解题方法
1 . 如图所示,在正方体
中,E,F分别为
,AB上的中点,且
,P点是正方形
内的动点,若
平面
,则P点的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68004768b879c6a052f45a2c45217cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8759f11769105049212e1f52aedbb3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1012e31eb8a9a3aed7e6cbba09534e0c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知函数
,对于任意的
,不等式
恒成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8a17a15811dc66b8d947493e29d67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46ecf935049473045cdebae68415657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0168c220dc243c185338de11f15fe8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 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
4 . 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)
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5 . 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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6 . 设复数
,
为虚数单位,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa3d3ca8ae9c034b384ba8267808553.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9686a6bd64d328579a4bc1c3e19326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579743813856e2a9183f5ec6eaaefbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcbe8b4bcd32e5a64ebfd873f8cbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70c2519610d6d1d6d0855b0f27dfc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa3d3ca8ae9c034b384ba8267808553.png)
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7 . 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)
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名校
解题方法
8 . 若不等式
在
上恒成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffcfff3f9f46e07ec6b88b3e7bde90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.1 | D.![]() |
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9 . 在
的展开式中,含
的项的系数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd8a80c31c66dd92ed30eef28da1711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
A.-280 | B.280 | C.560 | D.-560 |
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解题方法
10 . 已知双曲线
的实轴长等于虚轴长的2倍,则
的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd4f50a036a0e3b9fef4936db94115c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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