名校
1 . 足球教练带领运动员对“带球射门”进行专项训练.如图,教练员指导运动员沿着与边路
平行的路线带球并起脚射门,教练员强调要在路线上的相应位置
处起脚射门进球的可能性最佳(即点
对球门
所张的角
最大),假如每条虚线都表示在规定的区域
内为运动员预设的带球路线,而每条路线上都有一个最佳起脚射门点
,为了研究方便,如图建立坐标系,设
、
,
在
轴的上方.
,求此时
的外接圆的圆心坐标
(2)过点
作
轴的垂线,垂足为
,若
,求当
最大时,点
的坐标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb898663f98b8400a897913b4d3102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e7030cc9fb09f86c6cdab7d912ed31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506512c81d3523a4a6c307ccc14f1583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
2 . 若
,
,
,
,则
的值等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f07029c97c324d32f258f18a96654a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5059dca84cb4580174d8b911bbe0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efac3f630599fe34aadd7c51ca48c061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3884b343d76a26b4b85b48987d7064.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-26更新
|
422次组卷
|
5卷引用:上海市延安中学2023-2024学年高一下学期期中考试数学试题
上海市延安中学2023-2024学年高一下学期期中考试数学试题(已下线)考题猜想01三角-期末考点大串讲(沪教版2020必修二)(已下线)专题01 三角函数公式常考题型归类-期末考点大串讲(人教B版2019必修第三册)广西南宁市第三中学五象校区2024届高三最后套卷(四)数学试题江西省上高二中2024届高三适应性考试数学试卷
名校
解题方法
3 . 已知函数
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38e596d5cf8bd174544b8319940d6c2.png)
(1)求
的值
(2)若存在
,使得等式
成立,求实数
的取值范围;
(3)若对任意
都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2b27dfa7123e7bb2792632dc6a3f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38e596d5cf8bd174544b8319940d6c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3df2a0f63978a70bb9affcd2e1a693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06d4aa6849bbb8b543a0b361e1ebb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79d2951323344a72bce6bb2c700e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 如图是函数
的部分图象,其中点
在
轴上且过
点的竖直线经过图象的最高点,
是图象上一点,
是线段
与图象的交点,且
,则
点的纵坐标是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f552dba7c0d8c1038a91ba98fa9aa6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19c3dc7d68e709093f2b1aeea4ebb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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5 . 已知圆
为锐角
的外接圆,
.若动点P可在圆O上任意移动,则
的取值范围为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e83ac5efc4c142c43c5e7a3e156c407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a3e4a62eed6eb1eff42ed688801895.png)
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解题方法
6 . 函数
的值域为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6365d70625efb472663b899cf0847ebc.png)
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名校
解题方法
7 . 已知
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9da6f152a33ef475161c9e396647225.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcbe8b4bcd32e5a64ebfd873f8cbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2564d60c75ee81676e748474164267ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1ce72d88d211e733fd317f4c77b93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fed36a9711ee2f1c48db10420dc6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9da6f152a33ef475161c9e396647225.png)
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名校
8 . 如图,某公园有一块扇形人工湖OAB,其中
,
千米,为了增加人工湖的观赏性,政府计划在人工湖上建造两个观景区,其中荷花池观景区的形状为矩形PCOD,喷泉观景区的形状为△PBC,且C在OB上,D在OA上,P在
上,记
.
分别表示矩形PCOD和
的面积,并给出角
的取值范围;
(2)若在PD的位置架起一座观景桥,已知建造观景桥的费用为每千米8万元(包含桥的宽度费用),建造喷泉观景区的费用为每平方千米16万元,建造荷花池的总费用为6万元.求当
为多少时,建造该观景区总费用最低,并求出其最低费用.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac51bffb8f476896081027b33f7ec25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c20e5e01e88591113257c46fe308ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ff139f605ee0df463ad9f64089e542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若在PD的位置架起一座观景桥,已知建造观景桥的费用为每千米8万元(包含桥的宽度费用),建造喷泉观景区的费用为每平方千米16万元,建造荷花池的总费用为6万元.求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2024·全国·模拟预测
9 . 已知函数
,若
的图象在
上有且仅有两条对称轴,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611792520f93bc93445492610823eac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4b61d912f99e5583e7e17cf8fef558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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10 . 某临海地区为保障游客安全修建了海上救生栈道,如图,线段
、
是救生栈道的一部分,其中
,
,
在
的北偏东
方向,
在
的正北方向,
在
的北偏西
方向,且
.若救生艇在
处载上遇险游客需要尽快抵达救生栈道
,则最短距离为___________ m.(结果精确到1 m)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13067253e5dccb6962d8ac8f36273739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400227dcaf0d2206547d0a73f6edde7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391479c151307826c9765a47a5f10503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5d53e570a2f8516c7af8b22662c195.png)
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