2007年重庆高考数学(理科)试题答案

1. “英国高教会宁愿饶恕对它三十九个信条中的三十八个信条展开的攻击，而不饶恕对它现金收入的三十九分之一进行的攻击”。

马克思举这个例子是为了说明(ACDE)A.政治经济学的研究直接关系到各阶级的物质利益B.英国高教会容忍对其信条的攻击C.英国高教会也是英国社会的一种利益集团D.物质利益是社会其它利益的基础E.政治经济学是一门具有强烈阶级性的学科2. “一个社会即使探索到了本身运动的自然规律，……它还是既不能跳过也不能用法令取消自然的发展阶段。

但是它能缩短和减轻分娩的痛苦”。

这句话说明(BCDE)A.社会运动的规律就是自然运动的规律B.社会运动规律的作用和自然运动规律的作用一样不可抗拒C.社会运动规律决定社会发展的阶段不能人为的超越D.认识社会的运动规律有利于促进社会的发展E.认识了社会运动规律不等于就可以支配社会运动规律3. “我们也同西欧大陆所有其他国家一样，不仅苦于资本主义生产的发展，而且苦于资本主义生产的不发展”。

这句话的意思是说: 德国和西欧大陆其他国家(ABCDE)A.其资本主义生产关系均落后于英国B.同时存在着资本主义生产关系和前资本主义生产关系C.其工人阶级的生活状况不如英国的工人阶级D.其劳动者要遭受资本家阶级和封建贵族阶级的双重压迫E.在与英国的经济竞争中处于劣势4. 《资本论》第一卷是(D)A.《哲学的贫困》的续篇B.《雇佣劳动与资本》的续篇C.《1844年经济学哲学手稿》的续篇D.《政治经济学批判》的续篇E.《1957-1958经济学手稿》的续篇5. 《资本论》包括四大卷，它们的卷名分别是(ABDE)A.资本的生产过程B.资本的流通过程C.资本的分配过程D.资本主义生产的总过程E.剩余价值理论6. 《资本论》第一卷出版于(C)A.1843年3月B.1857年2月C.1867年9月D.1885年12月E.1895年12月7. 马克思研究资本主义经济(ABCE)A.其研究对象是资本主义生产关系B.其研究目的是为了揭示资本主义经济的运动规律C.其研究方法是唯物辩证法D.作为研究典型的国家是美国E.作为研究典型的国家是英国8. 马克思开始研究政治经济学是在(D)A.德国读大学期间B.德国担任“莱茵报”主编期间C.流亡英国伦敦期间D.流亡法国巴黎期间E.流亡比利时布鲁塞尔期间9. “我决不用玫瑰色描绘资本家和地主的面貌”。

