名校
1 . 已知函数
,如图,
是直线
与曲线
的两个交点,若
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1bba2a16b86470432ffcdb6ad84916.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad58e5f29712deaf99ab98bfbbfc3abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f3fa679bb55ded25a9b72a8e788cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e515607a0591459746f2ade643c45aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1bba2a16b86470432ffcdb6ad84916.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/20b572a8-98bc-44ee-879f-6da3e33a8cb6.png?resizew=184)
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2 . 如图,在正方形
中,点
为
上动点,点
为
上动点,满足
,将
、
分别沿
、
折起,使
、
两点重合于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/9700c52b-1c2c-4787-8826-871aee194fe4.png?resizew=315)
(1)证明:
;
(2)若
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38d97f03faed3152db2fd3bd1919944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eff00441c41fc516c37876d266fcbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/9700c52b-1c2c-4787-8826-871aee194fe4.png?resizew=315)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa8355d95bb4c8d7c004eab4c7ce784.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cca2d187a304eab931eedc2139c23ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f8c417f5c19cc076dc6baeb0c173a9.png)
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3 . 设
是奇函数,且在
上是减函数,
,则
的解集是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b03af66c2b6d916b41321d7bb292f1.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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4 . 在棱长为4的正方体
中,点
分别是线段
和
的四等分点,分别满足
建系如图,解答下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/707b19ee-7b73-4c76-b73b-ccc661925046.png?resizew=199)
(1)求
和
所成角的余弦值;
(2)点
是线段
的四等分点,满足
求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e57e2c1b68189c58a1d1eb5db8f018.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/707b19ee-7b73-4c76-b73b-ccc661925046.png?resizew=199)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfca8aa367e30ec87b8c80b9358c0d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
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解题方法
5 . 不等式
与不等式
是同解不等式,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb2f87452a6a5fe9dd73766b16d66bf.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee9165d56de268f25db548c1e791a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8023e1902803a7939d2aa32ba9e2d44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb2f87452a6a5fe9dd73766b16d66bf.png)
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2023-12-30更新
|
681次组卷
|
3卷引用:新疆乌鲁木齐市第十九中学2023-2024学年高一上学期第二次月考数学试卷
新疆乌鲁木齐市第十九中学2023-2024学年高一上学期第二次月考数学试卷四川省南充市阆中中学校2023-2024学年高一上学期12月月考数学试题(已下线)专题04 与指数函数、对数函数有关的复合函数及函数方程综合应用-【寒假自学课】(人教A版2019)
6 . 在直角坐标系中,曲线
的参数方程为
;在极坐标系(以原点为坐标原点,以轴正半轴为极轴)中曲线
的方程为
,则
与
的交点的距离为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8a231125afc3eb4eed9bcc65213a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76817e4d13d29c0644a6286a1f9e22ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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7 . 小明有一条长度为A的木棍,小华有一条长度为B的木棍,小明先将自己的木棍分成3段,然后小华也将自己的木棍分成3段,如果可用分成的6段木棍拼成2个三角形,则小华获胜;否则小明获胜,如果二人在采用最优策略的前提下小明必胜,那么有序数对
可能是下面的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 直线
被圆
截得的弦
的中点为
,且
,若点
关于原点的对称点
恰在圆
上,则圆
的标准方程为____ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bf4c5441af2933c5bd4422b3dfad28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce395dfb7eab4d1d58a19bce2bfdaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
9 . 设
,若
有三个不同的零点,则实数
的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2b79dea5aaa2f9e192d2237b0465cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0384a0466920e5bf00231a5c5bf77969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 用
表示
,
两个实数中的最大值.设
,则函数
的最小值是__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ad6b511253288bb1a39cf30a82e644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc889264f7ef9edb57326825bbe1eff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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