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1、江苏省东台市安丰中学2012-2013学年高一上学期期中考试数学试题闰土教育东台市安丰中学2012-2013学年度第一学期 高一数学期中试卷 分值160分 时间120分钟 一(填空题(本大题有14小题，每题5分共70分。请把答案填写在答题纸相应的位置上.) (A:B1(设集合，则等于 ? . A,1,2,3,4B,2,4,62(函数的定义域为 ? . f(x),2,x，ln(x,1)x,1a,0a,13(函数(且)的图象恒过点 ? . f(x),a，14(若幂函数的图象经过，则 ? . ，4,2fx()f(9),20.35(设，则三者的大小关系是 ? .(用“”连接) a,b,ca,0.3,b
2、,2,c,log0.3226(已知集合有且只有一个元素，则实数的取值集合为 ? . aA,x|ax,4x，2,0m(),1,7(已知函数是奇函数，则实数的值为 ? . fxmx5，1logx,x,013f(f(),8(已知函数 ，则 ? . f(x),x9x,02,xk(已知函数9的零点为，且，则整数, ? . xx,k,k，1f(x),2，x,80010(若为偶函数，在上是减函数，又，则的解集是 ? . fx(),0f(2)0,xfx()0,，,x,0x,011(设函数是定义在R上的奇函数，当时，则当时， ? . f(x)f(x),x(1，x)f(x),12. 已知yax,log(32)在上
3、为的减函数，则的取值范围为 ? . xa0,1ay,logx,13(定义:区间,的长度为.已知函数的定义域为,值域为0,2,则区间,长x,x(x,x)x,xa,ba,b0.5211212度的最大值为 ? . (已知函数14的图象如下所示: yfxygx,()()2,2和在yy 2211,21,2,12,1O2Oxx ,1 ,2,2 y,f(x)y,g(x)给出下列四个命题: personal and collective learning on your own, combining learning reading and discussion, read, learn, and under
4、standing of the original principles, focused learning around topics discussion, ongoing positive and negative type education. Members should close their own thoughts, work, real life, comparing reflection and further improve the pertinence and effectiveness of learning, continue to unlock the button
5、s, correct wrong, think of practical realization in mind, party rules discipline, firm and correct political orientation, develop discipline, and being a qualified member of the adherence to the Constitution Party rules and political discipline. Second, to do as the key, seriously, do try to do, to
6、set an example. Two lies in the doing. To learn to do, and the unity of knowledge, qualified party member, is the focus of this study and education and essential point. A qualified party members not only to watch his Constitution Party rules and talk to learn how, through, dark and light, and also w
7、hat does he end up doing, is not a unity. This study and education, is essential to enhance the partys political awareness, awareness of overall, core, par. In learning education in the, each members are to control told political, and has faith, do political qualified; told rules, and has discipline
8、, do implementation discipline qualified; told moral, and has conduct, do conduct qualified; told dedication, and has as, do play role qualified four told four has this put ruler, often measure himself, view himself, transformation himself, with actual action reflected learn of effectiveness, and re
9、flected belief faith of power. To firm to to Central par, to XI General Secretary par, to party of theory, and route, and approach par, to Central of the decision deployment par, strongly maintenance Central of authority, maintenance XI General Secretary this core, strongly obey Central of concentra
10、ted unified led, in thought, and political 有且仅有3个根 ?方程有且仅有4个根 ?方程ggx()0,gfx()0,?方程有且仅有5个根 ?方程有且仅有6个根 ffx()0,fgx()0,其中正确的命题的序号是 ? ( 二(解答题(本大题有6小题，共90分(请在答题纸指定区域内作答，解答时应写出文字说明、证明或演算步骤.) U,R15(本小题14分)设全集，已知集合，( ,B,x(4,x)(x,1),0A,xx,a,1A:Ba,4(1)若，求;A:B,A(2)若，求实数的取值范围( a16.(本小题14分)计算下列各题: 2(1); (lg5)，lg2
11、,lg5011,2,222a，a(2)已知a,a,1的值. 求，217.(本小题15分)已知函数. f(x),(logx),4logx，122(1)求f(8)的值; 2,x,16f(x)(2)当时,求的最大值和最小值. personal and collective learning on your own, combining learning reading and discussion, read, learn, and understanding of the original principles, focused learning around topics discussion,
12、 ongoing positive and negative type education. Members should close their own thoughts, work, real life, comparing reflection and further improve the pertinence and effectiveness of learning, continue to unlock the buttons, correct wrong, think of practical realization in mind, party rules disciplin
