2026届西安市九年级数学学业水平模拟原创模拟试卷第045套（含答案详解与评分标准）

2026届西安市九年级数学学业水平模拟原创模拟试卷第045套（含答案详解与评分标准）考试时间：120分钟满分：120分题号范围：1—23题注意事项：1.本试卷为九年级数学学业水平模拟用卷，所有题目均须在规定位置作答；选择题用对应字母作答，填空题只写最后结果，解答题写出必要的计算、推理或证明过程。2.全卷共三大题、23小题。选择题8小题，每小题3分，共24分；填空题5小题，每小题3分，共15分；解答题10小题，共81分。3.书写应工整，作图可用铅笔先画再描清；涉及根式、分式、方程、函数、概率和几何证明时，应保留关键步骤。4.答题中可使用直尺、圆规、三角板等常规作图工具；不得把参考答案写在试题页作答区域内。题型一、选择题二、填空题三、解答题总分题号1—89—1314—231—23分值241581120得分一、选择题（本大题共8小题，每小题3分，共24分。每小题只有一个选项符合题意）1.在数−3，0，，−1中，绝对值最小的是（）A.−3B.0C.D.−12.计算的结果是（）A.B.C.D.3.点P(−2，3)关于x轴的对称点坐标是（）A.(2，3)B.(−2，3)C.(−2，−3)D.(2，−3)4.方程的两个根是（）A.1和6B.2和3C.−2和−3D.−1和−65.五名同学一次数学小测成绩分别为86，90，88，92，84，则这组数据的平均数是（）A.88B.89C.90D.926.将直线向上平移3个单位长度后得到的直线表达式是（）A.B.C.D.7.一个正六边形的内角和为（）A.360°B.540°C.D.900°8.二次函数的图象的顶点和开口方向分别是（）A.(−2，−1)，向上B.(2，1)，向下C.(2，−1)，向上D.(−2，1)，向下二、填空题（本大题共5小题，每小题3分，共15分。请把答案写在题中横线上）9.分解因式：=__________。10.当时，代数式的值为__________。11.在平面直角坐标系中，A(1，2)，B(5，5)，则线段AB的长为__________。12.不等式组的解集是__________。13.一个扇形的半径为，圆心角为，则该扇形的面积为__________。三、解答题（本大题共10小题，共81分。解答应写出文字说明、证明过程或演算步骤）14.（6分）计算：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________15.（6分）解分式方程：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16.（7分）某校九年级数学组对80名学生“每天体育活动时长”进行抽样调查，整理结果如下表。时长t（分钟）人数8283212（1）写出本次抽样调查的样本容量，并求“”这一组的频率；（2）若该校九年级共有960名学生，请估计每天体育活动时长不少于60分钟的学生人数；（3）在“”的8名学生中有男生5人、女生3人，随机抽取2人访谈，求恰好抽到1名男生和1名女生的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17.（7分）已知一次函数的图象经过点A(−1，5)和B(2，−1)。（1）求这个一次函数的表达式；（2）求该函数图象与x轴、y轴的交点坐标；（3）当该函数的函数值不小于直线的函数值时，求x的取值范围。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（8分）数学兴趣小组在西安市某广场测量一根竖直景观灯杆的高度。同一时刻，高的直立标杆在水平地面上的影长为，灯杆影长为。若需要从灯杆顶端拉一根电缆到地面固定点，固定点与灯杆底端的水平距离为。（1）求灯杆的高度；（2）求电缆的长度；（3）求电缆与地面所成锐角的正弦值。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（8分）一个盒中有四张形状、大小完全相同的数字卡片，卡片上的数字分别为。每次从盒中随机抽取一张，记录数字后放回，再随机抽取一张。设第一次抽到的数为a，第二次抽到的数为b，得到有序数对。（1）共有多少种等可能结果？（2）求的概率；（3）求点在抛物线上的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（9分）如图形条件所述：⊙O的半径为4，点P在圆外，PA、PB分别切⊙O于A、B两点，且。连接OA、OB、OP。（1）说明OP平分∠APB；（2）求OP和PA的长；（3）求四边形AOBP的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（10分）某班开展数学文化义卖活动，制作“西安城墙主题书签”。每件书签的成本为8元。根据试售记录，当售价为x元/件时，每天可售出()件，其中。设每天利润为W元。（1）写出W关于x的函数表达式；（2）售价定为多少元时，每天利润最大？最大利润是多少元？（3）若希望每天利润不低于900元，求售价x的取值范围。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（10分）如图形条件所述：在矩形ABCD中，，。点E在边AD上，，连接CE；从点B作，垂足为F；点P为线段CE上的动点。（1）求CE的长；（2）求BF的长；（3）当的面积为12时，求CP的长。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（10分）在平面直角坐标系中，抛物线经过、、三点。（1）求该抛物线的函数表达式；（2）若点P在抛物线位于x轴下方的部分上，求以AB为底的面积的最大值及此时点P的坐标；（3）若点Q在抛物线上且位于x轴下方，并且的面积为6，求点Q的坐标。__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________