名校
解题方法
1 . 已知函数
的图象如图所示,则该函数的解析式为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/05488119-12ac-4db5-9244-1e1696648435.png?resizew=179)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/05488119-12ac-4db5-9244-1e1696648435.png?resizew=179)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-11更新
|
454次组卷
|
2卷引用:黑龙江省大庆铁人中学2023-2024学年高一上学期期末考试数学试题
名校
解题方法
2 . 中国古代数学著作《九章算术》中,记载了一种称为“曲池”的几何体,该几何体的上下底面平行,且均为扇环形(扇环是指圆环被扇形截得的部分),现有一个如图所示的曲池,它的高为
,
,
,
,
均与曲池的底面垂直,底面扇环对应的两个圆的半径分别为
和
,对应的圆心角为
,则
与
成角的余弦值为___________ ;以
点为球心,
为半径的球面与曲池上底面的交线长为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0468237bbc0d3df77435d98b817c10c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/a90920f7-d3d6-421e-8756-2d6b1bf9def3.png?resizew=128)
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解题方法
3 . 已知圆
直线
,点
在直线
上运动,直线
分别与圆
相切于点
.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131497b1be0dace1f59d13474d141694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6d2269875c74ebc793c8e4328c77f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
A.四边形![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.直线AB过定点![]() |
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解题方法
4 . 下列命题中,是真命题的是( )
A.![]() ![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
5 . 已知正项等比数列
中,
,
.
(1)求
的通项公式;
(2)在
和
之间插入
个数,使这
个数组成一个公差为
的等差数列,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b12e4642119f14a93a4afa25912f41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48622e094b93b42821e11e4a4f21ed4e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0526bcbb60d5258b461ab634e913212d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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6 . 数列
的通项公式为
,前
项和为
,下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d769bccbcfe1458ef7e63d1c2af451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() ![]() |
B.存在正整数![]() ![]() |
C.存在正整数![]() ![]() |
D.记![]() ![]() |
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7 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/bfa4f03abdc7547d7bb717ce82485dc8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36a1aec898dc75fa9d6f33a59ca35f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9472a54240208537e18535345a2bda94.png)
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8 . 设
是等比数列
的前
项和,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb28d9e94c098eb48d50dbc70995082b.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881eabb3eea4a9a9c8611a9910dbf9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb28d9e94c098eb48d50dbc70995082b.png)
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9 . 关于
的不等式
的解集是
,且
,则实数
的取值范围
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2664a158811bae27b518fa2b96fd51b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfe05b521eb1c6269c3a25ec05992dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9dd5409f7777490aefc775e71292b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://img.xkw.com/dksih/QBM/2024/1/15/3411722549526528/3411739445395456/STEM/17b20b48ef254e989baa02564c9d7f8c.png?resizew=4)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 已知全集为实数集
,集合
,
(1)分别求
,
,
;
(2)已知集合
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa26ede4564b80c035c146272384bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24429c22edcbe1e927dfec17e14b9fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b6709250c8c9bb7a3e77c6abda0317.png)
(1)分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b184e1cedfd0ed92151024de549d6a6.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5988337b7a0798b5d056d98bb60cf32a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6ca098b764e0366d043b69ae9d8f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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