2007年重庆市高考数学试卷（理科）一、选择题（共10小题，每小题5分，满分50分）1．（5分）若等差数列{a n}的前三项和S3=9且a1=1，则a2等于（）A．3 B．4 C．5 D．62．（5分）命题“若x2＜1，则﹣1＜x＜1”的逆否命题是（）A．若x2≥1，则x≥1或x≤﹣1 B．若﹣1＜x＜1，则x2＜1C．若x＞1或x＜﹣1，则x2＞1 D．若x≥1或x≤﹣1，则x2≥13．（5分）若三个平面两两相交，且三条交线互相平行，则这三个平面把空间分成（）A．5部分B．6部分C．7部分D．8部分4．（5分）若（x+）n展开式的二项式系数之和为64，则展开式的常数项为（）A．10 B．20 C．30 D．1205．（5分）在△ABC中，AB=，A=45°，C=75°，则BC=（）A．B．C．2 D．6．（5分）从5张100元，3张200元，2张300元的奥运预赛门票中任取3张，则所取3张中至少有2张价格相同的概率为（）A．B． C．D．7．（5分）若a是1+2b与1﹣2b的等比中项，则的最大值为（）A．B．C．D．8．（5分）设正数a，b满足，则=（）A．0 B．C．D．19．（5分）已知定义域为R的函数f（x）在（8，+∞）上为减函数，且函数y=f （x+8）函数为偶函数，则（）A．f（6）＞f（7）B．f（6）＞f（9）C．f（7）＞f（9）D．f（7）＞f（10）10．（5分）如图，在四边形ABCD中，++=4，•=•=0，•+•=4，则（+）•的值为（）A．2 B．C．4 D．二、填空题（共6小题，每小题4分，满分24分）11．（4分）复数的虚部为．12．（4分）已知x，y满足，则函数z=x+3y的最大值是．13．（4分）若函数的定义域为R，则实数a的取值范围是．14．（4分）设{a n}为公比q＞1的等比数列，若a2004和a2005是方程4x2﹣8x+3=0的两根，则a2006+a2007=．15．（4分）某校要求每位学生从7门课程中选修4门，其中甲、乙两门课程不能都选，则不同的选课方案有种．（以数字作答）16．（4分）过双曲线x2﹣y2=4的右焦点F作倾斜角为1050的直线，交双曲线于P、Q两点，则|FP|•|FQ|的值为．三、解答题（共6小题，满分76分）17．（13分）设f（x）=6cos2x﹣sin2x，（1）求f（x）的最大值及最小正周期；（2）若锐角α满足f（α）=3﹣2，求tanα的值．18．（13分）某单位有三辆汽车参加某种事故保险，单位年初向保险公司缴纳每辆900元的保险金、对在一年内发生此种事故的每辆汽车，单位获9000元的赔偿（假设每辆车最多只赔偿一次）．设这三辆车在一年内发生此种事故的概率分别为，且各车是否发生事故相互独立，求一年内该单位在此保险中：（1）获赔的概率；（2）获赔金额ξ的分布列与期望．19．（13分）如图，在直三棱柱ABC﹣A1B1C1中，AA1=2，AB=1，∠ABC=90°；点D、E分别在BB1，A1D上，且B1E⊥A1D，四棱锥C﹣ABDA1与直三棱柱的体积之比为3：5．（1）求异面直线DE与B1C1的距离；（2）若BC=，求二面角A1﹣DC1﹣B1的平面角的正切值．20．（13分）已知函数f（x）=ax4lnx+bx4﹣c（x＞0）在x=1处取得极值﹣3﹣c，其中a，b，c为常数．（1）试确定a，b的值；（2）讨论函数f（x）的单调区间；（3）若对任意x＞0，不等式f（x）≥﹣2c2恒成立，求c的取值范围．21．（12分）已知各项均为正数的数列{a n}的前n项和满足S1＞1，且6S n=（a n+1）（a n+2），n∈N*．（1）求{a n}的通项公式；（2）设数列{b n}满足，并记T n为{b n}的前n项和，求证：3T n+1＞log2（a n+3），n∈N*．22．（12分）如图，中心在原点O的椭圆的右焦点为F（3，0），右准线l的方程为：x=12．（1）求椭圆的方程；（2）在椭圆上任取三个不同点P1，P2，P3，使∠P1FP2=∠P2FP3=∠P3FP1，证明：++为定值，并求此定值．2007年重庆市高考数学试卷（理科）参考答案与试题解析一、选择题（共10小题，每小题5分，满分50分）1．（5分）（2007•重庆）若等差数列{a n}的前三项和S3=9且a1=1，则a2等于（）A．3 B．4 C．5 D．6【分析】根据等差数列的前n项和公式，结合已知条件，先求出d，再代入通项公式即可求解．【解答】解：∵S3=9且a1=1，∴S3=3a1+3d=3+3d=9，解得d=2．∴a2=a1+d=3．故选A．2．（5分）（2007•重庆）命题“若x2＜1，则﹣1＜x＜1”的逆否命题是（）A．若x2≥1，则x≥1或x≤﹣1 B．若﹣1＜x＜1，则x2＜1C．若x＞1或x＜﹣1，则x2＞1 D．若x≥1或x≤﹣1，则x2≥1【分析】根据逆否命题的定义，直接写出答案即可，要注意“且”形式的命题的否定．【解答】解：原命题的条件是““若x2＜1”，结论为“﹣1＜x＜1”，则其逆否命题是：若x≥1或x≤﹣1，则x2≥1．故选D．3．（5分）（2007•重庆）若三个平面两两相交，且三条交线互相平行，则这三个平面把空间分成（）A．5部分B．6部分C．7部分D．8部分【分析】画出图形，用三线表示三个平面，结合图形进行分析．【解答】解：可用三线a，b，c表示三个平面，其截面如图，将空间分成7个部分，故选C．4．（5分）（2007•重庆）若（x+）n展开式的二项式系数之和为64，则展开式的常数项为（）A．10 B．20 C．30 D．120【分析】根据二项式的展开式的二项式系数是64，写出二项式系数的表示式，得到次数n的值，写出通项式，当x的指数是0时，得到结果．【解答】解：∵C n°+C n1+…+C n n=2n=64，∴n=6．T r+1=C6r x6﹣r x﹣r=C6r x6﹣2r，令6﹣2r=0，∴r=3，常数项：T4=C63=20，故选B．5．（5分）（2007•重庆）在△ABC中，AB=，A=45°，C=75°，则BC=（）A．B．C．2 D．【分析】结合已知条件，直接利用正弦定理作答．【解答】解：∵AB=，A=45°，C=75°，由正弦定理得：，∴．故选A．6．（5分）（2007•重庆）从5张100元，3张200元，2张300元的奥运预赛门票中任取3张，则所取3张中至少有2张价格相同的概率为（）A．B． C．D．【分析】由题意知本题是一个古典概型，满足条件的事件包含的结果比较多，可以从它的对立事件来考虑，取出的三张门票的价格均不相同5×3×2=30种取法，试验发生的所有事件总的取法有C103，用对立事件概率得到结果．【解答】解：由题意知本题是一个古典概型，∵满足条件的事件包含的结果比较多，可以从它的对立事件来考虑，取出的三张门票的价格均不相同5×3×2=30种取法，试验发生的所有事件总的取法有（10×9×8）÷（3×2×1）=120种，三张门票的价格均不相同的概率是=，∴至少有2张价格相同的概率为P=1﹣=．故选C．7．（5分）（2007•重庆）若a是1+2b与1﹣2b的等比中项，则的最大值为（）A．B．C．D．【分析】由a是1+2b与1﹣2b的等比中项得到4|ab|≤1，再由基本不等式法求得．【解答】解：a是1+2b与1﹣2b的等比中项，则a2=1﹣4b2⇒a2+4b2=1≥4|ab|．∴．∵a2+4b2=（|a|+2|b|）2﹣4|ab|=1．∴≤===∵∴，∴．故选B．8．（5分）（2007•重庆）设正数a，b满足，则=（）A．0 B．C．D．1【分析】由题目中的已知式化简，得到a，b的关系，再代入化简求值．【解答】解：∵=4⇒4+2a﹣b=4⇒2a=b，∴．∴故选B．9．（5分）（2007•重庆）已知定义域为R的函数f（x）在（8，+∞）上为减函数，且函数y=f（x+8）函数为偶函数，则（）A．f（6）＞f（7）B．f（6）＞f（9）C．f（7）＞f（9）D．f（7）＞f（10）【分析】根据y=f（x+8）为偶函数，则f（x+8）=f（﹣x+8），即y=f（x）关于直线x=8对称．又f（x）在（8，+∞）上为减函数，故在（﹣∞，8）上为增函数，故可得答案．【解答】解：∵y=f（x+8）为偶函数，∴f（x+8）=f（﹣x+8），即y=f（x）关于直线x=8对称．又∵f（x）在（8，+∞）上为减函数，∴f（x）在（﹣∞，8）上为增函数．由f（8+2）=f（8﹣2），即f（10）=f（6），又由6＜7＜8，则有f（6）＜f（7），即f（7）＞f（10）．故选D．10．（5分）（2007•重庆）如图，在四边形ABCD中，++=4，•=•=0，•+•=4，则（+）•的值为（）A．2 B．C．4 D．【分析】先根据++=4，•+•=4，求出+=2，，再由•=•=0，确定∥，再由向量的点乘运算可解决．【解答】解：∵++=4，•+•=4，∴+=2，，由已知•=•=0，知⊥⊥，∴∥，作如图辅助线∴=+=，即三角形AEC是等腰直角三角形，∠CAE=45°|，∴（+）•=||cos∠CAE=2×=4，故选C．二、填空题（共6小题，每小题4分，满分24分）11．（4分）（2007•重庆）复数的虚部为．【分析】把复数整理变形，先变分母，再分子和分母同乘以分母的共轭复数，分子上要进行复数的乘法运算，最后写出代数形式，指出虚部【解答】解：．故答案为：．12．（4分）（2007•重庆）已知x，y满足，则函数z=x+3y的最大值是7．【分析】先画出可行域，再把目标函数变形为直线的斜截式，由截距的最值即可求得．【解答】解：画出可行域，如图所示解得C（1，2），函数z=x+3y可变形为，可见当直线过点C 时z取得最大值，所以z max=1+6=7．故答案为：7．13．（4分）（2007•重庆）若函数的定义域为R，则实数a 的取值范围是0≤a≤1．【分析】利用被开方数非负的特点列出关于a的不等式，转化成x2﹣2ax+a≥0在R上恒成立，然后建立关于a的不等式，求出所求的取值范围即可．【解答】解：函数的定义域为R，∴﹣1≥0在R上恒成立即x2﹣2ax+a≥0在R上恒成立该不等式等价于△=4a2﹣4a≤0，解出0≤a≤1．故实数a的取值范围为0≤a≤1故答案为：0≤a≤114．（4分）（2007•重庆）设{a n}为公比q＞1的等比数列，若a2004和a2005是方程4x2﹣8x+3=0的两根，则a2006+a2007=18．【分析】通过解方程可以求出a2004和a2005的值，进而求出q，根据等比数列的通项公式，a2006+a2007=a2004q2+a2005q2=（a2004+a2005）q2，从而问题得解．【解答】解：∵a2004和a2005是方程4x2﹣8x+3=0的两根，∴或．∴q=3或，∵q＞1，∴q=3；∴a2006+a2007=a2004q2+a2005q2=（a2004+a2005）×9=18．故答案为：18．15．（4分）（2007•重庆）某校要求每位学生从7门课程中选修4门，其中甲、乙两门课程不能都选，则不同的选课方案有25种．（以数字作答）【分析】从7门课程中选修4门，其中甲、乙两门课程不能都选，可从反面解决，分别求出从7门课程中选修4门的种数和两门都选的方法种数，做差即可；也可按分类原理分为两类：一类甲、乙两门课程都不选，另一类只选一门．【解答】解：所有的选法数为C74，两门都选的方法为C22C52，故共有选法数为C74﹣C22C52=35﹣10=25．故答案为：2516．（4分）（2007•重庆）过双曲线x2﹣y2=4的右焦点F作倾斜角为1050的直线，交双曲线于P、Q两点，则|FP|•|FQ|的值为．【分析】先由点斜式写出直线方程，设出两个交点坐标，再由弦长公式计算，作出解答．【解答】解：∵，．∴．代入x2﹣y2=4得：．设P（x1，y1），Q（x2，y2）．⇒x1+x2=．又|FP|=，|FQ|=，∴==，故答案为：．三、解答题（共6小题，满分76分）17．（13分）（2007•重庆）设f（x）=6cos2x﹣sin2x，（1）求f（x）的最大值及最小正周期；（2）若锐角α满足f（α）=3﹣2，求tanα的值．【分析】（I）利用三角函数的二倍角公式及公式化简为只含一个角一个函数名的三角函数，利用有界性及周期公式求出最大值最小正周期．（II）列出关于α的三角方程，求出α，求出正切值．【解答】解：（Ⅰ）===故f（x）的最大值为；最小正周期（Ⅱ）由得，故又由得，故，解得．从而．18．（13分）（2007•重庆）某单位有三辆汽车参加某种事故保险，单位年初向保险公司缴纳每辆900元的保险金、对在一年内发生此种事故的每辆汽车，单位获9000元的赔偿（假设每辆车最多只赔偿一次）．设这三辆车在一年内发生此种事故的概率分别为，且各车是否发生事故相互独立，求一年内该单位在此保险中：（1）获赔的概率；（2）获赔金额ξ的分布列与期望．【分析】（1）设A k表示第k辆车在一年内发生此种事故，k=1，2，3、由题意知A1，A2，A3之间相互独立，正难则反，该单位一年内获赔的对立事件是A1，A2，A3都不发生，用对立事件的概率做出结果．（2）由题意知ξ的所有可能值为0，9000，18000，27000，看出这四个数字对应的事件，做出事件的概率，写出分布列，求出期望，概率在解时情况比较多，要认真．【解答】解：（1）设A k表示第k辆车在一年内发生此种事故，k=1，2，3，由题意知A1，A2，A3独立，且P（A1）=，P（A2）=，P（A3）=∵该单位一年内获赔的对立事件是A1，A2，A3都不发生，∴该单位一年内获赔的概率为．（Ⅱ）ξ的所有可能值为0，9000，18000，27000，===，===，P（ξ=27000）=P（A1A2A3）=P（A1）P（A2）P（A3）=，综上知，ξ的分布列为ζ090001800027000P设ξk表示第k辆车一年内的获赔金额，k=1，2，3，则ξ1有分布列ζ109000P∴同理得，综上有Eξ=Eξ1+Eξ2+Eξ3≈1000+900+818.18=2718.18（元）19．（13分）（2007•重庆）如图，在直三棱柱ABC﹣A1B1C1中，AA1=2，AB=1，∠ABC=90°；点D、E分别在BB1，A1D上，且B1E⊥A1D，四棱锥C﹣ABDA1与直三棱柱的体积之比为3：5．（1）求异面直线DE与B1C1的距离；（2）若BC=，求二面角A1﹣DC1﹣B1的平面角的正切值．【分析】（1）因B1C1⊥A1B1，且B1C1⊥BB1，进而可推断B1C1⊥面A1ABB1，进而推断B1E是异面直线B1C1与DE的公垂线，设BD的长度为x，则四棱椎C﹣ABDA1的体积V1为，里用体积公式表示出V1，表示出四棱椎C﹣ABDA1的体积V1，同时直三棱柱ABC﹣A1B1C1的体积V2，根据V1：V2=3：5求得x，从而求得B1D，直角三角形A1B1D中利用勾股定理求得A1D进而利用三角形面积公式求得B1E．（2）过B1作B1F⊥C1D，垂足为F，连接A1F，因A1B1⊥B1C1，A1B1⊥B1D，故A1B1⊥面B1DC1．由三垂线定理知C1D⊥A1F，故∠A1FB1为所求二面角的平面角，先利用勾股定理求得C11D，进而求得BF，进而可求tan求得∠A1FB1．【解答】解：（Ⅰ）因B1C1⊥A1B1，且B1C1⊥BB1，故B1C1⊥面A1ABB1，从而B1C1⊥B1E，又B1E⊥DE，故B1E是异面直线B1C1与DE的公垂线设BD的长度为x，则四棱椎C﹣ABDA1的体积V1为而直三棱柱ABC﹣A1B1C1的体积V2为由已知条件V1：V2=3：5，故，解之得从而在直角三角形A1B1D中，，又因，故（Ⅱ）如图1，过B1作B1F⊥C1D，垂足为F，连接A1F，因A1B1⊥B1C1，A1B1⊥B1D，故A1B1⊥面B1DC1．由三垂线定理知C1D⊥A1F，故∠A1FB1为所求二面角的平面角在直角△C1B1D中，，又因，故，所以．20．（13分）（2007•重庆）已知函数f（x）=ax4lnx+bx4﹣c（x＞0）在x=1处取得极值﹣3﹣c，其中a，b，c为常数．（1）试确定a，b的值；（2）讨论函数f（x）的单调区间；（3）若对任意x＞0，不等式f（x）≥﹣2c2恒成立，求c的取值范围．【分析】（1）因为x=1时函数取得极值得f（x）=﹣3﹣c求出b，然后令导函数=0求出a即可；（2）解出导函数为0时x的值讨论x的取值范围时导函数的正负决定f（x）的单调区间；（3）不等式f（x）≥﹣2c2恒成立即f（x）的极小值≥﹣2c2，求出c的解集即可．【解答】解：（1）由题意知f（1）=﹣3﹣c，因此b﹣c=﹣3﹣c，从而b=﹣3又对f（x）求导得=x3（4alnx+a+4b）由题意f'（1）=0，因此a+4b=0，解得a=12（2）由（I）知f'（x）=48x3lnx（x＞0），令f'（x）=0，解得x=1当0＜x＜1时，f'（x）＜0，此时f（x）为减函数；当x＞1时，f'（x）＞0，此时f（x）为增函数因此f（x）的单调递减区间为（0，1），而f（x）的单调递增区间为（1，+∞）（3）由（II）知，f（x）在x=1处取得极小值f（1）=﹣3﹣c，此极小值也是最小值，要使f（x）≥﹣2c2（x＞0）恒成立，只需﹣3﹣c≥﹣2c2即2c2﹣c﹣3≥0，从而（2c﹣3）（c+1）≥0，解得或c≤﹣1所以c的取值范围为（﹣∞，﹣1]∪21．（12分）（2007•重庆）已知各项均为正数的数列{a n}的前n项和满足S1＞1，且6S n=（a n+1）（a n+2），n∈N*．（1）求{a n}的通项公式；（2）设数列{b n}满足，并记T n为{b n}的前n项和，求证：3T n+1＞log2（a n+3），n∈N*．【分析】（1）先根据题设求得a1，进而根据a n+1=S n+1﹣S n整理得（a n+1+a n）（a n+1﹣a n﹣3）=0求得a n+1﹣a n=3，判断出{a n}是公差为3，首项为2的等差数列，则数列的通项公式可得．（2）把（1）中的a n代入可求得b n，进而求得前n项的和T n，代入到3T n+1﹣log2（a n+3）中，令，进而判断出f（n+1）＞f（n），从而推断出3T n+1﹣log2（a n+3）=log2f（n）＞0，原式得证．【解答】解：（1）由，解得a1=1或a1=2，由假设a1=S1＞1，因此a1=2，又由，+a n）（a n+1﹣a n﹣3）=0，得（a n+1即a n﹣a n﹣3=0或a n+1=﹣a n，因a n＞0，故a n+1=﹣a n不成立，舍去+1﹣a n=3，从而{a n}是公差为3，首项为2的等差数列，因此a n+1故{a n}的通项为a n=3n﹣1（2）证明：由可解得；从而因此令，则因（3n+3）3﹣（3n+5）（3n+2）2=9n+7＞0，故f（n+1）＞f（n）特别地，从而3T n+1﹣log2（a n+3）=log2f（n）＞0即3T n+1＞log2（a n+3）22．（12分）（2007•重庆）如图，中心在原点O的椭圆的右焦点为F（3，0），右准线l的方程为：x=12．（1）求椭圆的方程；（2）在椭圆上任取三个不同点P1，P2，P3，使∠P1FP2=∠P2FP3=∠P3FP1，证明：++为定值，并求此定值．【分析】（Ⅰ）设椭圆方程为，由题意知a=6，，故所求椭圆方程为．（Ⅱ）记椭圆的右顶点为A，并设∠AFP i=αi（i=1，2，3），假设，且，，又设点P i在l上的射影为Q i，因椭圆的离心率，从而有|FP i|=|P i Q i|•e==（i=1，2，3）．由此入手能够推导出++为定值，并能求出此定值．【解答】解：（Ⅰ）设椭圆方程为因焦点为F（3，0），故半焦距c=3又右准线l的方程为，从而由已知，因此a=6，故所求椭圆方程为（Ⅱ）记椭圆的右顶点为A，并设∠AFP i=αi（i=1，2，3），不失一般性，假设，且，又设点P i在l上的射影为Q i，因椭圆的离心率，从而有|FP i|=|P i Q i|•e==（i=1，2，3）解得=（i=1，2，3）因此++=，而=，故++为定值．。

