名校
解题方法
1 . 已知等差数列
的前
项和为
,
,
.
(1)求
的通项公式;
(2)证明:
.
![](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/878c70d9a2c8da673f5cb88d26f7d16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf9f45329bae09f13ebc5a7fd2788a5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83dfb450d025aa482277a23dae8203b.png)
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2022-12-08更新
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1987次组卷
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10卷引用:新疆昌吉州行知学校2023届高三下学期第一次月考数学(文)试题
解题方法
2 . 从①AB⊥BC;②直线SC与平面ABCD所成的角为60°;③△ACD为锐角三角形且三棱锥S﹣ACD的体积为2这三个条件中任选一个,补充在下面的问题中,并完成解答.
如图,在四棱锥S﹣ABCD中,底面ABCD是菱形,SA⊥平面ABCD,E,F分别为AB,SC的中点.
(1)求证:直线EF∥平面SAD;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb9a768239f8efec81d9ef718c585c8.png)
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2022-12-05更新
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223次组卷
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3卷引用:新疆伊宁县第二中学2022-2023学年高二上学期期中考试数学(理)试题
名校
解题方法
3 . 在平面直角坐标系
中,已知点
在抛物线
上,圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
,
为圆
上的动点,求线段
长度的最小值;
(2)若点
的纵坐标为4,过
的直线
与圆
相切,分别交抛物线
于
(异于点
),求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2022-12-11更新
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3卷引用:新疆维吾尔自治区乌鲁木齐市第四十中学2023届高三下学期4月月考理科数学试题
名校
解题方法
4 . 如图,在正方体
中,E为
的中点,F为
的中点.
(2)求直线DE,BF所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
(2)求直线DE,BF所成角的余弦值.
您最近一年使用:0次
2022-11-04更新
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8卷引用:新疆维吾尔自治区伊犁哈萨克自治州霍城县江苏中学2022-2023学年高二上学期期中考试数学试题
新疆维吾尔自治区伊犁哈萨克自治州霍城县江苏中学2022-2023学年高二上学期期中考试数学试题贵州省黔东南六校联盟2022-2023学年高二上学期期中联考数学试题(A)贵州省黔东南六校联盟2022-2023学年高二上学期期中联考数学试题(B)河南省平顶山市叶县高级中学2023-2024学年高二上学期10月月考数学试题山西省朔州市怀仁市第一中学校2023-2024学年高二上学期第三次月考(11月)数学试题(已下线)高二上期中真题精选(压轴60题30个考点专练)【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)甘肃省武威市天祝一中、民勤一中2023-2024学年高二下学期5月期中考试数学试题云南省曲靖市宣威市第九中学2023-2024学年高二下学期第二次月考数学试卷
解题方法
5 . 如图,在
中,
,
,点
是
的中点,点
在
上,且
,求证:
、
、
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9656da701e229facaa1a5be081a4ccf.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/481ba75a-e05f-4b00-b959-3561eccd0398.png?resizew=168)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
.
(1)证明函数
为奇函数;
(2)解关于t的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34d64a7bea0629324b9105d94556ff.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解关于t的不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a655b42b5f8eb3cfbabf2f31170cd553.png)
您最近一年使用:0次
2022-12-28更新
|
1168次组卷
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8卷引用:新疆英吉沙县实验中学2024届高三上学期期中考试复习数学试题(四)
7 . 已知
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed4485745f1d259a3953c242b9cf2.png)
(1)求实数
的值;
(2)判断此函数的奇偶性并证明;
(3)判断此函数在
的单调性(无需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7355cbf9bdb3d727e968c0bb642bd1d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed4485745f1d259a3953c242b9cf2.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)判断此函数的奇偶性并证明;
(3)判断此函数在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3501cffd2b6c90c22a7d78b36493106.png)
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2022-09-12更新
|
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2卷引用:新疆柯坪县柯坪湖州国庆中学2021-2022学年高二下学期期末考试数学(理)试题
8 . 定义:在数列
中,若存在正整数
,使得
,都有
,则称数列
为“
型数列”.已知数列
满足
.
(1)证明:数列
为“3型数列”;
(2)若
,数列
的通项公式为
,求数列
的前15项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2627ec0b75380530d2df867be0ab1f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33362cb770e46d6af6268e1d7999d2a2.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ff259bff098430a6512d0e4f6fb2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973d17cd50a4905164d29b8449fafd52.png)
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2023-01-13更新
|
756次组卷
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7卷引用:新疆奎屯市第一高级中学2022—2023学年高二下学期期中考试数学试题
名校
9 . 如图,正三棱柱
中,D是
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8472e092-2492-4566-a4d3-e8c2c0f3cb13.png?resizew=145)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4639a9dc0bc99101cbde59fef04b4a2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8472e092-2492-4566-a4d3-e8c2c0f3cb13.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1006895256aad863fb283f5ecd1793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
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2023-01-12更新
|
568次组卷
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6卷引用:新疆阿勒泰地区2022-2023学年高二上学期期末联考数学试题
新疆阿勒泰地区2022-2023学年高二上学期期末联考数学试题广东省广州空港实验中学2022-2023学年高二上学期期末数学试题湖南省长沙市浏阳市第一中学2022-2023学年高二下学期入学考试数学试题重庆市乌江新高考协作体2023-2024学年高二上学期期中学业质量联合调研抽测数学试题广东省江门市鹤山市纪元中学2023-2024学年高二上学期期中数学试题(已下线)期末真题必刷常考60题(32个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
10 . 如图,在三棱柱
中,侧面
为矩形,平面
平面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/f950cd55-f20a-4155-ad11-690d248969e2.png?resizew=234)
(1)求证:
平面
;
(2)若侧面
是正方形,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/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047f00a89d08e79d45adde46af70c9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddef39ef9ed3da136c4ed8b5d28b73e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/f950cd55-f20a-4155-ad11-690d248969e2.png?resizew=234)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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2022-12-04更新
|
542次组卷
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4卷引用:新疆阿克苏市实验中学2022-2023学年高二上学期期末考试数学试题