1781059196255-2026年七年级数学七年级下册期中模拟试卷（全国版·原创命题A卷含答案详解与评分标准）

七年级数学七年级下册期中模拟试卷2026年七年级数学七年级下册期中模拟试卷（全国通用版·原创命题A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：七年级数学七年级下册期中阶段测评范围标签：全国通用版注意事项：1.本试卷共26题，满分120分。请在规定区域内作答，书写要清楚，步骤要完整。2.选择题每题只有一个正确选项；填空题只需填写最终结果；解答题必须写出必要的计算、推理或说明过程。3.本卷覆盖相交线与平行线、实数、平面直角坐标系、二元一次方程组及综合应用等内容，难度由基础到综合递进。4.允许使用直尺、三角板等常规作图工具，不得在试题区域之外标注与作答无关的信息。题型与分值结构题型题号题量每题分值合计选择题1—1010题3分30分填空题11—166题3分18分解答题17—2610题见各题72分全卷1—2626题—120分一、选择题（本大题共10小题，每小题3分，共30分）请把正确选项填入下方答题栏。题号12345678910答案1.在平面直角坐标系中，点P（-2，3）所在的象限是（）。A.第一象限B.第二象限C.第三象限D.第四象限2.25的算术平方根是（）。A.5B.-5C.±5D.6253.两条直线被第三条直线所截，如果有一组同位角相等，那么这两条直线（）。A.相交但不垂直B.互相垂直C.平行D.无法判断4.下列整数中，使n<√17<n+1成立的是（）。A.3B.4C.5D.65.二元一次方程组x-y=2，2x+y=7的解是（）。A.x=3，y=1B.x=1，y=3C.x=2，y=0D.x=4，y=-26.点A（-1，2）向右平移3个单位，再向下平移4个单位后得到点A′，则A′的坐标是（）。A.（-4，6）B.（2，6）C.（-4，-2）D.（2，-2）7.在下列数中，是无理数的是（）。A.√9B.-7/8C.0.2020020002…（相邻两个2之间0的个数逐次增加）D.1.358.若∠α与∠β互为补角，且∠α=118°，则∠β的度数为（）。A.28°B.52°C.62°D.72°9.某文具店中，5本同款练习本和3支同款中性笔共21元，3本同款练习本和5支同款中性笔共19元。设每本练习本x元、每支中性笔y元，列出的方程组正确的是（）。A.5x+3y=19，3x+5y=21B.5x+5y=21，3x+3y=19C.3x+5y=21，5x+3y=19D.5x+3y=21，3x+5y=1910.在坐标平面内，长方形ABCD的顶点为A（0，0）、B（6，0）、C（6，4）、D（0，4）。长方形EFGH的顶点为E（2，1）、F（5，1）、G（5，3）、H（2，3）。若阴影部分表示大长方形去掉小长方形后的区域，则阴影部分面积为（）。A.16B.18C.20D.24二、填空题（本大题共6小题，每小题3分，共18分）11.∛(-64)=__________。12.若∠A=35°20′，则∠A的补角为__________。13.若点M（a-2，a+1）在y轴上，则a=__________，点M的坐标为__________。14.方程组x+y=8，2x-y=1的解为__________。15.若n为正整数，且n<√50<n+1，则n=__________。16.点A（m，3）与点B（-2，n）关于x轴对称，则m=__________，n=__________。三、解答题（本大题共10小题，共72分）请写出必要的计算过程、推理依据或文字说明。17.（6分）计算与求值：（1）计算：√49+∛(-27)-|-5|；（2）求满足（x-1）²=16的x的值。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）解方程组：2x+y=13，3x-y=7。______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（6分）直线AB、CD被直线EF所截。已知∠1与∠2是一组同位角，∠1=68°，∠2=68°；∠3与∠2互为邻补角。（1）判断AB与CD的位置关系，并说明理由；（2）求∠3的度数。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（7分）某班准备购买练习本和圆珠笔作为数学活动奖品。购买3套练习本和2支圆珠笔共26元，购买2套练习本和5支圆珠笔共32元。设每套练习本x元，每支圆珠笔y元。（1）根据题意列出方程组；（2）求每套练习本和每支圆珠笔的单价；（3）若再购买4套练习本和6支圆珠笔，需要多少元？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（7分）在平面直角坐标系中，三角形ABC的三个顶点分别为A（-3，2）、B（1，2）、C（1，-1）。将三角形ABC向右平移5个单位，再向下平移3个单位，得到三角形A′B′C′。（1）写出A′、B′、C′的坐标；（2）求三角形ABC的面积；（3）判断点B′所在的象限。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（8分）某校七年级制作数学文化展示卡，计划购买正方形展示卡和长方形展示卡共40张。两种展示卡的单价与可展示题目数量如下表：展示卡类型单价每张可展示题目数正方形展示卡2元/张4题长方形展示卡3元/张6题若购买两种展示卡共花105元。（1）分别购买正方形展示卡和长方形展示卡多少张？（2）这些展示卡一共可以展示多少道题目？