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1、2012年高考数学 仿真模拟卷 文1 新课标版2012届高考数学仿真模拟卷新课标版(文1) 一、选择题:本大题共12小题，每小题5分(共60分(在每小题给出的四个选项中，只有一个是正确的，将正确答案的代号涂在答题卡上( 2MN:1(设函数的定义域为，集合，则等于( ) MNyyxxR,|,yx,2,N A( B( C( D(M1,)，, 2(已知等比数列中有f，数列是等差数列，且，则 abab,bb，,nn7759( ) A(2 B(4 C(8 D(16 1x3. 已知是函数fx,，的一个零点.若， 则 ()2xx,(1,)xx,(,x，,)1020,x1( ) A. B. fxfx()0,(
2、)0,fxfx()0,()0,1212C. D. fxfx()0,()0,fxfx()0,()0,12124(下列命题中是假命题的是 ( ) 2m,4m，3 A( 上递减 且在(0,，,)，m,R,使f(x),(m,1),x是幂函数,2 B( ,a,0,函数f(x),lnx，lnx,a有零点C(; ，,R,使cos(,，,),cos,，sin,1 2 1 D(都不是偶函数 ,，,R,()sin(2)函数fxx2 5(已知某几何体的三视图如图，其中正视图中半圆半径为1，侧视图 则该几何体体积为( ) 正视图 1 2 1 3, A(24- B(24- 233 , C(24- D(24- 2俯视图
3、S6(某程序框图如图所示，该程序运行后输出的的值是( ) 11,3,2A( B( C( D( 23R7(定义在上的函数满足，当时f(x)f(x，2),f(x)x,3,5f(x),2,x,4，则( ) ,ff(sin)(cos),Aff(sin1)(cos1), B( 66第6题图 - 1 - 用心 爱心 专心 22,C D( ,ff(sin)(cos)ff(sin2)(cos2),3328. 已知函数的图象在点A(1，f(1)处的切线与直线平行，3x,y，2,0f(x),x，bxl1若数列的前项和为,则的值为( ) SSnn2011f(n)2A( B( C( D( 32229(过点可作圆的两条
4、切线，则实数的取值范围为aA(a,a)x，y,2ax，a，2a,3,0( ) 33a,31,a,1,a, A(或 B( 223,31aa,3 C(或 D(或 a,1a,22y210. 设F，F是双曲线x,1的两个焦点，P是双曲线上的一点，且，3|PF|,4|PF|121224则的面积等于 ( ) ,PFF128342 A B( C(24 D(48 11(如图，四边形OABC是边长为1的正方形，OD,3，点P为?BCD内(含边界)的动点，设,，则的最大值等于 ,，OPOCODR,，,(,)( ) 14A( B( B C 43P 1 C( D( 1 3D O A 223212. 如图是函数的大致图
5、象，则等于 xx，fxxbxcxd(),，1224816y (A) (B) (C) (D) 3339x 2-1 x12 x O 二、填空题:本大题4个小题，每小题5分，共20分. 13(已知复数z满足(z-2)i=1+i ,(i是虚数单位)则|z| =_. x，y,4,22y,x14. 在区域M=(x,y)|内撒一粒豆子，落在区域N=(x,y)|x+(y-2)?2内的概,x,0,- 2 - 用心 爱心 专心 率为_. 15(边长是的正三角形ABC内接于体积是的球O，则球面上的点到平面ABC的最43,22大距离为 。 16(将全体正奇数排成一个三角形数阵: 1 3 5 7 9 11 13 15
6、17 19 按照以上排列的规律，第n 行(n ?3)从左向右的第3个数为( 三、解答题:本大题共6个小题，满分70分(解答时要求写出必要的文字说明、证明过程或推演步骤( 17(本题12分)某兴趣小组测量电视塔AE的高度H(单位m)，如示意图，垂直放置的标杆BC高度h=4m，仰角?ABE=，?ADE= (1)该小组已经测得一组、的值，tanE =1.24,tan=1.20,请据此算出H的值 (2)该小组分析若干测得的数据后，发现适当调整标杆到电视塔的距离d(单位m)，使与之差较大，可以提高测量精确度，若H 电视塔实际高度为125m，问d为多少时，C -最大, h ) ) A B D d 18(本
7、小题满分12分) 某水泥厂甲、乙两个车间包装水泥，在自动包装传送带上每隔30分钟抽取一包产品，称其重量，分别记录抽查数据如下: 99，98，103，98，99 甲:102，101，乙:110，115，90，85，75，115，110 (1)画出这两组数据的茎叶图; (2)求出这两组数据的平均值和方差(用分数表示);并说明哪个车间的产品较稳定( (3)从甲中任取一个数据x(x?100)，从乙中任取一个数据y(y?100)，求满足条件|x-y|?20的概率( - 3 - 用心 爱心 专心 19(本小题12分) ABCD，A,60:AB,6CD 如图，已知为平行四边形，点在上，AFFB,2EEF/B
8、CN，与相交于(现将四边形沿折起，使点BD,ADBDEFADEFEFDBCEFBC在平面上的射影恰在直线上( BCEF (?)求证:平面; BD,(?)求折后直线DN与直线BF所成角的余弦值; (?)求三棱锥NABF的体积( 20.(本小题满分12分) 22xy C已知椭圆:的一个焦点是(1，0)，两个焦点与短轴的一个端点构成，,1(0)ab22ab等边三角形. C(?)求椭圆的方程; xQlCABA(?)过点(4,0)且不与坐标轴垂直的直线交椭圆于、两点，设点关于轴的对A称点为. 1xAB(?)求证:直线过轴上一定点，并求出此定点坐标; 1OAB(?)求?面积的取值范围. 121.(本小题满
9、分12分) - 4 - 用心 爱心 专心 32,x，x，bx，c,x,1已知函数的图象过坐标原点O,且在点处的f(x),(,1,f(,1),axxln,1,5切线的斜率是. ,1,2b、c(?)求实数的值; (?)求在区间上的最大值; f(x)(?)对任意给定的正实数，曲线上是否存在两点P、Q，使得是以O为直角,POQay,f(x)顶点的直角三角形，且此三角形斜边中点在轴上,说明理由. y四、选做题 22(本小题满分10分)选修41 几何证明选讲 MN,ANP在直径是AB的半圆上有两点,设与BM的交点是.求N 2证: APANBPBMAB,，,M P A B 22(选修44 极坐标系与参数方程
