2026届福建省九年级数学中考三模模拟试卷（含答案详解与评分标准）

2026届福建省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分适用：2026届九年级节点：中考三模注意事项：1．本试卷为九年级数学中考三模模拟检测卷，着重考查基础知识、综合运用与考前规范表达能力。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；填空题只需写出最终结果；解答题应写出必要的文字说明、证明过程或演算步骤。4．作图、证明、计算和应用题请书写清楚，答案要与题号对应，过程不完整或表达不规范将按评分标准扣分。题型选择题填空题解答题分值10题×3分=30分6题×3分=18分6题共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）题号12345678910答案1．在实数，0，，中，的倒数是（）A．B．C．D．2．不等式的解集是（）A．B．C．D．3．福建某地三模质量分析中，样本误差率约为0.000072，将0.000072用科学记数法表示为（）A．B．C．D．4．在中，若，，则的度数为（）A．B．C．D．5．一次函数的图象与轴的交点坐标是（）A．B．C．D．6．一个不透明袋中装有除颜色外完全相同的3个红球和2个白球，从中随机摸出1个球，摸到红球的概率是（）A．B．C．D．7．方程的两个根之和为（）A．B．C．D．8．圆O中，圆心角，点C在圆上且与点A、B不重合，则所对同弧的圆周角为（）A．B．C．D．9．矩形的长为8cm，宽为6cm，则它的对角线长为（）A．B．C．D．10．某班6名学生一次限时训练的数学成绩为8，9，9，10，12，13，则这组数据的中位数是（）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．方程的解为__________。13．点关于轴的对称点坐标为__________。14．一个正多边形的每一个外角都是，则这个正多边形的边数是__________。15．二次函数的最小值是__________。16．用同样大小的正方形按规律摆成图案：第1个图案用1个，第2个用5个，第3个用9个，第4个用13个，依此规律，第个图案用__________个正方形；若用2025个正方形，恰好可摆成第__________个图案。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．（本小题10分）完成下列计算与求解。（1）计算：；（2）解方程组：。解答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本小题10分）为了解九年级学生中考三模考前复习方式，某校从九年级学生中随机抽取200人进行问卷调查，结果分为A“基础知识梳理”、B“专题限时训练”、C“综合模拟讲评”、D“错题重做”四类，统计表如下。类别ABCD人数4872m20百分比24%36%n%10%（1）求和的值，并指出被调查学生选择人数最多的复习方式；（2）若该校九年级共有650名学生，请估计选择C“综合模拟讲评”的学生人数；（3）该班推荐的错题讲解员中有2名男生、2名女生，从中随机抽取2名参加三模讲评展示，求恰好抽到1名男生和1名女生的概率。解答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本小题12分）在等腰三角形中，，点D、E在边上，且B、D、E、C依次在同一直线上，。设F为的中点。（1）证明F也是的中点，并证明；（2）证明；（3）若，，，求的长。解答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本小题12分）反比例函数的图象与一次函数的图象在第一象限交于点，两图象的另一个交点为Q。（1）求和的值；（2）求点Q的坐标；（3）求的面积；（4）在第一象限内，直接写出不等式的解集。解答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本小题14分）某校中考三模后整理校园测量实践数据。数学兴趣小组在水平地面上测量旗杆高度，测角仪镜头距地面的高度为1.6m。第一次在点A处测得旗杆顶端的仰角为；沿着指向旗杆底部的直线向前走12m到点C处，第二次测得旗杆顶端的仰角为。旗杆底部与A、C在同一直线上，忽略旗杆粗细。（1）根据题意画出关系示意并设未知量，写出等量关系；（2）求旗杆的高度，结果精确到0.1m；（3）说明本题中若把镜头高度忽略，会对结果产生怎样的影响。解答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22．（本小题14分）在平面直角坐标系中，抛物线与轴交于点A、B（点A在点B左侧），与轴交于点C，顶点为D。（1）求A、B、C、D的坐标；（2）求直线的表达式，并求它与抛物线对称轴的交点E的坐标；（3）点P在抛物线弧上运动，设，其中。求的面积S关于的函数表达式，并求S的最大值；（4）当时，求点P的坐标。解答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析一、选择题答案与关键理由题号12345678910答案AABCDCBBDB1．答案：A。倒数是乘积为1的两个数。因为，所以的倒数是。2．答案：A。由得，两边同除以正数2，得。3．答案：B。0.000072的小数点向右移动5位得到7.2，所以。4．答案：C。等腰三角形两底角相等，，且三角形内角和为，所以。5．答案：D。一次函数与轴交点令，得，交点为。6．答案：C。共有5个球，其中红球3个，随机摸出1个球，摸到红球的概率为。7．答案：B。