2026届上海市浦东新区九年级数学中考一模模拟试卷（含答案详解与评分标准）

2026届上海市浦东新区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分本卷用于九年级数学中考一模阶段复习检测。全卷共22题，选择题10题30分，填空题6题18分，解答题6题72分，合计120分。注意事项：1．答题前请填写学校、班级、姓名和考号；2．选择题每题只有一个正确选项；3．解答题应写出必要的文字说明、演算步骤或证明过程；4．作图、计算和推理应保持书写清楚，结果需化简；5．考试结束后请将试卷与答题纸一并交回。题型选择题填空题第17题第18题第19题第20题第21题第22题总分分值301881010121418120得分选择题答案填写区12345678910填空题作答区：11．__________12．__________13．__________14．__________15．__________16．__________一、选择题（本大题共10题，每题3分，共30分）下列各题的四个选项中，只有一个选项是正确的。请把正确选项填入上方答案填写区。1．下列实数中，属于无理数的是（）A．B．0.3131131113…（小数部分按规律延续）C．D．2．若代数式有意义，则实数的取值范围是（）A．B．C．且D．3．已知，化简的结果是（）A．B．C．D．4．一次函数的图像经过点和，则的值为（）A．1B．3C．5D．75．不等式组：，。它的解集是（）A．B．C．D．6．二次函数的顶点坐标是（）A．B．C．D．7．反比例函数的图像经过点。在每一个象限内，当增大时，的变化情况是（）A．随之增大B．随之减小C．先增大后减小D．无法确定8．在半径为5的圆中，弦AB的长为8，则圆心到弦AB的距离为（）A．2B．3C．4D．69．两个相似三角形的面积比为9:16，则它们的对应周长比为（）A．9:16B．3:4C．81:256D．4:310．一个不透明袋中有2个红球和3个白球，这些球除颜色外完全相同。从中一次摸出2个球，则至少摸到1个红球的概率为（）A．B．C．D．二、填空题（本大题共6题，每题3分，共18分）请将结果直接填写在答题区相应题号后，结果应化为最简形式。11．分解因式：________________。12．若方程有两个相等的实数根，则________________。13．一组数据为，则这组数据的方差是________________。14．一个正六边形的内角和为________________度。15．二次函数经过点和，则________________。16．小明在平地上观测旗杆顶端。点A、B与旗杆底部O在同一直线上，B在A、O之间，AB=10米。在A处测得顶端仰角为30°，在B处测得顶端仰角为45°，则旗杆高度为________________米。三、解答题（本大题共6题，共72分）解答应写出必要的文字说明、证明过程或演算步骤。每题后所留空白为学生作答区。17．（本题8分）计算与解方程。（1）计算：；（2）解方程：。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）已知关于的一元二次方程。（1）证明：无论实数m取何值，方程总有实数根；（2）若该方程的两个实数根均为正数，且两根之差的绝对值为3，求m的值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题10分）如条件所述，在△ABC中，点D在AB上，点E在AC上，DE∥BC，且AD:DB=2:3。已知△ADE的面积为12，BC=15，△ABC的周长为45。（1）求△ABC的面积；（2）求DE的长；（3）求四边形DBCE的周长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）某文具店销售一款九年级复习笔记本，每本进价为12元。市场调研发现，当每本售价为x元时，每日销量y（本）与售价x（元）之间近似满足一次函数关系：。（1）用含x的式子表示每日销售利润w（元）；（2）当售价为多少元时，每日销售利润最大？最大利润是多少元？（3）若店主希望每日销售利润不少于1800元，同时尽量降低售价以让利学生，求应定的最低售价。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题14分）在⊙O中，AB为直径，点C在圆上，AC=6，BC=8。过点C作⊙O的切线l，过点A作AD⊥l，垂足为D，连接OC。（1）求⊙O的半径；（2）求AD的长；（3）求△AOC的面积；（4）若点E在AB上，且CE平分∠ACB，求BE的长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本题18分）在平面直角坐标系xOy中，抛物线经过点、，与y轴交于点C。点P为该抛物线在第一象限内的一点，过点P作PD⊥x轴，垂足为D，连接PB、PC。（1）求抛物线的解析式及顶点坐标；（2）设点P的横坐标为t，求△PBC的面积S关于t的函数解析式，并求S的最大值；（3）若△PBC的面积为3，求点P的坐标；（4）设直线PB与y轴交于点E，且E在点C上方。当CE=9/2时，求点P的坐标。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与关键理由12345678910DBCBAAABBC1．答案D。关键理由：有理数包括整数、有限小数和无限循环小数，根号2不能化为两个整数之比，是无理数；根号9等于3，22/7为分数，均为有理数。2．答案B。关键理由：分母中的根式必须有意义且分母不为0，因此x+1必须大于0，所以x>-1；分子x-2不影响代数式是否有意义。3．答案C。关键理由：，再除以得。4．答案B。关键理由：两点纵坐标差为-4，横坐标差为2，所以k=-2；代入点(1,3)得b=5，故k+b=3。5．答案A。关键理由：第一个不等式解得x>2，第二个不等式解得x≥-3，取公共部分得到x>2。6．答案A。关键理由：，顶点为。7．答案A。关键理由：将点(-2,3)代入反比例函数，得m=-6。对于m<0的反比例函数，在每一个象限内y随x的增大而增大。8．答案B。关键理由：半径为5，弦长为8，半弦长为4。圆心、弦中点和弦端点构成直角三角形，距离为3。9．答案B。关键理由：相似三角形面积比等于相似比的平方。面积比为9:16，则对应边比为3:4，周长比也为3:4。10．答案C。关键理由：从5个球中摸出2个共有10种等可能组合；没有红球即两个都是白球共有3种组合，所以至少一个红球的概率为1-3/10=7/10。二、填空题答案与解析11．答案：。解析：寻找乘积为6、和为-5的两个数，得到-2和-3。12．答案：。解析：一元二次方程有两个相等实数根时，判别式为0，即36-4m=0，故m=9。13．答案：。解析：平均数为4，五个数据的离差平方和为4+0+0+1+1=6，方差为6/5。14．答案：。解析：n边形内角和为(n-2)×180°，正六边形的内角和为4×180°=720°。15．答案：。解析：两点(0,-3)、