名校
1 . 海宝塔位于银川市兴庆区,始建于北朝晚期,是一座方形楼阁式砖塔,内有木梯可盘旋登至顶层,极目远眺,巍巍贺兰山,绵绵黄河水,塞上江南景色尽收眼底.如图所示,为了测量海宝塔的高度,某同学(身高173cm)在点
处测得塔顶
的仰角为
,然后沿点
向塔的正前方走了38m到达点
处,此时测得塔顶
的仰角为
,据此可估计海宝塔的高度约为__________ m.(计算结果精确到0.1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e0c2455a9e796bba6861503f0fe31b.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea06b78df3f0847f358714357a18d30.png)
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7日内更新
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294次组卷
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3卷引用:福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题
福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题宁夏回族自治区银川九中、平罗中学、贺兰二高、西吉中学2024届高三第四次模拟考试联考数学(文)试题(已下线)【高一模块一】难度8 小题强化限时晋级练(较难2)
2 . 陶瓷茶壶是中国人很喜爱的一种茶具,不少陶瓷茶壶兼具实用性与艺术性,如图所示的陶瓷茶壶的主体可近似看作一个圆台型容器,忽略茶壶的壁厚,该圆台型容器的轴截面下底为10cm,上底为6cm,面积为
,则该茶壶的容积约为______ L(结果精确到0.1,参考数据:
;
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa574e9bd11e6f437175cccf618c87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8639b0b48393b0a99719216160822336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17e2352d0c9ec14cb23b702efe5ba30.png)
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2024-06-17更新
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298次组卷
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2卷引用:福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题
名校
3 . 已知双曲线
的上、下顶点分别为
.
(1)若直线
与
交于
两点,记直线
与
的斜率分别为
,求
的值;
(2)过
上一点
作抛物线
的切线
和
,切点分别为
,证明:直线
与圆
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ff07459dc1549f2a66429eca9829e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a8d6991873e79b298984a95b8954b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fda21944581898ccb13c7d4641b7f9.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
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4 . 甲企业生产线上生产的零件尺寸的误差
服从正态分布
,规定
的零件为优等品,
的零件为合格品.
(1)从该生产线上随机抽取100个零件,估计抽到合格品但非优等品的个数(精确到整数);
(2)乙企业拟向甲企业购买这批零件,先对该批零件进行质量抽检,检测的方案是:从这批零件中任取2个作检测,若这2个零件都是优等品,则通过检测;若这2个零件中恰有1个为优等品,1个为合格品但非优等品,则再从这批零件中任取1个作检测,若为优等品,则通过检测;其余情况都不通过检测.求这批零件通过检测时,检测了2个零件的概率(精确到0.01).
(附:若随机变量
,则
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c6adfd75c1091fa9b62ef534a7539a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4461881f5ce6f3c2b8d998784257b0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011d2d889100a1fe8fc948b33b881759.png)
(1)从该生产线上随机抽取100个零件,估计抽到合格品但非优等品的个数(精确到整数);
(2)乙企业拟向甲企业购买这批零件,先对该批零件进行质量抽检,检测的方案是:从这批零件中任取2个作检测,若这2个零件都是优等品,则通过检测;若这2个零件中恰有1个为优等品,1个为合格品但非优等品,则再从这批零件中任取1个作检测,若为优等品,则通过检测;其余情况都不通过检测.求这批零件通过检测时,检测了2个零件的概率(精确到0.01).
(附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6814d3993a9ff7100ccb592db3253e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508ef1c38ba5a4bef237bb0aa8c9107a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350cae728ba08282c79aab748b69b5f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3152d8e8d896808be44680cf14addb.png)
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5 . 计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca81f09e9a1d34577c6dbf743ba3ba9.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca81f09e9a1d34577c6dbf743ba3ba9.png)
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名校
解题方法
6 . 若实数集
对
,均有
,则称
具有Bernoulli型关系.
(1)若集合
,判断
是否具有Bernoulli型关系,并说明理由;
(2)设集合
,若
具有Bernoulli型关系,求非负实数
的取值范围;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2df79c96894e48585d810e2d1180b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de62c03953e609ea331280b1e27ba701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acae4bf2a6bead9d904b70d0480fc0.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5055c43ef4c493c056609f617f38e108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef4609431a6fc9f2755d8e8ca6617b0.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9d408eb7f234bea73e86bff6a453f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5596a9fe31bffbe73af20f611a9a574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953916e76840b10bf27302f42ad98cb9.png)
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2024-05-12更新
|
1030次组卷
|
3卷引用:福建省福州市2024届高三第三次质量检测数学试题
名校
解题方法
7 . 已知等腰梯形
,
,
,圆
为梯形
的内切圆,并与
,
分别切于点
,
,如图所示,以
所在的直线为轴,梯形
和圆
分别旋转一周形成的曲面围成的几何体体积分别为
,
,则
值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-11更新
|
657次组卷
|
6卷引用:福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题
福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)(已下线)【北京专用】高一下学期期末模拟测试A卷宁夏吴忠市吴忠中学2024届高三下学期第五次模拟理科数学试卷(已下线)专题07 立体几何初步(2)-期末考点大串讲(人教B版2019必修第四册)
8 . 如图,以正方形
的边
所在直线为旋转轴,其余三边旋转120°形成的面围成一个几何体
.设
是
上的一点,
,
分别为线段
,
的中点.
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cfa6b4db3a67fcd3c169fd8502a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4193fb98c610f41f9a6c89d046f13d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fb768fc63e1aabddbfb2b3e7c5b51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4d775e9fb8bca58a25e75d5b21b05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57043f1d131e9c7c8b71bf8a68bacbc.png)
您最近一年使用:0次
9 . 点
是椭圆
:
(
)上(左、右端点除外)的一个动点,
,
分别是
的左、右焦点.
(1)设点
到直线
:
的距离为
,证明
为定值,并求出这个定值;
(2)
的重心与内心(内切圆的圆心)分别为
,
,已知直线
垂直于
轴.
(ⅰ)求椭圆
的离心率;
(ⅱ)若椭圆
的长轴长为6,求
被直线
分成两个部分的图形面积之比的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa5d6092f598c7da4796f965e40525a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e43fcb2b96389a11d232758fad1e29.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7168c9b611be134a7a2752aff9d7261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(ⅱ)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7168c9b611be134a7a2752aff9d7261.png)
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名校
解题方法
10 . 记集合
,集合
,若
,则称直线
为函数
在
上的“最佳上界线”;若
,则称直线
为函数
在
上的“最佳下界线”.
(1)已知函数
,
.若
,求
的值;
(2)已知
.
(ⅰ)证明:直线
是曲线
的一条切线的充要条件是直线
是函数
在
上的“最佳下界线”;
(ⅱ)若
,直接写出集合
中元素的个数(无需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8ed79e83f9896873e80c3c4b5a935d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bf53ee2722352957ab61f90a49daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54ade3f669537d031a2be1b4f24a626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165beb63772ec0f7797a71646d0a1ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7cc26a0fe4103db9229df034d5aa70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf2f55da363aa19912ee465d3eb2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063bb2a5c220db357fa36417de213ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da66a74e8ab43f08d4b3949bb7d24e4.png)
(ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a669064772daefdeb12c3ebaf01a581f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a494f5a36475e96c7bc69589f70c3a86.png)
您最近一年使用:0次
2024-05-07更新
|
482次组卷
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2卷引用:福建省福州市2023-2024学年高三下学期4月末质量检测数学试卷