2027北京市朝阳区九年级数学训练卷

2027朝阳区九年级数学二模训练校本仿真训练·非官方试卷·PAGESCHOOL-BASEDMOCK/2027EDITION2027届北京市朝阳区九年级数学二模校本仿真训练卷（答案详解｜评分标准｜错题复盘）22题进阶训练·函数与几何综合·过程评分·考后复盘120分钟·120分校本训练制·学生卷+详解+评分使用边界：本卷为校本仿真训练资料，非教育考试院或区级教研部门官方试卷；具体考试结构、分值和安排以当年正式发布为准。

2027届北京市朝阳区九年级数学二模校本仿真训练卷（答案详解｜评分标准｜错题复盘）学校：________________班级：________________姓名：________________考号：________________考试时间：120分钟满分：120分注意事项1．本试卷为九年级数学中考二模考前检测用卷，题目围绕基础运算、几何推理、统计概率、函数应用与综合探究设置。2．答题前，请将学校、班级、姓名、考号填写清楚。选择题请将唯一正确答案填在题后括号内；填空题只填写最终结果。3．解答题应写出必要的计算过程、推理依据和结论。计算结果能化简的要化为最简形式。4．作图、表格和文字说明须清晰。全卷共三大题22小题，满分120分。题型题号题量每题分值合计一、选择题1—1010题3分30分二、填空题11—166题3分18分三、解答题17—226题见题目72分一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个选项符合题意）1．若，则所在的范围是（）A．B．C．D．2．某学习平台在二模复习周的访问量为21858000次，将21858000用科学记数法表示为（）A．B．C．D．3．一个正多边形的每一个外角都是，这个正多边形的边数是（）A．6B．8C．10D．124．一次函数的图象经过点和，下列说法正确的是（）A．，图象经过第一、三象限B．，图象经过第二、四象限和原点C．，图象与轴交于D．当增大时，随之增大5．在圆中，弦所对的圆心角，点在不含弦的优弧上，则的度数为（）A．B．C．D．6．九年级某小组6名同学一次限时训练的成绩依次为74，82，88，91，95，100，则这组数据的中位数是（）A．88B．89.5C．91D．927．关于二次函数，下列判断正确的是（）A．开口向下B．对称轴是直线C．最大值为D．与轴的交点横坐标为和38．反比例函数的图象经过点，当时，的值为（）A．B．C．1D．29．两个相似三角形的相似比为。若较小三角形的面积为，则较大三角形的面积为（）A．18B．24C．27D．3010．关于的一元二次方程有两个相等的实数根，则的值为（）A．B．2C．4D．6二、填空题（本大题共6小题，每小题3分，共18分）11．因式与整式运算中，__________。12．一个不透明袋中有3个红球和2个白球，这些球除颜色外完全相同。从袋中不放回地随机取出2个球，取出的2个球颜色相同的概率是__________。13．方程组，的解是__________。14．一次函数的图象与两坐标轴围成的三角形面积为__________。15．为圆的切线，切点为，，圆的半径为6，则__________。16．一列数按规律排列：2，6，12，20，30，……，第项可表示为，则第10项是__________。三、解答题（本大题共6小题，共72分。解答应写出文字说明、证明过程或演算步骤）17．（10分）先化简，再求值：要求写出因式分解、约分和代入计算的完整过程。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）解不等式组，并把解集在数轴上表示出来：作答时需写出每个不等式的变形依据，并用区间端点的实心、空心情况表达解集。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）为了解九年级学生二模前数学专项训练情况，某校从九年级学生中随机抽取40名同学，按训练成绩（满分110分）分组，得到如下统计表：成绩x（分）人数频率80.20120.30140.3560.15（1）补全统计意义：成绩在这一组的频率为0.35，对应扇形统计图的圆心角为多少度？（2）若该校九年级共有480名学生，请估计成绩不低于90分的学生人数。（3）在成绩为100分及以上的6名同学中，甲、乙两名同学均在其中。现从这6名同学中随机选2名作经验分享，求甲、乙恰好同时被选中的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）某文具店为服务中考二模复习，购进一种笔记本。每本成本为8元，销售单价为元。经试销发现，当时，月销售量（本）与销售单价（元）之间近似满足一次函数关系。设月利润为元。（1）当销售单价为14元时，求月销售量和月利润。（2）求与之间的函数关系式，并求月利润的最大值。（3）若文具店希望月利润不低于1260元，同时尽量让利给学生，则销售单价应定为多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）如图，为圆的直径，点在圆上，过点作圆的切线，过点作，垂足为，连接，，。已知，。（1）求的长；（2）证明：；（3）求的长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）已知二次函数的图象与轴交于，两点（点在点左侧），与轴交于点，顶点为。（1）求，，，的坐标；（2）设点在抛物线上，且。过点作平行于轴的直线，交直线于点。求线段的长和的面积关于的表达式，并求该面积的最大值；（3）在抛物线的对称轴上是否存在点，使为直角三角形？若存在，求出点的坐标。作答区：_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________