1 . 已知无穷数列
,构造新数列
满足
,
满足
,
,
满足
,若
为常数数列,则称
为
阶等差数列;同理令
,
,
,
,若
为常数数列,则称
为
阶等比数列.
(1)已知
为二阶等差数列,且
,
,
,求
的通项公式;
(2)若
为
阶等差数列,
为一阶等比数列,证明:
为
阶等比数列;
(3)已知
,令
的前
项和为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22e75bf99dcb0fe32f66fa90a74f9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc06ff2f65c456efb6a114e67b62cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d16e3ca4fb65342b0e9a0594d661ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf623a6dd661f87cf64ea150072fd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcbdf91bb5a49f293f9b52ac8dcfa35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab5abd104649f9a3c231df9a55813a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c653f3a05dd25f6affdba7baeab38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0606df3b6fbc6fcf863f9c59e0e54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab214e5f34d976717284bed52c645e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e796a0144ff9b3329c7064a01c5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a4b318fa151fab14b3857942ed3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07418f1fa0f6569b50944b5a13ffa021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7778648d93a10ed66ddd99672d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.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/a2a5a414f3f5d724058a2e887f3d1c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
名校
2 . 在等腰梯形
中,CD的中点为O,以O为坐标原点,DC所在直线为x轴,建立如图所示的平面直角坐标系,已知
.
;
(2)若点F在线段CD上,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2d09493b38fc4c41cb19f0c4b6f53c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1239d20fa03551421f0949d878fe541.png)
(2)若点F在线段CD上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aef759150f9e9a60042788fbf1a7ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980201d3fea976d86a818fee73faf1bd.png)
您最近一年使用:0次
7日内更新
|
275次组卷
|
4卷引用:河北省保定市定州市第二中学2023-2024学年高一下学期5月月考数学试题
名校
3 . 设
,
.
(1)若x,y均为锐角且
,求z的取值范围;
(2)若
且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d018fc39fe3a5feee51a08ee8c58483e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ebed1b93046c28dd4ce381df0ca441f.png)
(1)若x,y均为锐角且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3085600fba3d8ce8403ddc8b44996f88.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7204495706847fd4c8abc55e89c9a35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598caae9102ce0b49bdd2ea12189562d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eca80d80b6e1577762585b69145736b.png)
您最近一年使用:0次
2024-06-13更新
|
48次组卷
|
3卷引用:四川省成都市树德中学2023-2024学年高三下学期适应性考试数学(文)试题
4 . 现随机对
件产品进行逐个检测,每件产品是否合格相互独立,且每件产品不合格的概率均为
.
(1)当
时,记20件产品中恰有2件不合格的概率为
,求
的最大值点
;
(2)若这
件产品中恰好有
件不合格,以(1)中确定的
作为
的值,则当
时,若以使得
最大的
值作为
的估计值,求
的估计值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f260c8bc16d2564b65309a57a860053.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb2ad93be53f0838c8563903ad31b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a0be4eebc5d70c51f72f28dbfc11e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a0be4eebc5d70c51f72f28dbfc11e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b053ad342b809a8bbef2dd73d925b9f.png)
(2)若这
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc301d5e7f82a5c6f6a1aaa80becd900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b053ad342b809a8bbef2dd73d925b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e16f64a24257b2d244c5b26b2133a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090fad640f7d6942bc04bdd78ef9a4c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
解题方法
5 . 已知函数
的导函数为
,
的导函数为
,对于区间A,若
与
在区间A上都单调递增或都单调递减,则称
为区间A上的自律函数.
(1)若
是R上的自律函数.
(ⅰ)求a的取值范围;
(ⅱ)若a取得最小值时,
只有一个实根,求实数t的取值范围;
(2)已知函数
,判断是否存在b,c及
,使得
在
上不单调,且
是
及
上的自律函数,若存在,求出b与c的关系及b的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6710a9e70f5e01e62df02c7977fb99.png)
(ⅰ)求a的取值范围;
(ⅱ)若a取得最小值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e5b4bb2360c7df054d14d0a20186da.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a0c15b208d3096fdf206a6ac918c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2188a7cdcc9dac14ffbbc2239c81a7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfdd3d02b54e997cbec983d80f6bafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b14ccdd85f5f2f59f6b0ef3329f34a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1057fe66bead8b39e4099ca62a9d5a28.png)
您最近一年使用:0次
6 . 已知在平面直角坐标系中,直线
交坐标轴于A、B两点,直线
交坐标轴于C、D两点,已知点
,
.
