篇一：江苏省常州市第一中学、江阴南菁高中2016届高三数学两校联考试题
常州市第一中学、江阴南菁高中2016届高三两校联考
数学试题
一、填空题（本大题共14小题，每小题5分，计70分）
1．已知集合A?{2a}，B?{?1,1,3}，且A?B，则实数a的值是 ▲ ． 2．“a?1”是“(a?1)x?2对x?(1,??)恒成立”的 ▲ .条件（填“充分不必要、必要不充分、充要”）．
3．已知m，n为实数，若关于x的不等式x+mx+n＜0的解集为(—1，3)，则m+n的值为 ▲ ．
4．函数y?sinx?cosx?2(x?0)的值域是 ▲ .
5．已知抛物线y＝2px过点M(2，2)，则点M到抛物线焦点的距离为 ▲ ．
6. 底面边长为a的正四面体的体积为 ▲ ．
2
2
x2y2
7．已知F是椭圆2?2?1（a?b?0）的左焦点，A为右顶点，P是椭圆
ab
上一点，PF?x轴.若PF?
1
AF，则该椭圆的离心率是． 4
8．已知?ABC的一个内角为120?，并且三边长构成公差为4的等差数列，则?ABC的面积为 ▲ ．
9．已知f(x)是定义在R上的函数，且对任意x?R都有f(x?2)?f(2?x)?4f(2)，若函数
y?f(x?1)的图象关于点(?1,0)对称，且f(1)?3，则f(2015)?.
10．在等腰梯形ABCD中，已知AB//DC,∠ABC=60°,BC=
????????????1????????????
DC，则AE·BF的最小值为 ▲ ．且BE=?BC ，DF=2?
1
AB=2,动点E和F2
x
11．已知函数f(x)?e，对于实数m、n、p有f(m?n)?f(m)?f(n)f(m?n?p)?f(m)?f(n)?f(p)，则p的最大值等于．
g?x?a
12．已知函数f?x??x?(a?R), g?x??lnx，若关于x的方程2?f?x??2e(e为自然对数的
xx
底数)只有一个实数根, 则a=▲ ．
1
13．设a1，a2，?，an是各项不为零的n（n?4）项等差数列，且公差d?0．若将此数列删去某一项后，得到的数列（按原来顺序）是等比数列，则所有数对?n,
??a1?
?所组成的集合为 ▲ ． d?
14．已知P点为圆O1与圆O2公共点，圆O1:(x?a)2?(y?b)2?b2+1，圆O2:(x?c)2?(y?d)2?d2+1 ，若
ac?8,
ac
?，则点P与直线l：3x?4y?25?0上任意一点M之间的距离的最小值为 ▲ ． bd
二、解答题（本大题共6小题，计90分.解答应写出必要的文字说明，证明过程或演算步骤，并把答案写在答题纸的指定区域内） 15. （本题满分14分）
??????
2B?C在△ABC中，a,b,c分别为角A、B、C的对边，若m=(sin,1）, n?(?2,cos2A?1),且m?n. 2（1）求角A的度数；
222
（2）当a?，且△ABC的面积S?c的值和△ABC的面积。
▲ ▲ ▲
16．（本题满分14分）
已知直三棱柱ABC?A1B1C1中，D,E分别为AA1,CC1的中点，AC?BE,点F在线段AB上，且
AB?4AF．
（1）证:BC?C1D；
（2）若M为线段BE上一点，试确定M在线段BE上的位置，使得C1D//平面BFM． ▲ ▲ ▲
17．（本题满分14分）
如图，相距14km的两个居民小区M和N位于河岸l（直线）的同侧，M和N距离河岸分别为10km和8km．现要在河的小区一侧选一地点P，在P处建一个生活污水处理站，从P排直线水管PM，PN分别到两个小区和垂直于河岸的水管PQ，使小区污水经处理后排入河道．设PQ段长为t km（0 < t < 8）． M（1）求污水处理站P到两小区的水管的总长最小值（用t表示）； （2）请确定污水处理站P的位置，使所排三段水管的总长最小，并求出此时污水处理站分别到两小区水管的长度．
▲ ▲ ▲
18.（本题满分16分）
N
PQ河
l
x2y23
已知椭圆E2＋21过点D(1，)，且右焦点为F(1,0)，右顶点为A．过点F的弦为BC．直线BA，
ab2
直线CA分别交直线l:x＝m,(m＞2)于P?Q两点． (1) 求椭圆方程；
(2) （2）若FP⊥FQ，求m的值．
▲ ▲ ▲
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19. （本题满分16分）
已知函数f(x)?ax?x2?xlna(a?0,a?1). （1）求函数f(x)在点(0,f(0))处的切线方程； （2）求函数f(x)单调递增区间；
（3）若存在x1,x2?[?1,1]，使得f(x1)?f(x2)?e?1(e是自然对数的底数），求实数a的取值范围．
▲ ▲ ▲
20. （本题满分16分）
在数列{an}中，a1?1，且对任意的k?N*,a2k?1,a2k,a2k?1成等比数列，其公比为qk． （1）若qk=2(k?N*)，求a1?a3?a5?...?a2k?1；
（2）若对任意的k?N*，a2k，a2k?1，a2k?2成等差数列，其公差为dk，设bk? ① 求证：{bk}成等差数列，并指出其公差； ②若d1=2,试求数列{dk}的前k项的和Dk．
▲ ▲ ▲ 一、填空题：
1．1； 2．充分不必要； 3．－5； 4．［－4,0］； 5．10．l3；11．2ln2?ln3； 12. e?二、解答题：
4
2
1
． qk?1
533
a； 7．； 8
9．?3；；
6.
