2026届山东省九年级数学中考二模模拟试卷（含答案详解与评分标准）

2026届山东省九年级数学中考二模模拟试卷（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分注意事项：1．本卷为九年级数学中考二模考前综合检测卷，试题覆盖数与式、方程与不等式、函数、图形与几何、统计与概率、综合应用等内容。2．答题前请将学校、班级、姓名、考号填写清楚。选择题答案请填入答题栏，填空题直接写出结果，解答题须写出必要的文字说明、演算步骤或证明过程。3．全卷共三大题22小题。选择题10题，每题3分，共30分；填空题6题，每题3分，共18分；解答题6题，共72分。满分120分。4．计算结果需化为最简形式；涉及实际问题时，结果应符合实际意义；几何证明题应说明依据。题号一二三总分阅卷人得分一、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。请把正确选项填入下表。题号12345678910答案1．计算−22A．1B．−1C．5D．2．某种纳米材料的厚度约为0.00000072米，用科学记数法表示为（）A．7.2×10−6米B．7.2×10−73．如两条平行直线被一条截线所截，其中一个钝角为118∘A．28∘B．52∘C．624．不等式组2x−A．x≤3B．x>−5．二次函数y=xA．1B．−4C．4D．6．某学习小组8名同学一次限时训练的得分为7,A．9，10B．9.5，8C．9，8D．9.5，107．若两个相似三角形的相似比为3:2，较小三角形的面积为A．27B．18C．24D．368．分式方程2x−A．x=1B．x=29．点A,B在圆O上，直线PA与圆O相切于点A。若弦AB与切线PA所成的锐角∠A．40∘B．80∘C．10010．抛物线与x轴交于−1,0、3,0两点，且过点0A．x<−1或x>3B．x<−3二、填空题（本大题共6小题，每小题3分，共18分）请把正确结果直接填写在横线上。11．分解因式：x2−12．若a+b=5，ab13．半径为6、圆心角为120∘14．一个不透明袋中有2个红球、3个蓝球，这些球除颜色外完全相同。从中不放回地随机摸出2个球，摸出的2个球都是蓝球的概率为＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿。15．关于x的方程x2−4x+m16．已知点A2,3，B6,三、解答题（本大题共6小题，共72分）解答时应写出必要的文字说明、证明过程或演算步骤。17．（本题10分）（1）计算：18−（2）先化简，再求值：x2−4x答题区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）九年级二模前，某校对80名学生进行“数学核心知识模块掌握情况”抽样检测，按检测结果分为A、B、C、D四个等级，统计如下表。等级ABCD合计人数243216880百分比100%（1）补全表中A、B、C、D等级对应的百分比，并求D等级在扇形统计图中对应扇形的圆心角度数；（2）在A等级学生中，教师从5名候选学生甲、乙、丙、丁、戊中随机抽取2名进行复习经验分享。已知甲、乙、丙来自九年级1班，丁、戊来自九年级2班。求抽到的2名学生恰好来自不同班级的概率。答题区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）在△ABC中，点D,E分别在边AB,AC上，且（1）证明△A（2）求DE（3）求四边形DBC答题区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）二模后，学校计划在教学楼外墙边设置一个矩形复习展示区。展示区一边靠墙，另外三边用总长为48米的围栏围成。设垂直于墙的边长为x米，展示区面积为S平方米。（1）写出S关于x的函数关系式，并指出x的取值范围；（2）当展示区面积为256平方米时，求x的值及靠墙一边的长度；（3）在围栏长度不变的条件下，求展示区面积的最大值及此时展示区的尺寸。答题区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题14分）已知抛物线y=x2−4x+3与x轴交于点A,B，其中点A在点B的左侧，与（1）求点A,B（2）求直线BC（3）点P在抛物线上，横坐标为m，其中0<m<3。过点P作PQ∥y轴，交直线BC于点Q。求线段答题区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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