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2015-2016年度高三第一学期数学期中测试一、选择题（本大题有12小题，每小题5分，共60分。
在每小题给出的四个选项中，只有一项是符合题目要求的并填在答题卡上）1.设A ，B 是两个集合，则“AB A =”是“A B Í”的（ ）A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件 2.设命题p ：2,2n n N n $?，则p Ø为( )A ．2,2n n N n"? B.2,2n n N n $危 C. 2,2n n N n "危 D.2,=2n n N n $?3.下列函数为奇函数的是( )A ．y =B ．sin y x = C ．cos y x = D ．x x y e e -=-4.要得到函数sin 43y x p骣琪=-琪桫的图象，只需要将函数sin 4y x =的图象（ ） A.向左平移12π个单位 B.向右平移12π个单位C.向左平移3π个单位 D.向右平移3π个单位 5.已知菱形ABCD 的边长为a ，60ABC ? ,则BD CD ?（ ）A.232a -B.234a -C. 234a 错误！未找到引用源。
D. 232a 错误！未找到引用源。
6.函数()f x =cos()x w j +的部分图像如图所示，则()f x 的单调递减区间为( ) A.13(,),44k k k Z p p -+? B.13(2,2),44k k k Z p p -+? C.13(,),44k k k Z -+? D.13(2,2),44k k k Z -+?7..在ABC D中，已知,a c bb c a c-=-+则角A 的值是（ ）A ． 30B ．60C ．120D ．1508.设函数211log (2),1,()2,1,x x x f x x -ì+-<ï=í³ïî,2(2)(log 12)f f -+=( )A ．3B ．6C ．9D ．12 9.若非零向量a ，b 满足|a ||b |，且（a -b ）^（3a +2b ），则a 与b 的夹角为 （ ） A.4πB.2πC.34πD.π 10.已知定义在R 上的函数()21x mf x -=- （m 为实数）为偶函数，记()()0.52(log 3),log 5,2a f b f c f m === ，则,,a b c 的大小关系为( )A.a b c <<B.a c b <<C.c a b <<D.c b a << 11.已知符号函数1,0,sgn 0,0,1,0.x x x x ì>ïï==íï-<ïî ()f x 是R 上的增函数，()()()(1)g x f x f ax a =->，则（ ）A ．sgn[()]sgn g x x =B ．sgn[()]sgn g x x =-C ．sgn[()]sgn[()]g x f x =D ．sgn[()]sgn[()]g x f x =-12.设函数'()f x 是奇函数()()f x x R Î的导函数，(1)0f -=，当0x >时，'()()0xf x f x -<，则使得()0f x >成立的x 的取值范围是（ ）A ．(,1)(0,1)-? B ．(1,0)(1,)-+? C ．(,1)(1,0)-?- D ．(0,1)(1,)+?二、填空题（本大题有4小题，每小题5分，共20分。
2015-2016年度高三第一学期数学期中测试一、选择题（本大题有12小题，每小题5分，共60分。
在每小题给出的四个选项中，只有一项是符合题目要求的并填在答题卡上）1.设A ，B 是两个集合，则“AB A =”是“A B Í”的（ ）A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件 2.设命题p ：2,2n n N n $?，则p Ø为( )A ．2,2n n N n"? B.2,2n n N n $危 C. 2,2n n N n "危 D.2,=2n n N n $?3.下列函数为奇函数的是( )A ．y =B ．sin y x = C ．cos y x = D ．x x y e e -=-4.要得到函数sin 43y x p骣琪=-琪桫的图象，只需要将函数sin 4y x =的图象（ ） A.向左平移12π个单位 B.向右平移12π个单位C.向左平移3π个单位 D.向右平移3π个单位 5.已知菱形ABCD 的边长为a ，60ABC ? ,则BD CD ?（ ）A.232a -B.234a -C. 234aD. 232a 6.函数()f x =cos()x w j +的部分图像如图所示，则()f x 的单调递减区间为( )A.13(,),44k k k Z p p -+?B.13(2,2),44k k k Z p p -+? C.13(,),44k k k Z -+? D.13(2,2),44k k k Z -+?7..在ABC D 中，已知,a c bb c a c-=-+则角A 的值是（ ）A ． 30B ．60C ．120D ．1508.设函数211log (2),1,()2,1,x x x f x x -ì+-<ï=í³ïî,2(2)(log 12)f f -+=( )A ．3B ．6C ．9D ．12 9.若非零向量a ，b 满足|a ||b |，且（a -b ）^（3a +2b ），则a 与b 的夹角为 （ ） A.4πB.2πC.34πD.π 10.已知定义在R 上的函数()21x mf x -=- （m 为实数）为偶函数，记()()0.52(log 3),log 5,2a f b f c f m === ，则,,a b c 的大小关系为( )A.a b c <<B.a c b <<C.c a b <<D.c b a << 11.