1 . 如图,在直四棱柱
中,底面
是菱形,
,
,
分别为棱
,
的中点,
是棱
上的一点,
,
是棱
上的一点,
.
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f730fdcaa70886694a0367d708f2dcf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51914a865a3a2902af46635df4d62d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9af9708cd08585191681dc87a4c7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b5f967c7a8bfdb1dc8c6addcced5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
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解题方法
2 . 根据要求完成下列问题:
(1)设两个非零向量
,
不共线,如果
,
,
,证明A,B,D三点共线;
(2)设
,
是两个不共线的向量,
,已知
,
,
,若
恒成立,求k的值.
(1)设两个非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c37644fa9f227906c4e5b82c6905447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4330d48848aad9fa26d59516d042bdf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faea619ed35e8c52b295284bfbd4a7a0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1612505f2f7f38d1c6fb7d6c48029d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35811bc17681bb510bb593e0b3c1fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52e576eb4d80b3622bf2affab775699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ff35c6195ccff7a759e7b05e0e3ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d24632bdcdfffb47173e0064a47af8.png)
您最近一年使用:0次
3 . 在四棱锥
中,
是等边三角形,四边形ABCD是矩形,
,
,
,E是棱PD的中点.
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4746df85049d1651d3f6c30212a7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985905ab3559ed7ec54e745a493629af.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6405e9a84b771505dfeaf4d7129d0fc2.png)
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4 . 在
中,内角A,B,C的对边分别为a,b,c,且
.
(1)求角B;
(2)若
为锐角三角形,
,D是线段AC的中点,求BD的长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7cd8020fdf7ae5a64bc25d89293782.png)
(1)求角B;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,已知四棱锥
的底面是正方形,点E是棱PA的中点,
平面ABCD.
平面BDE;
(2)求证:平面
平面BDE;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2597b5554284e275367c25529c6750f.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
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名校
6 . 已知平面向量
,
,
,且
,
.
(1)求
和
;
(2)若
,
,求向量
和向量
的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27acda0d95efa6fb5ca9a57759e1702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bdb1cdb08ed2ed7e70b5246f45d0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e509349f83a9fb9340d4de7e90cd5c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03481e6a73207be03fdbc1f8e9965b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a36228810d0c2f6c6e53584c1ac176b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98cfc96a17c0ed837bd8bfabdda5217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd89e2066303543b96c0ee4b5d64d35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e163480714acc9dae5005cac65d217d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
您最近一年使用:0次
7 . 已知
,
.
(1)求
的值;
(2)若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75083d2a3f62c22971c6ef543e237420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bfdb5f50c0514b2b7cb83b2c29407b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a975174b697129d6cc7bdaeaa9d5de71.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db538adbb2706f0b3b9dae38cc438f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b2942c97548f9e6699d8d27209550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
您最近一年使用:0次
2024-06-14更新
|
499次组卷
|
2卷引用:甘肃省天水市第一中学2023-2024学年高一下学期第二次段中检测(6月)数学试题
名校
解题方法
8 . 已知非空集合
,
.
(1)若
,求
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55201a71f63e95aef66df1ca9e21551a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fbb02d5a584747b4a8287c6c24e0d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-06-10更新
|
327次组卷
|
4卷引用:甘肃省陇南市第一中学2023-2024学年高一上学期期末考试数学试题
9 . (1)解方程:
.
(2)求值:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638c5adc6e1300209246f802e8c69a23.png)
(2)求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e3915352d054290dbecaec123d54a6.png)
您最近一年使用:0次
2024-06-08更新
|
372次组卷
|
2卷引用:甘肃省陇南市第一中学2023-2024学年高一上学期期末考试数学试题
名校
解题方法
10 . 已知函数
.
(1)当
时,求
的最值;
(2)当
时,关于
的不等式
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b28b21dbae9edb360ea96c1edb96e6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691c1fc50ea793ea08748cb75bae70e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e74fc7479e44217bfa27dbd75992b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf755154fdddb396e7ed1a2352f1911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次