2026年八年级数学八年级下册期中模拟试卷（湖北专用版·学生练习版含答案详解与评分标准）

2026年八年级数学八年级下册期中模拟试卷（湖北专用版·学生练习版，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分注意事项：1.本卷为阶段性模拟测评，试题范围围绕八年级下册期中常见内容，重点考查二次根式、勾股定理、平行四边形及特殊平行四边形等知识的理解与运用。2.答题前请填写学校、班级、姓名和考号；选择题答案请填入答题栏，填空题只写最终结果，解答题须写出必要的计算、证明或说明过程。3.书写要清楚，作图或证明题要标明关键依据；本卷最后附参考答案、解析和评分标准，练习时建议先独立完成再核对。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。请将正确选项填入上方答题栏。1.式子√(x－2)在实数范围内有意义，则x的取值范围是（）A.x＞2B.x＜2C.x≥2D.x≤22.下列计算正确的是（）A.√12－√3=√3B.√8+√2=√10C.√(3×5)=√3+√5D.2√5－√5=23.下列各组数中，能作为直角三角形三边长的是（）A.4，5，6B.5，12，13C.6，8，9D.7，8，104.在平行四边形ABCD中，对角线AC、BD相交于点O。下列结论一定成立的是（）A.AC⊥BDB.AC=BDC.OA=OC，OB=ODD.∠ABC=∠BAD5.计算(√5+2)(√5－2)的结果是（）A.1B.3C.5D.96.矩形ABCD中，AB=6cm，BC=8cm，对角线AC、BD交于点O，则AO的长为（）A.4cmB.5cmC.6cmD.10cm7.菱形的一条对角线长为10cm，另一条对角线长为24cm，则它的边长为（）A.12cmB.13cmC.17cmD.26cm8.一架长5m的梯子斜靠在竖直墙上，梯脚离墙3m，若地面与墙面互相垂直，则梯子顶端离地面的高度为（）A.2mB.3mC.4mD.5m9.若a=√18，b=3√2，c=2√5，则a、b、c的大小关系是（）A.a＜b＜cB.a=b＜cC.c＜a=bD.b＜c＜a10.在平面直角坐标系中，平行四边形ABCD的顶点A(0，0)，B(6，0)，D(2，4)，则平行四边形ABCD的面积为（）A.20B.24C.28D.32二、填空题（本大题共6小题，每小题3分，共18分）请把正确答案直接写在题中横线上。11.（3分）化简：√50=________________。12.（3分）若a=√3+1，b=√3－1，则a²+b²=________________。13.（3分）直角三角形的两条直角边分别为9cm和12cm，则斜边长为________________cm。14.（3分）在平行四边形ABCD中，若∠A=70°，则∠B=________________°。15.（3分）矩形的一条边长为5cm，对角线长为13cm，则另一条边长为________________cm。16.（3分）四边形的两条对角线互相平分且互相垂直，则这个四边形是________________。三、解答题（本大题共10小题，共72分）解答应写出文字说明、证明过程或演算步骤。17.（6分）计算：（1）√27－2√12+√48；（2）(√5+√2)²－√40。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）已知x=√3+2，y=√3－2。求：（1）x+y；（2）xy；（3）x²+y²。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（7分）某社区准备在一块长方形活动场地内铺设一条从一个角到对角的直线健步道。已知长方形场地长24m，宽10m，健步道两端分别在长方形的一组对角处。

（1）求这条健步道的长度；

（2）若每铺1m需要材料费85元，材料费共需多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（7分）已知：在平行四边形ABCD中，E、F分别是AD、BC的中点。求证：四边形BEDF是平行四边形。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（7分）矩形ABCD中，AB=12cm，BC=5cm，对角线AC、BD相交于点O。

（1）求AC的长；

（2）求BO的长；

（3）说明△AOB是等腰三角形还是直角三角形，并写出理由。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（7分）已知m=√7+√3，n=√7－√3。

（1）求mn；

（2）求m²+n²；

（3）求m/n+n/m的值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（8分）某校园景观小品的平面轮廓为菱形ABCD，两条对角线AC、BD分别长16dm和12dm。

（1）求菱形的面积；

（2）求菱形的边长；

（3）若沿菱形四周安装装饰条，每分米装饰条费用为4元，至少需要多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（8分）矩形ABCD中，AB=12cm，AD=5cm，E是AB的中点，对角线BD的中点为O。

（1）求BD的长；

（2）求EO的长；

（3）请说明求EO时用到的几何依据。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（8分）学校劳动实践基地设计了一块直角三角形菜地ABC，其中∠C=90°，AC=18m，BC=24m。为了便于灌溉，计划从点C向边AB修一条垂直水渠CD，垂足为D。

