2026届湖北省九年级数学中考一模模拟试卷（含答案详解与评分标准）

第1页2026届湖北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分适用对象：2026届湖北省九年级中考一模阶段质量检测题号一二三总分得分注意事项：1．本卷共三大题、22小题，选择题10小题30分，填空题6小题18分，解答题6小题72分，合计120分。2．答题前请认真填写学校、班级、姓名和考号；作图题请使用铅笔先画，确认后再描清。3．选择题每题只有一个正确选项；填空题只写最终结果；解答题须写出必要的推理、计算或证明过程。4．本卷突出中考一模阶段的基础诊断、综合应用与考前复习反馈，答题时应注意规范书写和步骤完整。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，只有一项符合题意）1．在数-2，-√3，0，1/2中，最小的数是A．-2B．-√3C．0D．1/22．2025年某市新能源汽车年度充电量约为1.26×108千瓦时，将这个数还原成普通计数法是A．12600000B．126000000C．1260000000D．0.00000001263．如图形关系用文字表示：直线l截两条平行直线a，b，∠1与∠2是同旁内角。若∠1=58°，则∠2的度数为A．58°B．112°C．122°D．132°4．反比例函数y=k/x的图象经过点(-2,3)，则当x=3时，y的值为A．2B．-2C．6D．-65．关于x的一元二次方程x2-4x+m=0有两个相等的实数根，则m的值为A．-4B．0C．2D．46．一个不透明袋中有2个红球、3个白球，这些球除颜色外完全相同。从中不放回地连续摸出2个球，两个球都是红球的概率是A．1/5B．2/15C．1/10D．3/107．圆O的半径为5，弦AB到圆心O的距离为3，则弦AB的长为A．6B．8C．10D．128．二次函数y=-(x-1)2+4的图象，下列说法正确的是A．开口向上B．当x=1时，函数有最大值4C．对称轴是直线x=-1D．图象与y轴无交点9．某九年级数学一模小测成绩数据为：6分1人，7分2人，8分3人，9分2人，10分1人。关于这组数据，下列结论正确的是A．平均数是7.5B．中位数是9C．众数是7D．平均数与中位数都是810．已知m>0，关于x的方程x2-(m+1)x+m=0的两个根为x1，x2，且x12+x22=5，则m的值是A．1B．√5C．2D．5选择题作答栏：请将所选选项填入下表。题号12345678910答案二、填空题（本大题共6小题，每小题3分，共18分。请将答案直接填写在横线上）11．分解因式：x2-9=________________。12．在Rt△ABC中，∠C=90°，AC=6，tanA=4/3，则AB=________________。13．若α，β是方程x2-5x+2=0的两个实数根，则α2β+αβ2=________________。14．半径为6、圆心角为120°的扇形面积是________________。15．一次函数y=2x-1与y=-x+5的图象交点坐标是________________。16．用24米长的篱笆靠一面直墙围成一个矩形菜圃，篱笆只围另外三边，则菜圃面积的最大值为________________平方米。填空题作答栏：请按题号写出最终结果。题号111213141516答案三、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）本题考查实数运算与不等式组，是中考一模基础运算诊断题。（1）计算：(√12-√3)2+|1-√3|-2sin60°；（2）解不等式组：2x-1≤5，(x+2)/3>1。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）某校为了解2026届九年级学生在中考一模复习阶段整理数学错题的情况，随机抽取50名学生，统计其一周内整理错题的次数，结果如下表。组别A（0～1次）B（2次）C（3次）D（4次及以上）人数6141812（1）求D组在扇形统计图中对应的圆心角度数，并写出这组数据中出现次数最多的组别；（2）若该校九年级共有900名学生，估计一周内整理错题不少于3次的学生人数；（3）学校从甲、乙、丙、丁四名学生中随机选2名作复习经验交流，其中甲、乙为男生，丙、丁为女生，求选出的2名学生恰好一男一女的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）在平面直角坐标系中，一次函数y=ax+b的图象与反比例函数y=k/x的图象交于A(1,4)、B(4,n)两点，点A在反比例函数图象上。（1）求k、n及一次函数解析式；（2）结合图象，直接写出在x>0时不等式ax+b≥k/x的解集；（3）求△AOB的面积，其中O为坐标原点。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）如图形关系用文字表示：AB是⊙O的直径，点C在⊙O上，过点C作⊙O的切线l，点D在l上，且AD⊥l，连接AC、BC。（1）证明：∠DCA=∠ABC；（2）若AB=10，AC=6，求AD和CD的长；（3）在（2）的条件下，求△ACD的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）为服务2026届九年级中考一模后的阶段复习，某校准备购买A、B两类数学复习资料。已知购买A类资料30本、B类资料20本共需1240元；购买A类资料20本、B类资料30本共需1160元。（1）求A、B两类资料的单价；（2）若学校计划共购买100本资料，要求A类资料本数不少于B类资料本数的3/2，且总费用不超过2600元，求A类资料可购买的本数范围；（3）文印店推出一类“一模冲刺包”，每本进价为28元，原售价为36元。若每本售价提高p元，则预计销量为(90-3p)本，其中p为非负整数。求销售该冲刺包的最大利润。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）如图形关系用文字表示：在平面直角坐标系中，抛物线y=-x2+bx+c与x轴交于A(-1,0)、B(3,0)两点，与y轴交于点C，顶点为V。直线BC与抛物线围成中考一模综合探究图形。（1）求抛物线的解析式、点C坐标和顶点V坐标；（2）点P(t,-t2+2t+3)是第一象限内抛物线上的动点，过点P作PQ∥y轴交直线BC于点Q。求PQ的长度关于t的函数关系式，并求PQ的最大值；（3）当PQ取得最大值时，设R为抛物线对称轴上一点。求使PR+RQ最小的点R的坐标，并求此时四边形PBRQ中△BPQ的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________