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2024一2025学年度第一学期期末质量监测试卷
八年级数学
本试卷共6页，23小题，满分120分。考试用时120分钟。
注意事项：1.答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的学校、姓名和准考证号填写在答
题卡上。将条形码粘贴在答题卡“条形码粘贴处”
2,作答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂
黑；如需改动，用橡皮擦干净后，再选涂其他答案。
3.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内
相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂
改液。不按以上要求作答的答案无效。
4.考生必须保持答题卡的整洁。考试结束后，将试卷和答题卡一并交回。
一、选择题：本大题共10小题，每小题3分，共30分。在每小题列出的四个选项中，只
有一项是符合题目要求的。
1.中国剪纸是一种用剪刀或刻刀在纸上剪刻花纹，用于装点生活或配合其他民俗活动的
民间艺术.在中国，剪纸具有广泛的群众基础，交融于各族人民的社会生活，是各种
民俗活动的重要组成部分.下列剪纸图片中，是轴对称图形的是()
2.已知三角形两边分别为1cm和3cm,
则第三边可能是（)
A.1cm
B.2cm
C.3cm
D.4cm
B若分式的值为0，则x的值为(》
A.0
B.3
C.2
D.-2
4.如图，△DBC≌△ECB,且BE与CD相交于点A,下列结论错误的是()
B
A.BE=CD
B.AB=AC
C.∠D=∠E
D.BD=AE
八年级数学试卷第1页（共6页）
5.下列运算正确的是()
A.x2·x3=x6
B.(-2x2)=-4x4C.G3)2=x6
D.x5÷x=x
6.2024年3月25日鹊桥二号中继卫星顺利进入环月轨道飞行，其搭载的天线由精细的镀
金钼丝编织而成，这些钼丝的直径仅为0.0000015米，用科学记数法表示该钼丝的直径
是()
A.1.5×105米
B.1.5×106米
C.1.5×10-5米
D.1.5×10-6米
7.如图，∠BAC=30°，P是∠BAC平分线上一点，PM∥AC,PD⊥AC,PD=30,则AM
长度为()
M
P
A.30
B.40
C.50
D.60
8.如图，小明利用4张图①所示的长为α、宽为b的长方形卡片，拼成图②所示的图形，
则根据图②的面积关系能验证的恒等式为()
图①
图②
A.(a+2b)2=a2+4ab+4b2
B.(a+b)"=(a-b)+4ab
C.(2a+b)=4a2+4ab+b2
D.(a-b)"=a2-2ab+62
9.中国首列商用磁浮列车平均速度为akm/h,计划提速20km/h,已知从A地到B地路程
为360km,那么提速后从A地到B地节约的时间为()
3600
3600
7200
7200
A.
-a(a-20)h
B.
h
C.
D.
a(a+20)
a(a+20)
a(a-20)
八年级数学试卷第2页（共6页）2024—2025 学年度第一学期期末质量监测试卷
八年级数学参考答案及评分标准
一、选择题：本大题共 10小题，每小题 3分，共 30分。在每小题列出的四个选项中，只
有一项是符合题目要求的。
题号 1 2 3 4 5 6 7 8 9 10
答案 A C D D C D D B C B
二、填空题：本大题共 5 小题，每小题 3 分，共 15 分。请将下列各题的正确答案填写在
答题卡相应的位置上。
题号 11 12 13 14 15
答案 ( ＋5)( －5) (－1，－3) 24 2 3 7 81°
三、解答题（一）：本大题共 3小题，每小题 7分，共 21分。
16．解：（1）原式= 2 + 2，······················································· 2分
= ；······································································ 3分
（2）原式= 4 2 + 4 + 2 2 2 ··································· 5分
= 4 2 + 4 + 2 2 + 2 ········································6分
= 4 2 + 6 ····························································· 7分
= ( )( + ) 17．解：原式 +( )2 · ( + ) ，··············································· 3分
= +
，···································································4分
= +
，·········································································· 5分
当 = 1， = 2时，
= + 原式 =
1+2 = 1
1 2 3．·························································7分
18．证明：∵AB∥CD，
∴∠B＝∠C，···································································· 2分
∵CE＝BF，
∴CE＋EF＝BF＋EF，即 CF＝BE，········································4分
在△AEB和△DFC中，
八年级数学参考答案及评分标准 第 1 页 (共 7 页)
∠ = ∠
∠ = ∠ ，
=
∴△AEB≌△DFC（AAS），················································· 6分
∴AB＝CD．······································································7分
四、解答题（二）：本大题共 3小题，每小题 9分，共 27分。
19．解：∵ ⊥ ， ⊥ ，
∴∠ = ∠ = 90°，························································2分
∴∠ = 90° ∠ = 90° 68.2° = 21.8° = ∠ ，···············4分
在△ABC和△CDE中，
∠ = ∠
∠ = ∠ ，
=
∴△ABC≌△CDE（AAS），····················································7分
∴AB＝CD，········································································ 8分
∵ = 12 ，
∴ = 12 ，
答：教学楼高度 为 12 ．························································· 9分
20．解：（1）设第一次每双球鞋的进价是 x元，·····································1分
6300 40 = 4200，····························································· 2分
1.2
解得：x＝70，·································································3分
