21-22高一·全国·单元测试
名校
1 . 已知函数f(x)=ax﹣2(a>0且a≠1).
(1)求证函数f(x+1)的图象过定点,并写出该定点;
(2)设函数g(x)=log2(x+2)﹣f(x﹣1)﹣3,且g(2)
,试证明函数g(x)在x∈(1,2)上有唯一零点.
(1)求证函数f(x+1)的图象过定点,并写出该定点;
(2)设函数g(x)=log2(x+2)﹣f(x﹣1)﹣3,且g(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c70c0c5a061195b9941796b6a9acc4.png)
您最近一年使用:0次
2022-04-12更新
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1217次组卷
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4卷引用:云南省曲靖市会泽县大成高级中学2022-2023学年高二上学期开学数学试题
云南省曲靖市会泽县大成高级中学2022-2023学年高二上学期开学数学试题山东省青岛第一中学2022-2023学年高二上学期期初考试数学试题河北省石家庄市十五中2021-2022学年高一下学期3月开学考数学试题(已下线)专题4.12 指数函数与对数函数全章综合测试卷-2021-2022学年高一数学举一反三系列(人教A版2019必修第一册)
名校
解题方法
2 . 已知圆C:
和直线l:
相切.
(1)求圆C半径
;
(2)若动点M在直线
上,过点M引圆C的两条切线MA、MB,切点分别为A、B.
①记四边形MACB的面积为S,求S的最小值;
②证明直线AB恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dceb22241e283787a43ac2b006ee56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b905d12adb1d83dd79b0b6512a32ab.png)
(1)求圆C半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)若动点M在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446ffa300bde93a7f64368cb43bd3551.png)
①记四边形MACB的面积为S,求S的最小值;
②证明直线AB恒过定点.
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2024-04-14更新
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408次组卷
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3卷引用:云南省昆明市官渡区2022-2023学年高二上学期期中联考数学试卷
3 . 如图所示,已知正方体
的棱长为
分别是
的中点,
是
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/d13caa2e-602a-4bd1-81d1-18b5bc3d932c.png?resizew=174)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89952953873ddf693370dedd910d86be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c4bf3d636b63efd9cbc1b0de58f8be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520e213ecdc97d202c37ca8356a979fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/d13caa2e-602a-4bd1-81d1-18b5bc3d932c.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c08b9a48b3f89132f323efcdb014430.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becf2941e15d668d93ea6ed980afd0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c08b9a48b3f89132f323efcdb014430.png)
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解题方法
4 . 在四棱锥
中,底面
是直角梯形,
,E为
的中点,
是等边三角形,平面
平面
,且
.
(1)求证:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/70c66b94f6bc54b0c75063052410cb4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78aafccd397e9c88a567abf4993d40f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/68b81a3d-3a6d-4cbc-b0bd-2b81a7606d76.png?resizew=190)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
5 . 如图,在三棱锥
中,
为正三角形,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/28127681-d04b-4d6c-bf58-2852053953be.png?resizew=168)
(1)求证:
;
(2)若
是
的中点,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9c515dc5337d5ed8afe3f81b68c57a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/28127681-d04b-4d6c-bf58-2852053953be.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2023-12-11更新
|
1478次组卷
|
7卷引用:云南省沧源佤族自治县民族中学2021~2022学年高二上学期期末考试数学试题
云南省沧源佤族自治县民族中学2021~2022学年高二上学期期末考试数学试题云南省昆明市第三中学2023-2024学年高二下学期第一次综合测试数学试卷陕西省渭南市高级中学2023-2024学年高二上学期12月月考数学试题福建省龙岩市第一中学2023-2024学年高二上学期第三次月考数学试题(已下线)高二上学期数学期末模拟卷(一)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)6.3 空间向量的应用 (5)江西省宜春市丰城市第九中学2023-2024学年高二上学期期末考试数学试题
6 . 在直三棱柱
中,平面
平面
.
(1)求证:
;
(2)
,
,
为
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/b0a719ac-f72f-43a6-b8ad-a1c78199071c.png?resizew=137)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0830c440cb5f1b816d17dcdebdba71a3.png)
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7 . 记
为各项均为正数的等比数列
的前
项和,已知
.
(1)求数列
的通项公式
;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/cf0c2df3f977803ae33c8eac13afdea6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e473533450492900779dc8743cc98c8.png)
您最近一年使用:0次
解题方法
8 . 如图,三棱柱
的所有棱长都是
平面
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/342c09f5-4ce8-48d5-982b-d54d996262a5.png?resizew=172)
(1)求证:平面
平面
;
(2)在线段
(含端点)上是否存在点
,使点
到平面
的距离为
?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fdbbb4d0281a75bb9870ce232b56956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ab05980824d7403b26cc3d3aa5436f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d06f8edd1a1f18ca2dae700c6a29ab4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/342c09f5-4ce8-48d5-982b-d54d996262a5.png?resizew=172)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036a0d3b3c70d41060bc441ddd8003fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
您最近一年使用:0次
名校
9 . 如图,三棱柱
的侧棱与底面垂直,
,点
是
的中点.
;
(2)求
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/96fa89d526f7fa47b7565326cffbfd80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4cdc3a083d1263634d510f172dab09.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc7e774e4ae40c23bf4ceed179230ca.png)
您最近一年使用:0次
2024-03-29更新
|
1203次组卷
|
4卷引用:云南省沧源佤族自治县民族中学2022-2023学年高二上学期教学测评月考(二)数学试题
云南省沧源佤族自治县民族中学2022-2023学年高二上学期教学测评月考(二)数学试题江苏省淮安市金湖中学,清江中学,涟水郑梁梅高级中学等2023-2024学年高二下学期4月期中数学试题重庆市巴南育才实验中学校2023-2024学年高二下学期期中质量监测数学试题(已下线)专题06 空间直线﹑平面的垂直(一-《知识解读·题型专练》(人教A版2019必修第二册)
名校
10 . 如图,在四棱锥
中,
,
平面
,底面
为正方形,
,
分别为
,
的中点.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1365206d14224e0b2d40a7bd8b7965ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/578e3534-c0e1-4c0f-8a35-d416eab64d16.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
您最近一年使用:0次
2023-10-17更新
|
389次组卷
|
12卷引用:云南省砚山县第三高级中学2021-2022学年高二上学期期末考试数学试题
云南省砚山县第三高级中学2021-2022学年高二上学期期末考试数学试题云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(B卷)黑龙江省哈尔滨市第九中学校2020-2021学年高二上学期期中考试数学(理)试题天津市河西区梧桐中学2020-2021学年高二上学期第一次学情调研数学试题福建省尤溪县第五中学2021-2022学年高二上学期第一次月考数学试题北京市朝阳区北京工业大学附属中学2023-2024学年高二上学期10月月考数学试题2020届北京市高考适应性测试数学试题西藏拉萨市2020届高三第二次模拟考试数学(理)试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)专题20 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)北京师范大学亚太实验学校2021届高三上学期期中数学试题北京市第四十三中学2021届高三1月月考数学试题