名校
解题方法
1 . 如图,一块三角形铁片ABC,已知
,
,
,现在这块铁片中间发现一个小洞,记为点D,
,
.如果过点D作一条直线分别交AB,AC于点E,F,并沿直线EF裁掉
,则剩下的四边形EFCB面积的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c99fc553ecb3e2afdb7058201bc642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b566395b41fc587143d533f9756024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d54e182a943f960a1885b8556d07a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
2 . 设集合
,(
,
)且A中任意两数之和不能被5整除,则n的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bd3eec1b1e189c92c2db22ea773cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
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3 . 已知数列
:
的各项均为正整数,设集合
,记
的元素个数为
.
(1)若数列
:
,且
,
,求数列
和集合
;
(2)若
是递增的等差数列,求
的值(用
表示),并说明理由;
(3)请你判断
是否存在最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9ef2e730239fb441c867d6ab4d9b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f05a921b593d6e1bedfd6c28b60f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab8cdaf36beae93dd45c27981cb75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc668d959b811bef55a1e672eb1dcec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f255d89ed61b51eb161d74e518b9a763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)请你判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
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名校
解题方法
4 . 如图,圆
与
轴相切于
圆心
在直线
上运动.过点
向圆
作非
轴的切线,切点分别为
两条切线交于点
,设点
的轨迹为曲线
.
的方程;
(2)设
为线段
上一点(不含端点),过
的直线
交曲线
于
两点,且
为
的中点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380c4f18890b088ef62dcea9b52ec73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d324b8cc99df14a6418e7d0f7b7d7436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433486848d127b7f6dadc40c96d1aec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46dc74f006f8d176db51ffe97dd8af90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a74a141b1e4a6b441d17d3ef8db85f75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
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名校
解题方法
5 . 已知
均为正实数,其中
满足:
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b511bcbe94aa484c0a067891fbf7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c6362d9899ef5c2c274e2708ddd2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51693f186c0d198110811c2068e8210.png)
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6 . 三棱锥P-ABC中,
是边长为3的正三角形,
,
.则三棱锥P-ABC的体积最大为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5089d0790c09c65dc54a5aa57e47a67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307d38cc7012c328f1f22aa793fe76d7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-09更新
|
496次组卷
|
2卷引用:湖南省长沙市湖南师范大学附属中学2023-2024学年高二下学期第一次大练习数学试题
名校
解题方法
7 . 已知定义在
上的函数
是偶函数,当
时,
,若关于
的方程
有且仅有6个不同的实数根,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00147a0bfc0ce72b3a652c2abccccfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa47b2df21fca7a0dae406d541d1c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
8 . 双曲线
的左、右焦点分别为
、
,过
的直线与双曲线
的右支交于
,
两点(其中点
在第一象限).设
,
的内切圆半径为
,
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51524b03af28db4c6c5a7b30543916a.png)
![](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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.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/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd3d19b0c8b544d52b897ca30990b4.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
9 . 某商城进行促销活动,购买某产品的顾客可以参加一次游戏:在一个不透明箱子中放入红、蓝、黄三种颜色的小球各1个,顾客从中有放回地取出小球,直到取出的小球集齐了三种颜色则停止取球.设顾客停止取球时,取过的小球次数为
,
(1)求
;
(2)设
,数列
,求
的通项公式;
(3)顾客停止取球时,取过的小球次数为
,顾客可以获得对应的
元奖金,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beded6e21d93573807f67478c74e7e24.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2984cf03d31b5fa49437a49c393002c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)顾客停止取球时,取过的小球次数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faa95fff49f487cce3a4fdc58bb067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1269b45b8c9bcb0cada085cd86fd88.png)
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名校
解题方法
10 . 已知函数
,若
恒成立,则
,
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f7683cf752bbe2b6a5e5b3198a160d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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