上海市金山区2014—2015学年第一学期期末考试 高三数学试卷(一模).doc

上海市金山区20142015学年第一学期期末考试高三数学试卷(满分：150分，完卷时间：120分钟) （答题请写在答题纸上）一、填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分1若集合M=，xÎR，N=，x2，则MN= 2计算：= 3不等式：的解是 4如果复数z =（bÎR）的实部与虚部相等，则z的共轭复数= 5方程：sinx+cosx =1在0，上的解是 6等差数列an中，a2=8，S10=185，则数列an的通项公式an= (nÎN*) 7当a>0，b>0且a+b=2时，行列式的值的最大值是 8若的二项展开式中的常数项为m，则m= 9从一堆苹果中任取5只，称得它们的质量分别是：(单位：克)125，124，121，123，127，则该样本的标准差是 克 10三棱锥OABC中，OA=OB=OC=2，且BOC=45°，则三棱锥OABC体积的最大值是 11从集合1, 2, 3, 4, 5, 6, 7, 8, 9, 10中任取两个数，欲使取到的一个数大于k，另一个数小于k(其中kÎ5, 6, 7, 8, 9)的概率是，则k= 12已知点A(3,2)和圆C：(x4)2+(y8)2=9，一束光线从点A发出，射到直线l：y=x1后反射(入射点为B)，反射光线经过圆周C上一点P，则折线ABP的最短长度是 AGDEHBCMF第13题图13如图所示，在长方体ABCDEFGH中，AD=2，AB=AE=1，M为矩形AEHD内的一点，如果MGF=MGH，MG和平面EFG所成角的正切值为，那么点M到平面EFGH的距离是 14已知点P(x0, y0) 在椭圆C：(a>b>0)上，如果经过点P的直线与椭圆只有一个公共点时，称直线为椭圆的切线，此时点P称为切点，这条切线方程可以表示为：根据以上性质，解决以下问题：已知椭圆L：，若Q(u，v)是椭圆L外一点(其中u，v为定值)，经过Q点作椭圆L的两条切线，切点分别为A、B，则直线AB的方程是 二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15复数z1a+bi(a、bÎR，i为虚数单位)，z2b+i，且|z1|<|z2|，则a的取值范围是( )(A)a1 (B)a0 (C)la1 (D)a1或a116用1，2，3，4，5组成没有重复数字的五位数，其中偶数有( )(A) 60个 (B) 48个 (C) 36个 (D) 24个 17设k>1，f(x)=k(x1) (xÎR)，在平面直角坐标系xOy中，函数y=f(x)的图像与x轴交于A点，它的反函数y=f 1(x)的图像与y轴交于B点，并且这两个函数的图像相交于P点. 已知四边形OAPB的面积是3，则实数k等于( )(A) 3 (B) (C) (D) 18若集合A1、A2满足A1A2=A，则称(A1，A2)为集合A的一个分拆，并规定：当且仅当A1=A2时，(A1，A2)与(A2，A1)为集合A的同一种分拆，则集合A=a1，a2，a3的不同分拆种数是( )(A)8 (B)9 (C)26 (D)27三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤19(本题满分12分)a、b、c分别是锐角ABC的内角A、B、C的对边，向量=(22sinA，cosA+sinA)，=(sinAcosA，1+sinA)，且已知a=，ABC面积为，求b、c的大小20(本题满分14分)本题共有2个小题，第1小题满分8分，第2小题满分6分如图，在四棱锥PABCD的底面梯形ABCD中，ADBC，ABBC，AB=2，AD=3，ADC=45°.已知PA平面ABCD，PA=1求：(1)异面直线PD与AC所成角的大小 (结果用反三角函数值表示)；PDCBA第20题图(2)三棱锥CAPD的体积21(本题满分14分) 本题共有2个小题，第1小题满分7分，第2小题满分7分. 已知a>0且a¹1，数列an是首项与公比均为a的等比数列，数列bn满足bn=an×lgan(nÎN*)(1)若a=3，求数列bn的前n项和Sn；(2)若对于nÎN*，总有bn < bn+1，求a的取值范围 22（本题满分16分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分6分动点与点的距离和它到直线的距离相等，记点的轨迹为曲线(1) 求曲线的方程；(2) 设点2,动点在曲线上运动时，的最短距离为，求的值以及取到最小值时点的坐标；(3) 设为曲线的任意两点，满足(为原点)，试问直线是否恒过一个定点？如果是，求出定点坐标；如果不是，说明理由23(本小题满分18分) 本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.设函数f(x)=2kax+(k3)ax (a>0且a¹1)是定义域为R的奇函数(1) 求k值；(2) 若f(2)<0，试判断函数f(x)的单调性，并求使不等式f(x2x)+f(tx+4)<0恒成立的t的取值范围；(3) 若f(2)=3，且g(x)=2x+2 x 2mf(x)在2,+上的最小值为2，求m的值上海市金山区20142015学年第一学期期末考试评分标准一、填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分10, 5； 2； 30<x<1； 41i； 5或0； 63n+2； 7087920； 92； 10； 117； 1210； 13；14二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15C； 16B； 17B； 18D 三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤19(本题满分12分)解：，又(22sinA)(1+sinA)(cosA+sinA)(sinAcosA)=0， 即： 又为锐角，则，所以A=60°6分因为ABC面积为，所以bcsinA=，即bc=6， 又a=，所以7=b2+c22bccosA，b2+c2=13， 解之得：或12分20(本题满分14分)本题共有2个小题，第1小题满分8分，第2小题满分6分解：(1) 过点C作CFAB交AD于点F，延长BC至E，使得CE=AD，连接DE，则ACDE，所以PDE就是异面直线PD与AC所成的角或其补角，2分PDCBAFE因为ADC=45°，所以FD=2，从而BC=AF=1，且DE=AC=，AE=，PE=，PD=，在中，所以，异面直线与所成角的大小为8分(2) 因为VCAPD=VPACD， SACD=´CF´AD=3PA底面ABCD，三棱锥PACD的高为PA=1，VPACD=´ SACD ´ PA=1， 所以，三棱锥CAPD的体积为1.14分21(本题满分14分) 本题共有2个小题，第1小题满分7分，第2小题满分7分.(1) 由已知有， ，所以，. 7分(2) 即.由且，得，所以或即或对任意nÎN*成立，且，所以或14分22（本题满分16分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分6分(1) 根据抛物线的定义可知, 动点的轨迹是抛物线 所以曲线C的方程为x2=4y；4分(2) 设点T(x0, y0), x02=4y0 (y00)，|AT|=，a2>0，则当y0=a2时，|AT|取得最小值为2， 2=a1, a26a+5=0，a=5或a=1 (舍去)， 所以y0=a2=3，x0=±2，所以T坐标为(±2, 3)；10分(3) 显然直线OP1、OP2的斜率都必须存在，记为k，解之得P1(,)，同理P2(4k, 4k2)，直线P1P2的斜率为，直线P1P2方程为：整理得：k(y4)+(k21)x=0，所以直线P1P2恒过点(0, 4)16分23(本小题满分18分) 本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.