名校
解题方法
1 . 已知直线l经过点
,曲线
:
.
①曲线
经过原点且关于
对称;
②当直线l与曲线
有2个公共点时,直线l斜率的取值范围为
;
③当直线l与曲线
有奇数个公共点时,直线l斜率的取值共有4个
④存在定点Q,使得过Q的任意直线与曲线
的公共点的个数都不可能为2
以上说法正确的是___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9b41e8cc050a0616f10f13d6780bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17757aab2a5a4b5bf3cc88432bbfb0e.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
②当直线l与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd911f9faae39534b586eb4fc807bf4.png)
③当直线l与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
④存在定点Q,使得过Q的任意直线与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
以上说法正确的是
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名校
2 . 设函数
,
①若
有两个零点,则实数
的一个取值可以是______ ;
②若
是
上的增函数,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c87a9d6ceb62c7c17b2ce2b0f039199.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-28更新
|
809次组卷
|
3卷引用:北京市石景山区2024届高三下学期3月统一练习数学试卷
名校
解题方法
3 . 设函数
.
①若
存在最大值,则实数
的一个取值为___________ .
②若
无最大值,则实数
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c30374477744e492bd903a3a0e37e0.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
4 . 有穷数列{}共m项(
).其各项均为整数,任意两项均不相等.
,
.
(1)若{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7a1d739890a8951586e23b78b035bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668f1e1169ebc1dfcae1cdc484322a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9dbbde1c76faf80c2ff141086226f7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0f7f62693882ed8d31e0ffba8c3400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffec3878c7a5433a224d4388a8059bd9.png)
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5 . 设函数
,若函数
有且只有一个零点,则实数a的一个取值为__________ ;若函数
存在三个零点,则实数a的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5ecb70c86715deca41f55af4c827fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
6 . 若无穷数列
满足
,
,则称
具有性质
.若无穷数列
满足
,
,则称
具有性质
.
(1)若数列
具有性质
,且
,请直接写出
的所有可能取值;
(2)若等差数列
具有性质
,且
,求
的取值范围;
(3)已知无穷数列
同时具有性质
和性质
,
,且
不是数列
的项,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3567869af3e34bcf1dd5f2124e544785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6518163334e6b56dfa6ae7eb75f9a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bd31185a298a88fb51205d8b67aecd.png)
(3)已知无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0313eea2c65393728d83a287a8b799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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名校
解题方法
7 . 已知函数
若
的值域为R,则a的一个取值为____________ ;若
是R上的增函数,则实数a的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e372ebb8eae888f8db06520d6fc4316d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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8 . 设
,函数
,函数
,
.
(Ⅰ)判断函数
在区间
上是否为单调函数,并说明理由;
(Ⅱ)若当
时,对任意的
, 都有
成立,求实数
的取值范围;
(Ⅲ)当
时,若存在直线
(
),使得曲线
与曲线
分别位于直线
的两侧,写出
的所有可能取值. (只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e4b994dbe43b3dc59409507791ae05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b44ce1f38097acac14cd28b5dc07fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096f1be1cd0f6fb6856e9d147f076c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db2eb29042782efa4f96d82e6aa35d6.png)
(Ⅰ)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
(Ⅱ)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9234e2ee3ebf72645582a8319a0168b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bd3b259fabe06824f1abeca77a3dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c61ed9bb08a0a1bfff16f95ea95098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307da948a9e2f6f48cf86295bff9a61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f869c504d225b642b67137595a8be7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
9 . 设函数
,
①若
,则不等式
的解集为___________ ;
②若
,且不等式
的解集中恰有一个正整数,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711a65c36cdd87a7cdf26f9b84e5c49b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3b43fb07a1d631b294dbf6f0f58713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a023ef8a7a5d94029b08b4cb30422e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-05-05更新
|
1054次组卷
|
3卷引用:北京市海淀区2023届高三二模数学试题
解题方法
10 . 已知不等式
的解集为
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d76f450d21c04c9cc7db8377d8681d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次