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【一】:2016年青岛市中考自主招生青岛二中录取各学校学生名额
2 6 8 11
1 2 1 3 1 1 2 2
2 2 5 1 7
5 21
15
【二】:2016年广东省湛江市高考数学二模试卷(理科)(解析版)
2016年广东省湛江市高考数学二模试卷（理科）
一、选择题
1．已知全集U=R，集合A={x|x2≥4}，集合B={x|x＞1}，则∁U（A∪B）=（ ） A．{x|﹣2＜x＜2} B．{x|1≤x≤2} C．{x|﹣2＜x≤1} D．{x|﹣2≤x＜1} 2．已知i是虚数单位，a∈R，复数z1=3﹣ai，z2=1+2i，若z1•z2是纯虚数，则a=（ ） A．﹣ B． C．﹣6 D．6
3．某中学共有学生2000名，校卫生室为了解学生身体健康状况，对全校学生按性别分别采用分层抽样的办法进行抽样调查，抽取了一个容量为200的样本，样本中男生107人，则该中学共有女生（ ）
A．1070人 B．1030人 C．930人 D．970人
4．执行如图所示的程序框图，若输入x=2，则输出的结果为（ ）
A．2 B．5 C．11
5．给出以下四个结论： D．23
①a+b=0的充要条件是=﹣1；
②命题：“∀x∈R，sinx≤1”的否定是“∃x0∈R，sinx0＞1”；
③∀x＞0，2x＞x2；
④一组数据的方差越大，则这组数据的波动越小．
其中正确的个数是（ ）
A．0 B．1 C．2 D．3
6．函数f（x）=sin（ωx+）（ω＞0）的最小正周期为π，将其图象向右平移个单位后所得图象对应的解析式为（ ）
A．y=sin（2x﹣） B．y=﹣cos2x C．y=sin D．y=cos2x
7．如图，圆柱内有一个三棱柱，三棱柱的底面在圆柱底面内，且底面是正三角形，圆柱侧面积为16π，其底面直径与母线长相等，则此三棱柱的体积为（ ）
A．6 B．12 C．12 D．16
﹣）6的展开式中含x项的系数是（ ）
8．若a=，则二项式（a
A．210 B．﹣210 C．240 D．﹣240
9．y满足已知实数x， ，如果目标函数z=y﹣x的最大值为1，则实数m等于（ ）A．6 B．5 C．4 D．3
=1（a＞0，b＞0）的两条渐近线与抛物线y2=2px（p＞0）的准线
，则P10．已知双曲线分别交于M，N两点，O为坐标原点，若双曲线的离心率为2，△MON的面积为
的值为（ ）
A． B．3 C．4 D．2
11．设数列{an}为等差数列，{bn}为等比数列，若a1＜a2，b1＜b2，且bi=a（i=1，2，3），则数列{bn}的公比为（ ）
A．1+2 B．3+2 C．3﹣2 D．2﹣1
12．定义在R上的函数f（x）的导函数为f′（x），如对任意实数x，有f（x）＞f′（x），且f（x）+1为奇函数，则不等式f（x）+ex＜0的解集是（ ）
A．（﹣∞，0）
二、填空题
13．已知数列{an}满足a1=1，且对于任意n∈N*都有an+1=an+n+1，则
=
14．已知平面向量，是单位向量，且•=，若平面向量满足： •=•=||= ．
15．若∀x∈（0，），9x＜logax（a＞0且a≠1），则实数a的取值范围是 16．已知圆O：x2+y2=9，点A（2，0），点P为动点，以线段AP为直径的圆内切于圆O，则动点P的轨迹方程是 ．
三、解答题
17．B，C的对边分别为a，b，c，A为锐角，已知△ABC的内角A，向量=（2sinA，﹣），=（cos2A，2cos2﹣1），且∥．
（1）求A的大小；
（2）如果a=2，求△ABC面积的最大值．
18．某校数学文化节同时安排A、B两场讲座，已知甲、乙两寝室各有6位同学，甲寝室1人选择听A讲座，其余5人选择听B讲座，乙寝室2人选择听A讲座，其余4人选择听B讲座，现从甲、乙两寝室中各任选2人．
（1）求选出的4人均选择听B讲座的概率；
（2）设ξ为选出的4人中选择听A讲座的人数，求ξ的分布列和数学期望Eξ．
B．（0，+∞） C．（﹣∞，） D．（，+∞） +…+，则
