名校
1 . 下列说法正确的是( )
A.已知幂函数![]() ![]() ![]() |
B.函数![]() ![]() ![]() |
C.已知![]() ![]() ![]() ![]() |
D.已知函数![]() ![]() ![]() |
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2卷引用:湖北省咸宁市崇阳县第二高级中学2023-2024学年高一上学期期末模拟考试数学试题
2 . 已知点
为
图象上一点,点
为
图象上一点,
为坐标原点,设
,
的夹角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdad8acb5f4d31bfee990bf844b1a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() ![]() | B.![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() ![]() |
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解题方法
3 . 某学校为了普及防溺水安全知识,对本校1000名学生开展了一次防溺水安全知识竞赛答题活动,从中随机抽取100名学生的得分,按照
分成六段,整理得到如图所示的频率分布直方图,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f2545a52537ce09154671883356fe4.png)
A.根据直方图,该校竞赛得分落在![]() |
B.根据直方图,该校竞赛得分的第75百分位数估计大于130 |
C.根据直方图,该校竞赛得分的众数约为135 |
D.根据直方图,该校竞赛得分的平均分约为121 |
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4 . 已知
,过点
(
)作
图象的切线
.
(1)求切线
的斜率的最大值.
(2)证明:切线
与
在第一象限仅有一个交点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbad69de967d3873f571c72e4e4e49fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b151ae04f963028ab2df8b46a86b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a3a46e58d634eebaea7f5c6213fba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7ba4e6f59fcf28d820cb602698089c.png)
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5 . 已知
,
既是双曲线
:
的两条渐近线,也是双曲线
:
的渐近线,且双曲线
的焦距是双曲线
的焦距的
倍.
(1)任作一条平行于
的直线
依次与直线
以及双曲线
,
交于点
,
,
,求
的值;
(2)如图,
为双曲线
上任意一点,过点
分别作
,
的平行线交
于
,
两点,证明:
的面积为定值,并求出该定值.
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565bc68d208cd5e0c90a32851faf3814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/2/05fffea4-4f40-4d0c-a514-981af9399e17.png?resizew=146)
(1)任作一条平行于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](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/0c88d9142df6ba8e43c1a93bd04a1362.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/62fcbb76c923a883fee205e7a24fcd9b.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/b1241216f3c1cb5e73043dd1037f556d.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/2205cffebf8c4d5f81d15ed7b85c8936.png)
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|
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湖北省咸宁市2022-2023学年高二下学期期末数学试题(已下线)专题3.9 圆锥曲线中的定点、定值、定直线问题大题专项训练【九大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-1(已下线)第2章 圆锥曲线(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)通关练16 双曲线13考点精练(100题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
名校
解题方法
6 . 随着疫情结束,自行车市场逐渐回暖,通过调查,收集了5家商家对某个品牌的自行车的售价
(百元)和月销售量
(百辆)之间的一组数据,如下表所示:
根据计算可得
与
的经验回归方程是:
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
价格![]() | 9.6 | 9.9 | 10 | 10.2 | 10.3 |
销售![]() | 10.2 | 9.3 | ![]() | 8.4 | 8.0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6350f77bc5a2f3a93c575fefbeedae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.8.8 | B.8.9 | C.9 | D.9.1 |
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|
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湖北省咸宁市2022-2023学年高二下学期期末数学试题湖南省五市十校教研教改共同体、三湘名校教育联盟、湖湘名校教育联合体2022-2023学年高二下学期7月期末联考数学试题吉林省长春市十一高中2022-2023学年高二下学期期末数学试题(已下线)专题05 成对数据的统计分析(5大考点经典基础练+优选提升练)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)江苏省无锡市江阴市两校联考2023-2024学年高二下学期5月阶段性练习数学试题
7 . 如图,已知正六边形
的顶点分别是正六边形
的边
上的点,其中
,若正六边形
和
的面积分别为
,且满足
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5949184e158b99bbac9fa116feb0fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80edb3049a8391c224dba21094954766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e2b3b0497d1b7c8e798d72b082dfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5949184e158b99bbac9fa116feb0fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b368f407280d39c2f75e10a2d3c48f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3943cf7284199135a76add0186c92918.png)
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名校
8 . 已知集合
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4619dfeeec373d66511967ba6c065363.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知点
和直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d727778ea634df7c6607096bee39b0c8.png)
点
是点A关于直线
的对称点.
(1)求点
的坐标;
(2)
为坐标原点,且点
满足
.若点
的轨迹与直线
有公共点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9c730266ecf448c14608e24d37b986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d727778ea634df7c6607096bee39b0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3361eae6ffd24142f2e935dda5f552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3a18adae759548edaa008e80fd29d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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|
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4卷引用:湖北省咸宁市2022-2023学年高二上学期期末数学试题
名校
解题方法
10 . 若数列
满足
,
,则称该数列为斐波那契数列
如图所示的“黄金螺旋线”是根据斐波那契数列画出来的曲线
图中的长方形由以斐波那契数为边长的正方形拼接而成,在每个正方形中作圆心角为
的扇形,连接起来的曲线就是“黄金螺旋线”
记以
为边长的正方形中的扇形面积为
,数列
的前
项和为
,则 ( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/b771b941-bb0a-4431-9a09-4e7475fd758f.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be7f38256b38b88ac5c7d5cec9d407d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/b771b941-bb0a-4431-9a09-4e7475fd758f.png?resizew=158)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8卷引用:湖北省咸宁市2022-2023学年高二上学期期末数学试题
湖北省咸宁市2022-2023学年高二上学期期末数学试题湖北省部分地区2022-2023学年高二上学期元月期末数学试题(已下线)模块四 专题3 重组综合练(湖北)期末终极研习室(高二人教A版)第五章 数列(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教B版2019)安徽省滁州市定远县民族中学2022-2023学年高二下学期3月第一次月考数学试题(已下线)专题10 数列通项公式的求法 微点2 累加法(已下线)广东省深圳市深圳中学2023-2024学年高二上学期期中数学试题福建省厦门市第二中学2023-2024学年高二上学期第二次月考数学试题