名校
1 . 已知函数
.
(1)若函数
有3个不同的零点,求a的取值范围;
(2)已知
为函数
的导函数,
在
上有极小值0,对于某点
,
在P点的切线方程为
,若对于
,都有
,则称P为好点.
①求a的值;
②求所有的好点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261bed360289f37d94f742ab63676e45.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be20e3724274132cb83b16deaeecfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02af34501d48e2349967ecdfbfa6c1f8.png)
①求a的值;
②求所有的好点.
您最近一年使用:0次
2024-03-08更新
|
1397次组卷
|
4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
名校
解题方法
2 . 某商场周年庆进行大型促销活动,为吸引消费者,特别推出“玩游戏,送礼券”的活动,活动期间在商场消费达到一定金额的人可以参加游戏,游戏规则如下:在一个盒子里放着六枚硬币,其中有三枚正常的硬币,一面印着字,一面印着花;另外三枚硬币是特制的,有两枚双面都印着字,一枚双面都印着花,规定印着字的面为正面,印着花的面为反面.游戏者蒙着眼睛随机从盒子中抽取一枚硬币并连续投掷两次,由工作人员告知投掷的结果,若两次投掷向上的面都是正面,则进入最终挑战,否则游戏结束,不获得任何礼券.最终挑战的方式是进行第三次投掷,有两个方案可供选择:方案一,继续投掷之前抽取的那枚硬币,如果掷出向上的面为正面,则获得200元礼券,方案二,不使用之前抽取的硬币,从盒子里剩余的五枚硬币中再次随机抽取一枚投掷,如果掷出向上的面为正面,则获得300元礼券,不管选择方案一还是方案二,如果掷出向上的面为反面,则获得100元礼券.
(1)求第一次投掷后,向上的面为正面的概率.
(2)若已知某顾客抽取一枚硬币后连续两次投掷,向上的面均为正面,求该硬币是正常硬币的概率.
(3)在已知某顾客进入了最终挑战环节的条件下,试分别计算他选择两种抽奖方案最终获得的礼券的数学期望,并以此判断应该选择哪种抽奖方案更合适.
(1)求第一次投掷后,向上的面为正面的概率.
(2)若已知某顾客抽取一枚硬币后连续两次投掷,向上的面均为正面,求该硬币是正常硬币的概率.
(3)在已知某顾客进入了最终挑战环节的条件下,试分别计算他选择两种抽奖方案最终获得的礼券的数学期望,并以此判断应该选择哪种抽奖方案更合适.
您最近一年使用:0次
2024-03-08更新
|
2197次组卷
|
4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
名校
3 . 已知等差数列
的公差与等比数列
的公比相等,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
______ ;若数列
和
的所有项合在一起,从小到大依次排列构成一个数列
,数列
的前
项和为
,则使得
成立的
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684b935a7274130d081bfa7b2b938023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89b8821c758c29c8b02bd79425ecbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13624221ac7e06fc5ebd48b21ed0de10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/055bd850286feebbeac5df481988b1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2024-03-08更新
|
1248次组卷
|
4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
名校
4 . 函数
,
,
.已知
有极小值
,
有极小值
.
(1)求
的取值范围;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ea83afd86cb24bb191956d6dd68106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427352f1d09e1f6ee7c54cadaca64906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f371d431b6c91972b742c426c8a81ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
5 . 已知抛物线
,过焦点
的直线
与
交于
两点,且
的最小值为2.
(1)求
的方程;
(2)过
且与
垂直的直线交
于
两点,设直线
的中点分别为
,过坐标原点
作直线
的垂线,垂足为
,是否存在定点
,使得
为定值,若存在,求出点
坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa877db8dc1b03f1581106dfd5211ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9e6b473819e4e88341e2d98004de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
有两个不同的零点
.
(1)求实数
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f39c41fdb528c5568ae47945d093e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b0ebd86fc43bcf6d8261652ffef3d0.png)
您最近一年使用:0次
2024-02-12更新
|
1165次组卷
|
3卷引用:专题03 函数的概念与性质(含导数)
解题方法
7 . 设
为抛物线
的焦点,
是抛物线
的准线与
轴的交点,
是抛物线
上一点,当
轴时,
.
(1)求抛物线
的方程.
(2)
的延长线与
的交点为
,
的延长线与
的交点为
,点
在
与
之间.
(i)证明:
,
两点关于
轴对称.
(ii)记
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3baa6d3cf25af55055fb8e1c4dcccd91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323232ab36943d1d5d2831d70ffcff87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a780261d7c91ccf6b5dc0f580146b1a4.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a0c85deb80d8e63bc60127e803f7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d4c08ed526b54460c4d6fda1c11b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d7df4d3cf520d9d9355394c0a884bb.png)
您最近一年使用:0次
2024-02-05更新
|
525次组卷
|
3卷引用:河北省邢台市2024届高三上学期期末数学试题
8 . 已知函数
.
(1)证明曲线
在
处的切线过原点;
(2)讨论
的单调性;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47dd2852e029e5b030f26a5ad0543bb.png)
(1)证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68cb9f9f7935fd5703f46181db6e4db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-04更新
|
2312次组卷
|
5卷引用:专题03 函数的概念与性质(含导数)
9 . 已知函数
.
(1)设
且
,求
在区间
内的单调递减区间(用
表示);
(2)若
,函数
有且仅有2个零点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04ae16feb41a56b5495b0d1a4c788f0.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a898370f495ce22ad03a441a6ec778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c50021fcf7b959aa2fe77f676dc4d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
23-24高二·江苏·假期作业
名校
解题方法
10 . 已知定义在
上的函数
和
.
(1)求证:
;
(2)设
在
存在极值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d40624fc4d5a669a76185052ee6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8578c6d7d390a36d1728070bbd9cc14.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e312eca38032174f9739126b81d012.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4354638374e9db54f784e28d8b23c597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-01-30更新
|
614次组卷
|
3卷引用:河北省石家庄市第二中学2024届高三上学期第一次模拟测试数学试题