解题方法
1 . 如图所示,在五面体
中,四边形
是矩形,
和
均是等边三角形,且
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0acc93490a6a784eb62201d93dd93d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8977e6db26ea83d19d5f19f8179cb8.png)
A.![]() ![]() |
B.二面角![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-25更新
|
1736次组卷
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6卷引用:2024届福建省厦门市一模考试数学试题
2024届福建省厦门市一模考试数学试题福建省部分地市2024届高三上学期期末数学试题(已下线)专题06 立体几何 第一讲 立体几何中的证明问题(解密讲义)(已下线)第二章 立体几何中的计算 专题三 空间体积的计算 微点4 四面体体积公式拓展综合训练【培优版】(已下线)专题04 立体几何(已下线)压轴题04立体几何压轴题10题型汇总-1
名校
解题方法
2 . 如图所示,在长方体
中,
和
交于点
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/2b83e586-bde1-41eb-b785-6399c124ba90.png?resizew=162)
(1)根据上下文,在“直线
平行于平面
”的证明过程中完成填空;
证明:(1)如图所示,连接
.由
是长方体,得___①___,所以四边形
为平行四边形,从而
是
的中点;再由
是
中点,
是
中平行于
的中位线.于是,__②____,根据直线与平面平行判定定理,得直线
平行于平面
,证明完毕.
①___________________________________________________;
②___________________________________________________.
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bed5edf85db24ba3e6fa7e2d89f4afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/2b83e586-bde1-41eb-b785-6399c124ba90.png?resizew=162)
(1)根据上下文,在“直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
证明:(1)如图所示,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf8c670b78106a980fc98b6659627d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
①___________________________________________________;
②___________________________________________________.
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b8df87ef099eae61bb07018f2ab335.png)
您最近一年使用:0次
3 . 如图,在正方体
中,
均为棱的中点,现有下列4个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/e7adc206-fdc0-43d4-8fad-f52f29460469.png?resizew=180)
①平面
平面
;
②梯形
内存在一点
,使得
平面
;
③过
可作一个平面,使得
到这个平面的距离相等;
④梯形
的面积是
面积的3倍.
其中正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7fa1c1d6321b28a2a2b7ffd0b27253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/e7adc206-fdc0-43d4-8fad-f52f29460469.png?resizew=180)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46f725fb1c57d0855a0a6cc26bf562a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac66de8543430fd51e7c18042e626dd.png)
②梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac66de8543430fd51e7c18042e626dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2803a2949df8ff5494549cf41207f963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
③过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7f4d18c6a2e405bbd7ea1e814649c6.png)
④梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac66de8543430fd51e7c18042e626dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
其中正确的个数为( )
A.4 | B.3 | C.2 | D.1 |
您最近一年使用:0次
2023-12-27更新
|
509次组卷
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4卷引用:陕西省西安市部分学校2024届高三上学期12月联考数学(文)试题
陕西省西安市部分学校2024届高三上学期12月联考数学(文)试题陕西省西安市长安区教育片区2024届高三上学期模拟考试数学(理)试题陕西省西安市长安区教育片区2024届高三上学期模拟考试数学(文)试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)
4 . 如图,棱长为6的正四面体
,
是
的重心,
是
的中点过
作平面
,且
平面
.
(1)在图中做出平面
与正四面体
表面的交线,要求说明作法(无需证明),并求交线长;
(2)求点E到
平面的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b27b287cb884184ed3edfb0e554a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/e5f8873e-9b0f-4a10-a032-30f91e8d0110.png?resizew=160)
(1)在图中做出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点E到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
5 . 在直角梯形
中,
,
,
,
,
,
在
上,
,
在
上,
.将
沿直线
翻折至
的位置,将四边形
沿
翻折至四边形
的位置,使
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/4b686bc1-6d68-4593-8446-0e3ec579e0b2.png?resizew=323)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e901a932e409a3d432128fd60436a885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbd6f0a0412d0f43ce1f7c1d530e56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ef2dc657bd3b3c0f47642e607b142a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03952d664fba91020fc5f3bcf2f9746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f4248e8021130ab60365e3d2e9a694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3c5c8187180242e0e0a7cb3797f585.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/4b686bc1-6d68-4593-8446-0e3ec579e0b2.png?resizew=323)
A.![]() ![]() ![]() |
B.平面![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.四棱锥![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图1,山形图是两个全等的直角梯形
和
的组合图,将直角梯形
沿底边
翻折,得到图2所示的几何体.已知
,
,点
在线段
上,且
在几何体
中,解决下面问题.
