济南市平阴县2018-2019学年八年级上学期期末考试数学试题（扫描版） 15页

‎2018—2019学年度第一学期期末学习诊断检测 八年级数学试题参考答案 一、 单项选择题（共12小题，每小题4分，满分48分）‎ ‎1‎ ‎2‎ ‎3‎ ‎4‎ ‎5‎ ‎6‎ ‎7‎ ‎8‎ ‎9‎ ‎10‎ ‎11‎ ‎12‎ A B D C C A C D A B A B 二、填空题（共6小题，每小题4分，满分24分）‎ ‎13. 2 14. （-1，-3） 15. 87 ‎ ‎16. 240° 17. (3,0) 18. (0,21009) ‎ 三、解答题（共9小题，满分78分，解答应写出文字说明，证明过程或演算步骤）‎ ‎19. 计算:（本题满分8分,每小题4分）‎ ‎ (1) = ·······························2分 ‎ = ····························································4分 ‎ (2) =··············1分 ‎ =··················································2分 ‎ =·······················································3分 ‎ = -1 ·····························································4分 20. 解方程组: （本题满分8分,每小题4分）‎ (1) ‎ ‎ 解：得 ③‎ ‎ 得 ④‎ ‎ 得 ·······································2分 将代入①，得 ‎ ‎ ········································3分 所以原方程组的解是···········································4分 ‎(2) ‎ ‎ 解： 得 ······················2分 ‎ 将代入①，得 ·······················3分 ‎ 所以原方程组的解是········································4分 20. ‎（本题满分6分）‎ 证明：∵ ‎ ‎ ∴ ·························1分 ‎ ∴ ······················2分 ‎ 又∵ ‎ ‎ ∴························4分 ‎ ∴ ·························5分 ‎ ∴····························6分 21. ‎（本题满分6分） 解：∵ BE平分∠ABC ‎ ∴ ·······················1分 ‎ 又∵ DE∥BC ‎ ∴ ························2分 ‎∴ ························4分 ‎∴ ·····················5分 ‎∵点D是AB的中点 ‎∴ ················6分 ‎23.（本题满分8分）‎ ‎（1）众数___90_____，中位数___90_____；·································2分 ‎(2) ‎ ‎ ···2分 ‎（3）由题意可得，轻度污染的天数为30-3-15=12（天）················1分 下图是补全后的空气质量天数条形统计图 ‎······························2分 ‎（4）空气污染指数在100以下的天数为（天）··············1分 ‎ 所以：该市居民一年中适合做户外运动天数：（天）············2分 ‎24.（本题满分8分）‎ ‎ 解：（1）·································2分 ‎ （2）················································2分 ‎（3）‎ ‎ ‎ ‎ ·································2分 所以 ，所以△EFG为直角三角形······················3分 又因为 ,所以△EFG为等腰直角三角形··························4分 ‎25.（本题满分10分）‎ ‎ 解：（1）设本次试点投放的A型车x辆，B型车y辆··························1分 ‎ 由题意可得： ······························3分 ‎ 解 得··················································4分 ‎ 所以： 本次试点投放的A型车60辆，B型车40辆··························5分 ‎（2）设 B型车购进a辆，购车总费用为w元 ‎ 则 ‎ ‎ =················································2分 ‎ ∵‎ ‎ ∴ w随a的增大而减小 ‎ ∴当a取最大值300时，w有最小值，‎ 此时，购进A型车：500-300=200（辆）······································3分 ‎ ∴ （元）···························4分 ‎ 所以：当购进A型车200辆，B型车300辆时，购车费用最低，‎ 最低费用为176000元。 ··········································5分 ‎26.（本题满分12分）‎ 解：（1）在中 令，则 ············································1分 ‎∴B点坐标为：···················································2分 令，则，解得··································3分 ‎∴A点坐标为：····················································4分 ‎(2)过点P做x轴的垂线，交x轴于点M ‎∵A点坐标为：，∴·········1分 ‎∵△中，‎ ‎∴···············2分 把代入中，得 ‎∴P点坐标为：··················3分 把P代入中，‎ 可得： 解得：···········4分 ‎（3）∵C是直线上一点 ‎∴设C点坐标为 则点D坐标为，点E坐标为······················1分 ‎∴‎ ‎···········································2分 ‎∵CD=2ED ‎∴=‎ 解得······················································3分 ‎ 则 此时，C点坐标为········································4分 ‎27.（本题满分12分）‎ 解（1）∵OA=6,OB=10 ∴C点坐标为（6,10）‎ 即此时P点坐标为（6,10）··················1分 设直线DP解析式为 代入D点坐标（0,2），P点坐标（6,10）‎ 可得：····················2分 解，得························································3分 ‎∴直线DP解析式为···········································4分 ‎（2）若点P在线段AC上运动，则△OPD面积是一个定值：=6·····1分 所以若△OPD的面积为4，则点P位于线段CB上 此时 ················································2分 可得：·························································3分 此时点P运动的路程：10+6-4=12·········································4分 所以点P运动的时间：‎ ‎（秒） ··································5分 ‎（3）3或或 ············································3分