1 . 无字证明来源于《几何原本》卷2的几何代数法(以几何方法研究代数问题),通过这一原理,很多的代数的公理或定理都能够通过图形实现证明.现有如图所示
,其中
、
为
边上异于端点的两点,
,
,且
是边长为
的正三角形,则下列不等式一定成立的是( )
![](https://img.xkw.com/dksih/QBM/2021/5/28/2730657997660160/2732120371486720/STEM/621fc4e6-3dce-4375-a13c-06dab1195f8d.png?resizew=244)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9001f0c06cf2c8f893a38b1dabe6219e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62e0d7822af5b4dc4ae1920d8c906e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://img.xkw.com/dksih/QBM/2021/5/28/2730657997660160/2732120371486720/STEM/621fc4e6-3dce-4375-a13c-06dab1195f8d.png?resizew=244)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2021-05-30更新
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277次组卷
|
2卷引用:江西省临川一中暨临川一中实验学校2021届高三高考模拟押题预测卷数学(文)试题
名校
2 . 直线
的直角坐标方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a13485bc6288f31ebe1ed7e5c3cd910.png)
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名校
3 . 在
中,角
的对边分别为
.若
,则三角形的面积
,因为这个公式最早出现在古希腊数学家海伦的著作《测地术》中,故称之为海伦公式.将海伦公式推广到凸四边形(凸四边形即任取平面四边形一边所在直线,其余各边均在此直线的同侧)中,即“设凸四边形的四条边长分别为
,凸四边形的一对对角和的一半为
,凸四边形的面积为
,现有凸四边形
,
则四边形
的面积的最大值为( )
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841785778970624/2841982476681216/STEM/8d33a2c5-484f-439b-81c8-1c3dce777ac3.png?resizew=197)
![](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/71d788614f1841b4943b30fe6fd1eff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c667f76da3658f200fff8eadb24b8e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fc3adfff8ffffe53cfa08f07317215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690ef07cba7c9636c58c8dc28b93efc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4c12f00c0e6cb063775974a21cd010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841785778970624/2841982476681216/STEM/8d33a2c5-484f-439b-81c8-1c3dce777ac3.png?resizew=197)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2021-11-02更新
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250次组卷
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3卷引用:江西省抚州市七校联考2021-2022学年高二下学期期中考试数学(理)试题
4 . 下列“若
,则
”形式的命题中,满足“
是
的充分不必要条件”的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
A.若事件![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() |
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22-23高三上·江西南昌·阶段练习
5 . 现有下列四个命题:
①
;
②存在
,使得
为质数;
③
;
④若
,则
的最大值为
.
其中所有真命题的序号为( )
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009ff8f3c216ed7b4f6e0aeaf816a64e.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9444414de4b849ea3c8bd35e2a8f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b5a9de8a72dda70e3eefeb0a408ffd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780e4d198b42f80c6faca7694bb8572.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30632a857e3ce91b2b0dcc50b765deac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
其中所有真命题的序号为( )
A.②④ | B.①③ | C.③④ | D.②③④ |
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6 . 为了测量一个不规则湖泊
两端之间的距离,如图,在东西方向上选取相距
的
两点,点
在点
的正东方向上,且
四点在同一水平面上.从点
处观测得点
在它的东北方向上,点
在它的西北方向上;从点
处观测得点
在它的北偏东
方向上,点
在它的北偏西
方向上.
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841770437574656/2841790852603904/STEM/28679fdd-2cf5-43bc-a1e4-3f27d48b9e79.png?resizew=305)
(1)求
之间的距离;
(2)以点
为观测点,求点
的方位角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1890f0b4e81634bb7e013412698640f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841770437574656/2841790852603904/STEM/28679fdd-2cf5-43bc-a1e4-3f27d48b9e79.png?resizew=305)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
(2)以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2021-11-01更新
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215次组卷
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3卷引用:江西省2022届高三10月大联考数学(理)试题
名校
7 . 若点
在角
的终边上,则
的值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10be12fe42332ab8da8853faba491c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2017-02-08更新
|
2813次组卷
|
7卷引用:2016-2017学年江西省南昌市第二中学高一上学期期末考试数学试卷
解题方法
8 . 下列判断正确的是___________ (请填上所有你认为正确的结果的序号).
①若
,
,则
;
②已知
,向量
,
.若
与
的夹角为钝角,则实数
的取值范围是
;
③若数列
的前
项和
(
为常数,且
),则
是等比数列;
④在
中,内角
,
,
的对边分别为
,
,
,
,
.若
仅有一解,则边
的取值范围是
.
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a946e12aa82cd49792e179fe46243f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516be1d86e3ad60ec72b101b5efc746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f15a138dbcc056b0eaee44076425f0b.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6569e50f43b3d8645652ecc13b62066e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228ddd3d628aff7349e326c5e76c7303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe706d206d9bc18206c039cbd25a18b.png)
③若数列
![](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/eec92ccdc8f008c18e52cd9043282c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
④在
![](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/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/e54a36173cd9b7b28e91619d715cb569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109d06b8be2e402b5ffbb0aeb501009.png)
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名校
解题方法
9 . 如图,将边长为1的正
以边
为轴逆时针翻转
弧度得到
,其中
,构成一个三棱锥
.若该三棱锥的外接球半径不超过
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c430808cb91d66ce60b1e2f83f129db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476c1028ab48d8f3779e1217b8bf63d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bc09ca07b357a1ecf0c9588aa7030e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5f1b9a7dc93aa2cd57d6352d000bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 在中国文化中,八边形常常被看作是四平八稳、镇宅保平安的象征.比如,八角楼、八角塔、八边花窗、八角门环和八边园林门径等,都有着这样的寓意.如图,在边长为
的正八边形
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e246bc4a4d491259fabc9c7497d6242.png)
______ ,若
内的一点
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1475c82f3a5c6fd1b418444a2f5af73b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4ab3f511aea1a80d79c6ad865e1955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e246bc4a4d491259fabc9c7497d6242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc5c12b241539cc99487865f7d8bf34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbc58200da9c83866917019eae87a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1475c82f3a5c6fd1b418444a2f5af73b.png)
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