名校
解题方法
1 . 已知抛物线
的焦点为
,直线
交抛物线于
两点,
为抛物线
的准线与
轴的交点,直线
分别交抛物线于
两点(点
异于点
,
),
为坐标原点,则实数
的取值范围为__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b21b94a2bb768ccbc65c33f9c4ed923.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c654f3bb56ece42d29a9f14cca37bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb2d74932ede98011219d319f5b9995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b21b94a2bb768ccbc65c33f9c4ed923.png)
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解题方法
2 . 已知
,
,是双曲线C:
的左右焦点,过
的直线与双曲线左支交于点A,与右支交于点B,
与
内切圆的圆心分别为
,
,半径分别为
,
,若
,则双曲线离心率为________ .
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcccefb64de9d739bb52695c8cf38fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeaf446f8478f36f56884039d517104c.png)
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解题方法
3 . 已知长方体
中,
,点
为矩形
内一动点,记二面角
的平面角为
,直线
与平面
所成的角为
,若
,则三棱锥
体积的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a871dabec7b93bd9fcf74602ece936d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7a43b5f03e1e911ea2e82da91301a8.png)
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名校
4 . 已知函数
,下面命题正确的是_________ .
①存在
,使得
;
②存在
,使得
;
③存在常数
,使得
恒成立;
④存在
,使得直线
与曲线
有无穷多个公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3d74bc831a959f5d2a2b016548eba0.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5af267764227a538f13953d06341c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1260c6fa15a4d739a41c5de1533e9e5c.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81faf6ab77580b3d89b6aa1d802f84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee798d2d512f7342c55a0d580f4367e2.png)
③存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c46385268d3081043e04f4401b7973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf322b61457bd0bd7484b4349f537e6.png)
④存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
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解题方法
5 . 对于有穷数列
,从数列
中选取第
项、第
项、
、第
项
,顺次排列构成数列
,其中
,则称新数列
为
的一个子列,称
各项之和为
的一个子列和.规定:数列
的任意一项都是
的子列.则数列
的所有子列和的和为__________ .
![](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/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d034715f9b1dfb306f9c89d383582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e636879245230dd00a3ab3cbcfbfd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533484c347e86e6bb635006a94530dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa301d4a86341fd749f1f8c72c970565.png)
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6 . 已知
是
内一点,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932979fbd93c8f58f804a448d4a4983c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431e50511feb9d559aede83a55a49af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932979fbd93c8f58f804a448d4a4983c.png)
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解题方法
7 . 已知函数
.
①当
时,
,记
前
项积为
,若
恒成立,整数
的最小值是______________ ;
②对所有n都有
成立,则
的最小值是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c3613c9bdafd6f258c53dbf49776b.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef2639f7d9950f9481a5ddd92334be7.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c16b5df55ae677b721c5401ca1a8f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②对所有n都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f791e32e2606e39c024f26c7a02feb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知
,
分别是函数
和
图象上的动点,若对任意的
,都有
恒成立,则实数a的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc4d15605cedb4667a1bdcb00b2720b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9852d7433cf82fb187fcb796eb6d98d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6385e5564e8e04033873d9453615a24.png)
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名校
9 . 已知正数
,
满足
,则
的最大值为_________ .
![](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/60339f4fad87d3c19d28bcc1f864e172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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名校
解题方法
10 . 在圆台
中,圆
的半径是2,母线
,圆
是
的外接圆,
,
,则三棱锥体积最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d81d732204a3c2384a27606f858677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
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