与
交于点E,试判断
的形状,并说明理由;
(2)点P、Q在
的边上,且满足
与
全等(点Q异于点C),直接写出点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e24de76e6f9a6097f890bc2f395904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a01e2e3d40112fdeeb464f81eaac1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eae074b97ec3ff58fbd9d556aea81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5a48393681b882d719f5562235ba11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
(2)点P、Q在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9dc427a01582ec222446b352d40ab0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
您最近一年使用:0次
7 . 抛物线
与x轴交于A,B两点,与y轴交于点C,点P为抛物线上一动点,过点P作PQ平行BC交抛物线于点Q,P,Q两点间距离为m.
(2)取线段BC中点M,连接PM,当m最小时,判断以点P,O,M,B为顶点的四边形是什么四边形;
(3)设N为y轴上一点,在(2)的基础上,当
时,求点N的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9ca095c086211e4b676d3a948d046a.png)
(2)取线段BC中点M,连接PM,当m最小时,判断以点P,O,M,B为顶点的四边形是什么四边形;
(3)设N为y轴上一点,在(2)的基础上,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1a52ee810c2c090f61e8d4e1e788d7.png)
您最近一年使用:0次
8 . 如图,在平面直角坐标系中,抛物线
经过
、
、
.
(2)点D是线段BC上一动点,点D关于AC、AB的对称点分别为点M、N,连接MN交线段AC、AB于E、F.求
最小值;
(3)在(2)的条件下请直接写出线段MN的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6bbbb53aaeab0ab7a242228cc510fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0bc3a43265b63b6964476ca327fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850e01debd266a398b597a1876dbb3ea.png)
(2)点D是线段BC上一动点,点D关于AC、AB的对称点分别为点M、N,连接MN交线段AC、AB于E、F.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13106b48acf096f7fc9ac1e49559b130.png)
(3)在(2)的条件下请直接写出线段MN的取值范围.
您最近一年使用:0次
名校
9 . 今年6月份,永州市某中学开展“六城同创”知识竞赛活动,赛后,随机抽取了部分参赛学生的成绩,按得分划为A,B,C,D四个等级,
,
,
,
,并绘制了如图两幅不完整的统计图,请结合图中所给信息,解答下列问题:
(2)扇形统计图中
______,
______,B等级所占扇形的圆心角度数为______.
(3)该校准备从上述获得A等级的四名学生中选取两人参加永州市举行的“六城同创”知识竞赛,已知这四人中有两名男生(用
,
表示),两名女生(用
,
表示),请利用树状图法或列表法,求恰好抽到1名男生和1名女生的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b788f849213c9bede89249019d87808d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e507529b30a6ff85a1f089bd31a7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbfd347f5c3a2ae250f732fa9ab849f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4965f1128f8c5a418c24e39a51c364c0.png)
(2)扇形统计图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
(3)该校准备从上述获得A等级的四名学生中选取两人参加永州市举行的“六城同创”知识竞赛,已知这四人中有两名男生(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024e2379c58191758f8bd7602a6bcb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34a75c2a392f235c5f07b91d9fb58d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4450b959d69fdf09b38ba82fe132ec33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c89fcb4633216e492ed5a04cf45eed.png)
您最近一年使用:0次
名校
10 . 在平面直角坐标系
中,抛物线
经过点
和
,且在
轴上截得的线段长为
.
(1)求抛物线
的解析式;
(2)已知点
在抛物线
上,且在其对称轴右侧,点
在抛物线
的对称轴上,若
是以
为斜边的等腰直角三角形,求点
的坐标;
(3)将抛物线
向左平行移动3个单位得到抛物线
,直线
与
交于
两点,直线
与
交于
两点,若
分别为线段
和线段
的中点,连
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c7a611e99d7785f66cd22fd8ee5e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec40ff4479edca2ed18b6cadb8db72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e8b766829220981993a9bd024e6b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)将抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa841ce5d58b64f747a3c1b69bb20a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f5921423b5d7a0723968a8e32d974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次