22-23高三上·上海浦东新·开学考试
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解题方法
1 . 设
,其中
,已知
.
(1)求
的最小值;
(2)已知凸四边形
中,
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81dd9885bca00b3a5dcf3f86dec2ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a8c0233f56dabafb54c9e5a18f9e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628ea76f8ab52a325ce3d2c3ca8f969.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知凸四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d892643006733ca580b4b2d9834e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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22-23高三上·上海浦东新·开学考试
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2 . 对开区间
,定义
,当实数集合
为
段(
为正整数)互不相交的开区间
的并集时,定义
,若对任意上述形式的
的子集
,总存在
,使得
,其中
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095747cd995cc4524071c66ab76e5fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fa78977d3830bb863c4df4ba362064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53f84ec1c2416ead2a3f92d05af188a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ca25c7ef458ef1da40d7f1d2d99c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a7792efd7f82bfa7549db4cb6ca761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a593f20de490729bc067552e62661e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8145182f289fbed90bbce4fe773205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
3 . 正四棱锥
的展开图如图所示,侧棱
长为1,记
,其表面积记为
,体积记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e2bf084b-f7e5-47d8-add0-6ed4bfada543.png?resizew=202)
(1)求
的解析式,并直接写出
的取值范围;
(2)求
,并将其化简为
的形式,其中
为常数;
(3)试判断
是否存在最大值,最小值?(写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c55c1c441f921d874702a4f19ed17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9d76fb48eb30e7946cb96047e08206.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e2bf084b-f7e5-47d8-add0-6ed4bfada543.png?resizew=202)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d0adafeb8e5d088e974f1246880055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a296bb758c36b50b102a4ceb2dea42bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(3)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d0adafeb8e5d088e974f1246880055.png)
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2022-07-05更新
|
815次组卷
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7卷引用:上海市洋泾中学2022-2023学年高二上学期期中数学试题
上海市洋泾中学2022-2023学年高二上学期期中数学试题北京一零一中学2021-2022 学年高一下学期期末考试数学模拟试题(一)湖北省郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中2022-2023学年高二上学期10月联考数学试题湖北省五校(郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中)2022-2023学年高二上学期10月月考数学试题湖北省黄石市第二中学2023-2024学年高二上学期9月月考数学试题(已下线)湖南省长沙市雅礼中学2024届高三上学期月考(二)数学试题变式题19-22(已下线)期中测试卷01(测试范围:第10-11章)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
21-22高一下·上海浦东新·期末
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4 . 已知世界上倾斜度最高的摩天大厦坐落于阿联酋的阿布扎比,其倾斜度达到18°,请用弧度表示倾斜度______ .
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5 . 已知正实数C满足:对于任意
,均存在
,使得
,记C的最小值为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757161f2f2668dc65c8574c2a3f3fb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105083fd0315bceb804345eb116f2218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-06-18更新
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2513次组卷
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3卷引用:上海市华东师范大学第二附属中学2023届高三上学期10月月考数学试题
6 . 在△ABC中,角A、B、C所对边的长分别为a、b、c,下列结论正确的是( )
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若△ABC是锐角三角形,![]() ![]() ![]() |
D.若![]() ![]() |
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7 . 在直角坐标系
中,
轴在正半轴上一点
依逆时针方向做匀速圆周运动,若点
一分钟转过角
,
分钟到达第三象限,
分钟回到原来位置,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/5ea1ce5fef40c38080b28d5066ac0e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
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8 . 某动物园喜迎虎年的到来,拟用一块形如直角三角形
的地块建造小老虎的休息区和活动区.如图,
,
(单位:米),E、F为BC上的两点,且
,
区域为休息区,
和
区域均为活动区.设
.
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967900906315776/2968436869840896/STEM/0ee2bbce-9fa9-4749-ad59-80ce77eec527.png?resizew=208)
(1)求
、
的长(用
的代数式表示);
(2)为了使小老虎能健康成长,要求所建造的活动区面积尽可能大(即休息区尽可能小).当
为多少时,活动区的面积最大?最大面积为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0896521d46a6b47c995c58959bc1041b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192155e6a3aade305b76b1eb7c75e30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128021de1e3024a0ef8e70409b08dd30.png)
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967900906315776/2968436869840896/STEM/0ee2bbce-9fa9-4749-ad59-80ce77eec527.png?resizew=208)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)为了使小老虎能健康成长,要求所建造的活动区面积尽可能大(即休息区尽可能小).当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2022-04-29更新
|
734次组卷
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3卷引用:上海市洋泾中学2023届高三上学期开学考试数学试题
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9 . 设实数
.给出如下两个命题,则( ).
①存在x使得
,
,
,
按某种顺序可组成等差数列;
②存在x使得
,
,
,
按某种顺序可组成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77ce9ca93a0634c6302d116bf36439c.png)
①存在x使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66db91bb3be9e2b6ad567774e3699758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c5a05a11f731194a845e68a0479ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada1a099b4cb4863ef1a94927c221ff8.png)
②存在x使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66db91bb3be9e2b6ad567774e3699758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c5a05a11f731194a845e68a0479ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada1a099b4cb4863ef1a94927c221ff8.png)
A.①真②真 | B.①真②假 | C.①假②真 | D.①假②假 |
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10 . 已知
中的内角
满足
,则角
可表示为______ (限定用反三角符号
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c106915873fcb8d6b21c7fa80d393ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f5f59b2d27a6cc1516195eb6711b0f.png)
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