2007年普通高等学校招生全国统一考试数学 (重庆理卷)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. （1）若等差数列{n a }的前三项和93=S 且11=a ，则2a 等于（ ）A ．3 B.4 C. 5 D. 6（2）命题“若12<x ，则11<<-x ”的逆否命题是（ ）A ．若12≥x ，则1≥x 或1-≤x B.若11<<-x ，则12<x C.若1>x 或1-<x ，则12>x D.若1≥x 或1-≤x ，则12≥x（3）若三个平面两两相交，且三条交线互相平行，则这三个平面把空间分成（ ）A ．5部分 B.6部分 C.7部分 D.8部分 （4）若nxx )1(+展开式的二项式系数之和为64，则展开式的常数项为（ ） A10 B.20 C.30 D.120（5）在ABC ∆中，,75,45,300===C A AB 则BC =（ ）A.33-B.2C.2D.33+（6）从5张100元，3张200元，2张300元的奥运预赛门票中任取3张，则所取3张中至少有2张价格相同的概率为（ ）A ．41 B ．12079 C ． 43 D ．2423 （7）若a 是1+2b 与1-2b 的等比中项，则||2||2b a ab+的最大值为（ ）A.1552 B.42 C.55 D.22（8）设正数a,b 满足4)(22lim =-+→b ax xx 则=++--+∞→nn n n n ba ab a 2111lim（ ） A ．0 B ．41 C ．21D ．1 （9）已知定义域为R 的函数f(x)在),8(+∞上为减函数，且y=f(x+8)函数为偶函数，则（ ）A.f(6)>f(7)B.f(6)>f(9)C.f(7)>f(9)D.f(7)>f(10)（10）如图，在四边形ABCD 中，→→→→→→→⋅=⋅=++DC BD BD AB DC BD AB ,4||||||=0,CD→→→→=⋅+⋅4||||||||DC BD BD AB 则→→→⋅+AC DC AB )(的值为（ ）A.2B. 22C.4D.24二、填空题：本大题共6小题，共24分，把答案填写在答题卡相应位置上（11）复数322i i+的虚部为________.（12）已知x,y 满足⎪⎩⎪⎨⎧≥≤+≤-1421x y x y x ，则函数z = x+3y 的最大值是________.（13）若函数f(x) =1222--+aax x的定义域为R ，则a 的取值范围为_______.（14）设{n a }为公比q>1的等比数列，若2004a 和2005a 是方程03842=+x x 的两根，则=+20072006a a __________.（15）某校要求每位学生从7门课程中选修4门，其中甲乙两门课程不能都选，则不同的选课方案有___________种。

