2026届深圳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届深圳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分题型选择题填空题解答题总分分值30分18分72分120分注意事项1．本试卷为2026届深圳市九年级数学中考三模考前检测用卷，重点检验阶段复习后的基础落实、综合建模和规范表达能力。2．全卷共三大题、22小题。选择题10题，每题3分；填空题6题，每题3分；解答题6题，共72分。3．请将选择题答案填涂在答题卡相应位置；填空题和解答题写在规定作答区内，书写过程要清楚、步骤要完整。4．作图题可先用铅笔作辅助线，最终答案请用黑色字迹笔书写；不得使用计算器。一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个正确选项）1．计算的值是（）A．4B．5C．7D．92．三模质量分析中，某区九年级数学线上练习访问量约为6270000次，将6270000用科学记数法表示为（）A．6.27×10^5B．6.27×10^6C．62.7×10^5D．0.627×10^73．下列平面图形中，既是轴对称图形又是中心对称图形的是（）A．等边三角形B．矩形C．等腰梯形D．正五边形4．若一次函数的函数值随自变量的增大而减小，则的取值范围是（）A．m>2B．m<2C．m≥2D．m≤25．一个不透明袋中装有除颜色外完全相同的3个红球、2个白球和1个蓝球，从中随机摸出1个球，摸到的球不是白球的概率为（）A．1/3B．1/2C．2/3D．5/66．不等式组的解集是（）A．x>2B．x≤3C．2<x≤3D．2≤x<37．在半径为5的圆中，弦AB的长为8，则圆心到弦AB的距离为（）A．2B．3C．4D．68．一组数据6，8，8，10，12的中位数和众数分别是（）A．8，8B．8，10C．10，8D．8，129．关于的一元二次方程有两个不相等的实数根，则的取值范围是（）A．k<1B．k>1C．k≤1D．k≥110．如图意可作：在△ABC中，DE∥BC，D在AB上，E在AC上，AD:DB=2:3。若△ADE的面积为8，则四边形DBCE的面积为（）A．20B．32C．42D．50二、填空题（本大题共6小题，每小题3分，共18分。请把答案填写在题中横线上）11．分解因式：________________。12．在锐角中，若，则________________。13．同时抛掷两枚质地均匀的硬币，至少有一枚正面朝上的概率是________________。14．已知点，，则线段的长为________________。15．一个圆锥的底面半径为3，高为4，则这个圆锥的侧面积为________________。16．定义新运算。若，则________________。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）本题为三模考前基础运算与方程检测。（1）计算：；（2）解分式方程：。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）某校九年级数学组在中考三模后，对80名学生“每日错题整理时间”进行抽样调查，并将结果分为A、B、C、D四组：A组为0≤t<30分钟，B组为30≤t<60分钟，C组为60≤t<90分钟，D组为t≥90分钟。已知统计表如下，扇形统计图中D组对应的圆心角为90°。组别ABCD人数1228ab（1）求a、b的值，并写出C组所占百分比；（2）若全年级共有1200名学生，请估计每日错题整理时间不少于60分钟的学生人数；（3）D组中推选出甲、乙、丙、丁4名学生作为错题分享候选人，现随机抽取2人进行分享，请用列表或树状图求“甲被抽中”的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）如图，在△ABC中，AB=AC=10，BC=12。点E在AC上，AE=4，过点E作EF∥BC，交AB于点F。（1）证明△AEF∽△ACB；（2）求EF的长；（3）求四边形FBCE的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）某校在三模复盘阶段准备印制“数学错题复盘手册”。每本售价为p元（10≤p≤18），市场调查发现：当售价为10元时，可订购240本；售价每提高1元，订购量减少15本。每本手册的制作成本为6元，另需固定设计费180元。设订购量为q本，总利润为W元。（1）用含p的代数式表示q，并写出W关于p的函数关系式；（2）求售价为多少元时总利润最大，并求最大利润；（3）若要求总利润不少于1260元，且售价为整数，同时希望订购量不少于150本，请确定最合适的售价。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）如图，⊙O的半径为5，AB为直径，点C在⊙O上，AC=6。过点C作⊙O的切线，交AB的延长线于点D，且D在A的外侧；过C作CE⊥AB于点E。（1）求BC的长；（2）求CE和AE的长；（3）求切线段CD的长；（4）求tan∠CDA的值。作答区：_____________________________________________________________________________________________________________________________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___________________________________________________________________________________________________________________________________________________________22．（14分）如图，在平面直角坐标系中，抛物线y=-x²+4x+5与x轴交于A、B两点（A在B的左侧），与y轴交于点C，顶点为D。（1）求A、B、C、D的坐标；（2）设点P(t，-t²+4t+5)在第一象限内，若△PAB的面积为24，求点P的坐标；（3）点M在第一象限内的抛物线弧CB上，过M作MN∥y轴交直线BC于点N，求MN的最大值及此时点M的坐标。作答区：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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