解题方法
1 . “调和数列”被称为“和谐的数列”,在数学中的地位非常重要,广泛应用于音乐创作和建筑设计中.若数列
满足
(
为常数),则称数列
为“调和数列”.已知
为正项调和数列,
是
的前
项和,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c697bf8d59f10fa93f6a535b4ded6e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48b466ab970861ef47d1113d1146e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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2 . 某班级举行元旦文艺晚会,晚会有3个唱歌节目和2个小品节目,问:
(1)若2个小品节目彼此要隔开,有多少种排法?
(2)第一个节目和最后一个节目都是唱歌节目,有多少种排法?
(1)若2个小品节目彼此要隔开,有多少种排法?
(2)第一个节目和最后一个节目都是唱歌节目,有多少种排法?
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解题方法
3 . 在
的展开式中,下列叙述中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df47407b37a64b23e2a4a94901e2cc5f.png)
A.二项式系数之和为32 | B.各项系数之和为0 |
C.常数项为15 | D.![]() |
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4 . 乘积式
展开后的项数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011d8e80756a0019e991cb2c1c295e98.png)
A.8 | B.9 | C.18 | D.27 |
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5 . 在棱长为2的正方体
中,E,F分别是棱
的中点,直线
与平面
交于点
.
;
(2)求
;
(3)若点
在棱BC上,且
平面
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93fa937325f9d083ac2d059cae553c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4474f00be9b97176f1867c22162521e1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200038dad137ce1b81983f5ee4c1739b.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
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6 . 如图,在底面为平行四边形的四棱锥
中,
为
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
7 . 已知曲线
恒过
点,且
在抛物线
上.若
是
上的一点,点
,则点
到
的焦点与到点
的距离之和的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af28172001b8a530a98128a01af39594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646baa8667df433b0122bc40236db993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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8 . 设等差数列
的前
项和为
,已知
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](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/339f690070cf185f99f43d8f93a693d9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a6066bbcb82f522a296e6d44efdf16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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9 . 已知向量
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22332a5483b7ac6f5ccd17d61183773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a1ce5559b35b59016c834ab3c7e35b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知3是函数
的极小值点.
(1)求
的值;
(2)若
,且
有3个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99aa855128ded58e5ee664733051edd7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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