名校
解题方法
1 . 已知数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)证明:数列
为等差数列.
![](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/5635fbe6fabbf7eb4ab1670c06fba091.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
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解题方法
2 . 设函数
.
(1)求函数
的最小正周期;
(2)若
在
上的值域为
,
①若
,求m的值;
②若
,求m的取值范围.(①②两问直接写出答案)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29048efca57d47100104c47e3a21772c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d1a62f0c7627cf14ec8633514f5d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3888f94c47f6c7caf602f248d4cd9348.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/935b4035585dfe624ebdd0c758c6ea89.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
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3 . 对于分别定义在
,
上的函数
,
以及实数
,若存在
,
使得
,则称函数
与
具有关系
.
(1)若
,
;
,
,判断
与
是否具有关系
,并说明理由;
(2)若
与
具有关系
,求
的取值范围;
(3)已知
,
为定义在
上的奇函数,且满足:
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
判断
与
是否具有关系
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4413796ac3d5ca067bf70334101f5440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3ac1b540727626af78788a8e5f15de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6fc39a0cea8095683ad4a20a2f96f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da4f4bf9fb72cabd7afc5a67f6ecf1c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12959f65e9db83c446c35d3261a33171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976581d4a974fe50f9f29d430c1289f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677007fe2d220c74cbe3c9f4e9f8ccec.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3510b22fcf848f36cfaf5ff8964ce049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f318506aebfa6403ca8177d8db36d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da4f4bf9fb72cabd7afc5a67f6ecf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a78355986534b6e50bd7cabc9290a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0d3607cac89a65327549f87f20ba1c7.png)
判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca470d8c4a0a60e9f600d6aa264ad1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb41d5badc297be2d9b8931991ab7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1115793a13fb11c9e126cbb1fb2ac879.png)
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4 . 已知
,
,
,且
,
与
相交于点P.
(1)求点C和点P的坐标;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95963e8e4dcc511f0d86b1853ddcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0acc212c5c94602deb68c86c33369f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(1)求点C和点P的坐标;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a10f2c4a2a9c9cb4047f9f27cff1d7a.png)
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5 . 已知函数
.
(1)求函数
的图象在点
处的切线方程;
(2)求函数
在区间
上的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedaa6aad781cb80241b78ae9d4c97cc.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9770b18d9984172e6c08bf0921ec4200.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b63fb475fbdacbbb8eb2bf6a6716d2.png)
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解题方法
6 . 设
,
是不共线的两个向量.
(1)若
,
,
,求证:A,B,D三点共线;
(2)若
与
共线,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c08ebbac3d6784d6d3565192f36f91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5f8509784fc0cc4134e41f8dcc0a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af26762e8309eb14f2bcab0954f7165.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52395f0262abbf2a4b1a823b4b65caae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a126bb16b6ab8644a8e8d33f6909224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
7 . 诚信是立身之本,道德之基.某校学生会创设了“诚信水站”,既便于学生用水,又推进诚信教育,并用“
”表示每周“水站诚信度”.为了便于数据分析,以四周为一个周期,下表为该水站连续八周(共两个周期)的诚信度数据统计,如表1:
(1)计算表中八周水站诚信度的平均数
;
(2)从表中诚信度超过
的数据中,随机抽取2个,求至少有1个数据出现在第二个周期的概率;
(3)学生会认为水站诚信度在第二个周期中的后两周出现了滑落,为此学生会举行了“以诚信为本”主题教育活动,并得到活动之后一个周期的水站诚信度数据,如表2:
请根据提供的数据,判断该主题教育活动是否有效,并根据已有数据说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc891e44ebe17a1ffc956667a4112bf4.png)
第一周 | 第二周 | 第三周 | 第四周 | |
第一个周期 | ||||
第二个周期 |
(1)计算表中八周水站诚信度的平均数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
(2)从表中诚信度超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4426df5be4e96b6385de735db9f69772.png)
(3)学生会认为水站诚信度在第二个周期中的后两周出现了滑落,为此学生会举行了“以诚信为本”主题教育活动,并得到活动之后一个周期的水站诚信度数据,如表2:
第一周 | 第二周 | 第三周 | 第四周 | |
第三个周期 |
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解题方法
8 . 已知
和
都是直角三角形,
,E,F分别是边AB,AD的中点,现将
沿BD边折起到
的位置,如图所示,使平面
平面BCD.
平面BCD;
(2)求证:平面
平面
;
(3)请你判断,
与BD是否有可能垂直,做出判断并写明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ff103699fefbd87327b26b58fafd42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c967c9b3f669ea78edd838e1d8b59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(3)请你判断,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
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9 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)如果点
是角
终边上一点,求
的值;
(2)设
,求
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9688a68bd2d1b2c8dcd6568e1a5ac3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)如果点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e7c6b1e8d06e439c1ede19f99286c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f3b2cc4fc44eef6a51e1a4ae89ecb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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10 . 已知椭圆C:
(
)过点
,右焦点为
.
(1)求椭圆C的方程;
(2)过点F的直线l(不与x轴重合)交椭圆C于点M、N,点A是右顶点,直线MA、NA分别与直线
交于点P、Q,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a571f86f21d6455bd867cd06b4562070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
(1)求椭圆C的方程;
(2)过点F的直线l(不与x轴重合)交椭圆C于点M、N,点A是右顶点,直线MA、NA分别与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c32805e421aec6bce3624baa0c954f1.png)
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