1 . 若复数
满足
,则
在复平面内对应的点在第 象限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb5f7658a4bc2dc5f671e693bdcb7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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2016-12-04更新
|
163次组卷
|
2卷引用:2016届福建省厦门市高三5月月考理科数学试卷
2 . 已知
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3fb4f3c0ac3ee31dc7429a4bff51fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ed564cb43353affaf385c6accc522c.png)
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3 . 设复数
满足
,则
在复平面内所对应的点位于第_________象限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd9c4ce2ff42b6faa68e620d3b3ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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4 . 已知x∈R+,有不等式:x+
≥2
=2,x+
=
+
+
≥3
=3,….启发我们可能推广结论为:x+
≥n+1(n∈N*),则a的值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf35027e76f8ea593f82023973d4aba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68cadd7aee2cc660ecd7d0a517203038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8494b1b5d62b8fff80cfeac6ee648c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1020afcfd8b7de38dfd825373b86bdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1020afcfd8b7de38dfd825373b86bdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8494b1b5d62b8fff80cfeac6ee648c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bba62fcf0e6195360919bc7932797e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e170f086d4c5eebd5f57b2b3bff3745.png)
A.2n | B.nn | C.n2 | D.2n+1 |
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5 . 执行右面的程序框图,如果输入的
的值为1,则输出的
的值为
![](https://img.xkw.com/dksih/QBM/2016/7/27/1572941069762560/1572941075603456/STEM/ebe297aedfc446ae9a32b2d1507a8d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2016/7/27/1572941069762560/1572941075603456/STEM/ebe297aedfc446ae9a32b2d1507a8d4c.png)
A.4 | B.13 | C.40 | D.121 |
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6 . 式子
满足
,则称
为轮换对称式.给出如下三个式子:
①
;
②
;
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b237ea135e10ddd7e144ee7a1e6a446.png)
是
的内角).
其中为轮换对称式的个数是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064c998287edd05fb0af6afe4a66a33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bafb1f8ac52feb6b3f9837fc3efa461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064c998287edd05fb0af6afe4a66a33d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb5e62e1d254e15711a50e038975c50.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9689644a971f7bda369c4d7f0f946e26.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b237ea135e10ddd7e144ee7a1e6a446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7afb6976f7d8c60bf094be1bdc7af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
其中为轮换对称式的个数是
A.0 | B.1 | C.2 | D.3 |
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7 . 复数
满足方程
那么
在复平面内对应的点
组成的图形为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bdadcbf65f4338c4efb4a83f60ae1b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.以![]() ![]() | B.以![]() ![]() |
C.以![]() ![]() | D.以![]() ![]() |
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8 . 已知函数
,其中
为自然对数的底数.
(Ⅰ)当
时,求函数
的单调区间;
(Ⅱ)当
时,若函数
存在两个相距大于2的极值点,求实数
的取值范围;
(Ⅲ)若函数
与函数
的图象关于
轴对称,且函数
在
单调递减,在
单调递增,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e21b81b3e5c09491e86b1fb9241066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87cc4e28bb2bb026526712c64917179.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52ba9beded7726f79672d0187d6a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95431f03b592dee84cd01039dba94999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac038016867ce4e51b37ce31ef22f214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅲ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b144bb6a3250cfdf5e047053a9b6631c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec632e79346543e767661aa6e910d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719ea7d96512dc6bc650a8e9267376e7.png)
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9 . 根据下面的要求,求
┅
值.
(Ⅰ)请将程序框图补充完整;
(Ⅱ)求出(I)中输出S的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda02705c4c503797278dc27fd8598cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8de276d6e4d30b3d0fc77f1eacfbdc.png)
(Ⅰ)请将程序框图补充完整;
(Ⅱ)求出(I)中输出S的值.
![](https://img.xkw.com/dksih/QBM/2016/11/22/1573164033687552/1573164039905280/STEM/fb580fa39ba241f2802e32bac22a0a47.png)
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10 . 数列
的通项公式为
,设
,试求
的值,推导出
的公式,并证明.
![](https://img.xkw.com/dksih/QBM/2016/5/12/1572634487037952/1572634493313024/STEM/f7247edceff84fc1b6d609878374927c.png)
![](https://img.xkw.com/dksih/QBM/2016/5/12/1572634487037952/1572634493313024/STEM/b7b222a9139a4720928566b3af7a42cb.png)
![](https://img.xkw.com/dksih/QBM/2016/5/12/1572634487037952/1572634493313024/STEM/8685eaf8914c425db2d83a07c0f2deca.png)
![](https://img.xkw.com/dksih/QBM/2016/5/12/1572634487037952/1572634493313024/STEM/8030301c47e547fc94a0b0fe77f7b491.png)
![](https://img.xkw.com/dksih/QBM/2016/5/12/1572634487037952/1572634493313024/STEM/03c9a35595684a44aec872e58388572d.png)
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