13、e, firm and correct political orientation, develop discipline, and being a qualified member of the adherence to the Constitution Party rules and political discipline. Second, to do as the key, seriously, do try to do, to set an example. Two lies in the doing. To learn to do, and the unity of knowled
14、ge, qualified party member, is the focus of this study and education and essential point. A qualified party members not only to watch his Constitution Party rules and talk to learn how, through, dark and light, and also what does he end up doing, is not a unity. This study and education, is essentia
15、l to enhance the partys political awareness, awareness of overall, core, par. In learning education in the, each members are to control told political, and has faith, do political qualified; told rules, and has discipline, do implementation discipline qualified; told moral, and has conduct, do condu
16、ct qualified; told dedication, and has as, do play role qualified four told four has this put ruler, often measure himself, view himself, transformation himself, with actual action reflected learn of effectiveness, and reflected belief faith of power. To firm to to Central par, to XI General Secreta
17、ry par, to party of theory, and route, and approach par, to Central of the decision deployment par, strongly maintenance Central of authority, maintenance XI General Secretary this core, strongly obey Central of concentrated unified led, in thought, and political 盐阜路学习中心 Yanfu Rd Learning Center 18(
18、本小题15分)已知二次函数的最小值为1，且( fx()ff(0)(2)3,(1)求的解析式; fx()(2)若在区间上不单调，求实数的取值范围; afx()3,1aa，(3)在区间上，的图象恒在的图象上方，试确定实数的取值范围( m1,1,yfx,()yxm,，221x21,x,Rfx(),19(本小题16分)已知函数()( x21，fx(1)求函数的值域; ，fx(2)?判断并证明函数的奇偶性; ，fx?判断并证明函数的单调性; ，2(3)解不等式( f(1,m)，f(1,m),0R20.(本小题16分)已知函数fx()定义域为且同时满足: ?fx()图像左移1个单位后所得函数为偶函数;?f
19、afb()(),0对于任意大于1的不等实数ab,，总有成立. ab,fx()(,1),fx()(1)的图像是否有对称轴,如果有，写出对称轴方程.并说明在区间上的单调性; personal and collective learning on your own, combining learning reading and discussion, read, learn, and understanding of the original principles, focused learning around topics discussion, ongoing positive and neg
20、ative type education. Members should c闰土教育祝您成功 lose their own thoughts, work, real life, comparing reflection and further improve the pertinence and effectiveness of learning第 3 页 共 13 页 , continue to unlock the buttons, correct wrong, think of practical realization in mind, party rules discipline,
21、firm and correct political orientation, develop discipline, and being a qualified member of the adherence to the Constitution Party rules and political discipline. Second, to do as the key, seriously, do try to do, to set an example. Two lies in the doing. To learn to do, and the unity of knowledge,
22、 qualified party member, is the focus of this study and education and essential point. A qualified party members not only to watch his Constitution Party rules and talk to learn how, through, dark and light, and also what does he end up doing, is not a unity. This study and education, is essential t
23、o enhance the partys political awareness, awareness of overall, core, par. In learning education in the, each members are to control told political, and has faith, do political qualified; told rules, and has discipline, do implementation discipline qualified; told moral, and has conduct, do conduct
24、qualified; told dedication, and has as, do play role qualified four told four has this put ruler, often measure himself, view himself, transformation himself, with actual action reflected learn of effectiveness, and reflected belief faith of power. To firm to to Central par, to XI General Secretary