2412
1
； 13．?(4,?4),(4,1)?； 14．2. e
15. （本题满分14分）
???
【解】：（I）由于m?n，所以 ???B?CAm?n??2sin2?cos2A?1?1?2cos2?2cos2A?1?2cos2A?cosA?1
22
?(2cosA?1)(cosA?1)?0. ....................................3分
1
所以cosA??或1（舍去），....................................5分
2
又因为A?(0,?) ....................................6分
2
即角A的度数为?.....................................7分
3
222
（II
）由S?及余弦定理得：tanC?，....................................9分
3?
又因为A?(0,?) ∴C? ....................................10分
6
ac
?又由正弦定理得c?2，....................................12分 sinAsinC
1
所以?ABC的面积S?acsinB?。.....................................14分
2
16．（本题满分14分） 【解】：
⑴ 直三棱柱可
C
1
知
CC1?
平面ABC,AC?平面ABC,
1
所以
?CAC，....................................1分
B1又因为AC?BE,CC1?BE?E，CC1?平面BCE, BE?平面BCE,AC?面BCE， 故
D F AC?BC，....................................4分 又在直三棱柱中，CC1?BC,AC?CC1?C，AC?平面ACC1,CC1?平面ACC1,
故BC?面ACC1,C1D在平面ACC1内，所以BC?C1D....................................7分 (2)连结AE，在BE上取点M，使BE=4ME, ....................................8分 连结FM，B1M,FB1，在?BEA中，由BE=4ME，AB=4AF....................................10分 所以MF//AE， ....................................11分 又在面AA1C1C中，∵C1E?AD且C1E//AD，∴C1D//AE，又MF//AE，所以C1D//MF，
C1D?/平面B1FM，FM?平面B1FM，C1D//平面B1FM．...................................14分 17．（本题满分14分） 【解】： （1）如图，以河岸l所在直线为x轴，以过M垂直于l的直线为y
轴建立直角坐标系，则可得点M(0, 10)，
由MN=14,MO=10,NN’=8点N ...................................2分 设点P(s,t
)，过P作平行于x轴的直线m，作N关于m的对称点N?，则N?t?8)．
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篇二：江苏省南菁高级中学实验学校2015年中考一模英语试卷(含详细答案)
江苏省南菁高级中学实验学校2015年中考一模英语试卷
第一卷 选择题（50分）
一、单项填空 在A、B、C、D 四个选项中，选出可以填入空白处的最佳选项。（本大题共14 分，每小题1分）
1.I can't tell you________ way to the Webb's because there isn't________ Webb here.
A. the; aB. a; / C. the; the D. the; /
2._________ wonderful news report he wrote! The boss was really satisfied with it.
A. What a B. What C. HowD. How a
3.---Mum, when shall we go to the zoo?
---Sorry, I will have a meeting today. ________ Saturday ________ Sunday is OK.
A. Not only; but also B. Neither; norC. Either; or D. Both; and
4.My cousin served in the army ________ when he was ________.
A. in 1990's; in twenties B. in the 1990's; in the twenties
C. in the 1990s; in his twentiesD. in 1990's; in his twenties
5.Boris has a good brain. In fact, I don't think that anyone in the class has________ IQ.
A. a high B. a higherC. the higher D. the highest
6.How lucky Peter was! Some policemen arrived in time and_________ him out.
A. failed to help B. managed to helpC. succeeded to help D. tried to help
7.---Do the Smiths live next door to you? ---No, but they________.
A. used to B. used to do C. are used to D. used to be
8.Debbie spends________ money on clothes every year.
A. many B. a great deal of C. a great deal D. a number of
9.---So many people are standing outside the hall. ________ will the concert begin?
---________ seven o'clock.
A. How soon; Until B. How long; UntilC. How long; Not untilD. How soon; Not until
10.The boy_________ "Prince of Basketball" after his_________ in the match.
A. named; successB. was named; successC. named; succeeded D. was named; succeeded
11.What do you think________ if the car________?
A. can we do; is brokenB. can we do; breaks down
C. we can do; breaks downD. we can do; is broken down
12.You_________ be too careful while you are driving a car.
A. needn't B. mustC. mayD. can't
13.---Could you tell me_________?
---Sorry, I have no idea, either. You can ask the policeman over there.
A. what's happened to themB. how I can arrive the museum
C. when did the accident happen D. where they had gone to
14.---Whose advice should we take? ---________.
