名校
解题方法
1 . 如图,在三棱锥D-ABC中,已知△BCD是正三角形,AB⊥平面BCD,AB=BC=a,E为BC的中点,F在棱AC上,且AF=3FC.
(2)求三棱锥A-BDF的体积;
(3)若M为DB的中点,是否存在N在棱AC上,
,且
平面DEF?若存在,求
的值并说明理由;若不存在,给出证明.
(2)求三棱锥A-BDF的体积;
(3)若M为DB的中点,是否存在N在棱AC上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18da88f27cc36dbf1d01bcea7341bc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9cf9de9a49a343865199c29b329797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
2 . 如图所示,底面为正方形的四棱锥
中,
,
,
,
与
相交于点O,E为
中点.
平面
;
(2)
上是否存在点F,使平面
平面
.若存在,请指出并给予证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4ad370fe836accc1b2de6807d8ae62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe2fe5985a27babe0199e1c0865f49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f92fb805ed4f3b08ced4b8a385fa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-08-12更新
|
927次组卷
|
9卷引用:广东省茂名市华侨中学2022-2023学年高一下学期段考二数学试卷
广东省茂名市华侨中学2022-2023学年高一下学期段考二数学试卷陕西省铜川市宜君县高级中学2022-2023学年高一下学期期中数学试题四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题(已下线)第10讲 8.5.3 平面与平面平行-【帮课堂】(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)(已下线)8.5.3 平面与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)吉林省长春市东北师范大学附属中学净月实验学校2023-2024学年高一上学期期中质量监测数学试题(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
名校
3 . 已知函数
.
(1)证明:函数
在区间
上有2个零点;
(2)若函数
有两个极值点:
,且
.求证:
(其中
为自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a480c757668bd8d3177a7a2fe1049d25.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e093425cab3a441afb189d86513d6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987b5662225a45d45f3729b13ea472d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2976d45a26ec77149a05553e8eb13efb.png)
您最近一年使用:0次
2023-02-10更新
|
637次组卷
|
3卷引用:广东省茂名市第一中学奥林匹克学校2022-2023学年高二下学期期中数学试题
名校
解题方法
4 . 如图,在棱长为1的正方体
中,
分别为
、
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/d529a4c5-a788-4648-8047-41bb105d05ed.png?resizew=213)
(1)求异面直线
与
所成角的余弦值;
(2)求证:
平面
;
(3)试在棱
上找一点
,使
平面
,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446f0ebe5b33c905e29065cc52cdeb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/d529a4c5-a788-4648-8047-41bb105d05ed.png?resizew=213)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ff5ec52d9348020f5380e2de82e769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(3)试在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2022-09-07更新
|
950次组卷
|
3卷引用:广东省化州市林尘中学2023-2024学年高二上学期第一次月考数学试题
5 . 已知数列{
}的首项
=2,
(n≥2,
),
,
.
(1)证明:{
+1}为等比数列;
(2)设数列{
}的前n项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0016094d4c3ee9283e60749616ff6201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb23f1b6940b40353ca3d6397d5c21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1198d9a8c802928d39bb31c6c5db6110.png)
(1)证明:{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbb0a0bb77044ff507eb050821f1f16.png)
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2022-02-16更新
|
683次组卷
|
4卷引用:广东省茂名市五校联盟2021-2022学年高二上学期期末联考数学试题
名校
解题方法
6 . 已知数列
的首项
,
,
、
、
.
(1)求证:数列
为等比数列;
(2)记
,若
,求最大正整数
;
(3)是否存在互不相等的正整数
、
、
,使
、
、
成等差数列且
、
、
成等比数列,如果存在,请给出证明;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7643e8b7aa32ebf299048417a94432dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fa34d5a86d929757c2bc3db1a51e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f92693c8b5e2828929376a6fbb8e638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)是否存在互不相等的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb10dd730b827d3ec05aebe8c18c9e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff1721a696504d02a4c4b20e5ba7f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07812c89c11b5cb96c2eb573e681cbd3.png)
您最近一年使用:0次
2020-07-26更新
|
352次组卷
|
10卷引用:广东省茂名市电白区2018-2019学年高一下学期期中数学试题
广东省茂名市电白区2018-2019学年高一下学期期中数学试题江苏省南通市如皋中学2017-2018学年第一学期高三第二次阶段测试12月数学试题湖南省长沙市长郡中学2019-2020学年高三10月月考数学(理)试题湖南省长沙市长郡中学2019-2020学年高三上学期第二次月考理科数学试题江西省抚州市临川第一中学2019-2020学年高一下学期开学考试数学试题江苏省南通市2019-2020学年高三上学期开学模拟考试数学试题福建省永泰一中2021届高三上学期数学月考试题(已下线)专题07 《数列》中的最值问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)江西省景德镇一中2021-2022学年高一(19)班下学期期中考试数学试题广东省广州市第十七中学2023-2024学年高二下学期期中考试数学试卷
7 . 已知曲线C:
,其中
.
(1)求证:曲线C都表示圆,并且这些圆心都在同一条直线上;
(2)证明:曲线C过定点;
(3)若曲线C与x轴相切,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69169b830e66bae7ffffd41994c58ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5371fa518863c0d328d90b1e8d1c2deb.png)
(1)求证:曲线C都表示圆,并且这些圆心都在同一条直线上;
(2)证明:曲线C过定点;
(3)若曲线C与x轴相切,求k的值.
您最近一年使用:0次
2018-08-26更新
|
1177次组卷
|
2卷引用:广东省茂名地区2017-2018学年高二上学期期中数学(文)试题
2011·广东茂名·一模
8 . 已知数列
满足
,且
.
(Ⅰ)求证:数列
是等差数列,并求通项
;
(Ⅱ)若
,且
,求和
;
(Ⅲ)比较
与
的大小,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2d4ee4ca59ee21a52cdc88b8a7f994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a507879ed62acd7cfec1dbbfe91c1.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d17a1ac79d2fbc8481e319a64c11e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6372af2da3bc6ce6cda193a79a88c975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af884c9717e1584d130525fdda61815.png)
(Ⅲ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855e9b353277395dbfcea8e568182ea.png)
您最近一年使用:0次
解题方法
9 . 如图,在三棱柱
中,
,
,
,
平面
,
为
的中点,
为线段
上的动点.
为中点时,求证:
平面
;
(2)当
时,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4957406b21df59fdf7fa184752287b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4dda7809e1730bd133b0fd0deac685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89195bacd53d43195e70c12b5cfa041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd19c4db61254be8512edf741bf9f978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c529e5f1ddc9beb8b9b8c8e4ca8bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a0a3bb566b5d2404e4bb823abddfa9.png)
您最近一年使用:0次
10 . 已知集合
,其中
且
,
,若对任意的
,都有
,则称集合A具有性质
.
(1)集合
具有性质
,求m的最小值;
(2)已知A具有性质
,求证:
;
(3)已知A具有性质
,求集合
中元素个数的最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f12d3cd8f71a493b992647877b7da96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a80c5e31db0cd36e415229685de33e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8ecc8eb8eb4e2509897fcbff92db49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a578e8271c92160a8914460b09bfd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24a572b923f59906ebc90d3aa311cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e86a882ef57f44f0ad22836079afe1.png)
(1)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5892d36ab3e0df852a14b28a36296d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700537ac93b9dddbeb05d74067a03666.png)
(2)已知A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa9b9ef8fafe39ef9982a63a82590d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68dc3bd653ea503d500677612629ac8.png)
(3)已知A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa9b9ef8fafe39ef9982a63a82590d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次