2026届安徽省九年级数学中考一模模拟试卷（含答案详解与评分标准）

2026届安徽省九年级数学中考一模模拟试卷（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：中考一模适用对象：2026届九年级注意事项：1．本卷为九年级数学中考一模阶段考前综合检测卷，满分120分，考试时间120分钟。2．答题前，请将学校、班级、姓名、考号填写完整；保持卷面整洁，书写规范。3．选择题每小题只有一个正确选项，请将答案填入选择题答题栏；填空题只填写最终结果。4．解答题应写出必要的文字说明、演算步骤或证明过程；仅写答案不得满分。5．作图题可使用铅笔，计算题可使用无编程、无存储功能的科学计算器。6．本卷覆盖数与式、方程与不等式、函数、图形性质、圆、统计与概率等一模复习核心内容。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=72分一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个正确选项。）1．在下列四个数中，比-1小的数是（）A．-3B．0C．1/2D．22．2025年某市新能源汽车登记量约为1380000辆，将1380000用科学记数法表示为（）A．1.38×10⁵B．1.38×10⁶C．13.8×10⁵D．0.138×10⁷3．用4个相同的小正方体搭成一个几何体：底层3个小正方体排成一行，最左边小正方体上再放1个。则从正面看该几何体得到的图形是（）A．三列，高度依次为2、1、1B．三列，高度均为1C．三列，高度依次为1、2、1D．两列，高度均为24．计算下列式子的结果：，正确的是（）A．-8a⁶b³B．8a⁵b³C．-6a⁶b³D．-8a⁶b5．一元二次方程x²-5x+6=0的两个根为（）A．1和6B．2和3C．-2和-3D．-1和-66．若点A(-2，y₁)，B(1，y₂)，C(3，y₃)都在反比例函数的图象上，则y₁、y₂、y₃的大小关系是（）A．y₂＞y₃＞y₁B．y₃＞y₁＞y₂C．y₁＞y₂＞y₃D．y₁＞y₃＞y₂7．两条平行直线被同一条截线所截，若一组同旁内角中的一个角为118°，则另一个角为（）A．52°B．62°C．72°D．118°8．一个不透明袋中有除颜色外完全相同的3个红球、2个黄球和1个蓝球，随机摸出1个球，摸到的球不是黄球的概率是（）A．1/3B．1/2C．2/3D．5/69．如图意描述：AB是⊙O的直径，点C在⊙O上，若∠ABC=35°，则∠AOC的度数为（）A．35°B．55°C．70°D．110°10．若二次函数的图象顶点为(1，-4)，且与y轴交于点(0，-3)，则该二次函数的解析式为（）A．y=x²-2x-3B．y=x²+2x-3C．y=-x²+2x-3D．y=x²-2x+3选择题答题栏：12345678910二、填空题（本大题共6小题，每小题3分，共18分。请把答案填写在相应位置。）11．分解因式：=________。12．不等式的解集是________。13．若x=2，y=-1，则的值为________。14．正六边形的内角和为________度。15．若反比例函数的图象经过点A(-2，3)，则比例系数k=________。16．半径为6cm、圆心角为120°的扇形面积为________cm²。（可列式为）111213141516三、解答题（本大题共6小题，共72分。解答应写出必要的过程。）17．（10分）计算与解方程。（1）计算：；（2）解方程：。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）如图意描述，在平行四边形ABCD中，E，F分别为AD，BC的中点，连接BE，DF，EF。（1）求证：四边形BFDE是平行四边形；（2）设BE与DF交于点O，求证：点O为BE和DF的共同中点。说明：作答时可依据平行四边形性质、中点定义、平行线判定与平行四边形对角线性质进行证明。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）某校九年级为了解学生中考一模阶段数学复习状态，从全年级随机抽取50名学生进行问卷调查。调查结果分为四类：A类“基础扎实且能独立完成压轴题”，B类“基础较好但综合题需训练”，C类“基础题稳定但运算易失分”，D类“基础薄弱需专项巩固”。统计如下表。类别ABCD人数1520105（1）分别求A类、C类学生在样本中所占百分比；（2）若全年级共有600名学生，估计A类和B类学生共有多少人；（3）从样本中的50名学生中随机抽取2人进行学习方法访谈，求抽到的2人都属于C类的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）某书店在一模阶段销售数学复习资料。每本进价为10元，计划以x元的价格销售，且12≤x≤25。根据以往数据，售价每提高1元，每天销售量比售价12元时减少4本；当售价为12元时，每天可销售80本。（1）用含x的式子表示每天销售量y；（2）设每天销售利润为W元，求W与x之间的函数关系式；（3）在给定价格范围内，售价定为多少元时每天销售利润最大？最大利润是多少元？提示：销售利润可用公式建模。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）在⊙O中，AB为直径，点C在⊙O上，点D在AB的延长线上，DC与⊙O相切于点C，连接AC，BC。已知AB=10，BD=8。（1）求证：OC⊥DC；（2）求切线段CD的长；（3）求△ABC的面积。可用关系：，并结合勾股定理与三角形面积公式。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）如图意描述，抛物线与x轴交于A(-1，0)，B(3，0)两点，与y轴交于C(0，3)。点P为抛物线上第一象限内一点，设点P的横坐标为t。（1）求该抛物线的解析式和顶点坐标；（2）用含t的式子表示△PAB的面积，并求面积的最大值；（3）若直线y=m与抛物线交于M，N两点，且MN=2，求m的值。设抛物线为：。作答区：_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析评分说明：选择题与填空题按最终答案给分；解答题按步骤给分，若