经检验得出 x＝70是原方程的解，且符合题意，·····················4分
答：第一次每双球鞋的进价是 70元．········································5分
（2）设最低应打 y折，
依题意得：4200÷（70×1.2）＝50双，······························· 6分
160×25＋160×0.1y×25－4200≥2200，································ 7分
解得：y≥6，····································································8分
答：最低打 6折．··································································9分
21．（1）解：如图所示， ⊥ 即为所求；
八年级数学参考答案及评分标准 第 2 页 (共 7 页)
·············································· 4分
（2）证明：∵∠ = ∠ + ∠ ，∠ = ∠ + ∠ ，
∴∠ = ∠ ，即 是∠ 的角平分线，·················· 5分
∵∠ = 90°，
∴ ⊥ ，······························································· 7分
又∵ ⊥ ，
∴ = ．·······························································9分
五、解答题（三）：本大题共 2小题，第 22题 13分，第 23题 14分，共 27分。
22．解：（1） = + ；···························································· 2分
（2）第（1）题中的结论 = + 仍然成立，理由如下：········ 3分
如图 2中，延长 CD至 H，使 BE=DH，连接 AH，
∵∠ + ∠ = 180°，∠ + ∠ = 180°，
∴∠ = ∠ ，
在△ABE和△ADH中，
=
∠ = ∠ ，
=
∴△ABE≌△ADH（SAS）．···············································4分
∴ = ，∠ = ∠ ，
∵∠ = 1∠ ，
2
八年级数学参考答案及评分标准 第 3 页 (共 7 页)
∴∠ + ∠ = 1∠ = ∠ ．
2
∴∠ + ∠ = ∠ ，即∠ = ∠ ························ 5分
在△AFH和△AFE中，
=
∠ = ∠ ，
=
∴△AFH≌△AFE（SAS），··············································· 6分
∴ = ，即 = + ，
∴ = + ；··························································· 7分
（3）结论： = ，理由如下：····································· 8分
如图 3中，延长 CD至 I，使 BE=DI，连接 AI，
∵∠ + ∠ = 180°，∠ + ∠ = 180°，
∴∠ = ∠ ．
在△ABE和△ADI中，
=
∠ = ∠ ，
=
∴△ABE≌△ADI（SAS），················································9分
∴∠ = ∠ ， = ，
∴∠ + ∠ = ∠ + ∠ ，即∠BAD＝∠EAI，········ 10分
∵∠ = 1∠ ，
2
∴∠ = 1∠ ，
2
∴∠ = ∠ ，···························································11分
八年级数学参考答案及评分标准 第 4 页 (共 7 页)
∵ = ，
∴△AEF≌△AIF（SAS）， ·············································· 12分
∴ = ，
∵ = ，
∴ = ．··························································13分
23．解：（1）作 ⊥ 轴于 H，如图 1：
∵点 A的坐标是 1,0 ，点 B的坐标是 0,2 ，
∴ = 1， = 2，························································ 1分
∵△ABC是等腰直角三角形，
∴ = ，∠ = 90°，
∴∠ + ∠ = 90°，
∵∠ + ∠ = 90°，
∴∠ = ∠ ，···························································2分
在△ABO和△BCH中，
∠ = ∠
∠ = ∠ ，
=
∴△ABO≌△BCH（AAS），·············································· 3分
∴ = = 2， = = 1，
∴ = + = 2 + 1 = 3，
∴ 2，3 ；································································· 4分
（2）证明如下：如图 2，
八年级数学参考答案及评分标准 第 5 页 (共 7 页)
∵△ABC是等腰直角三角形，
∴ = ，∠ = 90°，················································5分
∴∠ + ∠ = 90°，
∵∠ + ∠ = 90°，
∴∠ = ∠ ，···························································6分
在△ABO和△BCD中
∠ = ∠
∠ = ∠ ，
=
∴△ABO≌△BCD（AAS），·············································· 7分
∴ = ， = ，
∵ = + = + ，
∴ = + ；···························································8分
（3） = 1 ，理由如下：···················································· 9分
2
如图 3，设 和 的延长线相交于点 D，
∵∠ = 90°，
∴∠ = 90°，
∵ ⊥ 轴，
∴∠ + ∠ = 90°，·····················································10分
∵∠ + ∠ = 90°，
八年级数学参考答案及评分标准 第 6 页 (共 7 页)
∴∠ = ∠ ，························································· 11分
在△ABE和△CBD中，
∠ = ∠
= ，
∠ = ∠
∴△ABE≌△CBD（ASA），
∴ = ，································································· 12分
∵x 轴平分∠ ， ⊥ 轴，
∴在△AFC和△AFD中，
∠ = ∠
= ，
∠ = ∠ = 90°
∴△AFC≌△AFD（ASA），············································· 13分
∴ = ，
∴ = 1 = 1 ．······················································ 14分
2 2
（本卷所有题参考答案只提供一种解法，其他解法只要正确，请参照本参考答案相应给分．）
八年级数学参考答案及评分标准 第 7 页 (共 7 页)
