1 . 我们称数集
为数域
,当且仅当数集
中的任意两个元素经过加法、减法、乘法、除法(除数不为0)四则运算后,其运算结果仍在数集
中,则下列数集能称作数域的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
A.自然数集 | B.整数集 | C.有理数集 | D.无理数集 |
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2 . 实数列
满足
为
前k项和,令
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4479bae6c067537f99bd8a74b69efb5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b823bb30ecbe7ea3a48e35d16cf0d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c00f1e8a107981c5b654608f55e0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f89080740f515f64a5077647b3ca927.png)
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3 . 已知集合
、
,
,若满足
,则称集合
为正序集合,
,若满足
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddf5a3a5b55043f5f08c91c821fcf72.png)
,称集合
为波浪集合,若
,则称集合
为正序集合
的波浪集合.如正序集合
的波浪集合为
.已知正序集合
,则集合
的波浪集合的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da789bf1d330f0fd9060e14fe30af393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55faf5a2518cfafbd16cd54542a16568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb4a0475eeaf8f3c163712c0ffc6aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b08e18d4cff5287425ec1ebb74cede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddf5a3a5b55043f5f08c91c821fcf72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8540d30ff822582b9f942f45a71d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26bbb11e932ddb26a9088e7fc33e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f51bdfe12a443002d2eb220c4f74a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4677f5df67e9727194c888a71e1727e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.13 | B.14 | C.15 | D.16 |
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解题方法
4 . 设
,
,则最接近于S的整数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e3c33e1cb283d72fe1a6cbc27eb462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0228777a871cf7f71d46fe39f6aa2fd7.png)
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解题方法
5 . 已知集合
,若
,则
,则称
为集合
的“亮点”,若
,则集合
中的“亮点”共有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898c0751f20302e2d001d48f1c90f79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a091fb4cc5cce92cafa6cf1dc10e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.2个 | B.3个 | C.1个 | D.0个 |
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解题方法
6 . 已知函数
为锐角,设
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef6aac49c48e1aa12ff1fad74700225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103506ffcbab54b205ab74449ada4248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 如图,在矩形
中放置了如图所示的5个大小相同的正方形,其中
,
,设
,考虑向量
与
可得正方形边长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae8221601c7bd5c51fd520615581fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb4a33e424150f5def117f0106b10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690ed857fecbea5575496c34c1c3067f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572ce9aed5ba709a84a6aa20b245dc58.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 下表中所列的是某地区一年中十天的白昼时间.表中日期为(月、日)
某同学以日期为
轴(天),以白昼时长为
轴(小时),建立直角坐标系,绘出了散点图(如图),他想用余弦曲线去拟合这些数据,经过查找资料,他建立了模型
,则
( )
日期 | 1月1日 | 2月28日 | 3月21日 | 4月27日 | 5月6日 | 6月21日 | 8月14日 | 9月23日 | 10月25日 | 11月21日 |
小时 | 5.59 | 10.23 | 12.38 | 15.91 | 16.71 | 19.40 | 15.93 | 12.61 | 9.14 | 5.44 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42401422a5bc0b6d2d2af0770cf7c460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.5 | B.6 | C.7 | D.8 |
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9 . 定义两个向量
之间的运算“
”为
.其中
,
,若向量
,则向量
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091e86ca89e484b331fd90125a5e5af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d845b425d73c24b6ba88ea5447ab03a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c857eec21dd64ccf0ba530883bb6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcab0226effeccd2a336c23079bc1be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf28ca5acd5f256d78677041aeec9776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5186ca272d0cbf0ee500e4a1dce008.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 如图,三个机器人
和检测台
位于同一直线上,三个机器人需把各自生产的零件送到
处进行检测,送检程序规定:当
把零件送到
处时,
立刻自动出发送检,当
把零件送到
处时,
立刻自动出发送检,设
的送检速度为
,且送检速度是
的2倍,
的3倍.
把各自生产的零件送到检测台
处的时间总和;
(2)现要求
送检时间总和必须最短,请你找出检测台
在该直线上的位置(
与
均不重合).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75193c2de6968a93cf0bffc2f77f807.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/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e05f91d7c92d26dc2ed37c4b4f6369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)现要求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e05f91d7c92d26dc2ed37c4b4f6369.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/71e05f91d7c92d26dc2ed37c4b4f6369.png)
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