解(1) 因为f(x)是定义域为R的奇函数，所以f(0)0， 所以2k+(k3)=0，即k=1，检验知，符合条件 4分(2) f(x)=2(axa x) (a>0且a¹1) 因为f(2)<0，<0，又a>0且a¹1，所以0<a<1 因为y=ax单调递减，y=a x单调递增，故f(x)在R上单调递减。7分不等式化为f(x2x)<f(tx4) 所以x2x >tx4，即x2+(t1)x+4>0恒成立， 所以=(t1)216<0，解得3<t<5. 10分(3) 因为f(2)=3，所以2()=3，即2a4 3a2 2=0，所以a=12分所以g(x)2x2x4m()()24m()2.令t=，由(1)可知t=为增函数，因为x2，所以t，令h(t)t24mt2(t2m)224m2 (t)15分若m，当t2m时，h(t)min24m22，m1 若m<，当t时，h(t)min6m2，解得m>，舍去综上可知m1.18分（英文版 ） Two regulations promulgated for implementation is in the party in power for a long time and the rule of law conditions, the implementation of comprehensive strictly strategic plan, implementation in accordance with the rules and discipline to manage the party, strengthen inner-party supervision of major initiatives. The two regulations supporting each other, the < code > adhere to a positive advocate, focusing on morality is of Party members and Party leading cadres can see, enough to get a high standard; < rule > around the party discipline, disciplinary ruler requirements, listed as "negative list, focusing on vertical gauge, draw the party organizations and Party members do not touch the" bottom line ". Here, the main from four square face two party rules of interpretation: the first part introduces two party Revised regulations the necessity and the revision process; the second part is the interpretation of the two fundamental principles of the revision of laws and regulations in the party; the third part introduces two party regulations modified the main changes and needs to grasp several key problems; the fourth part on how to grasp the implementation of the two regulations of the party. < code > and < Regulations > revised the necessity and revised history of the CPC Central Committee the amendment to the Chinese Communist Party members and leading cadres honest politics several guidelines > and < Chinese Communist Party discipline and Punishment Regulations > column 1 by 2015 to strengthen party laws and regulations focus. Two party regulations revision work lasted a Years, pooling the wisdom of the whole party, ideological consensus, draw historical experience, respect for the wisdom of our predecessors, which reflects the unity of inheritance and innovation; follow the correct direction, grasp the limited goals, adhere to the party's leadership, to solve the masses of the people reflect a focus on the problem. The new revision of the < code > and < rule >, reflects the party's 18 and the eighth session of the third, the spirit of the fourth plenary session, reflecting the experience of studying and implementing the General Secretary Xi Jinping series of important speech, reflects the party's eighteen years comprehensive strictly practice. (a) revised two regulations of the party need of < the ICAC guidelines > in < in 1997 Leaders as members of the Communist Party of China clean politics certain criteria (Trial) > based on revised, the promulgation and implementation of January 2010, to strengthen the construction of the contingent of leading cadres play an important role. But with the party to manage the party strictly administering the deepening, has not been able to fully meet the actual needs. Content is too complicated, "eight prohibition, 52 are not allowed to" hard to remember, and also difficult to put into practice; the second is concisely positive advocated by the lack of prohibited provisions excessive, no autonomy requirements; the third is banned terms and discipline law, both with the party discipline, disciplinary regulations