2025-2026年江苏版高中一年级数学下学期测试卷

2025-2026年江苏版高中一年级数学下学期测试卷姓名：_____ 准考证号：_____ 得分：__________

2025-2026年江苏版高中一年级数学下学期测试卷

一、选择题(每题2分，总共10题)

1.函数f(x)=sin(x)+cos(x)的最小正周期是

A.π

B.2π

C.3π

D.4π

2.若复数z=a+bi(a,b∈R)的模为√5，且z的辐角主值为π/4，则a的值为

A.√5/2

B.5/2

C.2√5

D.-√5/2

3.抛掷两个均匀的骰子，记事件A为"点数之和大于8"，事件B为"点数之和为偶数"，则P(A|B)等于

A.1/6

B.1/3

C.1/2

D.2/3

4.已知函数f(x)=x^3-ax^2+bx在x=1处取得极值，且f'(1)=0，则a+b的值为

A.3

B.4

C.5

D.6

5.在等差数列{a_n}中，若a_1=2，a_5=10，则a_10的值为

A.18

B.20

C.22

D.24

6.已知圆O的方程为x^2+y^2=9，直线l的方程为y=kx+3，若直线l与圆O相切，则k的值为

A.±2√2

B.±√3

C.±3√2

D.±√5

7.函数g(x)=|x-1|+|x+1|的最小值为

A.0

B.1

C.2

D.3

8.在△ABC中，若角A=60°，角B=45°，且a=√3，则边b的值为

A.1

B.√2

C.√3

D.2

9.已知向量u=(1,2)，v=(3,-4)，则向量u+v的模长为

A.√10

B.√26

C.√30

D.√50

10.已知直线l的参数方程为x=1+t，y=2-3t(t为参数)，则直线l的斜率为

A.-3

B.3

C.1/3

D.-1/3

二、填空题(每题2分，总共10题)

1.函数h(x)=log_2(x+3)的定义域为

2.若复数z=1+i的平方根为z_1和z_2，则z_1+z_2的值为

3.从5名男生和4名女生中任选3人参加比赛，则选出的3人中恰好有2名男生的概率为

4.已知函数f(x)=x^2-4x+3，则f(x)在区间[1,4]上的最大值为

5.在等比数列{b_n}中，若b_1=1，b_4=16，则b_3的值为

6.已知圆C的方程为(x-2)^2+(y+1)^2=4，则圆C的圆心坐标为

7.函数k(x)=x^2-2x+3的顶点坐标为

8.在直角坐标系中，点P(1,2)到直线x+y-1=0的距离为

9.已知向量a=(2,-1)，b=(-1,3)，则向量a·b的值为

10.已知直线l_1的方程为x-2y+1=0，直线l_2的方程为2x+y-3=0，则直线l_1与直线l_2的夹角余弦值为

三、多选题(每题2分，总共10题)

1.下列函数中，在区间(0,π)上单调递增的是

A.f(x)=sin(x)

B.g(x)=cos(x)

C.h(x)=tan(x)

D.k(x)=cot(x)

2.下列命题中，正确的是

A.若z_1=a+bi，z_2=c+di(a,b,c,d∈R)，则|z_1+z_2|=|z_1|+|z_2|

B.奇函数的图像关于原点对称

C.若事件A和事件B互斥，则P(A∪B)=P(A)+P(B)

D.若数列{a_n}是等差数列，则数列{a_n^2}也是等差数列

3.下列直线中，与圆(x-1)^2+(y+2)^2=5相切的是

A.x=1

B.y=-2

C.x+y=0

D.2x-y=1

4.下列数列中，是等比数列的是

A.2,4,8,16,...

B.3,6,9,12,...

C.1,1/2,1/4,1/8,...

D.1,-1,1,-1,...

5.下列函数中，在定义域内存在反函数的是

A.f(x)=x^3

B.g(x)=|x|

C.h(x)=e^x

D.k(x)=sin(x)

6.下列向量中，与向量(1,-1)平行的有

A.(2,-2)

B.(-1,1)

C.(3,3)

D.(0,0)

7.下列命题中，正确的是

A.若三角形ABC的三边长分别为a,b,c，且满足a^2+b^2=c^2，则三角形ABC是直角三角形

B.若数列{a_n}是递增数列，则对任意n，都有a_n<a_{n+1}

C.若函数f(x)在区间I上连续，则f(x)在区间I上必有界

D.若事件A和事件B相互独立，则P(A|B)=P(A)

8.下列图形中，是轴对称图形的有

A.正方形

B.等边三角形

C.矩形

D.梯形

9.下列不等式中，成立的有

A.log_2(3)>log_2(4)

B.sin(π/6)<sin(π/3)

C.e^2>e^3

D.√2>√3

10.下列函数中，是周期函数的有

A.f(x)=sin(x)

B.g(x)=cos(x)

C.h(x)=tan(x)

D.k(x)=x^2+1

四、判断题(每题2分，总共10题)

1.函数f(x)=sin(x)+cos(x)可以写成f(x)=√2sin(x+π/4)

2.若复数z=a+bi(a,b∈R)的模为0，则z必为0

3.抛掷三个均匀的骰子，事件"点数之和为12"的概率等于事件"点数之和为6"的概率

4.若函数f(x)在x=c处取得极值，则f'(c)必为0

5.在等差数列{a_n}中，若a_1=5，d=-2，则a_10=1

6.已知圆O的方程为x^2+y^2=16，直线l的方程为y=kx-4，若直线l与圆O相切，则k的值必为±2√2

7.函数g(x)=|x-2|+|x+2|的最小值为4

8.在△ABC中，若角A=30°，角B=60°，且a=2，则边b的值为2√3

9.已知向量u=(3,0)，v=(0,4)，则向量u+v的模长为5

10.已知直线l的参数方程为x=2-t，y=1+2t(t为参数)，则直线l的斜率为-1/2

五、问答题(每题2分，总共10题)

1.求函数f(x)=x^3-3x^2+2在区间[-1,3]上的最大值和最小值

2.已知数列{a_n}的前n项和为S_n=n^2+n，求a_5的值

3.求圆C：(x-1)^2+(y+2)^2=9的圆心坐标和半径

4.求直线l：3x+4y-12=0的斜率和y轴截距

5.求向量u=(1,2)和向量v=(3,-4)的夹角余弦值

6.写出函数f(x)=2cos(2x+π/3)的最小正周期

7.已知复数z=1+i，求z^4的值

8.从6名男生和4名女生中任选4人参加比赛，求选出的4人中恰好有3名男生的概率

9.求不等式|2x-1|<3的解集

10.证明：若函数f(x)在区间I上单调递增，且f(x)在区间I上连续，则f(x)在区间I上有界

试卷答案

一、选择题答案及解析

1.B解析：函数f(x)=sin(x)+cos(x)=√2sin(x+π/4)，最小正周期为2π。

2.A解析：复数z=a+bi的模为√5，即√(a^2+b^2)=√5，辐角主值为π/4，即tan^{-1}(b/a)=π/4，解得a=√5/2，b=√5/2。

3.C解析：抛掷两个均匀的骰子，点数之和大于8的组合有(4,5),(5,4),(3,6),(6,3),(5,6),(6,5)共6种，点数之和为偶数的组合有(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)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