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1、2013年江西省高考压轴卷数学文试题2013年江西省高考压轴卷 数学(文)试题 本试卷分第I卷和第II卷两部分(考试时间120分钟，满分150分(请考生按规定用笔将所有试题的答案涂、写在答题纸上( 参考公式: 1VShSSSS,，()1122棱台的体积公式 3其中分别表示棱台的上、下底面积，h表示梭台的高 SS,12球的表面积公式 2 S,4,R43球的体积公式 其中R表示球的半径 ,VR球3第I卷 一、选择题:本大题共10小题, 每小题5分,共50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( 1aAB:AB:,(1)已知集合若,则为 ABab,1,2,211111,1,1,1
2、,1,b A( B( C( D( ) 2222a，2iab，,i (2) 已知,，,babi(,)R，其中为虚数单位，则 i,1(A) (B)1 (C)2 (D)3 (3)在空间，下列命题正确的是 (A)平行直线的平行投影重合 (B)平行于同一直线的两个平面平行 (C)垂直于同一平面的两个平面平行(D)垂直于同一平面的两条直线平行 xx?0bR(4)设为定义在上的奇函数，当时， (为常数)，则fx()fxxb()22,，f(1),3(A) 3 (B) 1 (C)-1 (D) 11c,， (5) 已知a0,b,013, ,是 fxxx()sinsin(),(11) 函数的最小正周期为 ( 3输出
3、f(x) n,(12) 右程序框图中，当N(n1)时，函数表示函 fx()n,n数fx()的导函数.若输入函数fxxx(),，sincos，则输出的 n-11结束 函数fx()可化为_ _。 n第12题图 village temples Central Office every day, carry out their duties. Correspondence relating to education by the Chief of the first section marked my draft statement. Worked after a few months, Ive be
4、en buried in the official program, very rigid monotony of clerical career, flavourless. 1939 of 7 August between, County, and Secretary to I with to Office meeting, for Government established one years to work reported, for time rush, prior not for full prepared, had to in way by rank Ann Mr describ
5、ed one years to about people, and fiscal, and built, and taught, and insurance five aspects important matters, I accordingly detailed narrative finishing written, completed Wujiang Government established one years to of work report. Turn back and forth month Shan Road, apart from the Secretary, Mr r
6、ank foot disease immobility, bamboo car instead of walking outside, square foot (except for myself and 4 guards), the wuxing, peace, SI an, Guangde, doorway swing, Zhang Zhu to the destination-wearing Bu. At diwei to the important towns of troops is difficult to access, we have to change angles, Sha
7、n rugged trails, Sun and rain on the way, hardship exceptions, if the patriotic and passions of the war, than the successful completion of tasks. An old frail, rank, long-distance Lawton regrets, admirable! In November 1939, I was admitted to the Faculty of law, College of law and politics in Shangh
8、ai, but resigned from the post office, bid farewell to this short and memorable life. (J) the siazhen boat buried Japanese morning of October 18, 1937, siazhen sick to shun Tang Qiao-cutters, 1 from Nanxun town jiaxing to Japanese boats, caught dragging behind 3 small boats, loaded with military goo
9、ds. Siazhen too late to escape, jumped ashore Japan catch up with the boat, forcing him to row a boat. Meanwhile caught the migrants village Zhang Shun. Siazhen was sick for a long time, (13) 如图，若一个几何体的正视图、侧视图、俯视图相同，且均为面积等于2的等腰直角三角形，则该几何体的体积为 ( ,aaa,55,a，a,16(14) 已知是一个公差大于0的等差数列，且满足.令n36274m,b,nT,bT
10、，记数列的前项和为，对任意的，不等式(n,N)nN,n2nnna,1100n，1m恒成立，则实数的最小值是 . 2(1,3),a(15)(根据浙江高考题改编)若不等式的解集为，则实数的取值范,，,11axbxc围是 ( 三、解答题:本大题共6小题，共75分，解答应写出文字说明、证明过程或演算步骤( 16(本题满分11分) ,ABCADBC,BDDCAD:2:3:6,AD如图，在中，垂足为，且( ，BAC(?)求的大小; E,ABCCEEAB(?)设为的中点，已知的面积为15，求的长( BCD 17(本题满分11分)现有4个人去参加春节联欢活动，该活动有甲、乙两个项目可供参加者选择.为增加趣味性
