八年级数学秋季学期期中考试
八年级数学
| 题 号 | 一 | 二 | 三 | 总 分 | ||||||
| 1～10 | 11～18 | 19 | 20 | 21 | 22 | 23 | 24 | 附加题 | ||
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说明：1．可以使用计算器，但未注明精确度的计算问题不得采取近似计算，建议根据题型特点把握好使用计算器的时机．
2．本试卷满分120分，在120分钟内完成．相信你一定会有出色的表现！
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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 ．
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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76分．解答应写出文字说明或演算步骤．
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19．（本小题满分16分）
计算：（1）2＋－
（精确到百分位）；
（2）
＋π（保留2个有效数字）．
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20．（本小题满分12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？
21．（本小题满分12分）
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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（要求：着色出一个图形，并画出一条对称轴即可）．
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22．（本小题满分12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．
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23．（本小题满分12分）
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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．
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24．（本小题满分12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，并说明你的方案的正确性．
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附加题．（本小题满分10分）
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请你把上面的解答再认真地检查一遍，别留下什么遗憾，并估算一下成绩是否达到了80分，如果你的全卷得分低于80分，则本题的得分将计入全卷总分，但计入后全卷总分最多不超过80分；如果你全卷得分已经达到或超过80分，则本题的得分不计入全卷总分．
求下列各式中x的值：
（1）x2＝
；
（2）x3＝－0.125．
八年级数学参考答案及评分标准
一、填空题：（每小题2分，共20分）
1．1，2；2．＜；3．398.2；4．等腰；5．60°；6．12； 7．81007；8．6；
9．17；10．逆，90°或填顺，270°．
二、选择题：（每小题3分，共24分）
| 题号 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 答案 | D | D | C | A | B | C | A | B |
三、解答题：
19．解：（1）2＋－＝2＋1.414－1.732·············································································· 4分
≈1.68；······································································································ 8分
（2）＋π＝2.24＋3.14·········································································································· 4分
≈5.4．······················································································································ 8分
20．解：连结AC，在
△ABC中，由勾股定理得
AC2＝AB2＋BC2····························································································································· 4分
＝302＋402································································································································ 6分
＝2500．···································································································································· 8分
AC＝
＝50．··················································································································· 10分
答：小明至少要走50米．··································································································· 12分
21．解：图形有多种，如：
（每个图各4分）
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22．解：如右图．······································ 12分
23．解：成立.
在△ABC中，因为AB＝AC，所以∠ACB＝∠ABC．··············································· 4分
理由是：等边对等角．············································································································ 6分
因为∠ABD＝∠ACE，所以∠OBC＝∠OCB．····························································· 8分
在△OBC中，因为∠OBC＝∠OCB，所以OB＝OC．··········································· 10分
理由是：等角对等边．·········································································································· 12分
24．解：作等腰直角三角形底边上的中线CD，交AB于点D，将等腰△ABC分成两个全等的等腰直角三角形，如图翻折其中一个三角形使得DC与CD重叠就可得到一个含有45°角的．· 4分
因为CD是等腰△ABC底边上的中线，
所以AD＝BD，即AD＝CB′．
又因为△ABC是等腰，
所以∠A＝45°，AC＝CB，即AC＝DB′．
所以四边形ACB′D，是一个含有45°角的平行四边形．
理由是：有两组对边相等的四边形是平行四边形．·············································· 12分
附加题．（1）因为
＝
，········································································································· 3分
所以x＝±
；···················································································································· 5分
（2）因为（－0.5）3＝－0.125，·························································································· 3分
所以x＝－0.5．··················································································································· 5分