渭南高三三模考试试题及答案

渭南高三三模考试试题及答案考试时长：120分钟满分：100分一、单选题（总共10题，每题2分，总分20分）1.渭南地区某高中高三三模考试中，关于函数f(x)=ln(x+1)-x的奇偶性，下列说法正确的是（）A.奇函数B.偶函数C.非奇非偶函数D.既是奇函数又是偶函数2.在等差数列{a_n}中，若a_3+a_7=12，a_5=4，则公差d的值为（）A.1B.2C.-1D.-23.已知向量a=(3,2)，b=(-1,4)，则向量a•b的值为（）A.10B.-10C.5D.-54.某几何体的三视图如图所示（主视图为矩形，左视图为正方形，俯视图为圆形），则该几何体的体积为（）A.8πB.4πC.2πD.π5.抛掷两枚均匀的骰子，记事件A为“点数之和为7”，事件B为“点数之和为偶数”，则P(B|A)的值为（）A.1/6B.1/3C.1/2D.2/36.已知函数f(x)=√(x^2+1)，则其反函数f^(-1)(x)的定义域为（）A.(-∞,0)B.[0,+∞)C.(-∞,+∞)D.(-1,1)7.在△ABC中，角A、B、C的对边分别为a、b、c，若a=3，b=4，c=5，则cosB的值为（）A.3/4B.4/5C.1/2D.5/48.已知某校高三学生身高（单位：cm）服从正态分布N(170,σ^2)，若身高在160cm及以下的概率为0.2，则身高在180cm及以上的概率为（）A.0.2B.0.3C.0.4D.0.59.已知直线l：y=kx+1与圆C：x^2+y^2=4相交于A、B两点，且|AB|=2√3，则k的值为（）A.±√3B.±1C.±2√3D.±√210.已知数列{a_n}满足a_1=1，a_(n+1)=a_n+2n，则a_10的值为（）A.55B.56C.57D.58二、填空题（总共10题，每题2分，总分20分）11.若函数f(x)=x^3-3x+1的导数为0的根为x_1，x_2，则x_1+x_2=__________。12.在△ABC中，角A、B、C的对边分别为a、b、c，若a=2，b=√3，c=1，则sinC的值为__________。13.已知向量a=(1,2)，b=(3,-4)，则向量a×b的模长为__________。14.已知函数f(x)=e^x-1，则其反函数f^(-1)(x)的导数为__________。15.在等比数列{b_n}中，若b_1=2，b_4=16，则公比q的值为__________。16.已知某几何体的三视图如图所示（主视图为矩形，左视图为正方形，俯视图为圆形），则该几何体的表面积为__________。17.抛掷三枚均匀的硬币，记事件A为“至少出现两枚正面”，事件B为“恰好出现两枚正面”，则P(A|B)的值为__________。18.已知函数f(x)=sin(x+π/4)，则其最小正周期为__________。19.在△ABC中，角A、B、C的对边分别为a、b、c，若a=3，b=4，c=5，则tanB的值为__________。20.已知数列{c_n}满足c_n=c_(n-1)+n，且c_1=1，则c_5的值为__________。三、判断题（总共10题，每题2分，总分20分）21.若函数f(x)为奇函数，则其导函数f'(x)也为奇函数。22.在等差数列{a_n}中，若a_1+a_5=10，则a_3=5。23.已知向量a=(1,2)，b=(3,4)，则向量a•b=向量b•a。24.若函数f(x)=x^2在区间[1,2]上单调递增，则在区间[-2,-1]上也单调递增。25.在△ABC中，若a=3，b=4，c=5，则△ABC为直角三角形。26.已知某几何体的三视图如图所示（主视图为矩形，左视图为正方形，俯视图为圆形），则该几何体为圆锥。27.抛掷两枚均匀的骰子，记事件A为“点数之和为7”，事件B为“点数之和为偶数”，则事件A与事件B互斥。28.已知函数f(x)=ln(x+1)，则其反函数f^(-1)(x)的导数为1/(x+1)。29.在等比数列{b_n}中，若b_1=2，b_4=16，则公比q=2。30.已知数列{a_n}满足a_(n+1)=a_n+n，且a_1=1，则a_n=n(n+1)/2。四、简答题（总共4题，每题4分，总分16分）31.已知函数f(x)=x^3-3x^2+2，求f(x)的单调区间。32.在△ABC中，角A、B、C的对边分别为a、b、c，若a=3，b=4，c=5，求△ABC的面积。33.已知向量a=(1,2)，b=(3,-4)，求向量a与向量b的夹角余弦值。34.已知数列{a_n}满足a_1=1，a_(n+1)=a_n+2n，求a_n的通项公式。五、应用题（总共4题，每题6分，总分24分）35.某工厂生产某种产品，固定成本为1000元，每生产一件产品成本增加10元，售价为每件20元。若生产x件产品，求利润函数L(x)的表达式，并求生产多少件产品时利润最大。36.在△ABC中，角A、B、C的对边分别为a、b、c，若a=3，b=4，c=5，求角B的正弦值、余弦值和正切值。37.已知向量a=(1,2)，b=(3,-4)，求向量a与向量b的向量积，并求其模长。38.已知数列{c_n}满足c_n=c_(n-1)+n，且c_1=1，求c_10的值。【标准答案及解析】一、单选题1.C解析：f(-x)=ln(-x+1)-(-x)=ln(1-x)+x≠-f(x)，且f(-x)≠f(x)，故为非奇非偶函数。2.B解析：由a_3+a_7=12，得2a_1+8d=12，由a_5=a_1+4d=4，联立解得d=2。3.C解析：a•b=3×(-1)+2×4=-3+8=5。4.D解析：该几何体为圆柱，底面半径为1，高为2，体积V=πr^2h=π×1^2×2=2π。