2026届重庆市九年级数学中考三模模拟试卷（含答案详解与评分标准）

第1页/共1页2026届重庆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分适用：重庆市九年级中考三模考前检测注意事项：1．本试卷分选择题、填空题和解答题三部分，满分120分，考试时间120分钟。2．作答前请将学校、班级、姓名、考号填写清楚。3．选择题、填空题请把答案写在指定答题栏内；解答题须写出必要的文字说明、计算过程或证明过程。4．本卷用于三模阶段复习检测，重点考查基础落实、方法选择与综合运用。题型选择题填空题解答题总分分值30分18分72分120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，请将正确选项填入下方答题栏。1．在数轴上，与数对应点关于原点对称的点表示的数是（）A．B．C．D．2．重庆某区九年级参加第三次模拟测评的学生约为72300人，将72300用科学记数法表示为（）A．B．C．D．3．下列计算正确的是（）A．B．C．D．4．若代数式有意义，且为整数，则的最小值是（）A．B．C．D．5．一组数据6，8，8，9，12，13的中位数是（）A．8B．9C．8.5D．106．如两条直线被第三条直线所截，且两直线平行，若一对同旁内角中的一个角为64°，则另一个角的度数是（）A．26°B．64°C．116°D．128°7．一次函数的图象经过点，，则的值为（）A．B．C．D．8．一个不透明袋中有3个白球和2个黑球，这些球除颜色外完全相同。从中不放回地随机摸出2个球，两个球都是白球的概率为（）A．B．C．D．9．关于的方程有两个相等的实数根，则的值为（）A．1B．2C．4D．810．半径为6、圆心角为120°的扇形的弧长是（）A．B．C．D．题号12345678910答案二、填空题（本大题共6小题，每小题3分，共18分）11．计算：=________．12．不等式组的整数解共有________个．13．若，，则=________．14．反比例函数的图象经过点，当时，=________．15．一个圆锥的底面半径为3，母线长为5，则这个圆锥的侧面积为________．16．定义新运算：．若且，则=________．题号111213141516答案三、解答题（本大题共6小题，共72分）解答应写出必要的文字说明、证明过程或演算步骤。17．（10分）计算与化简。（1）计算：；（2）先化简，再求值：，其中．学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）解方程组与不等式组。（1）解方程组：（2）解不等式组：学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）为了解九年级学生在中考三模前的数学专项训练情况，某校随机调查了40名学生“每天完成数学专项训练的时间”（单位：分钟），并整理如下表。时间t/分钟20≤t<3030≤t<4040≤t<5050≤t<6060≤t<70人数4812106请根据表中信息完成下列问题：（1）以各组组中值作为该组数据的代表值，求这40名学生每天训练时间的平均数；（2）判断这40名学生每天训练时间的中位数所在的时间段；（3）若该校九年级共有1200名学生，估计每天训练时间不少于50分钟的学生人数；（4）在训练时间不足30分钟的4名学生中，有2名男生和2名女生。若从这4人中随机抽取2人进行访谈，求恰好抽到1名男生和1名女生的概率。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）某校附近文具店在中考三模复习阶段销售一种数学错题本。该错题本进价为8元/本，当前售价为15元/本时，平均每天可售出200本。根据试销发现：售价每提高1元，平均每天少售出12本。设每本提高元，且，为整数。（1）用含的式子表示每天的销售利润（元）；（2）当每天销售利润为1664元时，若售价仍按整元确定，求每本应提高多少元；（3）在售价按整元确定的条件下，求每天销售利润的最大值及此时的售价。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）如图形关系所述，在中，，点是的中点。点在直线上，且，连接，。（1）证明：四边形ABEC是菱形；（2）若，，求的长和四边形的面积；（3）若点是的中点，连接，证明，并求的长。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）如平面直角坐标系中，抛物线经过点，，。（1）求该抛物线的解析式；（2）求抛物线顶点的坐标，并写出抛物线的对称轴；（3）设点是抛物线上位于、之间的一点，过作轴，交直线于点。求线段的最大值及此时点的坐标。学生作答区：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________