1 . 物体在常温下的温度变化可以用牛顿冷却方程来描述:设物体的初始温度为
,环境温度为
,经过一段时间
(单位:分钟)后物体的温度是
,满足
.将85℃的热水放到21℃的房间中,如果热水降到37℃需要16分钟,那么从37℃降到29℃还需要多少分钟?( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d861b460f4d5e9718d1772c5416f717f.png)
A.2 | B.4 | C.6 | D.8 |
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解题方法
2 . 已知
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8395ec0d1086cd800bef037c0e1b319d.png)
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3 . 已知
,若
的展开式中含
项的系数为40,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ac51c120d9b040381246bdb014f69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3336c8ed5361c10c37300e41e03f9f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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2024-01-16更新
|
1079次组卷
|
4卷引用:天津市河北区2024届高三上学期期末质量检测数学试题
天津市河北区2024届高三上学期期末质量检测数学试题河北省石家庄市第二中学2024届高三上学期第一次模拟测试数学试题天津市蓟州区第一中学2024届高三第一次校模拟考数学试卷(已下线)专题17 二项式定理9种常见考法归类(3)
4 . 底面边长为
,且侧棱长为
的正四棱锥的体积和侧面积分别为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
A.![]() | B.![]() | C.32,24 | D.32,6 |
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5 . 将直线
向右平移一个单位后,被圆
截得的弦长为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0c4f7de0a94be0e0c6c0e2b68ad4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35465f3e40ce00a1dce54b943ae183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
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解题方法
6 . 如图,在平行四边形
中,
与
交于点
,
是线段
的中点,
的延长线与
交于点
.若
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe03f56946845cc0573e2ef6943da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4800094a6c5023668c9c9a826a0f6f17.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知集合
,集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b00b73f6e27e555749d5d8b725db0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a885bbc58543f2d8e460211d5a7e9f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 .
是虚数单位,复数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4233d750cc6f38507c25aa9bb830085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
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解题方法
9 . 一个体积为
的球在一个正三棱柱的内部,且球面与该正三棱柱的所有面都相切,则此正三棱柱的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bea86620b6ce1284536813e1a74837.png)
A.18 | B.27 | C.36 | D.54 |
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10 . 直线
将圆
分成两段圆弧,则较短圆弧与较长圆弧的弧长之比为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baabfd32465e9e50409413d9c1358279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8e5085828491f60b357024c3e72c66.png)
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