课后练习题据说有39道，本版本只有33道，希望大家注意下。

1.为什么说鸦片战争是中国近代史的起点？鸦片战争失败后，清政府被迫签订了中英《南京条约》及其补充条约、中美《望厦条约》和中法《黄埔条约》。

鸦片战争的失败和一系列不平等条约的签订，是中国人民遭受外国资本主义奴役的起点，给中国社会带来极大的影响。

鸦片战争后，中国社会性质开始发生根本变化，即由一个独立的封建社会一步步地变为半殖民地半封建社会。

鸦片战争前，中国在政治上是个独立自主的国家。

在经济上是一个自给自足的自然经济占统治地位的国家。

鸦片战争后，中国的自然经济由于遭受外国资本主义的冲击而开始解体。

中国社会的主要矛盾变为外国资本主义和中华民族的矛盾，封建主义和人民大众的矛盾。

在思想领域也发生了巨大的震动。

所以说鸦片战争是中国近代史的起点2、怎样认识近代中国的主要矛盾、社会性质及其基本特征？答：(1)两大主要矛盾是帝国主义和中华民族的矛盾、封建主义和人民大众的矛盾。

而前一个是主要矛盾。

(2)中国的社会性质由封建社会转变成半殖民地半封建的社会性质。

(3)中国半殖民地半封建社会有以下一些基本特征：①、资本----帝国主义势力操纵中国的经济命脉，控制了中国的政治②、中国封建势力和外国侵略势力相勾结，压迫奴役中国人民。

③、中国自然经济遭到破坏，但土地所有制依然存在，阻碍着中国走向现代化和民主化。

④、所兴的民族资本主义经济已经存在，但势力很弱。

⑤、政治势力不统一，各地区、政治、经济和文化发展不平衡。

⑥、在资本----帝国主义和封建主义的双重压迫下，中国的广大人民过着饥寒交迫，毫无政治权利的生活。

3、如何理解近代中国的两大任务及其相互关系？答：争取民族独立、人民解放和实现国家富强、人民富裕这两个任务，是互相区别又互相紧密联系的。

由于腐朽的社会制度束缚生产力发展，阻碍经济技术进步，必须先改变社会制度，争得民族独立和人民解放，才能为实现国家富强和人民富裕创造前提开辟道路。

２００７年普通高等学校招生全国统一考试（重庆卷）——数学试题卷（理工农医类）作者：来源：《数学教学通讯(教师阅读)》2007年第07期数学试题卷(理工农医类) 满分：150分时间：120分钟参考公式：如果事件A、B互斥，那么P(A+B)=P(A)+P(B) .如果事件A、B相互独立，那么P(A·B)=P(A)·P(B)如果事件A在一次试验中发生的概率是P，那么n次独立事件重复试验中恰好发生k次的概率Pn(k)=CknPk(1-P)n-k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.(1)若等差数列{an}的前三项和S3=9且a1=1，则a2等于().(A) 3 (B) 4(C) 5 (D)6(2)命题“若x2＜1，则－1＜x＜1”的逆否命题是().(A) 若x2≥1，则x≥1或x≤－1 ．(B) 若－1＜x＜1，则x2＜1．(C) 若x＞1或x＜－1，则x2＞1．(D) 若x≥1或x≤－1，则x2≥1．(3)若三个平面两两相交，且三条交线互相平行，则这三个平面把空间分成( ).(A) 5部分(B) 6部分(C) 7部分(D) 8部分(4)若(x+1x)n展开式的二项式系数之和为64，则展开式的常数项为()．(A) 10(B) 20 (C) 30 (D) 120(5)在△ABC中，AB=3,A=45°,C=75°,则BC =().(A) 3－3(B) 2(C) 2 (D) 3+3(6)从5张100元，3张200元，2张300元的奥运预赛门票中任取3张，则所取3张中至少有2张价格相同的概率为().二、填空题：本大题共6小题，共24分，把答案填写在答题卡相应位置上“本文中所涉及到的图表、注解、公式等内容请以PDF格式阅读原文”。

大学英语四级模拟试题四Part I writing (30 minutes)Directions: For this part, you are allowed 30 minutes to write a composition on the topic Chossing an Occupation . You should write at least 120 words following the outline given below in Chinese:1 选择职业是一个人要面对大众多难题之一。