已知符号函数1,0,sgn 0,0,1,0.x x x x ì>ïï==íï-<ïî ()f x 是R 上的增函数，()()()(1)g x f x f ax a =->，则（ ）A ．sgn[()]sgn g x x =B ．sgn[()]sgn g x x =-C ．sgn[()]sgn[()]g x f x =D ．sgn[()]sgn[()]g x f x =-12.设函数'()f x 是奇函数()()f x x R Î的导函数，(1)0f -=，当0x >时，'()()0xf x f x -<，则使得()0f x >成立的x 的取值范围是（ ）A ．(,1)(0,1)-? B ．(1,0)(1,)-+? C ．(,1)(1,0)-?- D ．(0,1)(1,)+?二、填空题（本大题有4小题，每小题5分，共20分。
卷11 安徽省蚌埠市2016届高三第一次教学质量检查[听力录音材料]Text 1W: Excuse me. Could you tell me where the TV station is?M: Yes, go two blocks and then turn left. The TV station is on the corner, opposite the post office.Text 2W: It must be the wind that makes it so cold. I'm freezing.M: Me, too. Let’s go inside.W: OK. It's no fun standing out here even if the sun is shinning.Text 3M: I just heard I passed my physics exam.W: Congratulations! I’m glad somebody is happy.M: Why? What’s the matter?W: Oh, I’m just worried I guess. I have to take a history exam next week.Text 4M: Excuse me. Is this seat taken?W: No, it isn’t.M: Would you mind moving over one? So my friend and I can sit together.W: No, not at all.Text 5W: Did you lock the doors?M: All except the back door. I left that open for Tim. He took the dog for a walk.W: Well, I'm going on to bed. I'm tired.Text 6[Knock]M: Hello?W: Hello. Mr. Johnson.M: Hello, Susan. What's up? How’s that report of mine going?W: Actually I've finished it.M: You have!W: Yes, I really wanted to help you since you had that meeting to go to.M: Ah, thanks a lot!W: Look, I'd like you to go over it to see if I missed anything. Shall I send it to your office some time this afternoon.M: Yes, that will be fine. You know. . .Text 7M: Hello, Ann. John speaking. It’s Saturday today. Are you doing anything tonight?W: Gee I’m sorry. But I’m afraid I'm busy tonight.M: Well, how about tomorrow? Maybe we could go to the cinema.W: That sounds good. What do you want to see?M: I was thinking we could see Bread and Chocolate. It’s playing on main street.W: Great, I’d love to.M: I guess we should meet about 8 o’clock then. I think the film starts at 8: 30. Where would be a good place to meet?W: There is a clock tower near the theater. We could meet there at about 8.M: OK, that sounds good. See you tomorrow then.W: See you.Text 8M: Was that the telephone ringing?W: I didn’t hear anything.M: I thought I heard it ring two or three times.W: Sometimes when the window is open, you can hear the neighbors’ phone.M: Well, I'm expecting an