____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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__________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（8分）如文字示意：AB∥CD，点E在两条平行线之间，射线EA交AB于A，射线EC交CD于C。已知∠BAE=35°，∠DCE=65°。（1）过点E作一条与AB平行的辅助线，说明这条辅助线也与CD平行；（2）求∠AEC的度数；（3）若把条件改为∠BAE=x°，∠DCE=2x+5°，且∠AEC=95°，求x的值。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.（8分）综合应用：某校七年级设计一面数学文化长廊。长廊整体是长方形ABCD，坐标为A（0，0）、B（12，0）、C（12，6）、D（0，6），单位为米。在长廊中间留出矩形标语区MNPQ，坐标为M（2，1）、N（10，1）、P（10，3）、Q（2，3），其余区域铺设两种展示板。A类展示板每块面积1平方米，B类展示板每块面积2平方米，共需36块，恰好铺满其余区域。A类展示板每块12元，B类展示板每块18元。（1）求长廊整体面积和标语区面积；（2）求需要铺设展示板的面积；（3）列方程组求A类、B类展示板各需多少块；（4）求展示板总费用。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析本部分给出1—26题参考答案、关键步骤与评分标准。主观题评分时，在不改变数学含义的前提下，方法正确、步骤合理均可按相应采分点给分。一、选择题答案与解析（每题3分，共30分）题号12345678910答案BACBADCCDB1.点P的横坐标为负、纵坐标为正，符合第二象限点的坐标特征，故选B。A项要求横纵坐标均为正，C项要求均为负，D项要求横坐标正纵坐标负，均不符合。2.算术平方根是非负平方根，25的非负平方根为5，故选A。C项“±5”是平方根而不是算术平方根，B项符号错误，D项是25的平方。3.“同位角相等，两直线平行”是平行线判定定理之一，故选C。A、B没有必然性，D没有使用同位角相等这一判定条件。4.因为4²=16，5²=25，且16<17<25，所以4<√17<5，符合n=4，故选B。5.由x-y=2得x=y+2，代入2x+y=7，得2(y+2)+y=7，解得y=1，x=3，故选A。主要干扰项是把x、y位置互换。6.向右平移3个单位，横坐标加3；向下平移4个单位，纵坐标减4，得A′（-1+3，2-4）=（2，-2），故选D。7.0.2020020002…的小数位不循环且无限，是无理数，故选C。√9=3、-7/8、1.35均为有理数。8.互为补角的两个角和为180°，所以∠β=180°-118°=62°，故选C。A、B、D均没有满足两角和为180°。9.5本练习本和3支中性笔共21元，应列5x+3y=21；3本练习本和5支中性笔共19元，应列3x+5y=19，故选D。10.大长方形面积为6×4=24，小长方形面积为（5-2）×（3-1）=3×2=6，阴影面积为24-6=18，故选B。二、填空题答案与解析（每题3分，共18分）11.答案：-4。解析：因为（-4）³=-64，所以∛(-64)=-4。12.答案：144°40′。解析：补角和为180°。180°00′-35°20′=179°60′-35°20′=144°40′。13.答案：a=2，M（0，3）。解析：点在y轴上时横坐标为0，因此a-2=0，得a=2；代入纵坐标a+1=3，故M（0，3）。14.答案：x=3，y=5。解析：由x+y=8得y=8-x，代入2x-y=1，得2x-(8-x)=1，3x=9，x=3，y=5。15.答案：7。解析：因为7²=49，8²=64，且49<50<64，所以7<√50<8，故n=7。16.答案：m=-2，n=-3。解析：关于x轴对称的两点横坐标相同、纵坐标互为相反数，所以m=-2，n=-3。三、解答题答案、解析与评分标准（共72分）17.（1）√49=7，∛(-27)=-3，|-5|=5，所以√49+∛(-27)-|-5|=7-3-5=-1。（2）（x-1）²=16，所以x-1=±4，得x=5或x=-3。评分标准：第（1）问正确求出三个基本值各1分，合并结果1分，共4分；第（2）问写出x-1=±4得1分，求出两个解得1分，共2分。18.方程组为2x+y=13，3x-y=7。两式相加，得5x=20，所以x=4。将x=4代入2x+y=13，得8+y=13，所以y=5。原方程组的解为x=4，y=5。评分标准：正确选择加减消元并得到5x=20给2分；求出x=4给1分；代入求得y=5给2分；写出完整解并检验或说明给1分。19.（1）AB∥CD。理由：∠1与∠2是一组同位角，且∠1=∠2=68°，根据“同位角相等，两直线平行”，可判定AB∥CD。（2）∠3与∠2互为邻补角，所以∠3+∠2=180°。∠3=180°-68°=112°。评分标准：判定AB∥CD得1分；写出同位角相等、两直线平行的依据得2分；写出邻补角和为180°得1分；求得112°得2分。20.（1）根据题意列方程组：3x+2y=26，2x+5y=32。（2）由3x+2y=26可得15x+10y=130；由2x+5y=32可得4x+10y=64。两式相减，得11x=66，所以x=6。代入3x+2y=26，得18+2y=26，y=4。因此每套练习本6元，每支圆珠笔4元。（3）4套练习本和6支圆珠笔需要4×6+6×4=48元。评分标准：设未知数清楚给1分；列出方程组给2分；消元过程正确给2分；求出两种单价给1分；求得48元给1分。21.（1）向右平移5个单位，横坐标加5；向下平移3个单位，纵坐标减3。A′（2，-1），B′（6，-1），C′（6，-4）。（2）AB水平，长度为1-(-3)=4；BC竖直，长度为2-(-1)=3。三角形ABC是直角三角形，