bài kiểm tra
Đề bài:
Câu1: ( 2 điểm )
Thực hiện phép tính nhân:
a) P= xy(x3+2x2y+2xy2+y3)-2x2(x2y+
2
1
y3)-xy4
b) Q=
2
1
x3(2x-3y+5y)+2xy(x+y+2) c) R=(2x+2)(4x+3+5)
d) F=(
2
1
x-xy)(2x4+5xy2+10xy+10) - (x+2)(y-2)
Câu 2 : ( 2 điểm )
a) P= ((5x+y)(5x-y) - (5x+y)(5x+y)+10
b) Q= (2x-2y)4x2+8xy+4y2) + (2x+y)(4x2-8xy+4y2)
c) R=
2
1
x3(2x4+2y2) - x5(x2+y2-x-2)
d) F= 2x(x+xy+y) - x(2x+xy+
2
1 y+8)
Câu 3 : (2 điểm)
Tìm x biết :
a) (x-3)(x+1)-(x+2)(2x-5)+x2=0
b) (3x+2)(5x+3)-(2x+7)(3x+2)-(3x-4)(3x+8)=0
Câu 4 : (2 điểm)
a) (3x+7y)(3x-7y)=9x2-79y2
b) Chứng minh hàm số sau không phụ thuộc vào biến
P= (2x2y-4xy)(4x4y2+8x3y2+8x3y2+16x2y2)-8x8y3+64x3y3+5
Câu 5 : (2 điểm)
a) (2ax+x)(
2
1 a+3)
A: ax2+6ax+3x C: a2x+
12
13
ax + 6x
B: ax+
12
13
ax+3x D: Cả A,B,C đều sai b) 2(25x+3) – 2x(x+1
A: 48x-2x2+6 C: x-x2 4
B: 48x+6 D: Cả A,B,C đều sai
Trang 2Bµi gi¶i vµ thang ®iÓm
Thùc hiÖn phÐp tÝnh nh©n:
a) P= xyx3+xy2x2y+xy2xy2+xyy3- 2x2x2y-2x2
2
1
y3-xy4 (0.05 ®iÓm) = x4y+2x3y2+2x2y3+xy4- 2x4y-x2y3-xy4 (0.2 ®iÓm) = -x4y+2x3y2+2x2y3 (0.25 ®iÓm) b) Q=
2
1
x32x+
2
1
x3(-3y)+5y
2
1
x3+2xyx+2xyy+2xy2 (0.05 ®iÓm)
=x4
-2
3
x3y+
2
5
x3y+2x2y+2xy2+4xy =x4+x3y+2x2y+2xy2+4xy (0.25 ®iÓm) c)R= 2x4x+2x3+2x5+2.4x+2.3+2.5 (0.25 ®iÓm) =8x2+6x+10x+8x+6+10 (0.45 ®iÓm) =8x2+24x+16 (0,30®iÓm)
d)F=
2
1
x2x4+
2
1 x5xy2+
2
1 x10xy+
2
1 x10-xy-x(-2)-2y-2(-2) (0.02 ®iÓm)
=x5+
2
5
x2y2+5xy+5x-xy+2x-2y+4 (0.2 ®iÓm)
=x5+
2
5
x2y+4xy+7x-2y+4
Rót gän biÓu thøc
a)P=5x5x+5x(-y)+y5x+y(-y)-5x5x-5xy-y5x-yy+10 (0.05 ®iÓm) = 25x2-5xy+5xy-y2-25x2-5xy-5xy-y2+10 (0.25 ®iÓm) =10-2y2 (0.2 ®iÓm) b)Q=2x4x2+2x8xy+2x4y2-2y4x2-2y8xy-2y4y2+2x4x2+2x(-8xy)+2x4y2+y4x2+y(-8xy)+y4y2 (0.2 ®iÓm)
=8x3+16x2y+8xy2-8x2y-16xy2-8y3+8x3-16x2y+8xy2+4x2y-8xy2+4y3 (0.2 ®iÓm) =16x3 -4x2y -8x y2-4y3 (0.05®iÓm)
c) R=
2
1
x32x4+
2
1
x32y2-x5x2-x5y2-x5(-x)-x5(-2) (0.05 ®iÓm) =x7+x3y2-x7-x5y2+x6+2x5 (0.25 ®iÓm) = x3y2-x5y+x6+2x5 (0.2 ®iÓm)
Trang 3d)F=2x.x+2x.xy+2xy-x.2x-x.xy-x
2
1 y-x8 (0.2 ®iÓm)
=2x2+2x2y+2xy-2x2-x2
y-2
1 xy-8x (0.25 ®iÓm)
=x2y+
2
3
xy-8x (0.2 ®iÓm)
C©u 3 : (2 ®iÓm)
T×m x biÕt
a) x.x+x.1-3x-3.1-x.2x-x(-5)-2.2x+2(-5)+x2=0 (0.25 ®iÓm)
⇒x2+x-3x-3-2x2+5x-4x-10+x2=0 (0.25 ®iÓm)
⇒x=7 (0.25 ®iÓm) b)3x.5x+3x.3+2.5x+2.3-2x.3x-2x.2-7.3x-7.2-3x.3x-3x.8+4.3x+4.8 =0 (0.25 ®iÓm)
⇒15x2+9x+10x+6-6x2-4x-21x-14-9x2-24x+12x+32=0 (0.25 ®iÓm)
3
4
(0.25 ®iÓm)
Chøng minh r»ng
a)3x.3x+3x(-7y)+7y3x+7y(-7y)=9x2-49y2 (0.5 ®iÓm)
⇒9x2-21xy+21xy-49y2=9x2-49y2 (0.75 ®iÓm)
⇒9x2-49y2=9x2-49y2 (0.5 ®iÓm)
⇒VÕ ph¶i b»ng vÕ tr¸i suy ra ®iÒu ph¶i chøng minh (0.25 ®iÓm) b)Chøng minh hµm sè sau kh«ng phô thuéc vµo biÕn
P=2x2y.4x4y2+2x2y.x3y2+2x2y.16x2y2-4xy.4x4y2-4xy.8x3y2-4xy.16x2y2-8x6y3+64x3y3+15 (0.7 ®iÓm) =8x6y3+16x5y3+32x4y3-16x5y3-32x4y3-64x3y3-8x6y3+64x3y3+15 (0.25 ®iÓm) VËy P=15 kh«ng phô thuéc vµo biÕn (0.05 ®iÓm)
C©u 5 : (2 ®iÓm )
a) B (1 ®iÓm)
b) A (1 ®iÓm)