A. Don't mention itB. It's your turnC. I'm sorry D. Up to you
二、完形填空 先通读下面的短文，掌握其大意，然后在每小题所给的四个选项中，选出可以填入空白处的最佳选项。（本大题共10分，每小题1分）
Barefoot and dirty, the girl just sat and watched the people go by. She never tried to speak. Many people
The next day I decided to go back to the park, being curious if the little girl would still be there. Right in the very spot as she was yesterday, she sat, with the look on her face.
As I began walking towards her, I could see the back of the little girl's dress which showed a deformity(畸形). As I got closer, the little girl slightly lowered her eyes to my eyes.
I sat down beside her and opened with a simple . The little girl stammered(结结巴巴地说) a hi. I smiled and she shyly smiled back. We talked until darkness fell and the park was completely empty.
"Why are you so sad?"
She replied slowly, "Because I'm "Little girl," I said in a soft voice, "You me of an angel because of your difference." She stood to her feet excitedly, "Really?"
"Yes, that's the thing. You're like a little angel sent to watch over all those people walking by." She nodded her head and smiled, " I am. And since you think of someone
yourself, my job here is done."
What a big surprise! I asked quickly, "Wait, so why did no one stop to help an angel?"
She bloomed(绽放) a big smile, "You are the one who could see me, because you care for others." With those words, she spread her wings and flew away from my sight.
From then on, I believe I am not all I have, for there is an angel always me. She is always watching over those who do good things for others.
15. A. passed B. looked C. asked D. helped
16. A. angriest B. coldest C. happiest D. saddest
17. A. avoid B. see C. touch D. meet
18. A. smile B. hello C. question D. word
19. A. different B. foolish C. beautiful D. poor
20. A. force B. treat C. turn D. remind
21. A. Indeed B. Happily C. Perhaps D. Luckily
22. A. beyond B. besides C. including D. except
23. A. clever B. great C. lucky D. only
24. A. on B. with C. in D. for
三、阅读理解 阅读下面的短文，然后根据短文内容，在每小题所给的四个选项中选出最佳选项。（本大题共26分，每小题2分）
A
If you want to see a thing well, touching can help you to "see" it better.
Your eyes can tell you that a glass ball is round. But by holding it in your hands, you can feel how smooth and cool the ball is. You can feel how heavy the glass ball is. When you learn all about the ball, you really see it well.
With your skin, you can feel better. For example, your fingers can tell the difference between two different coins in your pocket. You can feel a little drop of water on the back of your hand, too. You can even feel sounds against your skin. Have you ever wanted to know why some people like very loud music? They must like to feel the sounds of music.
All children soon learn what "Don't touch!" means. They hear it often. Yet most of us keep on touching things as we grow up. In shops, we touch things that we might buy. To see something well, we have to touch it. The bottoms of our feet can feel things, too. You know this when you walk on warm sand, cool grass or a hard floor. All feel different under your feet.
Most museums are just for looking. But today some museums have some things to touch. Their signs say, "Do touch!" There you can feel everything on show.
There are ways of learning to see well by feeling. One way is to close your eyes and try to feel everything that is touching your skin. Feel the shoes on your feet, the clothes on your body, the air on your skin.
If you want to see better, reach out and touch. Then you will really see!
25.The underlined word "these" in Paragraph 2 refers to________.
A. a glass ball is round
B. a glass ball is smooth and cool
C. a glass ball is smooth, cool and heavy
D. a glass ball is round, smooth, cool and heavy
26.Which of the following is NOT true?
A. People don't have to learn to feel.
B. Our skin may help us enjoy music.
C. By touching things, we can learn more about them.
D. We have to touch something in order to see it well.
27.________ can be the best title of the passage.
A. Feeling by Seeing B. To See or to Feel
C. To See Better---Touch D. Ways of Touching
B
Soon computers and other machines will be able to remember you by looking at your eyes! The programme works because everyone's eyes are different. Therefore, in the future you won't have to remember a number when you want to use a machine or take money out of a bank. You'll just have to look at the machine and it will be able to tell who you are.
The eye-recognition programme has already been tested in shops and banks in the USA, Britain, Spain, Italy and Turkey. Soon this technology will take the place of all other ways of finding out who people are.
However, scientists are also working on other systems. Machines will soon be able to know you from the shape of your face or hand or even your smell! We already have machines that can tell who you are from your voice or the mark made by your finger.
Eye-recognition is better than other kinds because your eyes don't change as you get older, a(转自：wWw.DXf5.Com 东星 资源网:南菁高中中考分数线)nd don't get dirty like hands or fingers, and even twins have different eyes. The eye-recognition programme can be up to 94% correct, depending on how good the technology is. However, some other programmes may only be 51% correct at present. In Britain, it was found that 91% of people who had tried it said that they liked the idea of eye-recognition.
In the future your computer will be looking at you in the eye. So smile!
28.Where has the eye-recognition programme already been tested in a few countries?
A. In shops and banks.B. In shops and schools.
C. In banks and schools. D. In schools and hospitals.
29.We already have machines that can tell who you are from________.
A. your eyes or your smell
B. your voice or the mark by your finger
C. your face or your voice
D. your face or your hand
30.Which of the following doesn't belong to the advantages of the eye-recognition programme?
篇三：盘点：全国100所一流中学名单一览
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