important phone call. And I don’t want to miss it.W: Is it anything I should know about?M: Not really. It has something to do with work and doesn’t really affect us here at home.W: Well, why don’t you go ahead and do what you wanted to do outside? I'll call you if the phone rings for you.M: Thanks! I think I will. I’ve been waiting so long now, I'm getting nervous. I need to calm down outdoors.Text 9W: So, Mr. Johns, are you ready for your trip?M: Ah, yes! I’m really excited about it. But could you tell me what I have to do at the airport?I’ve never flown before in my life. I’ve always preferred the train.W: I see. Well, luckily, the airport is small. So you can’t get lost. Now, as you enter, on your left, you’ll see a lot of checking desks. You should go to your airline desk, okay? Actually, that’s very close to the entrance. Once there show your ticket and your passport to the clerk and place your luggage on the scales. Try not to have more than 25 kilograms all together. Oh, and don’t check in your hand luggage as you’ll be taking that with you on the plane. Then the clerk will give you a boarding pass with your seat number printed on it.M: A friend of mine told me something about the departure tax. What’s that? Have I paid it?W: Don’t worry. It’s included in the price of your ticket.Text 10Usually, I’m in about 8:40, and the day usually starts with me typing a letter to a friend because I'm first in the office. So I spend a little time doing my own personal things. Then I'll go to the library where we have a computer on which we have a list of all our library books, er, which we keep an update until the new books coming. We put them onto the computer files. The otherthing we do out there is to deal with reports of problems other countries have come across in their computer systems. They send in forms called trouble reports, and we type them up and hand them out. And then, over the next few days, somebody in the department would solve the problem, write onto a platform, and we'll type that up, copy it to all and send it back so that everybody can change their system. But, um, it's pretty busy at the moment because the department’s closing down. And they're moving to China. So we're trying to get rid of all the library books and so on, and still carry on with the reports and replies. But then, suddenly comes a moment when everything goes from London to China when all the new problems are sent to the computer there. So we're building up towards that.。
