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1 . 有五本形状为长方体的书放置在方形书架中,如图所示,其中四本竖放,第五本斜放,点G正好在书架边框上,每本书的厚度为
,高度为
,书架宽为
,则FI的长______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a9eed64d225267a58cd001db67e2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57171806f407a98dd8a796d4d2d6bbd.png)
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2 . 如图四边形ABCD与BEFG是并列放在一起的两个正方形,O是BF与EG的交点.如果正方形ABCD的面积是9,
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6f6c04bc017ced739230d14ba31948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882475eea0be0fa89024b38d556fed0d.png)
A.1 | B.![]() | C.4 | D.![]() |
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3 . 如图,已知四边形
是平行四边形,将边AD绕点D逆时针旋转
得到
,线段
交边
于点
,连接
. 若
,
,
,则线段
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7e7cf4b8e0ef3e56123a504092dd8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60634341a9603e24b2bbc6960abe3d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5713d1a64003579a8daec80c5a55b939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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4 . 若实数x满足
,则x应满足的条件是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a577984141284e65ce4ed46723d393.png)
A.![]() ![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知直线
上横、纵坐标都是整数的点的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4236f8562bc9caef6ef91560cc0d9a8a.png)
A.0个 | B.1个 | C.不少于2个但有限个 | D.无数个 |
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6 . 甲乙丙丁四位同学各掷5次骰子并记录点数,方差最大的是( )
甲:4 5 4 5 5 乙:4 2 3 4 3
丙:2 3 2 3 4 丁:6 1 2 6 1
甲:4 5 4 5 5 乙:4 2 3 4 3
丙:2 3 2 3 4 丁:6 1 2 6 1
A.甲 | B.乙 | C.丙 | D.丁 |
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7 . 已知函数
,函数
.
(1)若
,求
的值域;
(2)若
:
(ⅰ)解关于
的不等式:
;
(ⅱ)设
,若实数
满足
,比较
与
的大小,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25d5c7479bf62d5c9fc71bf46b56866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6cc4bdc89f1475cd1b3e21808ff6a3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77589ec03475a3a653d684f6f23b467.png)
(ⅰ)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604be3e10ddd5e520c921a8e5ab923e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99a77bd57c52838c723803db147e17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
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8 . 三个人利用手机软件依次进行拼手气抢红包活动,红包的总金额数为
个单位.第一个人抢到的金额数为1到
个单位且等可能(记第一个人抢完后剩余的金额数为
),第二个人在剩余的
个金额数中抢到1到
个单位且等可能,第三个人抢到剩余的所有金额数,并且每个人抢到的金额数均为整数个单位.三个人都抢完后,获得金额数最高的人称为手气王(若有多人金额数相同且最高,则先抢到最高金额数的人称为手气王).
(1)若
,则第一个人抢到的金额数可能为
个单位且等可能.
(i)求第一个人抢到金额数
的分布列与期望;
(ii)求第一个人获得手气王的概率;
(2)在三个人抢到的金额数为
的一个排列的条件下,求第一个人获得手气王的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d69ffc5955738802bc80728d1f9770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0a33d3543384ad49fd97a23eeba4d5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680e9ef551b325387ab31dca1f893705.png)
(i)求第一个人抢到金额数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(ii)求第一个人获得手气王的概率;
(2)在三个人抢到的金额数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2afdbcee1468b98067081ae6df7fc52.png)
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解题方法
9 . 球面几何学是在球表面上的几何学,也是非欧几何的一个例子.对于半径为R的球
,过球面上一点
作两条大圆的弧
,
,它们构成的图形叫做球面角,记作
(或
),其值为二面角
的大小,点
称为球面角的顶点,大圆弧
称为球面角的边.不在同一大圆上的三点
,可以得到经过这三点中任意两点的大圆的劣弧
,这三条劣弧组成的图形称为球面
,这三条劣弧称为球面
的边,
三点称为球面
的顶点;三个球面角
称为球面
的三个内角.
的单位球面上有不同在一个大圆上的三点
.
(1)球面
的三条边长相等(称为等边球面三角形),若
,求球面
的内角和;
(2)类比二面角,我们称从点
出发的三条射线
组成的图形为三面角,记为
.
其中点
称为三面角的顶点,
称为它的棱,
称为它的面角. 若三面角
的三个面角的余弦值分别为
.
(ⅰ)求球面
的三个内角的余弦值;
(ⅱ)求球面
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcdeb8eb2d5a8a7f1c81071ae349504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2dcc2105ebb1c89bfb1572a7e076e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19c1bcb8431ae315ecd29c6478d3eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef528373d472534670a8fd7fb301492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1b98b1478ed9480a9e1a62ec3b82da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e037d52e5d75070cd02df4727b5922d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(1)球面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814dc3914cdf4d5af2f4cfadf41c260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)类比二面角,我们称从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f673831a6738e1c317fede2920436d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de938433cfaf25cb38dd5c9d915bb2b.png)
其中点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f673831a6738e1c317fede2920436d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c93fa5e252ef36adfbffa39410f2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27029c4cc0fe55c8f4dbdb33beca9980.png)
(ⅰ)求球面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(ⅱ)求球面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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10 . 函数
,
,如图所示,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d789e4a7ca6fe5e2501763c6a410fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7774026e395632d1326deecc8f084cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346363143f4c60f935e2c2376391e664.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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