1 . 如图,在四棱锥
中,
⊥平面
,正方形
的边长为
,
,设
为侧棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3b4b1972-387a-4e1f-ba7f-9019f00d6f13.png?resizew=146)
(1)求四棱锥
的体积
;
(2)求直线
与平面
所成角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3b4b1972-387a-4e1f-ba7f-9019f00d6f13.png?resizew=146)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2022-11-23更新
|
532次组卷
|
8卷引用:2019年上海市宝山区高三上学期期末教学质量监测(一模)数学试题
2 . 某校兴趣小组在如图所示的矩形区域
内举行机器人拦截挑战赛,在
处按
方向释放机器人甲,同时在
处按某方向释放机器人乙,设机器人乙在
处成功拦截机器人甲.若点
在矩形区域
内(包含边界),则挑战成功,否则挑战失败.已知
米,
为
中点,机器人乙的速度是机器人甲的速度的
倍,比赛中两机器人均按匀速直线运动方式行进,记
与
的夹角为
.
(1)若
,
足够长,则如何设置机器人乙的释放角度才能挑战成功?
(2)如何设计矩形区域
的宽
的长度,才能确保无论
的值为多少,总可以通过设置机器人乙的释放角度使机器人乙在矩形区域
内成功拦截机器人甲?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e62758f556745c4089a0b178c6f8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d00be47dcb89793f14a2fd10f4c522b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e62758f556745c4089a0b178c6f8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d868a22c50b4ad3dae8e438c9779d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/70768327-a170-4df8-a2bc-9e025e71f719.png?resizew=166)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)如何设计矩形区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
3 . 某公园计划在矩形空地上建造一个扇形花园如图①所示,矩形
的
边与
边的长分别为48米与40米,扇形的圆心
为
中点,扇形的圆弧端点
,
分别在
与
上,圆弧的中点
在
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/42c484aa-8b21-48d3-823e-7ba4dfeb255a.png?resizew=375)
(1)求扇形花园的面积(精确到1平方米);
(2)若在扇形花园内开辟出一个矩形区域
为花卉展览区.如图②所示,矩形
的四条边与矩形
的对应边平行,点
,
分别在
,
上,点
,
在扇形的弧上.某同学猜想:当矩形
面积最大时,两矩形
与
的形状恰好相同(即长与宽之比相同),试求花卉展览区
面积的最大值,并判断上述猜想是否正确(请说明理由).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/42c484aa-8b21-48d3-823e-7ba4dfeb255a.png?resizew=375)
(1)求扇形花园的面积(精确到1平方米);
(2)若在扇形花园内开辟出一个矩形区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
您最近一年使用:0次
2020-05-21更新
|
366次组卷
|
3卷引用:2020届上海市黄浦区高三二模(阶段性调研)数学试题
4 . 函数
的定义域是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002a93d72c59d6572f574b3bc6152194.png)
您最近一年使用:0次
2020-05-19更新
|
342次组卷
|
4卷引用:2020届上海市宝山区高三下学期二模数学试题
2020届上海市宝山区高三下学期二模数学试题上海市七宝中学2022届高三上学期十月月考数学试题上海市徐汇区2019-2020学年高一下学期期末数学试题(已下线)专题03 函数的概念与性质(模拟练)-1
名校
解题方法
5 . 在下列命题中:①在
中,
,
,
,则解三角形只有唯一解的充要条件是:
;②当
时,
;③在
中,若
,则
中一定为钝角三角形;④扇形圆心角
为锐角,周长为定值,则它面积最大时,一定有
;⑤函数
的单增区间为
,其中真命题的序号为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b86d43790babcdbbdc03493ee70928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d39e8c6fc9149d6290c493a65bdc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbf7575ec7f9c22f3b51084fe190b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc18e9d81eaa4c0e25f92b497058d9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72243f88f9041df51a76f7b2dd0fdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f44641a1d73c24b9b69145f312ca70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb80c0e955d5be2a4af9006d36347b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7814b93320e57e95ca4a1d80f87c4b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37ff6a9a24078fdd7bf21c180e40d78.png)
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6 . “
”是“
”的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7ec48efb61d5e0ddef3b4bacebdc1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d450aea0fb89e956fc4caa3a9c59fa.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2020-01-13更新
|
286次组卷
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7卷引用:上海市建平中学2020届高三上学期12月月考数学试题
名校
7 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a7cf1b543bad0c701f611ff4f525b1.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa09c570d50d400babf1eb178883aa83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a7cf1b543bad0c701f611ff4f525b1.png)
您最近一年使用:0次
2019-12-03更新
|
212次组卷
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8卷引用:上海市洋泾中学2018—2019学年高三下学期3月月考数学试题
2018·上海浦东新·三模
名校
8 . 已知平面直角坐标系中不垂直于
轴的直线
,则“
的斜率等于
”是“
的倾斜角等于
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35be73560c5a8a7b576e9ebf4230b5aa.png)
A.充要条件 | B.充分非必要条件 |
C.必要非充分条件 | D.既非充分又不必要条件 |
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9 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a7cf1b543bad0c701f611ff4f525b1.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93681425a0cddd63a9809f69648ac8f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a7cf1b543bad0c701f611ff4f525b1.png)
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10 . 若集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1407d6f2b3cd6490ad571e421370302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dee449dfc48159a5291f0ba968b4fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
您最近一年使用:0次
2019-12-03更新
|
119次组卷
|
2卷引用:上海市复旦大学附属中学2018-2019学年高三上学期期中数学试题