1 . 已知函数
的部分图象如图所示.
的解析式与单调增区间;
(2)若将
的图象向右平移
个单位,再向上平移1个单位得到
的图象,写出
图象的对称中心的坐标,并求当
时,
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6309e18f51f43800c0a16205c6a491b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31a8b7f6d3b664b2c9bae09c3a6f884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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2 . 设
是公比大于1的等比数列,
为数列
的前
项和.已知
,且
、
构成等差数列,令
.
(1)求数列
的通项公式;
(2)令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ccdc17b603871d20843ffccca2df0ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadfe0800c4dc2fe3434c488cf3fe9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0462c9dc4a0bd08a0ec1cc07f1d2f3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131d12bb9ea1eb58c7f0721a291598b0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f50ac3b1d543e1a09eb9e84da4f5a0.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf35e622dc7630e7f5d056b1b6af1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
3 . 已知
是复数,
为实数,
为纯虚数(
为虚数单位) .
(1)求复数
;
(2)求
的模.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf883aa12fa8e6da300253195f485de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79495891db61dcff5ffb44197043d097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
(1)求复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbeaada495870b36c4d17a3caa624704.png)
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名校
4 . 设复数
,
.
(1)若
是纯虚数,求
的值;
(2)若复数
在复平面内对应的点在第四象限,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1988e53b17687a87e751e9513c20a0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4ddcdc131d6f0a1f17d637b1179f77.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34b88f343ca5a4c29057465541b9cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7be74b3741e5b47713ed3ce08398f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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今日更新
|
162次组卷
|
2卷引用:黑龙江省哈尔滨市第三中学校2023-2024学年高一下学期期中考试数学试卷
解题方法
5 . 已知
,且
,
(1)求实数
的值.
(2)若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8e588364f28e37a013c9943231b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f804528bc4c32cd8dd33668376f3b1e.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986d1f7eb4776389f1bac84b40e60616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024高一下·上海·专题练习
解题方法
6 . 某校开展数学专题实践活动,要求就学校新建的体育馆进行研究,为了提高研究效率,小王和小李打算分工调查测量并绘图,完成两个任务的研究.
(1)小王获得了以下信息:
.教学楼
和体育馆
之间有一条笔直的步道
;
.在步道
上有一点
,测得
到教学楼顶
的仰角是
,到体育馆楼顶
的仰角是
;
.从体育馆楼顶
测教学楼顶
的仰角是
;
.教学楼
的高度是20米.
请帮助小王完成任务一:求体育馆的高度
.
.体育馆外墙大屏幕的最低处到地面的距离是4米;
.大屏幕的高度
是2米;
.当观众所站的位置
到屏幕上下两端
,
所张的角
最大时,观看屏幕的效果最佳.
请帮助小李完成任务二:求步道
上观看屏幕效果最佳地点
的位置.
(1)小王获得了以下信息:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c12e76fbd84eeec721386bd3b04cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
请帮助小王完成任务一:求体育馆的高度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/b5e8e435259ab192d798bb8bf7774cdf.png)
请帮助小李完成任务二:求步道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在三棱锥
中,
底面
,
,
,
分别是
,
的中点.
平面
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0653ca05309f7e7529e1f16a68d17fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7d545820fd1dfc7f13f331543b2523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da035673ef0edcfae6b72fb5e5ba34a.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad03d5a6171238170755a73f5dd20639.png)
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8 . 已知函数
的一系列对应值如表:
(1)求
的解析式;
(2)若在
中,
,
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f26765b493dcb0cb3ebe4f7ef74c3c6.png)
![]() | … | ![]() | 0 | ![]() | ![]() | ![]() | ![]() | … |
![]() | … | 0 | 1 | ![]() | 0 | -1 | 0 | … |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e43805b893f9aae4787a449aafa36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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9 . 已知边长为3的等边三角形
,求
边上的中线向量
的模
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0987a20a5648765bce6ae78a693106.png)
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10 . 已知向量
,
,设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7aa1233d7a93113281594c41f25c7db.png)
(1)求
的最小正周期;
(2)将
的图象向右平移
个单位后得到函数
的图象,求函数
的单调增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9469f0d04934f97d68470b4db674676e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e81f2bf88ac5b5d98f4d80e07f66e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7aa1233d7a93113281594c41f25c7db.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次