A组考点基础演练一、选择题1．(2014年高考浙江卷)设全集U＝{x∈N|x≥2}，集合A＝{x∈N|x2≥5}，则∁U A＝() A．∅B．{2}C．{5} D．{2,5}解析：∵A＝{x∈N|x≥5}＝{x∈N|x≥3}，∴∁U A＝{x∈N|2≤x<3}＝{2}，故选B.答案：B2．已知全集为R，集合A＝{x|x2>1}，B＝{x|log2x>0}，则下列关系正确的是()A．A∪B＝R B．A∪(∁U B)＝RC．(∁U A)∪B＝R D．A∩B＝A解析：A＝(－∞，－1)∪(1，＋∞)，B＝(1，＋∞)，∁U B＝(－∞，1]．答案：B3．设集合P＝{3，log2a}，Q＝{a，b}，若P∩Q＝{0}，则P∪Q＝()A．{3,0} B．{3,0,2}C．{3,0,1} D．{3,0,1,2}解析：由P∩Q＝{0}，得log2a＝0，所以a＝1，从而b＝0，P∪Q＝{3,0,1}．答案：C4．(2014年福建五校期中联考)已知全集U＝R，集合M＝{x|x2－x＝0}，N＝{x|x＝2n＋1，n∈Z}，则M∩N为()A．{0} B．{1}C．{0,1} D．∅解析：因为，M＝{x|x2－x＝0}＝{0,1}，N＝{x|x＝2n＋1，n∈Z}中的元素是奇数，所以，M∩N＝{1}，选B.答案：B5．已知集合M＝{y|y＝x2＋1，x∈R}，N＝{x|y＝x＋1}，则M∩N＝()A．(0,1) B．{(0,1)}C．{x|x≥－1} D．{y|y≥1}解析：∵M＝{y|y≥1}，N＝{x|x≥－1}，∴M∩N＝{y|y≥1}，选D.答案：D二、填空题6．已知集合U＝{2,3，a2＋2a－3}，A＝{|2a－1|,2}，∁U A＝{5}，则实数a的值为________．解析：根据已知得⎩⎪⎨⎪⎧a 2＋2a －3＝5|2a －1|＝3，解得a ＝2.答案：27．(2014年高考重庆卷)设全集U ＝{n ∈N |1≤n ≤10}，A ＝{1,2,3,5,8}，B ＝{1,3,5,7,9}，则(∁U A )∩B ＝________.解析：∁U A ＝{4,6,7,9,10}，∴(∁U A )∩B ＝{7,9}． 答案：{7,9}8．设全集U ＝{0,1,2,3,4,5}，集合A ＝{2,4}，B ＝{y |y ＝log3(x －1)，x ∈A }，则集合(∁U A )∩(∁U B )＝________.解析：由题意得∁U A ＝{0,1,3,5}，B ＝{0,2}，∁U B ＝{1,3,4,5}．所以(∁U A )∩(∁U B )＝{1,3,5}． 答案：{1,3,5} 三、解答题9．(2014年南昌二中月考)已知：全集U ＝R ，函数f (x )＝1x ＋2＋lg(3－x )的定义域为集合A ，集合B ＝{x |－2<x <a }．(1)求∁U A ；(2)若A ∪B ＝A ，求实数a 的范围．解析：(1)由题意知⎩⎪⎨⎪⎧x ＋2>03－x >0，解得－2<x <3，所以集合A ＝{x |－2<x <3}，所以∁U A ＝{x |x ≤－2或x ≥3}；(2)由A ∪B ＝A 得B ⊆A ，集合A 在数轴上的表示为：所以要保证B 完全落在A 内，所以a ≤3.10．设不等式4－xx －2>0的解集为集合A ，关于x 的不等式x 2＋(2a －3)x ＋a 2－3a ＋2<0的解集为集合B .(1)若B ⊆A ，求实数a 的取值范围； (2)若A ∩B ＝∅，求实数a 的取值范围．解析：由题意4－xx －2>0⇔(x －2)(x －4)<0，解得A ＝{x |2<x <4}，集合B ＝{x |(x ＋a －2)(x ＋a－1)<0}＝{x |1－a <x <2－a }．(1)若B ⊆A ，则⎩⎪⎨⎪⎧1－a ≥22－a ≤4，解得－2≤a ≤－1，即a ∈[－2，－1]；(2)若A∩B＝∅，则2－a≤2或1－a≥4，解得a∈(－∞，－3]∪[0，＋∞)．B组高考题型专练1．已知P＝{－1,02}，Q＝{y|y＝sin θ，θ∈R}，则P∩Q＝()A．∅B．{0}C．{－1,0} D．{－1,0，2}解析：P＝{－1,0，2}，Q＝{y|y＝sin θ，θ∈R}＝{y|－1≤y≤1}|，所以P∩Q＝{－1,0}．答案：C2．设全集U＝R，A＝{x|2x(x－2)<1}，B＝{x|y＝ln(1－x)}，则下图中阴影部分表示的集合为()A．{x|x≥1} B．{x|1≤x<2}C. {x|0<x≤1} D．{x|x≤1}解析：由图像知，图中阴影部分所表示的集合为{x|x∈A且x∉A∩B}，由于A＝{x|2x(x－2)<1}＝{x|x(x－2)<0}＝{x|0<x<2}，B＝{x|y＝ln(1－x)}＝{x|1－x>0}＝{x|x<1}，故图中阴影部分表示的集合为{x|1≤x<2}，故选B.答案：B3．设集合U＝{x∈N|0<x≤8}，S＝{1,2,4,5}，T＝{3,5,7}，则S∩(∁U T)＝()A．{1,2,4} B．{1,2,3,4,5,7}C．{1,2} D．{1,2,4,5,6,8}解析：由U＝{1,2,3,4,5,6,7,8}，S＝{1,2,4,5}，T＝{3,5,7}，所以∁U T＝{1,2,4,6,8}，因此S∩(∁U T)＝{1,2,4}．故选A.答案：A4．若集合A＝{x∈R|y＝lg(2－x)}，B＝{y∈R|y＝2x－1，x∈A}，则∁R(A∩B)＝() A．R B．(－∞，0]∪[2，＋∞)C．[2，＋∞) D．(－∞，0]解析：A＝{x∈R|2－x>0}＝{x∈R|x<2}，B＝{y∈R|0<y<2}，∁R(A∩B)＝(－∞，0]∪[2，＋∞)．答案：B5．