11、，约定:每个人通过掷一枚质地均匀的骰子决定自己去参加哪个项目联欢，掷出点数为1或2的人去参加甲项目联欢，掷出点数大于2的人去参加乙项目联欢. (I)求这4个人中恰好有2人去参加甲项目联欢的概率; (II)求这4个人中去参加甲项目联欢的人数大于去参加乙项目联欢的人数的概率; ,XYXY,(III)用分别表示这4个人中去参加甲、乙项目联欢的人数，记，求随机,E,变量的分布列与数学期望. ABCD,18(本题满分11分)如图，在三棱锥中， :ACBCCD,63,6，,，,，,ABCBCDCDA90A ， BCDAE设顶点在底面上的射影为( G 第village temples Central Off
12、ice every day, carry out their duties. Correspondence relating to education by the Chief of the firs 3 页 共 13 页 t section marked my draft statement. Worked after a few months, Ive been buried in the official program, very rigid monotony of clerical career, flavourless. 1939 of 7 August between, Coun
13、ty, and Secretary to I with to Office meeting, for Government established one years to work reported, for time rush, prior not for full prepared, had to in way by rank Ann Mr described one years to about people, and fiscal, and built, and taught, and insurance five aspects important matters, I accor
14、dingly detailed narrative finishing written, completed Wujiang Government established one years to of work report. Turn back and forth month Shan Road, apart from the Secretary, Mr rank foot disease immobility, bamboo car instead of walking outside, square foot (except for myself and 4 guards), the
15、wuxing, peace, SI an, Guangde, doorway swing, Zhang Zhu to the destination-wearing Bu. At diwei to the important towns of troops is difficult to access, we have to change angles, Shan rugged trails, Sun and rain on the way, hardship exceptions, if the patriotic and passions of the war, than the succ
16、essful completion of tasks. An old frail, rank, long-distance Lawton regrets, admirable! In November 1939, I was admitted to the Faculty of law, College of law and politics in Shanghai, but resigned from the post office, bid farewell to this short and memorable life. (J) the siazhen boat buried Japa
17、nese morning of October 18, 1937, siazhen sick to shun Tang Qiao-cutters, 1 from Nanxun town jiaxing to Japanese boats, caught dragging behind 3 small boats, loaded with military goods. Siazhen too late to escape, jumped ashore Japan catch up with the boat, forcing him to row a boat. Meanwhile caugh
18、t the migrants village Zhang Shun. Siazhen was sick for a long time,E D B C CEBD,(?)求证:; GACCGGA,2(?)设点在棱上，且， CEGD,试求二面角的余弦值( ABBCEFGH,8,4,ABCD19(本题满分14分)如图，在矩形中，分别为四边的中y,CQ,CF(,0)OP,OF点，且都在坐标轴上，设,( GCDGQEPM,Q(?)求直线与的交点的轨迹的方程; MoxHF222P(02),rxyr，,N(?)过圆上一点 BAEST,作圆的切线与轨迹交于两点， ,2NS,NT，r,0r若，试求出的值( 2f
19、xxax()2ln,20(本题满分14分)已知函数 fx()a,4(?)若，求函数的极小值; gxx()cos2,xi(1,2,3),i(?)设函数，试问:在定义域内是否存在三个不同的自变量使fxgx()(),aii得的值相等，若存在，请求出的范围，若不存在，请说明理由, 21、(本题满分14分) *nN,pq,ccpcq,，对于给定数列，如果存在实常数使得对于任意都成nnn，1Tc立，我们称数列是“数列”( n*nnN,Ta,2nab(?)若，b,32，数列、是否为“数列”,若是，指出它nnnnpq,对应的实常数，若不是，请说明理由; TTaa，a(?)证明:若数列是“数列”，则数列也是“数
20、列”; nn，1nn*2013aa,2aa，a,3t,2(n,N)t(?)若数列满足，为常数(求数列前n1n，nn1village temples Central Office every day, carry out their duties. Correspondence relating to education by the Chief of the first section marked my draft statement. Worked after a few months, Ive been buried in the official program, very rigid