平面
;
(2)若平面
平面
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10de2459bc376f9a3de90f74cc18ca7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde387abe3ecba7cde65df9c58131b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a39a7453e6994a580038828513c68c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3b8602719b3d371bc9ec6c441bb9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7513c5dc6e1d35f76020f8f60c95669.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
您最近一年使用:0次
2023-11-24更新
|
606次组卷
|
9卷引用:江西省部分地区2023-2024学年高三上学期11月质量检测数学试题
江西省部分地区2023-2024学年高三上学期11月质量检测数学试题河北省部分高中2024届高三上学期11月联考数学试题陕西省榆林市府谷县第一中学2024届高三上学期第五次月考数学(理)试题山西省运城市盐湖区第五高级中学2024届高三上学期一轮复习成果检测数学试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)(已下线)11.4.2平面与平面垂直-同步精品课堂(人教B版2019必修第四册)河北省唐山海港经济开发区第三中学2024届高三上学期11月质量检测数学试题
名校
解题方法
7 . 羡除是《九章算术》中记载的一种五面体.如图五面体ABCDEF,四边形ABCD与四边形ADEF均为等腰梯形,其中
,
,
,
,M为AD中点,平面BCEF与平面ADEF交于EF.再从条件①,条件②,条件③中选择一个作为已知,使得羡除ABCDEF能够确定,然后解答下列各题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/10/1e20e620-b7c4-4e7a-841e-ea3fa10898b2.png?resizew=146)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
平面CDE;
(2)求二面角
的余弦值.
(3)在线段AE上是否存在点Q,使得MQ与平面ABE所成的角的正弦值为
,若存在,求出
的值,若不存在,请说明理由.
条件①:平面
平面ABCD;
条件②:平面
平面ABCD;
条件③:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9398fe7da3972063a4a3cae5f4e2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c428f5201735597284c67d5d47a515d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a972f5d6110b87497fa71efe4ee9d7fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/10/1e20e620-b7c4-4e7a-841e-ea3fa10898b2.png?resizew=146)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96040590db621faa8ac1d862c319d2de.png)
(3)在线段AE上是否存在点Q,使得MQ与平面ABE所成的角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e468f168f3657d84d44be5eb89a62d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe34c49dc3e7c71956bd8cb9362912ad.png)
条件①:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c1acdd27cebb11e0266464b03b3afb.png)
条件②:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edbb7850e42abf006017b477d85dee5.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,几何体
为三棱台.
平面
.
(2)已知平面
平面
,求三棱台
的体积.
参考公式:台体的体积
,其中
分别为台体的上底面面积、下底面面积,
为台体的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7d82423b6f211a7ac51a850b55e73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546468c4f030e2474ab4485c59a7947b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
参考公式:台体的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0df98384885fe5d6b67eb6d03f42dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
您最近一年使用:0次
2023-10-19更新
|
184次组卷
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2卷引用:四川省部分名校2023-2024学年高三上学期10月联考文科数学试题
9 . 已知直线a,b异面,下列判断正确的是( )
A.过b的平面不可能与a平行 | B.过b的平面不可能与a垂直 |
C.过b的平面有且仅有一个与a平行 | D.过b的平面有且仅有一个与a垂直 |
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名校
10 . 如图,已知圆柱的轴截面
为正方形,
,
为圆弧
上的两个三等分点,
,
为母线,
,
分别为线段
,
上的动点(与端点不重合),经过
,
,
的平面
与线段
交于点
.
(1)证明:
;
(2)当
时,求平面
与圆柱底面
所成夹角的正弦值的最小值.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/24/a3435286-b6cd-4341-9e3a-51c680ec7bd2.png?resizew=119)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ce395d0a14f53004b815c5304afb4f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9398ffc304dcefeda7a865cf557f702f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2023-09-23更新
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2卷引用:贵州省黔西南州部分学校2024届高三上学期9月高考适应性月考(一)数学试题