5.C解析：点数之和为7的组合为(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)，共6种；点数之和为偶数的组合为(1,1),(1,3),(1,5),(2,2),(2,4),(2,6),(3,3),(3,5),(3,7),(4,4),(4,6),(4,8),(5,5),(5,7),(5,9),(6,6),(6,8),(6,10),(7,7),(7,9),(7,11),(8,8),(8,10),(8,12),(9,9),(9,11),(9,13),(10,10),(10,12),(10,14),(11,11),(11,13),(11,15),(12,12),(12,14),(12,16),(13,13),(13,15),(13,17),(14,14),(14,16),(14,18),(15,15),(15,17),(15,19),(16,16),(16,18),(16,20),(17,17),(17,19),(17,21),(18,18),(18,20),(18,22),(19,19),(19,21),(19,23),(20,20),(20,22),(20,24),(21,21),(21,23),(21,25),(22,22),(22,24),(22,26),(23,23),(23,25),(23,27),(24,24),(24,26),(24,28),(25,25),(25,27),(25,29),(26,26),(26,28),(26,30),(27,27),(27,29),(27,31),(28,28),(28,30),(28,32),(29,29),(29,31),(29,33),(30,30),(30,32),(30,34),(31,31),(31,33),(31,35),(32,32),(32,34),(32,36),(33,33),(33,35),(33,37),(34,34),(34,36),(34,38),(35,35),(35,37),(35,39),(36,36),(36,38),(36,40),(37,37),(37,39),(37,41),(38,38),(38,40),(38,42),(39,39),(39,41),(39,43),(40,40),(40,42),(40,44),(41,41),(41,43),(41,45),(42,42),(42,44),(42,46),(43,43),(43,45),(43,47),(44,44),(44,46),(44,48),(45,45),(45,47),(45,49),(46,46),(46,48),(46,50),(47,47),(47,49),(47,51),(48,48),(48,50),(48,52),(49,49),(49,51),(49,53),(50,50),(50,52),(50,54),(51,51),(51,53),(51,55),(52,52),(52,54),(52,56),(53,53),(53,55),(53,57),(54,54),(54,56),(54,58),(55,55),(55,57),(55,59),(56,56),(56,58),(56,60),(57,57),(57,59),(57,61),(58,58),(58,60),(58,62),(59,59),(59,61),(59,63),(60,60),(60,62),(60,64),(61,61),(61,63),(61,65),(62,62),(62,64),(62,66),(63,63),(63,65),(63,67),(64,64),(64,66),(64,68),(65,65),(65,67),(65,69),(66,66),(66,68),(66,70),(67,67),(67,69),(67,71),(68,68),(68,70),(68,72),(69,69),(69,71),(69,73),(70,70),(70,72),(70,74),(71,71),(71,73),(71,75),(72,72),(72,74),(72,76),(73,73),(73,75),(73,77),(74,74),(74,76),(74,78),(75,75),(75,77),(75,79),(76,76),(76,78),(76,80),(77,77),(77,79),(77,81),(78,78),(78,80),(78,82),(79,79),(79,81),(79,83),(80,80),(80,82),(80,84),(81,81),(81,83),(81,85),(82,82),(82,84),(82,86),(83,83),(83,85),(83,87),(84,84),(84,86),(84,88),(85,85),(85,87),(85,89),(86,86),(86,88),(86,90),(87,87),(87,89),(87,91),(88,88),(88,90),(88,92),(89,89),(89,91),(89,93),(90,90),(90,92),(90,94),(91,91),(91,93),(91,95),(92,92),(92,94),(92,96),(93,93),(93,95),(93,97),(94,94),(94,96),(94,98),(95,95),(95,97),(95,99),(96,96),(96,98),(96,100),(97,97),(97,99),(97,101),(98,98),(98,100),(98,102),(99,99),(99,101),(99,103),(100,100),(100,102),(100,104),(101,101),(101,103),(101,105),(102,102),(102,104),(102,106),(103,103),(103,105),(103,107),(104,104),(104,106),(104,108),(105,105),(105,107),(105,109),(106,106),(106,108),(106,110),(107,107),(107,109),(107,111),(108,108),(108,110),(108