2025-2026学年八年级数学八年级下册期末模拟试卷（福建专用版·基础巩固卷含答案详解与评分标准）

2025-2026学年八年级数学八年级下册期末模拟试卷（福建专用版·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：福建专用版·八年级下册期末基础巩固题型选择题填空题解答题总分分值30分18分72分120分注意事项与答题要求1.本试卷共26题，分为选择题、填空题和解答题三部分，满分120分，考试时间120分钟。2.答题前请将学校、班级、姓名、考号填写清楚；客观题答案填入答题栏，主观题写出必要的计算、推理或证明过程。3.作图、计算和证明应书写规范，结果能化简的必须化为最简形式；无特殊说明时，取值范围按题意确定。4.试题范围以八年级下册期末基础内容为主，覆盖二次根式、勾股定理、平行四边形及特殊平行四边形、一次函数、数据分析等内容。选择题答题栏（请将正确选项填入对应题号下方）：题号12345678910答案一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个正确选项）1.（3分）下列二次根式中，化简结果为3√2的是（）。A.√6B.√12C.√18D.√272.（3分）在直角三角形中，两条直角边长分别为6和8，则斜边长为（）。A.9B.10C.12D.143.（3分）若一次函数y＝-2x＋3，当x＝1时，y的值是（）。A.-5B.-1C.1D.54.（3分）平行四边形ABCD中，∠A＝70°，则∠C的度数为（）。A.70°B.90°C.110°D.140°5.（3分）一组数据6，8，8，10，13的中位数是（）。A.8B.9C.10D.136.（3分）计算√12－√3的结果是（）。A.√3B.2√3C.3√3D.97.（3分）一次函数y＝kx＋b的图象经过点(0，2)和(1，5)，则k的值为（）。A.-3B.2C.3D.58.（3分）矩形的一条对角线长为10，一条边长为6，则另一条边长为（）。A.4B.6C.8D.169.（3分）某水池原有水20m³，开始匀速注水，每分钟增加3m³。若注水x分钟后水量为ym³，则y与x之间的函数关系式是（）。A.y＝3xB.y＝20x＋3C.y＝20＋3xD.y＝23x10.（3分）菱形的两条对角线长分别为6和8，则该菱形的周长为（）。A.14B.20C.24D.48二、填空题（本大题共6小题，每小题3分，共18分）11.（3分）若a≥0，则√(25a²)＝____________12.（3分）一次函数y＝mx－1的图象经过点(2，5)，则m＝____________13.（3分）某同学三次数学小测成绩分别为80分、90分、x分，平均分为85分，则x＝____________14.（3分）正方形的对角线长为4√2，则它的边长为____________15.（3分）平行四边形相邻两个内角的度数之比为2∶3，则较小的内角为____________16.（3分）直角三角形两条直角边长分别为9和12，则斜边上的高为____________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）计算并化简：

（1）√48－3√12＋√27；

（2）(√5＋2)²－(√5－1)(√5＋1)。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）已知一次函数的图象经过A(2，5)、B(-1，-1)两点。

（1）求这个一次函数的表达式；

（2）求该函数图象与x轴的交点坐标；

（3）求它与两坐标轴围成的三角形面积。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（7分）某校八年级开展“基础计算能力”竞赛，甲、乙两组各6名同学成绩如下：

甲组：78，82，85，85，90，90；

乙组：75，80，85，87，90，93。

（1）分别求两组成绩的平均数和中位数；

（2）分别求两组成绩的方差；

（3）从稳定性角度分析哪一组成绩更稳定。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（7分）如图形关系所述：在平行四边形ABCD中，E、F分别是AD、BC的中点。

（1）求证：DE＝BF；

（2）求证：四边形EBFD是平行四边形；

（3）若∠DAB＝60°，AD＝6，AB＝10，说明四边形EBFD的一组相邻边长度。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（7分）某公园准备在一块长方形草坪ABCD中铺设从A到C的直线步道。已知AB＝60m，BC＝80m。

