1 . 在平面直角坐标系中,已知直线
与椭圆
在第二象限交于点
,交
轴于点
.设点
,若
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e7c8ae68ceea9ff4329bf58a20772c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b4afd16b79370532de44989d6c43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505b6a2ffbe5eee08156c30c8e41dbd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2 . 设实数
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a629ff9dcd6c23bf7846116c8581998b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb76c4956c01d52c178ae2ef29007689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9623f28eff10a0df572b338888f1ea62.png)
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3 . 符号
表示不超过
的最大整数,
为正整数,求:
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e90b41a295a4b424cf37f5640430dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b36ee2eebae5b276242089079dcace.png)
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4 . 如图,已知抛物线
的焦点为
,直线
与抛物线交于
两点,过
分别作抛物线的切线
,
交于点
.过抛物线上一点
(在
下方)作切线
,交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/7010be9e-22f0-4144-940a-0b3e5e66e9d7.png?resizew=256)
(1)当
时,求
面积的最大值;
(2)证明
四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91356fe1338cd458e4b1761b36873145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072104dd362a079309bcf3916901b7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5191fd3625bf6bd3744807e3ccdb030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5191fd3625bf6bd3744807e3ccdb030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cc6468ae954284918b1b54b188ae81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cc6468ae954284918b1b54b188ae81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92adfef6c3f4b8c041958fbf0b01f6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cc6468ae954284918b1b54b188ae81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86079725fcc03d623554ce82be14514.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/7010be9e-22f0-4144-940a-0b3e5e66e9d7.png?resizew=256)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dedff09ac873e40c3ee0ce3ecf2fa032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8b58ad3c066807c6b456932beafe39.png)
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解题方法
5 . 已知数列
,
,记
为
的前
项和,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb13237f04bd129ff52ad910d6d64bda.png)
,记
,
,
为
的前
项和.
(1)求数列
的通项公式;
(2)对
,使得
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065054f4e163585d630aa42cb6323a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4465705237c08e4e05d849cb28d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065054f4e163585d630aa42cb6323a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb13237f04bd129ff52ad910d6d64bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc21d3aa3d73897faff10fbafcfcca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d434bb9bd8d871e4cd1710adb4e92b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2a34ba3e0a669a77e76dc4e66edae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4465705237c08e4e05d849cb28d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065054f4e163585d630aa42cb6323a3e.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0790ada81b629938c80fb28b53f76282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e33cc462e26236015d48424f5fa207b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9faeed172ec5b88966b0d1c52748d41.png)
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解题方法
6 . 已知函数
.
(1)若
,求
的值;
(2)若
,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b1f44fdee4134fb55bf73722a67735.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63461019de0e1cc935f4cbad2efe140c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d383133a74f020784da99329bf597736.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd5308f1be49c12a7a8a29a219c1494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
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解题方法
7 . 从各位数字之和为
的所有四位数中任取两个,则
被取到的概率为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b632e7f3193aacab40ef3c9a9d69d7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb0c31687a3e30058e8ba13645c17cb.png)
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8 . 已知三棱锥
中,
两两垂直,
.若此三棱锥的体积为定值,当点
到平面
距离最大时,直线
与平面
所成角的正弦值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e43f6eb62e48e72e06361138e0d1e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14c10cd5801f3f84fa18a3a1d9faa8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dbacc8f5a9d6c606548dc11f19781e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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9 .
的边分别为a,b,c,且满足
,则
的取值范围为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff214d99784c6b23b7784bdaf3ed37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399461908ddad512b53d04d80f4ca580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51967992d093c51c7d28c46e3840a95.png)
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解题方法
10 . 在平面直角坐标系中,线段
的两端点分别落在
轴,
轴上,
,点
,则
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcf9bfbf771cb6118f8e631724314e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd8b8ceece9b2e576dff09c6cc670d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f76667e3a76e2c1de0a6b6805e1e496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853d44af78e164569cd514250d1abdb0.png)
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