2021年山东省青岛市市南区中考数学二模
山东
九年级
二模
2021-06-23
874次
整体难度:
容易
考查范围:
数与式、图形的变化、统计与概率、方程与不等式、函数、图形的性质
一、单选题 添加题型下试题
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 用科学记数法表示绝对值大于1的数解读
A.18个 | B.15个 | C.12个 | D.10个 |
【知识点】 用频率估计概率的综合应用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ec97789eca11fec8ede61572475070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503081984/STEM/eccd209a-08e5-4fb3-89a0-3409c93362d8.png?resizew=295)
A.![]() | B.2 | C.﹣1 | D.![]() |
【知识点】 求反比例函数解析式解读 求位似图形的对应坐标解读
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204696a289b1f47a176eb16c1cecf8b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc4622a5f65ffbece28e09206b0cb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d727d1b22093536a4a50024a99a0db2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503106560/STEM/e1d89761-7aec-44e6-9b27-c398dca96c17.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
【知识点】 反比例函数、二次函数图象综合判断解读
二、填空题 添加题型下试题
![](https://img.xkw.com/dksih/QBM/2022/1/9/2890780614868992/2891319307640832/STEM/2a4d9401285049308004f3dfed019d05.png?resizew=135)
【知识点】 同弧或等弧所对的圆周角相等解读 已知圆内接四边形求角度解读
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
【知识点】 根据实际问题列二元一次方程组解读
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503270400/STEM/e20a9a29-500a-44b7-b7d7-3fb8c7a06ac3.png)
【知识点】 正方形折叠问题 相似三角形的判定与性质综合
三、解答题 添加题型下试题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503286784/STEM/2347dc85-27fd-4d35-8c31-10a3002f2265.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503401472/STEM/8982312a-1c35-4b81-889c-01e0838b88e7.png)
【知识点】 列表法或树状图法求概率解读
成绩 | 频数 | 频率 |
不及格 | 4 | 0.08 |
及格 | 18 | 0.36 |
良好 | a | 0.24 |
优秀 | 16 | b |
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)已知“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89b2f8dbc36bc105e5398ede89dd67c.png)
(3)求参加本次测试学生的平均成绩;
(4)请估计全校九年级体质测试成绩为“良好”等级及以上的学生数.
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503450624/STEM/df109788-d42d-4a5c-b4a8-d83d87bdc64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503483392/STEM/87b99d3525f14e2d8bfd4e4155897b74.png?resizew=255)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(1)每个甲种和乙种礼盒所需包装纸的面积分别是多少?
(2)加工企业拟生产甲种礼盒
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)已知每个甲种礼盒利润是10元、每个乙种礼盒利润是8元,在(2)的前提下,若将两种礼盒全部卖出,该企业要获得21000元总利润,应如何安排甲、乙两种礼盒的生产数量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa8cee7d2463f6f7d352e8b65f47cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17064fbff0ecc9dffaf47c8c39319e91.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17064fbff0ecc9dffaf47c8c39319e91.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503868416/STEM/0481d851-fabb-46e9-ac0f-3bbf24cc48d7.png)
【知识点】 判断能否构成平行四边形解读 添一个条件使四边形是菱形解读
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b48040973927208cb8a7dfdc2d2c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e609320b04e7c36c30476842cba3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69641bf9a35ad95ad403829f1fff56f.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b48040973927208cb8a7dfdc2d2c78.png)
(2)在轨道距离地面5米处有两个位置
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)现需要在轨道下坡段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933ca21b38bd73fd4d1d88de90f8b543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23b355ef7b1116baf9ec6f024a54524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cf17ee13e937cd8b84879da17d15b4.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458503974912/STEM/2011a739-b42d-4363-bab5-ea3e1b53c618.png?resizew=334)
【知识点】 y=a(x-h)²的图象和性质解读
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
问题探究:
探究一:如果有两支队伍参赛,要求相邻的座位不能安排同一队的队员,那么共有多少种不同的安排方法?
不妨设两支队伍分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/86d60bf13e4c494a92b0ec9a580c61f9.png)
探究二:如果有三支队伍参赛,要求相邻的座位不能安排同一队的队员,那么共有多少种不同的安排方法?