2 需要时间去选择职业。

3 选择职业时可以向众多人寻求建议和帮助。

Choosing an OccupationPart 2 Reading Comprehension (Skimming and Scanning) (15 minutes)Direction: In this part, you will have 15 minutes to go over the passage quickly and answer the question on Answers Sheet 1For questions 1-7 mark.Y(for YES)if the statement agrees with the information given in the passageN(for NO)if the statement contradicts the information given in the passageNG(for NOT GIVEN)if the information is not given in the passageFor questions 8-10 , complete the sentences with the information given in the passage.Will We Run Out Of Water?Picture a “ghost ship” sinking into the sand, left to rot on dry land by a receding sea . Then imagine dust storms sweeping up toxic pesticides and chemical fertilizers from the dry seabed and spewing then across towns and villages.Seem like a scene from a movie about the end of the word? For people living near the Aral Sea in Central Asia, it’s all too irrigate (provide water for) farmland. As a result, the sea has shrunk to half its original size, stranding ships on dry land.The seawater has tripled in salt content and become polluted, killing all 24 native species of fish.Similar large scale efforts to redirect water in other parts of the world have also ended in ecological crisis, according to numerous environmental groups .But many countries continue to build massive dams and irrigation systems, even though such projects can create more problems than they fix why? People in many parts of the world are desperate for water, and more people will need more water in the next century.“Growing populations will worsen problems with water,” says Peter H. Gleick, an environmental scientist at the Pacific Institute for studies in Development, Environment, and Security, a research organization in California. He fears that by the year 2025, as many as one third of the world’s projected 8.3 billion people will suffer from water shortages.Where Water GoesOnly 2.5 percent of all water on Earth is freshwater, water suitable for drinking and growing food, says Sandra Postel, director of the Global Water Policy Project in Amherst, Mass. Two thirds of this freshwater is locked in glaciers and ice caps. In fact, only a tiny percentage of freshwater is part of the water cycle, in which waterevaporates and rises into the atmosphere, then condenses and falls back to Earth as precipitation（rain or snow）.Some precipitation runs off land to lakes and oceans, and some becomes groundwater, water that seeps into the earth. Much of this renewable freshwater ends up in remote places like the Amazon river basin in Brazil, where few people live. In fact, the world’s population has access to only 12,500 cubic kilometers of freshwater—about the amount of water in Lake Su perior. And people use half of this amount already. “If water demand continues to climb rapidly,” says Postel, “there will be severe shortages and damage to the aquatic environment.”Close to HomeWater woes may seem remote to people living in rich countries like the United States. But Americans could face serious water shortages, too especially in areas that rely on groundwater. Groundwater accumulates in aquifers, layers of sand and gravel that lie between soil and bedrock. （For every liter of surface water, more than 90 liters are hidden underground）.Although the United States has large aquifers, farmers, ranchers, and cities are tapping many of them for water faster than nature can replenish it. In northwest Texas, for example, over pumping has shrunk groundwater supplies by 25 percent, according to Postel.Americans may face even more urgent problems from pollution. Drinking water in the United States is generally safe and meets high standards. Nevertheless, one in five Americans every day unknowingly drinks tap water contaminated with bacteria and chemical wastes, according to the Environmental Protection Agency. In Milwaukee, 400,000 people fell ill in 1993 after drinking tap water tainted with cryptosporidium, a microbe that causes fever, diarrhea and vomiting.The SourceWhere so contaminants come from? In developing countries, people dump raw sewage into the same streams and rivers from which they draw water for drinking and cooking; about 250 million people a year get sick from water borne diseases.In developed countries, manufacturers use 100,000 chemical compounds to make a wide range of products. Toxic chemicals pollute water when released untreated into rivers and lakes. (Certain compounds, such as polychlorinated biphenyls, or PCBs, have been banned in the United States.）But almost everyone contributes to water pollution. People often pour household cleaners, car antifreeze, and paint thinners down the drain; All of these contain hazardous chemicals. Scientists studying water in the San Francisco Bay reported in 1996 that 70 percent of the pollutants could be traced to household waste.Farmers have been criticized for overusing herbicides and pesticides, chemicals that kill weeds and insects but insects but that pollutes water as well. Farmers also use nitrates, nitrogen rich fertilizer that helps plants grow but that can wreak havoc onthe environment. Nitrates are swept away by surface runoff to lakes and seas. Too many nitrates “over enrich” these bodies of water, encouraging the buildup of algae, or microscopic plants that live on the surface of the water. Algae deprive the water of oxygen that fish need to survive, at times choking off life in an entire body of water. What’s the Solution?Water expert Gleick advocates conservation and local solutions to water related problems; governments, for instance, would be better off building small scale dams rather than huge and disruptive projects like the one that ruined the Aral Sea.“More than 1 billion people worldwide don’t have access to basic clean drinking water,”says Gleick. “There has to be a strong push on the part of everyone governments and ordinary people—to make sure we have a resource so fundamental to life.”huge water projects have diverted the rivers causes the Aral Sea to shrink.2. The construction of massive dams and irrigation projects does more good than harm.3. The chief causes of water shortage are population growth and water pollution.4. The problems Americans face concerning water are ground water shrinkage and tap water pollution.5. According to the passage all water pollutants come from household waste.6. The people living in the United States will not be faced with water shortages.7. Water expert Gleick has come up with the best solution to water related problems.1.［Y］［N］［NG］2.［Y］［N］［NG］3.［Y］［N］［NG］4.［Y］［N］［NG］5.［Y］［N］［NG］6.［Y］［N］［NG］7.［Y］［N］［NG］8. According to Peter H. Gleick, by the year 2025, as many as of the world’s people will suffer from water shortages .9.Two thirds of the freshwater on Earth is locked in .10.In developed countries, before toxic chemicals are released into rivers and lakes, they should be treated in order to avoid .Part III Listening Comprehension(35 minutes)Section ADirections: In this section, you will hear 8 short conversations and 2 long conversations. At the end of each conversation, one or more questions will be asked about what was said. Both the conversation and the questions will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked ［A］,［B］,［C］and［D］, and decide which is the best answer. Then mark the corresponding letter on Answer Sheet 2 with a single line through the centre.11.［A］Wait for the sale to start. ［B］Get further information about the sale.［C］Call the TV station to be sure if the ad is true. ［D］Buy a new suit.12.［A］He doesn’t think that John is ill.［B］He thinks that perhaps John is not in very good health.［C］He is aware that John is ill.［D］He doesn’t think that John has a very good knowledge of physics.13.［A］Before six. ［B］At six. ［C］After six. ［D］After seven.14.［A］It is bigger. ［B］It is of a prettier color.［C］It has a larger yard. ［D］It is brighter.15.［A］Australian and American. ［B］Guest and host.［C］Husband and wife. ［D］Professor and student.16.［A］1∶30 ［B］11∶00 ［C］9∶30 ［D］10∶0017.［A］He prefers staying at home because the bus is too late.［B］He prefers staying at home because he doesn’t like to travel.［C］He prefers taking a bus because the plane makes him nervous.［D］He prefers traveling with the woman.18.［A］He thinks she should visit her cousin.［B］Her cousin doesn’t visit very often.［C］Her cousin is feeling a lot better today.［D］He doesn’t think her cousin has been at home today.Questions 19 to 22 are based on the conversation you have just heard.19.［A］Two different types of bones in the human body.［B］How bones help the body move.［C］How bones continuously repair themselves.［D］The chemical composition of human bones.20.［A］They defend the bone against viruses.［B］They prevent oxygen from entering the bone.［C］They break down bone tissue.［D］They connect the bone to muscle tissue.21.［A］They have difficulty identifying these cells.［B］They aren’t sure how these cells work.［C］They’ve learned how to reproduce these cells.［D］They’ve found similar cells in other species.22.［A］To learn how to prevent a bone disease.［B］To understand differences between bone tissue and other tissue.［C］To find out how specialized bone cells have evolved.［D］To create artificial bone tissueQuestions 23 to 25 are based on the conversation you have just heard.23.［A］A new fuel for buses. ［B］The causes of air pollution.［C］A way to improve fuel efficiency in buses. ［D］Careers in environmental engineering.24.［A］Her car is being repaired. ［B］She wants to help reduce pollution. ［C］Parking is difficult in the city. ［D］The cost of fuel has increased.25.［A］A fuel that burns cleanly.［B］An oil additive that helps cool engines.［C］A material from which filters are made.［D］An insulating material sprayed on engine parts.Section BDirections: In this section, you will hear 3 short passages. At the end of each passage, you will hear some questions. Both the passage and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked ［A］, ［B］, ［C］and ［D］.Then mark the corresponding letter on Answer sheet 2 with a single line through the centre.Passage OneQuestions 26 to 28 are based on the passage you have just heard.26.［A］From three to five months. ［B］Three months.［C］Five months. ［D］Four months.27. A］Watch traffic. ［B］Obey commands.［C］Cross streets safely. ［D］Guard the door.28.［A］Three weeks. ［B］Two weeks. ［C］Four weeks. ［D］Five weeks. Passage TwoQuestions 29 to 31 are based on the passage you have just heard.29.［A］Two to four times. ［B］Four to six times.［C］Four to eight times. ［D］Six to ten times.30.［A］Sleeping pills made people go into REM sleep quickly.［B］People had more dreams after they took sleeping pills.［C］People became angry easily because they didn’t take sleeping pills.［D］Sleeping pills prevented people from going into REM sleep.31.［A］People dream so as to sleep better.［B］People dream in order not to go into REM sleep.［C］Because they may run into difficult problems in their dreams.［D］Because in their dreams they may find the answers to their problems. Passage ThreeQuestions 32 to 35 are based on the passage you have just heard.32.［A］A sales representative. ［B］A store manager.［C］A committee chairperson. ［D］A class president.33.［A］To determine who will graduate this year.［B］To discuss the seating arrangement.［C］To choose the chairperson of the ceremonies.［D］To begin planning the graduation ceremonies.34.［A］Their names, phone numbers and job preference.［B］The names and addresses of their guests.［C］The names of the committee they worked on last year.［D］Their dormitory name, address and phone number.35.［A］In an hour. ［B］Next week.［C］In one month. ［D］Next year.Section CDirections: In this section, you will hear a passage three times. When the passage isread for the first time, you should listen carefully for its general idea. When the passage is read for the second time, you are required to fill in the blanks numbered from 36 to 43 with the exact words you have just heard. For blanks numbered from 44 to 46 you are required to fill in the missing information. For these blanks, you can either use the exact words you have just heard or write down the main points in you own words. Finally, when the passage is read for the third time, you should check what you have written.In the English (36)system, students take three very important examinations. The first is the eleven-plus, which is (37) at the age of eleven or a little past. At one time the (38)or (39)shown on the eleven-plus would have (40)if a child stayed in school. Now, however, all children continue in (41) schools, and the eleven-plus determines which courses of study the child will follow. At the age of fifteen or sixteen, the students are (42)for the Ordinary (43)of the General Certificate of Education. (44). Once students have passed this exam, they are allowed to specialize, so that two-thirds or more of their courses will be in physics, chemistry, classical languages, or whatever they wish to study at greater length. (45). Even at the universities, students study only in their concentrated area, and very few students ever venture out-side that subject again.