解题方法
1 . 如图,在复平面内,复数
,
对应的向量分别是
,
,则
对应的点位于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe615164ed2995bdeea0f5b0ba94231.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
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2 . 已知
是两条不同的直线,
是两个不同的平面,且
,下列命题为真命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ccc19a183b9ce7f82d2609a14b9a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9666cbc826c71f108c3e802fc764dd45.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() | B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() ![]() ![]() |
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3 . 已知
,若平面内满足到直线
的距离为1的点
有且只有3个,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e18fd813ef878b9d7292620c757f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692265c4b64c721bd3e567b8af832b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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解题方法
4 . 在
中,角
所对的边分别为
,已知
,角
的平分线交边
于点
,且
.
(1)求角
的大小;
(2)若
,求
的面积.
![](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/407cdd82791eaa0734efd8584f5bb2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133760237c0ccf2d6a83786925b6d23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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5 . 有序实数组
称为
维向量,
为该向量的范数,范数在度量向量的长度和大小方面有着重要的作用.已知
维向量
,其中
.记范数为奇数的
的个数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9bc06a8ca80e9f47ccda39308e7ba4.png)
______ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c351c3dcae1b29183e5e78496378396b.png)
______ .(用含
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2624bf8eae8ec856a5f0ba799cee719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70fd5ea91c137241e07d2d53568557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0681ee547b06d12a5f689b6c16c85181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5ac304996e908248a1f0d3eae50d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9bc06a8ca80e9f47ccda39308e7ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c351c3dcae1b29183e5e78496378396b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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6 . 已知函数
.
(1)若
,求函数
的单调区间;
(2)若
存在极小值点
,且
,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0168522cd94db25a52257022fc82b431.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7efe7748bee5a868259f231f1c23404a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc1e8ec684bc3dedb313882c840196c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944ede342597c070831052dc06bca45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6967f64fdbc9f97a28c263b7f962f0c7.png)
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7 . 已知点
在抛物线
上,
为抛物线
上两个动点,
不垂直
轴,
为焦点,且满足
.
(1)求
的值,并证明:线段
的垂直平分线过定点;
(2)设(1)中定点为
,当
的面积最大时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763353a1abb8ed4d79f18bc73418a44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e1bc08cc69d3d8e73b990f1236ed5c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设(1)中定点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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8 .
的展开式中
的系数为______ .(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4876dc1aadc8e38cff230cf40f5980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7554b2a0cfc2a6fae8af010a5175d959.png)
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9 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001e448bbc5e519d38005707ca27ef24.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3529f0a1f3b4c201674801eb3ad2a114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001e448bbc5e519d38005707ca27ef24.png)
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10 . 函数
与其导函数为
,满足
,其中
;若
,
,其中
.
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e49359c5c9d119d81b08e8ca91c404.png)
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa79527e9b1cc3839131d98ca2c46ee.png)
其中正确的命题有______ .(将正确的序号都写上,多写漏写均不得分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1532cefdaf4b6df045285000b288b6d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad0fbc31815c67dc97072bfbcfe7fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa3e99070c9d83a1b4620d151a0c945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee86fc3cc1700452e83ca45bccb9c55.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6800a8cc57f3655f62ca47f7846b8a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e49359c5c9d119d81b08e8ca91c404.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad4406d78858a1c6c5d9b37726e30ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa79527e9b1cc3839131d98ca2c46ee.png)
其中正确的命题有
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