21、 monotony of clerical career, flavourless. 1939 of 7 August between, County, and Secretary to I with to Office meeting, for Government established one years to work reported, for time rush, prior not for full prepared, had to in way by rank Ann Mr described one years to about people, and fiscal, and
22、 built, and taught, and insurance five aspects important matters, I accordingly detailed narrative finishing written, completed Wujiang Government established one years to of work report. Turn back and forth month Shan Road, apart from the Secretary, Mr rank foot disease immobility, bamboo car inste
23、ad of walking outside, square foot (except for myself and 4 guards), the wuxing, peace, SI an, Guangde, doorway swing, Zhang Zhu to the destination-wearing Bu. At diwei to the important towns of troops is difficult to access, we have to change angles, Shan rugged trails, Sun and rain on the way, har
24、dship exceptions, if the patriotic and passions of the war, than the successful completion of tasks. An old frail, rank, long-distance Lawton regrets, admirable! In November 1939, I was admitted to the Faculty of law, College of law and politics in Shanghai, but resigned from the post office, bid fa
25、rewell to this short and memorable life. (J) the siazhen boat buried Japanese morning of October 18, 1937, siazhen sick to shun Tang Qiao-cutters, 1 from Nanxun town jiaxing to Japanese boats, caught dragging behind 3 small boats, loaded with military goods. Siazhen too late to escape, jumped ashore
26、 Japan catch up with the boat, forcing him to row a boat. Meanwhile caught the migrants village Zhang Shun. Siazhen was sick for a long time, 项的和( 江西省高考压轴卷 数学(文)试题 参考答案 一、选择题:本大题共10小题，每小题5分，共50分 1aAB:(1)1(已知集合若,则为 AB:,ABab,1,2,21111 A( B(1, C(1, D(1,1,( ) ,1,b2222(选题意图:主要考查集合的表示、集合的运算。)选D a，2iab，, (
27、2) 已知，其中i为虚数单位，则 ,，,babi(,)Ri(A),1 (B)1 (C)2 (D)3 【答案】B a+2iab+2i=i-1ab+=【解析】由=+ib得,所以由复数相等的意义知,所以1. ab=1,=2,ia+2i,abi+2=+i=+ib另解:由得，则. (,)ab,R,，,abab1,2,1i故选B. 【命题意图】本题考查复数相等的意义、复数的基本运算，属保分题。 (3)在空间，下列命题正确的是 (A)平行直线的平行投影重合 (B)平行于同一直线的两个平面平行 (C)垂直于同一平面的两个平面平行 (D)垂直于同一平面的两条直线平行 【答案】D 【解析】由空间直线与平面的位置关
28、系及线面垂直与平行的判定与性质定理可以得出答案。 【命题意图】考查空间直线与平面的位置关系及线面垂直与平行的判定与性质，属基础题。 xx?0bR(4)设fx()为定义在上的奇函数，当时， (为常数)，则fxxb()22,，f(1), ,3(A) 3 (B) 1 (C)-1 (D) 【答案】D 第village temples Central Office every day, carry out their duties. Correspondence relating to education by the Chief of the firs 5 页 共 13 页 t section mar
29、ked my draft statement. Worked after a few months, Ive been buried in the official program, very rigid monotony of clerical career, flavourless. 1939 of 7 August between, County, and Secretary to I with to Office meeting, for Government established one years to work reported, for time rush, prior no
30、t for full prepared, had to in way by rank Ann Mr described one years to about people, and fiscal, and built, and taught, and insurance five aspects important matters, I accordingly detailed narrative finishing written, completed Wujiang Government established one years to of work report. Turn back
