1 . 设数列
的前
项和为
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba83359167d8ca8c9eafa8a23f34a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acac0a395f2315fdfe7014548dbc033.png)
A.![]() | B.![]() |
C.对任意的![]() ![]() | D.对任意的![]() ![]() |
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2 . 如图,在四棱台
中,
平面
,底面
为平行四边形,
,且
分别为线段
的中点.
.
(2)证明:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
平面
.
(3)若
,当
与平面
所成的角最大时,求四棱台
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e658d7985a600629fdf01517fc55c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac18faf9da6221b788020ac0ddf709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fab0d028634166a93c5d80add98dc27.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faec6f7381dbe8daf15b2969f379e3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
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3卷引用:广西重点高中2023-2024学年高一下学期5月阶段性联合调研考试数学试题
名校
3 . 刻画空间的弯曲性是几何研究的重要内容,用曲率刻画空间的弯曲性,规定:多面体顶点的曲率等于
与多面体在该点的面角之和的差,其中多面体的面的内角叫做多面体的面角,角度用弧度制.例如:正方体每个顶点均有3个面角,每个面角均为
,故其各个顶点的曲率均为
.如图,在直三棱柱
中,
,点
的曲率为
分别为
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62837b40813c7cd7959f4e77eeca8a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c9668ea27ff0d5323dbf8c65ddcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df332962ba616c7ef45a0523d410c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53477a5d40457f154d8afe0bcec4a549.png)
A.直线![]() ![]() |
B.在三棱柱![]() ![]() ![]() |
C.在四面体![]() ![]() ![]() |
D.二面角![]() ![]() |
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4卷引用:广西重点高中2023-2024学年高一下学期5月阶段性联合调研考试数学试题
4 . 已知函数
,其中
.
(1)若
,求
在
处的切线方程;
(2)若函数
存在两个极值点
.
(i)求实数a的取值范围;
(ii)当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88d158cacab265da551bdb84fad5318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
(i)求实数a的取值范围;
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e156df320e6b84a4e18961440b1ca078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eec001bfec02deb84bb9f3f24cb50d5.png)
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解题方法
5 . 已知定义域为
的函数
,满足
,且
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2505bf49deefcd20c06fc9059b64a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8718f486c48b09ffd904ddbf1dc7037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cc2d590d74ecaf47de3b501f355ff9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
6 . 现定义“
维形态复数
”:
,其中
为虚数单位,
,
.
(1)当
时,证明:“2维形态复数”与“1维形态复数”之间存在平方关系;
(2)若“2维形态复数”与“3维形态复数”相等,求
的值;
(3)若正整数
,
,满足
,
,证明:存在有理数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d830212489b316bb052455098108e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8299790d98621b87e73212a2ebb91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
(2)若“2维形态复数”与“3维形态复数”相等,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c136aaf9b5dedec254a92ce302f4a70c.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94742ebbb028c50d7a58e3e8f4ab329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35490c12e57ecd91af9934cb17b5c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed110fbfeb14003270a1039ba174d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f02f2606180ffeda602ff9ae747af6f.png)
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2024-05-11更新
|
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3卷引用:广西南宁市第二中学2023-2024学年高一下学期5月月考数学试卷
名校
解题方法
7 . 设函数
是定义在R上的奇函数,对任意
,都有
,且当
时,
,若函数
(
且
)在
上恰有4个不同的零点,则实数a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafce249be1aeee0581417db4ce841db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ea832b11f5a84b9bf3020271480631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900b106c2b44b211c60b0ba9c2cf6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0b226b2da37b802313e88a4cd8f987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77b96fc51eb8a9d03ced254ce8b78be.png)
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名校
8 . 在正三棱柱
中,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7e8dd831f4edc711c0f7d5f078f625.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若往正三棱柱中装水,当侧面![]() ![]() ![]() ![]() |
D.若D是![]() ![]() ![]() |
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9 . 已知对任意平面向量
,把
绕其起点沿逆时针方向旋转
角得到向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb4713985fd15713e52c5001059345c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceeeef52b8eca772c669980b8cda36.png)
叫做把点
绕点
沿逆时针方向旋转
角得到点
.已知平面点
,点
,把点
绕点
沿顺时针方向旋转
后得到点
,则点
的坐标为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bfd8ec5168694a721c9498a68e8640d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb4713985fd15713e52c5001059345c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceeeef52b8eca772c669980b8cda36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4555374420f2770ea23b95ca9dc3b364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1e95fb519f59c46f40e4ab44660073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b36c51be5f4b8ea60b1f8cf9f3c32dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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名校
10 . 如图,在直三棱柱
中,
,
,
,侧面
的对角线交点
,点
是侧棱
上的一个动点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d46c17903078e0b38279353c5430d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
A.直三棱柱的侧面积是![]() |
B.直三棱柱的外接球表面积是![]() |
C.三棱锥![]() ![]() |
D.![]() ![]() |
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2024-04-19更新
|
1064次组卷
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3卷引用:广西南宁市第三中学2023-2024学年高一下学期月考(三)数学试题
广西南宁市第三中学2023-2024学年高一下学期月考(三)数学试题浙江省杭州市西湖高级中学2023-2024学年高一下学期4月期中测试数学试题(已下线)专题6 组合体中的外接与内切问题【练】(高一期末压轴专项)