北京市平谷区2020届九年级中考统一练习（二）数学试题（PDF版）

北京市平谷区 2020 年中考统一练习（二） 数学试卷参考答案及评分标准 2020.6 一、选择题（本题共 16分，每小题 2分） 题号 1 2 3 4 5 6 7 8 答案 D B A B C C A D 二、填空题（本题共 16分，每小题 2分） 9． 3 3y( x )( x )  ； 10．45°； 11． x 1 ； 12．； 13．答案不唯一，如 2 2y x  ； 14．答案不唯一，如 a=-1； 15． 4 2 x y x y      ；或 3( xy ) 16．方案四． 三、解答题(本题共 68分，第 17-21题，每小题 5分，第 22-27题，每小题 6分，第 28 题 7分)解答应写出文字说明、演算步骤或证明过程. 17.解：原式= 32 1 2 +2-2 3  ········································································ 4 =1- 3 ······················································································· 5 18.解：由①得 2x-6<x-4 x<2·····················································································1 由②得 x-1<2x··················································································· 2 x>-1····················································································3 ∴-1<x<2··················································································· 5 19.（1）补全图形；..................................................2 （2） 证明：连接 BP ∵ AB=BC ∴ BCAB   ∴ ∠_CPB__=∠_APB___，..................................................3 又∵ OB=OP， ∴ ∠APB=∠OBP，..................................................4 ∴ ∠CPB=∠OBP， ∴CP∥l（___内错角相等两直线平行）..................................................5 20．解：(1) 2-1 4 k-2k  （ ） （ ） ······································································ 1 2 2 k -6k+9 = k-3  （ ） ················································································· 2 ∵ 0  ∴方程总有两个不相等的实数根·········································································3 (2) k=2当 ∴ 2x +x=0 ··················································································· 4 1 2x =0 x =-1解得 ， ．····································································· 5 （其他取法相应给分） 21．(1)证明：∵四边形 ABCD是菱形 ∴∠1=∠2，AD=AB..............................1 ∵BC=DF ∴AE=AF ∴AG⊥EF .............................................2 （2）证明: ∵菱形 ABCD ∴BD⊥AC ∵BM⊥EF，AG⊥EF ∴∠BOG=∠OGM=∠GMB=90 ∴四边形 OBMG是矩形................................