名校
解题方法
1 . 甲、乙两位同学参加一个游戏,规则如下:每人在
四个长方体容器中取两个盛满水,盛水体积多者为胜.甲先取两个容器,余下的两个容器给乙.已知
的底面积均为
,高分别为
的底面积均为
,高分别为
其中
).在未能确定
与
大小的情况下,请给出一个让甲必胜的方案(即指出甲取哪两个容器可以获胜),并说明此方案必胜的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db2ca6d163be93b18959beb75ac588b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64289a00d51858f6ee9f51fdc62823de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a476588acbf41d798cc234a52fa21a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/904288bd99217d66013c030bfb99c0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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解题方法
2 . 在复平面上有点
和点
,
所对的复数是
.已知小明在点
处休憩,有只小狗沿着
所在直线来回跑动.
(1)求
的面积;
(2)问:小狗在什么位置时,离小明最近?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ead24689501cc86576b06ffa85a68a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(2)问:小狗在什么位置时,离小明最近?
您最近一年使用:0次
2023-07-08更新
|
191次组卷
|
3卷引用:上海市长宁区2022-2023学年高一下学期期末数学试题
上海市长宁区2022-2023学年高一下学期期末数学试题福建省宁德市福安市第一中学2023-2024学年高一下学期3月月考数学试题(已下线)9.2 复数的几何意义-同步精品课堂(沪教版2020必修第二册)
3 . 科学家用死亡生物的体内残余碳
成分束推断它的存在年龄.生物在生存的时候,由于需要呼吸,其体内的碳
含量大致不变.生物死去后会停止呼吸,此时体内原有的碳
含量会按确定的比率衰减(称为衰减率),且大约每经过
年衰减为原来的一半,这个时间称为“半衰期”,设某一刚死亡生物体内碳
含量为
.
(1)按上述变化规律,此死亡生物体内碳
含量
与死亡年数
之间有怎样的关系?
(2)当死亡生物体内碳
的含量不足死亡前的千分之一时,用一般的放射性探测器就测不到碳
了,请问该生物死亡
年后,用一般的放射性探测器能测到它体内的碳
吗?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1824fea6ea80d1c805d75df4573ad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
(1)按上述变化规律,此死亡生物体内碳
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当死亡生物体内碳
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76524dc0c7a20c5870a79a2e3fd4bfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
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4 . 设复数
,
在复平面所对应的点为
与
,则关于点
、
与以原点为圆心,10为半径的圆
的位置关系,描述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b372191466358e8f8cad6397a25a228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d618a37760a2b378c03d53ee56ce06c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.点![]() ![]() ![]() ![]() | B.点![]() ![]() ![]() ![]() |
C.点![]() ![]() ![]() | D.点![]() ![]() ![]() |
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2022-06-28更新
|
280次组卷
|
3卷引用:上海市延安中学2021-2022学年高一下学期6月质量调研数学试题
名校
5 . 已知复数列
满足:
,
,设复数
在复平面中对应点
.当
无限增大时,点
越来越趋近于一个确定的点
,点
的坐标是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c916fd7ddb4e800d98b15ce54c4d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2103a934a70ceb3f67525a1bfe9200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176f249595624605402d8cb1bcb4eae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176f249595624605402d8cb1bcb4eae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
6 . 下列有关向量的命题正确的是( )
A.长度相等的向量均为相等向量 |
B.若ABCD是平行四边形,则必有![]() |
C.非零向量![]() ![]() ![]() ![]() |
D.若非零向量![]() ![]() ![]() ![]() ![]() |
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7 . 如图所示,
是一山坡,与地面成
,某人在点
看见一只山羊从山脚往山坡上爬.当此人看见山羊爬到点
时的仰角是
,当山羊继续爬
米到山顶
时,此人看见羊的仰角为
.问此人离山脚
有多远?(结果精确到
米)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1006d62fa5723dc36286b8f5494f993e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f959e5f8d89390f0f136f6acc9f6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965629902364672/2965870657257472/STEM/730e859f-8341-4c87-a2df-e9f6f6e90501.png)
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8 . 利用拉格朗日(法国数学家,1736-1813)插值公式,可以把二次函数
表示成
的形式.
(1)若
,
,
,
,
,把
的二次项系数表示成关于f的函数
,并求
的值域(此处视e为给定的常数,答案用e表示);
(2)若
,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5457d763fd9698e27fbcc1ef6d53f00a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf94d263ea1e5ddad405ccbc1eb2a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f6db131eb532855af41d5e84ad22cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0667df710a11c9f9f073babe66e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0667df710a11c9f9f073babe66e7a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27763d65ec630511141303dad69545b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0e86caa2ab1bd37b67efe864815c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68982e0dd0bb3d87b344d23df4c2213.png)
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解题方法
9 . 如图,在同一平面上,已知等腰直角三角形纸片
的腰长为3,正方形纸片
的边长为1,其中B、C、D三点在同一水平线上依次排列.把正方形纸片向左平移a个单位,
.设两张纸片重叠部分的面积为S.
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896473803669504/2899180820365312/STEM/e280f33c-4a24-4c5e-8cb7-78ca8065ccd2.png?resizew=198)
(1)求
关于a的函数解析式;
(2)若
,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dbee66892e61a6399e1c24e7541304.png)
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896473803669504/2899180820365312/STEM/e280f33c-4a24-4c5e-8cb7-78ca8065ccd2.png?resizew=198)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a39e043678dd84d41c32b042239a20.png)
您最近一年使用:0次
解题方法
10 . 设函数
.
(1)若对任意实数
,
有
成立,且当
时,
;
①判断函数的增减性,并证明;
②解不等式:
;
(2)证明:“
图象关于直线
对称”的充要条件是“任意给定的
,
”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe10ebb50c9dfcf2570083b9321d281.png)
(1)若对任意实数
![](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/1e36e45821cc161584ad64043772227a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
①判断函数的增减性,并证明;
②解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67748e1777567c2f05835fe6fe6f5303.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe10ebb50c9dfcf2570083b9321d281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3dbcdab81b677ce015ee99f0445864.png)
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