10、 222已知圆方程为( y,6ysin,，x,8xcos,，7cos,，8,0(1)求圆心轨迹的参数方程C; 2x，y(2)点是(1)中曲线C上的动点，求的取值范围( P(x,y)23(选修45 不等式选讲 227x，,(1)已知关于的不等式在上恒成立，求实数的最小值; xax,(a,，,)xa,x,1,y,11,xy,x,y (2)已知，求证:( 参考答案 一、选择题:本大题共12小题，每小题5分(共60分(在每小题给出的四个选项中，只有一个是正确的，将正确答案的代号涂在答题卡上(1 2 3 4 5 6 7 8 9 10 11 12 答D C B D A B C C A C B D - 5
11、- 用心 爱心 专心 案 二、填空题:本大题4个小题，每小题5分，共20分. ,13、 14、 10443215、 16、 n,n，53三、解答题:本大题共6个小题，满分70分(解答时要求写出必要的文字说明、证明过程或推演步骤( HHhHhH17(解:由AB=，BD=，AD=及AB+BD=AD，得+=，解tan,tan,tan,tan,tan,tan,41.24，htan,得H=124，因此，算出的电视塔的高度H是124m. 61.241.20,tantan,分 HHh,Hh(2)由题设知d=AB，得tan=，由AB=AD-BD=-，得tan=，所以,ddtan,tan,hhtantan,ta
12、n(-)=?， ,HHh(),1tantan，2()HHh,d，dHHh(),5当且仅当d=，即d=55时，上式取等号，所以HHh(),125(1254)，,d5当d=55时，tan(-)最大， ,5因为0，则0-，所以当d=55时，-最大，故所求的d是,22555m12分 18. (1)茎叶图略 4分 (2); ; 24 ; 71600 7 . ?，故甲车间产品比较稳定. 8分 - 6 - 用心 爱心 专心 (3)所有可能的情况有:(102,90),(102,85),(102,75),(101,90),(101,85),(101,75),(103,90),(103,85), (103,75)
13、,不满足条件的有:(102，75)，(101，75)，(103，75) 12所以P()=1- 12分 ,|x,y|,2033DNB19(解:(?)，得面 EF,EF,DN,EF,BNBDN,BCEF 则平面平面， BDN:BN,BCEF 由平面平面, BCEFBN 则在平面上的射影在直线上, DBCEFBC 又在平面上的射影在直线上, DBCEF 则D在平面上的射影即为点B, BCEF 故BD,平面( 4分 (?)法一(如图，建立空间直角坐标系， ?在原图中AB=6，?DAB=60?， 33 则BN=，DN=2，?折后图中BD=3，BC=3 13NF,CB ?N(0，0)，D(0，0，3)，C
14、(3，0，0)=(-1，0，0) 333 ?(-1，0)(0，-3) BF,BN，NF,DN,BF,DN3, ?= cos,BF,DN,4|BF|,|DN|3 ?折后直线DN与直线BF所成角的余弦值为 8分 4法二(在线段BC上取点M，使BM=BF，则MN?BF ?DNM或其补角为DN与BF所成角( 22 又MN=BF=2，DM=( BD，BM,10,DN,232223DNMN,DMcos，DNM, ? 24DN,MN3 ?折后直线DN与直线BF所成角的余弦值为 4(?)?AD?EF， ?A到平面BNF的距离等于D到平面BNF的距离， 13,VVVSBD ? N,ABFA,BNFD,BNF,B
15、NF323 即所求三棱锥的体积为 12分 2- 7 - 用心 爱心 专心 cC20(解:(?)因为椭圆的一个焦点是(1，0)，所以半焦距=1. 因为椭圆两个焦点与短轴的一个端点构成等边三角形. 22c1xy,所以，解得所以椭圆的标准方程为. 4分 ab,2,3.，,1a24322xyxxmy,，4l(?)(i)设直线:与联立并消去得:，,14322. (34)24360mymy，,24myy，,Axy(),Bxy(),记， 121122234m，36xyy,AAxy(,),t. 由A关于轴的对称点为，得，根据题设条件设定点为T(，121111234m，yy21,kk,0)，得，即.所以TBTA
16、1xttx,21xyyxmyymyy，(4)(4)2myy2121211212t,，,4431 yyyy，yy，121212T(1 ， 0). 8分 即定点m,2AB,0T(ii)由(i)中判别式，解得. 可知直线过定点 (1,0). 11244m,S|11,OAB214SOTyyyy,，|()|，243m所以 得, 令,OAB21211，m223m44/tm,|,，,()tt()1tt,2记，得，当时，. ,()0t,23t3t4428m，(2 , )，,，()tt,，,2在上为增函数. 所以 ， 3m3t33333,，,S(0 , )04得.故?OAB的面积取值范围是. 12分 1,OAB
17、1282322x,1,21.解:(?)当时，则。 f(x),x，x，bx，cf(x),3x，2x，bf(0),0c,0,b,c,0依题意得:，即 解得 4分 ,f(,1),5,3,2，b,5,32,x，x,x,1f(x),(?)由(?)知， ,axxln,1,22,1,x,1f(x),3x，2x,3x(x,)?当时， 3- 8 - 用心 爱心 专心 2,令得 x,0或x,f(x),03,当变化时，的变化情况如下表: xf(x),f(x)222 x(,1,0)0 (0,)(,1)333, f(x) 0 + 0 f(x)单调递减 单调递减 极小值 单调递增 极大值 24f(),又，。?在上的最大值
18、为2. f(,1),2f(0),0f(x),1,1)3271,x,2a,0?当时, .当时, ,最大值为0; f(x),alnxf(x),0f(x)a,0aln2当时, 在上单调递增。?在最大值为。 f(x)1,2f(x)1,22,1,2aln2,2a,综上，当时，即时，在区间上的最大值为2; f(x)ln22,1,2aln2,2aln2a,当时，即时，在区间上的最大值为。8分 f(x)ln2(?)假设曲线上存在两点P、Q满足题设要求，则点P、Q只能在轴两侧。 y,f(x)y32t,1不妨设，则，显然 P(t,f(t)(t,0)Q(,t,t，t),POQ是以O为直角顶点的直角三角形，? OP,
19、OQ,0?232即 (*) ,t，f(t)(t，t),0若方程(*)有解，存在满足题设要求的两点P、Q; 若方程(*)无解，不存在满足题设要求的两点P、Q. 32232320,t,1若，则代入(*)式得: f(t),t，t,t，(,t，t)(t，t),042t,1t,t，1,0即，而此方程无解，因此。此时， f(t),alnt1232,(t，1)lnt代入(*)式得: 即 (*) ,t，(alnt)(t，t),0a1,h(x),lnx，1,0令h(x),(x，1)lnx (x,1)，则 xt,1?h(x)在1,，,)上单调递增， ? ?h(t),h(1),0,?h(t)的取值范围是(0,，,)