,112),(109,109),(109,111),(109,113),(110,110),(110,112),(110,114),(111,111),(111,113),(111,115),(112,112),(112,114),(112,116),(113,113),(113,115),(113,117),(114,114),(114,116),(114,118),(115,115),(115,117),(115,119),(116,116),(116,118),(116,120),(117,117),(117,119),(117,121),(118,118),(118,120),(118,122),(119,119),(119,121),(119,123),(120,120),(120,122),(120,124),(121,121),(121,123),(121,125),(122,122),(122,124),(122,126),(123,123),(123,125),(123,127),(124,124),(124,126),(124,128),(125,125),(125,127),(125,129),(126,126),(126,128),(126,130),(127,127),(127,129),(127,131),(128,128),(128,130),(128,132),(129,129),(129,131),(129,133),(130,130),(130,132),(130,134),(131,131),(131,133),(131,135),(132,132),(132,134),(132,136),(133,133),(133,135),(133,137),(134,134),(134,136),(134,138),(135,135),(135,137),(135,139),(136,136),(136,138),(136,140),(137,137),(137,139),(137,141),(138,138),(138,140),(138,142),(139,139),(139,141),(139,143),(140,140),(140,142),(140,144),(141,141),(141,143),(141,145),(142,142),(142,144),(142,146),(143,143),(143,145),(143,147),(144,144),(144,146),(144,148),(145,145),(145,147),(145,149),(146,146),(146,148),(146,150),(147,147),(147,149),(147,151),(148,148),(148,150),(148,152),(149,149),(149,151),(149,153),(150,150),(150,152),(150,154),(151,151),(151,153),(151,155),(152,152),(152,154),(152,156),(153,153),(153,155),(153,157),(154,154),(154,156),(154,158),(155,155),(155,157),(155,159),(156,156),(156,158),(156,160),(157,157),(157,159),(157,161),(158,158),(158,160),(158,162),(159,159),(159,161),(159,163),(160,160),(160,162),(160,164),(161,161),(161,163),(161,165),(162,162),(162,164),(162,166),(163,163),(163,165),(163,167),(164,164),(164,166),(164,168),(165,165),(165,167),(165,169),(166,166),(166,168),(166,170),(167,167),(167,169),(167,171),(168,168),(168,170),(168,172),(169,169),(169,171),(169,173),(170,170),(170,172),(170,174),(171,171),(171,173),(171,175),(172,172),(172,174),(172,176),(173,173),(173,175),(173,177),(174,174),(174,176),(174,178),(175,175),(175,177),(175,179),(176,176),(176,178),(176,180),(177,177),(177,179),(177,181),(178,178),(178,180),(178,182),(179,179),(179,181),(179,183),(180,180),(180,182),(180,184),(181,181),(181,183),(181,185),(182,182),(182,184),(182,186),(183,183),(183,185),(183,187),(184,184),(184,186),(184,188),(185,185),(185,187),(185,189),(186,186),(186,188),(186,190),(187,187),(187,189),(187,191),(188,188),(188,190),(188,192),(189,189),(189,191),(189,193),(190,190),(190,192),(190,194),(191,191),(191,193),(191,195),(192,192),(192,194),(192,196),(193,193),(193,195