山东省烟台市2021-2022学年八年级下学期期中数学试题(word版含答案)

2021—2022学年度第二学期期中学业水平检测

初三数学

温馨提示：

1.本试卷共6页，共120分；考试时间120分钟.

2.答题前务必用0.5毫米黑色签字笔将自己的姓名、准考证号填写在答题卡规定的位置上.

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5.写在试卷上或答题卡指定区域外的答案无效.

一、卷面书写（满分3分）

二、选择题（本题共12个小题，每小题3分，满分36分）每小题都给出标号为A，B，C，D四个备选答案，其中有且只有一个是正确的.

1.下列关于x的方程是一元二次方程的是（    ）

A. B. C. D.

2.王师傅应客户要求加工4个长为4、宽为3的矩形零件.在交付客户之前，王师傅需要对4个零件进行检测.根据零件的检测结果，图中有可能不合格的零件是（    ）

A. B. C. D.

3.下列二次根式中，不能与合并的是（    ）

A. B. C. D.

4.下列等式成立的是（    ）

A. B. C. D.

5.已知关于x的方程有两个不相等的实数根，则a的取值范围是（    ）

A. B.且 C. D.且

6.当时，化简的结果是（    ）

A. B. C. D.

7.如图，四边形为菱形，点A、B、C、D在坐标轴上，点A的坐标为，长为3，则菱形的面积等于（    ）

A.20 B. C. D.

8.如图，在矩形中，点E是上一点，且，，垂足为点F，下列结论中，不一定正确的是（    ）

A. B. C. D.

9.如图，某小区有一块长为30m，宽为24m的矩形空地，计划在这块空地上划出四分之一的区域修建绿地，小明的设计方案如图所示，若设绿地的宽度为m，可列方程为（    ）

A. B.

C. D.

10.如图，四边形，都是正方形，点E，G分别在边，上，连接，过点E作交于点H.若，，则的长为（    ）

A.1 B.2 C.3 D.

11.若，则等于（    ）

A.-1 B.-5 C.5 D.1

12.下列说法：①关于x的一元二次方程（）无实数根；②无论m为何值，关于x的一元二次方程都有两个不相等的实数根；③若关于x的一元二次方程有两个不相等的实数根，则m的取值范围是且.其中说法正确的是（    ）

A.①②③ B.①② C.①③ D.②

三、填空题（本大题共6个小题，每小题3分，满分18分）

13.计算的结果是__________.

14.若关于x的一元二次方程的常数项为0，则m的值为__________.

15.若代数式有意义，则x的取值范围为__________.

16.m是方程的根，则代数式的值是__________.

17.如图，在矩形中，E为的中点，的角平分线交于点F.若，，则的长度为__________.

18.如图，在正方形中，和为直角三角形，，，，则的长是__________.

四、解答题（本大题共7个小题，满分63分）

19.（本题满分8分）

解方程：

（1）

（2）

20.（本题满分8分）

计算：

（1）

（2）

21.（本题满分9分）

已知关于x的方程是一元二次方程.

（1）求m的值；

（2）解这个一元二次方程.

22.（本题满分9分）

（1）在中，，，.求的周长和面积；

（2）已知，，求的值.

23.（本题满分9分）

如图，在菱形中，于点E，于点F.

（1）求证：；

（2）分别延长和相交于点G，若，，求的值.

24.（本题满分10分）

如图，已知正方形中，点E是边延长线上一点，连接，过点B作，垂足为点F，与交于点G.

（1）求证：；

（2）若，，求的长.

25.（本题满分10分）

如图，点E是平行四边形对角线上一点，点F在延长线上，且，与交于点G，连接，，.

（1）求证：；

（2）若，点G恰好是的中点，求证：四边形是矩形.

初三数学参考答案

一、卷面书写（满分3分）

二、选择题（每题3分，共36分）

BCDAD  CCDDD  AB

三、填空题（每题3分，共18分）

13.  14.-3  15.且  16.-2018  17.6  18.72

四、解答题（本题共7个题，满分63分）

19.（本题满分8分）

（1）；  （2），

20.（本题满分8分）

（1）；  （2）

21.（本题满分9分）

（1）-1；···········································································4分

（2）方程为，即，···································································5分

，·················································································9分

22.（本题满分9分）

（1）周长为，面积为；································································5分

（2）9·············································································9分

23.（本题满分9分）

（1）证明：∵四边形是菱形，∴，·······················································1分

∵于点E，于点F，∴，································································2分

∵，，，∴，········································································3分

∴，···············································································4分

∴；···············································································5分

（2）解：∵四边形是菱形，∴，∴，······················································6分

∵，∴，∴，∴，····································································8分

∴.················································································9分

24.（本题满分10分）

（1）证明：∵四边形是正方形，∴，，····················································1分

∵，∴，∵，∴.······································································3分

∴，···············································································4分

∴；···············································································5分

（2）解：由（1），，∴，·····························································6分

∵，，∴，，········································································8分

在中，············································································10分

25.（本题满分10分）

（1）证明：连接，交于点O，···························································1分

∵四边形是平行四边形，∴，····························································2分

∵，∴是的中位线，···································································3分

∴，即；···········································································4分

（2）证明：由（1）得，

∴，，

∵G是的中点，∴，···································································5分

∴，∴，···········································································6分

∴四边形是平行四边形，·······························································7分

∵四边形是平行四边形，∴，

∵，∴，∵，∴，

∴，···············································································9分

∴平行四边形是矩形.·································································10分