2026年七年级数学七年级月度质量检测质量检测卷（湖南专用版·基础巩固卷含答案详解与评分标准）

2026年七年级数学七年级月度质量检测质量检测卷（湖南专用版·基础巩固卷，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分适用范围：湖南专用版·基础巩固卷考查内容：七年级阶段数学基础内容，侧重有理数与整式、一次方程、线段与角、简单数据整理及数学应用。题号一二三总分得分注意事项1.本卷共三大题，26小题。选择题1-10题，每题3分；填空题11-16题，每题3分；解答题17-26题，共72分。2.请认真审题，书写过程要清楚。解答题应写出必要的计算、推理、作图说明或列式过程。3.选择题请将答案填入答题栏；填空题直接填写结果；解答题在相应作答区内完成。4.不得在试题主体中书写与答题无关内容，作答时注意单位、符号、步骤和结论完整。选择题答题栏题号12345678910答案一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个选项符合题意）1.-2的相反数是（）A.-2B.2C.1/2D.-1/22.已知a=-4，b=3，则a-b的值为（）A.-7B.-1C.1D.73.某校七年级参加一次校园跑活动的人数约为1320人，将1320用科学记数法表示为（）A.1.32×10²B.13.2×10²C.1.32×10³D.0.132×10⁴4.方程3x-5=10的解是（）A.x=3B.x=4C.x=5D.x=155.下列式子中，是单项式的是（）A.x+1B.2a²bC.m/nD.3x-2y6.数轴上点A表示-2，点B表示4，则线段AB的中点表示的数是（）A.-3B.-1C.1D.37.化简2(3x-1)-(x+4)的结果为（）A.5x-6B.5x+2C.7x-6D.6x-28.计算43°28′+16°45′的结果是（）A.59°73′B.60°13′C.60°73′D.59°13′9.已知点C在线段AB上，AB=12cm，且AC:CB=1:2，则AC的长为（）A.3cmB.4cmC.6cmD.8cm10.若m与n互为相反数，p与q互为倒数，则2(m+n)-3pq的值为（）A.-3B.-1C.0D.3二、填空题（本大题共6小题，每小题3分，共18分。请把答案填写在横线上）11.|-7|=__________。12.单项式-3x²y³的次数是__________。13.若x=2是方程5x-a=3的解，则a=__________。14.计算72°36′÷3=__________。15.某地早晨气温为-2℃，中午升高7℃，傍晚又下降4℃，则傍晚气温为__________℃。16.点M是线段AB的中点，AB=18cm，点C在线段MB上，MC=2cm，则BC=__________cm。三、解答题（本大题共10小题，共72分。请写出必要过程与结论）17.（6分）计算下列各题。（1）-12+7-(-5)-8；（2）2²×(-3)+18÷(-6)。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）先化简，再求值：3(2x-1)-2(x+5)，其中x=3。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（7分）解下列方程。（1）4x-7=2x+5；（2）(x-1)/2+(x+2)/3=5。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（7分）如图意描述：点O在直线AB上，射线OC在直线AB上方，∠AOC=58°，OD平分∠BOC。求∠COD的度数，并说明理由。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（8分）某校七年级四个班开展“绿色校园”塑料瓶回收活动，统计如下表。班级701班702班703班704班人数42404543回收瓶数252260270258（1）求四个班共回收塑料瓶多少个；（2）分别计算701班和702班的人均回收瓶数，并判断这两个班中哪个班人均回收较多；（3）若每个塑料瓶可兑换0.08元公益基金，四个班共可兑换多少元？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（8分）七年级组织研学活动，37名学生乘车。现有小车和中巴两种车，小车每辆可坐4人，租金80元；中巴每辆可坐7人，租金120元。若共租7辆车且恰好坐满，求小车和中巴各租多少辆，并计算总租金。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（8分）劳动课上，七年级同学整理一块长方形菜地。