解题方法
1 . 把一条线段分割为两部分,使较长部分的长度与全长的比值等于较短与较长部分的长度的比值,这个比值称为黄金分割比(简称黄金比).黄金比在建筑、艺术和科学等领域中都有广泛应用.我们把顶角为
的等腰三角形称为黄金三角形,它满足较短边与较长边的长度之比等于黄金比.由上述信息可求得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5bef7ce8a5dc9f61a9a795e41030432.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e411abb2d185fa546789b89e0fa5c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5bef7ce8a5dc9f61a9a795e41030432.png)
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2 . 已知集合
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493a867ea76c734d822dabdbbf3afaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad96b50521f4bbf3d436d05dc258083d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4753f4a4456d0df13843b71015bfa14.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
3 . 如图所示,已知角
的始边为
轴的非负半轴,终边与单位圆的交点分别为
,
为线段
的中点,射线
与单位圆交于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549f63e3b5c421f653613f7cf3e6f26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() |
B.![]() |
C.点![]() ![]() |
D.点![]() ![]() |
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2024-02-15更新
|
1998次组卷
|
6卷引用:山东省济南市2023-2024学年高一上学期1月期末数学试题
山东省济南市2023-2024学年高一上学期1月期末数学试题安徽省合肥一六八中学2024届高三“九省联考”考后适应性测试数学试题(三)(已下线)8.2.2两家和与差的正弦、正切-同步精品课堂(人教B版2019必修第三册)江西省鹰潭市2024届高三第一次模拟考试数学试题(已下线)信息必刷卷05广东省广州市真光中学2023-2024学年高一下学期期中考试数学试卷
解题方法
4 . 下列四组数中,满足
的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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5 . 水星是离太阳最近的行星,在地球上较难观测到.当地球和水星连线与地球和太阳连线的夹角达到最大时,称水星东(西)大距,这是观测水星的最佳时机(如图1).将行星的公转视为匀速圆周运动,则研究水星大距类似如下问题:在平面直角坐标系中,点A,
分别在以坐标原点
为圆心,半径分别为1,3的圆上沿逆时针方向做匀速圆周运动,角速度分别为
,
.当
达到最大时,称A位于
的“大距点”.如图2,初始时刻A位于
,
位于以
为始边的角
的终边上.
,当A第一次位于
的“大距点”时,A的坐标为______ ;
(2)在
内,A位于
的“大距点”的次数最多有______ 次
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3551176fd3003244122a34612d90113c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c896216c135b8c568a5f0987c23947e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f9341d51c827a29a4a0b0b3dded16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c7f579d5017888a314d681fe44db8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590e165e407098fcac9f871beb047dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf01af951cc03381ca19150c6fe5364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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解题方法
6 . 如图所示,某开发区有一块边长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
的正方形空地
.当地政府计划将它改造成一个体育公园,在半径为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
的扇形
上放置健身器材,并在剩余区域中修建一个矩形运动球场
,其中
是弧
上一点,
分别在边
上.设
,球场
的面积
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/168266f9-ffe2-4586-9398-e3218f8a6de0.png?resizew=163)
(1)求
的解析式;
(2)若球场平均每平方米的造价为
元,问:当角
为多少时,球场的造价
最低.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38a6341dbb03ec2c0c10e5353a07c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3029ea5516e56e8d20594c71929624f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340ecf16f5e8ef7f72f956fc02e86d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3029ea5516e56e8d20594c71929624f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99342ab6aac415bbf5bdecd08d2cccb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/168266f9-ffe2-4586-9398-e3218f8a6de0.png?resizew=163)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99342ab6aac415bbf5bdecd08d2cccb.png)
(2)若球场平均每平方米的造价为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd1535418f1f6a2dafcdd0846734f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
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名校
解题方法
7 . 雅各布·伯努利(Jakob Bernoulli,1654-1705年)是伯努利家族代表人物之一,瑞士数学家,他酷爱数学,常常忘情地沉溺于数学之中.伯努利不等式就是由伯努利提出的在分析不等式中一种常见的不等式.伯努利不等式的一种形式为:
,
,则
.伯努利不等式是数学中的一种重要不等式,它的应用非常广泛,尤其在概率论、统计学等领域中有着重要的作用.已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fe85f6383f5b2aca40ab15ba4bc248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d4045366a437d4003259050718e244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37510088319e438ceee842590ab6e3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56893c747445bebabfe192eca5b9eaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24311368ea9d298e36fdb3562093fc68.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 下列说法正确的是( )
A.![]() ![]() | B.若![]() ![]() |
C.当![]() ![]() | D.已知![]() ![]() |
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名校
9 . 如图,已知直线
,
分别在直线
,
上,
是
,
之间的定点,点
到
,
的距离分别为
,
,
.设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/947a1fd9-bd67-4420-9249-8d6f167bd310.png?resizew=156)
(1)用
表示边
,
的长度;
(2)若
为等腰三角形,求
的面积;
(3)设
,问:是否存在
,使得
?若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.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/7f9e8449aad35c5d840a3395ea86df6d.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/7f9e8449aad35c5d840a3395ea86df6d.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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289a5d041c76475437bf2ab8d1169280.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/947a1fd9-bd67-4420-9249-8d6f167bd310.png?resizew=156)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73f691e91c1a725fbd6fd3d719a24b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600369eee391636a0d3ab5e9d9bf655e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2024-01-31更新
|
399次组卷
|
2卷引用:河北省唐山市2023-2024学年高一上学期期末考试数学试题
10 . 在平面直角坐标系xOy中,半径为2的圆O与y轴非负半轴的交点为
,动点P从
出发,以1rad/s的角速度按顺时针方向在圆O上做匀速圆周运动,则2s时点P的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次