2026届九年级数学中考冲刺模拟试卷（含答案详解与评分标准）

2026届九年级数学中考冲刺模拟试卷（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分适用年级：九年级考试节点：中考冲刺注意事项1．本卷为2026届九年级数学中考冲刺阶段模拟检测，满分120分，考试时间120分钟。2．全卷共三大题22小题：选择题10题共30分，填空题6题共18分，解答题6题共72分。3．作答选择题时，请把正确选项填在括号内；作答填空题时，请把结果写在横线上。4．解答题必须写出必要的文字说明、计算过程、推理过程或作图依据，只写最后结果不得满分。5．本卷适合考前综合诊断与阶段复习使用，重点考查数与式、方程与不等式、函数、几何、统计概率及综合应用能力。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．计算的结果是（）A．8B．10C．18D．-82．若，且，则下列结论一定成立的是（）A．a+c<b+cB．ac<bcC．a-c<b-cD．a/c>b/c3．2026年某市预计参加中考人数约为人，把这个数写成普通数是（）A．8640B．86400C．864000D．0.0008644．如一组数据表示某小组5名同学一次数学限时训练的得分等级，则这组数据的中位数和众数分别是（）A．7，7B．7，8C．8，7D．8，85．若分式有意义，则化简后的结果为（）A．x+3，且x≠3B．x-3，且x≠-3C．x+3，且x≠-3D．x-3，且x≠36．在一个不透明袋中有3个红球、2个白球和1个黄球，除颜色外完全相同。随机摸出1个球，摸到白球的概率是（）A．1/6B．1/3C．1/2D．2/37．在圆O中，AB是直径，点C在圆上，若，则的度数是（）A．35°B．55°C．70°D．110°8．关于x的一元二次方程有两个相等的实数根，则m的值是（）A．-4B．0C．4D．89．二次函数中。下列说法正确的是（）A．图象开口向上B．当x=1时，y取得最大值3C．对称轴是直线x=-1D．函数没有最大值10．反比例函数（x>0）与一次函数的交点为A(1，4)、B(4，1)，则的面积是（）A．6B．7.5C．8D．10二、填空题（本大题共6小题，每小题3分，共18分）11．分解因式：____________________。12．若，且，则的值为____________________。13．在10张形状、大小完全相同的卡片中，有2张写有“基础”、3张写有“提升”、5张写有“综合”。随机抽取1张，抽到不是“综合”的概率为____________________。14．在平面直角坐标系中，点A(-2，3)，B(4，-1)，则线段AB的中点坐标为____________________。15．一个圆锥的底面半径为3cm，母线长为5cm，则该圆锥的侧面积为____________________cm²。16．二次函数在上的最大值为____________________。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、演算步骤或推理过程）17．（10分）本题考查实数运算与不等式组，是中考冲刺阶段的基础计算检测。（1）计算：；（2）解不等式组：，。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）某校九年级在中考冲刺复习中开展“错题整理习惯”调查，随机抽取50名学生，统计他们一周内整理数学错题的次数，结果如下表。整理次数0次1次2次3次4次人数4815185（1）求这50名学生一周内整理数学错题次数的平均数、众数和中位数；（2）若该校九年级共有900名学生，请估计一周内整理错题不少于3次的学生人数；（3）从整理4次的5名学生中选取2名进行经验交流。已知其中男生3名、女生2名，求恰好选到1名男生和1名女生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）已知一次函数的图象经过点A(-2，5)和点B(4，-1)。（1）求这个一次函数的表达式；（2）设该图象与x轴、y轴分别交于C、D两点，求的面积；（3）点P在x轴正半轴上，若与的面积相等，求点P的坐标。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）在中，AB=AC，D是BC的中点。点E在AC上，过点E作EF∥BC，交AB于点F。已知AB=10，BC=12，AE:EC=2:3。（1）证明：；（2）求EF和AF的长；（3）连接DF，求的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）某文具店为服务九年级中考冲刺复习，印制一套数学模拟试卷。已知每套成本为6元，按每套10元销售时，每日可售出100套。市场调查发现：售价每提高1元，每日销量减少5套。设每套提高售价x元，且x为非负数。（1）用含x的式子表示每日销量q和每日利润P；（2）若要求每日销量不低于70套，求每日利润的最大值；（3）在每日销量不低于70套的前提下，若要求每日利润不低于640元，求x的取值范围。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）在平面直角坐标系中，抛物线与x轴交于A、B两点（A在B的左侧），与y轴交于C点，顶点为D。（1）求A、B、C、D的坐标；（2）点P在抛物线对称轴上且位于x轴上方，若，求点P的坐标；（3）过点P作直线l∥AC，直线l交抛物线于M、N两点，求MN的长；（4）在x轴上是否存在点Q，使以A、C、D、Q为顶点的四边形为平行四边形？若存在，求点Q坐标；若不存在，请说明理由。作答区：___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案速查题号12345678910答案ABBAABCCBB二、选择题解析与评分标准1．答案：A。原式中，，，所以结果为9-5+4=8。四个选项中只有A与计算结果一致。评分标准：选A得3分；选错、多选或不选均得0分。2．答案：B。由不等式性质可知，不等式两边同时加同一个数，方向不变；同时减同一个数，方向也不变；但同时乘或除以负数时，不等号方向改变。因为且，所以。评分标准：选B得3分；若因未注意负数乘法方向改变而选错，得0分。3．答案：B。科学记数法表示把8.64的小数点向右移动4位，得到86400。A少移动一位，C多移动一位，D方向相反。评分标准：选B得3分；其他选项不得分。4．答案：A。将数据从小到大排列仍为6，7，7，8，10。第3个数是7，所以中位数是7；出现次数最多的数也是7，所以众数是7。评分标准：选A得3分；若只判断出其中一个统计量但选项错误，得0分。5．答案：A。分式有意义的条件是分母不为0，即x≠3。分子，约去公因式x-3后得x+3，但原分式的限制条件仍为x≠3。评分标准：选A得3分；只化简为x+3但遗漏限制条件对