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1 . 乒乓球,被称为中国的“国球”.某次比赛采用三局两胜制,当参赛选手甲、乙两位中有一位赢得两局比赛时,就由该选手晋级而比赛结束.每局比赛都要分出胜负,且每局比赛的胜负不受之前比赛结果影响.假设甲在任一局赢球的概率为
,有选手晋级所需要的比赛局数的期望值记为
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09ff35a01b538c6383ede0fc2aa7acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a0be4eebc5d70c51f72f28dbfc11e9.png)
A.打满三局结束比赛的概率为![]() | B.![]() |
C.函数![]() ![]() | D.![]() |
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解题方法
2 . 已知不等式
的解集为
,则以下选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5f28031b036e4a37be931d5ff28368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078d466170d2ed871ecb34534bc7c64c.png)
A.![]() |
B.![]() |
C.函数![]() |
D.![]() ![]() ![]() |
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解题方法
3 . 已知a为实数,函数
,
.
(1)设
,
,若函数
的最大值等于2,求a的值;
(2)若对任意
,都存在
,使得
,求a的取值范围;
(3)设
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6076f2c305797168a666280436eb6e8f.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605705b3da667e82dd7787b4741b261e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77156221148913fb706a2d57d9b9100c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327e81d90543aa594968112a73bfa2ad.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3a5b4f2b7279a7aa94f8ec12b3f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3b1d05315ce6c73c0ad0500845a409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cf4f9640637c4ec7804da532b6a819.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b200636f87441fc3e8788675391f39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
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4 . 下列命题正确的是( )
A.命题“![]() ![]() ![]() ![]() |
B.如果A是B的必要不充分条件,B是C的充分必要条件,D是C的充分不必要条件,那么A是D的必要不充分条件 |
C.函数![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() |
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5 . 二次函数
是常数,且
的自变量
与函数值
的部分对应值如下表:
且当
时,对应的函数值
.下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c53fa91aecb40438f8b53eb97b70bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28b08682efa2692b052f64fe1448fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
… | -1 | 0 | 1 | 2 | … | |
… | 2 | 2 | … |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57458464618fcf619375a93d3c66d69.png)
A.![]() |
B.![]() |
C.关于![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() |
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6 . 已知向量
,
,函数
,
.
(1)若
,求
的值;
(2)用
表示
,若
时,
的最小值为
,求实数
的值;
(3)设
为正整数,函数
在区间
上恰有2024个零点,请求出所有满足条件的
的值及相应
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24de0eae5db745b9e0f51963973e961d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae2a23e9e7ae7db55c3e114f2eba19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e95435f474caf8511be2679d1b8476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b87f4ef298bdeebf59a0d850aff72c.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93af88a7628c71d642d3a6df067c15f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bb700769d578c7ed2b6a650400b926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c07c496500d66cbd74e1070e1c7c1d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
7 . 如图,在平面四边形
中,
.若点
为边
上的动点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c0518ef6097a5f3bc3446f85d7fc61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53aec2ef0bbe7a2d482aa35b9826ec6.png)
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解题方法
8 . 已知函数
的定义域为R,且
,则下列结论一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c744ee4528f4803d5d5710e2b27bf8c.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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9 . 已知定义在
上的函数
满足
.
(1)求
;
(2)若函数
,
,是否存在实数
使得
的最小值为
?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e276006dc5b6f941be16860b8e3c0e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b201cf357856ffe5feffeaea3f763047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
10 . 已知函数
,设
,
.且关于
的函数
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26af862ac8e4e2fe03204b0463a7a789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5954cca8533e3392b0e88b5e618e7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8793f866a3eb72d4785604035e7f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0f5ae54c95fc4b8dbd885bc35fdfb8.png)
A.![]() ![]() |
B.![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() |
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