名校
1 . 从某小区抽取50户居民进行月用电量调查,发现其用电量都在50到350度之间,将用电量的数据绘制成频率分布直方图如下.
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321674727424/1924021284544512/STEM/60f9b90d3d4b45eca6793791934f3d7e.png?resizew=329)
(1)求频率分布直方图中
的值并估计这50户用户的平均用电量;
(2)若将用电量在区间
内的用户记为
类用户,标记为低用电家庭,用电量在区间
内的用户记为
类用户,标记为高用电家庭,现对这两类用户进行问卷调查,让其对供电服务进行打分,打分情况见茎叶图:
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321674727424/1924021284544512/STEM/3f5a2b37d23647d6a30ad334741a8d8f.png?resizew=362)
①从
类用户中任意抽取3户,求恰好有2户打分超过85分的概率;
②若打分超过85分视为满意,没超过85分视为不满意,请填写下面列联表,并根据列联表判断是否有
的把握认为“满意度与用电量高低有关”?
附表及公式:
,
.
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321674727424/1924021284544512/STEM/60f9b90d3d4b45eca6793791934f3d7e.png?resizew=329)
(1)求频率分布直方图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若将用电量在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27021654e26c879b0ca067e14425ff63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd912af5e2a64028abe0ef1e2dfe604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321674727424/1924021284544512/STEM/3f5a2b37d23647d6a30ad334741a8d8f.png?resizew=362)
①从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②若打分超过85分视为满意,没超过85分视为不满意,请填写下面列联表,并根据列联表判断是否有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b399e6815afcaa24f2889e58c79c10a1.png)
满意 | 不满意 | 合计 | |
![]() | |||
![]() | |||
合计 |
附表及公式:
![]() | 0.050 | 0.010 | 0.001 |
![]() | 3.841 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
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6卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
名校
解题方法
2 . 设
,
满足约束条件
,则
的最小值是
![](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/67f3e6bb8303ed6330846c6e66a4fcb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee51b0cac927e6445e4b94438c2ff3da.png)
A.0 | B.-1 | C.-2 | D.-3 |
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3卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
名校
3 . 已知复数
在复平面内对应的点在第二象限,则整数
的取值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf4798617f7f8ab31dac033c8e7a760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.0 | B.1 | C.2 | D.3 |
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4 . 执行如图所示的程序框图,则输出的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321674727424/1924021284282368/STEM/bfd86d3f7d5f465e8196aeafd9550ecf.png?resizew=121)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321674727424/1924021284282368/STEM/bfd86d3f7d5f465e8196aeafd9550ecf.png?resizew=121)
A.17 | B.33 | C.65 | D.129 |
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8卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题海南省2018届高三第二次联合考试数学理试题海南省2018届高三第二次联合考试数学(文)试题【全国百强校】陕西省西安市西北工业大学附属中学2019届第一次适应性训练理科数学试题(已下线)专题12.4 算法与程序框图(练)【理】-《2020年高考一轮复习讲练测》(已下线)专题11.3 算法与程序框图(练)【文】-《2020年高考一轮复习讲练测》(已下线)测试卷24 算法初步-2021届高考数学一轮复习(文理通用)单元过关测试卷【全国校级联考】湖北省孝感市重点高中协作体2017-2018学年高二下学期期末联考数学(文)试题
名校
解题方法
5 . 如图,在四棱锥
中,底面
为平行四边形,
,
,且
底面
.
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321631801344/1924013826408448/STEM/2dc1690b-eddc-4790-9743-683d985c347d.png)
(1)证明:平面
平面
;
(2)若
为
的中点,且
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdfd547c5cb12488099645da9bce79e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321631801344/1924013826408448/STEM/2dc1690b-eddc-4790-9743-683d985c347d.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87529e0d2e57c3a2bce351399b8717da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b4e098c6194f55462b24f552f5967.png)
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5卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
6 . 将曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba3522ee6b81e2c3552a82fc93def89.png)
向右平移
个单位长度后得到曲线
,若函数
的图象关于
轴对称,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba3522ee6b81e2c3552a82fc93def89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77144844a6377a45454e31b6c7813ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
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7 . [选修4-5:不等式选讲]
设函数
.
(1)若不等式
的解集为
,求
的值;
(2)在(1)的条件下,若不等式
恒成立,求
的取值范围.
设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed77faa76b091eec33038fed30d9f843.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e799e937076aa5a7dcd51cdc0f40f6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae966a0b705b01913e45508af829a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在(1)的条件下,若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30eecea8197f8b331e0f4dbac059ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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8卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
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8 .
的内角
,
,
所对的边分别为
,
,
.已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1e7e406819b8fc89f9fa3101ba72dc.png)
,且
.
(1)求角
;
(2)若
,且
的面积为
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1e7e406819b8fc89f9fa3101ba72dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20d383153926e7bb1f4a8535743c0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5030b196e6131e3c36e57e2f63dff9f.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a62f66ba24d6afef2b38482001e3182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c00f7e3c9b3ca278015e3ec031f102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
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6卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
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解题方法
9 . 等差数列
的前
项和为
,
,且
,则
的公差
( )
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a358086122d509098a4d541b167842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
A.1 | B.2 | C.3 | D.4 |
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10卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题
海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题海南省2018届高三第二次联合考试数学理试题海南省2018届高三第二次联合考试数学(文)试题湖南省长沙市第一中学2018届高三下学期高考模拟卷(三)数学(文)试题四川省遂宁市船山区第二中学校2020届高三高考适应(二)考试数学(文)试卷四川省遂宁市船山区第二中学校2020届高三高考适应(二)考试数学(理)试卷四川省泸州市泸县第二中学2020-2021学年高三上学期开学考试数学(理)试题四川省泸州市泸县第二中学2020-2021学年高三上学期开学考试数学(文)试题【全国百强校】湖南省衡阳市第八中学2017-2018学年高二(实验班)下学期期末结业考试数学(文)试题(已下线)4.2.2 等差数列的前n项和(精练)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第二册(人教A版)
名校
10 . 在平面直角坐标系
中,设动点
到坐标原点的距离与到
轴的距离分别为
,
,且
,记动点
的轨迹为
.
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321631801344/1924013826727936/STEM/78c8438d3db54aac9cfbfaa3db7a83e5.png?resizew=217)
(1)求
的方程;
(2)设过点
的直线
与
相交于
,
两点,当
的面积最大时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09475d26093175769e82cf6c334fefd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://img.xkw.com/dksih/QBM/2018/4/13/1923321631801344/1924013826727936/STEM/78c8438d3db54aac9cfbfaa3db7a83e5.png?resizew=217)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa71aa2ea224669698850108751a71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](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/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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5卷引用:海南省三亚市第二中学2020届高三年级下学期第二次考试数学试题