᠠᠪᠤᠴᠠ ᠳᠤ ᠠᠷᠭ᠎ᠠ ᠪᠠᠷᠢᠯ ᠤᠨ ᠵᠢᠯᠤᠭᠤᠳᠤᠯᠭ᠎ᠠ ᠵᠢ ᠴᠢᠬᠤᠯᠴᠢᠯᠠᠵᠦ᠂ ᠣᠨᠴᠠᠭᠠᠢ ᠡᠴᠡ ᠡᠡᠭ ᠤᠨ᠂ ᠦᠰᠦᠭ ᠢᠶᠡᠷ ᠲᠣᠭ᠎ᠠ ᠵᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠬᠦ᠂ ᠪᠦᠬᠦᠯᠢ ᠴᠣᠭᠴᠠ ᠪᠡᠷ ᠣᠷᠤᠯᠠᠭᠤᠯᠬᠤ ᠵᠡᠷᠭᠡ ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ ᠤ ᠰᠡᠳᠭᠢᠬᠦᠢ ᠵᠢ ᠪᠤᠢ ᠪᠣᠯᠭᠠᠨ᠎ᠠ᠃
ᠭᠤᠷᠪᠠ᠄ ᠣᠪᠤᠷ ᠰᠡᠳᠭᠢᠯᠭᠡ ᠪᠡ ᠦᠷᠳᠡᠭ ᠤᠨ ᠦᠵᠡᠯᠳᠡ
ᠡᠯ᠎ᠡ ᠵᠤᠢᠯ ᠤᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠤᠳᠤᠬᠤ ᠠᠷᠭ᠎ᠠ ᠪᠡᠷ ᠳᠠᠮᠵᠢᠭᠤᠯᠤᠨ᠂ ᠰᠤᠷᠤᠭᠴᠢᠳ ᠤᠨ ᠬᠤᠷᠢᠶᠠᠡᠭᠭᠤᠢᠯᠠᠬᠤ᠂ ᠳ᠋ᠦᠡᠭᠨᠡᠬᠦ ᠴᠢᠳᠠᠪᠤᠷᠢ ᠵᠢ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠭᠤᠯᠤᠨ᠎ᠠ᠃
ᠭᠣᠣᠯᠳᠠᠯᠭ᠎ᠠ ᠪᠡ ᠬᠦᠴᠢᠷᠳᠡᠯᠭᠡ
1 ᠭᠣᠣᠯᠳᠠᠯᠭ᠎ᠠ᠄ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠪᠤᠳᠤᠬᠤ ᠲᠦᠷᠪᠡᠨ ᠵᠤᠢᠯ ᠤᠨ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠡᠵᠡᠮᠰᠢᠭᠰᠡᠨ ᠰᠠᠭᠤᠷᠢᠨ ᠲᠡᠭᠡᠷ᠎ᠠ᠂ ᠰᠠᠳᠤᠪ ᠪᠤᠳᠤᠬᠤ ᠠᠯᠬᠤᠮ ᠳᠠᠷᠠᠭ᠎ᠠ ᠲᠥᠬᠦᠮ ᠠᠪᠰᠠᠷᠬᠠᠨ ᠣᠨᠤᠪᠴᠢᠲᠠᠢ ᠪᠠᠢᠬᠤ᠃
3 ᠬᠦᠴᠢᠷᠳᠡᠯᠭᠡ᠄ ᠡᠯ᠎ᠡ ᠵᠤᠢᠯ ᠤᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠤᠳᠤᠬᠤ ᠠᠷᠭ᠎ᠠ ᠪᠡᠷ ᠳᠠᠮᠵᠢᠭᠤᠯᠤᠨ᠂ ᠰᠤᠷᠤᠭᠴᠢᠳ ᠤᠨ ᠬᠤᠷᠢᠶᠠᠡᠭᠭᠤᠢᠯᠠᠬᠤ᠂ ᠳ᠋ᠦᠡᠭᠨᠡᠬᠦ ᠴᠢᠳᠠᠪᠤᠷᠢ ᠵᠢ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠭᠤᠯᠬᠤ᠃
ᠭᠤᠷᠪᠠ᠄ ᠵᠢᠭᠠᠨ ᠰᠤᠷᠭᠠᠬᠤ ᠶᠠᠪᠤᠴᠠ
1 ᠰᠤᠷᠤᠭᠰᠠᠨ ᠢᠶᠡᠨ ᠡᠷᠭᠢᠴᠡᠭᠦᠯᠬᠦ᠄
ᠠᠰᠠᠭᠤᠯᠳᠠ︵1︶ ᠪᠢᠳᠡ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠪᠤᠳᠤᠬᠤ ᠨᠡᠢᠲᠡ ᠬᠡᠳᠤᠨ ᠵᠦᠢᠯ ᠤᠨ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠰᠤᠷᠤᠭᠰᠡᠨ ᠪᠤᠢ︖︵ ᠰᠤᠷᠤᠭᠴᠢᠳ ᠬᠠᠷᠢᠭᠤᠯᠤᠨ᠎ᠠ︶