25、par, to party of theory, and route, and approach par, to Central of the decision deployment par, strongly maintenance Central of authority, maintenance XI General Secretary this core, strongly obey Central of concentrated unified led, in thought, and political11(2)设，如果，判断是否有负实根并说明理由; f(0)1,g(x),0gx(
26、),，fxx()2,(3)如果且，比较与的大小并简述理由( xx,0,0xx，,20fx(),fx(),121212东台市安丰中学2012-2013学年度第一学期 高一数学期中试卷答案 一(填空题(本大题有14小题，每题5分共70分。请把答案填写在答题纸相应的位置上.) (c,a,b1( 2( 3( 4( 3 5(，,，1,21,22,4 11,6(7( 8( 9( 2 10(0,2(,2)(0,2),: 24153,11( 12. 13( 14(? x(1,x)1,42, 二(解答题(本大题有6小题，共90分(请在答题纸指定区域内作答，解答时应写出文字说明、证明或演算步骤.) a,4,x3,
27、x,5,A,xx,4,115(【解析】(1)当，= ,B,x(4,x)(x,1),0xx,4或x,1=， A:B,xx,1或x,3= 7分 ,xa,1,x,a，1,A,xx,a,1(2)=， ,B,x(4,x)(x,1),0xx,4或x,1=， A:B,AA,B若，则 a，1,1a,1,4a,0a,5或 或14分 ？2216.【解析】(1)原式= (lg5)，lg2,(1，lg5),(lg5)，lg2,lg5，lg2personal and collective learning on your own, combining learning reading and discussion, r
28、ead, learn, and understanding of the original principles, focused learning around topics discussion, ongoing positive and negative type education. Members should close their own thoughts, work, real life, comparing reflection and further improve the pertinence and effectiveness of learning, continue
29、 to unlock the buttons, correct wrong, think of practical realization in mind, party rules discipline, firm and correct political orientation, develop discipline, and being a qualified member of the adherence to the Constitution Party rules and political discipline. Second, to do as the key, serious
30、ly, do try to do, to set an example. Two lies in the doing. To learn to do, and the unity of knowledge, qualified party member, is the focus of this study and education and essential point. A qualified party members not only to watch his Constitution Party rules and talk to learn how, through, dark
31、and light, and also what does he end up doing, is not a unity. This study and education, is essential to enhance the partys political awareness, awareness of overall, core, par. In learning education in the, each members are to control told political, and has faith, do political qualified; told rule
32、s, and has discipline, do implementation discipline qualified; told moral, and has conduct, do conduct qualified; told dedication, and has as, do play role qualified four told four has this put ruler, often measure himself, view himself, transformation himself, with actual action reflected learn of
33、effectiveness, and reflected belief faith of power. To firm to to Central par, to XI General Secretary par, to party of theory, and route, and approach par, to Central of the decision deployment par, strongly maintenance Central of authority, maintenance XI General Secretary this core, strongly obey
34、 Central of concentrated unified led, in thought, and political 盐阜路学习中心 Yanfu Rd Learning Center 7分,1,lg5,(lg5，lg2)，lg2,lg5，lg2 1111,2,12222(2) 由，得， a,a,1(a,a),a，a,2,1,1 10分 ？a，a,3,122,2 ？(a，a),a，a，2,92,2 14分 ？a，a,7217.【解析】(1)6分 f(8),(log8),4log8，1,222？2,x,16？1,t,4(2)令，8分 t,logx222原函数即为10分 y,t,4t，1,
35、(t,2),3(1,t,4)t,2x,4当，即时，;12分 f(x),3mint,4x,16当，即时，;15分 f(x),1max2a,218(【解析】(1)由已知，设，由，得， f(0)3,fxax()(1)1,，2故.5分 fxxx()243,，13a,1,a，10,a,(2)要使函数不单调，则，解得 10分 32243221xxxm,，,，(3)由已知，即在上恒成立， 1,1,2,m,x,3x，1在上恒成立， 1,1,2设, 则 g(x),1g(x),x,3x，1(,1,x,1)minm,1. 15分 ？1，yx2,19(【解析】(1)? ， 2分 1,yx20,11yfx,1,1又 ，
