名校
解题方法
1 . 已知数列
中
,关于
的函数
有唯一零点,记
.
(1)判断函数
的奇偶性并证明;
(2)求
;
(3)求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f4d4fa1b049045d58a9571a0709004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072010cccaa77474c07b66816ce4ae92.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f4d4fa1b049045d58a9571a0709004.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f8c399c162dbd37d2aa304a4a3a1fd.png)
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名校
解题方法
2 . 将平面直角坐标系中的一列点
.记为
,设
,其中
为与y轴正方向相同的单位向量若对任意的正整数n,都有
,则称
为T点列.
(1)判断点列
是否为T点列,直接写出结果;
(2)求证
是T点列:
(3)若
为T点列,且
.任取其中连续三点
,证明
为钝角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fa0a4178c2ab8acf3342d228ed8e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f4f7da7655b76971cdf3e11600a9f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869434cabde100f74953780653d3a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88364f251f3d8a14d9784588f45f7acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e972e658495ad2b603e2b11f3d5e20ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f4f7da7655b76971cdf3e11600a9f3.png)
(1)判断点列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf87e7e5ae1e3d45c2ccd73dd8d29a2.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6ec98836c8c456b45ab94f9aa5a7fb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f4f7da7655b76971cdf3e11600a9f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ed0fe3ab3607bcc987be7ba9ae5bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade2b9aa97d71e08923f71c8eba032a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d24dc108423b4ca4d3b94e9779089f73.png)
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3 . (1)已知
均为正数,且
,求证:
;
(2)根据生活常识“淡糖水再加糖会更甜”,请给出类似第(1)小题的命题,并予以证明;
(3)证明:
中,
.(可直接应用第(1);(2)小题的结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa556c0786c4facc7c5c44e8fe9101ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3085495517cf7b77cc88e513fa874cc.png)
(2)根据生活常识“淡糖水再加糖会更甜”,请给出类似第(1)小题的命题,并予以证明;
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452a8c9881d3b55ed7dd7ff08dca2d09.png)
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解题方法
4 . 在如图所示的几何体中,侧面
为正方形,底面
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/9aa4885b-d99d-4fd5-beec-e97d9b1aabd3.png?resizew=190)
(1)求证:
平面
;
(2)线段
上是否存在点
,使
平面
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679a911235fae7f028966b57f150ddee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4020513c097ba34df4b42e297f892cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5867254f6e74a3e31237279cd481f6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/9aa4885b-d99d-4fd5-beec-e97d9b1aabd3.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e51817ee1ebf17c73ed21171bcfc5b5.png)
(2)线段
![](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/05a162b0af925d3b18d0f7e2c3b32dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4291a7c647aaf6d00e48bed030b48c.png)
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名校
解题方法
5 . 如图,直四棱柱
中,侧棱
,底面
是菱形,
,
,
为侧棱
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/da5dd9fe-09c2-44f8-bdaa-17397a8da412.png?resizew=161)
(1)求证:
;
(2)在棱
上是否存在点
,使得二面角
的大小为
?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/da5dd9fe-09c2-44f8-bdaa-17397a8da412.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68263d477443994e54cea454ae5490e.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf29d1e4a907cf155e00c5baaed0f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
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6 . 用分析法证明:若
的三内角
成等差数列,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043714f337a44c343813c4e34f699211.png)
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7 . 证明锐角三角形中正弦定理成立,即在锐角
中,
所对边为
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c1e84aaa7e1b5c1283075b36c72fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1501d4035822b34fcc2378f1e316f159.png)
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11-12高二上·广东·期末
8 . 已知定义域为
的两个函数
、
,对于任意的
、
满足:
且
.
(1)求
的值并分别写出一个
和
的解析式,使它们满足已知条件(不要求说明理由);
(2)证明:
是奇函数;
(3)若
,记
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b8acf40088f0385734c68f7b2747f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a98717f40c32b9ed1a29edc6b9f527.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196c05daecd852ab814377d7fbff32b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79581020e07821a3460c1f14f7867fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efba990f1fca3fe00fb5e0a7fff0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a2335e6b3f9e909d19efee454a76f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f877249646e6c4613e2fcb64990dfd.png)
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9 . 先解答(1)(2),再通过结果类比解答(3).
(1)求证:
;
(2)写出函数
的最小正周期;
(3)定义在
上的函数
满足
(其中
为非零常数),试猜想
是否为周期函数,并证明你的结论.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870b39c0e1e837cee44a5eea25008384.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457eb5e0000350b102d387a80cf3476b.png)
(3)定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4fd86f5e6a24e6caf07d4248c1e308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
10 . 如图,在四棱锥
中,底面
为正方形,
平面
,
为
上的中点.
平面
;
(2)设
,求二面角
的大小.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeab80976db9b4689b9446cda06196a.png)
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2024-04-26更新
|
534次组卷
|
3卷引用:上海市复兴高级中学2023-2024学年高二下学期期中考试数学试卷
上海市复兴高级中学2023-2024学年高二下学期期中考试数学试卷上海市金山中学2023-2024学年高二下学期5月月考数学试卷(已下线)专题03 空间向量及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)