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1 . 样本数据
的第30百分位数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ea59ba9c066b71f4f11b55441360ee.png)
A.7 | B.7.5 | C.8 | D.8.5 |
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2 . 为了回馈长期以来的顾客群体,某健身房在五周年庆活动期间设计出了一种游戏活动,顾客需投掷一枚骰子三次,若三次投掷的数字都是奇数,则该顾客获得该健身房的免费团操券5张,且有2次终极抽奖机会(2次抽奖结果互不影响);若三次投掷的数字之和是6,12或18,则该顾客获得该健身房的免费团操券5张,且有1次终极抽奖机会;其余情况顾客均获得该健身房的免费团操券3张,不具有终极抽奖机会.已知每次在终极抽奖活动中的奖品和对应的概率如下表所示.
(1)已知某顾客有两次终极抽奖机会,求该顾客获得一个健身背包和一盒蛋白粉的概率;
(2)求一位参加游戏活动的顾客获得蛋白粉的概率.
奖品 | 一个健身背包 | 一盒蛋白粉 |
概率 | ![]() | ![]() |
(2)求一位参加游戏活动的顾客获得蛋白粉的概率.
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解题方法
3 . 函数
在
上的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca8323e91ce162e8cba418191356de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d79a1aff4e8c0a9d97dee259423ea7f.png)
A.5 | B.4 | C.3 | D.2 |
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4 . 定义:任取数列
中相邻的两项,若这两项之差的绝对值为1,则称数列
具有“性质1”.已知项数为
的数列
的所有项的和为
,且数列
具有“性质1”.
(1)若
,且
,写出所有可能的
的值;
(2)若
,证明:“
”是“
”的充要条件;
(3)若
,证明:
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4ac9c2787e5c2b6ce99f89b50b0dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a72be91e4148dbd19e935bd9e51a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e1a57b212411267bff20b97d6c3e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f2867385db84ec7fac034865ea91b6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f4aea81669864630ee9be6f69e43fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e12058f26dd0b9319a97bdf8e3b4702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a19410555c6ed7f5d55becd4516609.png)
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5 .
的虚部为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fba932e362a009ae8860a653546792.png)
A.-5 | B.5 | C.-1 | D.1 |
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解题方法
6 . 已知椭圆
的离心率为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc790695d3ff61ea27cce0777481053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.3 | B.![]() | C.2 | D.![]() |
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解题方法
7 . 已知函数
.
(1)若
,讨论
的单调性;
(2)若曲线
在
处的切线与直线
垂直,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cfe16275a7703fa5c7b7c910d10475.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512f4c29ff276b7f35052ad4cc255ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559250e7a91f36fe7a8ec6ce6a1550f.png)
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8 . 已知
中,角
所对的边分别为
的面积记为
,若
,则( )
![](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/718b5b48053888ab3b234b8cb56a0fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d6dae531265e6d528cbf1346e41aca.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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9 . 已知全集
,集合
,若
有4个子集,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b68095137c7e5a3e90af74b515d33f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5c5c7e2b86320b6d4204815f685ce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c093cbde3d3472d1f7f2b0dff2bc4881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
A.![]() | B.集合![]() |
C.![]() | D.![]() |
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10 . 过圆
外一点
做圆
的切线
,切点为
,若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e0db273061d0331e4e5da9ff1e955e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b0dd09a59056af579586ab8b69f4f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9817a48b819ab971e79bad7b20250294.png)
A.![]() | B.![]() | C.![]() | D.8 |
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