(46).Part ⅣReading Comprehension（Reading in Depth）（25 minutes）Section ADirections: In this section, there is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passage through carefully before making your choices. Each choice in the bank is identified by a letter. Please mark the corresponding letter for each item on Answer Sheet 2 with a single line through the centre. You may not use any of the words in the bank more than once.Questions 47 to 56 are based on the following passage.Shopping habits in the United States have changed greatly in the last quarter of the 20th century. 47 in the 1900s most American towns and cities had a Main Street. Main Street was always the heart of a town. This street was lined on the both sides with many 48 businesses. Here, shoppers walked into stores to look at all sorts of merchandise: clothing, furniture, hardware, groceries. In addition, some shops offered 49 . There shops included drugstores, restaurants, shoe repair stores, and barber or hairdressing shops. But in the 1950s, a change began to 50 place. Too many automobiles had crowded into Main Street while too few parking places were 51 to shoppers. Because the streets were crowded, merchants began to look with interest at the open spaces outside the city limits. Open space is what their car driving customers needed. And open space is what they got when the first shopping centre was built. Shopping centers, or rather malls, 52 as a collection of small new stores away from crowded city centers. 53 by hundreds of free parking space, customers were drawn away from 54 areas to outlying malls. And the growing 55 of shopping centers led in turn to the building of bigger and better stocked stores. By the late 1970s, manyshopping malls had almost developed into small cities themselves. In addition to providing the 56 of the stop shopping, malls were transformed into landscaped parks, with benches, fountains, and outdoor entertainment.［A］designed ［F］convenience ［K］cosmetics［B］take ［G］services ［L］started［C］Early ［H］fame ［M］downtown［D］Attracted ［I］various ［N］available［E］though ［J］popularity ［O］cheapnessSection BDirections: There are 2 passages in this section. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked ［A］, ［B］, ［C］and ［D］.You should decide on the best choice and mark the corresponding letter on Answer Sheet 2 with a single line through the centre. Passage OneQuestions 57 to 61 are based on the following passage.Culture is one of the most challenging elements of the international marketplace. This system of learned behavior patterns characteristic of the members of a given society is constantly shaped by a set of dynamic variables: language, religion, values and attitudes, manners and customs, aesthetics, technology, education, and social institutions. To cope with this system, an international manager needs both factual and interpretive knowledge of culture. To some extent, the factual knowledge can be learned; its interpretation comes only through experience.The most complicated problems in dealing with the cultural environment stem from the fact that one cannot learn culture one has to live it. Two schools of thought exist in the business world on how to deal with cultural diversity. One is that business is b usiness the world around, following the model of Pepsi and McDonald’s. In some cases, globalization is a fact of life; however, cultural differences are still far from converging.The other school proposes that companies must tailor business approaches to individual cultures. Setting up policies and procedures in each country has been compared to an organ transplant; the critical question centers around acceptance or rejection. The major challenge to the international manager is to make sure that rejection is not a result of cultural myopia or even blindness.Fortune examined the international performance of a dozen large companies that earn 20 percent or more of their revenue overseas. The internationally successful companies all share an important quality: patience. They have not rushed into situations but rather built their operations carefully by following the most basic business principles. These principles are to know your adversary, know your audience, and know your customer.57. According to the passage, which of the following is true?［A］All international managers can learn culture.［B］Business diversity is not necessary.［C］Views differ on how to treat culture in business world.［D］Most people do not know foreign culture well.58. According to the author, the model of Pepsi.［A］is in line with the theories of the school advocating the business is business the world around.［B］is different from the model of McDonald’s［C］shows the reverse of globalization［D］has converged cultural differences59. The two schools of thought.［A］both propose that companies should tailor business approaches to individual cultures［B］both advocate that different policies be set up in different countries［C］admit the existence of cultural diversity in business world［D］Both A and B60. This article is supposed to be most useful for those.［A］who are interested in researching the topic of cultural diversity［B］who have connections to more than one type of culture［C］who want to travel abroad［D］who want to run business on International Scale61. According to Fortune, successful international companies.［A］earn 20 percent or more of their revenue overseas［B］all have the quality of patience［C］will follow the overseas local cultures［D］adopt the policy of internationalizationPassage TwoQuestions 62 to 66 are based on the following passage.There are people in Italy who can’t stand s occer. Not all Canadians love hockey. A similar situation exists in America, where there are those individuals you may be one of them who yawn or even frown when somebody mentions baseball. Baseball to them means boring hours watching grown men in funny tight outfits standing around in a field staring away while very little of anything happens. They tell you it’s a game better suited to the 19th century, slow, quiet, and gentlemanly. These are the same people you may be one of them who love football because there’s the sport that glorifies “the hit”.By contrast, baseball seems abstract, cool, silent, still.On TV the game is fractured into a dozen perspectives, replays, close ups. The geometry of the game, however, is essential to understanding it. You will contemplate the game from one point as a painter does his subject; you may, of course, project yourself into the game. It is in this projection that the game affords so much space and time for involvement. The TV won’t do it for you.Take, for example, the third baseman. You sit behind the third base dugout and you watch him watching home plate. His legs are apart, knees flexed. His arms hang loose. He does a lot of this. The skeptic still cannot think of any other sports so still, so passive. But watch what happens every time the pitcher throws: the third basemangoes up on his toes, flexes his arms or bring the glove to a point in front of him, takes a step right or left, backward or forward, perhaps he glances across the field to check his first baseman’s position. Suppose the pitch is a ball. “Nothing happened,” you say. “I could have had my eyes closed.”The skeptic and the innocent must play the game. And this involvement in the stands is no more intellectual than listening to music is. Watch the third baseman. Smooth the dirt in front of you with one foot; smooth the pocket in your glove; watch the eyes of the batter, the speed of the bat, the sound of horsehide on wood. If football is a symphony of movement and theatre, baseball is chamber music, a spacious interlocking of notes, chores and responses.62.The passage is mainly concerned with .［A］the different tastes of people for sports［B］the different characteristics of sports ［C］the attraction of football D］the attraction of baseball63.Those who don’t like baseball may complain that.［A］it is only to the taste of the old ［B］it involves fewer players than football ［C］it is not exciting enough ［D］it is pretentious and looks funny64.The author admits that.［A］baseball is too peaceful for the young［B］baseball may seem boring when watched on TV［C］football is more attracting than baseball［D］baseball is more interesting than football65.By stating “I could have had my eyes closed.” the author means (4th paragraph last sentence).［A］The third baseman would rather sleep than play the game［B］Even if the third baseman closed his eyes a moment ago, it could make no different to the result［C］The third baseman is so good at baseball that he could finish the game with eyes closed all the time and do his work well［D］The consequent was too bad he could not bear to see it66.We can safely conclude that the author.［A］likes football ［B］hates football［C］hates baseball ［D］likes baseballPart ⅤCloze （15 minutes）Directions: There are 20 blanks in the following passage. For each blank there are four choices marked ［A］, ［B］, ［C］and ［D］on the right side of the paper. You should choose the ONE that best fits into the passage. Then mark the corresponding letter on Answer Sheet 2 with a single line through the centre.Who won the World Cup 1994 football game? What happened at the United Nations? How did the critics like the new play? 67 an event takes place; newspapers are on the streets 68 the details. Wherever anything happens in the world, reports are on the spot to 69 the news.Newspapers have one basic 70 , to get the news as quickly as possible from its source,from those who make it to those who want to 71 it. Radio, telegraph, television, and 72 inventions brought competition for newspapers. So did the development of magazines and other means of communication. 73 , this competition merely spurred the newspapers on. They quickly made use of the newer and faster means of communication to improve the 74 and thus the efficiency of their own operations. Today more newspapers are 75 and read than ever before. Competition also led newspapers to branch out to many other fields. Besides keeping readers 76 of the latest news, today’s newspapers 77 and influence readers about politics and other important and serious matters. Newspapers influence readers’ economic choices 78 advertising. Most newspapers depend on advertising for their very 79 .News papers is sold at a price that 80 even a small fraction of the cost of production. The main 81 of income for most newspapers is commercial advertising. The 82 in selling advertising depends on a newspaper’s val ue to advertisers. This 83 in terms of circulation. How many people read the newspaper? Circulation depends 84 on the work of the circulation department and on the services or entertainment 85 in a newspaper’s pages. But for the most part, circulation depe nds on a newspaper’s value to readers as a source of information 86 the community, city, country, state, nation, and world and even outer space.67.［A］Just when ［B］While ［C］Soon after ［D］Before68.［A］to give ［B］giving ［C］given ［D］being given69.［A］gather ［B］spread ［C］carry ［D］bring70.［A］reason ［B］cause ［C］problem ［D］purpose71.［A］make ［B］publish ［C］know ［D］write72.［A］another ［B］other ［C］one another ［D］the other73.［A］However ［B］And ［C］Therefore ［D］So74.［A］value ［B］ratio ［C］rate ［D］speed75.［A］spread ［B］passed ［C］printed ［D］completed76.［A］inform ［B］be informed ［C］to informed ［D］informed77.［A］entertain ［B］encourage ［C］educate ［D］edit78.［A］on ［B］through ［C］with ［D］of79.［A］forms ［B］existence ［C］contents ［D］purpose80.［A］tries to cover B］manages to cover ［C］fails to cover［D］succeeds in81.［A］source ［B］origin ［C］course ［D finance82.［A］way ［B］means ［C］chance ［D］success83.［A］measures ［B］measured［C］is measured ［D］was measured84.［A］somewhat ［B］little ［C］much ［D］something85.［A］offering ［B］offered ［C］which offered［D］to be offered86.［A］by ［B］with ［C］at ［D］aboutPart ⅥTranslation(5 minutes）Direction: Complete the sentences on Answer Sheet 2 by translating into English the Chinese given in brackets.87.There’s a man at the reception desk who seems very angry and I think he means(想找麻烦) .88.Why didn’t you tell me you could lend me the money? I (本来不必从银行借钱的) .89.(正是由于她太没有经验) that she does not know how to deal with the situation.90.I (将在做实验) from three to five this afternoon.91.If this can’t be settled reasonably, it may be necessary to (诉诸武力) .答案Part I Writing【写作思路】本文是一篇关于择业的议论文。