（1）求直线步道AC的长度；

（2）若原来从A到C需沿AB、BC两边行走，改走直线步道可少走多少米；

（3）若铺设步道每米造价65元，求铺设AC共需多少元。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（7分）某班准备租用车辆参加研学活动，有甲、乙两种计费方案：甲方案基础费80元，每千米3元；乙方案基础费20元，每千米5元。设行驶路程为x千米，总费用分别为y甲、y乙。

（1）分别写出y甲、y乙关于x的函数关系式；

（2）当x＝25时，选择哪种方案费用更少；

（3）当行驶路程为多少千米时，两种方案费用相同？【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（8分）在矩形ABCD中，AB＝12，BC＝5。点E在AB上，点F在CD上，且AE＝CF＝4。

（1）求证：四边形AECF是平行四边形；

（2）求矩形对角线AC的长；

（3）求四边形AECF的周长；

（4）若P是AC的中点，说明P与EF的位置关系。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（8分）在Rt△ABC中，∠C＝90°，AC＝3√2，BC＝4√2。

（1）求AB的长；

（2）求△ABC的周长和面积；

（3）若以AB为边作正方形，求该正方形的面积；

（4）指出本题计算中二次根式化简最容易出错的一步。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（8分）在平面直角坐标系中，一次函数y＝-1/2x＋6的图象与x轴交于点A，与y轴交于点B。

（1）求A、B两点坐标；

（2）点P在x轴正半轴上，设OP＝t，若△PAB的面积为18，求t的值；

（3）点Q在该函数图象上，且横坐标为4，求OQ的长；

（4）结合图象说明当y＞0时x的取值范围。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.（8分）如图形关系所述：在平面直角坐标系中，A(0，0)，B(8，0)，D(2，4)，C(10，4)，四边形ABCD为平行四边形。点M在AB上，点N在DC上，且AM＝DN＝x（0≤x≤8）。

