1 . 已知:如图,等腰三角形
中,
,
,直线
经过点
(点
、
都在直线
的同侧),
,
,垂足分别为
、
.
(1)求证:
;
(2)请判断
、
、
三条线段之间有怎样的数量关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13b505788d3d02bf232ac637fc3a8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e72d26eae9a5470ac982541c609b109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/b7efb7d9-2f61-428f-9220-09f39fa06f0b.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e9e5200fe1aed46fc8dc8fcdd916d5.png)
(2)请判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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解题方法
2 . (1)求函数
的单调区间.
(2)用向量方法证明:已知直线l,a和平面
,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b6a91900d0dfa6296cdee22fdd6fe6.png)
(2)用向量方法证明:已知直线l,a和平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c29f79e8e51e7c35213df9ebe697bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d2a947e3fdc214d40a7d3f54679a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9b2c3117321788078867bd0701743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad25ad7785af488a004cae4436019ff.png)
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2023高一·全国·专题练习
名校
解题方法
3 . 在集合论中“差集”的定义是:
,且
(1)若
,
,求
;
(2)若
,
,求
;
(3)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f4bcaec7926363d8f77c6e773920d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b998f1e3675e0fa3b790c416a751af63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e6ad1166c7625e63b80e75b2fb1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2755a85584173902f146eacf40102723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cb7961d2d6957cfd6b4af403450e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6846ad147da3f53658602eade09631d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7321a9fa7a6ef6be6e40c96709763930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6846ad147da3f53658602eade09631d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe3404ade72e644b48d19572c173c93.png)
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名校
解题方法
4 . 甲和乙分别记录了从初中一年级(2017年)到高中三年级(2022年)每年的视力值,如下表所示
(1)计算乙从2017年到2022年这6年的视力平均值;
(2)从2017年到2022年这6年中随机选取2年,求这两年甲的视力值都比乙高0.05以上的概率;
(3)甲和乙的视力平均值从哪年开始连续三年的方差最小?(结论不要求证明)
2017年 | 2018年 | 2019年 | 2020年 | 2021年 | 2022年 | |
甲 | 4.94 | 4.90 | 4.95 | 4.82 | 4.80 | 4.79 |
乙 | 4.86 | 4.90 | 4.86 | 4.84 | 4.74 | 4.72 |
(2)从2017年到2022年这6年中随机选取2年,求这两年甲的视力值都比乙高0.05以上的概率;
(3)甲和乙的视力平均值从哪年开始连续三年的方差最小?(结论不要求证明)
您最近一年使用:0次
2023-01-05更新
|
480次组卷
|
2卷引用:北京市西城区2022-2023学年高一上学期数学期末试题
名校
5 . 判断下列事件是必然事件,还是不可能事件,并证明.
(1)直线y=kx+2k+3经过定点;
(2)直线y=kx-3k和圆
一定有两个交点;;
(3)如果∠a为锐角,则
的结果一定是1.
(1)直线y=kx+2k+3经过定点;
(2)直线y=kx-3k和圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
(3)如果∠a为锐角,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5df6cacabf99ee420a7a294ede4571.png)
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真题
6 . 写出余弦定理(只写一个公式即可),并加以证明.
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7 . 某公司出产了一款美观实用的筷子笼,如图,是由与圆柱底面成一定角度的截面截圆柱所得.如果从截面的最底端到最高端部分还原圆柱,如下图所示,AB,
分别为圆柱
底面直径,
,
为圆柱的母线,
,过
的平面
截圆柱且与底面所在平面交于直线
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/e8c50ced-4ea3-475f-92fa-a78be6572be7.png?resizew=511)
(1)证明:
;
(2)若底面有一动点M从A点出发在圆O上运动,过动点M的母线与截面
交于点N,设
,
,其中
.
①求
与
的函数关系;
②将圆柱
侧面沿母线
剪开并展平,请在所给的展开图中画出平面
截圆柱侧面的截痕,并建立适当的平面直角坐标系直接 写出其解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3671adea94a33848afff9b2edb6a902e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae781496bb5bc79b67abced9aa3cd0c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/e8c50ced-4ea3-475f-92fa-a78be6572be7.png?resizew=511)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa812513cb17ffa7901d1f5e3fb25c5.png)
(2)若底面有一动点M从A点出发在圆O上运动,过动点M的母线与截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d685845e1baa7e66d2502eebfcbb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914d142641c85ea5454b1eb05ac4204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d7581e52d1fa9eb225928fabd57fe9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②将圆柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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8 . 如图,在
中,
为
的角平分线,将线段
绕点
顺时针方向旋转使点
刚好落在
的延长线上的点
处,此时作
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/121491d3-0e61-495b-9710-cb416923672e.png?resizew=212)
(1)求证:
;
(2)求证:
;
(3)若
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7018c4694e634448e2480b0de7dc8a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7cce4c2fe0717b72987226628f3528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/121491d3-0e61-495b-9710-cb416923672e.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f954855744e0a096adec767545ae3d3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148def1286d8600dccd565132761575e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76a31d25188ad7e6d0cca77a2d7a465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
名校
解题方法
9 . 对于实数构成的集合
.若对任意
都有
(其中“
”表示普通的乘法运算),则称集合
对“
”是封闭的.
(1)已知集合
,判断
是否属于集合
;
(2)在(1)的条件下,若
,证明
的充要条件是
;
(3)若集合
对“
”都是封闭的,试判断
是否对“
”封闭,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8af42f2ec410ad1b28be69d3415ed10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9f1ff137e76626b7b608cef7c36349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50dae68b646f975a8a0c6bed67d028ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57ed82958abb00776e75987aa62d723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ecef225b27b5857d2d76fbe5b34982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff58fdfe14af9fb8aa0e0cf0d60853a.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a3375139541ed61929fa658f16bb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
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真题
10 . 如图,
为圆的直径,P、C为圆上两点,连
,过C作
的垂线与
和
的延长线依次相交于A,B,D,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbbb13ac6a4773193f76ab21be9fbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098f2d934743e32a3668dd5e612716e3.png)
![](https://img.xkw.com/dksih/QBM/2022/11/7/3104399415574528/3104527860924416/STEM/4c16330b778e42d49a67369025ac878e.png?resizew=159)
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