陕西省榆林市第十中学2022-2023学年九年级上学期期末考试数学试题

这是一份陕西省榆林市第十中学2022-2023学年九年级上学期期末考试数学试题，共9页。试卷主要包含了答卷前将装订线内的项目填写清楚，把方程化成的形式，则的值是，已知正比例函数等内容，欢迎下载使用。
试卷类型：A（北师大版）2022~2023学年度第一学期期末调研试题（卷）九年级数学注意事项：1．本试卷共6页，满分120分，时间120分钟，学生直接在试题上答卷；2．答卷前将装订线内的项目填写清楚．一、选择题（共8小题，每小题3分，计24分．每小题只有一个选项是符合题意的）1．一元二次方程的解是（    ）A． B． C． D．，2．如图，已知两条直线m、n被三条平行线a、b、c所截，若，，则的值为（    ）A． B． C． D．3．关于如图所示的几何体的三视图，下列说法正确的是（    ）A．主视图和俯视图都是矩形 B．俯视图和左视图都是矩形C．主视图和左视图都是矩形 D．只有主视图是矩形4．把方程化成的形式，则的值是（    ）A． B．4 C． D．105．已知正比例函数（）和反比例函数（）的一个交点为，则另一个交点坐标为（    ）A． B． C． D．6．如图，在中，对角线AC与BD相交于点O，如果添加一个条件，可推出是菱形，那么这个条件可以是（    ）A． B． C． D．7．将分别标有“最”、“美”、“陕”、“西”四个汉字的小球装在一个不透明的口袋中，这些球除汉字不同外其他完全相同，每次摸球前先搅匀，随机摸出一球，不放回，再随机摸出一球，两次摸出的球上的汉字可以组成“陕西”的概率是（    ）A． B． C． D．8．如图，在矩形中，，，点P在对角线BD上，且，连接AP并延长，交DC的延长线于点Q，则DQ的长为（    ）A．5 B．6 C．7 D．8二、填空题（共5小题，每小题3分，计15分）9．如图，地面上的A处有一支燃烧的蜡烛（长度不计），一个人在A与墙BC之间运动，则他在墙上的投影长度随着他离墙的距离变小而________（填“变大”、“变小”或“不变”）．10．如图，四边形四边形，若，，，则FG的长为________．11．已知关于x的一元二次方程没有实数根，则m的值可能是________（写出一个即可）12．如图，点A是反比例函数图象上一点，过点A作轴于点D，且点D为线段AB的中点，若点C为x轴上任意一点，且的面积为4，则k的值为________．13．如图，BE，BF分别是与它的邻补角的平分线，，垂足为点E，，垂足为点F，EF分别交边AB，AC于点M和N．若，，则的长为________．三、解答题（共13小题，计81分．解答应写出过程）14．（5分）解方程：．15．（5分）在一个不透明的盒子中装有n个小球，它们只有颜色上的区别，其中有2个红球，每次摸球前先将盒中的球摇匀，随机摸出一个球记下颜色后再放回盒中，通过大量重复试验后发现，摸到红球的频率稳定于0.2，请你估计n的值．16．（5分）从棱长为2的正方体的一角，挖去一个棱长为1的小正方体，得到如图所示的几何体，请画出该几何体的三视图．17．（5分）在某一电路中，保持电压U不变，电流I（单位：A）与电阻R（单位：）成反比例关系，当电阻时，电流．（1）求I与R之间的函数关系式；（2）当电流时，求电阻R的值．18．（5分）为铸牢中华民族共同体意识，不断巩固民族大团结，某中学即将举办“中华民族一家亲，同心共筑中国梦”主题活动，学校拟定了演讲比赛、文艺汇演、书画展览、知识竞赛四种活动方案，九年级（1）班的王磊和李欣同学都准备参加此次活动，但不知选择哪一种活动方案，于是他们制定了A、B、C、D四张卡片（卡片背面完全相同），如图，将四张卡片背面朝上洗匀后，王磊先从中任意抽取一张，记录下卡片上的内容并放回，李欣再从中任意抽取一张．（1）王磊抽取的卡片上的活动方案是文艺汇演的概率为________；（2）请用列表法或画树状图的方法求王磊和李欣所抽取卡片上的活动方案相同的概率．19．（5分）如图，在平面直角坐标系中，的顶点均在网格格点上，且点A、B、C的坐标分别为，，．（1）以点O为位似中心，在第一象限画出的位似图形，使与的相似比为2：1；（2）在（1）的条件下，分别写出点B、C的对应点、的坐标．20．（5分）已知关于x的一元二次方程的两根、满足，求k的值．21．（6分）如图，小亮利用所学的数学知识测量某旗杆AB的高度，旗杆AB垂直于地面．（1）请你根据小亮在阳光下的投影，画出此刻旗杆AB在阳光下的投影；（2）已知直立于地面的小亮的身高为1.72m，在同一时刻测得小亮和旗杆AB在太阳光下的影长分别为0.86m和6m，求旗杆AB的高．22．（7分）如图，已知四边形是菱形，且于点E，于点F．（1）求证：；（2）若，，求菱形的面积．23．（7分）2022年我国已成为全球最大的电动汽车市场，电动汽车在保障能源安全，改善空气质量等方面较传统汽车都有明显优势．某汽车4S店销售某种型号的电动汽车，每辆进货价为19万元，该店经过一段时间的市场调研发现，当销售单价为25万元时，平均每月能售出18辆，而当销售价每降低1万元时，平均每月能多售出6辆，该4S店要想平均每月的销售利润为120万元，并且使每辆车的利润尽可能高，则每辆汽车应降价多少万元？24．（8分）如图，在平面直角坐标系中，已知点，，，点D为点B关于AC所在直线的对称点，反比例函数的图象经过点D．（1）求证：四边形为菱形；（2）求反比例函数的表达式．25．（8分）如图，和均为等腰三角形，且，，．（1）求证：；（2）连接BD、CE，若，的面积为9，求的面积．26．（10分）【问题探究】（1）如图①，在正方形中，点E在边AD上，点F在边CD上，且，线段BE与AF相交于点G，GH是的中线．①求证：；②试判断线段BF与GH之间的数量关系，并说明理由．【问题拓展】（2）如图，在矩形中，，，点E在边AD上，点F在边CD上，且，，线段BE与AF相交于点G，若GH是的中线，求线段GH的长． 试卷类型：A（北师大版）2022~2023学年度第一学期期末调研试题（卷）九年级数学参考答案及评分标准一、选择题（共8小题，每小题3分，计24分．每小题只有一个选项是符合题意的）1．B    2．A    3．C    4．D    5．A    6．C    7．A    8．D二、填空题（共5小题，每小题3分，计15分）9．变小 10．6 11．（答案不唯一）12． 13．5三、解答题（共13小题，计81分．解答应写出过程）14．解：，，，··············································································（3分）∴或，解得，．·········································································（5分）15．解：由题意，得，······························································（3分）解得，，经检验得：是原方程的解，且符合题意，∴估计n的值为10．·································································（5分）16．解：所画三视图如图所示．