1 . 已知二项式
的展开式中
项的系数为20,则实数a的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf116fb716976731a1fe24bde7d333d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
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2 . 有
辆车停放
个并排车位,货车甲车体较宽,停靠时需要占两个车位,并且乙车不与货车甲相邻停放,则共有_________________ 种停放方法.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
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3 . 已知直线
,若直线
与
垂直,则
的倾斜角是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13062d2d36619f5352102dcee1bb60cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 某足球训练基地有编号为
的
位学员,在一次射门考核比赛中,学员有两次射门机会.每人第一次射中的概率为
第二次射中的概率为
假设每位学员射门过程是相互独立的,比赛规则如下:
①按编号从小到大的顺序进行,第1号学员开始第1轮比赛,先第一次射门;
②若第
号学员第一次射门未射中,则第
轮比赛失败,由第
号学员继续比赛;
③若第
号学员第一次射门射中,再第二次射门,若该学员第二次射门射中,则比赛在第
轮结束,该学员第二次射门未射中,则第
轮比赛失败,由第
号学员继续比赛;
④若比赛进行到了第
轮,则不管第
号学员的射门情况,比赛结束.
(1)当
时,设随机变量
表示3名学员在第
轮比赛结束,求随机变量
的分布列;
(2)设随机变量
表示
名学员在第
轮比赛结束.
①求随机变量
的分布列;
②求证:
单调递增,且小于3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fda57f23706517a3b7c02218a1dbcef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095c3e3fa8dd8e454c52039a25c14520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e304cb3bcd353eee5749f5f402e8c441.png)
①按编号从小到大的顺序进行,第1号学员开始第1轮比赛,先第一次射门;
②若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a004043e329408a50f98d25691ca9652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12444d6e8d3b097a9d090e6ed06042e4.png)
③若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a004043e329408a50f98d25691ca9652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12444d6e8d3b097a9d090e6ed06042e4.png)
④若比赛进行到了第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4cbb3a50014fa18fab2e0de87ee22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4cbb3a50014fa18fab2e0de87ee22.png)
①求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51219b7f10c645e00bec49d9c446a79.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bcf3603979781255122ec2735cb9b5.png)
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5 . 在平面直角坐标系
中,设
是双曲线
的左、右焦点,过
的直线与双曲线的两支分别交于点
若
为正三角形,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578832b5e2b61bf599918028e68da17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a844f3fbe347454be52dd9fea2451cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
A.![]() | B.2 | C.![]() | D.![]() |
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6 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d8a45e1fb4fddf2dab137b15285afa.png)
(1)若对
均有
求实数
的取值范围;
(2)求证:对任意实数
函数
的图象总存在两条切线相互平行.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d8a45e1fb4fddf2dab137b15285afa.png)
(1)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b00f3a3d36376383ac2567e0aaa3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6413626e27fac27f583e45ca28709755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2187845526895307ea257ab5d609dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
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7 . 已知
下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852ce04bf92bfb78c1790c9349134c10.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若事件![]() ![]() ![]() ![]() |
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8 . 如图,在六面体
中,
三棱锥
为正四面体.
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5b8bfc1addf01ff19ddf51ce168dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb650f48c879ea25127662b47d16feec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fff0f219639442392ef08c6489df93.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5197d0fc2d6d6ec1bbfb5fdc9fb43b30.png)
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9 . 已知椭圆
的离心率为
,且经过点
,直线
与
轴交于点
,与椭圆
交于
两点.
(1)求椭圆
的方程;
(2)若点
坐标为
,线段
的垂直平分线分别交直线
和
于点
,若
,求直线
的斜率;
(3)若点
坐标为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323227dd8a7a31c078eac609b9acf472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465ad29754038f55bed90d1ccf8fec60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffbc423070f5d7ce2c72229066ee1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8431125d823e3b34a48f2ce2e4ca5a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23a03ca8f1729bfcadf513784817fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec2d512dbca05f9cf4fd329028ae789.png)
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10 . 各项不为0等差数列
中,
且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7017d83bdfaa074c3c330a2657c84151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3248626515f27b895bf929931a9057f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc2936f889aa2b19957a7097d8f3f15.png)
A.![]() | B.![]() | C.0 | D.2 |
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