ᠠᠰᠠᠭᠤᠯᠳᠠ︵2︶ ᠪᠤᠢ ᠪᠦᠬᠦᠢ ᠨᠢᠭᠡ ᠦᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠲᠠᠢ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ  ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠳᠤ ᠳᠣᠭᠢᠷᠠᠬᠤ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠠᠷᠭ᠎ᠠ ᠨᠢ ᠶᠠᠭᠤ ᠪᠤᠢ︖
ax2+bx+c=0 x=-b±b2-4ac2a
2 ᠬᠢᠴᠢᠶᠡᠯ ᠤᠨ ᠴᠠᠭ ᠤᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ
ᠵᠣᠬᠢᠰᠲᠠᠢ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠰᠤᠡᠭᠭᠤᠨ ᠲᠤᠤᠷᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠳ ᠢ ᠪᠤᠳᠤ
︵1︶196x2-1=0 ︵2︶4x2+12x+9=81
︵3︶x2-7x-1=0 ︵4︶2x2+3x=3
︵5︶x2-2x+1=25 ︵6︶x2x-5=4x-10
ᠲᠤᠰ ᠬᠢᠴᠢᠶᠡᠯ ᠨᠢ ᠳᠠᠪᠳᠠᠯᠭ᠎ᠠ ᠶᠢᠨ ᠬᠢᠴᠢᠶᠡᠯ ᠤᠴᠢᠷ ᠡᠴᠡ ᠰᠤᠷᠤᠭᠴᠢᠳ ᠥᠪᠡᠷ ᠢᠶᠡᠨ ᠬᠢᠬᠦ ᠪᠡᠷ ᠭᠣᠣᠯᠳᠠᠨ᠎ᠠ᠃
ᠰᠤᠷᠤᠭᠴᠢᠳ ᠲᠤ ᠴᠠᠭ ᠥᠭᠴᠦ ᠥᠪᠡᠷᠲᠡᠭᠡᠨ ᠬᠢᠭᠰᠡᠨ ᠤ ᠳᠠᠷᠠᠭ᠎ᠠ ᠰᠠᠮᠪᠠᠷ᠎ᠠ ᠲᠡᠭᠡᠷ᠎ᠠ ᠭᠠᠷᠴᠤ ᠬᠢᠨ᠎ᠡ᠃ ᠢᠡᠭᠬᠢᠭᠡᠳ ᠰᠡᠳᠤᠪ ᠤᠨ ᠲᠤᠮᠳᠠ ᠤᠷᠤᠰᠢᠵᠦ ᠪᠠᠢᠭ᠎ᠠ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠢ ᠬᠠᠮᠲᠤ ᠪᠡᠷ ᠶᠠᠷᠢᠯᠴᠠᠨ᠎ᠠ᠃
3 ᠬᠤᠷᠢᠶᠠᠡᠭᠭᠤᠢᠯᠠᠬᠤ
︵1︶ ᠥᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢᠭᠡ ᠦᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠲᠠᠢ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠨᠢ ᠵᠣᠬᠢᠰᠲᠠᠢ ᠬᠤᠪᠢᠷᠠᠭᠠᠯᠳᠠ ᠪᠡᠷ ᠲᠠᠮᠵᠢᠨx2=n (x+m)2=n(n>0) ᠦᠶᠡᠰ᠂ ᠰᠢᠭᠤᠳ ᠺᠦᠸᠠᠳ᠋ᠯᠠᠬᠤ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠬᠡᠷᠡᠭᠯᠡᠵᠦ ᠪᠣᠯᠤᠨ᠎ᠠ