（1）求AB的长；

（2）求水渠CD的长；

（3）若水渠每1.2m设置一个观察标记点，且两端点C、D不计入标记点，最多可设置多少个标记点？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.（8分）在平行四边形ABCD中，AB=10cm，AD=6cm，对角线BD=8cm。

（1）判断△ABD的形状，并说明理由；

（2）求平行四边形ABCD的面积；

（3）从点C作CE⊥BD，垂足为E，求CE的长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________备用演算区（可用于解答题补充作答）___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析本部分给出答案、关键步骤和评分标准。选择题、填空题重在结论正确；解答题既看结果，也看推理与书写过程。一、选择题答案与解析（每小题3分，共30分）题号12345678910答案CABCABBCBB1.【答案】C。【解析】二次根式√(x－2)有意义的条件是被开方数x－2≥0，因此x≥2。A项漏掉x=2，B、D项方向不符合非负条件。2.【答案】A。【解析】√12=2√3，所以√12－√3=√3。B项中√8=2√2，不能与√2相加成√10；C项应为√15；D项2√5－√5=√5。3.【答案】B。【解析】检验勾股关系：5²+12²=25+144=169=13²，所以5，12，13能构成直角三角形。其他选项平方和均不等于第三边平方。4.【答案】C。【解析】平行四边形的对角线互相平分，所以OA=OC，OB=OD。对角线垂直、相等不是一般平行四边形必有性质；相邻角通常互补而不一定相等。5.【答案】A。【解析】运用平方差公式：(√5+2)(√5－2)=(√5)²－2²=5－4=1。6.【答案】B。【解析】矩形对角线相等且互相平分。AC=√(6²+8²)=10cm，因此AO=AC/2=5cm。7.【答案】B。【解析】菱形对角线互相垂直平分，半对角线分别为5cm、12cm，边长为√(5²+12²)=13cm。8.【答案】C。【解析】梯子、墙、地面构成直角三角形，梯子为斜边。高度=√(5²－3²)=√16=4m。9.【答案】B。【解析】a=√18=3√2，b=3√2，所以a=b。c=2√5，比较平方：a²=18，c²=20，故a=b<c。10.【答案】B。【解析】AB在x轴上，AB=6；点D到AB所在直线的距离为4。平行四边形面积=底×高=6×4=24。二、填空题答案与解析（每小题3分，共18分）11.【答案】5√2。【解析】√50=√(25×2)=5√2。12.【答案】8。【解析】a+b=2√3，ab=(√3+1)(√3－1)=2。a²+b²=(a+b)²－2ab=(2√3)²－4=12－4=8。13.【答案】15。【解析】由勾股定理，斜边长为√(9²+12²)=√225=15。14.【答案】110。【解析】平行四边形邻角互补，∠A+∠B=180°，所以∠B=180°－70°=110°。15.【答案】12。【解析】设另一条边为x，则x²+5²=13²，x²=144，x=12。16.【答案】菱形。【解析】对角线互相平分的四边形是平行四边形；在此基础上对角线互相垂直，可判定为菱形。三、解答题参考答案、解析与评分标准（共72分）17.【参考答案与解析】（6分）（1）√27－2√12+√48=3√3－2×2√3+4√3=3√3－4√3+4√3=3√3。（2）(√5+√2)²－√40=5+2√10+2－2√10=7。评分标准：每小题3分。能正确化为最简二次根式得1分，合并或展开正确得1分，结果正确得1分。若因一个化简失误导致后续结果错误，按已体现的正确步骤酌情给分。易错点：√12应化为2√3，√48应化为4√3；(√5+√2)²中间项是2√10，不是√10。18.【参考答案与解析】（6分）x+y=(√3+2)+(√3－2)=2√3。xy=(√3+2)(√3－2)=3－4=－1。x²+y²=(x+y)²－2xy=(2√3)²－2×(－1)=12+2=14。评分标准：三问各2分。第（1）问写出合并同类根式并得2√3得2分；第（2）问能用平方差公式得1分，结果得1分；第（3）问公式或展开正确得1分，结果正确得1分。解析提示：本题可直接平方展开，也可利用完全平方关系，后者更简洁。19.【参考答案与解析】（7分）（1）长方形的一条对角线与长、宽构成直角三角形，健步道长为√(24²+10²)=√(576+100)=√676=26m。（2）材料费为26×85=2210元。评分标准：第（1）问5分，其中说明构成直角三角形得1分，列式24²+10²得2分，算出26m得2分；第（2）问2分，列式1分，结果1分。易错点：不能把长方形周长的一半当作对角线；单位应保持为米和元。20.【参考答案与解析】（7分）证明：因为四边形ABCD是平行四边