解题方法
1 . 如图,是南京博物馆展示的一件名为“陶三棱锥”的文物,该文物的出土,为研究吴越文化提供了重要价值,博物馆准备为该文物制作一个透明的球形玻璃外罩进行保护供游客观赏研究,经测量该文物的所有棱长都为
分米,则制作的球形玻璃外罩(玻璃外罩厚度忽略不计)的直径至少为____________ 分米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
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解题方法
2 . 欧拉函数
表示不大于正整数
且与
互素(互素:公约数只有1)的正整数的个数.已知
,其中
,
,…,
是
的所有不重复的质因数(质因数:因数中的质数).例如
.若数列
是首项为3,公比为2的等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c47847486c103fabb5b4ba4220c6a8.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc89a53c03cb86fb653bb82128f6cba.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/8ac535d98f300ff35496c66fe3c66a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b9bd3d8d836eb723be002c86a53740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9fa588c3a8ac4df1b963a1f2850163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c47847486c103fabb5b4ba4220c6a8.png)
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2024-06-03更新
|
591次组卷
|
3卷引用:贵州省黔南州2024届高三下学期第二次模拟统考数学试题
解题方法
3 . 已知四面体
的四个面都为直角三角形,
平面
,
为直角,且
,则四面体
的体积为______ ,其外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a72dfbf0138a611174c36ce077e0c47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db4241d0422534527b34cc4e7534637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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解题方法
4 . 已知正方体
的顶点均在半径为1的球
表面上,点
在正方体
表面上运动,
为球
的一条直径,则正方体
的体积是____________ ,
的范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
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5 . 已知函数
的最小正周期为
,则函数
图象的一条对称轴方程为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aabdcfd7cb767ec62811de7fbcbb4903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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6 . 已知双曲线
的左、右焦点分别为
,
,
为坐标原点,双曲线的离心率为2,过
作直线
的垂线,垂足为
,与双曲线右支和
轴的交点分别为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc80a1525c76e1890d8a4983186e6980.png)
________ ;
的内切圆在
边上的切点为
,若双曲线的虚轴长为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36dc57ee3ad90895adb9ef9d8a558aaa.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e04a6d711600fc4f8a8df876a85cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/bc80a1525c76e1890d8a4983186e6980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36dc57ee3ad90895adb9ef9d8a558aaa.png)
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7 . 已知直线
,直线
,
与
相交于点A,则点A的轨迹方程为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b1b5f4035eea8713b379e2d8dccd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68e261f470b13396badb3f358488a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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8 . 若实数a,b,c,d满足
,
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed4290447fbdc563027fec2a7f7960c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bfb41ec717c6782d0968266c665acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27562a5708b98d015cf417e65dc8e5f0.png)
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9 . 已知长轴与短轴长分别为2a与2b的椭圆围成区域的而积为
,现要切割加工一个底面半径为
、高为
的圆柱形零件(如图所示),截面经过圆柱的一个底面中心,并且与底面所成角为
,然后在切割后得到的两个部件表面都刷上油漆,则所刷油漆的面积为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8a3ce418b9a64e43cbd9813efea836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
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解题方法
10 . 已知集合
,集合
且
,若
,则
的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73461bdae8b2f6793d43afd2e5dfe09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47293d8b87516992971d6ba498bcf4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f1cfeb3f6ccc8573760d5776007321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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