2025-2026学年人教版七年级数学下册期末模拟试卷（含答案详解与评分标准）第350套

2025-2026学年人教版七年级数学下册期末模拟试卷（含答案详解与评分标准）第350套学校：____________________班级：____________姓名：____________考号：____________考试时间：90分钟满分：120分注意事项：1．本试卷为七年级数学下册期末综合检测，试题覆盖相交线与平行线、实数、平面直角坐标系、二元一次方程组、一元一次不等式与不等式组、数据的收集整理与描述等内容。2．请将选择题答案填在答题表中，填空题和解答题写在相应位置；解答题应写出必要的计算过程、推理依据和结论。3．全卷共26题，选择题12题共36分，填空题6题共18分，解答题8题共66分，总分120分。4．作图、列表或说明时，要求书写工整、步骤清楚；答案中含单位时应写明单位。本卷分值结构题型题号分值作答要求选择题1—1236分选出唯一正确答案，填入答题表填空题13—1818分只填写最终结果，注意单位和坐标格式解答题19—2666分写出必要步骤、理由和结论，按评分点给分选择题答题表题号123456789101112答案一、选择题（本大题共12小题，每小题3分，共36分。每小题只有一个选项符合题意）1．在平面直角坐标系中，点位于（）A．第一象限B．第二象限C．第三象限D．第四象限2．下列各数中，是无理数的是（）A．B．C．D．3．二元一次方程组的解是（）A．B．C．D．4．不等式的解集是（）A．B．C．D．5．两条平行直线被一条截线所截，若与一个的角是同位角，则的度数为（）A．B．C．D．6．将点向左平移3个单位，再向上平移5个单位，得到点的坐标是（）A．B．C．D．7．一组数据的众数和中位数分别是（）A．8，7B．7，7C．8，8D．7，88．若，则下列变形一定正确的是（）A．B．C．D．9．二元一次方程的正整数解的个数是（）A．1B．2C．3D．410．下列调查中，适合采用全面调查的是（）A．了解本班每名同学的身高B．了解某城市一天内各路段空气质量C．检测一批灯泡的使用寿命D．了解全国七年级学生每天阅读时间11．若与互为邻补角，且，则的度数为（）A．B．C．D．12．文具店中笔记本每本4元，签字笔每支2元。小华共买8件，付款20元，若买笔记本本、签字笔支，则的值为（）A．2B．4C．6D．8二、填空题（本大题共6小题，每小题3分，共18分。请把答案填写在题中横线上）13．点到轴的距离是__________。14．计算：＝__________。15．若，则＝__________。16．不等式组的整数解有__________个。17．三角形的顶点，，。若点平移后对应点为，则点对应点的坐标为__________。18．七（1）班40名学生参加期末体育测试，其中“优秀”等级占，则“优秀”等级人数为__________人。三、解答题（本大题共8小题，共66分。解答应写出文字说明、证明过程或演算步骤）19．（8分）计算与解方程。（1）；（2）解方程：。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（8分）解下列方程组或不等式组。（1）；（2）。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（8分）在平面直角坐标系中，已知，，。（1）求三角形ABC的面积；（2）将三角形向右平移4个单位、向下平移2个单位，写出的坐标；（3）判断点是否在边上，并说明理由。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（8分）如图可按下列文字描述理解：直线被截线所截，与是同旁内角，且，；在直线上，与互为邻补角。（1）判断直线a与直线b的位置关系，并说明理由；（2）求的度数；（3）若直线与直线相交形成的一个角等于，并且这个角与是同位角，判断直线与直线的位置关系，并说明理由。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23．（8分）为了解七年级学生期末体育兴趣项目选择情况，某校随机抽取40名七年级学生进行调查，得到如下统计表。项目跳绳篮球跑步足球人数12a106（1）求表中的值；（2）求选择“篮球”的学生所占百分比，并求其在扇形统计图中对应的圆心角度数；（3）若七年级共有420名学生，请估计选择“跳绳”的学生人数；（4）说明本次抽样要怎样做才更合理。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24．（8分）小明准备购买钢笔和笔记本。钢笔每支8元，笔记本每本5元。小明带了90元，计划买6支钢笔，并希望付款后至少剩10元，同时笔记本不少于3本。（1）设购买笔记本本，列出关于的不等式组；（2）求的整数取值；（3）小明最多可以买多少本笔记本？解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25．（9分）学校为七年级期末复习购买两种数学练习册，基础型每套16元，提高型每套22元。第一次共购买50套，合计花费920元。（1）第一次基础型和提高型各购买多少套？（2）第二次仍购买50套，要求基础型套数不少于提高型套数的2倍，且总费用不超过880元。求第二次提高型最多可购买多少套。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26．（9分）如图可按坐标描述理解：在平面直角坐标系中，，，，动点在轴上。（1）求三角形的面积；（2）若三角形的面积为6，求的值；（3）若点在线段上，且三角形的面积不小于三角形的面积，求的取值范围。解：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析及评分标准一、选择题答案（每小题3分，共36分）题号123456789101112答案BCCABADACABA1．B。横坐标为负、纵坐标为正，点在第二象限。本题3分。2．C。不能化成有限小数或无限循环小数，是无理数；其余三个数均为有理数。本题3分。3．C。由，相加得，，再得。本题3分。4．A。，移项得，所以。本题3分。5．B。两直线平行，同位角相等，所以。本题3分。6．A。横坐标，纵坐标，所以。本题3分。7．D。7出现3次，次数最多，众数为7；从小到大排列为，中位数为8。本题3分。8．A。不等式两边同时加同一个数，不等号方向不变；乘以负数时方向改变，所以B错误，C、D方向也不对。本题3分。9．C。取正整数且，可取，对应为，共3个。本题3分。10．A。本班人数少、对象明确，适合逐个调查；其余调查对象范围大或检测具有破坏性，适合抽样调查。本题3分。11．B。邻补角和为，，得，。本题3分。12．A。由，化简得，两式相减得。本题3分。二、填空题答案（每小题3分，共18分）题号131415161718答案13．5。点到轴的距离等于横坐标绝对值，。本题3分。14．1。，，所以结果为1。本题3分。15．。由，解得，，所以。本题3分。16．2。由得，由得，