2025-2026学年八年级数学下册期末函数几何综合模拟试卷（含答案详解与评分标准）

2025-2026学年八年级数学下册期末函数几何综合模拟试卷（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分注意事项1.本试卷共22题，包含选择题、填空题和解答题，重点考查一次函数、平面直角坐标系、三角形与四边形中的函数几何综合。2.选择题每题只有一个正确选项；填空题填写最简结果或符合题意的等价形式；解答题应写出必要的推理、计算过程和结论。3.作图、辅助线、坐标设点应标注清楚；涉及面积、长度、函数表达式时，应注意单位与取值范围。4.全卷满分120分。请在规定区域内作答，书写工整，步骤清楚。题型题号范围每题分值小计一、选择题1—83分24分二、填空题9—143分18分三、解答题15—228分、8分、9分、9分、10分、10分、12分、12分78分合计1—22—120分一、选择题（本大题共8小题，每小题3分，共24分。每小题只有一个正确选项）1.已知一次函数y=(2−m)x+m+1的图象经过第一、二、四象限，则m的取值范围是（）。

A.m<−1B.−1<m<2C.m=2D.m>22.在平面直角坐标系中，平行四边形ABCD的三个顶点为A(−1，2)，B(3，2)，D(1，5)，则点C的坐标是（）。

A.(3，5)B.(5，5)C.(1，−1)D.(−5，5)3.直线y=−3x+6与坐标轴围成的三角形面积为（）。

A.3B.4C.6D.124.下列条件中，能判定四边形一定是菱形的是（）。

A.两组对边分别相等B.对角线互相垂直且互相平分

C.对角线相等D.有一个角是直角5.若x与y满足一次函数关系，且有下表数据，则该函数表达式为（）。x−102y53−1A.y=−2x+3B.y=2x+3C.y=−x+4D.y=3x−26.一个矩形的一边长为6，对角线长为10，则该矩形的面积为（）。

A.30B.36C.48D.607.若点A(−2，4)、B(1，−2)都在同一个一次函数图象上，则该图象与x轴交点的横坐标为（）。

A.0B.1C.2D.−28.在第一象限内，点P(x，y)在直线y=−x+6上，过P分别向两坐标轴作垂线，垂足为M、N。若矩形OMPN的面积为8，则矩形OMPN的周长为（）。

