1 . 判断题(正确的填“正确”,错误的填“错误”):
(1)平行向量就是共线向量.( )
(2)若向量
的模小于
的模,则
.( )
(3)质量、动量、功、加速度都是向量.( )
(4)若
与
共线,则A,B,C,D四点必在一条直线上.( )
(5)若向量
与
平行,则
与
的方向相同或相反.( )
(6)在
中,
.( )
(7)若向量
与
有共同的起点,则以
的终点为起点,以
的终点为终点的向量等于
.( )
(8)若
且
,当
,则一定有
与
共线.( )
(9)若
,则
或
.( )
(10)若
且
,则
.( )
(11)向量
在
方向上的投影是一个模等于
,方向与
相同或相反的向量. ( )
(12)
.( )
(1)平行向量就是共线向量.
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de12437ea8219e16092749a45858053a.png)
(3)质量、动量、功、加速度都是向量.
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
(5)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(6)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71163a9fd0b7c3b86d1c7f3267bde28.png)
(7)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb667795acdfafa436ee35e152adbc4.png)
(8)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177bac525befae1da05679bba3735d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aeda90bd9777fda412249a37fc7a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(9)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5addd0c822fa3c5ac9c7db649f6682cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab00d21b5a95621c6b6164dfb9e08b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afff2ac07ebf0f4b8b498db0e256a72d.png)
(10)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa8f7351f41cbfc74f99de51c752ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6e8e539b10975174077d1fbf8d8099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fbeefcb60bff9eab8243d3b4931123.png)
(11)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69107a1f19902da9c610086e94c86daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(12)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7960dd509a123a8efe26a32e1f0ea396.png)
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2 . 能否从图形的直观分析中判断出直线
:
与椭圆C:
的交点个数?若存在交点,则求出交点坐标;若不存在交点,则求椭圆C上的点到直线l的最小距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a362b22d77130726c8dda391382eb186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
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名校
3 . 为了得到函数
的图象,只需将余弦函数
图象上各点( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c9577683bed1bbfce38f7135963af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
A.横坐标向左平移![]() |
B.横坐标向右平移![]() |
C.横坐标向左平移![]() |
D.横坐标向右平移![]() |
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2023-10-09更新
|
390次组卷
|
4卷引用:北师大版(2019)必修第二册课本习题 习题1-6
北师大版(2019)必修第二册课本习题 习题1-6(已下线)5.6 函数y=Asin(ωx+φ)精练-【题型分类归纳】(人教A版2019必修第一册)湖南省常德市汉寿县第一中学2023-2024学年高一下学期入学考试数学试题(已下线)习题 1-6
4 . (1)直线上有两点在一个平面内,则直线与平面的关系是什么?如何说明?
(2)两个不重合平面有两个公共点,则两个平面的关系是什么?如何说明?
(3)“两直线有一个公共点”能否说明两直线在一个平面内?为什么?
(2)两个不重合平面有两个公共点,则两个平面的关系是什么?如何说明?
(3)“两直线有一个公共点”能否说明两直线在一个平面内?为什么?
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5 . 图(1)是长、宽、高分别为
的长方体;图(2)是所有棱长均为2的正三棱锥,点
是
的中点.画出图中给出的所有侧面、底面与截面的真实平面图.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b44c694c8d0c29d0da8c4e73ab6cf5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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6 . 证明:若
,则
(
是任意的非零复数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de59a6da1ee210ccf04651ae53275dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740b5de15d571293281f351b78a20db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595044a7750ab4f84519041979c3d780.png)
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7 . 在复平面内,菱形
对角线交点为原点
,且两条对角线长度之比为2:1,顶点
对应的复数是
,设
,
,
三点对应的复数分别为
,
,
,求
,
,
,并计算出
,
,
三点所对应的复数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246d747e26000397caa6a2d0b88c80d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795493a60182973eaa42b4a65b29bb19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111739c84217132b98585838c6bf0c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e97bce30ba5879aa86338724584fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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8 . 试比较复数运算与平面向量运算的异同,谈谈你的感受.
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9 . 化简:
,
,
,
,
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af95b61a7e348dac2ba0e9663288da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d74cd0d356bab546ffd038cabd3ebc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27404cf78fcd9089ed4aa2a4e8dc436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61edd463546c93e4a58db673fda6095c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d53f57e7721519692bd7dffeb372b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af8342682e2fd493673352623e1a3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bf573e5f74d884d6ef940b87df0897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee0167a29fb8b1e0fbee889f87981.png)
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10 . 图中四边形ABCD,DCEF,FEGH都是正方形,用复数方法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6e7b446e3329dfe2894751f93cf0c1.png)
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