（1）用坐标或平行线性质证明四边形AMND是平行四边形；

（2）若BM＝3，求四边形AMND的面积；

（3）当M是AB的中点时，求四边形AMND的周长；

（4）若四边形AMND的面积不小于24，求x的取值范围。【作答区】________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析说明：本答案给出主要解法、关键步骤和采分点。学生若采用其他正确方法，且推理清楚、计算准确，可按相应步骤给分。一、选择题答案与解析题号12345678910答案CBCAAACCCB1.【答案】C【解析】√18＝√(9×2)＝3√2，符合题意。√12＝2√3，√27＝3√3，均不是3√2。【评分标准】选对得3分；选错、不选或多选均不得分。2.【答案】B【解析】由勾股定理，斜边＝√(6²＋8²)＝√100＝10。干扰项常来自把两直角边直接相加或开方错误。【评分标准】选对得3分；选错、不选或多选均不得分。3.【答案】C【解析】把x＝1代入y＝-2x＋3，得y＝-2×1＋3＝1。【评分标准】选对得3分；选错、不选或多选均不得分。4.【答案】A【解析】平行四边形对角相等，所以∠C＝∠A＝70°。相邻角才互补，不能把∠C误算成110°。【评分标准】选对得3分；选错、不选或多选均不得分。5.【答案】A【解析】数据已按从小到大排列为6，8，8，10，13，共5个数，中间的第3个数是8。【评分标准】选对得3分；选错、不选或多选均不得分。6.【答案】A【解析】√12＝2√3，因此√12－√3＝2√3－√3＝√3。【评分标准】选对得3分；选错、不选或多选均不得分。7.【答案】C【解析】由两点(0，2)、(1，5)可得k＝(5－2)/(1－0)＝3。点(0，2)说明b＝2，但本题只问k。【评分标准】选对得3分；选错、不选或多选均不得分。8.【答案】C【解析】矩形对角线、两边构成直角三角形，另一边＝√(10²－6²)＝√64＝8。【评分标准】选对得3分；选错、不选或多选均不得分。9.【答案】C【解析】初始水量为20m³，每分钟增加3m³，x分钟增加3xm³，所以y＝20＋3x。【评分标准】选对得3分；选错、不选或多选均不得分。10.【答案】B【解析】菱形对角线互相垂直平分，半对角线为3和4，边长＝√(3²＋4²)＝5，周长＝4×5＝20。【评分标准】选对得3分；选错、不选或多选均不得分。二、填空题答案与解析11.【答案】5a【解析】因为a≥0，所以√(25a²)＝5|a|＝5a。这里要注意二次根式化简后含绝对值，条件a≥0使其可直接写成5a。【评分标准】填对得3分；写成5|a|但未利用条件可得2分；写成±5a不得分。12.【答案】3【解析】将点(2，5)代入y＝mx－1，得5＝2m－1，2m＝6，m＝3。【评分标准】列出代入方程得1分，解得m＝3得2分。13.【答案】85【解析】平均数为85分，故(80＋90＋x)/3＝85，170＋x＝255，x＝85。【评分标准】列式正确得1分，计算正确得2分。14.【答案】4【解析】正方形对角线d＝a√2。由a√2＝4√2，得边长a＝4。【评分标准】写出或正确使用对角线关系得1分，结果正确得2分。15.【答案】72°【解析】设相邻两个内角为2k、3k。平行四边形相邻内角互补，2k＋3k＝180°，k＝36°，较小角为72°。【评分标准】列方程得1分，求出k得1分，写出较小角72°得1分。16.【答案】36/5【解析】斜边c＝√(9²＋12²)＝15。面积既可表示为1/2×9×12，也可表示为1/2×15×h，所以h＝(9×12)/15＝36/5。【评分标准】求出斜边得1分，建立面积等式得1分，结果正确得1分。三、解答题参考答案、解析与评分标准17.【答案】（1）√3；（2）5＋4√5。【解析】（1）√48＝4√3，√12＝2√3，√27＝3√3，所以原式＝4√3－3×2√3＋3√3＝√3。（2）(√5＋2)²＝5＋4√5＋4＝9＋4√5，(√5－1)(√5＋1)＝5－1＝4，所以原式＝9＋4√5－4＝5＋4√5。关键是二次根式化为最简二次根式，并正确使用完全平方公式与平方差公式。【评分标准】共6分。（1）化简三个根式各1分，合并得√3得1分，共3分；（2）正确展开或运用公式得2分，化简结果5＋4√5得1分，共3分。18.【答案】（1）y＝2x＋1；（2）(-1/2，0)；（3）1/4。【解析】设一次函数为y＝kx＋b。由A(2，5)、B(-1，-1)，k＝[5－(-1)]/[2－(-1)]＝2。把A(2，5)代入得5＝2×2＋b，b＝1，所以表达式为y＝2x＋1。令y＝0，得2x＋1＝0，x＝-1/2，故与x轴交点为(-1/2，0)。与y轴交点为(0，1)，与两坐标轴围成的直角三角形两直角边长分别为1/2和1，面积＝1/2×1/2×1＝1/4。【评分标准】共6分。求斜率k得2分，求b并写出表达式得2分；求x轴交点得1分；面积计算正确得1分。19.【答案】（1）甲平均数85，中位数85；乙平均数85，中位数86。（2）甲方差18，乙方差109/3。（3）甲组更稳定。【解析】甲组平均数为(78＋82＋85＋85＋90＋90)/6＝510/6＝85，中位数为第3、第4个数的平均数，即85。乙组平均数为(75＋80＋85＋87＋90＋93)/6＝510/6＝85，中位数为(85＋87)/2＝86。甲组方差＝[(78－85)²＋(82－85)²＋0²＋0²＋(90－85)²＋(90－85)²]/6＝(49＋9＋25＋25)/6＝18。乙组方差＝[(75－85)²＋(80－85)²＋0²＋(87－85)²＋(90－85)²＋(93－85)²]/6＝(100＋25＋4＋25＋64)/6＝109/3。平均数相同，甲组方差更小，成绩波动更小，因此甲组更稳定。【评分标准】共7分。两组平均数各1分，共2分；两组中位数各0.5分，共1分；甲方差计算正确1.5分，乙方差计算正确1.5分；稳定性判断及理由1分。20.【答案】（1）DE＝BF；（2）四边形EBFD是平行四边形；（3）一组相邻边可取3和√79。【解析】在平行四边形ABCD中，AD＝BC，AD∥BC。E、F分别是AD、BC的中点，所以DE＝1