1 . 甲、乙、丙三人从1楼乘电梯去商场的3到7楼,每层楼最多下2人,则下电梯的方法有___________ 种.
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2 . 设z为复数,若方程
表示一条圆锥曲线,则此曲线的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9b19dfc40f5ac92d489480c488a211.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba0faf86eda36bf50a0725d1d52722a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9b19dfc40f5ac92d489480c488a211.png)
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3 . 设
,且
,若
,则
的值___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0c5e972dd30f59425963ef568b5e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ffc0affbb5311cffa81936004a8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292e6cef540885a0b3f6f98f3d716a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853c0c03aa9086e9e6c53eb2af7f2d7d.png)
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4 . 已知二面角
的平面角为
,A,D为直线l上的两点,射线
在平面
内,射线
在平面
内,已知
,则
等于___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc4e18d1ac4f5119845b3ee4e8fd3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0860834d28d02fd66a5235671348b92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3217fa687c8a339e86fc482c826e2edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a096cc7ad0625b68858eb7549986d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9520604dc21bc8d5a6f4659725cecaec.png)
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5 . 如图,已知
内接于抛物线
,且边
所在直线分别与抛物线
相切,F为抛物线M的焦点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/9363e490-d4f9-4149-82da-1203d0f10886.png?resizew=200)
(1)边
所在直线与抛物线M相切;
(2)A,C,B,F四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bc980a6ff5fe01b746c65af072a05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19409d6d120387b3bccd934c4911bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd646f98b097a1b09f0b8a76ec399340.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/9363e490-d4f9-4149-82da-1203d0f10886.png?resizew=200)
(1)边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)A,C,B,F四点共圆.
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6 . 已知椭圆
的左右焦点为
,点P在直线
上,当
取最大值时,
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ec15606e83f0193fae69964aaec745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b799737e84f54908b8700fbaf1f96a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c18718d9550e3a2bc579d41f6de831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a436c08117d943c2e3b32cc68b6147b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24706bfc6eaa501211e3c0d4e184805.png)
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7 . 直角三角形
的三个顶点分别在等边三角形
的边
上,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839ce94689e556c5d3bbad67071a64de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8be9911089f6b0c48d50ac2eaf2091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5915a17fae38af0b2ef9ed98a81ec7ad.png)
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8 . (1)若实数x,y,z满足
,证明:
;
(2)若2023个实数
满足
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77bd83db721327f2875fb9ce218f797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f921846cfd2491c21fbe42fd29fd80.png)
(2)若2023个实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52011d2f4946b2ddd070bb20796a069d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7909872111d29739539041cb524eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4507435d75954f4991f50ad1376e5cb3.png)
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9 . 已知
,则不等式
的解集为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16dd5d855df241d4984f43ce057951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f581b04dd480d7b409bed4b9f2f9a3.png)
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10 . 设a,b都是正整数,且
,则
的个位数字是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3885147f2949fc1ebc203790a3f7a122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
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