19．如图，已知ABCDEF是正六边形，GA、ND都垂直于平面ABCDEF，平面FGN交线段DE于点R，点M是CD的中点，AB=DN=1，AG=2．
（1）求证：AM∥平面GFRN；
（2）求二面角A﹣GF﹣N的余弦值．
20．如图，已知抛物线C以坐标原点O为顶点，焦点F在x轴的正半轴上，且|OF|=． （1）求抛物线C的方程；
（2）过定点N（x0，y0）的动直线l与抛物线C相交于A、B两点（A、B异于点O），设OA、OB的倾斜角分别为α、β，若α+β（α+β∈（0，π））为定值，求x0的值．
21．已知函数f（x）=ex﹣e﹣x﹣xlna．
（1）若f（x）在R上单调递增，求实数a的取值范围；
（2）讨论f（x）的零点个数．
[选修4-1：几何证明选讲]
22．如图，直线AB为⊙O的切线，切点为B，点C、D在圆上，DB=DC，作BE⊥BD交圆于点E．
（1）证明：∠CBE=∠ABE；
（2）设⊙O的半径为2，BC=2，延长CE交AB于点F，求△BCF外接圆的半径．
[选修4-4：坐标系与参数方程选讲]
23．在直角坐标系xOy中，圆C的方程为（x﹣1）2+（y﹣2）2=1，以原点O为极点，以x轴正半轴为极轴建立极坐标系．
（1）求圆C的极坐标方程；
（2）若直线l的参数方程为=（t为参数），求圆C上的点到直线l的距离的取值范围．
[选修4-5：不等式选讲]
24．已知函数f（x）=|x+1|﹣2|x﹣1|．
（1）求不等式f（x）≥1的解集；
（2）求函数f（x）的图象与x轴围成的三角形的面积S．
2016年广东省湛江市高考数学二模试卷（理科）
参考答案与试题解析
一、选择题
1．已知全集U=R，集合A={x|x2≥4}，集合B={x|x＞1}，则∁U（A∪B）=（ ） A．{x|﹣2＜x＜2} B．{x|1≤x≤2} C．{x|﹣2＜x≤1} D．{x|﹣2≤x＜1}
【考点】交、并、补集的混合运算．
【分析】求出集合的等价条件，根据集合的基本运算进行求解即可．
【解答】解：由A={x|x2≥4}，得A={x|x≥2或x≤﹣2}，
则A∪B={x|x＞1或x≤﹣2}，
则∁U（A∪B）={x|﹣2＜x≤1}，
故选：C．
2．已知i是虚数单位，a∈R，复数z1=3﹣ai，z2=1+2i，若z1•z2是纯虚数，则a=（ ） A．﹣ B． C．﹣6 D．6
【考点】复数代数形式的乘除运算．
【分析】利用复数的运算法则、纯虚数的定义即可得出．
【解答】解：复数z1=3﹣ai，z2=1+2i，
∴z1•z2=（3﹣ai）（1+2i）=3+2a+（6﹣a）i是纯虚数，
∴，解得a=﹣．
故选：A．
3．某中学共有学生2000名，校卫生室为了解学生身体健康状况，对全校学生按性别分别采用分层抽样的办法进行抽样调查，抽取了一个容量为200的样本，样本中男生107人，则该中学共有女生（ ）
A．1070人 B．1030人 C．930人 D．970人
【考点】分层抽样方法．
【分析】设女生有x人，根据分层抽样比例相同，列出方程求出x的值即可．
【解答】解：设女生有x人，则
=，
解得x=930，
所以该校女生有930人．
故选：C．
4．执行如图所示的程序框图，若输入x=2，则输出的结果为（ ）www.fz173.com_2016年湛江二中高中录取学生。
【三】:湛江二中2016届高三上第二次月考英语试卷
第一部分 阅读理解（共两节，满分40分）
第一节 (共15小题；每小题2分，满分40分)
A
Larry was on another of his underwater expeditions(探险)but this time, it was different. He decided to take his daughter along with him. She was only ten years old. This would be her first trip with her father on what he had always been famous for.