不妨设三支队伍分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.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)
第一种:若②③号位队员来自同一队伍,则②号位有2种选择,③号只有1种选择,④号位会有2中选择,此时会有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a6c2b5c0a5f2a7cd7c1c2aadafa23d.png)
第二种:若②③号位队员来自不同的队伍,则②号位有2种选择,③号位只有1种选择,④号位也只有1种选择,此时会有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af734ffb87b91957a87944b700b8838.png)
把上述两种情况的结果加起来得到12+6=18,一共有18种不同的安排方法.
探究三:如果有四支队伍参赛,要求相邻的座位不能安排同一队的队员,那么共有多少种不同的安排方法?(请按照前面的探究方法,描述如果有四支参赛队伍时,会有多少种结果的推算过程)
归纳探究:如果有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
无论有多少支参赛队伍,我们都要考虑两种情况:②③号位队员来自同一个队伍;②③号位队员来自不同的队伍.
(1)如果有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若②③号位队员来自同一队伍,则③号位只有1种选择,④号位有 种选择,这样我们就有 种安排方法(结果不需化简);
(3)若②③号位队员来自不同队伍,则③号位有 种选择,④号位有 种选择,这样我们就有 种安排方法.(结果不需化简)
(4)如果有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458505023488/STEM/dfa0eed3-f6d8-4781-a049-7b690a0074c0.png)
【知识点】 用代数式表示数、图形的规律解读 数字类规律探索解读
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
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(1)当
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(2)正方形
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(3)当为
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(4)当
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![](https://img.xkw.com/dksih/QBM/2021/5/27/2730010431135744/2733458505449472/STEM/332b7bc2-5951-4ccd-bd29-5ce6478c012a.png)
试卷分析
试卷题型(共 24题)
试卷难度
知识点分析
细目表分析 导出
题号 | 难度系数 | 详细知识点 | 备注 |
一、单选题 | |||
1 | 0.85 | 绝对值的意义 求一个数的绝对值 实数的大小比较 | |
2 | 0.94 | 轴对称图形的识别 中心对称图形的识别 | |
3 | 0.94 | 用科学记数法表示绝对值大于1的数 | |
4 | 0.65 | 用频率估计概率的综合应用 | |
5 | 0.85 | 在数轴上表示不等式的解集 求不等式组的解集 | |
6 | 0.65 | 求反比例函数解析式 求位似图形的对应坐标 | |
7 | 0.85 | 反比例函数、二次函数图象综合判断 | |
8 | 0.65 | 根据旋转的性质求解 三角函数综合 | |
二、填空题 | |||
9 | 0.85 | 幂的混合运算 幂的乘方运算 积的乘方运算 同底数幂的除法运算 | |
10 | 0.85 | 同弧或等弧所对的圆周角相等 已知圆内接四边形求角度 | |
11 | 0.94 | 根据实际问题列二元一次方程组 | |
12 | 0.65 | 根据二次函数图象确定相应方程根的情况 | |
13 | 0.4 | 角平分线的性质定理 用勾股定理解三角形 求弧长 线段问题(轴对称综合题) | |
14 | 0.4 | 正方形折叠问题 相似三角形的判定与性质综合 | |
三、解答题 | |||
15 | 0.85 | 作角平分线(尺规作图) 画圆(尺规作图) 判断直线和圆的位置关系 | 问答题 |
16 | 0.85 | 分式化简求值 负整数指数幂 化为最简二次根式 求特殊角的三角函数值 | 计算题 |
17 | 0.85 | 列表法或树状图法求概率 | 问答题 |
18 | 0.85 | 由样本所占百分比估计总体的数量 频数分布表 频数分布直方图 求加权平均数 | 问答题 |
19 | 0.65 | 解分式方程 根据矩形的性质求线段长 仰角俯角问题(解直角三角形的应用) | 问答题 |
20 | 0.65 | 根据实际问题列二元一次方程组 分式方程的实际应用 列一次函数解析式并求值 | 问答题 |
21 | 0.65 | 判断能否构成平行四边形 添一个条件使四边形是菱形 | 证明题 |
22 | 0.4 | y=a(x-h)²的图象和性质 | 问答题 |
23 | 0.4 | 用代数式表示数、图形的规律 数字类规律探索 | 应用题 |
24 | 0.4 | 用ASA(AAS)证明三角形全等(ASA或者AAS) 根据正方形的性质与判定证明 相似三角形——动点问题 | 问答题 |