山西省临汾市曲沃县2026—2027学年度第一学期素养形成期中测试九年级数学

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2026—2027学年度第一学期素养形成期中测试

初三数学(华东版)

注意事项:

1.本试卷分第Ⅰ卷和第Ⅱ卷两部分.全卷共6页,满分120分,考试时间120分钟.

2.答卷前,考生务必将自己的姓名、准考证号填写在本试卷相应的位置.

3.答案全部在答题卡上完成,答在本试卷上无效.

4.考试结束后,将本试卷和答题卡一并交回.

第Ⅰ卷  选择题(共30分)

一、选择题(本大题共10个小题,每小题3分,共30分.在每小题给出的四个选项中,只有一项符合题目要求,请选出并在答题卡上将该项涂黑)

1.下列各式中,运算正确的是

A. B.

C. D.

2.杠杆原理在机械设计中应用广泛,如图是用杠杆提升重物的示意图,当施加动力时杠杆绕支点转动.动力臂,阻力臂,,则的长度是

A.  B.  C.  D.

3.将第一象限的“小旗”各点的横坐标保持不变,纵坐标乘以,符合上述要求的图形是

A.B.C.D.

4.在和中,,添加下列条件不能判定两个三角形相似的是

A.   B.

C.    D.page number 0

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5.若,则的值为

A.   B.   C.3   D.2

6.如图,,,,则的长为


A.  B.  C.  D.

7.秋冬季节是流感高发期,九年级某班有1名同学患了流感,已知经过两轮传染后,全校共有81人患了流感,设每轮传染中平均一个人传染x个人,则可列方程为

A. B.

C. D.

8.如图,四边形与四边形是位似图形,位似中心为点O,且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,则四边形与四边形的周长比为

A.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  B.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  C.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  D.eqWmf183GmgAAAAAAAMEC7QHsCQAAAADRXQEACQAAA0ABAAACAJoAAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4BGQAAAAUAAAALAgAAAAAFAAAADALAAYACCwAAACYGDwAMAE1hdGhUeXBlAAAwABIAAAAmBg8AGgD/////AAAQAAAAwP///8b///9AAgAAhgEAAAUAAAAJAgAAAAIFAAAAFAJgARAAHAAAAPsCgP4AAAAAAACQAQAAAAAAAgAQVGltZXMgTmV3IFJvbWFuAHCx8Xd5sfF3IFDzd9ciZgYEAAAALQEAAAwAAAAyCgAAAAADAAAAMTo5ANgAnAAAA5oAAAAmBg8AKgFBcHBzTUZDQwEAAwEAAAMBAABEZXNpZ24gU2NpZW5jZSwgSW5jLgAFAQAGCURTTVQ2AAATV2luQWxsQmFzaWNDb2RlUGFnZXMAEQVUaW1lcyBOZXcgUm9tYW4AEQNTeW1ib2wAEQVDb3VyaWVyIE5ldwATV2luQWxsQ29kZVBhZ2VzABEG0MLLzszlABEETVQgRXh0cmEAE1dpbkNoaW5hABEHy87M5S1QVUEAEgAIIS9Fj0QvQVD0EA9HX0FQ8h8eQVD0FQ9BAPRF9CX0j0JfQQD0EA9DX0EA9I9F9CpfSPSPQQD0EA9A9I9Bf0j0EA9BKl9EX0X0X0X0X0EPDAEAAQABAgICAgACAAEBAQADAAQABQAGAAoBAAIAiDEAAgCCOgACAIg5AAAACgAAACYGDwAKAP////8BAAAAAAAcAAAA+wIQAAcAAAAAALwCAAAAhgECAiJTeXN0ZW0AANciZgYAAAoAIQCKAQAAAAD/////xOYTAAQAAAAtAQEABAAAAPABAAADAAAAAAA=

9.如图,D、E分别是的边、上的点,,若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,则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的值为

A.   B.   C.   D.page number 1

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10.如图,正方形正方形,正方形的顶点G在正方形的边上运动,交的延长线于点H,若,,则正方形的边长为

A.4   B.  C.  D.5

第Ⅱ卷  非选择题(共90分)

二、填空(本大题共5个小题,每小题3分,共15分.)

11.若式子在实数范围内有意义,则x的取值范围是     ▲     .

12.若一个一元二次方程有一个根为,则这个一元二次方程可以是     ▲     .(写出一个即可)

13.如图,在中,D、E、F分别是、、上的点,且,,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,,则边的长为     ▲     .

14.如图,这是著名的“黄金螺旋”,它由一系列正方形中的四分之一圆弧拼接而成.已知最外侧的大矩形是一个黄金矩形(即长与宽的比符合黄金分割比).设该矩形水平边的最左端为点A,最右端为点B,且点C为线段的黄金分割点(),则     ▲     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.

15.如图,∽,若,,则     ▲     .

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