repeat and Criminal law and other laws and regulations repeat; the fourth is to "clean" the theme is not prominent, not for the existing problems, and is narrow, only needle of county-level leading cadres above. < rule > is in 1997 < Chinese Communist Party disciplinary cases (Trial) > based on revision, in December 2003 the promulgation and implementation, to strengthen the construction of the party play very important role. Along with the development of the situation, which many provisions have been unable to fully meet the comprehensive strictly administering the practice needs. One is Ji law, more than half of the provisions and criminal law and other countries laws and regulations Repetition; two is the political discipline regulations is not prominent, not specific, for violation of the party constitution, damage the authority of Party Constitution of misconduct lack necessary and serious responsibility to pursue; third is the main discipline for the leading cadres, does not cover all Party members. Based on the above situation, need to < the criterion of a clean and honest administration > and < rule > the two is likely to be more relevant regulations first amendment. By revising, really put the authority of Party discipline, the seriousness in the party tree and call up the majority of Party members and cadres of the party constitution of party compasses party consciousness. (II) two party regulations revision process the Central Committee of the Communist Party of China attaches great importance to two regulations revision . Xi Jinping, general books recorded in the Fifth Plenary Session of the eighth session of the Central Commission for Discipline Inspection, on the revised regulations < > made clear instructions. According to the central deployment, the Central Commission for Discipline Inspection from 2014 under six months begin study two regulations revision. The Standing Committee of the Central Commission for Discipline Inspection 4 review revised. Comrade Wang Qishan 14 times held a special meeting to study two regulations revision, amendment clarifies the direction, major issues of principle, path and target, respectively held a forum will listen to part of the province (area) secretary of the Party committee, Secretary of the Discipline Inspection Commission, part of the central ministries and state organs Department The first party committee is mainly responsible for people, views of experts and scholars and grassroots party organizations and Party members. Approved by the Central Committee of the Communist Party of China, on 7 September 2015, the general office of the Central Committee of the Party issued a notice to solicit the provinces (autonomous regions, municipalities) Party, the central ministries and commissions, state ministries and commissions of the Party (party), the General Political Department of the military, every 3 people organization of Party of two regulations revision opinion. Central Commission for Discipline Inspection of extensive solicitation of opinions, careful study, attracting, formed a revised sent reviewers. In October 8 and October 12, Central Committee Political Bureau Standing Committee and the Political Bureau of the Central Committee After consideration of the two regulations revised draft. On October 18, the Central Committee of the Communist Party of China formally issued two regulations. Can say, two laws amendment concentrated the wisdom of the whole