2026年高职单招数学招生考试模拟模拟试卷（含参考答案解析）

第页2026年高职单招数学招生考试模拟模拟试卷（含参考答案解析）学校：________________班级：________________姓名：________________考号：________________考试时间：120分钟满分：120分适用：高职单招科目：数学注意事项：1．本卷用于2026年高职单招数学招生考试模拟训练，满分120分，考试时间120分钟。请在规定时间内独立完成。2．选择题请将正确选项填入答题位置；填空题只写最终结果，结果应化简；解答题应写出必要的计算步骤、推理过程和结论。3．全卷题号为1—25题，题号连续。参考答案与解析单独分页，便于考后核对与教师讲评。4．作图、计算和文字说明均应清晰规范；使用草稿纸时，最终答案仍须写在试卷对应位置。一、选择题（本大题共10小题，每小题4分，共40分。在每小题给出的A、B、C、D四个选项中，只有一项符合题意。）1．已知集合，，则等于（）。A．B．C．D．2．设，，则的值是（）。A．B．C．D．3．一次函数，则的值为（）。A．B．C．D．4．方程的解为（）。A．或B．或C．或D．或5．不等式的解集是（）。A．B．C．D．6．等差数列首项a₁=5，公差d=-3，则第10项a₁₀为（）。A．22B．-20C．-22D．327．一个袋中有5个红球、3个蓝球，除颜色外完全相同。随机摸出1个球，摸到红球的概率为（）。A．B．C．D．8．点、所在直线的斜率为（），该直线可表示为（）。A．B．C．D．9．一个直角三角形的两条直角边分别为6和8，则它的面积为（）。A．B．C．D．10．二次函数的最小值为（）。A．B．C．D．二、填空题（本大题共5小题，每小题4分，共20分。请将正确答案填写在横线上。）11．计算：________________。12．方程的解是________________。13．一组数据2，4，5，10的中位数是________________。14．半径为的圆，其周长是________________。15．在直角三角形中，锐角满足，则________________。三、解答题（本大题共10小题，每小题6分，共60分。解答应写出文字说明、演算步骤或推理过程。）16．解二元一次方程组：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17．解方程，并写出该方程两个根的和与积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．某校为高职单招备考购买函数类、几何类两种练习册共60本。函数类每本18元，几何类每本22元，总费用为1200元。求两类练习册各购买多少本；若每本另需3元装订费，全部练习册的总支出是多少元？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．已知等差数列中，，。求公差、第10项以及前10项和。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．已知二次函数。（1）用配方法写出顶点式，并求函数的最大值；（2）求不等式的解集。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．一架长10米的梯子斜靠在竖直墙上，梯脚离墙6米。（1）求梯子顶端离地面的高度；（2）设梯子与地面所成锐角为，求和；（3）若梯脚向墙移动2米，梯子顶端升高多少米？结果可保留根号。_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24．某班10名学生一次数学小测成绩如下表。求这10名学生成绩的平均数、中位数、极差，并求成绩不低于80分的比例。成绩（分）7075808590人数12421________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25．某文具店购进A、B两种签字笔共40支，其中A种进价每支3元，B种进价每支5元，总进价为160元。A种售价每支4元，B种售价每支7元。（1）求A、B两种签字笔各购进多少支；（2）全部售出后总利润是多少元；（3）若将总利润的用于班级公益活动，剩余利润是多少元？_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________