数学（数学卷共2大题，17小题，满分100分）一、选择题（本题共14个小题，每小题5分，共70分；每小题只有一个正确答案）1．若a?b，则下列各式中正确的是（）A．a2?b2 B．a3?b3 C．log2a?log2b D．2．在复平面内，复数z?i(1?2i)对应的点位于（）A．第一象限 B．第二象限 C．第三象限 D．第四象限3．设集合A???1,0,1,2?，B?xx2?2x?3≤0，则A?B?（）A．??1,0? B．??1,0,1? C．?x?1≤x≤2? D．?x?1≤x≤1?4．已知平面向量a=（1 , 2），b=（m,?4），且a//b，则a?b=（）A．4 B．10 C．?6 D．?105．m??2是直线(m?1)x?y?2?0和直线mx?(2m?2)y?1?0相互垂直的（）A．充分不必要条件 B．必要不充分条件C．充分必要条件 D．既不充分也不必要条件6．已知sin??4π，???π，则tan??（） 523344A．? B． C．? D． 443311? ab??7．如下图所示，一个空间几何体的正视图和侧视图都是边长为1的正方形，俯视图是一个直径为1的圆，那么这个几何体的全面积为（）A．正视图侧视图俯视图ππ3 B． C．π D．π 1242文化课考试试卷（B卷）第6页（共14页）8．函数y??3sin2x是（）A．最小正周期为2π的奇函数 B．最小正周期为2π的偶函数C．最小正周期为π的奇函数 D．最小正周期为π的偶函数9．可作为函数y?f(x)的图像是（）ABCD10．给定下列三个命题：（1）若一个平面内的两条直线与另一个平面都平行，那么这两个平面相互平行；（2）垂直于同一直线的两条直线相互平行；（3）若一条直线与一个平面内的两条直线都垂直，则这条直线与这个平面垂直。
则正确的命题个数是（）A．3个 B．2个 C．1个 D．0个x2y2?1上的点，若F1、F2是椭圆的两个焦点，则PF1?PF2?（）11．设P是椭圆? 2516A．10 B．8 C．6 D．512．某公司招聘员工，经过笔试确定面试对象人数，面试对象人数按拟录用人数分段计1≤x≤10?4x,?算，计算公式为y??2x?10,10?x≤100，其中x代表拟录用人数，y代表面试对象人数。
?1.5x,x?100?若应聘的面试对象人数为60人，则该公司拟录用人数为（）A．15 B．25 C．40 D．13013．从甲、乙、丙三人中任选两名代表，甲被选中的概率为（）112A． B． C． D．1 323文化课考试试卷（B卷）第7页（共14页）14．阅读右边的程序框图，若输入的N?100，则输出的结果是（）101A．50 B． 2103C．51 D． 2二、解答题（本题有3小题，共30分；解答时需写出文字说明与演算步骤）15．（本小题满分8分）求过点(2,3)且与圆(x?3)2?y2?1相切的切线方程。
16．（本小题满分10分）在等比数列{an}中，已知a1?2，a4?16。
（1）求数列{an}的通项公式an；（2）若a3、a5分别为等差数列{bn}的第3项和第5项，试求数列{bn}的通项公式bn及前n项的和Sn。
17．（本小题满分12分）如图，位于A处的信息中心获悉：在其正东方向相距40海里的B处有一艘渔船遇险，在原地等待救援。
信息中心立即把消息告知在其南偏西30?，相距20海里C处的乙船，现乙船朝北偏东?的方向北东沿直线CB前往B处救援，求cos?的值。
AB?C?文化课考试试卷（B卷）第8页（共14页）英语（英语卷共4大题，62小题，满分100分）一、单项填空（本题有20小题，每小题1.5分，共30分；从A、B、C、D 四个选项中，选出可以填入空白处的最佳选项）1. —Where is Mr. Jack at this moment?—A. He comes from Tokyo.B. He loves basketball.C. He is playing basketball on the playgroundD. Basketball is hi s favorable sport.2. — Hello, may I speak to Bob please?—A. Thank you.B. I'm sorry.C. My name is Jack.D. Sorry, he's no t here.3. Do you know when_______________?A.will his shop be startedB.his shop will startC.his shop will be startedD.his shop will be begun4. —Would you like to go to Mount Tai with us?—A. Yes, I did.B. No, I didn't.C. Yes, of course.D. Oh, I am fed up with you.5. It suddenly occurred to me that we could _________ the police for help.A. askB. lookC. tellD. meet6. _______ Chinese we study English, maths, physics, chemistry and so on.A. ExceptB. BesideC. OutsideD. Besides7. You cannot imagine how much I A. cost B. paid C. spent D. boug ht8. This bridge is ________that one.A. as three times long asB. three times the length ofC. three time as long asD. three times as longer as9. The picture ______on the wall is painted by my nephew.A. having hungB. hangingC. hangsD. being hungA. newsB. knowledgeC. noticeD. message11.________we can't understand is___________he didn't join us in the discussion.A.What; whyB.What; howC.That; thatD.That; whether12.I’ll be very glad if you agree to this matter.文化课考试试卷（B卷）第9页（共14页）A. look upB. look forC. look intoD.look at13. We _______ everything into consideration before we drew up the plan.A. tookB. were takingC. did takeD. had takenA. missedB. wastedC. escapedD. failed15. It's so hot and dry. The trees __________.A. need to waterB. need wateringC. want to waterD. want to be watering16. Surely her daughter would make an even bigger effort ________ _ her.A. pleaseB. pleasedC. to pleaseD. having pleased17. A well-written composition good choice of words and clear org anizationamong other things.A. calls onB. calls upC. calls forD. calls off18. Most of the artists ________ to the party were from South Afr ica.A. to inviteB. invitedC. being invitedD. had been invited19. He speaks Chinese as fluently as if he ________ a Chinese.A. wereB. had beenC. isD. has been20. Only after they had done hundreds of experiments _______ in s olving the problem.A. they succeededB. they had succeededC. would they succeedD. did they succeed二、完形填空（本题有20小题，每小题1.5分，共30分；阅读下面的材料，掌握其大意，然后在21～40题所给的A、B、C、D四个选项中选出最佳选项）When Bob was eighteen, he bought a secondhand car for 200 so that he could travel to it.to buy a cheap car, but they all of them had any desire to buy it. Bob's friend Jack Bob told him, and Jack answered, "Well, what about advertising（广告宣传） it in the paper? （合理的）, he put an adver tisement in an evening paper, which read "For sale: small car, very l ittle petrol, only two owners. Bargain at 50."For two days after the advertisement first appeared, there was . But then on Saturday evening he had an inquiry（询问）about the car. "All right," Bob said, feeling happy. He asked the man whether ten o' clock the my wife. We intend （想要） to go for a ride in it to 35 it. "。