1 . 已知数列
满足
(
),且
.给出下列四个结论:
①
;
②
;
③
,当
时,
;
④
,
,当
时,
.
其中所有正确结论的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6601304f30b786d0dbc35a3ed07c084a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a95f98737192b55293edb36307ab27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245874c7590632dbfe943e38b645062e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279efbf5a2768db8064621fe997d5fe2.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0d92d11ac8d916de7858529b6b56fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6e1ad3cc94c60786612117ca27689b.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b133fe372537a59d8307d805dede37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f616248ea756e33bc9ab439feb199d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7c8e642529926f31c90ab0ccee9cca.png)
其中所有正确结论的个数为( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
2 . 设函数
的极值点为
,且
,则
可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42cd5920c27db7257886fece226833b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28319174975bd87487e49585c65a79a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 在平面直角坐标系
中,角
以
为始边,点
在角
终边上,则错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c617a8e7995c65746aac4aa84f30c70f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e840a7db5abc7322e629c08c4105f4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f219e145bb4c8409e11f0333f708ebe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
4 . 已知直线
的方程分别是
,点
的坐标为
.过点
的直线
的斜率为
,且与
分别交于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af3be509819cedd22f0ebb04e59e699.png)
的纵坐标均为正数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
(1)若
,且
为线段
中点,求实数
的值及
的面积;
(2)是否存在实数
,使得
的值与
无关?若存在,求出所有这样的实数
;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298a499784e70cd8487c97dd5da5b484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ae51a31048c032272dc0d531b670d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b93b1aca2f6d74a84e04eaef8e211b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec8d41d480faa56615c88703b244955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b93b1aca2f6d74a84e04eaef8e211b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa0a6cfe799d0ffc4666103fe0b17a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af3be509819cedd22f0ebb04e59e699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392c2d2cf5432b1aec405b6aa6571cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b93b1aca2f6d74a84e04eaef8e211b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bd94db69bac8b670ab113ce9be46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bd8b071b24e92e0b1fd38101ffe400.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2caac14fd6f2f4d683f734d6a1b4a155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
5 . 如图,在三棱柱
中,
平面
,
,
,
分别是
的中点.
(1)求证:
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
平面
;
(3)在棱
上是否存在一点
,使得平面
与平面
的夹角为
?若存在, 求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ba708880f5eb782acbf2c961c2494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dacc4f03e9421b55f870619808106bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec1de061cca3ed6432bff4e25081933.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/18bfb0c1-ca54-4d8b-b79b-31c7e8d9f449.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0af1e0cc19aca046902574cd3e4826.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0484b57e28f364f6a711d5b129af5.png)
您最近一年使用:0次
6 . 已知圆
经过点
和点
,且圆心
在直线
上.
(1)求圆
的方程;
(2)若线段
的端点
的坐标是
,端点
在圆
上运动,求线段
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1282cc43ebf4b459832fec04d805989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baabfd32465e9e50409413d9c1358279.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238f0ea276a00ae8d681ce00cc11c8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
解题方法
7 . 在长方体
中,
,
是
的中点.以
为原点,
、
、
所在直线分别为
轴、
轴、
轴,建立如图所示的空间直角坐标系.
(1)写出
在平面
上的投影向量的坐标;
(2)求点
到平面
的距离;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d0432a2fc0e82790bbb560b17888e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/23afbc7b-32c7-4939-8ab1-b8cea15b76e0.png?resizew=166)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9aad43adb48b03fab99a9670b7eda7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0758f3ff9f1f7109024c1ef65536c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7850e88507969a07a9515347b97c7b6e.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7850e88507969a07a9515347b97c7b6e.png)
您最近一年使用:0次
2023-11-09更新
|
159次组卷
|
2卷引用:北京市大兴区2023-2024学年高二上学期期中检测数学试题
解题方法
8 . 有3个相同的球,分别标有数字1,2,3,从中有放回的随机取两次,每次取1个球.用
表示试的样本点,其中
表示第一次取出球的数字,
表示第二次取出球的数字. 设事件
“第一次取出的球的数字是1”,事件
“两次取出的球的数字之和是4”.
(1)写出这个试验的样本空间;
(2)分别求出
的值;
(3)判断事件
和事件
是否相互独立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38bf64ec3a94d1c955913b462ab03fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
(1)写出这个试验的样本空间;
(2)分别求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2da0a2a15f6dfa881c4891b8da873b.png)
(3)判断事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
解题方法
9 . 已知
中,点
,点
,点
.
(1)求边
上的高所在直线的方程;
(2)求
角平分线所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5fd55dcd6c520c24d4e167aa810e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19b0b35111ccea1b1ebde0f355efcf1.png)
(1)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
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10 . 已知等腰三角形
的顶点为
,底边的一个端点为
,则底边的另一个端点
的轨迹方程为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84412505a0e343c80ef6cce9edd39db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4891a26274a2c396b8f5e67df868d1ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次