(2015年九江市七校联考)设集合M＝{－1,0,1}，N＝{a，a2}，若M∩N＝N，则a的值是()A．－1 B．0C．1 D．1或－1解析：M ∩N ＝N ，则N ⊆M ，当a ＝0时，N ＝{0,0}，与集合元素互异性相矛盾，当a ＝1时，N ＝{1,1}，与集合元素互异性相矛盾，当a ＝－1时，N ＝{－1,1}，符合题意．答案：A6．设集合M ＝{y |y ＝2sin x ，x ∈[－5,5]}，N ＝{x |y ＝log 2(x －1)}，则M ∩N ＝( ) A ．{x |1<x ≤5} B ．{x |－1<x ≤0} C ．{x |－2≤x ≤0}D ．{x |1<x ≤2}解析：M ＝{y |y ＝2sin x ，x ∈[－5,5]}＝[－2,2]，N ＝{x |y ＝log 2(x －1)}＝(1，＋∞)，M ∩N ＝[－2,2]∩(1，＋∞)＝(1,2]．答案：D7．(2015年江南十校联考)已知集合A ＝{y |y ＝2x ，x ∈R }，B ＝⎩⎨⎧⎭⎬⎫x |y ＝log 22－x 2＋x ，则A ∩B ＝________.解析：函数y ＝2x 的值域为(0，＋∞)，函数y ＝log 22－x2＋x 的定义域为(－2,2)，即A ＝(0，＋∞)，B ＝(－2,2)，∴A ∩B ＝(0,2)．答案：(0,2)8．(2015年苏锡常镇一调)已知集合A ＝{1,2,3,4}，B ＝{m,4,7}，若A ∩B ＝{1,4}，则A ∪B ＝________.解析：由A ∩B ＝{1,4}得m ＝1，所以A ∪B ＝{1,2,3,4,7}． 答案：{1,2,3,4,7}9．设常数a ∈R ，集合A ＝{x |(x －1)(x －a )≥0}，B ＝{x |x ≥a －1}，若A ∪B ＝R ，则a 的取值范围为________．解析：∵B ＝{x |x ≥a －1}，A ＝{x |(x －1)(x －a )≥0}，①当a >1时，A ＝{x |(x －1)(x －a )≥0}＝(－∞，1]∪[a ，＋∞)，由于A ∪B ＝R ，故有a －1≤1⇒a ≤2，故1<a ≤2；②当a ＝1时，A ＝{x |(x －1)(x －a )≥0}＝{x |(x －1)2≥0}＝R ，此时A ∪B ＝R ，合乎题意； ③当a <1时，A ＝{x |(x －1)(x －a )≥0}＝(－∞，a ]∪[1，＋∞)，由于A ∪B ＝R ，故有a －1≤a 对任意a <1恒成立；综上所述，实数a 的取值范围是(－∞，2]． 答案：(－∞，2]10．(2014年高考福建卷)若集合{a ，b ，c ，d }＝{1,2,3,4}，且下列四个关系： 有且只有一个是正确的，则符合条件的有序数组(a ，b ，c ，d )的个数是________． ①a ＝1；②b ≠1；③c ＝2；④d ≠4解析：若①正确，则②也正确，所以只有①正确是不可能的；若只有②正确，①③④都不正确，则符合条件的有序数组为(2,3,1,4)，(3,2,1,4)；若只有③正确，①②④都不正确，则符合条件的有序数组为(3,1,2,4)；若只有④正确，①②③都不正确，则符合条件的有序数组为(2,1,4,3)，(3,1,4,2)，(4,1,3,2)．综上，符合条件的有序数组的个数是6.答案：6。
蚌埠市2018届高三年级第一次教学质量检查考试数学（文史类）第Ⅰ卷（共60分）一、选择题：本大题共12个小题,每小题5分,共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．1）A2）A．1 B．2 C3（）A4）A．-3 B．0 C．-4 D．1 5）A ．B ．C ．D ．6． ）A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件7）A8表述正确的是（ ）A ．在定义域内为增函数 C ．周期函数 D ．在定义域内为减函数9．在“ ”中应填的执行语句是（ ）A ．2018n i =-B 10．如图，网格纸上小正方形的边长为1，粗线画出的是某几何体的三视图，则它的体积可能为（ ）A ．43π+B ．π11 ）AC12）A 第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上）1314.的值为 ．15．将2本相同的语文书和2本相同数学书随机排成一排，则相同科目的书不相邻的概率为 ．16的周长为．三、解答题（本大题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤．）17．（1（218．.（1（2.19．某图书公司有一款图书的历史收益率（收益率=利润÷每本收入）的频率分布直方图如图所示：（1）试估计平均收益率；（用区间中点值代替每一组的数值）（2）根据经验，若每本图书的收入在20（元）有较强线性相关关系，从历史销售记录中抽样得到如下5并求出该最大收益.20．（1（2.21．（1（2-2.请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分．22．选修4-4：坐标系与参数方程数）.（1（223．选修4-5：不等式选讲（1（2.全优试卷蚌埠市2018届高三年级第一次教学质量检查考试数学（文史类）参考答案及评分标准一、选择题1-5:ADCAD 6-10:BCCAA 11、12：CB二、填空题13．3三、解答题17．解：（1. （2）由（118．解：（1（219．解：（1）区间中值依次为：0.05，0.15，0.25，0.35，0.45，0.55取值的估计概率依次为：0.1，0.2，0.25，0.3，0.1，0.05平均收益率为（2360.20．解：（1（2此时直线与椭圆相切，不符合题意．-1．21．解：（1（222．解：（1（223．解：（1（2。