2007年普通高等学校招生全国统一·考试·理科数学本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分．第Ⅰ卷1至2页．第Ⅱ卷3至4页．·考试·结束后，将本试卷和答题卡一并交回．第Ⅰ卷注意事项：1．答题前，考生在答题卡上务必用直径0.5毫米黑色墨水签字笔将自己的姓名、准考证号填写清楚，并贴好条形码．请认真核准条形码上的准考证号、姓名和科目．2．每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号，在试题卷上作答无效．3．本卷共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的． 参考公式：如果事件A B ，互斥，那么 球的表面积公式()()()P A B P A P B +=+24πS R =如果事件A B ，相互独立，那么其中R 表示球的半径 ()()()P A B P A P B =球的体积公式如果事件A 在一次试验中发生的概率是p ，那么34π3V R =n 次独立重复试验中事件A 恰好发生k 次的概率其中R 表示球的半径()(1)(012)k k n k n n P k C p p k n -=-=，，，…， 一、选择题（1）α是第四象限角，5tan 12α=-，则sin α=（ ） A ．15 B ．15- C ．513 D ．513-（2）设a 是实数，且1i 1i 2a +++是实数，则a =（ ） A ．12 B ．1 C ．32D ．2（3）已知向量(56)=-，a ，(65)=，b ，则a 与b （ ） A ．垂直B ．不垂直也不平行C ．平行且同向D ．平行且反向（4）已知双曲线的离心率为2，焦点是(40)-，，(40)，，则双曲线方程为（ ） A ．221412x y -= B ．221124x y -= C ．221106x y -= D ．221610x y -=（5）设a b ∈R ，，集合{}10ba b a b a ⎧⎫+=⎨⎬⎩⎭，，，，，则b a -=（ ） A ．1B ．1-C ．2D ．2-（6）下面给出的四个点中，到直线10x y -+=的距离为2，且位于1010x y x y +-<⎧⎨-+>⎩，表示的平面区域内的点是（ ）A ．(11)，B ．(11)-，C ．(11)--，D ．(11)-， （7）如图，正四棱柱1111ABCD A BC D -中，12AA AB =，则异面直线1A B 与1AD 所成角的余弦值为（ ）A ．15B ．25C ．35D ．45（8）设1a >，函数()log a f x x =在区间[]2a a ，上的最大值与最小值之差为12，则a =（ ） AB ．2C．D ．4（9）()f x ，()g x 是定义在R 上的函数，()()()h x f x g x =+，则“()f x ，()g x 均为偶函数”是“()h x 为偶函数”的（ ） A ．充要条件 B ．充分而不必要的条件C ．必要而不充分的条件D ．既不充分也不必要的条件（10）21nx x ⎛⎫- ⎪⎝⎭的展开式中，常数项为15，则n =（ ）A ．3B ．4C ．5D ．6（11）抛物线24y x =的焦点为F ，准线为l ，经过Fx 轴上方的部分相交于点A ，AK l ⊥，垂足为K ，则AKF △的面积是（ ） A ．4B．C．D ．8（12）函数22()cos 2cos 2xf x x =-的一个单调增区间是（ ） A ．233ππ⎛⎫ ⎪⎝⎭，B ．62ππ⎛⎫ ⎪⎝⎭，C ．03π⎛⎫ ⎪⎝⎭，D ．66ππ⎛⎫- ⎪⎝⎭，第Ⅱ卷注意事项：AB1B1A1D1C CD1．答题前，考生先在答题卡上用直径0.5毫米黑色墨水签字笔将自己的姓名、准考证号填写清楚，然后贴好条形码．请认真核准条形码上的准考证号、姓名和科目．2．第Ⅱ卷共2页，请用直径0.5毫米黑色墨水签字笔在答题卡上各题的答题区域内作答，在试题卷上作答无效．3．本卷共10题，共90分．二、填空题：本大题共4小题，每小题5分，共20分．把答案填在横线上．（13）从班委会5名成员中选出3名，分别担任班级学习委员、文娱委员与体育委员，其中甲、乙二人不能担任文娱委员，则不同的选法共有 种．（用数字作答） （14）函数()y f x =的图像与函数3log (0)y x x =>的图像关于直线y x =对称，则()f x = ．（15）等比数列{}n a 的前n 项和为n S ，已知1S ，22S ，33S 成等差数列，则{}n a 的公比为 ． （16）一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上．已知正三棱柱的底面边长为2，则该三角形的斜边长为 ．三、解答题：本大题共6小题，共70分．解答应写出文字说明，证明过程或演算步骤． （17）（本小题满分10分）设锐角三角形ABC 的内角A B C ，，的对边分别为a b c ，，，2sin a b A =． （Ⅰ）求B 的大小；（Ⅱ）求cos sin A C +的取值范围． （18）（本小题满分12分） 某商场经销某商品，根据以往资料统计，顾客采用的付款期数ξ的分布列为商场经销一件该商品，采用1期付款，其利润为200元；分2期或3期付款，其利润为250元；分4期或5期付款，其利润为300元．η表示经销一件该商品的利润．（Ⅰ）求事件A ：“购买该商品的3位顾客中，至少有1位采用1期付款”的概率()P A ； （Ⅱ）求η的分布列及期望E η．（19）（本小题满分12分）四棱锥S ABC D -中，底面ABCD 为平行四边形，侧面SBC ⊥底面A B C D ．已知45ABC =∠，2AB =，BC =SA SB =（Ⅰ）证明SA BC ⊥；（Ⅱ）求直线SD 与平面SAB 所成角的大小．（20）（本小题满分12分） 设函数()e e x x f x -=-．（Ⅰ）证明：()f x 的导数()2f x '≥；（Ⅱ）若对所有0x ≥都有()f x ax ≥，求a 的取值范围． （21）（本小题满分12分）已知椭圆22132x y +=的左、右焦点分别为1F ，2F ．过1F 的直线交椭圆于B D ，两点，过2F 的直线交椭圆于AC ，两点，且AC BD ⊥，垂足为P ．（Ⅰ）设P 点的坐标为00()x y ，，证明：2200132x y +<； （Ⅱ）求四边形ABCD 的面积的最小值．（22）（本小题满分12分）已知数列{}n a 中12a =，11)(2)n n a a +=+，123n =，，，…． （Ⅰ）求{}n a 的通项公式； （Ⅱ）若数列{}n b 中12b =，13423n n n b b b ++=+，123n =，，，…，43n n b a -<≤，123n =，，，…．2007年普通高等学校招生全国统一·考试· 理科数学试题（必修+选修Ⅱ）参考答案一、选择题： （1）D （2）B （3）A （4）A （5）C （6）C （7）D （8）D （9）B（10）D（11）C（12）A二、填空题：（13）36（14）3()x x ∈R（15）13（16）三、解答题： （17）解：（Ⅰ）由2sin a b A =，根据正弦定理得sin 2sin sin A B A =，所以1sin 2B =， 由ABC △为锐角三角形得π6B =． （Ⅱ）cos sin cos sin A C A A π⎛⎫+=+π-- ⎪6⎝⎭cos sin 6A A π⎛⎫=++ ⎪⎝⎭1cos cos 2A A A =+3A π⎛⎫=+ ⎪⎝⎭．由ABC △为锐角三角形知，22A B ππ->-，2263B ππππ-=-=． 2336A πππ<+<，所以1sin 232A π⎛⎫+<⎪⎝⎭．由此有232A π⎛⎫<+< ⎪⎝⎭ 所以，cos sin A C +的取值范围为32⎫⎪⎪⎝⎭，． （18）解：（Ⅰ）由A 表示事件“购买该商品的3位顾客中至少有1位采用1期付款”．知A 表示事件“购买该商品的3位顾客中无人采用1期付款”2()(10.4)0.216P A =-=，()1()10.2160.784P A P A =-=-=．（Ⅱ）η的可能取值为200元，250元，300元．(200)(1)0.4P P ηξ====，(250)(2)(3)0.20.20.4P P P ηξξ===+==+=，(300)1(200)(250)10.40.40.2P P P ηηη==-=-==--=．η的分布列为2000.42500.43000.2E η=⨯+⨯+⨯ 240=（元）．（19）解法一：（Ⅰ）作SO BC ⊥，垂足为O ，连结AO ，由侧面SBC ⊥底面ABCD ，得SO ⊥底面ABCD ．因为SA SB =，所以AO BO =，又45ABC =∠，故AOB △为等腰直角三角形，AO BO ⊥，由三垂线定理，得SA BC ⊥．（Ⅱ）由（Ⅰ）知SA BC ⊥，依题设ADBC ∥，故SA AD ⊥，由AD BC ==，SA =AO 1SO =，SD =．SAB △的面积211122S AB SA ⎛=-= ⎝连结DB ，得DAB △的面积21sin13522S AB AD == 设D 到平面SAB 的距离为h ，由于D SAB S ABD V V --=，得121133h S SO S =， 解得h =A设SD 与平面SAB 所成角为α，则sin h SD α===． 所以，直线SD 与平面SBC所成的我为arcsin11． 解法二：（Ⅰ）作SO BC ⊥，垂足为O ，连结AO ，由侧面SBC ⊥底面ABCD ，得SO ⊥平面ABCD ．因为SA SB =，所以AO BO =．又45ABC =∠，AOB △为等腰直角三角形，AO OB ⊥． 如图，以O 为坐标原点，OA 为x0)A ，，(0B ，(0C ，(001)S ，，，(2，(0CB =，0SA CB =，所以SA BC ⊥．（Ⅱ）取AB 中点E ，022E ⎛⎫⎪ ⎪⎝⎭，，连结SE ，取SE 中点G ，连结OG ，1442G ⎛⎫⎪ ⎪⎝⎭，，． 1442OG ⎛⎫= ⎪ ⎪⎝⎭，，，122SE ⎛⎫= ⎪ ⎪⎝⎭，，(AB =． 0SE OG =，0AB OG =，OG 与平面SAB 内两条相交直线SE ，AB 垂直．所以OG ⊥平面SAB ，OG 与DS 的夹角记为α，SD 与平面SAB 所成的角记为β，则α与β互余．D ，(DS =． 22cos 11OG DS OG DSα==，sin 11β= 所以，直线SD 与平面SAB 所成的角为arcsin 11． （20）解：（Ⅰ）()f x 的导数()e e x xf x -'=+．由于e e 2x -x +=≥，故()2f x '≥． （当且仅当0x =时，等号成立）． （Ⅱ）令()()g x f x ax =-，则()()e e x x g x f x a a -''=-=+-，（ⅰ）若2a ≤，当0x >时，()e e 20x x g x a a -'=+->-≥，故()g x 在(0)+，∞上为增函数， 所以，0x ≥时，()(0)g x g ≥，即()f x ax ≥．（ⅱ）若2a >，方程()0g x '=的正根为1ln 2a x =，此时，若1(0)x x ∈，，则()0g x '<，故()g x 在该区间为减函数．所以，1(0)x x ∈，时，()(0)0g x g <=，即()f x ax <，与题设()f x ax ≥相矛盾． 综上，满足条件的a 的取值范围是(]2-∞，． （21）证明：（Ⅰ）椭圆的半焦距1c ==，由AC BD ⊥知点P 在以线段12F F 为直径的圆上，故22001x y +=， 所以，222200021132222y x y x ++=<≤． （Ⅱ）（ⅰ）当BD 的斜率k 存在且0k ≠时，BD 的方程为(1)y k x =+，代入椭圆方程22132x y +=，并化简得2222(32)6360k x k x k +++-=． 设11()B x y ，，22()D x y ，，则2122632k x x k +=-+，21223632k x x k -=+ 22212221221)(1)()432k BD x x k x x x x k +⎡=-=++-=⎣+；因为AC 与BC 相交于点P ，且AC 的斜率为1k-，所以，221132k AC k⎫+⎪⎝⎭==⨯+． 四边形ABCD 的面积222222222124(1)(1)962(32)(23)25(32)(23)2k k S BD AC k k k k +24+===++⎡⎤+++⎢⎥⎣⎦≥． 当21k =时，上式取等号．（ⅱ）当BD 的斜率0k =或斜率不存在时，四边形ABCD 的面积4S =．综上，四边形ABCD 的面积的最小值为9625． （22）解：（Ⅰ）由题设：11)(2)n n a a +=+1)(1)(2n a =+1)(n a =11)(n n a a +=．所以，数列{n a -是首项为21的等比数列，1)n n a ，即n a的通项公式为1)1nn a ⎤=+⎦，123n =，，，…． （Ⅱ）用数学归纳法证明．（ⅰ）当1n=2，112b a ==，所以11b a <≤，结论成立．（ⅱ）假设当n k =43k k b a -≤， 也即430k k b a -< 当1n k =+时，13423k k k b b b ++=+(3(423k k b b -+-=+(3023k k b b -=>+，又1323k b <=-+所以1(32)2)23k k k b b b +-=+2(3(k b <-4431)(k a -≤41k a +=也就是说，当1n k =+时，结论成立．43n n b a -<≤，123n =，，，…．笔记卡。