已知菜地的长比宽多8m，周长为80m。（1）设菜地的宽为xm，用含x的式子表示菜地的长；（2）列方程求菜地的长和宽；（3）若每平方米需施肥0.5kg，整块菜地需施肥多少千克？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（8分）用火柴棒按下列方式摆成一排相邻的正方形：1个正方形用4根，2个相邻正方形用7根，3个相邻正方形用10根。（1）摆成n个相邻正方形需要多少根火柴棒；（2）摆成20个相邻正方形需要多少根；（3）若正好有2026根火柴棒，能摆成多少个相邻正方形？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（7分）一条步道上有甲、乙两地，相距1200m。小明从甲地出发向乙地行走，速度为80m/min；小华从乙地出发向甲地行走，速度为70m/min。（1）若两人同时出发，几分钟后相遇；（2）若小华先出发2min，小明再出发，求小明出发后几分钟两人相遇，并求此时小明行走的路程。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.（7分）在数轴上，点A表示-6，点B表示10。点P从A出发以每秒2个单位长度的速度向右运动，点Q从B出发以每秒1个单位长度的速度向左运动，P、Q同时出发。（1）出发2秒后，点P、点Q分别表示什么数，PQ的长度是多少；（2）几秒后P、Q相遇；（3）几秒后PQ=4？_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析说明：评分时以步骤、结论和书写规范为主要依据。若解法合理、过程完整且结果正确，可按相应采分点给分。一、选择题答案与解析（每小题3分，共30分）1.答案：B。解析：相反数是只有符号不同的两个数，-2的相反数为2。A项仍为-2，C、D项是倒数相关形式，不符合题意。评分标准：选对得3分，未选、错选或多选不得分。2.答案：A。解析：a-b=-4-3=-7。易把减去正数看成加正数而得到-1，应注意减法转化为加相反数。评分标准：选对得3分，未选、错选或多选不得分。3.答案：C。解析：科学记数法写成a×10ⁿ，其中1≤a<10。1320=1.32×10³，指数3表示小数点向右移动3位。评分标准：选对得3分，未选、错选或多选不得分。4.答案：C。解析：由3x-5=10，得3x=15，所以x=5。检验：3×5-5=10，成立。评分标准：选对得3分，未选、错选或多选不得分。5.答案：B。解析：单项式是数与字母乘积的形式，2a²b符合。A、D是多项式，C含字母分母，在七年级整式范围内不作为单项式。评分标准：选对得3分，未选、错选或多选不得分。6.答案：C。解析：中点表示的数为(-2+4)/2=1。也可理解为从-2到4相距6个单位，中点向右3个单位，到1。评分标准：选对得3分，未选、错选或多选不得分。7.答案：A。解析：2(3x-1)-(x+4)=6x-2-x-4=5x-6。括号前是减号时，去括号后x和4都要变号。评分标准：选对得3分，未选、错选或多选不得分。8.答案：B。解析：43°28′+16°45′=59°73′。因为60′=1°，所以59°73′=60°13′。A项未进位。评分标准：选对得3分，未选、错选或多选不得分。9.答案：B。解析：AC:CB=1:2，线段AB分成3等份，每份12÷3=4cm，AC占1份，故AC=4cm。评分标准：选对得3分，未选、错选或多选不得分。10.答案：A。解析：m与n互为相反数，所以m+n=0；p与q互为倒数，所以pq=1。原式=2×0-3×1=-3。评分标准：选对得3分，未选、错选或多选不得分。二、填空题答案与解析（每小题3分，共18分）11.答案：7。解析：绝对值表示数到原点的距离，|-7|=7。评分标准：结果正确得3分。12.答案：5。解析：单项式-3x²y³中，字母指数和为2+3=5，所以次数为5。评分标准：填5得3分。13.答案：7。解析：把x=2代入5x-a=3，得10-a=3，所以a=7。评分标准：代入思路正确且结果为7得3分。14.答案：24°12′。解析：72°36′÷3可分别计算，72°÷3=24°，36′÷3=12′，结果为24°12′。评分标准：结果正确得3分。15.答案：1。解析：傍晚气温=-2+7-4=1℃。评分标准：列式或结果正确得3分。16.答案：7。解析：M是AB中点，MB=18÷2=9cm。C在线段MB上且MC=2cm，所以BC=9-2=7cm。评分标准：求出MB得1分，求出BC得2分。三、解答题答案、解析与评分标准（共72分）17.计算下列各题。（1）-12+7-(-5)-8=-12+7+5-8=(-12-8)+(7+5)=-20