名校
解题方法
1 . 如图,在四棱锥
中,底面
为正方形,
平面
,
,
为
中点,
为
中点,
为线段
上动点.
为
中点,求证:
平面
;
(2)证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a4950a6e4202efd609507964af238b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19129982fd8389238b303e091bd94c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
2 . 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)
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3 .
个有次序的实数
所组成的有序数组
称为一个
维向量,其中
称为该向量的第
个分量.特别地,对一个
维向量
,若
,
,称
为
维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在14个两两垂直的14维信号向量;
(3)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27bb33ccdad573e2b2b0e7facbcca07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d038f2967ee70acc7777c32c8b43c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9925b25d5708cbd87f69cca1b5c66c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143f87bed8eee1f43d3e67be747b7d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcadd9ce3631b6e230fe7b21a0719c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e0d46fb5c7c978e4fe9c23f33ba151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143f87bed8eee1f43d3e67be747b7d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777dac26504cae699de348ec1df9dc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8346ea7024dd0c905cc4c80cb16dc6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在14个两两垂直的14维信号向量;
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cae65660b220cc622b87ed9eea092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2024-02-23更新
|
697次组卷
|
6卷引用:广东韶关实验中学2023-2024学年高一下学期3月月考数学试题
广东韶关实验中学2023-2024学年高一下学期3月月考数学试题(已下线)模块一 专题3 平面向量的应用(B)(已下线)模块一专题3 《平面向量的应用》B提升卷(苏教版)(已下线)模块三专题4大题分类练(专题3 平面向量数量积)【高一下人教B版】(已下线)高一数学下学期期中模拟卷(新题型)-同步题型分类归纳讲与练(人教A版2019必修第二册)湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)
4 . 已知
为坐标原点,
,
.
(1)判断
的形状,并给予证明;
(2)若
,求证:
、
、
三点共线;
(3)若
是线段
上靠近点
的四等分点,求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51116e96f4c35d90677e91e0aa914111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9612a17c77d5d6ded6123e12f9c8914.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bdb30cad5418d2b634e697d2d8e46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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5 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5ff2705eb737adef9a6dc70559d79.png)
(1)已知
为单调递增函数,请判断
的单调性,并用单调性定义证明;
(2)若
,求证:方程
在区间
上有且仅有一个实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72eb501bf5451af98ab894176fb2a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5ff2705eb737adef9a6dc70559d79.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b67287da8b741b449aa283c688fd080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
.
(1)求证:
是奇函数;
(2)判断
在
上的单调性,并证明;
(3)已知关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47024cb8062925596b0b902917d3a779.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa6024d1514f7598e197ad3d7f8d720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-11-09更新
|
942次组卷
|
2卷引用:广东省广州市育才中学2023-2024学年高一上学期期中数学试题
23-24高一上·广东深圳·期中
名校
7 . 已知函数
的图像过点
.
(1)求实数
的值;
(2)判断函数的奇偶性并证明.
(3)求证:函数
在
上是减函数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acce899605cc4c8f3edd448d3698dbff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ce2f5e22175e3ff8ab5e0afca58f9c.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断函数的奇偶性并证明.
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ce82779a834a6871c96515eaaa5571.png)
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解题方法
8 . 在数学中,不给出具体解析式,只给出函数满足的特殊条件或特征的函数称为“抽象函数”.我们需要研究抽象函数的定义域、单调性、奇偶性等性质.对于抽象函数
,当
时,
,且满足:
,均有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367936b458618efb6b2eadc843e5d6ba.png)
(1)证明:
在
上单调递增;
(2)若函数
满足上述函数的特征,求实数
的取值范围;
(3)若
,求证:对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6571b33b56c6cd88f2f6e091031bcf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367936b458618efb6b2eadc843e5d6ba.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c5f8b7a1a268c904d04356f0d1b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be9b79f42bbf0de1851607050c3e8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219598f1289ddb370d632ea141731d52.png)
您最近一年使用:0次
名校
解题方法
9 . (1)已知函数
,
,若
,都有
,求证:
为奇函数.
(2)设函数
定义在
上,证明:
是偶函数,
是奇函数.
(3)已知
是定义在
上的函数,设
,
,试判断
与
的奇偶性;根据
,
与
的关系,你能猜想出什么样的结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c7798e8266916b8501e3837194407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e36e45821cc161584ad64043772227a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c3cfb21d60dc4bea0083dbbba146c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1836fe79a57e10d585d267c50d67d421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625e475c73bdfd992254680dc7d6b7f.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c9abee0619dcc5cd3bf7f40c4edadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2ea8a2a6013eb18b53ea3aeb6ef56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-08-20更新
|
252次组卷
|
2卷引用:广东省广雅中学2023-2024学年高一上学期期中数学试题
解题方法
10 . 已知函数
.
(1)当
为何值时,
为偶函数,说明理由;
(2)若
,证明:
;
(3)若
,求证:
有两个不相等的实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caef851640adfb3514851b0225e7114b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b896371aa9ee32182684a06d72cf63.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa6e9df5ed46e9a0ddba84d4b82813b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
您最近一年使用:0次
2023-08-06更新
|
154次组卷
|
2卷引用:广东省佛山市南海区2022-2023学年高一上学期期中数学试题