（画对主视图得1分，画对左视图和俯视图各得2分，共5分）17．解：（1）根据题意，得．∵当电阻时，电流，∴，∴，∴I与R之间的函数关系式为．·························································（3分）（2）当时，解得．··········································································（5分）18．解：（1）····································································（1分）（2）根据题意画树状图如下：················································································（3分）由树状图可知，共有16种等可能的结果，其中王磊和李欣所抽取卡片上的活动方案相同的情况有4种，∴王磊和李欣所抽取卡片上的活动方案相同的概率为．······································（5分）19．解：（1）如图所示．················································································（3分）（2）、．········································································（5分）20．解：根据题意，得，．············································································（2分）∵∴，解得．··········································································（5分）21．解：（1）如图所示，BC即为此刻旗杆AB在阳光下的投影．················································································（2分）（2）∵DE，AB都垂直于地面，且光线，∴，，∴，············································································（4分）∴，即，∴，即旗杆AB的高为12 m．··························································（6分）22．（1）证明：∵四边形是菱形，∴．·················································（2分）∵，∴．·········································································（3分）（2）解：∵四边形是菱形，∴．∵，∴，·········································································（5分）∴，∴．············································································（7分）23．解：设每辆汽车应降价x万元，根据题意，得，···································································（4分）解得，，∵使每辆车的利润尽可能高，∴．答：每辆汽车应降价1万元．··························································（7分）24．（1）证明：∵，，，∴，，··········································································（2分）∵D点为B点关于AC所在直线的对称点，∴，，··········································································（3分）∴，∴四边形为菱形···································································（4分）（2）解：∵四边形为菱形，，························································（5分）又∵，，∴，·····································································（6分）把代入得，∴反比例函数的表达式为．···························································（8分）25．（1）证明：∵，，∴．··························································（2分）又∵，∴．·······································································（3分）（2）解：∵，∴，，··········································································（4分）∴，即，∴，且相似比为．··································································（6分）∴与的面积比为．∵的面积为9，∴的面积为4．·························································（8分）26．（1）①证明：∵四边形是正方形，∴，．在和中，，，，∴．············································································（2分）②解：，理由如下：∵，∴．∵，∴，∴．∵GH是的中线，∴．·······························································（5分）（2）解：∵四边形是矩形，∴．∵，，，，∴，∴，·········································································（6分）∴．∵，∴，∴，∴．·········································································（8分）∵GH是的中线，∴．∵四边形是矩形，∴，，，∴，∴，∴．············································································（10分）