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1 . 设复数
(
为虚数单位),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f6329d8c9b339a1a6d3b69f2fa68b.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317f24346dd1d24fc50acdb22e003af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f6329d8c9b339a1a6d3b69f2fa68b.png)
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2 . 写出一个同时满足下列性质①②③的椭圆的标准方程为___________ .
①中心在原点,焦点在y轴上;②离心率为
;③焦距大于8.
①中心在原点,焦点在y轴上;②离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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3 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b4809ab36f25dfa6c7e00750581662.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b885b617cfaa1e1884e9c806e5e76c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b4809ab36f25dfa6c7e00750581662.png)
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4 . 已知
的半径是1,点P满足
,直线PA与
相切于点A,直线PB与
交于B,C两点,D为BC的中点,设
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
___________ 时,
取得最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2099708046b5e3f94e6500939ba5d05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a9f13126fc3789b2d8a585ef60535f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992907998c85cf872f6e66df0b0c1030.png)
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5 . 已知正四面体
的棱长为2,
为
的中点,
为
中点,
是棱
上的动点,
是平面
内的动点,则当
取得最小值时,线段
的长度等于___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2977ae4bfa32de8c6f0fb136205c4fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb806883030a6fd2c6825c95b864421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
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6 . 设
是面积为1的等腰直角三角形,D是斜边AB的中点,点P在
所在的平面内,记
与
的面积分别为
,
,且
.当
,且
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05c938fd42f5cb0b9d21cd44acbec6e.png)
________ ;记
,则实数a的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fa5b7ee3c02add5668fcdfd13e4b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779f538be94aff22b3eedabfc4c11be4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e81f85f2c7f054f32a01e17f4aa8fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51336413ab117b448511bdcd4758e39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05c938fd42f5cb0b9d21cd44acbec6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169436bf1e8baa899a0179a1c0409947.png)
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7 . 法国数学家加斯帕·蒙日被称为“画法几何创始人”“微分几何之父”.他发现椭圆的两条互相垂直的切线的交点的轨迹是以该椭圆的中心为圆心的圆,这个圆被称为该椭圆的蒙日圆.若椭圆
的蒙日圆为
,则
的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8bd7057c0f2247b350f41062285811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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8 . 如图,在长方体
中,
,
,异面直线
与
所成角的余弦值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67b3f4690dc8d3fb60de49755797e17.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e3b64a79d5668efcd92dc98cee255d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67b3f4690dc8d3fb60de49755797e17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/29d75f01-9476-415b-bcc8-55c291edd967.png?resizew=166)
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9 . 若函数
的图象在点
处的切线平行于
轴,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f65f3ec12749ac6b369b54bc4ac5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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福建省十一校2024届高三上学期期末联考数学试题广东省湛江市2024届高三上学期1月联考数学试题宁夏吴忠市2024届高三下学期高考模拟联考(一)理科数学试题河南省信阳市信阳高级中学2023-2024学年高二下学期易错题回顾测试(开学)数学试题(已下线)2.4 导数的四则运算法则3种常见考法归类-【帮课堂】2023-2024学年高二数学同步学与练(北师大版2019选择性必修第二册)
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10 . 某美食套餐中,除必选菜品以外,另有四款凉菜及四款饮品可供选择,其中凉菜可四选二,不可同款,饮品选择两杯,可以同款,则该套餐的供餐方案共有_________ 种.
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