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2015年普通高等学校招生全国统一考试(安徽卷)

2015年普通高等学校招生全国统一考试(安徽卷)
2015年普通高等学校招生全国统一考试(安徽卷)

2015年普通高等学校招生全国统一考试(安徽卷)

数学(文科)

一、选择题

1.设i 是虚数单位,则复数()()112i i -+=

(A )3+3i (B )-1+3i (3)3+i (D )-1+i

2.设全集{}123456U =,,,,,,{}12A =,,{}234B =,,,则()R A C B =

(A ){}1256,,

, (B ){}1 (C ){}2 (D ){}1234,,, 3.设p :x<3,q :-1

(A )充分必要条件 (B )充分不必要条件

(C )必要不充分条件 (D )既不充分也不必要条件

4.下列函数中,既是偶函数又存在零点的是

(A )y=lnx (B )2

1y x =+ (C )y=sinx (D )y=cosx 5.已知x ,y 满足约束条件0401x y x y y -≥??+-≤??≥?

,则z=-2x+y 的最大值是

(A )-1 (B )-2 (C )-5 (D )1

6.下列双曲线中,渐近线方程为2y x =±的是

(A )22

14y x -= (B )2

214x y -= (C )22

12y x -= (D )2

212x y -= 7.执行如图所示的程序框图(算法流程图),输出的n 为

(A )3 (B )4 (C )5 (D )6

8.直线3x+4y=b 与圆22

2210x y x y +--+=相切,则b=

(A )-2或12 (B )2或-12 (C )-2或-12 (D )2或12

9.一个四面体的三视图如图所示,则该四面体的表面积是

(A )1 (B )1+ (C )2 (D )10.函数()32

f x ax bx cx d =+++的图像如图所示,则下列结论成立的是

(A )a>0,b<0,c>0,d>0

(B )a>0,b<0,c<0,d>0

(C )a<0,b<0,c<0,d>0

(D )a>0,b>0,c>0,d<0

二;填空题

(11)=-+-1)2

1(2lg 225lg 。

(12)在ABC ?中,6=AB , 75=∠A , 45=∠B ,则=AC 。

(13)已知数列}{n a 中,11=a ,211+

=-n n a a (2≥n ),则数列}{n a 的前9项和等于 。

(14)在平面直角坐标系xOy 中,若直线a y 2=与函数1||--=a x y 的图像只有一个交点,则a 的值为 。

(15)ABC ?是边长为2的等边三角形,已知向量b a 、满足a AB 2=→,b a AC +=→2,

则下列结论中正确的是 。(写出所有正确结论得序号)

①a 为单位向量;②b 为单位向量;③b a ⊥;④→BC b // ;⑤→⊥+BC b a )4( 。

三.解答题

16.已知函数2()(sin cos )cos 2f x x x x =++

(1)求()f x 最小正周期;

(2)求()f x 在区间[0,]2π

上的最大值和最小值.

17.某企业为了解下属某部门对本企业职工的服务情况,随机访问50名职工,根据这50名职工对该部门的评分,绘制频率分布直方图(如图所示),其中样本数据分组区间为

[40,50],[50,60],,[80,90],[90,100]

(1)求频率分布图中a 的值;

(2)估计该企业的职工对该部门评分不低于80的概率;

(3)从评分在[40,60]的受访职工中,随机抽取2人,求此2人评分都在[40,50]的概率.

18.已知数列{}n a 是递增的等比数列,且14239,8.a a a a +==

(1)求数列{}n a 的通项公式;

(2)设n S 为数列{}n a 的前n 项和,11

n n n n a b S S ++=,求数列{}n b 的前n 项和n T 。 19.如图,三棱锥P-ABC 中,PA ⊥平面ABC ,1,1,2,60PA AB AC BAC ===∠=o .

(1)求三棱锥P-ABC 的体积;

(2)证明:在线段PC 上存在点M ,使得AC ⊥BM ,并求PM MC

的值。

20.设椭圆E 的方程为22

221(0),x y a b a b

+=>>点O 为坐标原点,点A 的坐标为(,0)a ,点B

的坐标为(0,b ),点M 在线段AB 上,满足2,BM MA =直线OM (1)求E 的离心率e;

(2)设点C 的坐标为(0,-b ),N 为线段AC 的中点,证明:MN ⊥AB 。

21.已知函数)0,0()()(2

>>+=r a r x ax x f (1)求)(x f 的定义域,并讨论)(x f 的单调性;

(2)若400=r

a ,求)(x f 在),0(+∞内的极值。

2015年江苏卷高考英语真题与答案

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2015年安徽省江南十校高三联考英语试卷

姓名______ 座位号______ (在此卷上答题无效) 绝密★启用前 2015年安徽省"江南十校"高三联考 英语 本试卷分第I卷(选择题)和第II卷(非选择题)两部分,第I卷第1至第13页,第II卷第14至第16页。全卷满分150分,考试时间120分钟。 考生注意事项: 1.答题前,务必在试题卷、答题卡规定的地方填写自己的姓名、座位号,并认真核对答题卡上所粘贴的条形码中姓名、座位号与本人姓名、座位号是否一致。务必在答题卡背面规定的地方填写姓名和座位号后两位。 2.答第I卷时,每小题选出答案后,用2B铅笔把答题卡上对应题目的答案标号涂黑。如需改动,用橡皮擦干净后,再选涂其他答案标号。 3.答第II卷时,必须使用0.5毫米的黑色墨水签字笔在答题卡上书写,要求字体工整、笔迹清晰。作图题可先用铅笔在规定的位置绘出再用0.5毫米的黑色墨水签字笔描清楚。必须在题号所指示的答题区域作答,超出答题区域书写的答案无效。 在试题卷,草稿纸上答题无效。 4.考试结束,务必将试题卷和答题卡一并上交。 第I卷 第一部分听力(共两节,满分30分) 做题时,先将答案标在试卷上。录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。 第一节(共5小题,每小题1.5分,满分7.5分) 听下面5段对话。每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。 1. What does the man mean? A. He’d like to come along. B. He knows the way to the river. C. The weather is quite hot. 2. What did the man think of the exam? A. It wasn't too difficult. B. It was easy. C. It was very difficult. 3. When does the train for Xuancheng start? A. 11:30. B. 9:34. C. 9 : 30 4. What does the man want to do? A. Go on a diet. B. Have a health check. C. Have his own doctor. 5. What can we learn from the conversation? A. The girl was probably not telling the truth. B. Students shouldn't ride bikes to school on Mondays. C. There is no doubt that bikes break down easily. 第二节(共15小题;每小题1.5分,满分22.5分) 听下面5段对话或独白。每段对话或独白后有几个小题,从题中所给的A、B、C、三个选项中选出最佳选项,并标在试卷的相应位置,听每段对话或独白前,你将有时间阅读各小题,每

2015年高考英语全国卷阅读解析

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完整word2015年高考英语江苏卷

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1.铺设树皮覆盖层的主要目的是: A.为植物提供养分 B.控制雨水渗漏速度 C.吸附雨水污染物 D.保持土壤水分 2.对下渗雨水净化起主要作用的填充层是 A. 树皮覆盖层和种植土层 B. 种植土层和砂层 C. 砂层和砾石层 D. 树皮覆盖层和砾石层 3. 雨水花园的核心功能是 A. 提供园林观赏景观 B. 保护生物多样性性 C. 控制雨洪和利用雨水 D. 调节局地小气候 甘德国际机场(图2)曾是世界上最繁忙的航空枢纽之一,当时几乎所有横跨北大西洋的航班都要经停该机

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