数学选修2-3第一章测试

第一章测试(时间：120分钟满分：150分)一、选择题(本大题共12小题，每小题5分，满分60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)13名学生报名参加艺术体操、美术、计算机、航模课外兴趣小组，每人选报一种，则不同的报名种数有()A3B12C34 D43解析每位学生都有4种报名方法，因此有44443种答案D2从1,3,5,7,9中任取3个数字，从2,4,6,8中任取两个数字，一共可以组成没有重复数字的五位偶数的个数为()A2880 B7200C1440 D60解析先取后排，CCAA2880.答案A312名同学合影，站成了前排4人后排8人，现摄影师要从后排8人中抽2人调整到前排，若其他人的相对顺序不变则不同调整方法的种数是()ACA BCACCA DCA解析从后排8人中选2人的方法有C种设选出的2人为A、B，安排A到前排有A种方法，再安排B到前排有A种方法共有CAACA种方法故选C.答案C4(x1)(x1)4的展开式中x4的系数是()A3 B3C5 D5解析(x1)4中x3，x4的系数分别是C，C，(x1)(x1)4的展开式中x4的系数是CC3.答案B5若(x2)n的展开式中含有常数项，则正整数n的最小值是()A5 B4C6 D7解析Tr1C(x2)nr()r(1)rCx2n5r(r0,1,2，n)令2n5r0，即nr.当r2，n5时，T3C为常数项答案A62010年南非世界杯足球赛参赛球队共32支，分成8个小组，每小组4支球队进行单循环赛，各组前两名出线，再按排定的签位进行淘汰赛，决出前4名，则比赛进行的场数共有()A8A12 B8A16C8C12 D8C16解析每小组单循环赛需C场.8个小组共8C场，16支出线的球队淘汰赛又需比赛12场共需8C12场答案C78个人坐成一排照相，现要调换其中3个人中每一个人的位置，其余5个人的位置不变，则不同的调换方式有()A56 B112C118 D336解析先从8人中选出5人使其位置不变，有C种选法，其他三人不能坐在原来的位置上，只有2种方法故共有C2112种排法答案B8若对于任意的实数x，有x3a0a1(x2)a2(x2)2a3(x2)3.则a2的值为()A3 B6C9 D12解析设x2t，则xt2，原式化为(2t)3a0a1ta2t2a3t3a2C26，故选B.答案B9在(x23x2)5的展开式中x的系数为()A160 B240C360 D800解析把(x23x2)5看作5个因式(x23x2)相乘其中一个因式取3x，其他4个因式取2，得C3xC24240x.x的系数为240.答案B10下图是著名的杨辉三角，则表中所有各数的和是()A225 B256C127 D128解析由图可知，表中所有各数的和是20212226271127.答案C11已知集合A5，B1,2，C1,3,4，从这三个集合中各取一个元素构成空间直角坐标系中点的坐标，则确定的不同点的个数为()A33 B34C35 D36解析分类：若横坐标选5，有1CCA111(其中(5,1,1)重复)若横坐标选B中的元素有：2CCA12，若横坐标选C中的元素有3CCA210(其中(1,5,1)，(1,1,5)与前重复)共33个不同点答案A12设(1x)8a0a1xa2x2a8x8，则a0，a1，a2，a8中奇数的个数为()A2 B3C4 D5解析a0C1，a1C8，a2C28，a3C56，a4C70，a8C1.答案A二、填空题(本大题共4小题，每小题5分，共20分把答案填在题中横线上)13某校安排5个班到4个工厂进行社会实践，每个班去一个工厂，每个工厂至少安排一个班，不同的安排方法共有_种(用数字作答)解析由题设知，必有两个班去同一工厂，所以把5个班分成四组，有C种分法，每一种分法对应去4个工厂的全排列因此，共有CA240(种)答案24014(12x)6a0a1xa2x2a8x8，则|a0|a1|a2|a8|_.解析(12x)6的展开式中各项系数绝对值的和，相当于x1时，(12x)6的值，即36729.答案72915一个集合A含有n个元素，则集合A的所有子集的个数为_解析所有子集的个数为CCCC2n.答案2n16(2008广东)已知(1kx2)6(k是正整数)的展开式中， x8的系数小于120，则k_.解析x8的系数为Ck415k4.15k4120，k40且c0，因此共有CCC27(条)满足条件的抛物线(2)只需ac0，共有A6(条)；第三类，与x轴负半轴有两个交点，则必须满足b3，a，c在1,2中取，有2条综上可知，共有186226(条)20(2010重庆)(12分)在甲、乙等6个单位参加的一次“唱读讲传”演出活动中，每个单位的节目安排在一起，若采用抽签的方式随机确定各单位的演出顺序(序号为1,2，6)，求(1)甲、乙两单位演出序号均为偶数的概率；(2)甲、乙两单位的演出序号不相邻的概率解考虑甲、乙两个单位的排列，甲、乙两单位可能排列在6个位置中的任意两个，有A30种等可能结果(1)设A表示“甲、乙的演出序号均为偶数”，则A包含的结果有A6种，故所求的概率为P(A).(2)设B表示“甲、乙两单位演出序号不相邻”，则表示甲、乙两单位为演出序号相邻，包含的结果有5A10种，故所求的概率为P(B)1P()1.21(12分)设f(x)是定义在R上的一个给定的函数，函数g(x)Cfx0(1x)nCfx(1x)n1Cfxn(1x)0(x0,1)(1)当f(x)1时，求g(x)；(2)当f(x)x时，求g(x)解(1)当f(x)1时，g(x)C(1x)nCx(1x)n1Cxn(1x)0(1x)xn1.(2)当f(x)x时，g(x)0Cx(1x)n1Cx2(1x)n2Cxn(1x)0xC(1x)n1Cx(1x)n2Cxn1(1x)0x(1x)xn1x.22(12分)袋中装有大小相同的4个红球和6个白球，从中取出4个球(1)若取出的球必须是两种颜色，则有多少种不同的取法？(2)若取出的红球个数不少于白球个数，则有多少种不同的取法？(3)取出一个红球记2分，取出一个白球记1分，若取4球的总分不低于5分，则有多少种不同的取法？解(1)分三类：3红1白，2红2白，1红3白这三类，由分类加法计数原理有：CCCCCC194(种)(2)分三类：4红，3红1白，2红2白，由分类加法计数原理共有：CCCCC115(种)(3)由题意知，取4球的总分不低于5，只要取出的4个球中至少一个红球即可因此共有取法：CCCCCCC195(种)技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，17栋建筑层数为11层，812栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed,