南京市玄武区2016-2017学年度第一学期期九年级试卷

南京市玄武区2016-2017学年度第一学期期九年级试卷
南京市玄武区2016-2017学年度第一学期期九年级试卷

2016~2017学年度第一学期期末学情调研试卷

九年级数学

注意事项:

1.本试卷共4页.全卷满分120分.考试时间为120分钟.考生答题全部答在答题卡上. 2.请认真核对监考教师在答题卡上所粘贴条形码的姓名、考试证号是否与本人相符合,再将自己的姓名、准考证号用0.5毫米黑色墨水签字笔填写在答题卡及本试卷上. 3.答选择题必须用2B 铅笔将答题卡上对应的答案标号涂黑.答非选择题必须用0.5毫米黑色墨水签字笔写在答题卡上的指定位置,在其他位置答题一律无效. 4.作图必须用2B 铅笔作答,并请加黑加粗,描写清楚.

一、选择题(本大题共6小题,每小题2分,共12分.在每小题所给出的四个选项中,恰有一项是符合题目要求的,请将正确选项前的字母代号填涂在答题卡...相应位置....上) 1.方程x 2=2x 的解是 A .x =2

B .x 1=2,x 2=0

C .x =0

D .x 1=2,x 2=1

2.在比例尺为1∶500000的工程图上,南京地铁四号线全长约6.76 cm ,它的实际长度约

A .3.38 km

B .338 km

C .33.8 km

D .0.338 km 3.抛掷一枚质地均匀的骰子一次,向上一面点数大于4的概率是

A .12

B .13

C .23

D .56

4.如图,AB 为⊙O 的直径,CD 为⊙O 的弦,CD ⊥AB ,垂足为E ,OE =3,CD =8,AB =

A . 27

B .10

C .7

D .5

5.两个相似三角形的一组对应边的长分别为5 cm

和3 cm ,如果它们的面积之和为136 cm 2,则面积较大的三角形的面积是 A .100 cm 2

B .96 cm 2

C .85 cm 2

D .36 cm 2

6.如图为二次函数y =ax 2+bx +c 的图像,下列说法:

①c <0;②a +b +c <0;③9a +3b +c =0;④3a +c =0.其中正确的有 A .1个

B .2个

C .3个

D .4个

二、填空题(本大题共10小题,每小题2分,共20分)

7.若a b =2

3,则a +b 2a

= ▲ .

B

(第4题)

8.已知P 是线段AB 的黄金分割点,AP >PB ,AB =2,则AP = ▲ .

9.把二次函数y =x 2的图像沿x 轴向左平移3个单位长度,再沿y 轴向上平移1个单位长度后,所得图像的函数表达式为 ▲ .

10.若一组数据1,2,x ,3,4的平均数是3,则这组数据的极差是 ▲ . 11.在二次函数y =ax 2+bx +c 中,y 与x 的部分对应值如下表:

则m 、n 的大小关系为 m ▲ n .(填“<”,“=”或“>”) 12.如图,点A 、B 、C 在⊙O 上,若∠BOC =150°,则∠A = ▲ °. 13.若二次函数y =x 2-3x +a 的图像与x 轴只有一个公共点,则a 的值为 ▲ . 14.若圆锥的底面圆的半径为2 cm ,母线长为8 cm ,则这个圆锥侧面展开图的面积为 ▲

cm 2.

15.如图,在△ABC 中,AB =9,AC =6,BC =12,点M 在边AB 上,AM =3,过点M 作

直线MN 与边AC 交于点N ,使截得的三角形与原三角形ABC 相似,则MN 的长为 ▲ .

16.如图,直线l 与⊙O 相切于点

A ,M 是⊙O 上的一个动点,设点M 与点A 间的距离为

a ,点M 到直线l 的距离为

b .若⊙O 的半径为1,则a -b 的最大值为 ▲ . 三、解答题(本大题共11小题,共88分.解答时应写出文字说明、推理过程或演算步骤) 17.(10分)解下列方程

(1)x 2-2x -1=0; (2) (x +3)2

=(x +3).

18.(7分)甲、乙两人分别进行了5次射击训练,成绩如下(单位:环).

(1)甲射击成绩的中位数是 ▲ 环,乙射击成绩的众数是 ▲ 环; (2)求甲射击成绩的方差.

19.(8分)一只不透明的袋子中装有1个蓝球和2个红球,这些球除颜色外都相同.

(第12题)

A

(第15题)

(第16题)

(1)搅匀后从中任意摸出1个球,求摸到蓝球的概率;

(2)搅匀后从中任意摸出1个球,记录颜色后放回、搅匀,再从中任意摸出1个球.

求至少有1次摸到红球的概率.

20.(8分)如图,在Rt △ABC 中,∠C =90°,矩形DEFG 的顶点G 、F 分别在AC 、BC

上,DE 在AB 上.

(1)求证:△ADG ∽△FEB ; (2)若AG =5,AD =4,求BE 的长.

21.(7分)已知二次函数的图像经过点(0,3)、(3,0)和(1,4).

(1)求该二次函数的表达式;

(2)若该二次函数图像的顶点为P ,与x 轴分别交于点A 、B ,求△ABP 的面积.

22.(8分)如图,已知⊙O 的直径为10,点A 、B 、C 在⊙O 上,∠CAB 的平分线交⊙O

(第20题)

图②

图①

于点D .

(1)图①,当BC 为⊙O 的直径时,求BD 的长; (2)图②,当BD =5时,求∠CDB 的度数.

23.(7分)已知二次函数y =x 2+(k -1)x -2k -3.

(1)求证:该二次函数图像与x 轴总有两个公共点;

(2)若点A (-1,y 1)、B (1,y 2)在该二次函数的图像上,且y 1>y 2,求k 的取值

范围.

24.(6分)如图,边长为1的小正方形组成了网格,点A 、B 均是格点,请你仅用无刻度

的直尺画出满足下列条件的点P ,并在图中标出点P . (1)图①中, 点P 在线段AB 上且AP =12AB ; (2)图②中, 点P 在线段AB 上且AP =1

3AB .

25.(9分)如图,在△ABC 中,AB =AC ,AD 为△ABC 的中线,O 为AB 上一点,以O

(第24题)

图①

A B

图②

A

B

(第22题)

为圆心,AO 为半径的⊙O 与AB 交于点F ,与BC 交于点E .连接AE ,AE 平分∠BAD . (1)求证:BC 与⊙O 相切于点E ; (2)若AB =10,BC =16,求⊙O 的半径;

(3)若AD 与⊙O 的交点为△ABC 的重心,则△ABE 的面积△ABC 的面积的值为 ▲ .

26.(9分)某水果店经营某种水果,顾客的批发量x (kg )与批发单价y (元/kg )之间的

关系如图所示.图中线段AB 表示:批发量x 每增加1

kg ,批发单价y 降低0.1元/kg . (1)求m 的值;

(2)已知该水果进价为6元/kg ,设该水果店获利w 元.

①求w 与x 的函数表达式; ②当0<x ≤m 时,求w 的最大值.

27.(9分)在矩形ABCD 中,AB =4,BC =10,E 是直线AD 上任意一点(不与点A 重合),

(第25题)

kg )

y (元(第26题)

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