2026届广州市九年级数学中考三模模拟试卷（含答案详解与评分标准）

2026届广州市九年级数学中考三模模拟试卷（含答案详解与评分标准）学校：________________班级：________________姓名：________________考号：________________考试时间：120分钟满分：120分考试节点：中考三模适用：九年级数学注意事项：1．本卷为考前第三次模拟检测，试题覆盖数与式、方程与不等式、函数、图形与几何、统计与概率等核心内容。2．全卷共三大题22小题，满分120分，考试时间120分钟。请在规定位置填写学校、班级、姓名和考号。3．选择题每小题只有一个正确选项；填空题只写最终结果；解答题应写出必要的文字说明、演算步骤或证明过程。4．作图、证明和计算应规范清晰；因书写不清、过程缺失造成无法判断的，按评分标准酌情处理。5．答题过程中可先易后难，注意检验单位、定义域和实际意义。一、选择题（本大题共10小题，每小题3分，共30分）每小题给出的四个选项中，只有一项是符合题目要求的。1．在数轴上表示数的点到原点的距离为，若，则的值是（）A．B．C．D．2．据统计，某科普场馆去年线上预约浏览量约为5730000次，将5730000用科学记数法表示为（）A．B．C．D．3．如图形情境：两条平行直线被一条截线所截，若其中一个内错角为，则它的同旁内角的度数为（）A．B．C．D．4．不等式组，的解集是（）A．B．C．D．5．一个不透明袋中有3个红球、2个黄球、1个蓝球，这些球除颜色外完全相同。从袋中随机摸出1个球，摸到的球不是黄球的概率为（）A．B．C．D．6．一次函数的图象经过点和，则该函数的表达式为（）A．B．C．D．7．点在同一圆上，圆心为。若，且点在不含弧的另一段圆弧上，则的度数为（）A．B．C．D．8．某小组6名同学的数学训练成绩（单位：分）为78，82，85，85，90，94。该组成绩的中位数是（）A．82B．84C．85.5D．859．若二次函数的图象与轴只有一个公共点，则的值为（）A．B．C．D．10．在边长为6的正方形中，为边的中点，连接，过点作于点，则的长为（）A．B．C．D．二、填空题（本大题共6小题，每小题3分，共18分）11．分解因式：________________。12．计算：________________。13．若，，则________________。14．在直角三角形中，，，，则该三角形的面积为________________。15．一组数据4，6，8，，10的平均数为8，则________________。16．反比例函数的图象经过点，则________________。三、解答题（本大题共6小题，每小题12分，共72分）解答应写出必要的证明、运算或推理过程。17．（12分）计算与解方程：（1）计算：；（2）解分式方程：。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（12分）某校九年级数学备课组为了解学生中考体育备考情况，随机抽取80名学生，统计他们每周课外体育锻炼时长，分成四组：A组（少于2小时），B组（2小时至不足4小时），C组（4小时至不足6小时），D组（不少于6小时）。统计结果如下表。组别每周锻炼时长人数A少于2小时8B2小时至不足4小时20C4小时至不足6小时32D不少于6小时20（1）求样本中C组人数所占百分比；（2）若该校九年级共有960名学生，估计每周锻炼时长不少于4小时的学生人数；（3）另有4名体能训练志愿者，其中甲、乙为男生，丙、丁为女生。从中随机选2名参加展示，求恰好选到1名男生和1名女生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）如图形关系所示，在平面直角坐标系中，直线分别与轴、轴交于点。反比例函数的图象经过直线上的点，且的横坐标为1。（1）求点的坐标；（2）求反比例函数的表达式；（3）若点在该反比例函数图象的第一象限部分，且，求点的坐标。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）如图形关系所示，矩形中，，。点是的中点，点是的中点，连接。（1）求证：四边形是平行四边形；（2）求四边形的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（12分）已知二次函数图象经过点，，。（1）求该二次函数的表达式；（2）求图象的对称轴和顶点坐标；（3）点在抛物线的对称轴上且位于第四象限，若，求点的坐标。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（12分）在直角三角形中，，，。点从出发沿向匀速运动，速度为每秒1cm；点从出发沿向匀速运动，速度为每秒2cm。两点同时出发，运动时间为秒，，连接。（1）用表示和；（2）设的面积为，求与的函数关系式；（3）当时，求的值；（4）在给定运动范围内，求的最小值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解答题备用作答区（请标明题号）：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析评分总则：客观题按题目分值给分；解答题依据过程、结果和表达综合评分，等价正确方法均可按相应步骤给分。一、选择题答案与关键理由12345678910BADCBACDBC评分标准：第1—10题每小题3分，选对得3分，错选