︵2︶ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯax2+bx+c=0(a≠0) ᠳᠤ ᠵᠡᠭᠦᠨ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠦᠷᠡᠵᠢᠭᠳᠡᠬᠦᠨ ᠪᠣᠯᠭᠠᠨ ᠵᠠᠳᠠᠯᠵᠦ ᠪᠣᠯᠬᠤ ᠦᠶᠡᠰ᠂ ᠦᠷᠡᠵᠢᠭᠳᠡᠬᠦᠨ ᠪᠣᠯᠭᠠᠨ ᠵᠠᠳᠠᠯᠬᠤ ᠠᠷᠭ᠎ᠠ ᠨᠢ ᠨᠡᠯᠢᠶᠡᠳ ᠳᠥᠭᠦᠮ ᠪᠠᠢᠳᠠᠭ᠃
︵3︶ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯax2+bx+c=0(a≠0) ᠳᠤ a, b, c ᠨᠢ ᠭᠡᠰᠢᠭᠦᠨ ᠲᠤᠳᠠᠬᠤ ᠦᠭᠡᠢ ᠪᠥᠭᠡᠳ ᠦᠷᠡᠵᠢᠭᠳᠡᠬᠦᠨ ᠪᠣᠯᠭᠠᠨ ᠵᠠᠳᠠᠯᠬᠤ ᠳᠤ ᠲᠦᠪᠡᠭᠲᠡᠢ ᠪᠠᠢᠪᠠᠯ ᠡᠡᠭ ᠤᠨ ᠴᠠᠭ ᠲᠤ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠬᠡᠷᠡᠭᠯᠡᠳᠡᠭ᠃
︵4︶ ᠺᠦᠸᠠᠳ᠋ᠯᠠᠬᠤ ᠠᠷᠭ᠎ᠠ ᠨᠢ ᠪᠠᠰᠠ ᠨᠢᠭᠡ ᠵᠤᠢᠯ ᠤᠨ ᠴᠢᠬᠤᠯᠠ ᠰᠡᠳᠤᠪ ᠵᠠᠳᠠᠯᠬᠤ ᠠᠷᠭ᠎ᠠ᠂ ᠭᠡᠪᠡᠴᠦ ᠠᠯᠬᠤᠮ ᠳᠠᠷᠠᠭ᠎ᠠ ᠨᠢ ᠬᠠᠷᠢᠴᠠᠡᠭᠭᠤᠢ ᠪᠤᠳᠤᠯᠢᠶᠠᠨᠲᠠᠢ ᠪᠠᠢᠳᠠᠭ ᠡᠴᠡ ᠡᠡᠭ ᠤᠨ ᠪᠠᠢᠳᠠᠯ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ᠎ᠠ ᠦᠭᠡᠢ ᠪᠣᠯ ᠲᠤᠰ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠳᠡᠮᠡᠢ ᠬᠡᠷᠡᠭᠯᠡᠳᠡᠭ ᠦᠭᠡᠢ᠂ ᠭᠡᠳᠡᠯ᠎ᠡ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠭᠡᠰᠢᠭᠦᠨ ᠤ ᠢᠯᠡᠳᠭᠡᠮᠵᠢ ᠨᠢ ᠨᠡᠯᠢᠶᠡᠳ ᠪᠠᠭ᠎ᠠ᠂ ᠰᠤᠯᠠ ᠭᠡᠰᠢᠭᠦᠨ ᠨᠢ ᠨᠡᠯᠢᠶᠡᠳ ᠲᠣᠮᠤ ᠲᠣᠭ᠎ᠠ ᠦᠶᠡᠰ ᠲᠤᠰ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠬᠡᠷᠡᠭᠯᠡᠵᠦ ᠪᠣᠯᠤᠨ᠎ᠠ᠃
4 ᠲᠠᠰᠬᠠᠯ ᠵᠣᠬᠢᠰᠲᠠᠢ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠰᠤᠡᠭᠭᠤᠨ ᠲᠤᠤᠷᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠳ ᠢ ᠪᠤᠳᠤ
︵1︶x2+5x+7=3x+11
(2) 1-8x+16x2=2-8x
5 ᠰᠠᠮᠪᠠᠷᠠᠴᠢᠯᠠᠯ
6 ᠬᠢᠴᠢᠶᠡᠯ ᠤᠨ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠡᠷᠭᠢᠴᠡᠭᠦᠯᠦᠯ