八年级数学综合测试卷

八年级数学综合测试卷
八年级数学综合测试卷

八年级数学综合测试卷

一.选择题:(每小题4分,共48分)

1.在实数,0,﹣,506,π,0.1中,无理数的个数是()

A.2个B.3个C.4个D.5个

2.已知等腰三角形的一个内角为70°,则另两个内角的度数是()

A.55°,55°B.70°,40°

C.55°,55°或70°,40°D.以上都不对

3.下列各式中,运算正确的是()

A.a6÷a3=a2B.(a3)2=a5C.=±11 D.(ab3)2=a2b6

4.下列是因式分解的是()

A.a2﹣a+1=a(a﹣1)+1 B.x2﹣4y 2=(x+4y)(x﹣4y)

C.x2y2﹣1=(xy+1)(xy﹣1) D.x2+y2=(x+y)2

5.如图,矩形纸片ABCD的边AD=9,AB=3,将其折叠,使点D与点B重合,则折叠后DE的长为()

A.4 B.5 C.6 D.7

6.如图,已知∠1=∠2,要得到△ABD≌△ACE,从下列条件中补选一个,则错误的是()

A.AB=AC B.DB=EC C.∠ADB=∠AEC D.∠B=∠C

7.下列图形中,既是中心对称图形,又是轴对称图形的是()

A.菱形B.平行四边形C.等边三角形D.梯形

8.下列说法不正确的是()

A.一组邻边相等的矩形是正方形

B.对角线相等的菱形是正方形

C.对角线互相垂直的矩形是正方形

D.有一个角是直角的平行四边形是正方形

9.已知等腰三角形的周长为20cm,底边长为ycm,腰长为xcm,则y与x之间的函数关系式为()

A.y=20﹣2x(0<x<10)B.y=10﹣x(0<x<10)

C.y=20﹣2x(5<x<10)D.y=10﹣x(5<x<10)

10.如图,有一块直角三角形纸片,两直角边AC=6,BC=8.现将直角边AC沿直线AD折叠,使它落在斜边AB上,且与AE重合,则CD的长为()

A. 4 B. 3 C. 2 D. 1

11.某校对初二年级1600名男生的身高进行了测量,结果身高(单位:m)在1.58~1.65这一小组的频率为0.4,则该组的人数为()

A.640人B.480人C.400人D.40人

12.如图,在△ABC中,∠ABC=90°,分别以BC,AB,AC为边向外作正方形,面积分别记为S1、S2、S3,若S2=4,S3=6,则S1=()

A.2 B.4 C.6 D.10

二.填空题:(每小题4分,共28分)

13.的平方根是.

14.分解因式:x3﹣4x=.

15.在数轴上与表示的点的距离最近的整数点所表示的数是.

16.如图所示,直线l过正方形ABCD的顶点B,点A、C到直线l的距离分别是AE=1,CF=2,则EF长

为.

17.如图,?ABCD的对角线AC、BD交于点O,点E是AD的中点,△BCD的周长为18,则△DEO的周长是.

18.如图,在矩形ABCD中,对角线AC与BD相交于点O,∠AOB=60°,AE平分∠BAD,AE交BC于E,则∠BOE的大小为.

19.在平面直角坐标系中,已知线段AB的两个端点分别是A(﹣3,1),B(1,3).把线段AB平移后得到线段A′B′,A与A′对应,B与B′对应.若点A′的坐标是(﹣1,﹣1),则点B′的坐标为.

三.解答题:

20.(6分)先化简,再求值:(a﹣2b)(a+2b)+ab2÷(﹣ab),其中a=2,b=﹣1.

21.((6分1)解方程:4(2x+1)2﹣16=0 (2)分解因式:x3﹣6x2+9x.

22(12分.如图,直线m的表达式为y=﹣3x+3,且与x轴交于点B,直线n经过点A(4,0),且与直线m交于点C(t,﹣3)

(1)求直线n的表达式.

(2)求△ABC的面积.

(3)在直线n上存在异于点C的另一点P,使△ABP与△ABC的面积相等,请直接写出点P的坐标.

青山埋白骨,绿水吊忠魂。

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