Time will pierce the surface or youth, will be on the beauty of the ditch dug a shallow groove ; Jane will eat rare!A born beauty, anything to escape his sickle sweep .-- Shakespeare2007年普通高等学校招生全国统一考试（重庆卷）数学（理科）试卷参考答案 一、选择题（每小题5分，满分50分）1．A 2．D 3．C 4．B 5．A6．C 7．B 8．B 9．D 10．C二、填空题11．4512．713．[－1，0]14．1815．2516．833三、解答题17．（本小题13分）解：（I ）f （x ）=1cos 263sin 22xx+-=3c os2x － 3si n 2x +3 =2313(cos 2sin 2)322x x -+ =23cos(2)36x π++故f （x ）的最大值为233+最小正周期T=22ππ= （II ）由f （α）=323-得23cos(2)33236πα++=-，故cos(2)16πα+=- 又0<α<2π得2666πππαπ<+<+，故26παπ+=，解得512πα= 从而4tan tan353πα==18．（本小题13分） 解：设A k 表示第k 辆车在一年内发生此种事故，k =1，2，3。

由题意知A 1，A 2，A 3独立，且P （A 1）=19，P （A 2）=110，P （A 3）=111（I ）该单位一年内获赔的概率为1－P （123A A A ）=1－123()()()p A P A p A =1－891039101111⨯⨯= （II ）ξ的所有可能值为0，9000，18000，27000。

P （ξ=0）= P （123A A A ）=123()()()p A P A p A =891089101111⨯⨯=， P （ξ=9000）=P （123A A A ）+P （123A A A ）+P （123A A A ）=P （A 1）P （2A ）P （3A ）+ P （1A ）P （A 2）P （3A ）+ P （1A ）P （2A ）P （A 3） =19108110891910119101191011⨯⨯+⨯⨯+⨯⨯ =2421199045= P （ξ=18000）=P （123A A A ）+P （123A A A ）+P （123A A A ） =1110191811910119101191011⨯⨯+⨯⨯+⨯⨯ =273990110= P （ξ=27000）=P （A 1 A 2 A 3）= P （A 1）P （A 2）P （A 3）=111191011990⨯⨯= 综上所述，ξ的分布列为 ξ0 9000 18000 27000 P（II ）求ξ的期望有两种解法：解法一：由ξ的分布列得E ξ=811310900018000270001145110990⨯+⨯+⨯+⨯ =2990011≈2718.18（元） 解法二：设ξk 表示第k 辆车一年内的获赔金额，k =1，2，3。