1 . 已知向量
,
,定义运算
,同时定义
.
(1)若
,求实数
的取值集合;
(2)已知
,求
;
(3)已知定义域为
的函数
满足
为奇函数,
为偶函数,且
时,
,是否存在实数
,使
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec6dba44a83ae69146c26a2eec325c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66717aa3e7a771427c1d4433c77a5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4817c9821c3c5268e665a3ebcfe2e9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153f8261059b286d175e53adb666d0bd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e993a236a70e4a094013a28c07079f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237b1a6f3e6ee0ef92b4aef7bffe58ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5285f8cfbab2baf73267d7649a58ac.png)
(3)已知定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91340ce6d32493c33527a32c2d448896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffde73ff7d3cd5125eb8d8a17a9f01c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994dcf841d356002fcebaed37497013c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de03de9f4bea859252f0158b32acf378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb0b435b3f1a00ee1df0d02384d6e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
解题方法
2 . 如图,点
均在
轴的正半轴上,
,
,…,
分别是以
为边长的等边三角形,且顶点
均在函数
的图象上.
个等边三角形的边长
;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e670062f54fef9f2af635014f22c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a619e2751f422ae187505e95339d02fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b80801bd92f36541707eea1229685e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43534ea1b9c007f961148b68e2adad1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02163d48486b66a17dd434e57877cc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cfa1efc047521bc9f9b60ab3122752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2024-06-08更新
|
661次组卷
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2卷引用:江西省宜春市丰城中学2023-2024学年高一下学期第三次段考(5月月考)数学试题
名校
3 . 已知数列
是公差为
的等差数列,若它的前
项的和
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5596e3d616cd804ad9a29a98b720831d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079f16bbd0704ecb6e5e44c5725af1d9.png)
A.若![]() ![]() ![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2024-06-08更新
|
340次组卷
|
2卷引用:江西省宜春市丰城中学2023-2024学年高一下学期第三次段考(5月月考)数学试题
解题方法
4 . 如图,在
中,边
上的点
满足
,边
上的点
满足
,线段
上的点
满足
,点
为线段
上任意一点(不包括端点),连接
并延长交直线
于点
,若
,则实数
的取值可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f7b7aef85de2d4babbc025d4329007.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/0a72599cfdfa9cd0a491b831100a2ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ecdfca7c17c5598214b977a090b1f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f8f4051b5dbc94620f44d93a862d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.1 |
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解题方法
5 . 在中国文化中,八边形常常被看作是四平八稳、镇宅保平安的象征.比如,八角楼、八角塔、八边花窗、八角门环和八边园林门径等,都有着这样的寓意.如图,在边长为
的正八边形
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e246bc4a4d491259fabc9c7497d6242.png)
______ ,若
内的一点
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1475c82f3a5c6fd1b418444a2f5af73b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4ab3f511aea1a80d79c6ad865e1955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e246bc4a4d491259fabc9c7497d6242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc5c12b241539cc99487865f7d8bf34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbc58200da9c83866917019eae87a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1475c82f3a5c6fd1b418444a2f5af73b.png)
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解题方法
6 . 春节过后,某大学四年级的5名大学生相约去人才市场应聘,其中小红、小东学的是建筑专业,小军、小英学的是通讯专业,小青学的是电气工程专业.
(1)若从这5人中随机采访3人,求3人中至少有1人是通讯专业的概率;
(2)若小红应聘成功的概率是
,小军应聘成功的概率是
,小青应聘成功的概率是
,这3名大学生的应聘结果相互独立,求这3人中至少有2人应聘成功的概率.
(1)若从这5人中随机采访3人,求3人中至少有1人是通讯专业的概率;
(2)若小红应聘成功的概率是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
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7 . 某届国际羽联世界锦标赛单打决赛在甲、乙两人之间进行,比赛采用五局三胜制.按以往比赛经验,每一局甲获胜的概率为
,则下列说法一定正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
A.当![]() |
B.当![]() |
C.当![]() |
D.当![]() |
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2024-05-08更新
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526次组卷
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3卷引用:江西省宜春市宜丰中学创新部2023-2024学年高一下学期6月月考数学试题
名校
8 . 已知
中,点
满足
,点
在
内(含边界),其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b487df3bd4826ed3e266f4f8677fee5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5331e29182b4a87e2d68127932ced86.png)
A.若![]() ![]() ![]() | B.若![]() ![]() |
C.若存在![]() ![]() | D.存在![]() ![]() |
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2024-05-07更新
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157次组卷
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4卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
9 . 已知
,
,
,
,则在
,
,
,
,
,
这6个数中最小的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785dac87206d5a2fde58dc629575440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cebc1007b5d36761f8049826077df50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0595ddf421f5eb6304903870905adf06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44db1ac4ff914ce499c4f650ca9e517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1103ddae6ffaba2b15808c6df09c0248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77fa8d7b2895886fb1a63a127acbe69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94720967984b2ab27d9637569ee1c146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1afc5679cf6db93d692a4e38ea07c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc952bb461a420a6877211ce32ac50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb00b6918dfb251c1a63acdc07464b92.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-02更新
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632次组卷
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2卷引用:江西省宜春市丰城中学2023-2024学年高一下学期4月期中考试数学试题
10 . 若
,则称
为
维空间向量集,
为零向量,对于
,任意
,定义:
①数乘运算:
;
②加法运算:
;
③数量积运算:
;
④向量的模:
,
对于
中一组向量
,若存在一组不同时为零的实数
使得
,则称这组向量线性相关,否则称为线性无关,
(1)对于
,判断下列各组向量是否线性相关:
①
;
②
;
(2)已知
线性无关,试判断
是否线性相关,并说明理由;
(3)证明:对于
中的任意两个元素
,均有
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d935457799f234e86a59e2f662d5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554f144d15fc567b25935b38917430c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1156e087d0c92bf15ea7a53d021fcc.png)
①数乘运算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee3d2d5f39d4050799537d5ad6bb375.png)
②加法运算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374036b2d97be3bb771c6d1bfd2ae6eb.png)
③数量积运算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3760d1b114cab294d2b8af405de49814.png)
④向量的模:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e7f7030526d65d5fff785d0d35a6ba.png)
对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab882b48940b6e1a185a513a0d8e8d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3e3f607c7d170c8a9e614bfd2cb5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946f81ae87f9c8cdc1017af6c1ec2fb2.png)
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56eb5f6747ea94d1075210265214211.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6432103414cd0efd40a0c0017eb11b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf1bee58a691b31e06e088afed4c25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76eb5fb9c09b830eecb5ba7efea4e09.png)
(3)证明:对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c21920a0a39b1604e130601f061b056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1120f6ff618146c9851df5dea05c1f55.png)
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