A.8B.12C.16D.24二、填空题（本大题共6小题，每小题3分，共18分）9.经过点A(2，−1)、B(6，7)的直线的斜率为__________。10.菱形的两条对角线长分别为6和8，则该菱形的边长为__________。11.对于一次函数y=2x−4，当y<0时，x的取值范围是__________。12.若函数y=(a−1)x+a²−4是正比例函数，则a的值为__________。13.菱形的一组对角线长分别为16和30，则该菱形的周长为__________。14.一次函数图象与直线y=−3x+2平行，且经过点(2，5)。当x=−1时，y的值为__________。三、解答题（本大题共8小题，共78分。解答应写出必要过程）15.（本题8分）已知一次函数的图象经过A(1，2)、B(3，6)。（1）求该一次函数的表达式；（2）判断点C(−1，−2)是否在该函数图象上，并说明理由；（3）求该函数图象、直线x=4与x轴围成的三角形面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16.（本题8分）如图形条件所示，在平行四边形ABCD中，E、F分别是AB、CD的中点。连接DE、BF。（1）求证：DE=BF；（2）求证：四边形DEBF是平行四边形。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17.（本题9分）某校八年级组织研学活动，租车总费用y（元）与行驶路程x（千米）之间满足一次函数关系。已知行驶20千米收费500元，行驶35千米收费725元。（1）求y与x之间的函数表达式；（2）若本次往返共64千米，应付多少元；（3）若班级租车预算不超过1400元，在此收费方式下最多可行驶多少千米？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（本题9分）在矩形ABCD中，AB=12，AD=9，点E在AB上，AE=4，连接CE、DE。（1）求CE的长；（2）求△DCE的面积；（3）若DF⊥CE，垂足为F，求DF的长。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（本题10分）在平面直角坐标系中，直线l经过A(−3，0)、B(0，6)。点P(t，0)在x轴上，且位于点A的右侧。（1）求直线l的函数表达式；（2）若△PAB的面积为18，求t的值；（3）在（2）的条件下，若以A、B、C、P为顶点的四边形ABCP是平行四边形，求点C的坐标。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（本题10分）阅读材料并完成问题。材料：在平面直角坐标系中，一次函数图象上任取两点，若横坐标差为Δx，纵坐标差为Δy，则斜率k=Δy÷Δx。两条非竖直直线的斜率分别为k₁、k₂，当k₁·k₂=−1时，这两条直线互相垂直。已知直线l₁：y=1/2x+3与x轴交于点A，与y轴交于点B。（1）求A、B两点坐标及△AOB的面积；（2）过点B作直线l₂，使l₂⊥l₁，求l₂的函数表达式；（3）若l₂与x轴交于点C，判断△ABC的形状，并求BC的长。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（本题12分）如图，在平面直角坐标系中，直线l：y=−x+8与x轴、y轴分别交于点A、B。点P在第一象限内的线段AB上，过P作PM⊥x轴于M，PN⊥y轴于N，形成矩形OMPN。（1）若点P的横坐标为3，求矩形OMPN的面积；（2）若矩形OMPN的面积为12，求点P的坐标；（3）是否存在点P，使矩形OMPN为正方形？若存在，求出点P坐标；若不存在，请说明理由。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（本题12分）如图，在矩形OABC中，O(0，0)，A(8，0)，B(8，6)，C(0，6)。动点P从点O沿OA运动，设OP=t（0≤t≤8）。过点P作PQ∥OB，交边AB于点Q，点R为PQ的中点。（1）求直线OB的函数表达式，并用t表示点Q的坐标；（2）设四边形OPQB的面积为S，求S与t之间的关系式；（3）当S=18时，求t的值和点Q的坐标；（4）求点R所在直线的函数表达式，并判断R是否可能落在矩形对角线AC上。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与解析题号12345678答案DBCBACAB1.答案D。一次函数图象经过第一、二、四象限，应满足斜率小于0、截距大于0。由2−m<0得m>2，由m+1>0得m>−1，综合得m>2。2.答案B。平行四边形对角线互相平分，也可用向量关系C=B+D−A，得C=(3，2)+(1，5)−(−1，2)=(5，5)。3.答案C。直线与x轴交点为(2，0)，与y轴交点为(0，6)，所围三角形面积为1/2×2×6=6。4.答案B。对角线互相平分可判定为平行四边形，在此基础上对角线互相垂直，可判定为菱形。5.答案A。由x每增加1，y减少2，可知斜率为−2；当x=0时y=3，所以表达式为y=−2x+3。6.答案C。矩形中相邻两边与对角线构成直角三角形，另一边长为√(10²−6²)=8，面积为6×8=48。7.答案A。斜率k=(−2−4)÷(1−(−2))=−2，代入点B得−2=−2×1+b，所以b=0，图象与x轴交于原点，横坐标为0。8.答案B。点P在y=−x+6上，所以x+y=6。矩形OMPN的长、宽分别为x、y，周长为2(x+y)=12；面积条件保证P不在坐标轴上。二、填空题答案与解析题号91011121314答案25x<2a=2或a=−268149.斜率k=(7−(−1))÷(6−2)=8÷4=2。10.菱形对角线互相垂直平分，半对角线为3和4，边长为√(3²+4²)=5。11.由2x−4<0，得x<2。12.正比例函数应满足常数项为0且一次项系数不为0。由a²−4=0得a=±2，且a−1≠0，两个值均符合。13.半对角线为8和15，边长为√(8²+15²)=17，周长为4×17=68。14.平行直线斜率相同，所以设y=−3x+b。代入(2，5)得5=−6+b，b=11。当x=−1时，y=3+11=14。三、解答题参考答案、解析与评分标准15.参考答案（8分）设函数表达式为y=kx+b。由点A(1，2)、B(3，6)在图象上，得k=(6−2)÷(3−1)=2。代入A(1，2)：2=2×1+b，得b=0，所以函数表达式为y=2x。当x=−1时，y=2×(−1)=−2，与点C的纵坐标一致，所以C(−1，−2)在该函数图象上。直线x=4与函数图象交于(4，8)，又与x轴交于(4，0)。所围三角形底为4，高为8，面积为1/2×4×8=16。评分标准：求斜率2分；求b并写出表达式2分；判断点C并说明理由2分；求面积2分。易错点：把斜率算成倒数，或将直线x=4误写成点的横坐标长度。16.参考答案（8分）在平行四边形ABCD中，AB∥CD且AB=CD。因为E、F分别是AB、CD的中点，所以BE=AB/2，DF=CD/2，从而BE=DF，且BE∥DF。在四边形DEBF中，一组对边BE、DF平行且相等，所以四边形DEBF是平行四边形。由平行四边形对边相等，得DE=BF。评分标准：写出AB∥CD、AB=CD共2分；由中点得到BE=DF共2分；说明BE∥DF共1分；判定四边形DEBF为平行四边形2分；得出DE=BF共1分。易错点：只写“中点”而不说明对应线段平行相等，证明链不完整。17.参考答案（9分）设y=kx+b。由(20，500)、(35，725)可得k=(725−500)÷(35−20)=15。代入(20，500)：500=15×20+b，得b