名校
解题方法
1 . 如图,在三棱锥
中,
,
,
平面ABC,E为CD的中点,则直线BE与AD所成角的余弦值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802941607869601748f8efcaa364afc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
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2 . 若椭圆
的左,右焦点分别为
,离心率为
,点
在椭圆
上,
的内切圆的半径为1,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee9d4ad39e56940f519bd3acc5e85ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5040ccc0d21519fc2ea911fce42e22d9.png)
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3 . 某工厂利用随机数表对生产的50个零件进行抽样测试,先将50个零件进行编号,编号分别为01,02,…,50,从中抽取5个样本,下面提供随机数表的第1行到第2行:
66 67 40 37 14 64 05 71 11 05 65 09 95 86 68 76 83 20 37 90
57 16 03 11 63 14 90 84 45 21 75 73 88 05 90 52 23 59 43 10
若从表中第1行第9列开始向右依次读取数据,则得到的第4个样本编号是________ .
66 67 40 37 14 64 05 71 11 05 65 09 95 86 68 76 83 20 37 90
57 16 03 11 63 14 90 84 45 21 75 73 88 05 90 52 23 59 43 10
若从表中第1行第9列开始向右依次读取数据,则得到的第4个样本编号是
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4 .
表示不小于x的最小整数,例如
,
.已知等差数列
的前n项和为
,且
,
.记
,则数列
的前10项的和______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa5efc9350c3ad41f456d434564f82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c314bd3e07c88abd2931344a30d11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739718565082441c3e1a9b3e22e1735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6760775a38ed18ab8f346346e25de2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac51814852f7070293f0e7ddcf4a0691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2dbf1896e958f7b0b715be6ab1b799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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5 . 若向量
满足
,
,则
在
上的投影向量为______ (用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da55c225932dfff8999c7a67ef87c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cab4a159676f892d37605751744abad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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6 . 设
,若
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582066df000f70b6b4fa5ab11e931bdb.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc0fee842afa40cbb8674fa8eb9edac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553a2b13547ab9fabd8878fbbb8780db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8e7a2df4185211339d84892de2ddf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582066df000f70b6b4fa5ab11e931bdb.png)
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7 . 已知
,当
时,则
的值是_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb9f992de6398e5de944d14d246eef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764eff906937f9b1fb58e5abfb2eb8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ccfc43be1d95f5a308ffbdfea60fd4.png)
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8 . 袋中装有大小相同的黑球和白球共9个,从中任取2个都是白球的概率为
.现甲、乙两人从袋中轮流摸球,甲先取,乙后取,然后甲再取…,每次摸取1个球,取出的球不放回,直到其中有一人取到白球时终止.用X表示取球终止时取球的总次数.则数学期望![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223770da09feb2fc824764188e924d7e.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16d09692f7b0fb5633964437202d21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223770da09feb2fc824764188e924d7e.png)
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9 . 赵爽是我国古代数学家,大约在公元222年,他为《周髀算经》一书作序时,介绍了“勾股圆方图”,亦称“赵爽弦图”.(以弦为边长得到的正方形由4个全等的直角三角形再加上中间的一个小正方形组成,如图①),类比“赵爽弦图”,可构造如图②所示的图形,它是由3个全等的三角形与中间一个小等边三角形拼成的一个较大的等边三角形,其中
,则
的值为______ ;设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bbe0491dc037390ef465b4deef4a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412e959d8e97ae6bee534a319662e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e507d3941363e9dbeac8be35134727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
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10 . 已知函数
(
)的图象关于直线
对称,若存在
,使得
(其中
,
),则
的最小值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d566cc50283930e80764affd45c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8973254e0eeb29a0add0e4677ce5337b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b965dbffd61b1e3e3c6f3ecd00b377e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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