party, embodies the party. Second, < code > and < Regulations > revision of the basic principles of two party regulations revision work and implement the party's eighteen, ten eight plenary, the spirit of the Fourth Plenary Session of the Eleventh Central Committee and General Secretary Xi Jinping important instructions on the revised < low political criterion > and < Regulations >, highlighting the ruling party characteristics, serious discipline, the discipline quite in front of the law, based on the current, a long-term, advance as a whole, with Bu Xiuding independent < rule > and < rule >. Main principle is: first, adhere to the party constitution to follow. The constitution about discipline and self-discipline required specific, awaken the party constitution of party compasses party consciousness, maintaining the authority of the constitution. General Secretary Xi Jinping pointed out that "no rules, no side round. Party constitution is the fundamental law, the party must follow the general rules. In early 2015 held the eighth session of the Central Commission for Discipline Inspection Fifth Plenary Session of the 16th Central Committee, Xi Jinping again pointed out that constitution is the party must follow the general rules, but also the general rules." the revision of the < code > and < rule > is Method in adhere to the regulations established for the purpose of combining rule of virtue is to adhere to the party constitution as a fundamental to follow, the constitution authority set up, wake up the party constitution and party rules the sense of discipline, the party constitution about discipline and self-discipline specific requirements. 4 second is to adhere to in accordance with the regulations governing the party and the party. The Party of rule of virtue "de", mainly refers to the party's ideals and beliefs, excellent traditional style. The revised the < code > closely linked to the "self-discipline", insisting on the positive initiative, for all members, highlight the "vital few", emphasized self-discipline, focusing on the morality, and the majority of Party members and the ideological and moral standards. The revised < > Ji method separately, Ji, Ji Yan to Method, as a "negative list", emphasizing the heteronomy, focusing on vertical gauge. Is this one high and one low, a positive reaction, the strict party discipline and practice results transformation for the integration of the whole party to observe moral and discipline requirements, for the majority of Party members and cadres provides benchmarking and ruler. Third, insist on to. In view of the problems existing in the party at the present stage, the main problems of Party members and cadres in the aspect of self-discipline and abide by the discipline to make clearly defined, especially the party's eighteen years strict political discipline and political rules, organization and discipline and to implement the central eight provisions of the spirit against the four winds and other requirements into Disciplinary provisions. Not one pace reachs the designated position, focusing on in line with reality, pragmatic and effective. After the revision of major changes, major changes in the < code > and < rule > modified and needs to grasp several key problems (a) < code > < code > adhere to according to regulations governing the party and party with morals in combination, for at the present stage, the leadership of the party members and cadres and Party members i