福建省福州福清市2023-2024学年上学期九年级期中数学试卷

{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}2023-2024学年第一学期九年级校内期末质量检测数学试卷评分标准一、选择题（共10小题，每小题4分，共40分）12345678910CCBDBDACCC二、填空题（共6小题，每小题4分，共24分）11.xx112.7213.202316.1214.60°15.，0）二、解答题．（共9小题，共8617.（本题8解：方法一：（配方法）xx224x7..................................................................................................................2分4x474......................................................................................................4分（x）................................................................................................................6分2x2...............................................................................................................7分x211,x2......................................................................................8分12方法二：（公式法）a=1b=4，c=-7..........................................................................................................1分b244241(7)0...................................................................3分ꢁ2−4ꢂꢃ−4±ꢀ===−2±11..............................................................6分2x211,x2......................................................................................8分1218.（本题8解：∵a=1b=3，c=m......................................................................................................1分∴b4341m94m...................................................................3分22∵方程有两个实数根..................................................................................................4分∴9-4m0..........................................................................................................6分9∴m....................................................................................................................8分4九年级校内期中质量检测评分标准第1页共6页{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}19.（本题8解：依题意得：OA=OC=5，∵CD，CD=6...............................................................................................2分1∴3.....................................................................................................4分2在△中，OEC=90°，根据勾股定理得：∴225234..................................................................6分2∴=OA+OE=5+4=9..........................................................................................7分答：门的高度AE的长是9m....................................................................................8分20.（本题8:设该快递公司投递总件数的月平均增长率为，......................................................1分依题意得：x)2.......................................................................................4分x0.110%,x2.10(不合题意，舍去）解得：.............................7分12答：该快递公司投递总件数的月平均增长率是10%....................................................8分．（本题8分，2+2+2+2解：（1）a=15.........................................................................................................................1分如图所示..................................................................................................................3分2x=2.......................................................................................................................5分3）当y=15-5x220x15................................................................................6分∴xx3..................................................................................................................7分12答：高尔夫球飞行高度为15m时所用的时间是13........................................8分九年级校内期中质量检测评分标准第2页共6页{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}．（本题10分，4+6分）1）如图所示.................................................................................................................4分2）证明：如图，连接∵A∴BOC=2A=90°..............................................................................................5分∴OB..................................................................................................................6分∴OCD=180°-∠90°..................................................................................7分∴CD..................................................................................................................8分∵OC是⊙O的半径..................................................................................................9分∴是⊙O的切线................................................................................................10分．（本题10分，4+4+2）（y2)2................................................................................................................2分y=5................................................................................................................................4分2）设点P的坐标为P（xyM（，0..................................................................5分∴yy，x∵2(y2)..............................................................................6分2∴yx2(y2)2y2x2(y2)2...............................................................7分1∴yx21..................................................................................................................8分43）1y.........................................................................................................................10分九年级校内期中质量检测评分标准第3页共6页{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}．（本题12分，4+4+4（1）将A-4，0，-4＝-x﹣bxc得：-16bc0.....................................................................................................2分..........................................................................................................3分c4b5解得：c4∴抛物线的解析式为：y＝﹣5x-4................................................................4分2）①在抛物线y＝﹣5x-4上，当时，-x﹣5x-解得：xx112∴（-10）∵A（-40（0-4）∴AC的解析式为：yx4....................................................................................5分∵点P在线段AC上，设（m-m-4D（m-m﹣5m-4）∴＝﹣5m-4-(-m-4m=-（m+2）+4.................................................6分13S四边形△△(m2)26∴22当m＝-2时，四边形ADBP的面积最大，此时PD=4=OC....................................7分∵PDx轴∴PD//OC∴四边形OCPD是平行四边形....................................................................................8分②由得：A-4，（-22P（-2-2）l:yx4.........................................................................................................9分iPQ//AD时，∠ADP＝∠∴直线l:yx...................................................................................................................10分x351x25x4依题意得：yx35(yx2∴-3-3........................................................................................................11分ii）∵点OE关于直线的对称，∴∠＝∠DPQ＝∠ADP此时点QA重合，∴Q-4，0）综上所述，-3-3或-40................................................................12分九年级校内期中质量检测评分标准第4页共6页{#{QQABbYaQggAgQABAAAhCAwFiCAKQkAECACoGBBAEIAABARNABAA=}#}．（本题14分，4+5+51）证明：如图，CA=CBCE=CF，ACE＝∠BCA-∠BCE=90°-BCE，BCF＝∠-BCE=90°-∠BCE，∴∠ACE＝∠BCF.....................................................................................................1分△ACE≌△∴∠EAC=∠.............................................∵∠∠2........2分∴∠BMA＝∠BCA=90°...................................BM⊥AE...............................................................3分.........4分(2)解：如图，取ABO，连接OMOQ.....................................................................5分∵∠AMB＝∠BCA＝90°，∴28.21OM＝BA=4，....................................6分2Q为AC的中点，1∴22.....................................7分2当M、、Q三点共线时，最大.............8分11此时，MQ=OM+OQ=422...........................................................9分223）方法一：如图，连接MC，过点B作BHH，过点C作CP⊥DA交DA延长线，CNN，∴∠＝∠CNB90°∠PCN90°∴∠ACP＝90°-ACN＝∠∵CA=CB∴△ACP≌△CP=CN...............................................................................................................10分1∴∠CMN＝AMN＝45°=MCN2∵CA=CB=42∴2∵∠105°∠BAC=45°∴∠BAM60°1∴AM=AB=4BM=3AM=43.................................................................11分2九年级校内期中质量检测评分标准第5页共6页{#{QQABbYaQggAgQABAAAhCAwFiCAK