Larry first began diving when he was his daughter’s age. Similarly, his father had taken him along on one of his expeditions. Since then, he had never looked back. Larry started out by renting diving suits from the small diving shop just along the shore. He had hated them. They were either too big or too small. Then, there was the instructor. He gave him a short lesson before allowing him into the water with his father. He had made an exception. Larry would never have been able to go down without at least five hours of theory and another similar number of hours on practical lessons with a guide. Children his age were not even allowed to dive.
After the first expedition, Larry’s later diving adventures only got better and better. There was never a dull moment. In his black and blue suit and with an oxygen tank fastened on his back, Larry dived from boats into the middle of the ocean. Dangerous areas did not prevent him from continuing his search. Sometimes, his was limited .com to a cage underwater but that did not bother him. At least, he was still able to take photographs of the underwater creatures.
Larry’s first expedition without his father was in the Cayman Islands.There were numerous diving spots in the area and Larry was determined to visit all of them .Fortunaly for him,a man offered to take him around the different
Spots for free. creatures that Larry saw more than thirty varieties of creatures.
Larry looked at his daughter.She looked as excited as he had been when he was her age.He hoped she would be able to continue the family tradition.Already,she looked like she was much braver than had been then.This was the key to a successful underwater expedition.
20.In what way was this expedition different for Larry?
A.His daughter had grown up.B.He had become a famous diver.
C.His father would dive with him.D.His daughter would dive with him.
21.What can be inferred from Paragraph2?
A.Larry had some privileges.B. Larry liked the rented diving suits.
C.Divers had to buy diving equipment.
D.Ten-year-old children were permitted to dive.
22.What did Larry expect his daughter to do?
A.Become a successful diver.B. Make a good diving guide.
C. Take a lot of photo underwater.D. Have longer hours of training.
B
HOLIDAY FUN AT THE POWERHOUSE
500 HARRIS STREET ULTIMO ·TELEPHONE (02)9270111
Join in the holiday fun ay the powerhouse this month linked to our new exhibition,
Evolution & Revolution: Chinese dress 1700s to now. DON’T FORGET our other special event, the Club Med Circus School which is part of the Circus（马戏团）！150 years of circus in Australia exhibition experience!
◆ Chinese Folk Dancing: Colorful Chinese dance and musical performances by The Chinese Folk Dancing School of Sydney. Dances include: the Golden and the Chinese drum dance. A feature will be the Qin dynasty Emperor’s count dance. Also included is a show of face painting for Beijing opera performances.
Sunday 29 June and Wednesday 2 July in the Turbine Hall, at 11.30 am & 1.30 pm.
◆ Australian Chinese Children’s Arts Theatre: Well-known children’s play experts from Shanghai leas this dynamic youth group. Performance include Chinese fairy tales and plays.
Thursday 3 to Sunday 6 July in the Turbine Hall, at 11.30 am & 1.30 pm.
◆ Chinese Youth League: A traditional performing arts group featuring
performance highlights such as Red scarf and Spring flower dances, and a musician playing Er Hu.
Sunday 6 to Tuesday 8 July in the Turbine Hall, 11.30 am to 1.30 pm.
◆ Kids Activity : Make a Paper Horse: Young ch
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