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仁寿县坝达初级中学八年级上期数学期中检测题

满分:120分 时间:120分钟

一、选择题:(每题3分,共36分)

1、下列计算正确的是( )。

A 、a 22a 3=a 5

B 、a+a=a 2

C 、(a 2)3= a 5

D 、a 2(a+1)= a 2+1 2、在7

22,8,-3.1416,π,25,0.6161161……,39中,无理数有( )。

A 、2个

B 、3个

C 、4个

D 、5个

3、若4y 2+my+1是一个完全平方式,则m 的值为( )。

A 、±4

B 、4

C 、±2

D 、2

4、下列各式能用完全平方公式分解因式的是( )。

A 、x 2+4x+4

B 、x 2+x+1

C 、x 2-y 2

D 、x 2+2x -1

5、(a+m )(a+2

1

)的结果中不含关于字母a 的一次项,那么m 为( )。

A 、2

B 、-2

C 、21

D 、-错误!链接无效。

6、如图,已知∠1=∠2,那么添一个条件后,仍无法判定△ADC 和△BDC 全等的是( )。

A 、∠3= ∠4

B 、∠A=∠B

C 、AD=B

D D 、AC=BC

7、下列命题是真命题的是( )。 A 、若b a =,则a=b B 、若a 2

=b 2

,则a=b C 、若x =3,则x=9

D 、若x 2=4,则x=2

8、若x 2+mx -15=(x+3)(x+n ),则m 的值为( )。

A 、-5

B 、5

C 、-2

D 、2 9、判断两直角三角形全等的方法不.正确的有( )。 A 、两直角边对应相等 B 、斜边和一锐角对应相等 C 、斜边和一直角边对应相等

D 、两锐角对应相等

10、若2)4(-x =4-x ,则x 的取值范围是( )。

A 、x >4

B 、x <4

C 、x ≥ 4

D 、x ≤4

11、若a+b=3,则2a 2+4ab+2b 2-6的值是( )。

A 、12

B 、6

C 、3

D 、0 12、如图,在△ABC 中,AD ⊥BC 于D ,B

E ⊥AC 于E ,BE 与AD 并于点

F ,AD=BD=5,

则AF+CD 的长度为( )。

A 、52

B 、6

C 、5

D 、4.5

二、填空题:(每题3分,共24分) 1、(-2ab 2)3= ;(-x 2)32x 4= 。 2、若a+b=3,ab=2,则a 2+b 2= 。 3、分解因式:a 3-4a= 。 4、“直角三角形的两个锐角互余”改成“如果……,那么……”的形式为 。

5、若x -x 1=3,则x 2+21

x = 。

6、若m x =3,m y =2,则m x -2y =。 。

7、如图,∠1=∠2,要使△ACE ≌△ABE ,还需要添加一个条件是 (只填一个条件即可)。

8、已知x 、y 都为有理数,且y=322+-+-x x ,则y x 的算术平方根为 。 三、算术题:(1题8分,2题12分,3题7分) 1、因式分解:(每小题4分,共8分)

1)ab 2-4ab+4a 2)(x 2+4)2-16x 2

姓名: 班级: 考号:

……………………………………密……………………………………封……………………………………线………………………………………

2、计算:(每小题6分,共12分) 1)(x+7)(x -6)-(x -2)(x+1)

2)a (a -2b )+2(a+b )(a -b )-(a -b )2

3、化简求值:(7分)

[(x -y )2+(x -y )(x+y )]÷x ,其中x=-1,y=2

1

四、解答题:(4、5、6题8分,7题9分)

4、如图,点B.F.C.E 在同一直线上,FB=CE ,AB//ED ,AC//FD ,求证:AC=DF 。

5、如图,AD=AE ,BE=CD ,∠1=∠2,∠BAE=60°,∠3=40°,求∠CAE 的度数。

6、若一个三角形的三边长为a 、b 、c ,满足a 2+b 2+c 2-2a -2b -2c+3=0,求三角形的

周长?

7、两个大小不同的等腰直角三角形三角板如图1所示放置,图2是由它抽象出的几何图形,B 、C 、E 三点在同一条直线上,连结DC 。 (1)求证:△ABE ≌△ACD 。

(2)观察DC 、BE 之间有什么特殊的位置关系?你能够说明理由吗?

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