江西省南昌市八一中学、洪都中学、麻丘高中等六校2017-2018学年高二10月联考数学试题

适用年级:高二
试卷号:596199

试卷类型:月考
试卷考试时间:2017/10/27

1.单选题(共10题)

1.
在约束条件下,当时,目标函数的最大值的变化范围是(   )
A.B.C.D.
2.
若圆始终平分圆的周长,则a,b应满足的关系式是(   )
A.B.
C.D.
3.
与圆的位置关系为()
A.内切B.相交C.外切D.相离
4.
如下图,在同一直角坐标系中表示直线y=ax与y=x+a,正确的是( )
A.B.C.D.
5.
已知直线与圆心为的圆相交于两点,且为等边三角形,则实数(   )
A.B.C.D.
6.
已知直线l1xy+1=0,l2:2x+2y-3=0,则l1,l2之间的距离为(  )
A.B.C.D.
7.
如图所示,定圆半径为,圆心为,则直线与直线的交点在(  )
A.第四象限B.第三象限C.第二象限D.第一象限
8.
若{(xy)|ax+2y-1=0}∩{(xy)|x+(a-1)y+1=0}=,则a等于(  )
A.B.2C.-1D.2或-1
9.
直线的倾斜角的大小为(  )
A.30°B.60°C.120°D.150°
10.
已知圆C:(x-1)2+(y-2)2=2截y轴所得线段与截直线y=2xb所得线段的长度相等,则b=(  )
A.B.C.D.

2.选择题(共2题)

11.

    Charlie was about to climb into bed when he found there was a light on in his garden shed(棚). Then he noticed some people who were busy stealing his things.
    He call the police right away. The policeman asked, “Are there any intruders(闯入者)in your house?” Charlie replied “no” and explained what was happening.
    The policeman said, “All patrol cars(巡逻车) have gone out, and a policeman will go to your house when one is free.”
    Charlie hung up, waited 30 seconds, and then called the police again. “Hello, I just called a short while ago because there were people stealing things from my shed. I want to let you know that they're not a problem anymore because I've just shot every one of them.”
    Charlie then hung up the phone. In five minutes, three patrol cars, nearly twenty policeman and an ambulance arrived at his house. Of course, the police caught the thieves.
    One policeman said, “I thought you said that you shot every one of them!”
    Charlie replied, “I thought you said there were no patrol cars free!”

12.

    Charlie was about to climb into bed when he found there was a light on in his garden shed(棚). Then he noticed some people who were busy stealing his things.
    He call the police right away. The policeman asked, “Are there any intruders(闯入者)in your house?” Charlie replied “no” and explained what was happening.
    The policeman said, “All patrol cars(巡逻车) have gone out, and a policeman will go to your house when one is free.”
    Charlie hung up, waited 30 seconds, and then called the police again. “Hello, I just called a short while ago because there were people stealing things from my shed. I want to let you know that they're not a problem anymore because I've just shot every one of them.”
    Charlie then hung up the phone. In five minutes, three patrol cars, nearly twenty policeman and an ambulance arrived at his house. Of course, the police caught the thieves.
    One policeman said, “I thought you said that you shot every one of them!”
    Charlie replied, “I thought you said there were no patrol cars free!”

3.填空题(共4题)

13.
若点在不等式组所表示的平面区域内,则的取值范围是_________;
14.
若直线l1yk(x-6)与直线l2关于点(3,1)对称,则直线l2恒过定点________;
15.
已知点A(3,2)和B(-1,4)到直线axy+1=0的距离相等,则a的值为________;
16.
在平面直角坐标系中,已知圆C:,直线经过点,若对任意的实数m,直线被圆C截得的弦长都是定值,则直线的方程为

4.解答题(共6题)

17.
已知以点CtRt≠0)为圆心的圆与x轴交于点O和点A,与y轴交于点O和点B,其中O为原点.
(1)求证:△OAB的面积为定值;
(2)设直线y=-2x+4与圆C交于点MN,若OMON,求圆C的方程.
18.
如图,分别是通过某城市开发区中心O的两条东西和南北走向的街道,连接MN两地间的铁路是圆心在上的一段圆弧.若点M在点O正北方向,且,点N的距离分别为5km和4km

(1)建立适当的坐标系,求铁路路线所在圆弧的方程.
(2)若该城市的某中学拟在点O正东方向选址建分校,考虑环境问题,要求校址到点O的距离大于4km,并且铁路上任意一点到校址的距离不能小于km,求该校址距点O的最近距离.
19.
已知菱形中,边所在的直线经过点.
(1)求边所在的直线方程;
(2)求对角线所在的直线方程.
20.
自点A(-3,3)发出的光线L射到x轴上,被x轴反射,其反射光线所在直线与圆x2+y2-4x-4y+7=0相切,求光线L所在直线的方程.
21.
已知点,动点P 满足:|PA|=2|PB|.
(1)若点P的轨迹为曲线,求此曲线的方程;
(2)若点Q在直线l1: x+y+3=0上,直线l2经过点Q且与曲线只有一个公共点M,求|QM|的最小值.
22.
过原点O的圆C,与x轴相交于点A(4,0),与y轴相交于点B(0,2).
(1)求圆C的标准方程;
(2)直线lB点与圆C相切,求直线l的方程,并化为一般式.
试卷分析
  • 【1】题量占比

    单选题:(10道)

    选择题:(2道)

    填空题:(4道)

    解答题:(6道)

  • 【2】:难度分析

    1星难题:0

    2星难题:0

    3星难题:0

    4星难题:0

    5星难题:0

    6星难题:0

    7星难题:0

    8星难题:0

    9星难题:20