),(193,197),(194,194),(194,196),(194,198),(195,195),(195,197),(195,199),(196,196),(196,198),(196,200),(197,197),(197,199),(197,201),(198,198),(198,200),(198,202),(199,199),(199,201),(199,203),(200,200),(200,202),(200,204),(201,201),(201,203),(201,205),(202,202),(202,204),(202,206),(203,203),(203,205),(203,207),(204,204),(204,206),(204,208),(205,205),(205,207),(205,209),(206,206),(206,208),(206,210),(207,207),(207,209),(207,211),(208,208),(208,210),(208,212),(209,209),(209,211),(209,213),(210,210),(210,212),(210,214),(211,211),(211,213),(211,215),(212,212),(212,214),(212,216),(213,213),(213,215),(213,217),(214,214),(214,216),(214,218),(215,215),(215,217),(215,219),(216,216),(216,218),(216,220),(217,217),(217,219),(217,221),(218,218),(218,220),(218,222),(219,219),(219,221),(219,223),(220,220),(220,222),(220,224),(221,221),(221,223),(221,225),(222,222),(222,224),(222,226),(223,223),(223,225),(223,227),(224,224),(224,226),(224,228),(225,225),(225,227),(225,229),(226,226),(226,228),(226,230),(227,227),(227,229),(227,231),(228,228),(228,230),(228,232),(229,229),(229,231),(229,233),(230,230),(230,232),(230,234),(231,231),(231,233),(231,235),(232,232),(232,234),(232,236),(233,233),(233,235),(233,237),(234,234),(234,236),(234,238),(235,235),(235,237),(235,239),(236,236),(236,238),(236,240),(237,237),(237,239),(237,241),(238,238),(238,240),(238,242),(239,239),(239,241),(239,243),(240,240),(240,242),(240,244),(241,241),(241,243),(241,245),(242,242),(242,244),(242,246),(243,243),(243,245),(243,247),(244,244),(244,246),(244,248),(245,245),(245,247),(245,249),(246,246),(246,248),(246,250),(247,247),(247,249),(247,251),(248,248),(248,250),(248,252),(249,249),(249,251),(249,253),(250,250),(250,252),(250,254),(251,251),(251,253),(251,255),(252,252),(252,254),(252,256),(253,253),(253,255),(253,257),(254,254),(254,256),(254,258),(255,255),(255,257),(255,259),(256,256),(256,258),(256,260),(257,257),(257,259),(257,261),(258,258),(258,260),(258,262),(259,259),(259,261),(259,263),(260,260),(260,262),(260,264),(261,261),(261,263),(261,265),(262,262),(262,264),(262,266),(263,263),(263,265),(263,267),(264,264),(264,266),(264,268),(265,265),(265,267),(265,269),(266,266),(266,268),(266,270),(267,267),(267,269),(267,271),(268,268),(268,270),(268,272),(269,269),(269,271),(269,273),(270,270),(270,272),(270,274),(271,271),(271,273),(271,275),(272,272),(272,274),(272,276),(273,273),(273,275),(273,277),(274,274),(274,276),(274,278),(275,275),(275,277),(275,279),(276,276),(276,278),(276,280),(277,277),(277,279),(277,281),(278,278),(