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1 . “
”是“复数
是纯虚数”的( )条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90822b111f1de80eae5ef0e31a276952.png)
A.必要不充分 | B.充分不必要 | C.充要 | D.既不充分又不必要 |
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2 . 平面直角坐标系中
,设点
是线段
的
等分点,其中
.
时,试用
表示
;
(2)当
时,求
的值;
(3)当
时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c26ad9deaf1c845754137638bb4e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa963c9dbb012bb08c2fdf5e5e41034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c941130c5d1166ced3b09aa0c883b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c12f9c428675ab178fc31e01f4334ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349eef3a3e97e2718ed5e77f313a4292.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ea0392d4bd0374c8a2b12a355e4655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60f5e90b85f837727d1148b18b9a0db.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b87fd0258955a65d55b1daf41eac0.png)
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3 . 对于实数
,用
表示不超过
的最大整数,例如
.已知
,则下列3个命题中真命题的个数为__________ .
(1)函数
是周期函数;
(2)函数
的图像关于直线
对称;
(3)方程
有2个实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d23555720f4938189847b3531bd7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2297ab933ad7b37e272c0ac367f150d.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
(3)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f277209e43e8881f3b0ec4b1bc0df082.png)
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4 . 已知向量
和
,则
在
方向上的投影是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6058a2d06b42c223208e37b901b7ff9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1076214bf555193967326cf2215c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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5 . 已知复数
,且复数
满足
,则
在复平面内对应的点位于第__________ 象限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad316d30f407b32b74564c6177723c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a10de1216740ff1542ddb2968de5832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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解题方法
6 . 若
为锐角,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207b77aa3cf9351cf7ee25827f0688fd.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9da049c686ff81df5d6645ef51e993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207b77aa3cf9351cf7ee25827f0688fd.png)
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解题方法
7 . 已知
,且
,则点
在第__________ 象限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca599151dae2ca77bd53af8b38b69684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9faccebbd12ce0332647b3ba6d2474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f42664269cd3e00de2e4dd8d02e886.png)
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8 . 窗花足贴在窗纸或窗户玻璃上的剪纸,是中国古老的传统民间艺术之一,图中所示的窗花轮廓可以看作是一个正八边形.已知该正八边形
的边长为10,点
在其边上运动,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fdc52a27396f7a067d2fdeda888725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d594aa525e62e5bcedbeddb094a25110.png)
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7日内更新
|
261次组卷
|
2卷引用:上海市徐汇中学2023-2024学年高一下学期期末考试数学试卷
名校
解题方法
9 . 设
均为正数且
,则使得不等式
总成立的k的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8d26087a321c3276225c55f2829764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dced4c4dfdec458b4d7319ee75d51f.png)
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10 . 已知各项均不为0的数列
满足
(
是正整数),
,定义函数
,
是自然对数的底数.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)记函数
,其中
.
(i)证明:对任意
,
;
(ii)数列
满足
,设
为数列
的前
项和.数列
的极限的严格定义为:若存在一个常数
,使得对任意给定的正实数
(不论它多么小),总存在正整数m满足:当
时,恒有
成立,则称
为数列
的极限.试根据以上定义求出数列
的极限
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bf7b5dc247fe10b6bfd984413a5e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd9ea8ffdea8c77370ea3e5f563dc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fec2729d8e927de9392ee90d1e0389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6f0a55fa53bf5f8e6654897975bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3324481138f2dc750f9ad889054abe1.png)
(i)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a72de4d0030203a867cc3b7b95d83.png)
(ii)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9de1835c164233db8b623489fbda0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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