名校
解题方法
1 . 已知无穷数列
的各项均为整数.设数列
的前
项和为
,记
中奇数的个数为
.
(1)若
,试写出数列
的前5项;
(2)证明:“
为奇数,且
为偶数”是“数列
为严格增数列”的充分非必要条件;
(3)若
(
为正整数),求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41274819307283f0a931fb244401733e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a229173b0f235a4da8aeb6d35f1325f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549d08f011d91ff3f40426a1db0adf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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名校
解题方法
2 . 已知椭圆
经过
两点
为坐标原点,且
的面积为
.过点
且斜率为
的直线
与椭圆
有两个不同的交点
、
,且直线
、
分别与
轴交于点
.
(1)求椭圆
的方程;
(2)设
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9896a087ec2b6e197ed41bb6ef6723fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf0631722901bd70cbb85b8b38a3f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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3 . 数列
中,若
,则下列命题中真命题个数是( )
(1)若数列
为常数数列,则
;
(2)若
,数列
都是单调递增数列;
(3)若
,任取
中的
项
构成数列
的子数
(
),则
都是单调数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6828e5ae7104f4cf73337536bc02c94.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6990e60949881829c2c334eb40ce760d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882b660047bb6ded500cedba57958e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774891ed3a49afbc2c87cca80a1e4752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9e5fb431bcae1c560e5ea55ed35644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1432ec910f245d324bda02930c92311d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 设集合
,其中
.
(1)写出集合
中的所有元素;
(2)设
,证明“
”的充要条件是“
”
(3)设集合
,设
,使得
,且
,试判断“
”是“
”的什么条件并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2745900c1c3372a3b37dfecc224d23e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576ea0f23e66276d14e99a90c149c0dc.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834919b3ab3c1c09a39f9c9840a9416c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f13b50acd120eb4c51efe6523c7b525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1c6fbf72f69e70f9d3fe3c8fa39fc1.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71de73e8625a91a3abb2bdc98f63cf60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfacc023f7aa57ab1f1421e68fafb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f06294bbd9e425f20a00dd606c923d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e185c096328c1d3b9dccd704261b3269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ed9b5d83428b4b7beb856825554703.png)
您最近一年使用:0次
2019-09-23更新
|
1035次组卷
|
2卷引用:上海市上海中学2018-2019学年高一下学期期末数学试题
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6a1a187bee0ac1a1a7849bfd06b17d.png)
的部分图象如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/f6aeee0a-c304-4b66-836b-515cadc2e475.png?resizew=137)
(1)求
与
的值;
(2)设
的三个角
、
、
所对的边依次为
、
、
,如果
,且
,试求
的取值范围;
(3)求函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326d5521d697c3f69a2574d9599f973.png)
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6a1a187bee0ac1a1a7849bfd06b17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1459ed6a7d1dc04ea2f0f38813df11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/f6aeee0a-c304-4b66-836b-515cadc2e475.png?resizew=137)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83596176a9b25814fd6b309c56520273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060b0f7f488b28d57e8d6d87abaa2056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326d5521d697c3f69a2574d9599f973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a09894a5af03a3d4b7d9d010e8876b.png)
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