2022年山东省菏泽市单县中考三模数学试题(word版含答案)

这是一份2022年山东省菏泽市单县中考三模数学试题(word版含答案)，共14页。试卷主要包含了下列运算正确的是，已知二元一次方程组，则的值为，已知，，则的值是等内容，欢迎下载使用。
2022年初中学业水平模拟测试数学试题（三）注意事项：1.本试题共24个题，满分120分，考试时间120分钟。2.请把答案写在答题卡上，选择题用2B铅笔填涂，非选择题用0.5毫米的黑色墨水签字笔书写在答题卡的指定区域内，写在其它区域不得分。一、选择题（本大题共8个小题，每小题3分，共24分，在每小题给出的四个选项中，只有一个选项是正确的，请把正确选项的序号涂在答题卡的相应位置.）1.实数a，b在数轴上的位置如图所示，则下列式子正确的是（    ）A. B. C. D.2.一列数4，5，6，4，4，7，x的平均数是5，则中位数和众数分别是（    ）A.4，4 B.5，4 C.5，6 D.6，73.下列运算正确的是（    ）A. B. C. D.4.已知二元一次方程组，则的值为（    ）A.2 B.6 C.-2 D.-65.已知，，则的值是（    ）A.2 B. C.3 D.6.如图，在中，，，，将绕点A逆时针旋转得到，使点落在边上，连结，则的值为（    ）A. B. C. D.7.如图，是的外接圆，交于点E，垂足为点D，，的延长线交于点F.若，，则的长是（    ）A.10 B.8 C.6 D.48.如图，二次函数的图象经过点，，与y轴交于点C.下列结论：①         ②当时，y随x的增大而增大  ③  ④.其中正确的个数有（    ）A.1个 B.2个 C.3个 D.4个二、填空题（本大题共6个小题，每小题3分，共18分.把结果填写在答题卡相应区域内）9.若一个扇形的圆心角为60°，面积为，则这个扇形的弧长为_________（结果保留）.10.已知是一元二次方程的一个根，则m的值为_________.11.关于x的不等式组恰好有2个整数解，则实数a的取值范围是_________.12.如图，在平面直角坐标系中，的顶点A、B的坐标分别为、.把沿x轴向右平移得到，如果点D的坐标为，则点E的坐标为_________.13.如图所示，反比例函数的图象经过矩形的边的中点D，则矩形的面积为________.14.如图，在平面直角坐标系中，将边长为1的正方形绕点O顺时针旋转45°后得到正方形，依此方式，绕点O连续旋转2019次得到正方形，那么点的坐标是_________.三、解答题（本大题共78分，把必要的证明过程或演算步骤写在答题卡的相应区域内）15.（6分）计算：.16.（6分）先化简，再求值：，其中a，b满足.17.（6分）如图，在和中，，.（1）求证：；（2）若，，求的长.18.（6分）由我国完全自主设计，自主建造的首艘国产航母于2018年5月成功完成首次海上试验任务.如图，航母由西向东航行，到达B处时，测得小岛A在北偏东60°方向上，航行20海里到达C点，这时测得小岛A在北偏东30°方向上，小岛A周围10海里内有暗礁，如果航母不改变航线继续向东航行，有没有触礁危险？请说明理由.19.（7分）如图，已知反比例函数（）的图象和一次函数的图象都过点，过点P作y轴的垂线，垂足为A，O为坐标原点，的面积为1.（1）求反比例函数和一次函数的表达式；（2）设反比例函数图象与一次函数图象的另一交点为M，过M作x轴的垂线，垂足为B，求五边形的面积.20.（7分）某电商在抖音上对一款成本价为40元的小商品进行直播销售，如果按每件60元销售，每天可卖出20件.通过市场调查发现，每件小商品售价每降低5元，日销售量增加10件.若日利润保持不变，商家想尽快销售完该款商品，每件售价应定为多少元？21.（10分）为加快推进生活垃圾分类工作，其中，可回收物用蓝色收集桶，有害垃圾用红色收集桶，厨余垃圾用绿色收集桶，其他垃圾用灰色收集桶.为了解学生对垃圾分类知识的掌握情况，某校宜传小组就“用过的餐巾纸应投放到哪种颜色的收集桶”在全校随机采访了部分学生，根据调查结果，绘制了如图所示的两幅不完整的统计图.根据图中信息，解答下列问题：（1）此次调查一共随机采访了_________名学生，在扇形统计图中，“灰”所在扇形的圆心角的度数为_________度；（2）补全条形统计图（要求在条形图上方注明人数）；（3）若该校有3600名学生，估计该校学生将用过的餐巾纸投放到红色收集桶的人数；（4）李老师计划从A，B，C，D四位学生中随机抽取两人参加学校的垃圾分类知识抢答赛，请用树状图法或列表法求出恰好抽中A，B两人的概率.22.（10分）如图，已知是的直径，C为上一点，的角平分线交于点D，F在直线上，且，垂足为E，连接、.（1）求证：是的切线；（2）若，的半径为3，求的长.23.（10分）如图1，在中，，，点D、E分别在边、上，，连接，点M，P，N分别为、、的中点.（1）观察猜想；图1中，线段与的数量关系是___________，位置关系是___________.（2）探究证明：把绕点A逆时针方向旋转到图2的位置，连接，，，判断的形状，并说明理由；（3）拓展延伸：把绕点A在平面内自由旋转，若，，请直接写出面积的最大值.24.（10分）如图，抛物线与x轴交于A、B两点，与y轴交于C点，，，连接和.（1）求抛物线的表达式；（2）点Ｄ在抛物线的对称轴上，当的周长最小时，点D的坐标为___________.（3）点E是第四象限内拋物线上的动点，连接和.求面积的最大值及此时点E的坐标；（4）若点M是y轴上的动点，在坐标平面内是否存在点N，使以点A、C、M、N为顶点的四边形是菱形？若存在，请直接写出点N的坐标；若不存在，请说明理由. 2022年九年级数学模拟三参考答案一、选择题（本大题共8个小题，每小题3分，共24分.）题号12345678答案BBCACCAB二、填空题（本大题共6个小题，每小题3分，共18分.）9.    10.-1    11.    12.    13.4    14.三、解答题：（本大题共10个小题，共78分，解答应写出必要的文字说明、证明过程或演算步骤）15.解：原式········································································（2分）·················································································（4分）.·················································································（6分）16解：原式·········································································（2分）·················································································（3分），················································································（4分）∵，∴，，，，··············································································（5分）原式.（6分）17证明：（1）∵.∴，∴，··············································································（2分）又∵，∴；·········································································（4分）（2）∵；∴，··············································································（5分）又∵，∴.··········································································（6分）18解:如果渔船不改变航线继续向东航行，没有触礁的危险，理由如下：过点A作，垂足为D，························································（1分）根据题意可知，，···································································（2分）∵，∴，∴，··············································································（3分）在中，，，，∴，··············································································（4分）∴，··············································································（5分）∴渔船不改变航线继续向东航行，没有触礁的危险.···········································（6分）19:解（1）∵过点P作y轴的垂线，垂足为A，O为坐标原点，的面积为1.