名校
解题方法
1 . 记
.
(1)若
,求
和
;
(2)若
,求证:对于任意
,都有
,且存在
,使得
.
(3)已知定义在
上
有最小值,求证“
是偶函数”的充要条件是“对于任意正实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80225e12934cd8d4ffc73d5fad815d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1b9f62690647a1597f4000ad5a64b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28034dcafe542a98d95d4504ad7d8a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4def7108b0a2338f07a0143b00b48271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3761d7ab4d00c91177fdbde67af36089.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625e9d3c298a595678933b59583632c2.png)
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2 . 下列命题正确的是( )
A.复数![]() ![]() |
B.复数![]() ![]() |
C.复数![]() ![]() |
D.已知![]() ![]() ![]() |
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3 . 小王去秦始皇兵马俑博物馆游玩,买了8个不同的兵马俑纪念品,其中将军俑3个,骑兵俑3个,跪射俑2个,将这8个纪念品排成一排,要求同种类型相邻,则不同的排法共有( )种.
A.48 | B.72 | C.216 | D.432 |
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解题方法
4 . (1)计算
;
(2)已知关于
的方程
有实数解,求纯虚数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6e91f961e6c375860251f88519329.png)
(2)已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752a8ba32cdcfb5d8e77f2f84d5acdb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 小明将一套斜边相等的三角板拼在一起,构成四边形
(如图1),其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6c64254d7fc695596dfb4206d610ab.png)
的长
(2)求
的值
(3)如图2,四边形
中,
,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6c64254d7fc695596dfb4206d610ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc0f23e79770ac886bf6c4f5937d0dc.png)
(3)如图2,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c5b4a8729b03d974a83d53141a2938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc0f23e79770ac886bf6c4f5937d0dc.png)
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6 . 已知数列
的通项公式为
,
,在
中依次选取若干项(至少3项)
,
,
,
,
,
,使
成为一个等比数列,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48873417a7667f628e5c7052c96f416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8ebcd5b8f8ae04513834a70575816f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3aaabba90eefb861068bf014f9d0b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d745f422af19d28303b7fbc3a08a9ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b625d02d9054af978b5fb6ec9bee787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
A.若取![]() ![]() ![]() |
B.满足题意的![]() |
C.在![]() ![]() |
D.如果把![]() ![]() |
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解题方法
7 . 下列说法正确的是( )
A.![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.![]() ![]() ![]() |
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8 . (多选)已知数据
,若去掉
后剩余6个数的平均数比7个数的平均数大,记
,
,
,
的平均数与方差为
,
,记
,
,
,
的平均数与方差为
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5587aea6e1e8fc73232325868e982d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848dac3d6db7c23c58f399970b3f9b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbc29b47b83fdc5368770b7b1acb439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9b42973c53907f09f2de384c42fc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20c1e5866f81c045a596079ac4a7671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e382c9bafdc5d09498b92f5248d01c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0da8a9d862e0005c44a8cb8fd262bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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2024-03-07更新
|
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|
2卷引用:贵州省贵阳市清华中学2023-2024学年高二下学期4月月考数学试题
9 . 折纸既是一种玩具,也是一种艺术品,更是一种思维活动.如图,有一张直径为4的圆形纸片,圆心为
,在圆内任取一点
,折叠纸片,使得圆周上某一点刚好与点
重合,记此时的折痕为
,点
在
上,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f68815ee48560500c184da6f76bced7.png)
A.5 | B.4 | C.3 | D.2 |
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|
379次组卷
|
7卷引用:贵州省贵阳市清华中学2023-2024学年高二下学期4月月考数学试题
名校
解题方法
10 . 球面三角学是研究球面三角形的边、角关系的一门学科.如图,球
的半径为
,
,
,
为球面上三点,劣弧
的弧长记为
,设
表示以
为圆心,且过
,
的圆,同理,圆
,
的劣弧
,
的弧长分别记为
,
,曲面
(阴影部分)叫做曲面三角形,若
,则称其为曲面等边三角形,线段
,
,
与曲面
围成的封闭几何体叫做球面三棱锥,记为球面
.设
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7874b563ba2f6954d767ef8d14942f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/a9569bb48ec5f56fb51930fe2fadd751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb63917915784933ee066a41d455eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbec8352ce3dbfbf3b173045d0ba8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9468931aa396efbdd7f50cc79f95f392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca45259311faa9f0a9cc61bc36b9a7c.png)
A.若平面![]() ![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若平面![]() ![]() ![]() |
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2024-02-23更新
|
1056次组卷
|
5卷引用:贵州省贵阳市清华中学2023-2024学年高二下学期4月月考数学试题