20、。 - 9 - 用心 爱心 专心 a,0?对于，方程(*)总有解，即方程(*)总有解。 因此，对任意给定的正实数，曲线上存在两点P、Q，使得是以O为直角顶,POQay,f(x)点的直角三角形，且此三角形斜边中点在轴上。12分 y,22(证明:作于为直径,) EPEAB,？AB？，,，,ANBAMB90？PEBN,PEAM,四点共圆,四点共圆. (6分) AEABAPAN,(1),ABAEBEAPANBPBM()，,，, (1)+(2)得9分 ,BEABBPBM,(2),2 即10分 APANBPBMAB,，,2223(解:将圆的方程整理得:(x-4cos)+(y-3sin)=1 设圆心坐标为P
21、(x,y) ,x,4cos, 则 ,0,360:),y,3sin, -5分(2)2x+y=8cos+3sin =,73sin(,，,) 7373?2x+y? - -10分24(解: 22？2x，,7？2(x,a)，,7，2a,7，2a,4 (1)， x,ax,a3？a,5分 2 22221,xy,x,y,(1,a)(1,b),0,所以1,xy,x,y (2)因为10分 - 10 - 用心 爱心 专心 (英文版 ) easily blame, to prevent the broken window effect. Supervise the leading cadres to play an
22、exemplary role, take the lead in the strict implementation of the and , lead to safeguard the solemnity and authority of the party discipline, ensure that the party discipline and the laws and regulations for implementation in place. Throughout the discipline in the daily supervision and management
23、, strengthen supervision and inspection, from the thorough investigation of violations of discipline behavior. Strengthen to key areas, key departments and key projects as well as the masses reflect the concentration of the units and departments for supervision. - strengthening supervision, discipli
24、ne inspection and supervision of cadres to set an example for compliance with the and is a man must be hexyl, blacksmith needs its own hardware. Discipline inspection organs as the executor of the party discipline, and supervisor of the defenders, for its supervision must be more strictly, disciplin
25、e inspection and supervision of cadres to firmly establish the awareness of Party Constitution, sense of discipline and rules consciousness, politics loyalty, sense obey. Action speak Ji Ordinance to set an example of the regulations of the rule of law, strengthen supervision and accept the supervis
26、ion of the firmness and consciousness, do comply with and . To firmly establish the discipline must first be disciplined, the supervisor will be subject to the 11 用心 爱心 专心 supervision of concept, and consciously safeguard and implement party compasses party, take the lead in practicing three strict
27、real strict, so loyal, clean, play. To be good at learning, the Constitution and the as morality, politics and brought to fruition; to implement , do not want to, dare not, not with disciplinary ruler to supervision; to discipline a ruler, often the control inspection, and consciously in the ideolog
28、ical red line to draw the row Ming Good accumulation is indeed the bottom line, so that the heart has fear, said to have quit, the line has ended. Attached: indifferent to heart, calmly to the table in our life, there are many unpredictable things will happen, some good, some bad things, we cannot c