31、and forth month Shan Road, apart from the Secretary, Mr rank foot disease immobility, bamboo car instead of walking outside, square foot (except for myself and 4 guards), the wuxing, peace, SI an, Guangde, doorway swing, Zhang Zhu to the destination-wearing Bu. At diwei to the important towns of tro
32、ops is difficult to access, we have to change angles, Shan rugged trails, Sun and rain on the way, hardship exceptions, if the patriotic and passions of the war, than the successful completion of tasks. An old frail, rank, long-distance Lawton regrets, admirable! In November 1939, I was admitted to
33、the Faculty of law, College of law and politics in Shanghai, but resigned from the post office, bid farewell to this short and memorable life. (J) the siazhen boat buried Japanese morning of October 18, 1937, siazhen sick to shun Tang Qiao-cutters, 1 from Nanxun town jiaxing to Japanese boats, caugh
34、t dragging behind 3 small boats, loaded with military goods. Siazhen too late to escape, jumped ashore Japan catch up with the boat, forcing him to row a boat. Meanwhile caught the migrants village Zhang Shun. Siazhen was sick for a long time,0【解析】由为定义在上的奇函数可知， Rfx()fbbb(0)210,1,，,，,于是，故选D. ff(1)(1)
35、(221)3,，,11(5) 已知a0,b0,a+b=-2若，则c的最值为 ( ) c,，abA(最小值-1 B(最小值-2 C(最大值-2 D(最大值-1 (编题意图:本题考查基本不等式的应用及函数最值问题。)选C (6)样本中共有5个个体，其值分别为.若该样本的平均值为1，则样本方差为 a,0,1,2,366(A) (B) (C) (D) 2255【答案】D 1a,1【解析】由题意知，解得，故样本方差为 (0123)1a，,51222222,故选D. S,，,，,，,，,(11)(01)(11)(21)(31)25【命题意图】本题考查样本平均数、方差的计算，属于基础题. 22xx22(7)
36、【原创】已知有相同两焦点F、F的椭圆+ y=1和双曲线- y=1，P是它们的一1253个交点，则FPF的面积是( ) 12A(2 B(3 C(1 D(4 (8)设数列a是等比数列，则“aaa,”是数列a是递增数列的 123nn(A)充分而不必要条件 (B)必要而不充分条件 (C)充分必要条件 (D)既不充分也不必要条件 【答案】C 2qaaa,aqa,1,0【解析】由，设数列的公比为, 得，则，数aaqaq,1231n111aaqa,1,0列为递增数列;反之，若数列是递增数列，则公比所以1nn2aaa,aaa,aaaqaq,，即，故“”是数列是递增数列的充分必要条123123n111件. 【命
37、题意图】本题主要考查等比数列以及充分必要条件的相关知识，属于基础题. village temples Central Office every day, carry out their duties. Correspondence relating to education by the Chief of the first section marked my draft statement. Worked after a few months, Ive been buried in the official program, very rigid monotony of clerical c
38、areer, flavourless. 1939 of 7 August between, County, and Secretary to I with to Office meeting, for Government established one years to work reported, for time rush, prior not for full prepared, had to in way by rank Ann Mr described one years to about people, and fiscal, and built, and taught, and
39、 insurance five aspects important matters, I accordingly detailed narrative finishing written, completed Wujiang Government established one years to of work report. Turn back and forth month Shan Road, apart from the Secretary, Mr rank foot disease immobility, bamboo car instead of walking outside,
40、square foot (except for myself and 4 guards), the wuxing, peace, SI an, Guangde, doorway swing, Zhang Zhu to the destination-wearing Bu. At diwei to the important towns of troops is difficult to access, we have to change angles, Shan rugged trails, Sun and rain on the way, hardship exceptions, if the patriotic and passions of the war, than th