36、? ?函数的值域为4分 ，(2)证明:?函数定义域为R ,xx2112,fxfx？()(),， 6分 ,xx2112，fx?函数为奇函数 7分 ，personal and collective learning on your own, combining learning reading and discussion, read, learn, and understanding of the original principles, focused learning around topics discussion, ongoing positive and negative type e
37、ducation. Members should c闰土教育祝您成功 lose their own thoughts, work, real life, comparing reflection and further improve the pertinence and effectiveness of learning第 5 页 共 13 页 , continue to unlock the buttons, correct wrong, think of practical realization in mind, party rules discipline, firm and cor
38、rect political orientation, develop discipline, and being a qualified member of the adherence to the Constitution Party rules and political discipline. Second, to do as the key, seriously, do try to do, to set an example. Two lies in the doing. To learn to do, and the unity of knowledge, qualified p
39、arty member, is the focus of this study and education and essential point. A qualified party members not only to watch his Constitution Party rules and talk to learn how, through, dark and light, and also what does he end up doing, is not a unity. This study and education, is essential to enhance th
40、e partys political awareness, awareness of overall, core, par. In learning education in the, each members are to control told political, and has faith, do political qualified; told rules, and has discipline, do implementation discipline qualified; told moral, and has conduct, do conduct qualified; t
41、old dedication, and has as, do play role qualified four told four has this put ruler, often measure himself, view himself, transformation himself, with actual action reflected learn of effectiveness, and reflected belief faith of power. To firm to to Central par, to XI General Secretary par, to part
42、y of theory, and route, and approach par, to Central of the decision deployment par, strongly maintenance Central of authority, maintenance XI General Secretary this core, strongly obey Central of concentrated unified led, in thought, and politicalx221,? = ,1fx(),xx，21，21在定义域R内任取两个实数,且， 8分 xx,xx,121
43、2xx12,222，则 10分 fxfx,()()12xx12，2121，xx12，从而 11分 ？xx,？,022fxfx()(),01212?函数在上为单调增函数 12分 fxR，(3)由(2)得函数为奇函数，在R上为单调增函数 fx，22? 即， fmfm110,，,fmfm11,，2211,mm?， 14分 fmfm11,，?原不等式的解集为 16分 ,，,21,:，x,120.【解析】(1)由条件?得的图像关于直线对称2分 f(x)a,b,1由条件?得时，恒成立， f(a),f(b)b,a,1时，恒成立， f(b),f(a)在上单调递增4分 f(x)(1,，,)？x,1又的图像关于直
44、线对称， f(x)？在上单调递减5分 f(x)(,1)？11(2)若x有负根，则g(x),，,0， g(x),000f(x)2,x00f(x),x,2 ？00， 在上单调递减， f(0),1f(x)(,1)？f(x),1x,2,1x,3x,0 ，与矛盾， ？ 0000故g(x),0无负实根10分 x,1(,x,f(,x)(2，x,f(2，x)(3)点f(x)与点为上关于直线对称的两点， 1111xx，,202,x，2,xf(x)(1,，,)，又在上单调递增， ？1212personal and collective learning on your own, combining learnin
45、g reading and discussion, read, learn, and understanding of the original principles, focused learning around topics discussion, ongoing positive and negative type education. Members should close their own thoughts, work, real life, comparing reflection and further improve the pertinence and effectiv
46、eness of learning, continue to unlock the buttons, correct wrong, think of practical realization in mind, party rules discipline, firm and correct political orientation, develop discipline, and being a qualified member of the adherence to the Constitution Party rules and political discipline. Second
47、, to do as the key, seriously, do try to do, to set an example. Two lies in the doing. To learn to do, and the unity of knowledge, qualified party member, is the focus of this study and education and essential point. A qualified party members not only to watch his Constitution Party rules and talk to learn how, through, dark and light, and also what does he end up doing, is not a unity. This stud