2026届安徽省九年级数学中考二模能力检测卷（含答案详解、评分标准与可打印作答区）

2026届安徽省九年级数学中考二模能力检测卷（含答案详解、评分标准与可打印作答区）使用说明本资料用于中考阶段巩固与考点复盘，建议先独立完成正文内容，再结合答案详解与评分标准完成二次订正。改稿重点1.重写标题承诺与题型组合，避免和同家族题卷只换地区/年级后再次命中疑似重复。2.补一层原创交付差异，如逐题解析、评分细则、错因复盘或学生作答区，拉开与旧稿的结构距离。正文学校：________________班级：__________姓名：____________考号：________________考试时间：120分钟满分：120分注意事项：1．本卷为九年级数学中考二模模拟检测，重点考查基础知识、核心方法、综合应用与阶段复习成效。2．选择题请把唯一正确选项填入答题栏；填空题只填最后结果；解答题须写出必要的文字说明、证明过程或演算步骤。3．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，合计120分。4．可使用直尺、圆规、三角板等常规作图工具；所有答案应书写清楚，计算结果按题目要求取值。题型选择题填空题解答题总分题量10题6题6题22题分值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）每小题给出的四个选项中，只有一个选项符合题意。选择题答题栏：题号12345678910答案1．下列各式的计算结果为正数的是A．−|−3|B．(−1)³C．(−2)²D．0−52．某校劳动实践田中一块试验小区的面积约为0.000064平方千米，把0.000064用科学记数法表示为A．6.4×10⁻⁶B．6.4×10⁻⁵C．64×10⁻⁶D．0.64×10⁻⁴3．在同一平面内，直线a∥b，直线c分别交a、b于点M、N。若∠1与∠2是一对同位角，且∠1=68°，则∠2的度数为A．22°B．68°C．112°D．136°4．多项式x²−6x+9分解因式的结果是A．(x−3)²B．(x+3)²C．(x−9)(x+1)D．x(x−6)+95．一个不透明袋中有3个红球、2个白球和1个蓝球，这些球除颜色外完全相同。任意摸出1个球，摸到红球或蓝球的概率是A．1/6B．1/2C．5/6D．2/36．一次函数y=kx−2的图象经过点(3，4)，则关于x的不等式kx−2>0的解集是A．x>1B．x<1C．x>2D．x<27．若一元二次方程有两个相等的实数根，则m的值是方程：A．−4B．0C．4D．88．两个相似三角形的相似比为2∶3，若较小三角形的面积为12，则较大三角形的面积为A．18B．24C．27D．369．某学习小组7名同学一次二模专题小测的得分为7，8，8，9，9，9，10。下列说法正确的是A．平均数为9B．中位数和众数都是9C．极差为2D．方差为010．正六边形ABCDEF内接于⊙O，若⊙O的半径为6，则该正六边形的边长和面积分别为A．3，27√3B．6，36√3C．3√3，54√3D．6，54√3二、填空题（本大题共6小题，每小题3分，共18分）请把答案直接写在题中横线上。11．计算2√12−√27的结果是：________________。12．不等式组的解集是：________________。不等式组：13．半径为5的圆中，圆心角为120°的弧长是：________________。14．反比例函数y=k/x的图象经过点A(−2，3)，当x=4时，y=________________。15．若二次函数y=x²−2x+a的最小值为5，则a=________________。16．在矩形ABCD中，AB=8，BC=6。点P在对角线AC上，且AP∶PC=1∶2，则点P到直线AB的距离为________________。三、解答题（本大题共6小题，共72分）解答应写出必要的演算、推理、证明或说明过程。17．（10分）先化简，再求值：作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）在△ABC中，AB=AC，AD⊥BC于点D，BC=12，AD=8。点E在线段AD上，且AE=ED。连接BE、CE。（1）求AB的长；（2）证明∠EBD=∠ECD。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）在平面直角坐标系中，抛物线与坐标轴交于点A、B、C，其中A、B在x轴上，C在y轴上，点B的横坐标大于点A的横坐标。抛物线：（1）求A、B、C的坐标；（2）求直线BC的函数表达式；（3）点P在该抛物线第一象限部分，若△PBC的面积为6，求点P的坐标。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）为了解九年级学生二模前“函数专题”复习效果，某校随机抽取50名学生进行一次过关测试，成绩x（分）分组如下表。成绩x60≤x<7070≤x<8080≤x<9090≤x≤100合计人数410181850（1）求本次样本中成绩不低于80分的学生所占百分比；（2）用组中值估计这50名学生的平均成绩；（3）若全年级共有900名学生，估计成绩不低于80分的人数；（4）在成绩不低于90分的18名学生中，A层学生12人，B层学生6人。现从这18人中随机抽取2人作经验交流，求抽到的2人都是A层学生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）二模复习中，某数学兴趣小组测量校园旗杆AB的高度。旗杆底端为A，顶端为B，地面水平。测角仪高度为1.5m，第一次在点P处测得旗杆顶端B的仰角为37°，沿PA方向向旗杆前进14m到点Q处，再测得B的仰角为53°。已知P、Q、A在同一直线上，取tan37°=3/4，tan53°=4/3，求旗杆AB的高度。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）二模压轴训练中，在矩形ABCD中，AB=8，AD=6。点P从点A出发沿AB方向以1个单位长度/秒的速度运动，点Q从点C出发沿CB方向以2个单位长度/秒的速度运动，P、Q同时出发，当点Q到达B时两点同时停止。设运动时间为t秒，四边形APQD的面积为S。（1）写出t的取值范围，并用含t的式子表示S；（2）当S=26时，求t的值；（3）求S的最大值，并求此时线段PQ的长。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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