1 . 如图所示,海尔学校要在操场上一个扇形区域内开辟一个矩形花园ABCD,现已知扇形圆心角为
,扇形半径为10
,则该矩形花园的面积的最大值为__________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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2 . 临沂一中校本部19、20班某数学兴趣小组在探究扇形时,发现如下现象:如图所示,⊙B向⊙A靠近的过程,就像月亮被磨弯一样.已知在某一时刻,圆A和圆B处于图1的状态,简化后如图2,
,
,
.则S阴影=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c88df39a169407053491a8f6690d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aed85ba8001c6ef155efb6f0f26b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb3d1070981fed5ca65a34bb2282e6f.png)
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2024-02-20更新
|
456次组卷
|
5卷引用:山东省临沂第一中学2023-2024学年高一上学期期末模拟数学试题
山东省临沂第一中学2023-2024学年高一上学期期末模拟数学试题(已下线)5.1.2弧度制(已下线)1.2&1.3 任意角与弧度制-同步精品课堂(北师大版2019必修第二册)河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期3月月考数学试题(已下线)第一章三角函数章末十九种常考题型归类(1)-【帮课堂】(北师大版2019必修第二册)
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3 . 下列四个命题中,
①集合
,且
,则实数
的取值集合是
;
②使得不等式
成立的一个充分条件是
;
③已知
,则
的取值范围是
;
④若
,则
的最小值是8;
⑤若
,则
的取值范围是
;
其中真命题的序号是__________ .
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd9a3d1537cb3ad4a6f538334f79ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbbe46a98a8fdebfc46fcbc45dc88e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebd7c565ca0e0f8b73fedda791479c5.png)
②使得不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9628a52a2d66782e5ea1a5dadf28444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccaa6e503b61e9ae78d8439cba2e328.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cbceb0d573d213b8f8ae91cf0b57d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20c6ab2d0f475b20bb945c1692b6c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342338eded5a03c00eb02ef7f7cf836e.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0bd65eb59d0acde6f5955490696c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2bd515c3c7f10f253d03d494fbb392a.png)
⑤若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2603458b29d71ebfb1b0432f991836ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d89f74ade1b380747d247f0eed0da0.png)
其中真命题的序号是
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2023-10-08更新
|
295次组卷
|
5卷引用:山东省淄博实验中学2023-2024学年高一上学期数学10月月考数学试题
4 . 在平面直角坐标系xOy中,函数
的图象与x轴交于点A,与直线
交于点B,C.现定义横坐标和纵坐标都是整数的点叫做整点,记线段AB,BC,AC围成的区域(不含边界)为P.若区域P内恰好有3个整点,则m的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efefec1202859f52d09ae00c2094b398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509c7095601da30b432ffe912cd607e3.png)
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5 . 在平面直角坐标系xOy中,已知以原点为圆心,2为半径的
,如图.现有直线l:
交x轴于点C,在该坐标系中作
,使
,
,线段AB关于直线l对称的对应线段
恰好为
的弦.当b取得最大值时,相应的BC的长为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520b2367c68ffc046e0e5381f92dada6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/23/a9b8c70f-ee3d-41b8-a521-1567f55963f5.png?resizew=121)
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6 . 将形如
和
为正整数)的正整数从小到大排列,并依次记为
若第
个数
,则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade9841a8e6840efddcfd8620a6fc1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092cde2151622e2aaf5a8770d932256d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5784f3ed0a37b512f313833f5d5b19d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1575182262e509760d01263df9360795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7 . 设
是正整数,且是15的倍数,
.已知
是完全平方数,
是完全立方数,
是完全5次方数,则
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627c25c462b941ad286de74a0ea94aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd479b1ab6ae715f99d21811f5026e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1ecac96594bae0d53a744fb9ceb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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8 . 在《数书九章》(宋·秦九韶)中记载了一个测量塔高的问题:如图所示,
表示塔的高度,
表示竹竿顶端到地面的高度,
表示人眼到地面的高度,
、
、
在同一平面内,点A、C、E在一条水平直线上.已知
米,
米,
米,
米,人从点F远眺塔顶B,视线恰好经过竹竿的顶端D,可求出塔的高度.根据以上信息,塔的高度为______ 米.
![](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/49b50357a6545cae8348e3059312f520.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0566be94b1ed3e5d250ca530eeb529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052d471177df219bfec13448f539f19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a6241af8eadb720f601ee48f74cb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1ceb0742d31738f59ee2c5271c1571.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/b2801555-6cd8-41ab-b241-8467a09ce18b.png?resizew=188)
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9 . 如图,将菱形纸片ABCD沿过点A的直线折叠,点C,D的对应点分别是
,且
,折痕AP交BC于点P.若
,
,则PC的长等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c37547156910f5307b8a0c496909f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b12244133a814fe29c3e781046695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4d00b86b2f067b902baf6e52f0faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/33c93223-1736-4d0e-86ba-86cd74827cf1.png?resizew=213)
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10 . A,B两地相距60km,甲、乙两人骑车分别从A,B两地同时出发,相向而行,匀速行驶.乙在途中休息了0.5h后按原速度继续前进.两人到A地的距离s(km)和时间
(h)的关系如图所示,则出发______ h后两人相遇.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/a9c44b1a-5bac-4614-9628-d1260f37de72.png?resizew=168)
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