1 . 如图,2024年元宵节在浙江桐乡凤凰湖举行“放孔明灯”活动.为了测量孔明灯的高度,在地上测量了一根长为200米的基线
,在点
处测量这个孔明灯的仰角为
,在
处测量这个孔明灯的仰角为
,在基线
上靠近
的四等分点处有一点
,在
处测量这个孔明灯的仰角为
,则这个孔明灯的高度![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a548e8a2e2205f2faa87e25180a083.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ec007c9c7ce7e13af3ca8b84c64ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc0c3626d9b2c9cc92403e99e727912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c0b52fdca650c96f803556a514b08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a548e8a2e2205f2faa87e25180a083.png)
您最近一年使用:0次
解题方法
2 . 已知
,且
,点P的轨迹为C.
(1)求C的方程;
(2)直线l:
与C相交于M,N两点,第一象限上点T在轨迹C上.
(ⅰ)若
是等边三角形,求实数k的值;
(ⅱ)若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8440227efdc641333e2b39c8497a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55388e2f910665e103b168af61c1fa76.png)
(1)求C的方程;
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf66a5f30d94390f59c6a3d1ae6c46.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e849753c1b4bbab8327c5ade6cc2469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf66a5f30d94390f59c6a3d1ae6c46.png)
您最近一年使用:0次
3 . 已知复数
,
是方程
的解,复平面内表示
的点A在第四象限,O是原点.
(1)点A关于虚轴的对称点为点B,求向量
对应的复数;
(2)将复数
对应的向量
绕原点逆时针旋转
得到向量
,
对应的复数为
,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd94ededc533b2bd356576d94e1ea6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
(1)点A关于虚轴的对称点为点B,求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
(2)将复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f28b09c6074898b0bf992928336eb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f28b09c6074898b0bf992928336eb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeaaa82e920b2caa9d11b9071fab385a.png)
您最近一年使用:0次
4 . 平行四边形ABCD中
,且
,AB、CD的中点分别为E、F,将
沿DE向上翻折得到
,使P在面BCDE上的投影在四边形BCDE内,且P到面BCDE的距离为
,连接PC、PF、EF、PB,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
A.![]() |
B.![]() |
C.三棱锥![]() ![]() |
D.点Q在线段PE上运动,则![]() ![]() |
您最近一年使用:0次
解题方法
5 . 若函数
有且仅有一个极值点
,函数
有且仅有一个极值点
,且
,则称
与
具有性质
.
(1)函数
与
是否具有性质
?并说明理由.
(2)已知函数
与
具有性质
.
(i)求
的取值范围;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0112af71e654cc86c8d5056fdbb2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861433f0c552c5bef8d8c03682d91858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0112af71e654cc86c8d5056fdbb2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861433f0c552c5bef8d8c03682d91858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d77fbccb3ae7f7836d16dfb4952e4cc.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d2a4a953934dcaf87f2ce64c6dab4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0482361cb97998139441fe0deb23578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9d58d2cef0d86281fdde5895a129a6.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b00477b17f5248a7301290d260a6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5eef1c41c5ed94a4944e062bcfeeeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36ea881341f274252964bc3a9fc5693.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926521541bf1c18ac229afc5ec2d9b51.png)
您最近一年使用:0次
6 . 小明进行足球射门训练,已知小明每次将球射入球门的概率为0.5.
(1)若小明共练习4次,求在射入2次的条件下,第一次没有射入的概率;
(2)若小明进行两组练习,第一组射球门2次,射入
次,第二组射球门3次,射入
次,求
.
(1)若小明共练习4次,求在射入2次的条件下,第一次没有射入的概率;
(2)若小明进行两组练习,第一组射球门2次,射入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8aa586c1ddb027aa28b40f5af8089d3.png)
您最近一年使用:0次
7 . 已知实数
,若
,且这四个数的中位数是3,则这四个数的平均数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f231fa3b79f7545a0ac5e70c6e924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4477f01e29104dafaadb67f1813b4eb2.png)
A.![]() | B.3 | C.![]() | D.4 |
您最近一年使用:0次
名校
8 . 已知函数
其中
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4911900ac1c8fb5b0bc6b64f1ad6f030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166cc3bc78f3870fc454556a1c8b5dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
A.![]() | B.函数![]() |
C.![]() | D.![]() |
您最近一年使用:0次
7日内更新
|
523次组卷
|
3卷引用:浙江省杭州市西湖高级中学2024届高三下学期数学模拟预测数学试题
解题方法
9 . 颐和园的十七孔桥,初建于清乾隆年间;永定河上的卢沟桥,始建于宋代;四川达州的大风高拱桥,修建于清同治7年,这些桥梁屹立百年而不倒,观察它们的桥梁结构,有一个共同的特点,那就是拱形结构,这是悬链线在建筑领域的应用.悬链线出现在建筑领域,最早是由十七世纪英国杰出的科学家罗伯特·胡克提出的,他认为当悬链线自然下垂时,处于最稳定的状态,反之如果把悬链线反方向放置,它也是一种稳定的状态,后来由此演变出了悬链线拱门,其中双曲余弦函数就是一种特殊的悬链线函数,其函数表达式为
,相应的双曲正弦函数的表达式为
.若关于x的不等式
对任意的
恒成立,则实数m的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac589ba73bc40a28bad3d87a04aef28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28a8261e70a026905cd74ed17d13845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b08048f0922fc9ef6f70d790b41d8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 已知函数
.
(1)当
时,求
,并判断函数
零点的个数;
(2)当
时,
有三个零点
,记
,
,2,3.证明:①
;②
.
参考公式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dc59a1edc821f4cbd77ef908dff3c7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6fb3c74056a4b4ebbda9d2be78de34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e6f74fdd5c57d4454f8e840563771a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722f025aeed67dbc2c16f60c3b06061d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b41b7154250380217e8dc70ff2a7591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4142405dce1c99e4c58474c00b2bd6e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65021f540ac58a37746758611f2fd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69673c72476d11a283eb5e4d1f7a72.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26aa2c8a73ca9a054ed46e16eb5811e5.png)
您最近一年使用:0次