名校
1 . 记“抛掷一颗骰子,向上的点数是4,5,6”为事件
,“抛掷一颗骰子,向上的点数是1,2”为事件
,“抛掷一颗骰子,向上的点数是1,2,3”为事件
, “抛掷一颗骰子,向上的点数是1,2,3,4”为事件
,下列判断正确的有 ( )个
①
与
互斥; ②
与
对立; ③
与
对立; ④
与
互斥;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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解题方法
2 . 甲、乙两人组成“星队”参加猜成语活动,每轮活动由甲、乙各猜一个成语,已知甲每轮猜对的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
乙每轮猜对的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
在每轮活动中,甲和乙猜对与否互不影响,各轮结果也互不影响,记甲在第
轮猜对成语为事件
,乙在第
轮猜对成语为事件![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc5c895153932c3e827a464664cef90.png)
.
(1)求甲在两轮活动中恰好猜对1个成语的概率;
(2)求“星队”在两轮活动中共猜对3个成语的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc5c895153932c3e827a464664cef90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b52faa6703492e49a2058ce6fc29f2.png)
(1)求甲在两轮活动中恰好猜对1个成语的概率;
(2)求“星队”在两轮活动中共猜对3个成语的概率.
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3 . 已知向量
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d69e851b0080e8f162e1f3b17e552c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e331d462d9c49348f44e56b626e18b6.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() ![]() ![]() | D.若![]() ![]() ![]() |
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4 . 如图,在正三棱柱
中, 点 D在边
上,
.
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)如果点E是
的中点, 求证:
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc80093eab6bfbba801d92b57d576b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)如果点E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35850dbc661ded6456b70767cc6cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d560542b646924eaf577480ac73281b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
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5 . 将函数
图象上每个点的横坐标变为原来的
倍,在将得到的图象向左平移
个单位,所得图象的解析( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 从参加环保知识竞赛的学生中抽出 60 名学生,将其成绩 〔均为整数〕整理后画出的频率直方图如图所示,则( )
A.估计 ![]() | B.估计这组数据的众数74.5 |
C.估计该次环保知识竞赛的平均成绩是72.5 | D.估计这组数据的中位数是72.8 |
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7 . 已知
则复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd6ffa9a48b87b3bd61dacc83c56674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
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8 . 在
中, 已知
,
,
, 求
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb6362bc99fba4bcd7331db9aee922c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe7a93172d308a58200e3c722fe1072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e1d0f65817ba32a732040518f41440.png)
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9 . 已知平面
和直线m,n,下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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10 . 若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626a3c22317e3d98ac5a2110f6e3eb69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb37406253b2dc9a2838e1ce08f1ac5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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