2023年安徽省合肥市第四十五中学中考模拟数学试题（含答案）

这是一份2023年安徽省合肥市第四十五中学中考模拟数学试题（含答案），共9页。试卷主要包含了选择题，填空题等内容，欢迎下载使用。
合肥市第四十五中学中考数学模拟试卷一、选择题（本题共10小题，每小题4分，满分40分）1.-2023的相反数是（    ）A. B. C.-2023 D.20232.下面计算正确的是（    ）A. B. C. D.3.2023年3月5日，李克强总理代表国务院作《政府工作报告》.报告中指出，2022年我国经济结构和区域布局继续优化，粮食产量13700亿斤，创历史新高，把数据13700亿用科学记数法表示为（    ）A. B. C. D.4.如图所示的手提水果篮，其俯视图是（    ）A. B. C. D.5.如图是一款手推车的平面示意图，其中，，，则的度数为（    ）A.56 B.66 C.98 D.1046.在一次演讲比赛中，七位评委为某位选手打出的分数如下：87，95，89，99，87，93，97（单位：分）.若去掉一个最高分和一个最低分，则去掉前与去掉后没有改变的一个统计量是（    ）A.平均分 B.众数 C.中位数 D.方差7.已知直线经过第一、二、三象限，且点在该直线上，设，则m的取值范围是（    ）A. B. C. D.8.如图，在平行四边形中，，，的平分线交的延长线于点E，交于点F，则等于（    ）A.7∶4 B.7∶3 C.4∶3 D.4∶79.已知a，b，c为实数，且，，则a，b，c之间的大小关系是（    ）A. B. C. D.10.已知抛物线的图象如图所示，其对称轴为直线，那么一次函数的图象大致为（    ）ABCD二、填空题（本题共4小题，每小题5分，满分20分）11.因式分解：______________.12.如图，四边形内接于，是的直径，过点C作的切线交的延长线于点P，若，则______________.13.如图，已知直角三角形中，，，将绕O点旋转至的位置，且为中点，在反比例函数上，则k的值______________.14.如图，已知矩形中，，，点M，N分别在边，上，沿着折叠矩形，使点B，C分别落在，处，且点在线段上（不与两端点重合）.（1）若为线段的中点，则____________；（2）折痕的长度的取值范围为_____________.三、（本题共2小题，每小题8分，满分16分）15.解不等式组：16.如图，的顶点坐标分别为，，.将绕原点O逆时针旋转90°的图形得到.（1）画出的图形，并写出的坐标.（2）若点在边上，直接写出点P旋转后对应点的坐标.四、（本题共2小题，每小题8分，满分16分）17.甲工程队新建公路，每名工人每天工作8小时，则甲工程队每天可完成800米新建公路.乙工程队比甲工程队少15名工人，每名工人每天工作12小时，则乙工程队每天可完成600米新建公路，假定甲、乙两工程队的每名工人每小时完成的工作量相同，求乙工程队的工人有多少名？18.观察以下等式：第1个等式：，第2个等式：，第3个等式：，……按照以上规律，解决下列问题：（1）按照此规律下去，第4个等式是：_______________________；（2）写出你猜想的第n个等式（用含n的式子表示），并证明.五、（本题共2小题，每小题10分，满分20分）19.周末爬大蜀山，是合肥市民周末娱乐休闲、锻炼身体的方式之一.如图，某个周末小张同学从大蜀山西坡沿坡角为37°的山坡爬了280米，到达点E处，紧接着沿坡角为45°的山坡又爬了160米，到达山顶A处；请你计算大蜀山的高度.（结果精确到个位，参考数据：，，，，.）20.学校即将开展红色经典诵读活动，李老师给学生推荐了3种不同的名著A，B，C.甲，乙两位同学分别从中任意选一种阅读，假设选任意一种都是等可能的.（1）甲同学选中名著B的概率是（2）请你利用画树状图或列表的方法，求甲、乙两位同学选中的名著不相同的概率.六、（本题满分12分）21.如图1，已知是的内接三角形，是的直径，是的弦，连接，交于点E.（1）求证：；（2）如图2，连接、，若，且，，求的长.七、（本题满分12分）22.已知：如图1，在中，，是的平分线，连接、，且于点D.（1）求证：；（2）如图2，点E、F分别是边、上的点，且于点E，求的值.八、（本题满分14分）23.如图，抛物线与x轴交于点A、B，与y轴交于点C，点A的坐标为，点B的坐标为.（1）求抛物线的表达式；（2）当时，抛物线有最小值5，求a的值；（3）若点P是第四象限内抛物线上一动点，连接、，求的面积S的最大值.  参考答案一、选择题（本题共10小题，每小题4分，满分40分）1-5 DCDBA  6-10 CBBAD二、填空题（本题共4小题，每小题5分，满分20分）11.  12.40°  13.  14.（1）  （2）三、（本题共2小题，每小题8分，满分16分）15.解：··················································································3分··················································································6分∴原不等式组的解集为.································································8分16.（1）如图所示，即为所求；··················································································3分··················································································5分（2）··············································································8分四、（本题共2小题，每小题8分，满分16分）17.解：设乙工程队的工人有x名，由题意得，··········································································4分解得，经检验，是原分式方程的解且符合题意，答：乙工程队的工人有15名.·····························································8分18.（1）；··········································································3分（2）第n个等式：证明：即·················································································8分五、（本题共2小题，每小题10分，满分20分）19.解：过点A作于D，过点E作于F，于G，则四边形为矩形，∴，在中，，则（米），··········································································4分在中，，则（米），··········································································8分∴（米），答：大蜀山的高度约为281米.···························································10分20.解：（1）∵共有3种不同的名著A，B，C，∴其名著B的概率是：；································································3分（2）根据题意画图（图略）共有9中等可能的情况数，其中甲、乙两位同学选中的名著不相同的有9种，则甲、乙两位同学选中的名著不相同的概率为：.············································10分六、（本题满分12分）21.（1），弧弧，推出∴·················································································5分（2）·············································································12分七、（本题满分12分）22.（1）证明：∵证明：过点D作于点E，于点F，可证∴·················································································5分或证A、C、B、D四点共圆（2）可证，∵，∴为等腰直角三角形，∵为等腰直角三角形∴，∴，∴∵，∴，∴∴················································································12分八、（本题满分14分）23.（1）············································································4分（2）或6···········································································9分（2）的面积S的最大值································································14分