2026届武汉市九年级数学中考一模模拟试卷（含答案详解与评分标准）

2026届武汉市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分注意事项：1．本试卷为九年级数学中考一模模拟卷，主要检测中考第一轮阶段复习质量。全卷共三大题，22小题，满分120分。2．选择题请把正确选项填入答题栏；填空题只写最后结果；解答题应写出必要的文字说明、证明过程或演算步骤。3．允许使用直尺、圆规、三角板等常规作图工具。不得在试卷上写与答题无关的内容。4．本卷中取π为精确符号；未说明取近似值的题目，结果可保留根号、分数或含π的形式。一、选择题（本大题共10小题，每小题3分，共30分）下列各题均有四个备选答案，其中只有一个是正确的。请把正确答案的字母填入答题栏。1．计算−3−A．−5B．−1C．12．武汉某区2026届九年级参加一模质量检测的学生约为42000人，将42000用科学记数法表示为（）A．4.2×103B．4.2×3．两条平行直线a，b被直线c所截，若其中一组同旁内角中较小的角为70∘A．20∘B．70∘C．1004．下列图形中，既是轴对称图形又是中心对称图形的是（）A．等边三角形B．一般平行四边形C．圆D．等腰梯形5．若关于x的一元二次方程x2−4x+mA．−4B．0C．2D．6．一个不透明袋中有3个红球、2个黑球，这5个球除颜色外完全相同。从袋中不放回地随机摸出2个球，恰好摸到2个红球的概率是（）A．310B．25C．37．反比例函数y=kx的图象经过点−2,3。若点3A．2B．−2C．6D．8．一组数据为8,A．20B．21C．643D．9．点P是圆O外一点，过点P作圆O的两条切线PA，PB，切点分别为A，B。已知PA=6，∠A．3B．6C．62D．10．二次函数y=x2−4xA．−3B．0C．−1选择题答题栏：1______2______3______4______5______6______7______8______9______10______二、填空题（本大题共6小题，每小题3分，共18分）请把答案直接填写在相应横线上。11．计算12−12．将x2−13．不等式组2x−14．在半径为3的圆中，圆心角为120∘15．将抛物线y=x2−2x−3向上平移m个单位后，所得抛物线与16．在矩形ABCD中，AB=6，BC=8。点P填空题答题栏：11__________12__________13__________14__________15__________16__________三、解答题（本大题共6小题，每小题12分，共72分）解答应写出必要的文字说明、证明过程或演算步骤。17．（12分）完成下列计算或求解。（1）计算：12（2）解一元二次方程：x2作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（12分）某校为了解九年级学生中考一模阶段数学复习情况，从全年级随机抽取40名学生的数学阶段检测成绩，按成绩x分为四个等级：A等级90≤x≤100，B等级80≤x<等级ABCD合计人数10m12640（1）求m的值，并求B等级在扇形统计图中所对应扇形的圆心角度数；（2）若全年级共有240名学生，请估计全年级成绩达到A等级或B等级的学生人数；（3）在样本的A等级学生中，有6名男生、4名女生。现从A等级学生中随机抽取2名学生进行复习经验交流，求抽到一名男生和一名女生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）如文字描述的图形：在矩形ABCD中，点E是边BC的中点，点F是边AD的中点，连接AE，（1）求证：四边形AEC（2）若AB=8，BC=作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）在圆O中，AB为直径，点C在圆O上，且AC=6，BC=8。过点C作圆O的切线l，过点B（1）求圆O的半径；（2）求证：△B（3）求BD作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（12分）某文具店销售一款中考错题整理本，每本进价为8元。市场调查发现：当每本售价为12元时，平均每天可售出100本；售价每提高1元，平均每天少售出5本。设每本售价为x元，其中12≤x≤22，平均每天销售量为y本，平均每天获得利润为（1）求y关于x的函数表达式；（2）求w关于x的函数表达式，并求平均每天利润的最大值；（3）若该店希望平均每天利润不低于700元，求每本售价x的取值范围。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（12分）如文字描述的平面直角坐标系：抛物线y=ax2+bx+c与x轴交于A−1,0，B3,0两点，与y轴交于C0,−3。点D为该抛物线的顶点。点P是抛物线在第四象限内的一点，过点P作（1）求抛物线的函数表达式及顶点D的坐标；（2）用含t的式子表示线段PE的长，并求△P（3）当△PBC的面积最大时，记此时点P为点M。求直线DM与x轴交点作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析一、选择题答案与关键解析1．答案：C。解析：−3=3，4=2．答案：B。解析：42000=4.2×100003．答案：D。解析：两条平行线被第三条直线所截，同旁内角互补。另一个角为180∘4．答案：C。解析：圆关于任意一条过圆心的直线对称，也关于圆心成中心对称。等边三角形不是中心对称图形，一般平行四边形不是轴对称图形，等腰梯形通常不是中心对称图形。5．答案：D。解析：一元二次方程有两个相等的实数根，则判别式Δ=0。由−42−4m6．答案：A。解析：从5个球中不放回摸2个球共有52=10种等可能结果；摸到2个红球共有32=7．答案：B。解析：将点−2,3代入y=kx，得k=−8．答案：C。解析：数据按从小到大排列为8,9,10,11,12,159．答案：B。解析：切线长定理得PA=PB=6。又∠AP10．答案：C。解析：y=x2−4x+3=x−2选择题评分标准：每小题3分，选对得3分，错选、多选或不选均不得分。二、填空题答案与解析11．答案：3。解析：12−1=2，12．答案：x+解析：利用平方差公式a2−b213．答案：−2解析：由2x−1≤5得x≤3；由x+14．答案：2π解析：弧长公式为l=nπr180。将n=12015．答案：4。解析：y=x2−2x−3=x−12−4。向上平移m16．答案：413解析：把点B关于直线AD对称到点B′。对任意点P在AD上，有PB=PB′，所以PB+PC=PB′+PC。当B′、填空题评分标准：每小题3分，结果正确得3分；形式等价的正确答案均可得分；结果中出现计算错误不得分。三、解答题答案、解析与评分标准17．答案与解析：（1）12−2=4，12=2原式为4−（2）x2−4x所以x−5=0或x