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1 . 已知半径为3和5的两个圆
和
内切于点
,点
分别在两个圆
和
上,则
的范围是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
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2 . 如图,圆锥底面是以
为圆心,直径
的圆,
为圆
上一点,且
为圆锥顶点,
,
分别是
、
、
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/7d6d0148-5a72-4047-b6a6-ee3e296e9b7c.png?resizew=220)
(1)求二面角
的大小(结果用反三角函数值表示);
(2)求点
到过点
的截面的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2ba439d81a5965786c24e0d250bcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/7d6d0148-5a72-4047-b6a6-ee3e296e9b7c.png?resizew=220)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89f615a3799591b96e6efbc941b8ef3.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4817f6d025306bfcba653b4e8d4dc6.png)
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3 . 有3本不同的数学书和4本不同的外语书从左到右依次排放在书架的某一层上,那么其中数学书甲不排在左边第一个并且英语书
不排在左边第二个的概率为_______ .(结果用数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
4 . 已知曲线
上一动点
到两定点
,
的距离之和为
,过点
的直线
与曲线
相交于点
,
.
(1)求曲线
的方程;
(2)动弦
满足:
,求点
的轨迹方程;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f7a7cf83fb9706134edb619d8aa90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cc3f576dcf32e3ec2de59ea8059a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14dd75003428d5b4071aabbaa4d11cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)动弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55899a55390743a4dd830402641d2122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979df095c33a0d8edce5c1fab7cad04.png)
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2022-09-06更新
|
382次组卷
|
2卷引用:上海市行知中学2022届高三上学期开学考试数学试题
5 . 在“立体几何”知识中:①两直线所成角的取值范围是
;②直线与平面所成角的取值范围是
;③二面角的平面角取值范围是
.在“解析几何”知识中;④直线的倾斜角取值范围是
;⑤两直线的夹角取值范围是
;在“向量”知识中:⑥两向量的夹角的取值范围是
;以上概念叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa898d5280ab56f52aeedc2cce370bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14bdd7f2b48c0ce6ba8696c89fbf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b1d28a098ea5555c89b332fad25b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917ae6fcf56fa6b4fc9852854cd8f78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
A.②①④⑤ | B.②③④⑥ | C.③④⑤⑥ | D.②③④⑤ |
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6 . 一个棱长为2的正方体容器,将8个直径均为1的球放入容器内,容器正中央能放入的最大的球的直径为________ .
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7 . 直线
(
为常数,且
),则直线倾斜角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
________ (结果用反正切表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cff0bbf16b63e3ee0d68f2ab8f9236d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
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8 . 已知
,
,
,
,
,
,则下列关于集合P,Q,S关系的表述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d4fbd66baf902402983c2135e31296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f9383bb648072cb607f403e3c2c7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dd9391a6f99d841bfc7f334faf2b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907ee062a0d2154bf1d97a4a70df437a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9a5c46a95fcdd8dd7910e90af2d4a6.png)
A.P=Q | B.Q=S | C.Q⊂P | D.P⊂S |
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9 . 如图,有一个半径为
的半球,过球心
作底面的垂线
,
上一点
满足
,过
作平行于底面的截面将半球分成两个几何体,其中较大 部分的体积为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068b914cd2f1080a396237d7a61e66e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://img.xkw.com/dksih/QBM/2021/11/13/2850628311859200/2851111543136256/STEM/282a711c-d6f1-40f6-83f6-92ce4200e6d0.png?resizew=537)
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10 . 一种玻璃饰品外形是简单多面体,表面是由三角形和平面八边形两种拼接而成.它共有24个顶点,每个顶点恰好在三条棱上.设该多面体表面有x个三角形,y个平面八边形,则
的值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
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