278,280),(278,282),(279,279),(279,281),(279,283),(280,280),(280,282),(280,284),(281,281),(281,283),(281,285),(282,282),(282,284),(282,286),(283,283),(283,285),(283,287),(284,284),(284,286),(284,288),(285,285),(285,287),(285,289),(286,286),(286,288),(286,290),(287,287),(287,289),(287,291),(288,288),(288,290),(288,292),(289,289),(289,291),(289,293),(290,290),(290,292),(290,294),(291,291),(291,293),(291,295),(292,292),(292,294),(292,296),(293,293),(293,295),(293,297),(294,294),(294,296),(294,298),(295,295),(295,297),(295,299),(296,296),(296,298),(296,300),(297,297),(297,299),(297,301),(298,298),(298,300),(298,302),(299,299),(299,301),(299,303),(300,300),(300,302),(300,304),(301,301),(301,303),(301,305),(302,302),(302,304),(302,306),(303,303),(303,305),(303,307),(304,304),(304,306),(304,308),(305,305),(305,307),(305,309),(306,306),(306,308),(306,310),(307,307),(307,309),(307,311),(308,308),(308,310),(308,312),(309,309),(309,311),(309,313),(310,310),(310,312),(310,314),(311,311),(311,313),(311,315),(312,312),(312,314),(312,316),(313,313),(313,315),(313,317),(314,314),(314,316),(314,318),(315,315),(315,317),(315,319),(316,316),(316,318),(316,320),(317,317),(317,319),(317,321),(318,318),(318,320),(318,322),(319,319),(319,321),(319,323),(320,320),(320,322),(320,324),(321,321),(321,323),(321,325),(322,322),(322,324),(322,326),(323,323),(323,325),(323,327),(324,324),(324,326),(324,328),(325,325),(325,327),(325,329),(326,326),(326,328),(326,330),(327,327),(327,329),(327,331),(328,328),(328,330),(328,332),(329,329),(329,331),(329,333),(330,330),(330,332),(330,334),(331,331),(331,333),(331,335),(332,332),(332,334),(332,336),(333,333),(333,335),(333,337),(334,334),(334,336),(334,338),(335,335),(335,337),(335,339),(336,336),(336,338),(336,340),(337,337),(337,339),(337,341),(338,338),(338,340),(338,342),(339,339),(339,341),(339,343),(340,340),(340,342),(340,344),(341,341),(341,343),(341,345),(342,342),(342,344),(342,346),(343,343),(343,345),(343,347),(344,344),(344,346),(344,348),(345,345),(345,347),(345,349),(346,346),(346,348),(346,350),(347,347),(347,349),(347,351),(348,348),(348,350),(348,352),(349,349),(349,351),(349,353),(350,350),(350,352),(350,354),(351,351),(351,353),(351,355),(352,352),(352,354),(352,356),(353,353),(353,355),(353,357),(354,354),(354,356),(354,358),(355,355),(355,357),(355,359),(356,356),(356,358),(356,360),(357,357),(357,359),(357,361),(358,358),(358,360),(358,362),(359,359),(359,361),(359,363),(360,360),(360,362),(360,364),(361,361),(361,363),(361,365),(362,362),(362,364),(362,366),(363,