∴，∴，··········································································（1分）∵在第一象限，∴，∴反比例函数的表达式为；·························································（2分）∵反比例函数（）的图象过点，∴，∴，··········································································（3分）∵一次函数的图象过点，∴，解得，∴一次函数的表达式为；······························································（4分）（2）设直线交x轴、y轴于C、D两点，∴，，解得或，∴，，············································································（5分）∴，，，，·········································································（6分）∴五边形的面积为.·················································································（7分）20解：设售价应定为x元，则每件的利润为元，日销售量件，···································（1分）依题意，得：，·····································································（3分）整理，得：，·······································································（5分）解得：，（舍去）.···································································（6分）答：售价应定为50元；································································（7分）21.解：（1）此次调查一共随机采访学生（名），············································（1分）在扇形统计图中，“灰”所在扇形的圆心角的度数为，········································（2分）故答案为：200，198；（2）绿色部分的人数为（人），························································（3分）补全图形如下：·····································································（4分）（3）估计该校学生将用过的餐巾纸投放到红色收集桶的人数（人）；····························（5分）（4）列表如下：····································································（8分） ABCDA B C D 由表格知，共有12种等可能结果，其中恰好抽中A，B两人的有2种结果，⋯（9分）所以恰好抽中A，B两人的概率为.························································（10分）22.解：（1）如图，连接，·····························································（1分）∵，∴，∵平分，∴，∴，··············································································（2分）∴，∴， （3分）∵，∴，∴，即，∴是的切线；·······································································（4分）（2）∵是的直径，∴，∴，则，··········································································（5分）在中，，，∴，即，··········································································（6分）解得，············································································（7分）由（1）知是的切线，∴，∵，∴，∴，则，··········································································（8分）在中，，由勾股定理可得，，即，解得，则，·········································································（9分）由（1）知，∴，即，解得.·······································································（10分）23.解：（1），，∵点P，N是，的中点，∴，，∵点P，M是，的中点，∴，，············································································（1分）∵，，∴，∴，··············································································（2分）∵，∴，∵，∴，∵，∴，··············································································（3分）∴，∴，··············································································（4分）故答案为：，，（2）由旋转知，，∵，，∴，∴，，············································································（5分）同（1）的方法，利用三角形的中位线得，，，∴，∴是等腰三角形，.（6分）同（1）的方法得，，∴，同（1）的方法得，，∴，∵，∴，················································································（7分）∵，∴，∴，∴是等腰直角三角形，································································（8分）（3）如图2，同（2）的方法得，是等腰直角三角形，∴最大时，的面积最大，∴且在顶点A上面，∴最大，··········································································（9分）连接，，在中，，，∴，在中，，，∴，∴.···············································································（10分）24.解：（1）∵，，∴，，∵抛物线过点A、C，∴················································································（1分）解得，∴抛物线解析式为；··································································（2分）（2）∵当时，，解得，，，∴，抛物线对称轴为直线，∵点D在直线上，点A、B关于直线对称，∴，，∴当点B、D、C在同一直线上时，最小，············································································（3分）设直线的表达式为，∴，解得，，∴直线：，∴，∴，故答案为；·········································································（4分）（3）过点E作轴于点G，交直线与点F，设（），则，∴，··············································································（5分）∴，················································································（6分）∴当时，面积最大，∴，∴点E坐标为时，面积最大，最大值为.····················································（7分）（4）存在点N，使以点A、C、M、N为顶点的四边形是菱形.∵，，∴，·········································································（8分）①若为菱形的边长，如图3，则且，，∴，，；··········································································（9分）②若为菱形的对角线，如图4，则，，设，∴，解得，，∴，··············································································（10分）综上所述，点N坐标为，，，.（以上各题如有其它解法，酌情给分）