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解题方法
1 . 在
中,三个内角
所对的边分别为
.已知
的面积为
,
.
(1)求
的值
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf8c9594a0dc9767b5e84b9d55c5d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eb259fab57e11a4b98d4448a0e65fe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6732580ffff616408c0985d7175a4c2.png)
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2 . 在四边形
中,
,则实数
的值为______ ,若
是线段
上的动点,且
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4fec47150e684e8b270289048aff7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d92b9548115581546be6f0a3c5a7057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ab157cd50abfa3a6de8027f3f0b424.png)
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3 . 如图所示,正方体
的棱长为1,线段
上有两个动点
,且
,则下列结论中正确的有( )
;
②三棱锥
的体积为定值;
③
的面积与
的面积相等;
④二面角
的正切值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f115f2683c0422042f1846450885e7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc3bf74119692ac98eb24fcfa2a3f9f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
④二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd41f11a3360662c09b042a9f987e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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4 . 如图,平面
平面
是等腰直角三角形,
,四边形ABDE是直角梯形,
分别为
的中点.
平面
;
(2)求直线BO和平面
所成角的正弦值;
(3)能否在EM上找一点
,使得
平面ABDE?若能,请指出点
的位置,并加以证明;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31effd1d3f7ce1f6e57be80c7f3af4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cfd6b6a7e911d10d1a4bed9ca5e749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb28bb4b1149885a1ee5765b2f95fade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb38e548308137e2bef269a18e03ec80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6748d9b9948485c5ba87ca8751c6e053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线BO和平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc97b3d966e2a95e19d006a9de713ee.png)
(3)能否在EM上找一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038b331d32c87fbd86c3accec0841fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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5 . 设
是三个不同平面,且
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad6e7a4c010074d364c686124cbf664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a63f6aa604e3d7fc7ae8c7b587069a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.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 |
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解题方法
6 . 已知在锐角
中,角A,
,
所对的边分别为
,
,
,且
.
(1)求角
的大小;
(2)当
时,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0a6936d370d6a238a608ca56f87198de.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/95921d7458b14d0f4335f6c8dd5b0a56.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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7 . 如图,圆O内接边长为1的正方形
是弧
(包括端点)上一点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462d9d51496fa5250f55e7368111e056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83b9f01e806bf74042ba41b26423022.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 设
,
,
,
是同一个半径为
的球的球面上四点,
是斜边为
的直角三角形,则三棱锥
体积的最大值为( )
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
A.![]() | B.64 | C.![]() | D.128 |
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395次组卷
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5卷引用:期末模拟卷(范围:人教A版2019必修第二册)-期末真题分类汇编(天津专用)
(已下线)期末模拟卷(范围:人教A版2019必修第二册)-期末真题分类汇编(天津专用)江苏省邗江中学2023-2024学年高一下学期5月阶段性测试数学试题福建省泉州市安溪第八中学2023-2024学年高一下学期6月份质量检测数学试题(已下线)专题07 立体几何小题常考题型归类-期末考点大串讲(人教B版2019必修第四册)(已下线)专题6 组合体中的外接与内切问题【练】(高一期末压轴专项)
名校
9 . 如图,在三棱锥
中,
平面
,E,F分别为BC,PC的中点,且
.
;
(2)求直线EF与平面ABC所成角的正弦值;
(3)求
到平面AEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a219cbad3454275ec748c3e00d535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)求直线EF与平面ABC所成角的正弦值;
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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10 . 某公司为了解所经销商品的使用情况,随机问卷50名使用者,然后根据这50名的问卷评分数据,统计得到如图所示的频率分布直方图,其统计数据分组区间为
,
,
,
,
,
.
的值;
(2)估计这50名问卷评分数据的中位数、众数、平均数;
(3)从评分在
的问卷者中随机抽取2人,求此2人评分都在
的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fc138be9688253cbdeae2808eb74ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486c7705dbd7b7b9ec5dd17b4891088b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea146d8ec45e63ad14683fd31064de66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77699e3d1ddc6e698a640573a7ef787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d90faf85d1548242098a6fe3accd84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1a32a9f2b04fc931c6a0da0b7485e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)估计这50名问卷评分数据的中位数、众数、平均数;
(3)从评分在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4204a934372022fa08a7e739ab46a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486c7705dbd7b7b9ec5dd17b4891088b.png)
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