29、ontrol is powerless to stop, but with time, you will find in life sometimes turns out to be not good, some bad things finally turned out to be a good thing, but then we muddy however did not know, this is the life teach us things. 1, life can be complex, can also be simple. Want simple life of preci
30、pitation, to have enough time to reflect, to make Become more perfect. Life is the most important thing is not to win, but the struggle; not to have conquered, but to have fought well. 2, the plain is the background of life. Live a plain life, give up on themselves is not a coward, but the wise answ
31、ers; not disillusioned after the heart, such as ashes, but experience the storm after the enlightenment; not unrewarding perfunctorily, but calm attitude of life of unrestrained self-confidence. Plain living, there is no noise noisy, no earthly troubles, more did not fill in the discontent of desire
32、, 12 用心 爱心 专心 some just a calm, a calm. 3, memory of heart will not good things to erase the, life is a When no movie, pain is a beginning, the struggle is a kind of process, death is a kind of ending. Give up this giving up is the helpless, do not give up the abandoned, do not give up this giving u
33、p is ignorance, do not give up should not give up is persistent. 4, a thing figured is heaven, think impassability is hell. Since the living, to live better. Sometimes we because of too narrow-minded, too care around the chores and penny wise and pound foolish, not worth the candle. Some things to a
34、ttract trouble and worry, completely depends on how we look at and deal with it. Dont always take everything back to things, and dont get into a blind alley, dont want to face, dont be narrow-minded. Poke to care, is a kind of open-minded, a free and easy. 5, I am not afraid of others behind me a kn
35、ife, I afraid to look back and see stab me, is my intention to treat people; I am not afraid of the truth to tell the best friend, Im afraid he turned to it as a joke to tell dont 6, when we are in a positive frame of mind, you will find many good things; and when we are in a negative state of mind,
36、 you will find many depressed things; life happy and worry, all is you of life attitude, optimistic, good luck; loss of sink, Eritrea company. When you are in adversity, may wish to change a point of view to think everything over to the good Think, because good mentality decided the fate of the! 7,
37、people are tired, rest; heart tired, calm. Grow up, mature, this society read. Tired and sad, squat down, to their a hug. Because the world no one can 13 用心 爱心 专心 sympathize with you, have mercy on you. You cry, tears is your own; you pain, no one can understand. Then you only tears to smile. 8, eac
38、h people have youth, Each youth are a story, the life of the world never gets easier, I want what, wish the world all know, as has been the same; now want anything, for fear that others know, or like to lose the same. 9, the heart move, everything in the world is followed by birth, Rangrang, importa
