2019秦淮区二模试题及答案

23．（8分）点A（－1，0）是函数y＝x2－2x＋m2－4m的图像与x轴的一个公共点． （1）求该函数的图像与x轴的另一个公共点的坐标以及m的值；

（2）将该函数图像沿y轴向上平移 ▲ 个单位后，该函数的图像与x轴只有一个公共点．

24．（8分）两个运输小队分别从两个仓库以相同的工作效率调运一批物资，两队同时开始工作．第二小队工作5天后，由于技术问题检修设备5天，为赶上进度，再次开工后他们将工作效率提高到原先的2倍，结果和第一小队同时完成任务．在两队调运物资的过程中，两个仓库物资的剩余量y t与第一小队工作时间x天的函数图像如图所示． （1）①求线段AC所表示的y与x之间的函数表达式； ②求点F的坐标，并解释点F的实际意义．

（2）如果第二小队没有检修设备，按原来的工作效率正常工作，那么他们完成任务的天数是 ▲ 天．

O D 5 （第24题）

F y／t 360 A B E C 12 x／天

10 25．（8分）已知线段AB与点O，利用直尺和圆规按下列要求作△ABC（不写作法，保留作图痕迹）．

（1）在图①中，点O是△ABC的内心； （2）在图②中，点O是△ABC的重心．

A

①

B

A

②

B

O O

（第25题）

九年级数学试卷 第 5 页( 共 11 页 )

26．（10分）某商店第一个月以每件100元的价格购进200件衬衫，以每件150元的价格售罄．由于市场火爆，该商店第二个月再次购进一批衬衫，与第一批衬衫相比，这批衬衫的进价和数量都有一定的提高，其数量的增长率是进价增长率的2.5倍，该批衬衫仍以每件150元销售．第二个月结束后，商店对剩余的50件衬衫以每件120元的价格一次性清仓销售，商店出售这两批衬衫共盈利17500元．设第二批衬衫进价的增长率为x．

（1）第二批衬衫进价为 ▲ 元，购进的数量为 ▲ 件．（都用含x的代数式表示，不需化简） （2）求x的值．

27．（10分）如图，在矩形ABCD中，AB＝5，BC＝12，E为BC的中点．⊙O与边BC相切于点E，并交边AD于点M、N，AM＝3． （1）求⊙O的半径；

（2）将矩形ABCD绕点E顺时针旋转，旋转角为?（0°＜?≤90°）．在旋转的过程中，⊙O和矩形ABCD的边是否能够相切，若能，直接写出相切时，旋转角?的正弦值；若不能，．．请说明理由．

九年级数学试卷 第 6 页( 共 11 页 )

B E （第27题）

C O A M N D

2018/2019学年度第二学期第二阶段学业质量监测试卷

九年级数学参考答案及评分标准

说明：本评分标准每题给出了一种或几种解法供参考，如果考生的解法与本解答不同，参照本评分标准的精神给分．

一、选择题（每小题2分，共计12分）

题号 答案 1 D 2 B 3 D 4 A 5 B 6 D 二、填空题（每小题2分，共计20分）

7．4.655×109 12．①②

8．22 13．33

9．－x(x－1)2 14．30

10．＜ 215．

5

11．0＜x＜1 22021

16．2019 3

三、解答题（本大题共11小题，共计88分） 17．（本题6分）

1

解：原式＝－1＋6×－3 ····································································································

2

＝－1＋3－3 ·····················································································································

＝－1． ···························································································································18．（本题6分）

x－3?x2－45?解：原式＝÷?－ ···························································································

x－2?x－2x－2??＝＝

x－3x－2· ··········································································································x－2(x＋3)(x－3)

1

． ·························································································································x＋3

19．（本题8分）

（1）④． ························································································································（2）证明：∵ AC⊥BD，∴ ∠AOB＝∠AOD＝90°．

∵ AC平分∠BAD，∴ ∠BAO＝∠DAO． 又∵ AO＝AO，∴ △AOB≌△AOD．

A

O

C B ∴ AB＝AD． ·················································································································

D 九年级数学试卷 第 7 页( 共 11 页 )

∵ AD∥BC，∴ ∠DAO＝∠BCO．

又∵ ∠BAO＝∠DAO，∴ ∠BAO＝∠BCO．

∴ BA＝BC． ··················································································································∴ AD＝BC．

又∵ AD∥BC，∴ 四边形ABCD是平行四边形． ·································································

又∵ AC⊥BD，∴ □ABCD是菱形．·················································································20．（本题8分）

（1）1． ·························································································································（2）解：将2个黄色小球分别记作“黄1”、“黄2”．从袋中随机摸出1个小球，记录好颜色后放回袋中并搅匀，再从袋中任意摸出1个小球，可能出现的结果有16种，即（红，红），（红，黄1），（红，黄2），（红，黑），（黄1，红），（黄1，黄1），（黄1，黄2），（黄1，黑），（黄2，红），（黄2，黄1），（黄2，黄2），（黄2，黑），（黑，红），（黑，黄1），（黑，黄2），（黑，黑），并且它们出现的可能性相同．其中两次摸出的都是黄色小球（记为事件A）的结果有4种，即（黄1，黄1），（黄1，黄2），（黄2，黄1），（黄2，黄2），

1

所以P（A）＝． ·············································································································

421．（本题8分）

解：（1）设专业技能笔试得分占总成绩的百分比是a．

根据题意，得90a＋70(1－a)＝78． ·······················································································解这个方程，得a＝40%． 1－40%＝60%．

所以专业技能笔试得分和课堂教学展示得分占总成绩的百分比分别是40%，60%． ·························

（2）2号考生总成绩为70×0.4＋90×0.6＝82（分）． ······························································

3号考生总成绩为86×0.4＋80×0.6＝82.4（分）． ····································································

4号考生总成绩为75×0.4＋86×0.6＝81.6（分）． ····································································

因为82.4＞82＞81.6＞78，所以3号考生会被录取． ·································································22．（本题8分）

A 九年级数学试卷 第 8 页( 共 11 页 )

B D C