1 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbefef7b3281be333606691debb669a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ff48f4efdacbd38514d1be76d50114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbefef7b3281be333606691debb669a.png)
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2 . 下列四个命题,真命题的个数是________ .
①若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63af71b9e6f71cd26e6e97541154cd8c.png)
②
的充分不必要条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
③命题“
,
”的否定为“
,
”
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63af71b9e6f71cd26e6e97541154cd8c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c22b9d08cf536bbb76bce1b0f135772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
③命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899301a636c6ca1b072877441bcbcc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3119d53efb32cd36255815c962be6ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2a51de282f71171aeb8284c4a9cb1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f9fdc01e564d4c2e5f7d3c8d0f3db3.png)
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3 . 设
是等差数列,
是等比数列,且
.
(1)求
与
的通项公式;
(2)设
的前
项和为
,求证:
;
(3)若
,且数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6eba282321f5d17e3de9b6544e9f6f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702b31070b4001b47426d73831e585b5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc79e006b192782170fdb16384ba5879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0022c073e919d163032a4f5923e893ef.png)
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解题方法
4 . 已知各项为正数的等比数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795be30bf3f8437b2b47370c69493790.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91bf6f3383066988d2982da500c31fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
5 . 设函数
.
(1)求函数
的最小正周期;
(2)求函数
的单调递减区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d3e59d288480f39da4d0ad73ca4f95.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806e889c307fdab82687627d38d831e0.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9568ef7be7ce3acb03c01d4a2e04ad.png)
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6 . 已知数据
的平均数为
,方差为
,中位数为
,极差为
.由这组数据得到新数据
,其中
,则下列命题中错误 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994541b4b1f1fb999ebee19925875868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f89a46609995acbef7e36fc03952ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d379a3a9979d209b621f9f055fbae5.png)
A.新数据的平均数是![]() | B.新数据的方差是![]() |
C.新数据的中位数是![]() | D.新数据的极差是![]() |
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7 . 奥林匹克运动会会旗中央有5个互相套连的圆环,颜色自左至右,上方依次为蓝、黑、红,下方依次为黄、绿,象征着五大洲.在手工课上,老师将这5个环分发给甲、乙、丙、丁、戊五位同学,每人分得1个,则事件“甲分得红环”与“乙分得红环”是( )
A.对立事件 | B.互斥且对立事件 |
C.互斥但不对立事件 | D.既不互斥又不对立事件 |
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解题方法
8 . 在
中,内角
的对边分别为
,若
,则
是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f549abc307c50bf8187555643c86589e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.锐角三角形 | B.直角三角形 | C.等边三角形 | D.钝角三角形 |
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9 . 在
中,
,则
外接圆的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ef91c74fc133fd045440f6d060e05d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 已知数列
的前
项和
,则数列
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce817f902302ebdd5a599e43df77614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.是等差数列 | B.是等比数列 |
C.既是等差数列又是等比数列 | D.既不是等差数列也不是等比数列 |
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