[]山西省平定县2018届九年级12月月考数学试题(图片版）

平定县 2017－2018 学年第一学期九年级教学质量调研试题（卷） 数学参考答案 一、选择题： 题号 1 2 3 4 5 6 7 8 9 10 答案 C C D D C B A B A B 二、填空题： 11. （5，3） 12. 5 2 13. 40° 14. 3 15. 3 5 π 三、解答题: 16.（1）解：（x－5）2 =2（5－x）， （x－5）2+2（x－5）=0，····································································· 1分 （x－5）（x－5+2）=0，·······································································2分 x－5=0或 x－5+2 =0，·········································································· 3分 x1=5，x2=3．······················································································ 5分 （2）解：∵一元二次方程     0332 22  mxmx 有两个不相等的实数根， ∴   3)432 22  mm （ ＞0 ．····························································1分 即 1249124 22  mmm ＞0 ． ·······················································2分 解得m＜ 4 7 ．·····················································································4分 ∴m的取值范围是m＜ 4 7 ．··································································5分 17. 解：（1）如图所示：△A′B′C′，即为所求；·········································2分 （2）如图所示：△A″B″C″，即为所求；·················································· 4分 （3）将△ABC绕原点 O旋转 180°，点 A的对应点 A1的坐标是（2，－3）．··6分 18. 解：（1）x=－2 ；·········································································2分 （2）解：原方程可化为 2x2－3x－5 = 0， Δ= b2－4ac = (－3)2－4×2×(－5) = 49＞0， ∴方程有两个不相等的实数根． 设两根为 x1，x2，则 x1＋ x2= 3 2 ，···························································· 4分 x1x2= －5 2 ．························································································6分 19. 解：（1）若他去买一本笔记本，则他买到 A种笔记本的概率是： ；····· 2分 （2）根据题意，画出如下的树状图：（用树状图或列表法均可） ···················································· 6分 由树状图可以看出，所有可能出现的结果共有 12种，恰好买到 A种笔记本和 C种笔记 本的有 2种情况，并且每种结果出现的可能性相等，··································7分 ∴恰好买到 A种笔记本和 C种笔记本的概率为：P= = ．······················9分 20.（1）证明：连接 OD，································ 1分 ∵OB=OD， ∴∠ABC =∠ODB．·········································2分 ∵AB =AC， ∴∠ABC =∠C． ∴∠ODB =∠C．...................................................