39、nt thing is often the most difficult to open ones mouth, because words will reduce its importance; to let strangers people care about your life in the good things, the original is not easy 10, do not blame, do not laugh at who, also dont envy who. Like a person is a kind of feeling, not like a perso
40、n is true. The truth is easy to explain, I feel Is unspeakable. The best travel life is that you in a strange place found a long lost touched. 11, happy life not in the bustling in, and in the peace of mind; no matter how many grievances, how uncomfortable, and ultimately to heal themselves or their
41、 own, others may got you to comfort, but never know your heart is how wanjianchuanxin. 12, maam, like a movie, learn to appreciate, learn to be grateful, learn tolerance, and goodness, helping others. Instead of accusing the society, as into one; and an exception is better to give than to what 13, d
42、ont envy him A sum of, dont lose your life and the life, respectively is: the former is a we experienced cannot escape in a day finally will last minute, while the latter is our persistent, we want to cherish the memory of those people and things. 14 用心 爱心 专心 14, learn to smile, learn to strong, the
43、 world you know so many people, so many people and you are, you cannot change also cant let everyone like you, so also do not want to do. Life is too short to go crazy to love to go to waste, to chase the dream to regret. 15, when temper, a blessing to go. A wounding elegant people, the key is to co
44、ntrol their own emotions. With the mouth is the most stupid behavior. A control negative emotions than a can take a city more powerful water flow slow, language is expensive. People spent two years of time to learn to speak, but to spend a few years time to shut up. That is a kind of ability, that i
45、s a kind of wisdom. 16, life is not perfect, sometimes, growth is not a cry, not an eyeful of tears, there is no trace of emotion, there is no gleam of hope, no desire, no action, no static, there is only one kind of downward sinking feeling, sink A murky? 6? 7? 6? 7 sink? 6? 7? 6? 7 toward the bott
46、om of the sink. 17, in some way, do not go, you will not know the other side scenery is beautiful. To you is not good, you do not mind too much, no one has an obligation to you; you learn knowledge, is you have weapons, you can start from scratch, but not unarmed; how do you treat people, does not r
47、epresent how others treat you, if cannot see through this point, only inviting worry. 18, time is like a sponge in the water, as long as you are willing to squeeze, the total water is still there. Every life, after the ups and downs The best test of live, to life, survival and continuation, do not stop the struggle in the joys and s