解题方法
1 . 如图,在直三棱柱
中,
为
的中点,点
分别在棱
和棱
上,且
.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9032b9800022c2f661217bbe4ee6d314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3648c864f9f58da1dbb166fee84cfeaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0ecf394142be16e4d62b450ef7f2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383bc7dd1960c2892a37ec0a90119556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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解题方法
2 . 在三棱锥
中,
平面
,
,
,
,
分别是棱
,
,
的中点,
,
,则直线
与平面
所成角的余弦值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
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名校
解题方法
3 . 如图,弧AEC是半径为
的半圆,AC为直径,点
为弧AC的中点,点
和点
为线段AD的三等分点,平面AEC外一点
满足
平面
.
;
(2)求点
到平面FED的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b5a90e556da12d63b7f481bd8e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee332f9a2d473022aeb62e79cd8af705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fe5c17d533c3bd30d6c32cbe94815c.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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解题方法
4 . 如图,在空间直角坐标系
中,正方形
与矩形
所在平面互相垂直(
与原点
重合),
在
上,且
平面
,则
点的坐标为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/4/7f81f22c-3080-4950-b4eb-f0de029f279f.png?resizew=187)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbc4482145feccd25000e1ab5ee0a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/4/7f81f22c-3080-4950-b4eb-f0de029f279f.png?resizew=187)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 如图,在直三棱柱
中,
,
为
的中点.
到平面
的距离.
(2)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352778470650c08ef29deccd03c202b9.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31228c7fd89c98d6235ad993d51d413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
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解题方法
6 . 若不等式
(其中
)的解集中恰有一个整数,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245ad3cdbf4c9e7061fe464e9cd795f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d217c7b12e12e5fb67472452518859ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-05-31更新
|
426次组卷
|
2卷引用:甘肃省兰州第一中学2023-2024学年高二下学期4月期中数学试题
名校
7 . 在空间直角坐标系
中,点
关于x轴对称的点的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1873c5e3346880fae651b32776642d08.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 作为上海市副中心之一,徐汇区的建设不仅是上海市发展战略的关键节点,也肩负着医治上海市“大城市病”的历史重任,因此,徐汇区的发展备受瞩目.2017年发布的《上海市徐汇区统计年鉴(2017)》显示:2016年徐汇区全区完成全社会固定资产投资939.9亿元,比上年增长
,下面给出的是徐汇区2011~2016年全社会固定资产投资及增长率,如图一.又根据徐汇区统计局2018年1月25日发布:2017年徐汇区全区完成全社会固定资产投资1054.5亿元,比上年增长
.
(2)通过计算2011~2017这7年的平均增长率约为
,现从2011~2017这7年中随机选取2个年份,记X为“选取的2个年份中,增长率高于
的年份的个数”,求X的分布列及数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c717a4d3ebb93976aa865e09bcbe90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56c6def59a2f032873442ffe5742e1f.png)
(2)通过计算2011~2017这7年的平均增长率约为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e925ad9bcf419c237ad5ee26c890b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e925ad9bcf419c237ad5ee26c890b69.png)
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9 . 对于三次函数
.定义:①
的导数为
,
的导数为
,若方程
有实数解
,则称点
为函数
的“拐点”;②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
恒成立,则函数
的图象关于点
对称.
(1)已知
,求函数
的“拐点”
的坐标;
(2)检验(1)中的函数
的图象是否关于“拐点”
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abde3621d19a60d8b0cad42c06d8891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5f97843013ef486e10f66543562a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
10 . 若函数
的导函数分别为
,满足
且
,则称c为函数
与
的一个“好位点”,记作“C点”.
(1)求
与
的“C点”.
(2)判断函数
与
是否存在“C点”,若存在,求出“C点”,若不存在,请说明理由.
(3)已知函数
,若存在实数
,使函数
与
在区间
内存在“C点”,求实数q的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53b75fa1fb33883c267d68cf329b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33ad170e5cd38220229a78c0c587100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3280a5562b30d78418eaa12eef4075fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e10aefd603b8d01ca3356787be8da0.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc4bf8b5b2a018b4a035823c10e2a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe8684da8476dea3c8d58637f1392ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f23debd9399295609268cf9c800532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
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