解题方法
1 . 环保生活,低碳出行,电动汽车正成为人们购车的热门选择.某型号电动汽车,在一段平坦的国道进行测试,国道限速.经多次测试得到,该汽车每小时耗电量
(单位:
)与速度
(单位:
)的下列数据:
0 | 10 | 40 | 60 | |
0 | 1325 | 4400 | 7200 |
为了描述国道上该汽车每小时耗电量与速度的关系,现有以下三种函数模型供选择:,
,
.
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2580bb2f3ca0015aca06cf7730fcbe4c.png)
(2)现有一辆同型号汽车从
![](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/dc598e0a0ebea206db23c06ac75fb3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870cd01b72fc36199688bc1be099a86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7759b26a9a0741248bf2bb87ebd01dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc81b52d38d0a8e500860d4ca74415e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6b1a808a8fb5b9834ee114592dca2e.png)
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2024-03-21更新
|
153次组卷
|
2卷引用:湖北省荆门市2023-2024学年高一上学期1月期末学业水平检测数学试题
2 . 在三棱锥
中,M是线段
的中点,
,
,
,
.
(1)证明:P在平面
内的射影O为
的垂心;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3735a467f788624fe63946e0da5b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c327b3e91d8bea53255d9308a952a276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827c7d9ca8f0e06a09bd37e930b3c3ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/d44cbe49-473b-42e9-a1e4-0a171e6be968.png?resizew=156)
(1)证明:P在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
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解题方法
3 . 如图,在平面直角坐标系
中,点
,直线
,设圆C的半径为1,圆心在l上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/5426adc8-1854-4d34-b385-3a24824b222a.png?resizew=147)
(1)若圆心C也在直线
上,过点A作圆C的切线,求切线的方程;
(2)若圆C上存在点M,使
,求圆心C的横坐标a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc878a5fd7b508cf817cbb65d3940547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db0a1cbf7b0ed76c443b953af8734d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/5426adc8-1854-4d34-b385-3a24824b222a.png?resizew=147)
(1)若圆心C也在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c1212804e6d784756d48083d166e8.png)
(2)若圆C上存在点M,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a464b0c729f294287d3d89119a585293.png)
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解题方法
4 . 已知函数
.
(1)当
时,求不等式
的解集;
(2)对于函数
,若
,
,
,
,
,
为某一三角形的三边长,则称
为“可构造三角形函数”,已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8448fbfa60e97f53e28122d84d8efa2d.png)
是“可构造三角形函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fbd668d9bee284aa0bc0b48c9114b42.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf0f2d083b8f2faa1626d1626dea127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(2)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f276b82d4e984675615cc27f9a764cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b9b582f8426f1269b54ee910b97f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49570402aa09e78a4b821c60e2e6881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8448fbfa60e97f53e28122d84d8efa2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
5 . 已知函数
.
(1)求
在
上的值域;
(2)
,若对
,
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68916e8f272c7a4eb2e1c84c996c367c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c40aeeec9aa219c0af917fd34258282.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c1156df7a89ce47a748ffe234a8b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e023a4eb85e27e54f1761063c368c7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc1d824c067f6b4c535de2bb9a7ad57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45095f19fc704de2e45bec5cad78530f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5492182a37d89038c162b06021ca7dd2.png)
(1)求
的定义域,并判断其奇偶性;
(2)判断函数
在
上的单调性,并用单调性的定义加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5492182a37d89038c162b06021ca7dd2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109d06b8be2e402b5ffbb0aeb501009.png)
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7 . 已知函数
的定义域为集合
,集合
.
(1)若
,求
;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759336bc4a1d02713f41320503423d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbcb06cf20c2e87fd69513c117936f1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170ed92b09d13465657b81d1defedec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc454b923ea3f9394accae361b18b0c0.png)
(1)化简
;
(2)若
为第三象限角,且
,求
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc454b923ea3f9394accae361b18b0c0.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38844d9998a21f63551955e75880b4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
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解题方法
9 . 已知椭圆
的离心率为
,
,
,
,
,设P为椭圆C上一点
的面积的最大值为
.
(1)求椭圆C的方程;
(2)当P在第三象限,直线
与y轴交于点M,直线
与x轴交于点N,求证:四边形
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87e24ea042ecf3f25150338e22b45b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆C的方程;
(2)当P在第三象限,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
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解题方法
10 . 已知数列
的前n项和为
,且
,
.
(1)求数列
的通项公式;
(2)在
与
之间插入n个数,使这
个数组成一个公差为
的等差数列,在数列
中是否存在3项
,
,
(其中
成等差数列)成等比数列?若存在,求出这样的3项,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb08c935c5a6dae2b2e53cfa8eac740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8598379ec01edc16c72c1d3fa3ce81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904e7018ec79c8b0efdcb3ba67cb7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2554efe1860dc6c769c34d8cfa6de3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7955013519718c9ac993531062495e95.png)
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