江宁初级中学2007—2008学年八年级数学

第一学期期中考试试卷

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一、填空题：本大题共10小题；每小题2分，共20分．请将答案填写在题中的横线上．

1．化简：＝       ，＝           ．

2．比较大小：           （用“＞”或“＜”填空）．

3．对398.15取近似值，精确到十分位是           ．

4．如图的格点三角形ABC是       三角形．

5．在△ABC中，∠A＝60°，∠B＝         时，△ABC是等边三角形．

6．在△ABC中，∠C＝90°，若AB＝13 cm，BC＝5 cm，则AC＝          cm．

7．是从镜子中看到的一串数字，这串数字应为           ．

8．如图，在△ABC中，∠C＝90°，AD平分∠BAC，若

CD＝6 cm，则点D到AB的距离是           cm．

9．如图，等腰梯形ABCD中，AD∥BC，AD＝3，AB＝6，BC＝8.

且DE∥AB，则△DEC的周长是           ．

10．如图，△ABC是等腰直角三角形，D是斜边BC上的中点，

△ABD绕点A旋转到△ACE的位置，恰好与△ACD组成正方

形ADCE，则△ABD按     时针方向旋转了          ．

二、选择题：本大题共8小题；每小题3分，共24分．在每小题给出的四个选项中，只有一项是正确的，请将正确答案前的字母填入题后的括号内．每小题选对得3分，选错，不选或多选均得零分．

11．近似数2.023的有效数字是···································································································· （    ）．

     （A）1个                 （B）2个                 （C）3个                 （D）4个

12．····························································································································································· 的平方根是       （    ）．

     （A）±12                （B）12                    （C）－12                （D）±

13．····························································································································································· 下列各数组中，不是勾股数的是····························································································································································· （    ）．

     （A）5，12，13                                        （B）7，24，25      

     （C）8，12，15                                        （D）3k，4k，5k（k为正整数）

14．····························································································································································· 用刻度尺分别画下列图形的对称轴可以不用刻度尺上的刻度画的是···························································································· （    ）．

     （A）①④                （B）②③                （C）③④                （D）①②

15．····························································································································································· 在4，3.5，π，，五个数中，无理数有·············································································································································· （    ）．

     （A）1个                 （B）2个                 （C）3个                 （D）4个

16．某数的平方根等于它的立方根，则这个数··································································· （    ）．

     （A）1                     （B）－1                  （C）0                     （D）以上都不对

17．····························································································································································· 下列条件中，能说明四边形ABCD是平行四边形的是·························································································································· （    ）．

     （A）∠A＝30°，∠B＝150°，∠C＝30°，∠D＝150°

     （B）∠A＝60°，∠B＝60°，∠C＝120°，∠D＝120°

     （C）∠A＝60°，∠B＝90°，∠C＝60°，∠D＝150°

     （D）∠A＝60°，∠B＝70°，∠C＝110°，∠D＝120°

18．····························································································································································· 下列说法中，正确的是     （    ）．

     （A）在成中心时称的图形中，连结对称点的线段不一定都经过对称中心

     （B）在成中心对称的图形中，连结对称点的线段都被对称中心平分

     （C）若两个图形的对应点连成的线段都经过某一点．那么这两个图形一定关于这一点成中心对称

     （D）以上说法都正确

三、解答题：本大题共6小题，共56分．解答应写出文字说明或演算步骤．

19．（本小题满分9分）求下列各式中x的值：

（1）x²＝；                        （2）x³＝－0.125．

（3）计算：

20．（本小题满分6分）如图，一个长方形的运动场，有一个球落到了点C，小明要从点A走到点C捡球，至少要走多少米？H₂

21．（本小题满分6分）在5×7的方格纸上，任意选出5个小方块，涂上颜色，使着色图形为轴对称图形，并画出其对称轴

22．（本小题满分6分）

△ABC的边AB绕点B旋转到图中BA′的位置，点A′是A的对应点，画出△ABC绕点B旋转后的图形．

23．探究与操作:1．（8分）如图，在△ABC中，AB＝AC，∠ABD＝∠ACE，BD，CE相交于点O，猜想：BO＝CO成立吗？并说明理由．

2、（8分）如图，□ABCD的周长是36，且AB∶BC＝5∶4，对角线AC、BD相交于点O，且BD⊥AD，求OB的长。

3、如图，在平行四边形ABCD中，点E、F在对角线AC上，且AE=CF

   求证：四边形BEDF是平行四边形（7分）

24．（本小题满分6分）

现有一块等腰直角三角形木板，你能通过剪切，使它成为一个含有45°角的平行四边形吗？请你设计一个最简的方案，画出图形,并说明你的方案的正确性．